Mathematical, Astronomical, and Geometrical Lexicon, that is, a collection and explanation of all things in one way or another pertaining to both and almost to all mathematics

Creator: Girolamo Vitale | Date: 1668 | Notes: Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio An alphabetical Latin lexicon of the mathematical sciences, defining and explaining terms from astronomy, geometry, optics, chronology, arithmetic, geography, and related natural-astrological topics. The work also includes an appended digression on sympathy and the magnetic cure of wounds, while repeatedly distinguishing licit natural philosophy and astronomy from judicial astrology and other condemned superstitions. 👉 <a href="https://tryleo.ai/collections/exlatinis/eden-on-the-moon-how-a-theatine-cleric-catalogued-forbidden-astrology-without-burning-a-page">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/bub_gb_Qs8dKhStZZcC">View the original file on Internet Archive</a> This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.

Title
Mathematical, Astronomical, and Geometrical Lexicon, that is, a collection and explanation of all things in one way or another pertaining to both and almost to all mathematics
Creator
Girolamo Vitale
Date
1668
Notes
Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio An alphabetical Latin lexicon of the mathematical sciences, defining and explaining terms from astronomy, geometry, optics, chronology, arithmetic, geography, and related natural-astrological topics. The work also includes an appended digression on sympathy and the magnetic cure of wounds, while repeatedly distinguishing licit natural philosophy and astronomy from judicial astrology and other condemned superstitions. 👉 <a href="https://tryleo.ai/collections/exlatinis/eden-on-the-moon-how-a-theatine-cleric-catalogued-forbidden-astrology-without-burning-a-page">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/bub_gb_Qs8dKhStZZcC">View the original file on Internet Archive</a> This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.

Document notes

Original title: Lexicon mathematicum astronomicum geometricum, hoc est rerum omnium ad utramque immò & ad omnem ferè mathesim quomodocumque spectantium, collectio, & explicatio An alphabetical Latin lexicon of the mathematical sciences, defining and explaining terms from astronomy, geometry, optics, chronology, arithmetic, geography, and related natural-astrological topics. The work also includes an appended digression on sympathy and the magnetic cure of wounds, while repeatedly distinguishing licit natural philosophy and astronomy from judicial astrology and other condemned superstitions. 👉 Read our introductory primer, full report, and finding guide here 📜 View the original file on Internet Archive This text was transcribed and translated as part of the ExLatinis project—an effort by Leo to make English translations of every published text in Latin in early modern Europe (between 1450 and 1750) available to the public for free online.

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Y.2. 14-22-D-23

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Y.2. 14-22-D-23

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VITALLS VORDORE RERVM. Vid lac posse duquod ponere MINVITVR, VT ELEMENTA REPLEAT. Ambros. PONDERE, ET MEN SVEA. TURBANT VIRI AVGIT OVASSATIO LVDITVR ARTE LABOR. HIERONYMI VITALIS CLER REGVL. LEXICON MATHEMA TICVM. Ponderibus librorum fuit Cam ad memi canuicam mensa BIBLIOTECA NAZ. ROMA VITTORIO EMANUELE

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VITALLS VORDORE RERVM. Vid lac posse duquod ponere MINVITVR, VT ELEMENTA REPLEAT. Ambros. PONDERE, ET MEN SVEA. TURBANT VIRI AVGIT OVASSATIO LVDITVR ARTE LABOR. HIERONYMI VITALIS CLER REGVL. LEXICON MATHEMA TICVM. Ponderibus librorum fuit Cam ad memi canuicam mensa BIBLIOTECA NAZ. ROMA VITTORIO EMANUELE

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LEXICON MATHEMATICVM ASTRONOMICVM GEOMETRICVM, Hoc est Rerum omnium ad utramque immò & ad omnem ferè Mathesim quomodocumque spectantium, Collectio, & explicatio. Adjecta breui nouorum Theorematum expensione, verborumque exoticorum dilucidatione vt non injuriâ Disciplinarum omnium Mathematicarum summa, & Promptuarium dici possit. Auctore HIERONYMO VITALE Capuano Clerico Regulari vulgò Theatino. PARISIIS, Ex Officina LUDOVIC. BILLAINE, in Palatio Regio. DC. LXVIII. Cum Licentijs. BIBLIOTECA NAZ. ROMA VITTORIO EMANUELE

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LEXICON MATHEMATICAL ASTRONOMICAL, GEOMETRICAL, that is, A collection and explanation of all things in every respect, and indeed of nearly everything pertaining in any way to Mathematics. To which is added a brief examination of new theorems, and an elucidation of exotic words, so that it may not unjustly be called the sum and repository of all Mathematical disciplines. By HIERONYMUS VITALIS, a Capuan Regular Cleric, commonly called Theatine. AT PARIS, From the workshop of LUDOVIC. BILLAINE, in the Royal Palace. 1668. With Licenses. BIBLIOTECA NAZ. ROME VITTORIO EMANUELE

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EMINENTISSIMO AC REVERENDISSIMO PRINCIPI D. GVIDOBALDO S.R.E. CARDINALI DE THVN ARCHIEPISCOPO ET PRINCIPI SALISBURGENSI, AC RATISSONENSE GERMANIÆ PRIMATI. AC S. R. SEDIS LEGATO PERPETVO S. R. Imperij Principi, &c. Hieronymus Vitalis æternam felicitatem. ERVBESCEREM ad in- fularum purpuram, Cardinalis amplissime, nisi animorum con- ciliatrix humanitas promican- tem ab ea fulgorem blandissimè temperaret. Auersaris enim pessimam optima- tum indolem, qui quoad sublimius gloriæ apo- gaum euehuntur, hoc magis eripiunt se popu- lorum aspectui, id vnum commune cum sideri- bus habentes, quod subiecta sibicapita despiciant mortalium oculis imperuj (quasi verò in gloria fiat, & abiecta, qua sub oculos cadit celsitudo.) a ij

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TO THE MOST EMINENT AND MOST REVEREND PRINCE D. GVIDOBALD CARDINAL OF THE HOLY ROMAN CHURCH OF THVN ARCHBISHOP AND PRINCE OF SALZBURG, AND OF RATISBON, PRIMATE OF GERMANY. AND PERPETUAL LEGATE OF THE HOLY ROMAN SEE TO THE PRINCE OF THE HOLY ROMAN EMPIRE, &c. Hieronymus Vitalis wishes eternal happiness. I WOULD blush at the purple of the cardinals, most illustrious Cardinal, unless the humanity that conciliates minds most kindly tempered the brilliance advancing from it. For you reject the worst trait of the great, who, as they are borne up to the loftier summit of glory, so much the more withdraw themselves from the sight of peoples, having this one thing in common with the stars, that they look down with mortal eyes upon the heads subject to them under their rule (as though, indeed, there were glory in what is lofty and cast down, the eminence that falls beneath the eyes.) a ij

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Quin potius regiam amularis Iouis alitem, quæ ita se Cælo permittit, vt terris interdu[m] illabi non dedignetur; Imò sic te præstas omnibus æqualem, nulla vt re supra hominum vulgus eminere videaris, quam meritis. Accedit quod libertatem non relinquis spectatoribus tuis, quos in te semel intenderint, torquere oculos alio possint, adò sunt intui vnius admiratione defixi: ea propter vitio dare non potes, si te importanus adeam, cum totus cuilibet te intuenti pateas, teque adeunti, facias sine fastidio copiam tui. Atque hîc ego non committam, velatiùs excurratoratio indagatura quænam ex tot quibus præfulges virtutibus, te ad tantum honoris fastigium promouerit; an probitas morum singularis? an rerum Ciuilium, & Ecclesiasticarum peritia? an maximarum rerum ponderi, non impar animus? an denique studium pietatis, & in tuendâ bellantis Ecclesiæ gloria inuictâ strenuitas? constat enim omnes vnà conspirasse virtutes, vt te ad tantam dignitatem certatim proucherent, cum quid quid in hierophantis, & præsidibus Religionis effusum est, in te vno ad inuidiam expressum miretur orbis, adeò vt tibi vni plausisse vates videatur cum cecinit. Sparguntur in omnes In te mixta fluunt, & quæ diuisa, beatos Efficiunt, collecta tenes. CLAYD. Qua propter si virtus est vera animarum

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Why rather imitate the royal bird of Jupiter, which so commits itself to the sky that it does not disdain to alight on the earth now and then; nay, so do you present yourself as equal to all, that you seem to excel in nothing above the common crowd of men, except in merit. There is also this: you do not leave your spectators the freedom, once they have fixed their gaze on you, to be able to turn their eyes elsewhere, for they are so held fast by the admiration of beholding one man. For that reason you cannot take it amiss if I approach you too importunately, since you are wholly open to anyone who looks at you, and, as he comes to you, you allow him access to yourself without displeasure. And here I shall not undertake, by a more elaborate course of reasoning, to investigate which among the many virtues with which you shine forth has promoted you to so great a height of honor: whether singular integrity of character? whether skill in civil and ecclesiastical affairs? whether a mind not unequal to the weight of the greatest matters? or finally a zeal for piety, and unconquerable energy in defending the glory of the Church at war? For it is clear that all the virtues have conspired together, to advance you in rivalry to so great a dignity, since whatever has been bestowed in the high priests and rulers of Religion the world marvels to see expressed in you alone, and expressed to the point of envy, so that the poet seems to have applauded you alone when he sang: “Scattered among all Are things which, mixed in you and divided elsewhere, make men blessed; you hold them gathered together.” CLAYD. Wherefore, if virtue is truly the health of souls

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illustrium purpura, antequam de te Roma co- gitaret, iam totus purpuratus eras, & priusquam in humeris ostrum igneum diradiaret, iam ru- tilabas præclarè gestorum fama conspicuus. Quæ res incertum animi tenet, plusne tibi quam Ger- mania, vel Ecclesiæ potius vniuersæ applaudendum sit, tibi, qui quod virtus tua merebatur di- uinâ (vt aiunt) virgulâ consecutus es, Germania, quæ suas inter Aquilas Phoenicem adnume- rat, Ecclesiæ quæ suo diademati nonum florem intexuit. Quinetiam nostro potissimum Ordini gratulandum arbitror, qui se iam expertus est ingenità ad benefaciendum voluntate adeò pro- cliuem, vt latè patentem munificentiam in an- gustum cogere non dubitaueris. Ad id autem officij quod mihi cum cæteris com- mune est, accedit priuata ratio, tuum quod votis omnibus ambio patrocinium quò nostra lucubra- tiones tanto insignita nomine securius prodeans in lucem, & grauius apud omnes, cum te vin- dicem nactæ fuerint, authoritatis pondus obti- neant. Huius honoris ambitu supplices, tuos ad pedes deuoluuntur, tua requirunt vestibula è quibus pendent tot doctissimorum anathemata ingeniorum; nec repulsam (vt spero) patientur, cum oceanus non reijciat ad se concurrentia mi- nora flumina, nec terra locum neget ponderi- bus, nec Cælum deprimat fauillas ad se liberiùs euolantes. Quæstum ambierint veteres, aut am- bitum quæsierint, cum sua Principibus opera

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The purple of the illustrious: before Rome had thought of you, you were already wholly clad in purple; and before the fiery purple should flash upon your shoulders, you were already glowing, conspicuous in the fame of your splendid deeds. This matter leaves the mind uncertain whether more applause is due to you than to Germany, or rather to the whole Church: to you, who have obtained by a divine wand, as they say, what your virtue deserved; to Germany, which counts a Phoenix among its Eagles; to the Church, which has woven a ninth flower into its diadem. Indeed I think our own Order especially should be congratulated, which has already experienced you as so naturally inclined to do good that you have not hesitated to compress wide-open munificence into narrow bounds. To that duty, however, which I share in common with the rest, there is added a private reason: your patronage, which I seek with all my prayers, so that our writings, adorned with so great a name, may come forth into the light more securely and, when they have found in you their defender, may carry among all a weightier authority. In pursuit of this honor, suppliant, they throw themselves at your feet, seek your threshold, from which depend the anathemas of so many most learned minds; nor, as I hope, will they suffer a refusal, since the ocean does not reject the smaller rivers flowing together to it, nor does the earth deny a place to weights, nor does heaven press down sparks flying more freely toward it. The ancients sought profit, or sought favor, when they offered their works to princes

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consecrauerunt; Antonini gratiam aucupetur suâ Oppianus Icthyologiâ, Vitruuius Augustum Architecturâ sibi conciliet, Commodi fauores ex- petas Pollucis Onomatologia, dignitates à Vespasiano suâ Plinius Physicâ emendicet: ego sane post habitis quibuscumque emolumentis perituro operi, Mecanatis immortalitate consulo. Futurum enim speraui vt quâ olim industriâ, Phydias dum elegantem illam Mineruam effingeret, proprium in ægide calauit, celauitque vultum, vt æternum sibi nomen compararet, sic me tibi dicatitiâ hacce epistolâ insinuarem, vibrantisque illius gloriæ, qua circunfusus coruscas, quosdam operi meo radios inspirares. Hac ergo ratione abundè mihi satisfactum putabo, si tuis sub auspicijs prodeat Lexicon hoc Mathematicum, neque enim timebit Stoica censorum supercilia, nec temporis omnia deprædantis reformidabit ingluuiem. Quapropter tuos affusus ad pedes illud depono, vt sin minus purpuræ tuæ innoluatur ambitu, extremam saltem laciniam delibans, tutissimum nanciscatur inter tot debachantis inuidiamorsus præsidium. Vale.

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They have been consecrated; let Oppianus, with his Icthyologia , court the favor of Antoninus, let Vitruvius win Augustus to himself with his Architecture , let you seek the favor of Commodus with Pollux’s Onomatologia , and let Pliny beg dignities from Vespasian with his Physics : for my part, having set aside whatever advantages there may be, I look to the immortality of Maecenas for this work, though it is doomed to perish. For I have hoped that, as Phidias once, while shaping that elegant Minerva, concealed and covered his own face within the shield, in order to win himself an everlasting name, so I might insinuate myself to you by this dedicatory letter, and inspire my work with some rays of that shining glory with which you are surrounded. In this way, then, I shall think myself abundantly satisfied, if this Mathematical Lexicon is brought forth under your auspices; for it will neither fear the stern brows of Stoic critics nor dread the rapacious greed of time, which devours all things. Wherefore I lay it at your feet, humbly commending it to you, that, if it cannot be wholly enveloped in the folds of your purple, it may at least, by grazing its outer fringe, obtain the safest possible protection amid the many hostile bites of envy. Farewell.

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PRÆFATIO AD LECTOREM In qua operis Idea, Auctoris mens, ac di- cendorum ratio explicatur. Athematicas discipli- nas, quò cæteris præ- stantiores, eò homi- nibus huius sæculi de- spectiores, atque odio- siores, inter nouissimas curas à paucis admo- dum coeli à plurimis eleuati, ab omnibus vniuersim, ceu stu- diorum retrimenta, & quisquilias cæteris artibus post haberi, Amice Lector, ama- rissimè semper indolui. Quippe cum eæ fint, quæ animum nostrum virtutibus im- buunt, ad nobilissimâ erigunt, ad Dei for- mam efformant, ac divinæ illius sapientiæ vniuersa bellissimè ordinantis semitas cal- care edocent, mirum est, quàm malè apud quosdam audiant; vt inter euanidas scien- tias, otiosas inutiles, ac poenè dixerim perniciosas connumerentur. Diogenes ille à

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PREFACE TO THE READER In which the idea of the work, the author’s intention, and the method of what is to be said are explained. I have always most bitterly lamented, dear Reader, that the mathematical disciplines, the more excellent they are above the rest, the more despised and hateful they are to the men of this age; that, among the latest concerns of very few, and of many scarcely lifted toward heaven, they are by all in general, as though the dregs and refuse of studies, set after the other arts. For since they are those which imbue our mind with virtues, raise it to the noblest things, shape it to the likeness of God, and teach it to tread the paths of that divine wisdom which orders all things most beautifully, it is strange how ill they are received among some; so that they are numbered among the vain, idle, useless, and I might almost say pernicious sciences. That Diogenes from

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consecrauerunt; Antonini gratiam aucupetur suâ Oppianus Icthyologiâ, Vitruuius Augustum Architecturâ sibi conciliet, Commodi fauores ex- petat Pollucis Onomatologia, dignitates à Vespasiano suâ Plinius Physicâ emendicet: ego sane post habitis quibuscumque emolumentis perituro operi, Mecanatis immortalitate consulo. Futurum enim speraui vt quâ olim industriâ, Phydiæ dum elegantem illam Mineruam effingeret, proprium in agide cælauit, celauitque vultum, vt æternum sibi nomen compararet, sic me tibi dicatitiâ hacce epistolâ insinuarem, vibrantisque illius gloria, qua circufusus coruscas, quosdam operi meo radios inspirares. Hac ergo ratione abundè mihi satisfactum putabo, si tuis sub auspicijs prodeat Lexicon hoc Mathematicum, neque enim timebit Stoica censorum supercilia, nec temporis omnia deprædantis reformidabit ingluuiem. Quapropter tuos affusus ad pedes illud depono, vt sin minus purpuræ tuæ innoluatur ambitu, extremam saltem laciniam delibans, tutissimum nanciscatur inter tot debachantis inuidiamorsus præsidium. Vale.

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...they have consecrated. Oppian seeks the favor of Antoninus through his Ichthyology; Vitruvius wins over Augustus by his Architecture; Pollux seeks the favor of Commodus through his Onomasticon; Pliny begs dignities from Vespasian through his Natural Philosophy: for my part, caring nothing for whatever profit there may be, I devote myself to an undertaking destined to perish, and I look to Mecenas-like immortality. For I have hoped that, just as once Phidias, while fashioning that elegant Minerva, secretly carved his own likeness and even hid his face, in order to win himself an everlasting name, so I might insinuate myself to you by this dedicatory letter, and that you, surrounded by the radiant glory in which you shine, would inspire some beams of that splendor into my work. For this reason, therefore, I shall think myself abundantly satisfied, if this Mathematical Lexicon comes forth under your auspices; for it will fear neither the haughty brows of Stoic critics, nor dread the greed of Time, which ravages all things and devours them. Wherefore I lay it down at your feet, that, if it cannot at least be enwrapped in the folds of your purple, yet by grazing the very edge of your mantle it may find the safest protection amid the many bites of envious detractors. Farewell.

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PRÆFATIO AD LECTOREM In qua operis Idea, Auctoris mens, ac di- cendorum ratio explicatur. Mathematicas discipli- nas, quò cæteris præ- stantiores, eò homi- nibus huius sæculi de- spectiores, atque odio- siores, inter nouissimas curas à paucis admo- dum coeli à plurimis eleuati, ab omnibus vniuersim, ceu stu- diorum retrimenta, & quisquilias cæteris artibus post haberi, Amice Lector, ama- rissimè semper indolui. Quippe cum eæ sint, quæ animum nostrum virtutibus im- buunt, ad nobilissimâ erigunt, ad Dei for- mam efformant, ac divinæ illius sapientiæ vniuersa bellissimè ordinantis semitas cal- care edocent, mirum est, quàm malè apud quosdam audiant; vt inter euanidas scien- tias, otiosas inutiles, ac poenè dixerim perniciosas connumerentur. Diogenes ille â

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PREFACE TO THE READER In which the idea of the work, the author’s intention, and the method of what is to be said are explained. I have always most bitterly grieved, dear Reader, that the mathematical disciplines, the more excellent they are than the rest, the more despised and hated they are among the people of this age, and, in the latest concerns, by very few lifted up toward heaven, by almost all, indeed by everyone universally, as though the refuse and offscouring of studies, are placed after all the other arts. For since they are the ones that imbue our mind with virtues, raise it up to the most noble things, shape it into the form of God, and teach it to tread the paths of that divine wisdom which most beautifully orders all things, it is astonishing how ill they fare in the judgment of some; so that they are counted among empty sciences, idle, useless, and, I had almost said, harmful. That Diogenes

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PRAEFATIO. Cynicus, homo, inquam, ad hominum irrisionem factus, qui sua Philosophia tu- midus cæteros aspernabatur, cuidam Ho- roscopon ostendenti Bellum, inquit, hercle instrumentum! Verum tamen ne frustremur cæ- na: invidè carpens ac sugillans geometri- cas artes, quasiearum ope coenam quidem sibi quisque parare queat. At enim si Allæ sunt facultates ad humanæ vitæ ratio- nem ineundam conducentes, si vllæ Rei- publicæ necessariæ, ciuibus opportunæ, eæ sunt Mathematicæ, & quæ in Mathe- matica fundantur artes, hoc est mechani- cæ. Quandoquidem ipsa olim scientiarum rudimenta, ipsa naturalis Philosophia, vt auctor est Gellius à Mathesis ruderibus in- cipiebant. Etenim refert Philosophiæ no- men vti ex Pythagora effluxisse ita & Ma- thematicæ appellationem â [sulphur] Ma[n]d[en]na. hoc est disciplina, seu à [mercurius] Martirio, quod est dis- co, & doceo deriuatam. Mathemata enim dicuntur artes, quæ firmis demonstrationibus constant: quæ quidem idcircò ad disciplinam animo inserendam aptissimæ inveniuntur. Namque ita Natura facti su- mus, vt nihil tenere mente possimus, ni aliquo modo sub sensu cadat, ac speciem aliquam præse ferant entis extensi. Cum igitur Mathematicæ disciplinæ totæ sint in rebus quantis, vt quantis exhibendis, ac

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PREFACE. The Cynic, I say, a man made for the ridicule of men, who in the pride of his own Philosophy despised others, when one showed him an Horoscope, said, “By Hercules, what an instrument for War! Yet let us not be cheated of our supper:”—jeeringly picking at and vilifying the geometric arts, as though by their aid one could indeed provide a supper for oneself. But if there are any faculties conducing to the ordering of human life, if there are any necessary to the Commonwealth and serviceable to citizens, these are Mathematics, and the arts founded upon Mathematics, that is, the mechanical arts. For even the very rudiments of the sciences of old, even natural Philosophy itself, as Gellius is author, began from the rudiments of Mathesis. Indeed it is related that the name of Philosophy flowed from Pythagoras, and likewise the designation of Mathematics from [sulphur] Ma[n]d[en]na; that is, discipline, or from [mercurius] Martirio, which is derived from “I learn” and “I teach.” For those things are called Mathemata, which are arts consisting in firm demonstrations; and for that very reason they are found most fit for implanting discipline in the mind. For we are so made by Nature that we can hold nothing in the mind unless in some way it falls under the senses and presents some form of an extended being. Since therefore the mathematical disciplines are wholly concerned with things quantitative, in that they exhibit quantities, and

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PRAEFATIO. proponendis, in eisque mensurandis, & co- parandis inter se, iure ipsarum notitia an tonomasticè disciplinæ nomen promeruit, quandoquidem ipsæ solæ sunt, quæ mentis nostræ duritiam superare, ignorantiæ te- nebras discutere, ac scientiis omnibus adi- tum aperire valent, atque ad id factæ sunt. Hinc testatur idem Gellius, triplicem fuis- se ordinem eorum, qui sub Pythagora pro- ficiebant. Quidam enim dicebantur Anusinot, hoc est, auditors, qui ab ingressu silere, atque audire tantum iubebantur ad certum tempus, quo durante nihil eis percontari licebat, quamvis non rectè quæ ab aliis docebantur perciperent, neque etiam commentari, quæ audierant, concessum erat: Veruntamen, vbi tacere & audire didicerant, jamque coepissent esse silentio eruditi, mox verba facere, & quæritare de iisque, quæ audierant scribere, ac diffi- cultates expromere, dabatur illis aditus, atque hi Madnunxmot appellabantur ab iis ar- tibus quas iam dicere, & meditari eæpe- rant. Posteà his scientiarum suppetiis in- structi, ad percipienda mundi opera, Na- turæque principia procedebant, quo tem- pore quonit audiebant, quod iam exinde ob Mathematicas disciplinas, superiores scientias sublimioraque studia capessenda apti inveniebantur. Proindeque pueris â ij

Transcription: Translated (English)

PREFACE. in proposing them, and in measuring and comparing them among themselves, the very knowledge of them has deserved the name of a discipline par excellence; since they alone are able to overcome the hardness of our mind, dispel the darkness of ignorance, and open the way to all sciences, and were made for this purpose. Hence the same Gellius testifies that there was a threefold order among those who made progress under Pythagoras. For some were called Anusinot, that is, auditors, who from the outset were commanded to be silent and to listen only for a fixed time, during which they were allowed to ask them nothing, even though they did not rightly understand what was being taught by others, nor was it permitted even to make notes of what they had heard. However, when they had learned to be silent and to listen, and had already begun to be instructed by silence, then, after a while, they were given leave to speak, to inquire about, to write down what they had heard, and to express their difficulties; and these were called Madnunxmot, from the arts which they had already begun to speak about and to contemplate. Afterwards, equipped with these aids to learning, they proceeded to understand the workings of the world and the principles of Nature, at which time they listened, since by reason of the Mathematical disciplines they were found fit to undertake the higher sciences and more elevated studies. Therefore, for boys

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Transcription: ATR-1

PRÆFATIO. Geometriæ, Musices, & Arithmetica rudimenta tanquam certa, fundataque scientiarum principia primò in scholis exhibebantur, vt iis demum exerciti ad majora Philosophiæ studia inienda redderentur idonei. Vnde est quod id perperam assumens Picus lib. 12. aduersus Astrologos cap. 2. exinde mathematicas facultates elevare nititur, & graphicè contra eas inuehitur, inquiens: Mathematica sapientes non facit, quare veteribus puerorum studium fuit imò qui ei soli totum se tradit, occasiones errorum in Philosophia maximas parit. At enim verò tantum abest quod Mathesis Philosophiam destruat atque in errores abducat, ut eam solam Philosophiæ studiis adeò necessariam censuerit Plato, teste Io. Grammatjco in p. Phys. c.45. vt in Gymnasij limine inscriptum vellet id est æquum hoc est Geometriæ ignarus huc non adueniat: & Xenocrates Platonis auditor cuidam Mathesis ignaro scholam suam frequentare expostulanti dixisse fertur. Abi, cares enim ansis, & adminiculis Philosophiæ. Quod autem pueris olim addiscenda traderetur, id potiùs eius necessitatem, atque vtilitatem arguit, quam, quod quicquam contra illam evincat. Porrò Mathematicarum disciplinarum dignitatem, commoda, atque vtilitates quis

Transcription: Translated (English)

Preface. The rudiments of Geometry, Music, and Arithmetic were first presented in the schools as certain and well-founded principles of the sciences, so that those trained in them might afterwards become fit to undertake the greater studies of Philosophy. Hence it is that Picus, wrongly assuming this, in book 12, Against the Astrologers, chapter 2, strives from this to disparage the mathematical disciplines, and openly attacks them, saying: Mathematics does not make men wise, therefore it was the study of children among the ancients; indeed, whoever gives himself wholly to it alone brings about the greatest occasions of error in Philosophy. But in truth it is so far from the case that Mathematics destroys Philosophy and leads it into errors, that Plato judged it alone so necessary for the studies of Philosophy, as Io. Grammatjcus testifies in p. Phys. c. 45, that he wished it inscribed at the threshold of the Gymnasium, namely: Let him who is ignorant of Geometry not enter here: and Xenocrates, Plato’s pupil, is said to have replied to someone ignorant of Mathematics who complained about being excluded from attending his school: Go away, for you lack the handles and supports of Philosophy. And the fact that in former times it was handed over to be learned by boys proves rather its necessity and usefulness than anything that would prove against it. Moreover, who could [adequately speak of] the dignity, benefits, and usefulness of the mathematical disciplines?

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PRAEFATIO: explicare poterit? e[ss]e in summo certitudinis gradu positæ sunt, vt Philosophus ipse testatur. eædem ad ciuium pacem, ad gentium communicationem, ad bellorum ordinem factæ sunt: per eas militarem disciplinam, vrbium stabilimenta, ædificiorum ordinem, locorum interualla, menium commoda, negotiantium fidem, totius orbis commercium, cælestium notitiam, & cum terrenis hisce communicationem habemus: Has Ægyptiorum Sacerdotes, cum liberos suos liberalibus artibus instruendos traderent, curabant inprimis eos ediscere, vt metari agros nolent, vbi Nili excursu confusi forent: sicque posset ciuium concordia custodiri, quod & Strabo, & Herodotus, ac de Persis etiam scribit Alexander ab Alexandro lib. 2. dier. genial. cap. 25. Has leges summe commendant & præcipiunt in C. Artem Geometriæ. ad has addiscendas cogi homines posse vult Penna in lib. 2. c. de excurs. art. lib. 10. Bartholus quoque in sua Tiberina figuris Geometricis vten, has facultates Iurisperitis vtiles esse ostendit, & Arist. in rebus Philosophiæ difficillimis explicandis mathematicis demonstrationibus vsus est. Medicina nonne sine Astronomiæ directione ægris esset incommoda atque exitialis? quæ enim sub certo stellarum positu exhi- â iij

Transcription: Translated (English)

Preface: can it explain? They are placed at the highest degree of certainty, as the Philosopher himself testifies. They were made for the peace of citizens, for the intercourse of nations, and for the order of wars: through them military discipline, the foundations of cities, the arrangement of buildings, the intervals of places, the convenience of walls, the trust of merchants, the commerce of the whole world, the knowledge of heavenly things, and our communication with these earthly matters are maintained. The Egyptian priests, when they handed over their children to be instructed in the liberal arts, took care above all that they should learn this, that they might not wish to measure fields when they had been confused by the overflow of the Nile; and thus the concord of citizens could be preserved, as Strabo also says, and Herodotus, and Alexander ab Alexandro writes about the Persians as well, lib. 2. dier. genial. cap. 25. These laws are highly commended and prescribed in C. Artem Geometriæ. That men can be compelled to learn these things is the view of Penna in lib. 2. c. de excurs. art. lib. 10. Bartholus too, in his Tiberina on Geometric figures, shows that these faculties are useful to jurists, and Aristotle used mathematical demonstrations in explaining the most difficult matters of philosophy. Would medicine not be inconvenient and even deadly to the sick without the guidance of astronomy? For those things which are administered under the fixed position of the stars are- â iij

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PRAEFATIO. bita prodesse compertum est, hæc incongruo tempore data euocant mortem; quod & Ouidius obseruauit cum cecinit. Temporibus medicina valet: data tempore prosunt. Et data non apto tempore vina nocent. Theologia etiam & Sacrarum Scripturarum notitia, & explanatio multum à Mathesi adjuvatur vt probat D. Augustinus lib. 2. de doctrina Christiana cap. 16 & seqq. ac testatur etiam D, Hieromymus to. 1. 1 p. 5. Vnde & sacræ paginæ Deum ipsum sæpius introducunt omnia inpondere & mensura, & numero disponentem; & Ecclesia secundum Astronomiæ regulas ritus suos instituit, ac nouillunia, & temporum rationes ordinat, sidelibusque exhibet observandas. Tandem nulla est scientia quæ nos adeò in Deum erigit, ac supernæ Patriæ desiderium in nobis excitat, quàm exilestium rerum notitia. Siquidem, vt ait, Psaltes Cæli enarrant gloriam Dei. Per eam enim tenetur quodammodo in manibus coelum ac fit vt cæteris omnibus spretis, ad idem seriò possidendum animum applicemus. Felices animæ, quibus hæc cognoscere primis, Inque domos superas scandere cura fuit, Credibile est illos pariter vitiisque, iocisque Altius humanis exercuisse caput.

Transcription: Translated (English)

PREFACE. What has been found to be useful at a suitable time, if given at an unsuitable time, brings death; as Ovid observed when he sang: At the right time medicine is effective; when given in time it is beneficial. And wine given at the wrong time is harmful. Theology also, and the knowledge and explanation of Holy Scripture, are greatly aided by Mathematics, as St. Augustine proves lib. 2, de doctrina Christiana cap. 16 and following, and St. Jerome likewise testifies, t. 1, p. 5. Hence the sacred pages themselves more than once present God as arranging all things in weight and measure and number; and the Church, according to the rules of Astronomy, has instituted its rites, and orders the new moons and the times, and presents them to the faithful to be observed. Finally, there is no science that so much lifts us up to God and awakens in us the desire of the heavenly Fatherland as the knowledge of celestial things. For, as it says, The heavens declare the glory of God. Through them, indeed, heaven is, as it were, held in our hands, and it comes about that, despising all else, we seriously apply our mind to possessing that same heaven. Happy are the souls for whom it was a first concern to know these things, and to ascend to the heavenly homes. It is credible that they likewise exercised their minds higher than human vices and pleasures.

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Transcription: ATR-1

PRAEFATIO. Nam Venus, & vinum sublimia pectora fregit, Officiumque fori, militiaue labor. Nec levis ambitio, perfusaque gloria fuco: Magna neque fames sollicitauit opum. Admouere oculis distantia sidera nostris, Ætheraque ingenio supposuisse suo. Sic petitur cælu, non vt ferat Ossam Olympus, Summaque Peliacus sidera tangat apex. Sic fatus verè Ovidius Pastorum 1. Cùm igitur tantæ sint Mathematicæ disciplinæ præstat hîc causam tantæ contrarietatis auertere, & invidiam, quam apud homines contraxerint aperire: quî factum sit, vt quæ ex se ipsis tam bonæ, tam vtiles, tam innocentes sunt, tam malè postea olere cæperint: vt ex iis quædam tanquam inutiles censeantur, quædam etiam vti perniciosæ ac Reipublicæ pestis abolitæ, atque in disciplinæ dedecus Imperatorum lege professores, ac mathematici vniuersim Vrbe proscriberentur. Equidem nil est in rerum natura tam bonum, quod non Daemonis astu, suorumque fraudibus corrumpi queat: Et quia ea est bonitatis conditio, vt præteruersa monstrosa fiat, ac deformissima (corruptionamque optimi pessima) inde fit, vt quæ maximè bona sunt, ea si tricis & sordidis adulterentur, nil illis perniciosius sit,

Transcription: Translated (English)

PREFACE. For Venus and wine have broken lofty spirits, as have duty at the forum and the labor of war. Nor has light ambition, nor glory bedaubed with false paint, nor great hunger for wealth urged them on. They have brought distant stars within our sight, and the heavens beneath the reach of our mind. Thus is heaven sought, not that Olympus may bear up Ossa, and the summit of Pelion touch the stars on high. So spoke, in truth, Ovid in the Pastors 1. Since, then, the Mathematical disciplines are so great, it is better here to turn away the cause of so great a contradiction and to explain the envy they have incurred among men: how it has come to pass that things which of themselves are so good, so useful, so innocent, should afterward begin to smell so badly; so that some are judged as though useless, and some even abolished as pernicious and a pest to the Commonwealth, and that, to the disgrace of learning, by the law of emperors professors and mathematicians in general were proscribed from the City. Indeed, there is nothing in nature so good that it cannot be corrupted by the Devil’s craft and by his own frauds. And because such is the condition of goodness, that when distorted it becomes monstrous and most deformed — corruption of the best being the worst — it follows that those things which are most good, if they are adulterated with petty tricks and sordidness, nothing is more harmful to them,

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PRÆFATIO. nil euadat insensius. Videmus id passim in alimétis, quæ quo salubriora, si postea cor- rumpantur, aut venenis inficiantur, eò sunt humanæ vitæ exitialiora. Cùm igitur dia- bolus ab initio Dei similitudinem ex arrogantia appetierit, postmodum superna patria pullus, nil magis affectet, quam Dei simiam facere, & perfectissima quæque in Dei contemptum corrumpere, atque hominibus exhibere. Quod & D. Petrus Chrysologus aliò respiciens adnotauit serm. 155. sic inquiens. Vbi Christus piè nostram natus est ad salutem mox diabolus diuinæ bonitati numerosa genuit, & perniciosa portenta, vt ridiculum de religione componeret in sacrilegium verteret sanctitatem, de honore Dei Deo pararet injuriam. Nonne Theologia scientia est omnium nobilissima, & diuina, quæ nos in Dei cognitionem ducit, quæ mores instruit, quæque altissima rimatur mysteria, atque illius beatificæ visionis, quæ æternæ gloriæ summa est, speculum esse, æmulam & primum gradum non inani gloriatione se jactat? At quid ea corrupta execrabilius? Quid scelestius? Quid Ecclesiæ perniciosius? Nonne ex ea tot hæreses pullularunt? Nonne tot infandæ dogmatum aborsiones? Religio nonne virtutum omnium Princeps est, ac Regina? At enim hanc in superstitionem transformare

Transcription: Translated (English)

PRÆFATIO. nothing more disastrous can happen. We see this everywhere in foods, which, the more wholesome they are, if later they become corrupted or are infected with poisons, are so much more deadly to human life. Since therefore the devil from the beginning, out of arrogance, sought the likeness of God, and afterward, as an outcast from the heavenly homeland, desires nothing more than to make himself God’s ape, and to corrupt whatever is most perfect to the contempt of God, and to present it to men. This also St. Peter Chrysologus, looking elsewhere, noted in sermon 155, saying thus: When Christ was born piously for our salvation, straightway the devil gave birth to numerous and pernicious monstrosities to the divine goodness, so that he might compose a mockery of religion, turn holiness into sacrilege, and from the honor of God prepare an insult to God. Is not Theology the most noble and divine of all sciences, which leads us to the knowledge of God, which instructs morals, and which explores the highest mysteries, and which boasts, not with empty vainglory, of being a mirror of that beatific vision, the summit of eternal glory, its rival and first step? But what is more execrable than it when corrupted? What more wicked? What more harmful to the Church? Did not so many heresies spring from it? Did not so many unspeakable abortions of dogmas? Is not Religion the Prince and Queen of all virtues? But to transform this into superstition

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Transcription: ATR-1

PRAEFATIO. studet nequissimus hostis, vt de honore Dei, Deo parare possit iniuriam. Naturæ dona, & maxima adjumenta suis tricis sæpe maculat, & corrumpit inuidus, vt ijs vel religione adducti non vtamur in nostrum commodum tamquam suspectis, vel sanè tanquam ab eo exhibitis, ac deprauatis. Hoc ipsum plane efficit in sublimioribus mathesis disciplinis: etenim nil ipsis ab initio innocentius, nil vtilius; nil humano generi conducentius fuit: At enim vel inde, quia nobis proficue, quia earum legitimus vsus homines ad vitæ optimè instituendi rationem conducit, ideò eas potissimu[m] superstitionibus satagit conspirare, & cum ex alia parte futura præsciendi à nostræ conditionis exordio naturalis nobis insit affectus, ex hoc genio ad naturæ limites transigendos nos studet impellere, ac non modò quæ à naturalibus causis necessario pendent, prænoscere, verum etiam, quæ vltrà captum sunt, quæ à libera voluntate pendent, tanquam ex astris ortum ducant, perscutari curiosos quosque minusque cautos extimulat, adigitque. Hinc Astronomiæ Astrologia succedit, & quia hæc notitia experimentalis tantum erat, & curiosa nimis, quæ mire animos hominum titillabat, Chaldæi super omnes superstitiosiores in eam toti incubuerunt:

Transcription: Translated (English)

PREFACE. The most wicked enemy strives so that, from the honor of God, he may be able to prepare an outrage against God. He often stains and corrupts with his tricks the gifts of nature and the greatest helps, the enemy of the human race, so that we either do not use them for our own advantage, being persuaded by religion to regard them as suspect, or indeed as having been provided and perverted by him. He plainly brings this about even in the more exalted disciplines of mathematics: for in the beginning nothing was more innocent, nothing more useful, nothing more conducive to the human race. Yet because they are profitable to us, because their legitimate use leads men to the method of ordering life in the best way, he especially endeavors to combine them with superstitions; and since on the other hand there is in us, from the beginning of our condition, a natural desire to know future things, from this impulse he seeks to drive us to go beyond the limits of nature, and not only to foreknow what necessarily depends on natural causes, but also what lies beyond our grasp, what depends on free will, as though it drew its origin from the stars; he incites and urges the curious and the less cautious to investigate these things. Hence Astrology follows Astronomy; and because this knowledge was merely experimental and excessively curious, and wonderfully tickled the minds of men, the Chaldeans, more superstitious than all others, devoted themselves wholly to it:

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Transcription: ATR-1

PRAEFATIO. Vnde omnes Philosophiæ limites prætergressi ad diuinatoriam simpliciter, siue ambitione ducti, siue spe quæstus illecti se conuerterunt. Vnde iam omnis Mathesis co[n]spurcata, omnis Mathematica disciplina iam malè audire coepit, proindeque & Mathematici Vrbe pulli, & omnis eoru[m] scientia tanquam infamis, & Reipublicæ exitialis est habita. Eapropter operæ pretium me facturum existimaui, si laruam tandem nobilissimis his facultatibus tollerem, ac zizania à tritico segregarem: eas suo nitori suæ innocentiæ restituendo, quod vt assequeret, in hoc opere id mihi præfixi, vt non tam Mathesis principia veræ Philosophiæ innixa, quam etiam vanitates, quibus conspurcata fuit, ostenderem, vt ijs perspectis Mathesis studiosus eam tutò capesseret, bonam doctrinam teneret, fallam reijceret, atque à se toto animo ablegaret. Opus equidem magni laboris, & quod Atlanthæos humeros expostulasset, ni bonorum amicorum, ac præcipuè eruditissimi conciuis mei Angeli Duratij, (qui & opera, & libris iugiter mihi astitit) in eo exornando auxilium accessisset, ac plurima suppeditasset. Lexicon ergò Mathematicum, ex omnibus Mathesis scriptoribus compilaui, in id præcipuè incumbens

Transcription: Translated (English)

PREFACE. Whence all the bounds of Philosophy having been overpassed, men turned themselves simply to divination, whether driven by ambition or enticed by hope of gain. Hence now the whole of Mathematics was defiled, and the entire mathematical discipline began to fall into ill repute; and thus Mathematicians were driven from the City, and all their science was held as infamous and destructive to the Commonwealth. For this reason I thought I should do something worthwhile if I would at last remove the mask from these most noble faculties, and separate the tares from the wheat: restoring them to their own splendor and their innocence; and in order to accomplish this, I set this aim before myself in this work, that I should show not so much the principles of Mathematics, founded upon true Philosophy, as also the vanities with which it was defiled, so that, these things being understood, the student of Mathematics might safely take it up, hold fast to sound doctrine, reject falsehood, and banish it from himself with all his heart. Truly a work of great labor, and one that would have required Atlantean shoulders, had not the help of good friends, and especially of my most learned fellow citizen Angelo Durati, who continually assisted me both with his work and his books, come to aid in embellishing it and supplied very many things. Therefore I compiled this Mathematical Lexicon from all the writers on Mathematics, chiefly applying myself to that end.

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Transcription: ATR-1

PRAEFATIO. vt & abstrusiora vocabula, vt plurimum Araba, Aegyptiaca, Barbara (quandoquidem apud has nationes Mathematicæ disciplinæ potissimum floruerunt) explicarem, & vniuersæ Mathesis Principia, Canones, Pronuntiata, Demonstrationes, Problemata, ordinatissima methodo dilucido scribendi genere, atque absoluta verborum descriptione traderem, ac penè ad viuum delineata oculis exhiberem. Vt proptereà facile sit cuiuis haud rudis ingenij, suo Marte plenam harum scientiarum notitiam comparare, aut saltem quemvis Authorem expedite percurrere. Quod adeò difficile Anatolius æstimauit, vt vel ob id Mathematicas scientias, disciplinas dixerit appellatas, quod cum cæteræ facultates libroru[m] lectione, ac solo discursu percipi possint; hæ nonnisi Magistro docente ac demonstrante: quandoquidem vt rectè monebat M. Tullius, Mathematici in magna rerum obscuritate, recondita arte multiplici ac subtili versantur: vt proptere à non ab re nec sine magno consilio censendum sit, veteres illos, ac prudentes viros constituisse, vt à teneris annis pueri in eiusmodi artibus erudirentur. Sed enim hac in re, ni fallor, palmam proripuisse me arbitror, clauumque nodo fixisse. Etenim cum rerum intelligentia magna ex parte ex terminorum

Transcription: Translated (English)

PREFACE. so that I might explain the more obscure terms, for the most part Arabic, Egyptian, Barbarian (since among these nations the Mathematical disciplines flourished especially), and might hand down the Principles, Canons, Assertions, Demonstrations, Problems, of the whole of Mathematics, by the most orderly method, in a clear style of writing, and with a complete description of the words, and might exhibit them, as it were, delineated to the very life before the eyes. So that therefore it may be easy for anyone not devoid of intelligence, by his own effort to acquire a full knowledge of these sciences, or at least to run through any author with ease. This Anatolius judged to be so difficult, that for that very reason also he said the mathematical sciences were called disciplines, because whereas the other branches may be grasped by reading books and by reasoning alone; these only with a teacher instructing and demonstrating: since, as M. Tullius rightly warned, mathematicians in a great darkness of things are engaged in a hidden art, manifold and subtle: so that therefore it may not be without reason nor without great deliberation to judge that the ancients, those prudent men, established that from tender years boys should be trained in such arts. But indeed in this matter, unless I am mistaken, I think I have snatched the palm and driven the nail home. For when the understanding of things largely arises from the terms

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PRAEFATIO. notitia pendeat, hæque potissimum facul- tates vocabulorum multitudine, diuersita- te, ac barbarie opprimantur, vt vel hæc vna consideratio me olim ab his studiis ab- Iteruerit; profecto de litteraria republi- ca me optime meriturum credidi, si quam ipse prouinciam duram, & cespitosam of- fendi, hanc aliis complanarem: in qua la- nè re, si scopum attigi, Lectoris esto iudi- cium. Nec tamen Novitiis solum scribo: habebunt ipsi, quæ ad probam scientiarum notitiam necessaria sunt, atque emeritis Professoribus obuia, habebunt & doctio- res, quibus non tædio afficiantur, sed no- uarum rerum pabulo animum nutriant; va- rietate recreent, soliditate stabiliant. E- quidem plus fortè in ipsa operis excursione inveniet Lector, quàm simplex titulus præ- se fert: videbit enim me ibi non purum compilerator emagere, sed vbi res postula- uerit, nouas ealque grauissimas specula- tiones subnectere, examinare, deducere; è meique tenuis licet ingenij poena merces adhuc invisas depromere, quibus totam fere Naturam expendo, atque areanorum eius conuenientissimam rationem afferre, vt probum decet Philosophum nitor. Quod ideò vt lectoribus morem gererem, placuit peculiarem sillabum centum plus quæstio- num, quæ in hoc opere non perfunctoriè

Transcription: Translated (English)

PREFACE. knowledge depends, and these faculties are especially oppressed by the multitude, diversity, and barbarity of words, so that even this one consideration once turned me away from these studies; indeed, I believed that I would best serve the literary commonwealth if I made smooth for others whatever rough and uneven province I myself encountered. In this matter, if I have attained my aim, let the reader judge. Nor do I write for beginners alone: they will find here what is necessary for a sound knowledge of the sciences, and what is suited also to accomplished Professors; the more learned too will find it, so that they may not be wearied, but may nourish their minds with the sustenance of new things, refresh them with variety, and strengthen them with solidity. Indeed, the reader will perhaps find more in the course of the work itself than the simple title suggests: for he will see that I am not there merely a compiler, but that, where the matter requires it, I add new and very serious speculations, examine them, and draw them out; and, though it be but the reward of my slight talent, I bring forth long-hidden things, by which I set forth almost the whole of Nature, and offer the most fitting account of its hidden matters, as beseems an upright Philosopher I strive. Therefore, to accommodate readers, it seemed good to add a special syllabus of more than a hundred questions, which in this work not perfunctorily

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PRÆFATIO. examinantur, attexere, atque ipsi præfigere, quò quivis quidquid non ita vulgarè, non ita obuium quætitate præsto sit inuenire; sicque doctiores haberet, quæ non multo labore, atque vnico ictu oculi in multis possent ingenij auiditatem explere. Alia verò non vulgaria, quæ incidenter quidem non tamen minus obseruatione digna sparsim in opere dicta sunt, huius signi ad margine appinxionem indigitauimus. Cæterum quæ hic puriora, atque innocentiora præcepta ex Astrologicis allegauero, ea non nisi ex Ptolemæo, aut ab Ecclesia probatis scriptoribus sumpti, ve in operis excursione prudens lector videre poterit. Quod si quid adhuc ex Pontano, aut Firmio nimis audenter, præsertim de stellis fixis, dictum inuenerit, id vel vbi opus fuerit explico moderor, castigo aut Philosophicis rationibus comprobo; aut sanè ad purum ornatum appono: cum aliàs hi auctores magni nominis sint non tam doctrinæ veritate quam stili elegantia, vnde & eorum opera ab Ecclesia permissa sunt in Pontano quidem ob poëtis excellentiam, quæ cum primoribus poësis pugnat; in Firmicò autem ob Sermonis amoenitatem: quod ideo ab Latinæ linguæ Professoribus præsertim Ambrosio

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Preface. ...are examined, to which I have added, and before which I have prefixed, so that anyone may find whatever is not so commonplace, not so readily at hand, by searching; and thus the more learned may have things which, with little labor and with a single glance of the eye, may satisfy a thirst for knowledge in many matters. Other uncommon things, which have been mentioned incidentally in the work, though not less worthy of observation, we have indicated by the insertion of this sign in the margin. Moreover, those purer and more innocent precepts from Astrology which I have here set forth are taken only from Ptolemy, or from writers approved by the Church, as the prudent reader will be able to see in the course of the work. And if he should find anything still too boldly stated from Pontanus or Firmius, especially concerning the fixed stars, I either explain it where necessary, moderate it, correct it, or confirm it by philosophical reasons; or else I set it down merely as graceful ornament. For otherwise these authors are of great name, not so much for the truth of their doctrine as for the elegance of their style, and therefore their works have been permitted by the Church: in Pontanus’ case because of his excellence in poetry, which conflicts with the foremost rules of poetry; but in Firmicus’ case because of the pleasantness of his language: which therefore by teachers of the Latin language, especially Ambrose

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PRAEFATIO. Calepino ex eo sæpissime testimonia desumuntur. Quæ verò à me minus cautè, minus fundatè in hoc opere dicta sunt non modò S. R. E. censuræ sed & tuæ humanissime lector castigationi lubens subiicio.

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PREFACE. From Calepino, testimonies are very often drawn. Whatever, however, has been said by me less cautiously, less soundly in this work, I willingly submit not only to the censure of the Holy Roman Church, but also to your correction, most courteous reader.

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Censura Patrum Reuisorum. ADMODVM REVERENDE PATER. Lexicon Mathematicum à Patre D. Hieronymo Vitali nostrę Congregationis Theologo elaboratum, demandato Admodum R.P vestrę perlegimus; nihilque ineodatum est offendere, quod Catholicæ Fidei, aut bonis moribus adversetur. Perutile profectò opus, & quod vel terminorum elucidando proprietates, vel idemtidem varias exoticasque dirimendo quæstiones, vberem Mathematicarum scientiarum studiosis offerat segetem. Typis proinde dignum existimavimus Neapoliprid. Kal. Augusti 1663. D. ANTONIVS CARAFA Cler. Reg. S. Theol. Prof. electus Episcopus Vgentinus. D. CAROLVS PIGNATELLVS Cler. Reg. Sac. Theol. Profess. Approbatio. D. Angelus Pistachius Prepositus Generalis Clericorum Regularium. Hoc opus inscriptum, Lexicon Mathematicum, à P. D. Hieronymo Vi-

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Approval of the Reviewing Fathers. MOST REVEREND FATHER. The Mathematical Lexicon, worked out by Father D. Hieronymus Vitali, theologian of our Congregation, at your Most Reverend request, we have read through; and we have found nothing to object to, insofar as it is contrary to the Catholic Faith or to good morals. Indeed, it is a very useful work, and one that, by clarifying the properties of terms or by resolving various and foreign questions from time to time, offers a rich harvest to those devoted to the mathematical sciences. We therefore judged it worthy of the press at Naples, on the Kalends of August 1663. D. ANTONIVS CARAFA, Royal Cleric, Elect of the Bishopric of Ugento, Professor of Sacred Theology. D. CAROLVS PIGNATELLVS, Royal Cleric, Professor of Sacred Theology. Approbation. D. Angelus Pistachius, Prepositus General of the Clerics Regular. This work, entitled Lexicon Mathematicum, by P. D. Hieronymus Vi-

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tali nostræ Congregationis Theologo compositum, & iuxta præfixam assertionem P.P. Theologorum, quibus id commisimus, approbatum, vt Typis mandetur, quoad nos spectat, facultatem concedimus. In quorum fidem præsentes litteras manu propria subscripsimus, & solito nostro sigillo firmauimus. Romæ Kalendis Februarij 1664. D. ANGELVS PISTACHIVS Præpositus Generalis Cleric. Regul. Locus † sigilli. D. CAROLVS LOBELLS C. R. Secret. -------------------------------------------------------- Opus attitulatum de vulnerum, aliorumque morborum curatione magnetica quæstiones tres Auctore Admod. Reu. Patre Hieronimo Vitali Clerico Regulari à me reuisum, potest ad publicam vtilitatem typis mandari, cum nihil contineat contra Orthodoxam & Catholicam doctrinam & bonos mores. In quorum fidem has propriam manu subsignaui in Conuentu S. Augustini de Padua Ordinis Prædicatorum tertio nonas Februarij 1659. Ego F. CYPRIANVS PHILIPPINVS Ordin. Prædicatorum Sac. Theol. Magister & in vniuersitate Patauina eiusdem facultatis publicus Professor.

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...of our Congregation, composed for the Theologian, and, according to the previously stated approval of the Theologians, to whom we entrusted this matter, approved to be committed to print, so far as pertains to us, we grant permission. In witness whereof we have signed these letters with our own hand, and confirmed them with our customary seal. At Rome, on the Kalends of February 1664. D. ANGELVS PISTACHIVS, General Prelate of the Clerics Regular. Place of the seal. D. CAROLVS LOBELLS, C. R. Secretary. -------------------------------------------------------- The work entitled de vulnerum, aliorumque morborum curatione magnetica , three questions, by the Very Reverend Father Hieronimo Vitali, Cleric Regular, having been revised by me, may be committed to print for the public benefit, since it contains nothing against Orthodox and Catholic doctrine and good morals. In witness whereof I have signed these presents with my own hand in the Convent of St. Augustine of Padua, of the Order of Preachers, on the third day before the Nones of February 1659. I, F. CYPRIANVS PHILIPPINVS, of the Order of Preachers, Master of Sacred Theology, and public Professor of the same faculty in the University of Padua.

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HIERONYMI VITALIS CLERICI REGULARIS LEXICON MATHEMATICVM ALPHABETICO ORDINE digestum, & compilatum. A , FIGVRA celebtis est, ac familiaris omnibus Ma- thematicis: non quidem quà prima litteraru[m] nota, atque Alphabeti vtriusque tam Græci, quàm Larini maximum, primumque in ordine Elementum; sed quà Mathesis janua, præcipuumque Mechani- Corum omnium, quæ à Mathesi prodeunt: instrumetum: in quo velut in compendio, omnia ferè Geometrica Elementa, omnis Triangulorum proportio, omnis quantitatis mensura, omnis Sinuum, Secantium, & Tangentium praxis, & omnia denique instrumenta ad Mathesin quovis modo spectantia restricta sunt. Quadram vulgus Italorum vocat: Latini Normam, seu Amussim, constantem duabus regulis planis in rectum angulum coëuntibus, atque aliâ in media distantia vtrique transuersâ, quæ eas inuicem nectat, ac Triangulum æquilaretum cum illis constituat, efformetque. Hanc Suem humi nostro delin- easse non sine coelesti consilio scribit Cicero lib. 1. de Diui- nacione: Hanc è Phoenice in Græciam à Cadmo allaram testatur Plinius lib. 7. c. p. 56. de rerum inuentoribus agens. Egregium sanè inuentum, ac propè dixerim s diuinum. Nec, quia vulgare, & vel ipsis Cæmentarijs obuium, à sublimiolum disciplinarum Professoribus aspernandum; vt proptereà eius laudes hic accensere, munia explicare, nostro instituto æstimenus indignum. Etenim & in hoc instrumento, Circini non obcuram speciem, & in eo Regulam spectare est. Duo, inquam, A

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HIERONYMI VITALIS CLERICI REGULARIS MATHEMATICAL LEXICON ARRANGED IN ALPHABETICAL ORDER digested and compiled. A , a celebrated and familiar figure to all mathematicians: not indeed as the first letter, and the first and greatest element of the alphabet, both Greek and Latin; but as the gate of mathematics, and the chief instrument of all mechanical things that arise from mathematics: in which, as it were in a compendium, almost all geometrical elements, every proportion of triangles, every measure of quantity, all the practice of sines, secants, and tangents, and, finally, all instruments in any way pertaining to mathematics are contained. The common people of Italy call it the square; the Latins, a rule or set-square, consisting of two straight rules meeting at a right angle, and another crosspiece midway between them, which joins them together and forms with them an equilateral triangle. Cicero writes in Book 1 of De Divinatione that this was drawn by a pig on the ground, not without heavenly counsel: Pliny testifies that it was brought from Phoenicia into Greece by Cadmus, in Book 7, chapter 56, where he speaks of inventors of things. Surely an excellent invention, and I might almost say a divine one. Nor, because it is common and even found in the hands of craftsmen, should it be despised by the more eminent professors of the disciplines; so that for that reason we should think it unworthy of our purpose to set forth here its praises and explain its uses. For in this instrument one can see, not without some appearance of the compass, and in it the rule as well. Two, I say,

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LEXICON tentissima Geometrarum subsidia, quibus omnes ferè Mathematicæ operationes co[m]plentur, & circa quos veluti Polos, omnis doctrina recti & curui, plani & sphærici, laterum ac angulorum voluitur, & versatur. Summus apex denotat punctum omnis dimensionis expers: latera, lineas. Si vno pede, præsertim acuminato in plana superficie fixo, alter circumducatur, Circulus describetur; cuius centrum referet similiter punctum. Si eius figuram directè intuearis, Triangulu[m] æquilaterum, vt supra innui, tibi in promptu erit: Si perpendiculum ad transversi quascumque partes figas, iam omnem Acutangulorum, Obtusangulorum speciem exhibebit. Si demum extrema latera arcu compleas, vel sanè, vt in aliquibus fieri assolet, ea non rectus, sed curius connectat axis nonaginta gradibus interstinctus, profectò Circuli quadraturam explicare poterit, & Quadrantis Geometrici subire vices; eius, inquam, instrumenti, quo regula proportionum traditur, sidera speculamur, horas distinguimus, distantias venamur, ac ferè omnes geometricas operationes perficimus, cuius laudes, atque officia in loco, vbi de eo recurret sermo prosequemur. Refert quidem pro miraculo Aristoteles lib. 5. Mor. Eud. apud Lesbum inuentum nescio quod instrumentum è plumbo tàm benè compactum, vt si mensurandis solidis, durisque lapidibus aptaretur, suam formam ad illorum formam redigeret; itaut modò triangulare, modò quadrangulare, modò etiam circulare, pro eorum se varietate præberet: Verùm si mollius applicaretur, eadem repensâ vice in sui similitudinem efformabat; vt proinde non vniùs regulæ solùm, sed & quam plurium instrumentorum sæpè onus subiret. At enim hæc & longè digniora miracula in nostro instrumento videmus. Quæ qui per partes ediscere, ac demirari volet, adeat Celeberrimi illius nostri sæculi Galilæi Circinum, eiusque vsum non ab se, sed à Balthassare Capra peculiari libello descriptum, vbi sanè inuenier quidquid studiosissimum harum disciplinarum animum possit complere. Interim fausto omine aggrediatur benignus Lector nostri Operis excursionem: cuius specimen vel in ipso eius vestibulo exhibet fortuita nobis occurrens, A, figuræ consideratio: quando ex vulgari, ac noto instrumento, quod oculis corporeis obiicit, totius Mathesis summam, atque ideam exhibet oculis mentis inspiciendam; proindeque animum addit ad eius studia feliciter capessenda. AB 4. ABACVL vocabantur olim, teste Plinio lib. 36. cap. 26. Calculi numerales, quibus rudis Antiquitas Arithmeticæ adhuc ignara in supputationibus computationibusque vtebatur: vnde

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The most useful aids of geometers, by which almost all mathematical operations are completed, and around which, as around poles, the whole doctrine of the straight and curved, the plane and the spherical, of sides and angles, turns and revolves. The highest point denotes a point devoid of all dimension; the sides, lines. If, with one foot, especially a pointed one, fixed upon a flat surface, the other is turned around, a circle will be described, whose center likewise represents a point. If you look directly at its figure, an equilateral triangle, as I hinted above, will be ready to hand for you. If you set the plumb line to any parts of the crossbar, it will now display every kind of acute-angled and obtuse-angled figure. If at last you complete the outer sides with an arc, or indeed, as happens in some cases, if an axis, marked off by ninety degrees, joins them not by a straight but by a curved line, it will certainly be able to explain the squaring of the circle, and to serve the purposes of a geometrical quadrant; namely, that instrument by which the rule of proportions is handed down, by which we observe the stars, distinguish the hours, pursue distances, and perform almost all geometrical operations; its praises and functions we shall discuss in the place where further mention of it will recur. Aristotle indeed relates, as a marvel, in book 5 of the Moral Eudemian Ethics, a certain instrument found near Lesbos, made of lead so well compacted that, if it were fitted to measuring solid and hard stones, it would reduce its own shape to the shape of those stones; so that it would present itself now triangular, now quadrangular, now even circular, according to the variety of their forms. But if it were applied more softly, by the same sudden turn it would be shaped into its own likeness, so that it would often bear not the burden of one rule alone, but of very many instruments. Yet in our instrument we see miracles both greater and far more deserving of wonder. Whoever wishes to learn and admire these things in detail should turn to the Circinum of that most celebrated Galileo of our century, and to its use described not by himself, but by Balthassare Capra in a special little book, where indeed he will find whatever can satisfy a mind most devoted to these disciplines. Meanwhile let the kindly reader, under a happy omen, undertake the excursion of our work, a specimen of which even at its very threshold is presented by the figure A, fortuitously meeting us: for from a common and familiar instrument, which presents itself to bodily eyes, it displays the sum and idea of the whole of Mathematics to be inspected by the eyes of the mind; and thus it encourages the mind to take up its studies happily. AB 4. ABACVL were formerly called, as Pliny bears witness, book 36, chapter 26, the counting pebbles, which rude antiquity, still ignorant of arithmetic, used in reckonings and computations: whence

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METHEMATICVM. ortum erediderim vulgare nomen, Abacum, quo nos Itali Arithmeticas notas promiscuè explicamus: eas inquam, quæ certo ordine ac methodo inter se dispositæ, quemuis nume- rum vel innumerabilem comprehendunt. Vt mirum sit totam Arithmeticam, hoc est amplissimam facultatem omnium Ma- thematicarum potissimam, sine qua nec vlla comparari po- rest, nec ( poenè dixerim) diu Orbis consistere, in paruo, de- cem videlicet numeralium Elementorum ambitu contineri. Ea sunt 1.2.3.4.5.6.7.8.9.0. Quæ ab vnitate vsque ad nouem progrediendo, singulorum numerorum per ordinem notæ unt & characteres: numerus autem denarius per o. cifram, talis Zero dictam exprimitur, non quidem se sola, sed alte- ius notæ additione quam in decuplum auget, totque denarios indicat, quot vnitates, numerus; seu nota illi præposita si- gnificare habet: itaut si hæc fuerit 1. cum fulcimento illius ci- liæ o. (se sola nihil significantis) exprimar decem, hoc est num denarium: si 2. eidem p[ro]xponatur, indicet viginti, hoc est duos denarios: si tres, triginta, hoc est tres denarios, & e deinceps vsque ad nonaginta. Hinc præpositâ, & superad- itâ aliâ figurâ, explicatur numerus centenarius, eodem ordine rogrediendo. Quòd si quarta nota addatur, ea erit numeri millenarij; si quinta, tot vnitates millenarij, hoc est tot mille- orum numerum, quot ea nota quæ cæteris anteponitur, se sola nitates significaret. Si sexta, tot centenoru[m] millium index est: demum seprima, per eam habetur numerus millenorum mil- um: itaut semper nota superaddita numerum posteriorem pro ii qualitate multiplicet ad caput semper reuertendo vsque in finitum. Itaque (vt id compendio repetam) vltima nota (si ioqui est significatiua) se sola, seu aliis comitata, indicat umerum simplicium vnitatum: penultima denarij: antepenul- na centenarij: quæ his omnibus anteponitur, tor indicat de- rios millenarij: quæ adhuc superadditur, centenos millena- rs, & sic deinceps prosequendo in infinitum, atque ad caput nper regrediendo. Ex hac numerorum connexione, propor- ne, collisione, ac respondentia tot miracula exantlantur, vt ritò Libellus non ità pridem in lucem editus, quo per varios merorum ordines arcana multa operari, perscrutarique ocemur, Thaumaturgus Mathematicus sit appellatus. Eum vi- sit curiosus lector, & non pigebit. BALANTICA siue Alantica, Arabicè Armillam sonat suspen- iam in summitate Astrolabij, Planisphærij, aut aliûs consi- lis instrumenti sitam ad illud perpendiculariter statuen- n; quo siderum distantias, positûs, altitudines, aliaque multa exquisitè contemplari possimus. A ij

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Mathematicum. I would take it to be the common name, Abacus, by which we Italians indiscriminately explain the numerical signs: I mean those which, arranged among themselves in a certain order and method, comprehend any number whatsoever, even the innumerable. So it is wonderful that the whole of Arithmetic, that is, the most extensive faculty and the chief of all the Mathematical sciences, without which none can be compared, nor, I may almost say, can the world long subsist, should be contained within a small compass, namely within the range of ten numeral elements. These are 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. These, advancing from unity up to nine, are the notes and characters of the individual numbers in order. But the number ten is expressed by 0, a cipher, called Zero, not indeed by itself alone, but by the addition of another figure, which increases it tenfold, and indicates as many tens as there are units signified by the number, or the figure placed before it; so that if this be 1, supported by that cipher 0 (which by itself signifies nothing), it expresses ten, that is, one ten: if 2 be prefixed to the same, it indicates twenty, that is, two tens: if 3, thirty, that is, three tens, and so on up to ninety. Hence, with another figure added before and above it, the hundred number is expressed, proceeding in the same order. If a fourth figure be added, it will be that of the thousands; if a fifth, it will denote so many units of thousands, that is, so many thousand as the figure placed before the others would, by itself, signify units. If a sixth, it is the sign of so many hundreds of thousands; finally, by the seventh, the number of thousands of thousands is obtained: so that each figure added above always multiplies the following number according to its value, always returning to the head, even to infinity. And thus, to repeat it briefly, the last figure (if it is significant by itself, or accompanied by others) indicates the number of simple units; the penultimate, of tens; the antepenultimate, of hundreds; that which is placed before all these, indicates as many tens of thousands; that which is added yet above, hundreds of thousands; and so on, continuing into infinity, and always returning to the beginning. From this connection, proportion, collision, and correspondence of numbers, so many wonders are wrought that a little book published not long ago, in which we are taught to work out and investigate many hidden things by various orders of numbers, was rightly called The Mathematical Thaumaturgus. Let the curious reader consult it, and he will not regret it. BALANTICA, or Alantica, in Arabic signifies the armilla suspended at the summit of the Astrolabe, Planisphere, or some other such instrument, placed there to set it perpendicularly; by means of which we may exquisitely contemplate the distances, positions, heights, and many other things of the stars.

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4 LEXICON 6. ABEN RAS, vel Ras Eltanin, latinè Caput Draconis: dicitur apud Arabes stella fixa pellucida in Capite Draconis sideris ad polum Arcticum, quod ipsum polum Zodiaci ambit & circumplectitur. Ipsa autem stella distat nunc à polo Arctico 15. ferè gr. estque tertiæ magnitudinis de natura mixta ex Ioue, Saturno, & Marte, Vide fusius in Veibo Draco. 7. ABRACHALEVS Chaldaicè, seù, vt passim corrupto nomine circumfertur, Garacles: Caput Herculis, seù Pollucis alterius Geminorum, & subsequentis: stella videlicet rufa, & subflaua de natura Martis secundæ magnitudinis, inter Regias quidem computata, sed tamen est etiam vna ex violentis De qua proinde nugantur Astrologi, quod si cum Luminari Conditionario reperta fuerit, altero in signo violento existente, mortem portendat itidem violentam. Existit nunc in gradu ferè 19. Cancri cum gr. 6. latitudinis borealis. 8. ABSCISSIO LUMINIS, Arab. Almana, est deterioratio Planetæ, quæ contingit quoties tres Planetæ fuerint intia fines suorum Orbium, itaut medius sit ponderosus; alius leuior in paucioribus gradibus signi eidem ponderoso applicans, ac rettius, qui sit in pluribus gradibus, desluatque à ponderoso post partitem cum eo coniunctionem; vetum antequam primus directè gradiens corpore iungatur ponderoso illi, tertius interim factus retrogradus eidem denuò retrocedens iungatur: tunc iste tertius diceretur lumen prioris abscindere. Potest id etiam accidere alio modo: is est, cum ex tribus medius applicat ad coniunctionem posterioris, sed alius leuior, qui est in paucioribus partibus, cursu illum anteuenit, eoque relictio, prius corpore iungatur tertio, quam secundus id prius affectans. Quod sæpissimè præstat Luna omnium velocissima. In eo igitur casu diceretur abscissum lumen eius, qui prior alteri applicabat ab eo qui postremò eidem applicans, ociùs tamen ad illum pertingit. 9. ABSIS, seu Apsis, Græcè, Suida teste, propriè significat fornicis curuaturam. Hinc apud Astronomos transferri solet ad significandam tum summam, & superiorem Circuli partem, in qua planetæ existens maximè à terra elongatur; tum infimam, in qua sit terræ proximior, quam fieri possit. Et illud quidem punctum in quo maximè elongatur, dicitur Apogæum, ab Arabibus verò Aux: hoc autem Perigæum, & Oppositum Ausis in quo manens Planeta à Græcis appellatur Hypaugus, hoc est tertæ vicinus. Potiò huiusmodi puncta considerantur tàm in Eccentricis, quàm in Epicyclis? quæ quidem (licet lentissimo motu) cientur, & locum permutant in Zodiaco; ac singuli planetæ proprias Absides habent in certis Zodiaci gradibus, vt

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4 LEXICON 6. ABEN RAS, or Ras Eltanin, in Latin Caput Draconis: it is said among the Arabs to be a bright fixed star in the Head of the Dragon, near the Arctic pole, which pole itself embraces and encompasses the Zodiac. That star is now distant from the Arctic pole about 15 degrees, and is of the third magnitude, of a mixed nature from Jupiter, Saturn, and Mars. See more fully in the word Draco. 7. ABRACHALEVS in Chaldaic, or, as it is commonly corruptedly called, Garacles: the Head of Hercules, or of the other Pollux of the Gemini, and the following one: namely a reddish star, and somewhat yellow, of the nature of Mars, of the second magnitude, reckoned among the Royal stars, yet it is also one of the violent ones. Astrologers therefore prattle that if it is found together with the Conditionary Luminary, with the other being in a violent sign, it likewise portends a violent death. It is now in about the 19th degree of Cancer, with 6 degrees of northern latitude. 8. ABSCISSIO LUMINIS, Arab. Almana, is the deterioration of a planet, which happens whenever three planets are within the bounds of their own orbits, so that the middle one is ponderous; another lighter one, in fewer degrees of the same sign, approaching the ponderous one more directly, and the one that is in more degrees, falling away from the ponderous one after a partial conjunction with it; but before the first, moving directly and joining itself bodily to the ponderous one, the third, meanwhile having become retrograde, again going back and joining the same: then that third would be said to cut off the light of the first. This can also happen in another way: namely, when out of three the middle one applies to the conjunction of the later one, but another lighter one, which is in fewer degrees, outstrips it in course, and leaving it behind, is bodily joined to the third before the second, who is striving for this first, does so. The Moon, the swiftest of all, very often does this. In that case the light of him who first was applying to the other would be said to be cut off by him who last applies to the same, yet reaches him more quickly. 9. ABSIS, or Apsis, in Greek, according to Suidas, properly signifies the curvature of an arch. Hence among astronomers it is commonly transferred to signify both the highest, and upper part of a Circle, in which a planet exists most distant from the earth; and also the lowest, in which it is nearest to the earth as much as possible. And that point indeed in which it is most distant is called the Apogee, by the Arabs however Aux: this is called the Perigee, and the opposite of Ausis in which the planet abiding is called by the Greeks Hypaugus, that is, nearest to the earth. Moreover such points are considered both in eccentrics and in epicycles, which indeed (though with a very slow motion) are moved, and change their place in the Zodiac; and each of the planets has its own Absides in certain degrees of the Zodiac, as

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MATHEMATICVM. 5 suo loco dicemus. Ex hac mutatione Absidum, ac transitu de vno in aliud signum, Astrologi Iudicarii sua solita vanitate ma- < *> gnas in mundo mutationes fieri contendunt, Regnorumque vicissitudines deriari. Quod & in maguis coniunctionibus, atque in mutationibus obliquitatis Ecclipticæ, quippequæ non nisi rarò eueniunt idipsum asserunt. Hinc Cardanus in Com- < 10.> mentar. ad Centiloquium Ptolemæi propos. 37. hæc habet. Mutationes Absidum regns, regiones, & religiones mutant. Et lib. 5. Aphor. 129. differens de mutatione Ausis Solis, hæc au- det tanquam ex Cathedra pronunciare. Absis, inquit, Solis ab < 11.> Ariete in Cancrum proficisciens inhabitabilem reddit Austrinam par- tem, Borealem autem habitabilem facit: à Cancro ad Libram benè habitabilem Borealem, & Australi dominantem: à Libra ad Ca- pricornum Austrinam habitabilem, sed Boreali partimimè im- perantem: à Capricorno ad Arietem, Australem imperantem Bo- < 11.> reali desolata efficit. Hæc Cardanus. At quo tandem fundamento id profert? Ratione forsitan ductus, vt bonus Philosophus; an verò experimento pluries repetito, vt Astrologus? Rationem vllam non affert, sed nec apparens elucet: Experimentum hac in se nullum habere potuit: Nam vt benè aduertit Ricciolus in < *> Almagesto nouo, lib. 7. sect. 5. in Scholis, ab initio Mundi < 11.> Apogæum Solis vix primum quadrantem confecit, cum nunc temporis sit in primis partibus Cancri, atque adeò in initio se- cundi quadrantis, nec tertium, nec quartum vnquam confecit, nec forte vnquam conficiet, cum simus iam in Mundi senecta. Quomodò igitur scire potuit Cardanus quæ posteris sæculis < *> futura sunt, & fortasse non erunt? Benè quidem ex hac muta- < 11.> tione Absidum coniectari poterit habitabilitas regionum ra- tione Climatum, qua ex accessu Solis ad Apogæum, vel Peri- < 11.> gæum variari debeant, ac proinde alicubi habitatio euadat moderatior, aut immoderatior, idque ratione maioris pro- < 11.> pinquitatis, & radiorum vel rectiorum, vel obliquiorum traiectione. Sic Sole nunc Apogæo in Cancro, & Perigæo in < 11.> Capricorno, quia in æstate remotior, atque in hyeme proxi- < 11.> mior sit telluri in nostris Borealibus regionibus, ideò modera- < 11.> tior est, ac magis magisque sit in æstate calor, & frigus in < 11.> hyeme, quam si foret Apogæus in Capricorno & Perigæus in < 11.> Cancro, vt sane ex historijs, & collatione priscorum tempo- < 11.> rum cum nostris præsentibus liquet. Econtra in regionibus < 11.> trans Æquatorem, ac maximè Australioribus, quia in æstate < 11.> Sol Perigæus in Capricorno terræ sit proximus, eamque di- < 11.> rectionibus radijs verberat; atque in hyeme constitutus in < 11.> Apogæo in Cancro ab ea maximè elongatur, & insuper obli- < 11.> quis valdè radiis illustrat, ideò immoderatior semper sit vtra < 11.> A iij

Transcription: Translated (English)

MATHEMATICVM. 5 we shall speak in its proper place. From this change of the Apogees, and the passage from one sign into another, Judicial Astrologers, with their accustomed vanity, contend that great changes occur in the world, and that the vicissitudes of kingdoms are brought about. The same thing they assert also with regard to the great conjunctions, and to the changes in the obliquity of the Ecliptic, since these happen only rarely. Hence Cardanus, in the Commentary on Ptolemy’s Centiloquium, proposition 37, has this to say. Changes of the Apogees change kingdoms, regions, and religions. And in book 5, Aphorism 129, speaking of the change of the Sun’s Apogee, he dares to pronounce as though from the chair: The Sun’s Apogee, he says, going from Aries to Cancer makes the southern part uninhabitable, but the northern part habitable: from Cancer to Libra it makes the northern part well habitable, and the southern part dominant: from Libra to Capricorn it makes the southern part habitable, but the northern part by no means dominant: from Capricorn to Aries it makes the southern part dominant, the northern desolate. Such is Cardanus. But upon what foundation does he finally put this forward? Perhaps guided by reason, as a good philosopher; or rather by experiment repeatedly tried, as an astrologer? He gives no reason at all, nor does any appear evident: he could have had no experiment in this matter. For, as Riccioli observes well in the New Almagest, book 7, section 5, in the schools, from the beginning of the world the Sun’s Apogee has scarcely completed its first quadrant, whereas at the present time it is in the first parts of Cancer, and therefore in the beginning of the second quadrant; it has never completed the third or the fourth, nor perhaps will it ever complete them, since we are now in the world’s old age. How then could Cardanus know what will be in later ages, and perhaps will not be? It may indeed be reasonably conjectured from this change of the Apogees that the habitability of regions may vary according to the climates, insofar as by the Sun’s approach to the Apogee, or Perigee, they ought to change, and consequently habitation may become more moderate, or less moderate, and that too by reason of a greater proximity, and of rays projected either more directly or more obliquely. Thus now, with the Sun Apogee in Cancer, and Perigee in Capricorn, because in summer it is farther from the earth, and in winter nearer to it in our northern regions, it is therefore more moderate, and heat becomes greater and greater in summer, and cold in winter, than if the Apogee were in Capricorn and the Perigee in Cancer, as is indeed clear from histories, and from the comparison of ancient times with our present ones. On the other hand, in regions beyond the Equator, and especially in the more southern ones, because in summer the Sun, being Perigee in Capricorn, is near the earth and strikes it with direct rays; and in winter, being situated in the Apogee in Cancer, it is greatly removed from it, and besides illuminates it with very oblique rays, therefore the climate is always more extreme in either direction. A iij

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LEXICON 8 que anni tempestas, quoadusque Apogæo Solis ad Libram perueniente, par sit earum regionum cum nostris conditio. Cæterum hæc obiter dicta sint, ex occasione incidentis de Absidum mutatione sermonis. De earum motus proportione, ac legibus vide apud citatum Ricciol. lib. 3 cap. 24. ß 25. 12. ABTERRANII dicuntur venti quidam impetuosi altè è terra spirantes (vnde & Altani audiunt) & in Mare progredientes illud subitis motibus quatiendo, ac terribiles tempestares cien- do. Vocantur autem græcè Apogæi quasi è terra spirantes. De his multa Plinius lib. 2. cap. 43. AC 13. ACARNAR, siue Acharnahar, aut Acharnaharim, Arab. dicitur extrema fluuij, fixa primæ magnitudinis de natura Iouis, & Ve- neris in extremitate Eridani posita atque in logitudine sub gr. 21. Arietis cum latir. australi gr. fere 60. Hæc in Horoscopo inuenta magnam fortunam pollicetur, vt author est Ptolemeus: idque præsertim si Iouis, aut Veneris benigno radio fulciatur. Badem in Tabulis Persicis vocatur Aulax, id est salus. 14. ACENTACER in sphæra barbarica dicitur terrius Decanus Arietis, cuius dispositio spectat ad Venerem; proindeque habet iudicium solestix, mansuetudinis, ludorum, munditarum, io- corum, &c. 15. ACTINOBOLIVM vocat sæpissimè Ptolemeus motum dire- ctionis rectum, quo scilicer dirigatur significator in co[n]sequen- tia signa: sicut econtra Horinaum appellat motum directionis conuersum, qui fiat in præcedentia loca: ea inquam, quæ suc- cessiuè acquirantur per motum diurnum, cuiusmodi est directio Aphætæ constituti inter decimam domum, & septimam, ad cardinem Occidentis. Qua de re plura vide in V. Directio. 16. ACHRONICVS, seu Achronichius, idem sonat Græcè ac La- tinè temporalis: coque nomine significatur certus ortus, & oc- casus siderum, ad differentiam ortus, & occasus Cosmici, nec- non Heliaci, de quibus in suis locis. Est autem propriè orris & occasus Achronicus, cùm stella, aut quodlibet coeli punctum vespere, sole ad occasum vergente suprà horizontem ad orientem emergit; vel cum ipso sole infra horizontem descen- dit. Verùm adhuc licet impropriè, achronicè oriri dicitur quælibet stella, quæ noctis tempore, sole sub inferiori he- mispherio delitescente, ipsa interim quauis hora suprà hori- zontem ascendit, ac nostrum hemisphærium lustrar: sicut & occidere achronicè semper, cum de nocte vergit ad occasum, & infà horizontem deprimitur. Hinc sequitur, semper signum illud in quo sol reperitur, vespere occidere achronicè, cum ra- men mauè non achronicè, sed cosmicè oriatur. Econtrà si-

Transcription: Translated (English)

LEXICON 8 for such a season of time, until, when the Sun’s apogee has come to Libra, the condition of those regions may be equal with ours. But let these things be mentioned in passing, on the occasion of this digression concerning the change of the Absidum. On the proportion of their motion and its laws, see the cited Ricciolus, book 3, chapter 24, § 25. 12. ABTERRANII are called certain violent winds blowing strongly from the earth (whence they are also called Altani) and advancing into the sea, shaking it with sudden motions and causing terrible storms. They are called in Greek Apogæi, as it were blowing from the earth. Much about these is found in Pliny, book 2, chapter 43. AC 13. ACARNAR, or Acharnahar, or Acharnaharim, in Arabic, is said of the end of a river, a fixed star of the first magnitude, of the nature of Jupiter and Venus, placed at the extremity of Eridanus and in longitude under 21 degrees of Aries, with southern latitude about 60 degrees. Found in the horoscope, it promises great fortune, as Ptolemy says; especially if supported by the benign ray of Jupiter or Venus. The same in the Persian Tables is called Aulax, that is, salvation. 14. ACENTACER in the barbaric sphere is called the third decan of Aries, whose disposition pertains to Venus; therefore it has the signification of solstice, gentleness, games, cleanliness, jokes, and so forth. 15. ACTINOBOLIVM Ptolemy very often calls the direct motion of direction, by which, namely, a significator is directed to the succeeding signs: just as, on the contrary, he calls Horianum the reversed motion of direction, which is made to the preceding places; that is, those which are successively acquired by the diurnal motion, such as the direction of the Aphæta placed between the tenth house and the seventh, to the western angle. On this matter see more in V. Directio. 16. ACHRONICVS, or Achronichius, means in Greek and Latin the same as temporal; and by that name is signified a certain rising and setting of the stars, as distinct from the cosmic, and also heliacal rising and setting, about which in their proper places. Properly, however, an achronic rising and setting is when a star, or any point of the heavens, in the evening, the sun inclining to setting, emerges above the horizon in the east; or when it descends below the horizon together with the sun itself. Yet, though improperly, a star is said to rise achronically when, during the night, the sun lying hidden under the lower hemisphere, it meanwhile at any hour ascends above the horizon and illuminates our hemisphere; and likewise to set achronically always when at night it inclines to the west and is depressed below the horizon. Hence it follows that that sign in which the sun is found always sets achronically in the evening, although in the morning it rises not achronically, but cosmically. On the contrary, si-

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MATHEMATICVM. 7 gnum oppositum ei in quo sol repetitur, vespere otiri achronicè, & manè cosmicè occidere. Plura exempla huius orris, & occasus stellarum exhibent nobis Poëræ: qui volet, videat apud Iunctinum in Commentarijs ad spharam 10. de Sacro-Bosco. ACTISAL, seu etiam Alectisal arab. idem sonat ac coniunctio, 17. seu potiùs applicario ad coniunctionem: hoc est, cum planeta leuior existens intra fines orbis, quantum se extendit lux planetæ ponderosi, pergit ad eius coniunctionem partilem, hoc est in minuto. Huius dictionis frequentem vsum inuenies in Qua- dripartiro Ptolemæi, necnon in Centiloquio ex versione Ara- bica Hali Rodoan. ACONTIÆ gtecè cometes sunt, seù potiùs aëræ impressiones 18. instar iaculi (vnde & nomen hauserunt) quia iaculi modo, in- quir Plinius lib. 2. cap. 25. vibrantur ocissimo significatu. Ex ijs quædam breuiores sunt, instar muctonis, omnium pallidissi- mæ, & quodam fulgore gladij renitentes, verum sine radijs quas Xyphias vocauere. Vide sub hac dictione. Ac vtrvs dicitur angulus apud Geomerras, qui minor est recto, 19. magisque acuminatus, qua de re vide in V. Angulus. AD ADALOR Arabicè dicitur ventus ab occidente spirans, quem 20. nos Fauonium appellamus. Sumitur etiam à quibusdam generi- cè pro quolibet vento occidentali, qui lateraliter ipsi cardinali Fouonio aduiuat. ADIGEGE corrupto nomine, Arab. dicitur Cignus, Gallina, 21. Olor, sidus videlicet in octaua sphæra ad borealem plagam constans stellis 17. inter quas præcipua est quæ Vulgò dicitur Cauda Caigni, Arabice Deneb. Adigege, secundæ magnitudinis. Notat autem Kircherus in Oedipo se in emendatis codicibus reperisse scriptum Eldegiigi b. Schiscardus autem Addigagato. ADOR apud Prolemæum in textu arabico idem sonat, ac debi- 22. itas planetæ, cum videlicet fuerir in locis cadentibus, aut in iuo casu, vel detrimento: siue etiam quacumque fuerit debili- ate affectus ex ijs quæ in proprijs locis connumerantur. ADORINGEN, seu vt habetur in textu Alkabirij, Adorogen, 23. dem sonat, ac dominus Decanorum: Diuidebant enim antiqui professores Astronomiæ tam Arabes quàm Iudæi vnumquod- ue signum in tres partes æquales, dando singulis planetis pat- em, hoc est decem gradus illius signi, qui proinde dicebarur ominus illius Decani. Cuius rei inquisitio sic traditur ab odem Alkabitio, & illustratur ab eius Commentatore Io. de axonia. Diuide, inquit Ascendens in tres partes æquales, aut quælibet pars constet ex decem gradibus, & si quidem scendat prima pars, seu facies signi, erit Adoringen, seu A iiij

Transcription: Translated (English)

MATHEMATICUM. 7 the opposite sign to that in which the sun returns, to rise in the evening achronically, and to set in the morning cosmically. The poets present us with many examples of this rising and setting of the stars; whoever wishes may see in Iunctinus, in the Commentaries on the Sphere of Sacro-Bosco, 10. ACTISAL, or also Alectisal in Arabic, sounds the same as conjunction, 17. or rather application to conjunction: that is, when a lighter planet, remaining within the bounds of its orbit, as far as the light of the heavier planet extends, proceeds to its partial conjunction, that is in minute. You will find frequent use of this word in Ptolemy’s Quadripartitum, as well as in the Centiloquium from the Arabic version of Hali Rodoan. ACONTIA, in Greek, are comets, or rather impressions in the air, 18. in the form of a javelin (whence they took the name), because, as Pliny says, book 2, chapter 25, they flash with the speed of a dart. Among them some are shorter, like a broadsword, the palest of all, and shining with a certain brightness of a sword, yet without rays; these they called Xyphias. See under that word. Acutus is the angle called among geometers which is less than a right angle, 19, and more pointed; on this see under V. Angulus. AD ADALOR in Arabic is said of a wind blowing from the west, which we call Favonius. It is also taken by some more generally for any western wind, which laterally assists the cardinal Favonius itself. ADIGEGE, under a corrupted name, in Arabic means Swan, Hen, Olor; namely the star in the eighth sphere fixed in the northern region, consisting of 17 stars, among which the principal is the one commonly called the Tail of the Swan, in Arabic Deneb. Adigege, of second magnitude. Kircher notes, however, in Oedipus, that in corrected manuscripts he found it written Eldegiigi, while Schiscard wrote Addigagato. ADOR, in Ptolemy’s Arabic text, means the debility of a planet, namely when it is in falling places, or in its decline or detriment; or even when it is affected by some debility from those things that are reckoned among its proper places. ADORINGEN, or as it is found in the text of Alkabir, Adorogen, means the lord of the decans: for the ancient teachers of astronomy, both Arabs and Jews, divided every sign into three equal parts, giving to individual planets a share, that is, ten degrees of that sign, which for that reason were called the lord of that decan. Inquiry into this matter is thus handed down by the same Alkabitius, and illustrated by his commentator Johannes of Saxony. Divide, he says, the ascendant into three equal parts, or let each part consist of ten degrees; and if the first part, or face of the sign, rises, it will be Adoringen, or A iiij

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8 LEXICON dominator Decani ipse dominus signi: si verò ascendat secunda facies signi, dominus Decani erit secundus dominus triplicitatis, hoc est dominus signi eiusdem triplicitatis cum Ascendente, quod per successionem signorum consequitur, eritque necessariò in quinta Domo, vel circà. Si demum ascendat tertia facies signi; tunc pro domino Decani accipiendus est terrius dominus triplicitatis, quod necessario cadere debet est in nonam Domum. Sic pro exemplo: Ascendant in alicuius Natiuitate, duo, tres, &c. vsque ad decem gradus Arietis. Eius Decanus est Mars, quia ipse etiam est dominus eiusdem signi: Si verò ascendant vndecim gradus, aut alia quæuis pars secundæ faciei Arietis; tunc eius Decanus est Sol, quia ipse est dominus signi Leonis, quod est secundum signum immediatè sequens in ea triplicitate. At si ascendat tertia facies Arietis; tunc dominus Decani erit Iupiter, qui est dominus tertij signi eiusdem triplicitatis, nempè Sagittarij: Similiter, si ascendat prima facies Tauri, dominus eius Decani erit Venus: si secunda, Mercurius dominus Virginis secundi signi, eiusdem cum Tauro triplicitatis: si tertia, Saturnus dominus Capricorni tertij signi eiusdem triplicitatis. Et hæc est doctrina Decanorum, quam solum ad ornatum, & operis complementum explicare volui, ne curioso Lectori quid desit; cum aliàs, res sit euanida, superstitiosa, & mera Arabum nugamenta. 24. ADONCADO idem est, ac separatus à natura gubernante corpus. Vide Ptolem. in cap. 14. lib. 3. ex versione Arabica, & eius Commentatorem Hali super eum. Æ 25. ÆGIPAN hoc est Hircus æquoris, dicitur Persis, Capricorni signum, seu sidus, eoquod habeat figuram hirci-marini, seù potiùs, quia sit æquori maximè infensus, & procellosus. Hinc etiam aliquibus dicitur pelagi procella, imbrifer, &c. Arabicè Ægedi vel Alcanarus. 26. ÆQVOCEROS item Græcè dicitur Capricornus apud Hyginu[m]. Qua de re vide exposit. Hermann. Cælaris in Arab. Phænomenon. 27. ÆQVATOR græcè pimerinos est Circulus maximus Sphæram æqualiter diuidens in duas partes, quarum vna ad polum Arcticum, altera ad Antarcticum vergit, ipso interim in medio consistente, & partes omnes æquante, vnde & nomen sortitus est: à priscis Astronomis dictus etiam Cingulum Mundi. Dicitur adhuc 28. ÆQVINOCIALIS, eoquod diem nocti æqualem faciat. Qui enim ipsum verticalem habent, semper quouis anni tépore dies noctibus æquales experiuntur: & nos, Sole eundem circulum tenente, quod bis in anno sit, cu[m] primas Arietis, & Libræ parte[m]

Transcription: Translated (English)

8 LEXICON The lord of the decan is himself the lord of the sign; but if the second face of the sign rises, the lord of the decan will be the second lord of the triplicity, that is, the lord of the sign of the same triplicity as the Ascendant, which by the succession of the signs follows, and it will necessarily be in the fifth House, or thereabouts. If finally the third face of the sign rises, then the third lord of the triplicity is to be taken as the lord of the decan, which must necessarily fall in the ninth House. Thus, for example: Let in someone’s nativity there rise two, three, &c. up to ten degrees of Aries. Its decan is Mars, because he is also the lord of the same sign. But if there rise eleven degrees, or any other part of the second face of Aries, then its decan is the Sun, because he is the lord of the sign of Leo, which is the second sign immediately following in that triplicity. But if the third face of Aries rises, then the lord of the decan will be Jupiter, who is the lord of the third sign of the same triplicity, namely Sagittarius. Likewise, if the first face of Taurus rises, the lord of its decan will be Venus; if the second, Mercury, lord of Virgo, the second sign of the same triplicity as Taurus; if the third, Saturn, lord of Capricorn, the third sign of the same triplicity. And this is the doctrine of the decans, which I wished to explain only for ornament and the completion of the work, lest anything be lacking to the curious reader; since otherwise the matter is vain, superstitious, and mere Arabian trifles. 24. ADONCADO is the same as separated from the nature governing the body. See Ptolemy in ch. 14 of book 3, from the Arabic version, and his commentator Hali on him. 25. ÆGIPAN, that is, the goat of the sea, is so called by the Persians, the sign of Capricorn, or the constellation, because it has the figure of a sea-goat, or rather because it is most hostile to the sea and stormy. Hence also by some it is called the storm of the sea, rain-bringer, etc. In Arabic Ægedi or Alcanarus. 26. ÆQVOCEROS is likewise called Capricorn in Greek by Hyginus. On this matter see the exposition of Hermannus Cælaris in the Arabic Phenomena. 27. ÆQVATOR, in Greek pimerinos, is the greatest circle, equally dividing the sphere into two parts, of which one inclines toward the Arctic pole, the other toward the Antarctic, while it stands in the middle, and making all parts equal, whence it also received its name: by the ancient astronomers it was also called the Girdle of the World. It is still called 28. ÆQVINOCIALIS, because it makes day equal to night. For those who have it vertical always, at whatever season of the year, experience days equal to the nights; and we, when the Sun holds the same circle, which happens twice in the year, with the first degree of Aries, and a part of Libra

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MATHEMATICVM. 5 ingreditur, in quauis mundi plaga vniuersale æquinoctium ex- perimur. Dicitur etiam Circulus rectus, non quia rectè semper ascendat, sed quia rectè, & æqualiter ex eisdem punctis Hori- zontis ad differentiam Zodiaci, qui vbiuis inæqualiter & obli- què semper ascendit, vt proptereà circulus obliquus & iste intonomasticè sit appellatus. Potro plura sunt Æquatoris officia, quæ fusè nimis recenset 29. lunctinus in sphæram 10. de Sacro-Bosco. Nos breuiter ea hic epi- ogabimus. Primò igitur haber secare quemuis Meridianum, d angulos rectos, & insuper in Sphæra recta p[er]sum Horizon- em, qui incidit in ipsos mundi polos. Secundò est mensura notus diurni, seù primi Mobilis, qui est communis cunctis ideribus: atque adeò qualibet hora ascendunt quindecim gra- lus Æquatoris, & Parallelorum ipsius. Tertiò est causa diuersi- aris dierum ac noctium artificialium, & vnfiformitatis inte- quæ dici naturalis ex die ac nocte artificiali conflatæ. Quartò lesignar duo puncta cardinalia ortus, & occasus in Horizon- e, vnde noscuntur qualitates ventotum. Quintò est mensura, mò & subiectum Ascensionum, & Descensionum. Sextò est mensura longitudinis Geographicæ, quæ tanta est, quanta ars, seu arcus Æquatoris interceptus inter Meridianum om- ium primum constitutum in insulis Canatijs, & Meridianum sci, cuius longitudinem quærimus. Septimò tandem concurrit un Ecliptica ad reliquos anni dies determinandos, qui tam ingi sunt, quam plures, & plures Æquatoris gradus ascendunt ipsa Horizontem eo reimpore, quo sol ab ortu ad occasum urtur. Hæc & alia munia habet Æquaror; quæ qui exactius oler, adeat Lunctinum citatum. ÆQUICRVRIA figura apud Astronomos est constitutio lumi- 30. riu[m] cum Maleficis in coelesti Themate tam dira, & infausta, : qui sub ea in lucem edi comperiantur, enutriri non possint, d mox extinguantur. Quippè cum in ea ambo luminaria, à nibus hominum vita pendet, vel sanè alterutrum, quod sit ditionatium, plurimum à Maleficis infestetur; inde sit, vt tæ vsuram diu naro communicare non possint, sed ob ni- iam siccitarem humidum radicale protinùs absumatur, ex- iguaturque calor naturalis; vnde editus natus tanram influ- s sæuitiem sustinere non possit, sicque demum vitam cum orre commutet. De hac re fusè agir Ptolemæus lib. 3. Qua- p. cap. 9. innumeraque affert experimenta Lunctinus. Est tur figura Æquicruia constitutio angulorum & luminarium in Maleficarum altera, vel vtraque, ità vt exactè effoiment iangulum æquilaterum, vt explicat ipsemet Ptolemæus. quodcunque igitur luminare, vel alterum, vel vtrumque,

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MATHEMATICVM. 5 it enters, in whatever part of the world we experience a universal equinox. It is also called the right circle, not because it always ascends straight, but because it ascends straight and evenly from the same points of the Horizon, in distinction from the Zodiac, which everywhere always ascends unevenly and obliquely, so that for that reason the one is called the oblique circle and this one, by excellence, the right circle. Moreover, there are many offices of the Equator, which Lunctinus in his exposition of the sphere of Sacro-Bosco 29 sets out at too great length. We shall briefly enumerate them here. First, therefore, it serves to cut any Meridian at right angles, and moreover in the sphere to stand straight through the Horizon, which passes through the very poles of the world. Secondly, it is the measure of the daily motion, or of the Primum Mobile, which is common to all the stars: and thus at any hour fifteen degrees of the Equator and of its Parallels rise. Thirdly, it is the cause of the diversity of artificial days and nights, and of the uniformity of the natural day, which is said to be composed of the artificial day and night. Fourthly, it indicates the two cardinal points of sunrise and sunset in the Horizon, from which the qualities of the winds are known. Fifthly, it is the measure, subject, and basis of ascensions and descensions. Sixthly, it is the measure of geographical longitude, which is as great as the portion, or arc, of the Equator intercepted between the first established Meridian in the Canary Islands and the Meridian of the place whose longitude we seek. Seventh and finally, the Ecliptic concurs with it to determine the remaining days of the year, which are so many, and so much, as more and more degrees of the Equator rise above the Horizon at the time when the sun proceeds from east to west. The Equator has these and other functions; whoever wishes to know them more exactly should consult the aforesaid Lunctinus. ÆQUICRVRIA is, among astrologers, a configuration of the luminaries with the malefics in a celestial figure so dire and unlucky that those who are found to have been born under it cannot be nourished, but are soon extinguished. For since in it both luminaries, on which human life depends, or certainly one of them, whichever is dominant, are greatly afflicted by the malefics; it comes about that they cannot long communicate the use of life, but, because of excessive dryness, the radical moisture is immediately consumed and natural heat diminished; whence the born child cannot endure such cruelty of influence, and thus at last exchanges life for terror. On this matter Ptolemy treats at length in Book 3 of the Quadripartitum, chapter 9, and Lunctinus adduces countless experiments. Æquicruia is also the configuration of the angles and luminaries with one or both of the malefics, so that they exactly form an equilateral angle, as Ptolemy himself explains. Therefore, whatever luminary, either one or both,

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10 LEXICON vna, vel ambæ Malesiæ, & angulorum aliquis præsertim Ascendens, aut medium cæli ità inter se disponuntur, vt efficiant perfectum Triangulum Orchogonium; tunc id quod nascetur sub tali constitutione cæli, aut mortuum ex vtero extrahetur, aut viuere desinat (iuxta naturæ cursum loquor) necesse est. Sed iam rem clariùs explicemus, atque omnem modum huius perniciosissimæ constitutionis declaremus. Omnium pessima est, cum ambo luminaria ex angulis affliguntur à Malescis, aut præsentia, aut oppositione, vel sane altera, præsertim Mars, in medio cæli, altera in Occidentis cardine sit constituta: ita tamen, vt coniunctio vel oppositio sit ad vnguem tam in longum, quam in latum. Tunc equidem, cum ambæ Malesiæ concurrant, & ambo luminaria affligantur, foetus vel mortuus, vel semiuiuus extrahetur. Secunda constitutio huic in malignitate proxima est, si alterum tantum luminare sit in angulo, & Malesicus fuerit illi iunctus, aut oppositus, aut suprà, partiliter; aut si non partiliter, concurrant tamen ambo Malesici ad affligendum dictum luminate constitutum in angulo, vel vnus eorum vtrumque luminare ex angulis infestet, tunc enim id quod nascetur diù ali non poterit Et hæ quidem numerantur à Ptolemæo species figuræ Æquierurix: in quibus profectò semper, posito luminari in angulo, videre est Triangulum Æquilaterum, siue æqualium erurium, quorum vnum sit à luminari posseffum, alterum à Malesica illi diametraliter opposita, vel ambo per coniunctionem efficiant vnum angulum; reliquos duos cardines summi, & imi cæli, si ij reperiantur in Oriente, vel Occidente, aut duo puncta ortus, & occasus, si luminare à Malesica infestatum fuerit in Meridiano 31. constitutum, vt consideranti patet. Cæterum, quia Antiscia, siue intuentia, siue imperantia, & obedientia æquiparantur coniunctioni, & oppositioni, vt aliàs diceretur; fortasse etiam hanc figutam Æquieruriam efformabunt luminaria à Malescis per Antiscium infestata, etiamsi in angulo minimè reperiantur. Nam vt benè aduertit Iunctinus in Commentar. ad hoc Ptolemæi caput, per æquam distâriam à punctis Tropicis, vel Æquinoctialibus, formatur perfectum Trigonum Æquilaterum. Si enim, inquit, ponatur Sol in gr. 12. Geminorum, & Mars in 18. Cancri, Solis Antiscium est in loco Martis, & econtra Antiscium Martis est in loco Solis, quia æquè distant à Tropico: vnde arcus Arietis ad locum Solis æqualis est areui à 18. gradu Cancri ad Libram: & arcus Æquatoris correspondentes illis sunt æquales: Deinde cum declinationes eclipticæ sint æquales, figura illa erit æquieruria & sic sunt duo latera æqualia. Huc vsque Iunctiùs, rem medullitus conspicatus: & ideò

Transcription: Translated (English)

10 LEXICON Venus, or both Malefics, and some of the angles, especially the Ascendant, or the Midheaven, are so disposed among themselves that they form a perfect equilateral triangle; then whatever is born under such a constitution of the heavens must either be brought forth dead from the womb, or cease to live (I speak according to the course of nature). But now let us explain the matter more clearly, and declare every mode of this most pernicious configuration. The worst of all is when both luminaries are afflicted from the angles by the Malefics, either by presence or by opposition, or indeed when one, especially Mars, is placed in the Midheaven and the other at the western angle: yet so that the conjunction or opposition is exact both in longitude and in latitude. Then indeed, when both Malefics concur and both luminaries are afflicted, the fetus will be born either dead or half alive. The second configuration, next to this in malignity, is if only one luminary is in an angle, and a Malefic is joined to it, or opposed to it, or above it in partial aspect; or if not by a partial aspect, yet both Malefics concur in afflicting the said luminary placed in an angle, or one of them assails both luminaries from the angles; then whatever is born will not be able to be nourished for long. And these indeed are counted by Ptolemy among the species of the equilateral figure: in which, certainly, whenever a luminary is placed in an angle, one always sees an equilateral triangle, that is, of equal sides, one side of which is occupied by the luminary, the other by the Malefic diametrically opposite to it, or both make one angle by conjunction; the remaining two corners are those of the upper and lower heaven, if they be found in the East or West, or the two points of rise and set, if the luminary attacked by the Malefic be placed in the meridian, 31. as is clear to one who considers the matter. Moreover, because antiscia, or opposite-shadow, or commanding and obeying, are equated with conjunction and opposition, as would be said elsewhere; perhaps the luminaries attacked by the Malefics through antiscium will also form this equilateral figure, even if they are not found in an angle at all. For, as Iunctinus rightly observes in his commentary on this chapter of Ptolemy, by equal distance from the tropical or equinoctial points a perfect equilateral triangle is formed. For if, he says, the Sun be placed at 12° Gemini and Mars at 18° Cancer, the antiscium of the Sun is in the place of Mars, and conversely the antiscium of Mars is in the place of the Sun, because they are equally distant from the Tropic: whence the arc of Aries to the place of the Sun is equal to the arc from 18° Cancer to Libra, and the corresponding arcs of the equator are equal. Then, since the ecliptic declinations are equal, that figure will be equilateral, and thus the two sides are equal. Thus far Iunctinus, having examined the matter to the very core; and therefore

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MATHEMATICVM. 11 Titus eos, Parallelos declinationis vocauir, qua notione melius explicatur hæc æquipotentia. Qui profectò eadem ratione par- allelosis mundo adinuenit, qui sunt æquidistantiæ duorum siderum à Meridiano, vt esset, si v.g. alterum eorum consi- steret in cuspide vndecimæ, alterum in octauæ: inde enim es- formaretur perfectum Triangulum ex punctis in quibus ipsa consistunt, & angulo medij coeli. Vnde etiam in hac consti- tutione luminaris cum Malesica natus fortè non superuiuer, ( vt ego sæpiùs obseruaui) quia Malesicus luminare affligir ab angulo, atque in figura æquicuria, ac perinde est, ac si foret illi pattiliter iunctus, aut oppositus ex diametro, vt conside- ranti patet. Verum id benè intelliget Lector, cum probè noue- rit naturam, atque efficaciam horum parallelorum, quam nos fusè in loco explicabimus. ÆQVIDIVM, & Æquidiale dicebatur ab antiquis id ipsum < 32.> quod nos dicimus Æquinoctium, & Æquinoctiale: forsan po- riori iute, eoquod nox diei potiùs sublternitur, ac famulari debet, quam dies nocti ( vt obseruar etiam August. in Psal. 70.) eò quòd Gen. 1. dicatur: Factum est vespere & manè dies vnus. Sed enim cedat nunc Antiquitas posteritati; quæque olim omnium magistra singulis quibusque rebus conuenientia indidit nomina, iam modo se recentioribus conformare, atque eorum placitis morem gerere necesse est. Igitur ÆQVINOCTVM dicitur tempus illud, quo sol initio Veris, & < 33.> Autumni prima puncta Arietis, & Libræ tangens toto terrarum orbe dies noctibus æquales facit: tunc enim exquisitè est in medio Sphæræ in ipso circulo Æquatoris, non magis ad Bo- ream, quam ad Austrum declinans: quî sit, vt motu suo diur- no non magis suprà quam infra horizontem degat, moretur- que, cum Æquator æqualiter semper procedat, sitque pars eius media, hoc est gr. 180. semper supra Horizontem, altera infra consistat, opus est Hinc circulus ille, vt suprà notauimus ab æqualitare quam facit dierum ac noctium, Æquinoctialis etiam dictus fuit. Porrò Æquinoctium semper, & vbique fie- < 34.> si Sole in Æquatote existente, nulli dubium est: At verò sem- per id fieri sole attingente initia Arietis, & Libræ non satis constat, ob motum irregularem octauæ spheræ. Qua in recol- ligenda maximè insudarunt præclarissimi Astronomi Georgius Peurbachius, Ioannes Regiomontanus, Nicolaus Copernicus, ac Tycho Brahe, qui in cælestium motuum obseruatione quin- quaginta amplius annos consumpsit, ac tandem comperuit, non semper, cum Sol fuerit in principio Arietis, & Libræ acci- dere æquinoctia, sicut nec etiam cùm fuerit in inirijs Cancri, & Capricorni, solstitia; sed aliquando ante, aliquando post, ali-

Transcription: Translated (English)

MATHEMATICVM. 11 Titus called these Parallelos declinationis , by which notion this equivalence is better explained. Indeed, in the same way one who devised parallels for the world, which are the equidistances of two stars from the Meridian, would do so—for example, if one of them stood in the cusp of the eleventh house and the other in that of the eighth; for then a perfect triangle would be formed from the points in which they themselves stand, and from the angle of the mid-heaven. Whence also in this constitution of the luminary with Malesicus, one born may perhaps not survive, as I have often observed, because Malesicus afflicts the luminary by an angle, and in an equicurial figure, and it is just as if it were joined to it on the side, or opposite it diametrically, as is clear to one who considers it. But the reader will understand this well, when he has properly learned the nature and efficacy of these parallels, which we shall explain at length in its place. ÆQVIDIVM, and Æquidiale was called by the ancients the same thing that we call Æquinoctium, and Æquinoctiale; perhaps for a better reason, because night ought rather to be subject to day and serve it, than day to night (as Augustine also observes in Psalm 70), because in Genesis 1 it is said: “And the evening and the morning were one day.” But let Antiquity now give way to posterity; and whatever once, as teacher of all things, assigned fitting names to individual matters, must now conform itself to the more recent and comply with their opinions. Therefore ÆQVINOCTVM is called that time when the sun, at the beginning of Spring and Autumn, touching the first points of Aries and Libra, makes day equal to night throughout the whole earth; for then it is exactly in the middle of the sphere, in the very circle of the Equator, inclining no more toward the North than toward the South. Hence it is that by its daily motion it stays and moves no more above than below the horizon, while the Equator always advances evenly, and since its middle part, that is, 180 degrees, is always above the Horizon and the other part below, it is necessary. From this, that circle, as we noted above, was also called the Equinoctial, from the equality it makes of days and nights. Moreover, an equinox always and everywhere occurs if the Sun is on the Equator; of this there is no doubt. But that it always happens when the sun reaches the beginnings of Aries and Libra is not sufficiently established, on account of the irregular motion of the eighth sphere. In investigating this, the most illustrious astronomers Georgius Peurbachius, Ioannes Regiomontanus, Nicolaus Copernicus, and Tycho Brahe labored greatly; Brahe, who spent more than fifty years in observing the motions of the heavens, and finally discovered that the equinoxes do not always occur when the Sun is at the beginning of Aries and Libra, just as the solstices do not always occur when it is at the beginnings of Cancer and Capricorn, but sometimes before, sometimes after, an

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12 LEXICON quando etiam, sed rarissimè, in eisdem punctis, eoquod ob deniationem Eclipticæ octauæ sphæræ ab Ecliptica primi Mo- bilis, non semper Ecliptica octauæ sphæræ rangit Æquinoctia- lem primi Mobilis, in principijs Arietis & Libræ, sed aliquan- do ante, aliquando post. Si quis autein viam obseruandi mo- mentum Æquinoctij scire desideret, videar apud Blacanum pag. 103. & erit voti compos. Cæterum in Æquinoctijs, pi- tuita in hominibus crescere solet vsque ad Virgiliarum exor- tum in Vere, aut earundem occasum in Autumno. Eoque po- tissimum tempore succosa, acriaque assumi debent, & corpus exerceri. 35. ÆQUILATERVM dicitur corpus, aut siguta geometrica Trian- gularis, Quadrangularis, &c. quæ æqualia habeas latera: Vnde & anguli quos efformant æquales quoque esse conuenit: vt ex quinta propositione lib. 1. Elementorum Euclidis manifestè colli- gitur. 36. AER proptè dicitur tota illa regio quæ est inter sphæra ignis, & terram: Elementum quidem crassius igne, sed longè inferio- ribus leuius; cuius descriptionem pulchre tradit Seneca in qua- stionibus naturalibus lib. 2. cap. 4. Quicælum, inquit, terram- que connectit, ima, & summa sic separat, vt tamen iungat; sepa- rat, quia medius interuenit, iungit, quia vtrique per hoc consen- sus est. Suprà se dat quidquid accepit a terris; rursus v. m siderum in terrena transfundit. In tres diuiditur regiones ab Arist. 1. 37. Meteor. text. 4. & reliquis Philosophis, supremam, mediam, & infimam. Hæc est quam nos respiramus, & extenditur vsque ad eam partem, quæ ex reflexione solarium radiorum non am- plius incalescit, & in ea generantur ros, pruina, trabes, &c. Media, vbi Meteora omnia efformantur, vt imbres, nuces grandines, &c. & frigidissima est, vt sæpiùs testatur Aristo- teles præsertim 2. Meteor. textu 9. cuius rei ratio est antiperi- stasis, eo quod vndique calore obsideatur; tum quia cum illuc vapotes peruenerint reducunur ad pristinam frigiditatem, adeoque aërem circumfusum infrigidam: tum denique quia ibi nec reflexio solarium radiotum, vt infetiora, nec feruor ignis elementaris pertingit. Dicitur hæc regio ab aliquibus obscura, 38. ac renebrosa, non quia fortè sit talis, sed quia à dæmonibus inhabitetur, qui sæpissimè inibi coruscationes, imbres, & to- nitrua faciunt, de quibus ait Apostolus. Non est nobis collectatio aduersus carnem & sanguinem, sed aduersus principatus, & pose- states, contra spiritualia nequitia in cælestibus, mundi rectores tene- brarum harum. Cur autem huic aëris regioni destinari fuerint huiusmodi Angeli reprobi, explicat Augustinus his verbis. Nunquam Deus quos prasciebat futuros malos fecisset, nisi pariter

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12 LEXICON when even, though very rarely, in the same points, because, owing to the declination of the Ecliptic of the eighth sphere from the Ecliptic of the first Mobile, the Ecliptic of the eighth sphere does not always meet the Equinoctial of the first Mobile in the beginnings of Aries and Libra, but sometimes before, sometimes after. If anyone, however, wishes to know the way of observing the moment of the Equinox, he may look in Blacanus, page 103, and he will be successful in his wish. Moreover, at the Equinoxes, phlegm is wont to increase in men until the rising of the Virgiliae in Spring, or their setting in Autumn. And at that time especially succulent and sharp things should be taken, and the body exercised. 35. AEQUILATERVM is said of a body, or geometrical figure, triangular, quadrangular, etc., which has equal sides: whence also the angles which it forms ought likewise to be equal, as is manifestly gathered from the fifth proposition of book 1 of Euclid’s Elements. 36. AER properly is called that whole region which lies between the sphere of fire and the earth: indeed a thicker element than fire, but much lighter than the lower elements; a beautiful description of which is given by Seneca in the Natural Questions, book 2, chapter 4. “It,” he says, “connects heaven and earth; it separates the lowest from the highest, yet so as to join them; it separates, because it intervenes in the middle; it joins, because through it there is agreement to both. It gives upward whatever it has received from the earth; in turn it pours down to earthly things the force of the stars.” It is divided into three regions by Aristotle, Meteorologica 1, text 4, and other philosophers: the highest, middle, and lowest. This is the air we breathe, and it extends as far as that part which, because of the reflection of the sun’s rays, no longer grows warm; and in it are generated dew, hoarfrost, comets, etc. The middle region, where all meteors are formed, such as rains, hailstones, etc., is the coldest, as Aristotle often testifies, especially Meteorologica 2, text 9. The reason for this is antiparistasis, because it is surrounded on all sides by heat; then because when vapors have reached there they are reduced to their former coldness, and thus the surrounding air is chilled; and finally because there reaches there neither the reflection of the sun’s rays, as in lower regions, nor the heat of the elementary fire. This region is called by some obscure, 38. and gloomy, not because perhaps it is such by nature, but because it is inhabited by demons, who very often in that place produce flashes, rains, and thunder, concerning which the Apostle says: “We do not wrestle against flesh and blood, but against principalities and powers, against spiritual wickedness in heavenly places, the rulers of the darkness of this world.” Why, however, such fallen angels were assigned to this region of the air, Augustine explains in these words. “Never would God have made those whom he foresaw would be evil, unless at the same time...”

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MATHEMATICVM. 15 nosset quibus v[er]sibus eos accommodaret. Aer enim caliginosus propter caliginem conuenit tenebrositati culpa, sed propter nobilissatem & subtilissatem, conuenit velocitati Angelica. Tertia demum regio, & suprema calidissima est ob ignis vicinitatem atque exhalationes calidas è terra illuc attractas, atque ab igne, vel certe à solaribus radiis accensas: quæ etiam ab aliquibus vocatur Æther. Credibile est aërem motu vniuersitatis moueri raptu à primo < 39.> Mobili, præsertim sub zona torrida, licet non tanta velocitate, vt superiores sphæræ vt multis probat Io. Baptista Porta de aëris transmut. & colligitur præcipuè ex motu cometarum inibi < 40.> consistentium. Cæterum aëris figura rotunda est, quemadmodum reliquorum elementorum; quod vel inde patet, quia cum natura sua sit tenuis, & fluidus, facile se dispositioni elementorum sibi contiguorum accommodat, vnde cum tetra, & aqua sit rotunda, eius extima superficies concaua est: superna verò quæ infra concauum ignis, aut Lunæ clauditur, conuexa. Ex eo quod est omninò purus, & diaphanus, sequitur ipsum < 41.> non esse lucis capacem, sed eam rotam in nos trasfundere: licet qua parte terris vicinior est ex classitate humorum, qui è terra prosiliunt aliquantulum lucis accipiat à solaribus radijs ex inferiori hæmisphærio ibi reflexis. Hinc lux illa crepera & subobscura manè ante solis ortum, & vespere post illius occasum, quam nos crepusculinam vocamus, qua de re vide Blazonum in sphæra mundi cap. 4. & 5. ÆREASIGNA dicutur quæ à qualitatibus aëris quibus pollent < 42.> denominantur, nempe calore & humiditate, constituuntque Trigonum aëreum ex Geminis, Libra, & Aquario. Et quia signa masculina sunt, in ijsque potissimas dignitates obtinent Mercurius, & Saturnus, ideo excluso Marte ij constituti sunt huius Trigoni moderatores: ac Saturnus quidem de die propter suam constitutionem, Mercurius verò de nocte. Quæ autem regiones & ciuitates subsunt huic Trigono aëreo, vide in Prolem. lib. 2. cap. 2. ÆROBO Caldaice dicitur signum Scorpij octauum ab Ariete, < 43.> teste Kirchero in Oedipo Ægyptiaco. ÆSCVLAPIVS. Vide Ophiucus apud Hebræos, autem Ækrab. < 44.> ÆSTAS ea olim anni pars dicebatur, quæ ab Æquinoctio ver- no v[er]sque ab autunnale protèditur, sicque sex integros menses, seu anni dimidium includebat: Nunc verò, anno in quatuor < 45.> quadrantes diuiso, accipitur pro ea parte in qua sol à solstitio æstiuo, hoc est à primo puncto Cancri, in quo est in maxima altitudine, propiusque accedit ad nostrum verticem, pergit ad æquinoctium autunnale, ac primum gradum Libræ, trium mensium spatio. Hinc æstatis nomen ad tempus maximè ferui-

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MATHEMATICVM. 15 would know by what verses to adapt them. For a cloudy air, because of its gloom, is suited to the darkness of guilt; but because of its nobility and subtlety, it is suited to the swiftness of the Angelic. The third region, and the highest, is very hot because of its nearness to fire and the hot exhalations drawn from the earth up there, and kindled by fire, or certainly by solar rays: which also by some is called Æther. It is credible that the air is moved by the motion of the universe, carried along by the first Mover, especially under the torrid zone, though not with such great speed as the higher spheres, as Io. Baptista Porta proves at length in de aëris transmut. and it is gathered especially from the motion of comets there existing. Moreover, the figure of the air is round, as are the other elements; which is evident even from this, because since by its nature it is subtle and fluid, it easily accommodates itself to the disposition of the elements contiguous to it, whence, since earth and water are round, its outer surface is concave; but the upper surface, which is enclosed below by the concavity of fire, or of the Moon, is convex. From the fact that it is entirely pure and diaphanous, it follows that it is not capable of light, but transmits it to us: although insofar as it is nearer to the earth, from the density of the humors that spring from the earth, it receives some light from the solar rays reflected there from the lower hemisphere. Hence that dim and somewhat obscure light in the morning before the sunrise and in the evening after sunset, which we call crepuscular, concerning which see Blazonum in sphæra mundi cap. 4 and 5. AIR SIGNS are those which are named from the qualities of the air they possess namely heat and moisture, and they constitute the airy Trigon from Gemini, Libra, and Aquarius. And because they are masculine signs, and in them the chief dignities are held by Mercury and Saturn, therefore, with Mars excluded, these were constituted rulers of this Trigon: and Saturn indeed by day because of his constitution, Mercury by night. What regions and cities are subject to this airy Trigon, see in Prolem. lib. 2. cap. 2. ÆROBO is said in Chaldean to be the sign of Scorpio, eighth from Aries, according to Kircher in Oedipus Ægyptiacus. ÆSCVLAPIVS. See Ophiucus among the Hebrews, but Ækrab. SUMMER was formerly called that part of the year which extends from the Vernal Equinox to the autumnal, and thus included six whole months, or half the year: but now, the year being divided into four quadrants, it is taken for that part in which the sun, from the summer solstice, that is, from the first point of Cancer, in which it is at its greatest altitude and comes closer to our zenith, proceeds to the autumnal equinox and the first degree of Libra, in the space of three months. Hence the name of summer for the time most fer-

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14 LEXICON dum accessumque Solis ad nostrum verticem significandum translatum est. Vnde ijs qui sub Æquatore degunt, quia bis in anno Sol accedit ad eorum verticem, in æquinoctijs nempe atque initijs Arietis, & Libræ, ideo binas æstates experiri contingit, binas etiam hyemes, seù potius calores remissiores in eiusdem recessu ad puncta solstitialia. Quod & Plinius tradidit lib. 6. cap. 17. & nos alibi obseruauimus. Cæterum Æstatis conditiones, ac vices, vide apud Plinium eumdem lib. 2. cap. 38. 45. ÆETHER propriè audit apud Græcos sphæra ignis. Aristoteles verò in libris de Mundo hoc nomine intellexit coeli siderumque substantiam. Vnde hodie Philosophi Astronomique omnes, Ætherem pro omni eo quod supra aërem elementaremque regionem consistit, accipiunt: proindeque vniuersum mundum in elementarem & æthereum dispescunt; atque in elementari collocant elementa ipsa, terram, aquam aërem, & sphæram ignis (si ea detur) in ætherea verò corpora cælestia, siue ea vnum coelum sint siue plures, sidera, planetas, aliaque phænomena, quæ de nouo in coelo generantur. Qua de re vide Argolum in Astronomicis lib. 1. cap. 4. & cap. 17. A F 46. AFETA Heleg. Vitæ dator. Vide Apheta. 47. AFLALEN Græcè pes, alter Geminorum Latine dicitur Stella fixa secundæ magnitudinis de natura Martis, & Mercurij in capite Geminorum præcedentis consistens: Arabicè Auellar. Vnde nescio qua ratione pes latinè interpretetur ab Hali in Commentar. ad Quadrip. Ptolemæi, cum alias extremus pes de natura Mercurij, & quartæ magnitudinis proprio nomine Propus appelletur, vt videre est apud Iunctinum in Catalogo stellarum fixarum, qui est in fine Commentarij ejusdem in Sphæram Io. de Sacro-Bosco. 48. AFRICVS ventus occidentalis lateralis Fauonio spirans immediatè à brumali occasu, oppositus directè Cæciæ, sic dictus, ab Africa, vnde exsufflat. Dicitur etiam Lybicus à Lybia. Natura sua frigidus est, & humidus, pluuiosus, & tempestatis index: de quo sic cecinit Manilius. Africus est nimbis creber, creberque procellis. Flatu suo foeminas concipere facit, vt author est Plinius lib. 18. cap. 34. Ex eo cognominati sunt Mesofricus, & Ypafricus collaterales venti de quibus suo loco. A G 49. AGATICHI Græcè, hoc est bona fortuna, appellatur quinta Domus ab Horoscopo succedens angulo imi coeli; eoquia ex ea sumatur significatio de voluptatibus, gaudijs, conuiuijs, libe- ris, &c. respicit de trino Ascendens. Consignificator eius est

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14 LEXICON has been transferred to signify the passage of the Sun to our zenith. Hence for those who dwell under the Equator, because the Sun comes to their zenith twice in the year, namely at the equinoxes and at the beginnings of Aries and Libra, it so happens that they experience two summers, and also two winters, or rather milder heats in its recession to the solstitial points. This also Pliny relates, book 6, chap. 17, and we have observed elsewhere. Moreover, see in Pliny himself the conditions and changes of Summer, book 2, chap. 38, 45. ÆETHER properly among the Greeks means the sphere of fire. Aristotle, however, in his books De Mundo understood by this name the substance of the heavens and the stars. Hence today all philosophers and astronomers take Æther for everything that exists above the elemental region of air; and therefore divide the whole world into elemental and æthereal; and place in the elemental the elements themselves, earth, water, air, and the sphere of fire (if there be such), but in the æthereal the celestial bodies, whether there be one heaven or several, the stars, planets, and other phenomena newly generated in the heavens. On this matter see Argolus in Astronomical Matters, book 1, chap. 4, and chap. 17. A F 46. AFETA Heleg. Giver of life. See Apheta. 47. AFLALEN in Greek, that is, the other foot of Gemini, is called in Latin a fixed star of the second magnitude, of the nature of Mars and Mercury, situated in the head of Gemini preceding it. In Arabic, Auellar. Whence I know not on what grounds it is translated “foot” in Latin by Hali in the Commentary on Ptolemy’s Quadripartitum, whereas elsewhere the hindmost foot, of the nature of Mercury and of the fourth magnitude, is properly called Propus, as may be seen in Juntinus in the Catalog of the fixed stars, which is at the end of the same Commentary on the Sphere of Jo. de Sacro-Bosco. 48. AFRICVS a western side wind blowing immediately from the winter sunset, directly opposite to Cæcias, so called from Africa, whence it blows. It is also called Lybicus from Libya. By nature it is cold and humid, rainy, and a sign of storm: concerning which Manilius sang thus. Africus is thick with showers, and thick with squalls. By its blast it causes women to conceive, as Pliny is author, book 18, chap. 34. From it were derived the names Mesofricus and Ypafricus, lateral winds of which in their proper place. A G 49. AGATICHI in Greek, that is, good fortune, is called the fifth House succeeding the Horoscope at the angle of the lower heaven; because from it is taken the signification concerning pleasures, joys, banquets, children, etc. It aspects the Ascendant by trine. Its significator is

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MATHEMATICVM. 15 ercurius, qui etiam inibi gaudet similiter. AGOTHODAMON id est Bonus genius, Græcè audit vndecima 50. nus proximè succedens culmini, ac modò memoratæ op- ita. Ex ea sumitur significatio amicorum, felicitatis, rerum- speratarum. Gaudet in ea Iupiter. AGGLUTINATIO, seù contactus, teste Valla, dicitur quando- 51. : apud Astronomos coniunctio, & conuenientia duarum vel rimum stellarum in eadem parte signiferi: sed præsertim ipitur agglutinatio pro agglomeratione plurium fixarum in im, cuiusmodi sunt Nubeculæ duæ ad polum Antarcticum; iades, nec non omnes stellæ obscuræ, ac nebulosæ, quæ aliud sunt, vt obseruauit nouissimè Galilæus in suo Nuntio reo quam congeries plurium stellarum in vnum conue- ntium, quæ obnimiam distantiam discerni singillatim non sunt, sed perinde, ac si vna esset se nostris obtutibus ex- pent. AGITATOR idem quod Æricthonius, vel Auriga, fidus ad Bo- 52. dem plagam existens in longitudine sub signo Geminorum. intinet stellas quatuordecim secundum Prolomæum, at Ke- rus in eo ponit stellas 27. & Baierus 31. omnes ferè de natu- Martis, ac Mercurij, inter quas vna est insignior primæ gnitudinis in sinistro humero fulgens nomine Hircus. Dux in obscuræ seù potiùs quartæ magnitudinis in vola manus istæ, quæ hædi vulgo audiunt, valdè procellosæ, quippe- æ pluuias in ortu suo generant, ventos excitant, & tem- states faciunt, sicut & Hircus. De quo multa Plinius lib. 18. ap. 26. vsque ad 29. Ideoque inimicum Nautis canit Germa- :us. Alia eius significata, vide in V. Auriga. AH AHARPH Saturni dicitur in sphæta barbarica tertius Deca- 53. s Tauri competens Saturno, vnde extrahuntur significatio- s seruitutis, miseræ, feritatis, necessitatis. AI AICHARD. Arab. Latinè, redditus luminis, & est cum vnsus 54. : plures planetæ transmittunt suum lumen vni tertio, qui ta- :n existat valdè debilis, vt puta retrogradus, vel combustus: :ic enim ob imbecillitatem suam retinere non valens trans- :llum lumen, reddit ipsis planetis immittentibus, seu potiùs :illos recidit lumen, quod alteri transmittebant. AIz, seu vt alij scribunt Alaiz, est conformitas planetæ cum 55. :no, in sexu, & conditione temporis vt quando masculinus & :rnus, de die est in signo masculino, & suprà terram, & :ontrà foemininus, sit in signo foeminino, & si nocturnus, de :cte sit suprà terram. Alij rectius scribunt Haye.

Transcription: Translated (English)

MATHEMATICVM. 15 Mercurius, who likewise rejoices there in a similar manner. AGOTHODAMON, that is, the Good Genius, in Greek, is called the eleventh 50. next succeeding the summit, and to the aforesaid op- portunity. From it is taken the signification of friends, happiness, things hoped for. Jupiter rejoices in it. AGGLUTINATIO, or contact, according to Valla, is said to occur when 51. : among astronomers, the conjunction and agreement of two or more stars in the same part of the zodiac: but especially agglutination is taken for the clustering of several fixed stars in one place, such as the two little clouds at the Antarctic pole; the Pleiades, as well as all the dim and nebulous stars, which are nothing else, as Galileo most recently observed in his Nuntius Sidereus, than a gathering of several stars into one con- tinuous body, which, because of their great distance, cannot be distinguished separately, but appear to our sight as if one were present. AGITATOR, the same as Erichthonius, or Auriga, faithful to Bo- 52. otes, situated on the western side in longitude under the sign of Gemini. It contains fourteen stars according to Ptolemy, but Ke- pler places in it 27 stars, and Bayer 31, almost all of the na- ture of Mars and Mercury, among which one is more notable, a star of first magnitude shining on the left shoulder, called the Kid. A group of stars of the obscure or rather fourth magnitude in the palm of the hand These, which are commonly called the Kids, are very stormy, since they cause rains at their rising, stir up winds, and make storms, as does also the Kid. Much on this matter by Pliny, book 18, chap. 26 up to 29. Therefore Germanicus sings that it is hostile to sailors. For its other meanings, see under Auriga. AH AHARPH is said, in the barbaric sphere, to be the third Deca- 53. n of Taurus, belonging to Saturn, whence are drawn significations of servitude, misery, fierceness, and necessity. AI AICHARD, in Arabic, in Latin, “returning of light,” and it is when 54. several planets transmit their light to a third one, which may then be very weak, as when retrograde or combust: for then, being unable by its weakness to retain the transmitted light, it returns it to the planets sending it, or rather it throws back to them the light which they were transmitting to another. AIz, or as others write, Alaiz, is the conformity of a planet with the Sun, in sex and in condition of time, as when masculine and diurnal, it is in a masculine sign and above the earth, and contrariwise, feminine, if it is in a feminine sign; and if nocturnal, it is by night above the earth. Others more correctly write Haye.

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16 LEXICON AI. 56. ALAAZEL Azimech, corrupto vocabulo apud Nubianos Astrologos vocatur spica Virginis, Stella fixa primæ magnitudinis de natura Veneris, & Mercurij, nunc temporis existens in gr. 19. Libræ cum grad. 2. latitudinis Australis. Estque Stella regia benignissima, honores, divitias adducens, atque ad pietatem naturali quadam propensione inclinans, si in præcipuis figuæ locis reperiatur, aut cum beneficis ac luminaribus iuncta. Arabicè dicitur Sombales Eleadari, vt testatur Kircherus in suo Oedipo. 57. ALACAE seu Alazaph Arabice dicitur Stella fixa secundæ magnitudinis in ala septem trionali Virginis consistens de natura Saturni, & Mercurij. Nostiis Vindemiasor, qua Vindemiæ tempore oritur. 58. ALACEHA idem quod Nubilosus. Ptolemæus in Quadripartito ex versione Arabica Hali. 59. ALACANTHABVT Arabice dicitur Rete Astrolabij, Sphæram cum suis circulis, ac stellis fixis insignioribus in plano repræsentans. 60. ALAGOBAL audit Sol apud Salmasium in lib. de annis Climactericis. 61. ALAHORE Arab. Latinè Fidicula, sicut etiam Albegaladè qua mox infia. 62. ALAIM Arab. idem quod Hayr. 63. ALALICEH Arab. Stella in extremo caudæ Vrsæ maioris. Vide in V. Bennenax. 64. ALAMAC Arab. pes dexter Andromedæ. 65. ALANGA Arab. Latine lagitta, sidus. 66. ALANGVE idem quod serpentarius. Vide Ophiucus. 67. ALANTHICA. Vide in V. Abalantica. 68. ALARAPH, vel Alcalf Arabice etiam dicitur spicitur spica Virg. Alasaph, Vide in V. Alacaf. 69. ALASCHA Arab. vocatur aculeus scorpij, quasi morsus scorpionis. 70. ALACHA Arab. idem quod Nubes. Eo nomine appellantur apud Ptolem. in textu arabico omnes stellæ nebulosæ. 71. ALATRAB, vt testatur Baiei, dicitur arab. Cor scorpij: Verum Kircherus in Oedipo legit dægrab vel cum articulo Elaakrab. 72. ALAYOTH, seu Alioth Arab. Stella fixa primæ magnitudinis in Auriga de natura Martis, & Mercurij, Latine Capella. 73. ALBAHVIM dicitur Arabice figura sexdecim laterum peragrationis Lunæ ab initio moti visque ad finem, quâ obseruare debent Medici ad eius mutationes siue in bonum siue in malum auspicandum. Hoc verbo, vtitur Ptolemæus siue quicumque tandem

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16 LEXICON A.I. 56. ALAAZEL Azimech, by a corrupt form of the word among the Nubian astrologers, is called the ear of Virgo, a fixed star of the first magnitude, of the nature of Venus and Mercury, now at 19 degrees of Libra with 2 degrees of south latitude. And it is a most benign royal star, bringing honors and wealth, and inclining toward piety by a certain natural tendency, if it is found in the principal places of the figure, or joined with benefics and luminaries. In Arabic it is called Sombales Eleadari, as Kircher testifies in his Oedipus. 57. ALACAE, or Alazaph, is called in Arabic a fixed star of the second magnitude, situated in the northern wing of Virgo, of the nature of Saturn and Mercury. Nostiis Vindemiasor, because it rises at the time of the vintage. 58. ALACEHA means the same as Nubilosus. Ptolemy in the Quadripartitum from the Arabic version of Hali. 59. ALACANTHABVT in Arabic is called the astrolabe net, representing the sphere with its circles, and the more notable fixed stars, on a plane. 60. ALAGOBAL is the name given to the Sun by Salmasius in the book on the Climacteric Years. 61. ALAHORE, Arabic; in Latin Fidicula, as also Albegaladè, which follows immediately below. 62. ALAIM, Arabic, the same as Hayr. 63. ALALICEH, Arabic, a star at the end of the tail of Ursa Major. See under V. Bennenax. 64. ALAMAC, Arabic, the right foot of Andromeda. 65. ALANGA, Arabic; in Latin lagitta, a star. 66. ALANGVE, the same as serpentarius. See Ophiucus. 67. ALANTHICA. See under V. Abalantica. 68. ALARAPH, or Alcalf, in Arabic is also called the ear of Virgo, Alasaph. See under V. Alacaf. 69. ALASCHA, Arabic, is called the sting of Scorpio, as it were the bite of the scorpion. 70. ALACHA, Arabic, the same as Nubes. By this name, in Ptolemy’s Arabic text, all nebulous stars are called. 71. ALATRAB, as Baiet testifies, is called in Arabic the heart of the scorpion: but Kircher in Oedipus reads dægrab, or with the article Elaakrab. 72. ALAYOTH, or Alioth, Arabic, a fixed star of the first magnitude in Auriga, of the nature of Mars and Mercury, in Latin Capella. 73. ALBAHVIM is called in Arabic the figure of sixteen sides of the Moon’s course from the beginning of motion up to the end, which physicians ought to observe for its changes, whether to prognosticate good or evil. Ptolemy, or whoever finally

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MATHEMATICVM. 17 tandem sit author Centiloquij in V. 60. secundum versionem Hali, sic inquiens: Super agroris criticos dies inspice ac Luna peragrassionem in angulis Albaburim. Vbi enim eos angulos bene affectos inueneris, bene eris languenti: contrà malè, si afflictos inueueris. Cuius autem ponderis sic hæc figura, & quomodò instituenda sit, dicemus in V. Figura sexdecim laterum 74. ALBEGALA siue etiam Alahore dicitur Arabicè fidus, quod nos vulgò Vulturem cadentem seù Lyram vocamus à decem stellis quibus tanquam fidibus constat. 75. ALBEMENIÆ item in Centiloquio Arab. in V. 36 audiunt stellæ fixæ de natuta Iouis, & Veneris, quas, vt aduertit Hali, vult author præfici in ascendente Vrbis condendæ. 76. ALBETATRAN Arab. Græcè Anepatros dicitur Genitura trium masculorum, in quam conueniant Saturnus, Iupiter, & Mars. 77. ALBIREO Arabicè dicitur stella fixa, consistens in rostro Cygni. 78. ALBOARAN, dicitur item in textu Arab. Centiloquij in V. 62. ex versione Hali, Dominator Anguli figuræ, vnde docet author, sumendam esse iudicium de mutatione sëris in illo mense: Erst enim, inquit, suxtà dominatorem angulis figura cujusque facta etiam consideratione de præsentis temporis qualitate. 79. ALBVZIC, siue (vt habet Io. de Saxonia in Commentar. Alkabitij) Albustum. Est ratio quædam dominij Planetarum super singulas duodenas horas à Luminarium coitione ad nouam synodum, quam maximè seruabant Indi, nescio superstitiosè ne magis, an fatuè. Dicam tamen, vt innotescat eorum deliramentum, & dignis cachinnis excipiatur. Itaque indorum vanitas numerabat duodecim horas immediatè sequentes conjunctionem Solis cum Luna, quas & Soli tribuebant: inde, diuisis illis in tres partes, dijudicabant secundum qualitatem Domini triplicitatis loci Solis. Postea dabant item Veneri duodecim horas sequentes diuidendo similiter eas in tres partes, quatum primam dijudicabant secundum natutam primi Domini triplicitatis loci Veneris hora coniunctionis: secundam, secundum iudicium secundi Domini triplicitatis: tertiam, secundum tertium. Idipsum de Mercurio faciebant; ac de reliquis Planetis, donec reuerteretur orbis ad Solem post octoginta quatuor horas, eodem modo prosequendo vlsque ad nouam synodum. Addebant autem (quod magis, ac magis ridendum) primas duodecim horas à Luminarium coniunctione esse infortunatas, in quibus non liceret, nec bonum esset aggredi vllum opus, adeoque eas vocabant combustas: & post has alix horæ sequebantur septuaginta duæ fortunatæ B

Transcription: Translated (English)

MATHEMATICVM. 17 at last let the author of the Centiloquium in V. 60, according to the version of Haly, be thus quoted: “Look at the critical days of illnesses and the Moon’s passage through the angles of Albaburim. For when you find those angles well disposed, you will do well with the sick person; contrariwise, badly, if you find them afflicted.” Of what weight this figure is, and how it should be constructed, we shall say in V. Figure of sixteen sides 74. ALBEGALA, or also Alahore, is called in Arabic the faithful one, which we commonly call the Falling Vulture or the Lyre, from the ten stars of which it is made, as it were of strings. 75. ALBEMENIA likewise in the Arabic Centiloquium in V. 36 are called the fixed stars of the nature of Jupiter and Venus, which, as Haly notes, the author wishes to have placed in the ascendant of the city to be founded. 76. ALBETATRAN in Arabic, in Greek Anepatros, is called a nativity of three males, in which Saturn, Jupiter, and Mars come together. 77. ALBIREO in Arabic is called a fixed star, situated in the beak of Cygnus. 78. ALBOARAN is likewise so called in the Arabic text of the Centiloquium in V. 62, from Haly’s version, “Ruler of the Angle of the figure,” whence the author teaches that judgment must be taken about a change of circumstances in that month: “For,” he says, “according to the ruler of the angles of each figure, judgment is made also with consideration of the quality of the present time.” 79. ALBVZIC, or (as Io. de Saxonia has it in his Commentary on Alkabitij) Albustum. It is a certain rule of planetary rule over each group of twelve hours from the conjunction of the luminaries to the new synod, which the Indians observed, perhaps more superstitiously than foolishly. Yet I shall mention it, so that their madness may be made known and received with due laughter. Thus the vanity of the Indians counted the twelve hours immediately following the conjunction of the Sun with the Moon, which they also attributed to the Sun: then, dividing them into three parts, they judged according to the quality of the lord of the triplicity of the Sun’s place. Afterward they likewise assigned the next twelve hours to Venus, dividing them similarly into three parts, of which they judged the first according to the nature of the first lord of the triplicity of Venus’s place at the hour of conjunction: the second, according to the judgment of the second lord of the triplicity: the third, according to the third. The same they did with Mercury; and with the remaining planets, until the sphere returned to the Sun after eighty-four hours, proceeding in the same manner up to the new synod. They also added (which is even more laughable) that the first twelve hours from the conjunction of the luminaries were unfortunate, in which it was not permitted, nor was it good, to undertake any work, and therefore they called them burned: and after these there followed seventy-two fortunate hours. B

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18 LEXICON omnes, & incombustæ, in quibus viilis foret inceptio cuiuscumque operis: inde iterum sequebantur aliæ duodecim horæ infottunatæ, combustæ, & post has aliæ 72. incombustæ ac bonæ vsque ad coniunctionem sequentem. Ratio autem diuisionis est, quod omnes horæ duodecim, quæ dantur soli secundum ordinem planetarum sunt combustæ, & infortunatæ, quæ verò reliquis planetis ascendentes ad summam 72. horarum sunt bonæ, & incombustæ. Et hoc est arcanum inanitatio quod includitur sub hoc Verbo Albuzie, siue Albutem. Qui plura volet videat Alkabitium. 80. ALCANTARVS promiscuè ac Alsedi apud Arabes dicitur Capricorni sidus; de quo vide in V. Capricornus. 81. ALCALEE, vel Alatraph, & Almuredin apud Nubianos dicitur Spica Virginis. 82. ALCHATIS Arabicè, Græcè lencos apud Ptolem. in Quadring. lib. 3. c. 3. ex versione Arabica audit Genitura trium foeminarum in vno pattu, in quam conveniant Venus, Luna & Mercurius? 83. ALCHENIB dicitur dextrum latus planetæ. 84. ALCHETIB Arab. idem sonat, ac virtus, & fortitudo planetæ. 85. ALCHIA DAPHA. Vide in V. Alkia. 86. ALCHENIRA Arab. est idem quod Haye: hoc est, quod Planeta masculinus, & diurnus, de die sit supra terram, & in signo masculino, ac diurno: de nocte verò sub terra. Similiter, quod Planeta foemininus, & nocturnus de nocte sit supra terram, de die sub terra, atque in signo foemino, & nocturno. 87. ALCHITOT Arab. Latinè Claus, seu vectis teres in medio Astrolabij nectens rete, ac tabulas intra matrem medio alio clauunculo omnia in vnum premente, qui ob formam equi, quam vt plurimum præ se ferr, Latinè Caballus dicitur, Arabicè verò Alpharatz Stoflerin. 88. ALCOBOL. Arab. Latinè idem sonat, ac receptio: fitque cùm Planeta ponderosus, ac tardi motus recipit intra suum orbem alium leuem ad se aduentantem, vt cum eo corpore iungatur. 89. ALCOCODEN siue Alcochoden Arab. dicitur planeta dispositior loci hylegi, ad quem spectat in genituris vitæ prorogatio: iravt qui plures prærogatiuas obtinuerit in dicto loco, is gaudeat Alchocodea virtute, quæ in eo consistit, vt pro sui constitutione valida aut debili in coelesti figura, definiri possit numerus annorum nati. Proindeque si fortis sit in Angulo, in suis dignitatibus, non retrogradus, non combustus. is addat ad vitam nati (quam in genere significat vitæ datur)

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18 LEXICON all, and unburnt, in which there would be the initiation of any work. Then there followed again another twelve unfortunate, burnt hours, and after these another 72 unburnt and good ones until the next conjunction. The reason for the division is this: all the twelve hours that are allotted to the Sun according to the order of the planets are burnt and unfortunate; but those which belong to the remaining planets, rising to the total of 72 hours, are good and unburnt. And this is the secret of inanitatio, which is included under this word Albuzie, or Albutem. Whoever wishes to know more, let him see Alkabitium. 80. ALCANTARVS is said promiscuously, and Alsedi among the Arabs, of the constellation of Capricorn; see under V. Capricornus. 81. ALCALEE, or Alatraph, and Almuredin among the Nubians, is said of the Spica Virginis. 82. ALCHATIS in Arabic, in Greek lencos, according to Ptolemy in Quadring. lib. 3, c. 3, from the Arabic version, is called the Genitura trium foeminarum in uno pattu, in which Venus, Luna, and Mercury come together? 83. ALCHENIB is said of the right side of the planet. 84. ALCHETIB in Arabic signifies the same as the virtue and strength of the planet. 85. ALCHIA DAPHA. See under V. Alkia. 86. ALCHENIRA in Arabic is the same as Haye: that is, that a masculine and diurnal planet by day be above the earth, and in a masculine and diurnal sign; but by night under the earth. Likewise, that a feminine and nocturnal planet by night be above the earth, by day under the earth, and in a feminine and nocturnal sign. 87. ALCHITOT in Arabic, in Latin, means a rod, or round bar, in the middle of the astrolabe, joining the rete and the plates inside the mater, pressing everything together with another little pin in the middle; because of its form, which it usually bears, it is called in Latin Caballus, but in Arabic Alpharatz, according to Stofler. 88. ALCOBOL. In Arabic, in Latin, it has the same meaning as reception: and this occurs when a heavy, slow-moving planet receives within its own orbit another lighter one approaching it, so that it may be joined with that body. 89. ALCOCODEN, or Alcochoden in Arabic, is said to be the planet better disposed in the place of the hyleg, to which in nativities the prolongation of life pertains: thus he who has obtained the greater prerogatives in the said place enjoys the Alchocodean virtue, which consists in this, that by reason of its valid or weak constitution in the heavenly figure, the number of the native's years may be determined. Therefore, if it is strong in an angle, in its own dignities, not retrograde, not combust, it adds to the life of the native (which in general signifies life is given)

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MATHEMATICVM. 19 suos annos maiores: si mediocriter fortis, medios: ac tandem, si debilis minores; aut sanè, si nimium debilis, & afflictus, pro annis det menses, aut dies. Ad quamrem circumfertur quædam tabella, quam nos, quia gratis effectam existimamus, imò, si verum dicere liceat, totam hanc Alehocoden doctrinam, ideò missam facimus. Qui eius fuerit curiosus, alios consulat. ALCOR Arab. dicitur stellula quædam minima quæ est pro- <90.> pe mediam è tribus quæ sunt in cauda Vrsæ maioris ab Agri- colis Equitator dicta: estque adeò exilis, vt non nisi ab acutissimis oculis discerni possit. Ex quo ortum vulgare illud Adagium apud Arabes de homine, qui maxima non videt ac negligit, & minutissima quæque perspicit, aut perspexisse se iactat. Vidisti Alcor, sed non Lunam plenam. ALCYONII dies vocantur septem, qui proximè præcedunt <91.> brumam, aut subsequuntur, qui maximè sereni sunt ac mi- tiores; vnde vulgò Aestas sancti Martini indigitantur. Quod a- deò verum est, vt eo tempore Alcyones aues, vt inquit Pli- nius passeribus paulò grandiores in maris littore ob securita- rem nidificare soleant, quod sanè non auderent, nisi natura dictante pernoscerent maximam tunc temporis instare aëris tranquillitatem; vt profectò ex eorum nidificatione his die- bus sit nomen inditum. Oritur autem hæc serenitas, vt habet Nyphus, eò quia, nimia solis absentia vapores pluuiatiles sur- sum non eleuantur, atque adeò nec pluuiis nec ventis locum turbandi aërem dare queunt. ALDEBARAN Latinè Lampas, seu Oculus Tauri, stella fixa <92.> primæ magnitudinis ad instar lampadis ardens in oculo austra- li Tauri octaux sphæræ, tunc temporis existens in grad. 4. Geminorum, cum latitudine meridiana gr. ferè 3. Vna est ex ijs quæ regiæ dicuntur: verum etiam est ex violentis, cum sic de natura Martis, adeoque volunt Astrologi eam cum Lumi- naribus aut Malesicis præsertim in ascendente violentam mor- tem minari. Dicitur etiam Romanis hæc stella Palilirium eo- <93.> quod olim Romæ eo tempore oriebatur, quo festa Palilia ce- lebrabantur. Qua de re vide Plinium, lib. 18. cap. 26. ALDERAIMIN Arab. Dexter humerus Caphes: stella fixa ter- <94.> tix magnitudinis de natura Saturni, & Iouis, in gradu ferè 8. Arietus tunc temporis sita cum maxima latitudine boreali; ideoque in nostro hæmispherio nunquam occidens. ALDHAFERA Arab. Latinè Iuba Leonis, stella fixa tertix <95.> magnitudinis de natura Saturni, & Mercurij; tunc temporis <96.> existens in gradu ferè 23. Leonis. ALFANTIA Vide Alphantia. ALFAZIN Arab. idem sonat, ac frustratio: estque cum pla- B ij

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MATHEMATICVM. 19 their greater years: if moderately strong, the middle ones; and at last, if weak, the smaller ones; or indeed, if excessively weak and afflicted, let him assign months or days instead of years. For this purpose a certain table is circulated, which we, because we consider it to have been produced without charge, indeed, if the truth may be spoken, we dismiss the whole of this doctrine of Alehocoden. Whoever is curious about it should consult others. ALCOR, in Arabic, is said of a certain very small star which is near the middle one of the three that are in the tail of Ursa Major, called by the farmers the Rider: and it is so tiny that it can be distinguished only by the sharpest eyes. From this arose that common Arabic proverb about a man who does not see and neglects the greatest things, yet perceives, or pretends that he has perceived, the smallest: “You saw Alcor, but not the full Moon.” ALCYONII days are called the seven days which immediately precede the winter solstice, or follow it, and which are most serene and mild; whence they are commonly called Saint Martin’s Summer. And this is so true that at that time the halcyon birds, as Pliny says, slightly larger than sparrows, are accustomed to build their nests safely on the seashore, which they certainly would not dare to do unless, instructed by nature, they knew that then the greatest calm of the air was at hand; so that from their nesting on these days the name has evidently been given. This serenity arises, as Nyphus has it, because, from the excessive absence of the sun, rain-bearing vapors are not lifted upward, and therefore can give neither rains nor winds any opportunity to disturb the air. ALDEBARAN, in Latin Lampas, or the Eye of Taurus, a fixed star of the first magnitude, burning like a lamp in the southern eye of Taurus, in the eighth sphere, then being in the 4th degree of Gemini, with a southern latitude of about 3 degrees. It is one of those called royal; but it is also of a violent nature, since it is of the nature of Mars, and therefore astrologers wish that, when joined with the luminaries or with malefics, especially in the ascendant, it threatens a violent death. This star is also called by the Romans Palilirium, because in former times in Rome it rose at the time when the Palilia festival was celebrated. On this matter see Pliny, book 18, chapter 26. ALDERAIMIN, in Arabic, the right shoulder of Cepheus: a fixed star of the third magnitude, of the nature of Saturn and Jupiter, then situated at about the 8th degree of Aries, with the greatest northern latitude; and therefore never setting in our hemisphere. ALDHAFERA, in Arabic, in Latin the Lion’s Mane, a fixed star of the third magnitude, of the nature of Saturn and Mercury; then being at about the 23rd degree of Leo. ALFANTIA. See Alphantia. ALFAZIN in Arabic means the same as frustration: and it is with pla- B ij

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LEXICON 40 neta alteri applicans coniunctione, manensque intrà sphæram lucis illius, interim fit retrogradus, & sine suo frustratur: est genus quoddam debilitatis, quod in maledicis semper in bonum cedit. 97. ALFRECA siue Alphetal dicitur Arabicè Lucida in Corona Gnossia hoc est aperisso, ea enim exoriente tellus aperitur, & flores germinat. In tabulis Persicis dicitur Piramis, vel Pinacis hoc est pupilla, & sertum pupillæ. Est Stella splendidissima secundi honoris de natura Veneris & Mercurij. De qua vide plura in V. Corona Gnossia. 98. ALFELTA item stella fixa in Dracone ad polum arcticum de natura Veneris & Mercurij: alio nomine Foca. 99. ALFRIDARIE, seu Fridaria, vel Ferdaria apud Arabes est quædam temporaria potestas, quam sibi arrogant Planetæ super vitam Nati, quæ à decenniorum dispositione patum differre videtur. Quandoquidem quilibet Planeta habet quandam determinatam, ac definitam temporis periodum, super quam disponit; vtpote Sol in natiuitate diurna gubernat vitam nati cum aliorum planetarum participatione, spatio annorum decem, sed ipse primus sibi vendicat septimam partem suorum annorum, nempe annum vnum solarem, menses quinque & dies circiter quatuor: Deinde intrant in eius domini participationem cæteri planetæ per otdinem sequentes, singuli per septimam partem. Quod, quia vanum est, atque à bonis omnibus deridetur, lubens omitto. 100. ALGEBAR fixa in sinistro Orionis pede. Vide Rigel. 101. ALGEBRA Arab. est certa regula de occulta numerorum parte, tam absolutorum, quam respectiuorum cognoscenda; qua de re erudite scripserunt Claius, & Nicolaus Tartalea 102. ALGEBRAVAR Arab. Latinè Diuisor, seu Dominus terminorum, in quibus incidit Directio, aut Profectio annua; apud Persas Zamoctar dictus. Estque is cui competit dominium finium, intrà quos comprehenduntur certi quidam gradus singulorum signorum Zodiaci siue ad mentem Prolemxi siue Ægyptiorum, quorum diuisio magis probatur à Professoribus, atque à Tiris in sua Cælestis Philosophia eorum ratio elacidatur. Eius inuestigatio ex Arabum schola talis est: Ascensionibus obliquis Horoscopi adjice annos fluentes, dando singulis annis gradam ferè vnum ( eo modo quo explicabimus sub V. Directio) & aggregatum, reiecto si opus fuerit integro circulo, reperiatur in tabulis primi mobilis sub eleuatione poli tuæ regionis; nam gradus Zodiaci illi respondens erit terminus, in quem incidit Directio; & Planeta Dominus illius termini

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LEXICON 40 neta, applying it by conjunction to another, and remaining within the sphere of that light, in the meantime becomes retrograde, and is frustrated without its own; there is a certain kind of weakness, which in malefics always turns to good. 97. ALFRECA or Alphetal is called in Arabic the Bright one in the Gnossian Crown, that is, aperisso; for at its rising the earth is opened, and it puts forth flowers. In Persian tables it is called Piramis, or Pinacis, that is, the pupil, and the garland of the pupil. It is a most splendid star of the second honor, of the nature of Venus and Mercury. Concerning which see more in V. Corona Gnossia. 98. ALFELTA likewise a fixed star in Draco toward the arctic pole, of the nature of Venus and Mercury: by another name Foca. 99. ALFRIDARIE, or Fridaria, or Ferdaria among the Arabs, is a certain temporary power, which the planets arrogate to themselves over the life of the Native, and which seems to differ little from decennial disposition. For each planet has a certain determined and defined period of time over which it governs; for example the Sun, in a diurnal nativity, governs the life of the native with the participation of the other planets, for a space of ten years, but itself first claims for itself the seventh part of its years, namely one solar year, five months and about four days: then the other planets enter into the participation of its lordship in order, each for the seventh part. Which, because it is vain, and is mocked by all good men, I willingly omit. 100. ALGEBAR fixed in the left foot of Orion. See Rigel. 101. ALGEBRA, from Arabic, is a certain rule for recognizing the hidden part of numbers, both absolute and relative; on which matter Claius and Nicolaus Tartalea have written learnedly. 102. ALGEBRAVAR, Arabic, in Latin Divisor, or Lord of the terms, in which Direction or annual Profection falls; among the Persians called Zamoctar. And he is the one to whom belongs the lordship of the bounds, within which are comprehended certain degrees of the individual signs of the Zodiac, whether according to Ptolemy's meaning or the Egyptians, whose division is more approved by the Professors, and by Tiris in his Celestial Philosophy their reasoning is explained. Its investigation from the school of the Arabs is as follows: to the oblique ascensions of the Horoscope add the passing years, giving to each year about one degree (in the way we shall explain under V. Direction) and the aggregate, the whole circle being rejected if need be, is found in the tables of the first mobile under the elevation of the pole of your region; for the degree of the Zodiac corresponding to that will be the term, into which the Direction falls; and the Planet Lord of that term

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erit Divisor, atque Algebubatar, ad quem spectabit definire qualitatem directionis. ALGEDI DEINE. Cauda Cappicotni, stella fixa tertia ma- 105. gnitudinis, de natura Saturni, & Louis existens in gr. ferè 17. Aquarij. ALGENMEE idem sonat, ac collectio luminis, sicut Almane 104. idem quod vetatio. ARGENSE, siue Algensis, Castot, alter Geminorum. Vide 105. Apollo. ALGENIBI Arab. fixa secundæ magnitudinis de natura lo- 106. uis & Saturni fulgens in dextro Persei latere; tunc temporis existens in gr. ferè 27. Tauri ad plagam borealem, ideoque in nostro hæmisphætio numquam occidens. ALGETI, siue Alghesi Arab. vocatur Hercules, hoc est Geni- 107. culator alio nomine Elathi vel Elzegiale. ALGOL RAS, Gotgonis caput, seu Medusæ, stella fixa 108. violentissima secundæ magnitudinis de natura Saturni, & lo- uis in constellatione Persei ad plagam borealem posita in gra- du ferè 22. Tauri. Hæc verticalis, aut cum Luminaribus con- stituta maximas adducit calamitates: ideoque aduertit Argo- lus, in Pandosio spherico Græciam elapsis annis, maximis cladi- bus, bellis, euersionibusque vexatam fuisse, eoquia Caput Medusæ habuit verticalem, ob eandemque causam in poste- rum Neapolitano Regno, ad cuius vetticem paulatim accedit, easdem clades imminere præfatus est: quas vrinam hisce die- bus expetti non fuissemus. Sed faxit Deus hic sistant, & am- plius non progrediantur. Huius stellæ malignitatem agnouit etiam D. Th. in opusc. 24. art. 4. dicens eam maximè fune- ream esse: vt nos etiam alibi memorauimus. ALGOMEYSA, Græci Procyon; Canis minor, stella fixa pri- 109. mæ magnitudinis de natura Mercurij, & Martis, tunc tem- poris sita in grad. ferè 21. Cancri cum latitud. australi gt. 16. Alio nomine Antecanis dicta, eoquia ante Canem maiorem exoriatur. Quo tempore notat Hippocrates in Aphor. mor- bos esse difficilis curationis. ALGORAB Arabicè dicitur ala dextra Corui; fixa tertiæ ma- 110. gnitudinis de natura Veneris & Saturni. Vide sub V. Cornus. ALHABOR Arabicè audit Canis Maior, Sirius, fixa fulgen- 111. tissima in ote canis existens, primæ magnitudinis, imò om- nium astrotum maximum, & vt aliqui volunt ipsum Solem magnitudine superans. Stella est magni toboris, & potentiæ de natura louis & Martis, eos qui sub hoc ardentissimo sidere oriuntur numquam aqua interituros testatur Cicero in lib. de faso. B iii

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erit Divisor, and Algebubatar, to which it will belong to determine the quality of the direction. ALGEDI DEINE. The tail of Capricorn, a fixed star of the third ma- 105. gnitude, of the nature of Saturn and Jupiter, then in about 17 degrees of Aquarius. ALGENMEE means the same as a gathering of light, just as Almane 104. means the same as prohibition. ARGENSE, or Algensis, Castot, the other of Gemini. See 105. Apollo. ALGENIBI, Arab., a fixed star of the second magnitude, of the nature of Ju- 106. piter and Saturn, shining on the right side of Perseus; at that time situated at about 27 degrees of Taurus, toward the north, and therefore never setting in our hemisphere. ALGETI, or Alghesi, Arab., is called Hercules, that is, Geniculator, by another name Elathi or Elzegiale. 107. ALGOL RAS, the head of Gorgon, or of Medusa, a most violent fixed 108. star of the second magnitude, of the nature of Saturn and Ju- piter, situated in the constellation of Perseus toward the north, at a de- gree of about 22 Taurus. When this is on the Midheaven, or in con- junction with the Luminaries, it brings the greatest calamities; and therefore Argo- lus notes, in the Pandosion sphericum, that Greece, in years past, was afflicted with the greatest de- structions, wars, and upheavals, because the Head of Medusa was on the Midheaven; and for the same reason he foretold that in the Neapolitan Kingdom in the future, to whose summit it is gradually approaching, the same disasters were impending: which, alas, in these days we have not hoped to see spared from. But may God cause them to stop here and advance no farther. The malignity of this star was also acknowledged by D. Th. in opusc. 24, art. 4, saying that it is most funereal: as we have also elsewhere mentioned. ALGOMEYSA, called by the Greeks Procyon; Canis Minor, a fixed star of the first magnitude, of the nature of Mercury and Mars, then situated at about 21 degrees of Cancer with southern latitude gt. 16. It is also called Antecanis, because it rises before the Greater Dog. At that time Hippocrates notes in the Aphorisms that diseases are difficult to cure. ALGORAB is the Arabic name for the right wing of the Crow; a fixed star of the third magnitude, of the nature of Venus and Saturn. See under V. Cornus. ALHABOR, in Arabic, is called Canis Major, Sirius, the brightest fixed star, 111. existing in the dog star, of the first magnitude, indeed the largest of all stars, and, as some claim, surpassing even the Sun in size. It is a star of great power and potency, of the nature of Jupiter and Mars; Cicero, in book De fato, testifies that those born under this most fiery star will never perish by water. B iii

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113. LEXICON Præterea ipso cum Sole exorient, vt notat Plinius, tota Na- tura reparitur, canes aguntur in rabiem, fluctuant in dolijs vina, febres ardentes grassantur, & maximos calores experi- mur, vt proprereà solemne omnibus obseruare sit dies ab eo dictos Cansculares. Est nunc in gradu 9. Cancri cum latitudine australi gr. ferè 40. Otitur tamen Romæ cum gr. 8. Leonis circa Kalendas Augusti. 112. ALHABOR item vocatur teste Stosloetino, clauus Astrolabij, timpana, & rete in vnum intra Matrem nectens. 113. ALHAISETH, teste Baiero vocatur ab Hermete spica Vir- ginis, stella fixa, primæ magnitudinis: Arabicè Azimech. 114. ALHANTICA sine Alphansia dicitur Arab. Armilla suspen- soria astrolabij. Sicut &c 115. ALHADIDA appellatur Ostensor seu, quam vulgo vocant linea fiducia, Græcis Dioptra in medio Astrolabij sita, & ad limbum vsque protracta ad venandas stellarum altitudines, & cuiuscunque loci ascensiones rectas, aut descensiones. 116. ALHIRTO Arab. dicitur rostrum Gallina, stella fixa tettia magnitudinis de natura Veneris, & Mercurij, existens in gr. 26. Capricotni cum maxima latitudine boteali. Non longè ab hac Stella, anno 1600. apparuit aliud nouum Phænomenon, quod durauit vsque ad annum 1621. quo euanuit linguens ta- men loco suo quendam hiatum, qui vt testatur Argolus, ad hæc vsque tempora cernitur. 117. ALIBD Arab. idem sonat, ac Latinè deterioratio, & est cùm Planeta in cælesti themate reperitur in domibus cadenti- bus, quales sunt tertia, sexta, nona, & duodecima, in quibus multum deteriotatur. Sicut econtrà 118. ALICHEL, hoc est, profectus Planeta, dicitur quando est in Angulo, vel succedentibus, vbi mirum in modum proficit, & eius vis duplicatur. Qua de re vide quæ diximus suo loco. 119. ALICORAB, seu Alichorad idem est, ac Latinè contrarietas. Quod euenit, cùm aliquis Planeta leuis fuerit multotum gra- duum in signo, & alter illo ponderosior in paucioribus: ter- tius quoque leuior vadens ad coniunctionem ponderosi: sed antequam corpore iungantur, ille, qui primus in pluribus gra- dibus existens potius à ponderoso videbatur patate discessum, fit retrogradus, ac per ponderosum transiens, post coniun- ctionem cum eo iungitur etiam tertio leuiori, & sic destruitur coniunctio, quam ille, vt ita dicam, moliebatur cum poderoso. 120. ALICTISAL, seu Ictisal Arab. idem sonat, ac Latinè appli- catio, & est cum planeta leuis existens in coniunctione platica alterius ponderosi, vadit ad eius coniunctionem partilem. Econtrà

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113. LEXICON Moreover, at the rising of the Sun itself, as Pliny notes, all of Nature is renewed; dogs are driven into rabies, wines ferment in barrels, burning fevers spread, and we experience the greatest heats, so that it is customary for all to observe the days called Caniculares, or Dog Days. It is now in the 9th degree of Cancer with southern latitude of about 40 minutes. Yet in Rome it occurs at the 8th degree of Leo, around the Kalends of August. 112. ALHABOR is also called, according to Stosloetinus, the pin of the Astrolabe, joining the tympana and the rete into one within the Mother. 113. ALHAISETH, according to Bayer, is called by Hermes the ear of Virgo, a fixed star of the first magnitude; in Arabic, Azimech. 114. ALHANTICA, or Alphansia, is called in Arabic the suspensory armlet of the astrolabe. And so on. 115. ALHADIDA is called the pointer, or what is commonly called the line of faith, in Greek the Dioptra, placed in the middle of the Astrolabe and drawn out to the rim for observing the altitudes of stars and the right ascensions or descensions of any place. 116. ALHIRTO is called in Arabic the rooster’s beak; a fixed star of the third magnitude, of the nature of Venus and Mercury, situated at the 26th degree of Capricorn with the greatest northern latitude. Not far from this star, in the year 1600, there appeared another new phenomenon, which lasted until the year 1621, when it vanished, leaving in its place a certain gap which, as Argolus testifies, is seen even to these times. 117. ALIBD, in Arabic, has the same meaning as in Latin deterioration, and is when a planet in a celestial figure is found in the cadent houses, such as the third, sixth, ninth, and twelfth, in which it is much weakened. Likewise conversely 118. ALICHEL, that is, the progress of a planet, is said when it is in an angular house or in the succedent houses, where in a wondrous way it advances, and its force is doubled. On this matter see what we have said in its place. 119. ALICORAB, or Alichorad, is the same as in Latin contrariety. This happens when one planet, lighter and in more degrees in a sign, and another, heavier than it, in fewer; and a third, also lighter, going toward conjunction with the heavier: but before they are joined in body, the one which first, being in more degrees, seemed rather to depart from the heavy one, becomes retrograde, and passing through the heavy one, after conjunction is joined with him also by the third lighter one; and thus the conjunction is destroyed, which he, so to speak, was attempting to make with the stronger. 120. ALICTISAL, or Ictisal in Arabic, has the same meaning as in Latin application, and is when a lighter planet, existing in the platick conjunction of another heavier one, goes toward its partile conjunction. On the contrary

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MATHEMATICVM. 23 ALINCIRAF idem est, ac separatio: cum videlicet planeta 111. leuis separatur à conunctione partili alterius ponderosi; sed tamen adhuc est in platica, hoc est intrà quantitatem orbis illius. ALIOT, Latinè equus. Eo nomine appellant promiscuè 122. Arabes singulas trium stellatum quæ sunt in cauda Vrsæ Ma- ioris, eoquia præseferunt quasi tres equos ex ordine dispositos ad trahendum Plaustrum. ALKAIR, siue Alkir, Aquila, Vultur volans, Stella fixa se- 123. cundæ magnitudinis de natura louis, & Martis existens in gr. ferè 27. Capricorni cum gr 30. latitudinis borealis. ALKIA DATHA Latinè idem sonat, ac pulsatio vireutis: & 124. est cùm Planeta existens in suis dignitatibus respicit tardio- rem, qui nullam dignitatem habeat in loco alterius: tunc enim iste velocior pulsat, & mirrit propitiam virtutem ad tardio- rem. Vide in V. Pulsatio. ALKINDVS, seu Dominus Ascone, est Cometæ species ad 125. instar Cornu (vnde & nomen hausit) de natura Mercurij, cum carda oblonga coloris cerulei. ALKINIRA, Vide Alchinira. 126. ALKIREM Arabicè dicitur locus præcedentis luminarium 127. conunctionis ad inuestigandum quis totius illius lunationis dominium sortiatur. Sicut etiam ALLVRE dicitur cardo ipse interluniorum. Eo potissimum 128. verbo vtitur Author Centiloquij secundum versionem Ara- bicam Hali Rodoan præsertim propos. 46. sicut & præceden- tis meminit in propositione 58. ALMAGSTVM. Sic intitulatur Liber magnæ constructionis 129. Ptolemæi ex Arab. Al quod significat ordo, & Græco Megiston, vel Ægyptio Megasice quod maximum, atque per- fectum sonat. Opus planè diuinum, ac singulare in quo tota sphæricorum doctrina traditur, & explicatur. ALMANACH apud Arabes idem sonat, ac Latinè numeratio, 130. vel distributio: ab radice Hebræa Mach, quod distribuit, seu numerauit, significat. Hinc apud Astronomos annotationes, & computationes cælestium motuum in dies singulos, quas Græce Ephemerides dixere, Almanach trito iam vel apud ipsum vulgus vocabulo audiunt. Eoque potissimum titulo Astrolo- gorum libri, in quibus astrorum motus, eclipses, aspectus planetarum, & alia huiusmodi oculis exhibentur, gaudent. ALMANAR Arab. idem sonat, ac supereminent a, & præ- 131. ponderaui vnius Planetæ super alium: Nos elevationem, seù Altitudinem dicimus Arabes tunc dicunt alicui planetæ com- petereius Almanar super alium, quando is fuerit situ emi- B itij

Transcription: Translated (English)

MATHEMATICVM. 23 ALINCIRAF is the same as separation: namely, when a light planet is separated from a partile conjunction of another, heavier one; but it is still in the platic, that is, within the quantity of that orb. ALIOT, in Latin, horse. By that name the Arabs promiscuously call the three stars which are in the tail of the Greater Bear, because they present themselves as if three horses arranged in order to draw the Wagon. ALKAIR, or Alkir, Aquila, Flying Vulture, a fixed star of the second magnitude, of the nature of Jupiter and Mars, situated at about 27 degrees of Capricorn with 30 degrees of northern latitude. ALKIA DATHA in Latin sounds the same as the pulsation of virtue: and it is when a planet, existing in its dignities, aspects the slower one, which has no dignity in the place of the other; for then the swifter one beats, and infuses a favorable virtue into the slower. See under V. Pulsation. ALKINDVS, or Dominus Ascone, is a kind of comet in the shape of a horn, from which also it takes its name, of the nature of Mercury, with an elongated head of blue color. ALKINIRA, see Alchinira. 126. ALKIREM is said in Arabic to be the place of the conjunction of the preceding luminaries, for investigating who shall obtain the rulership of that whole lunation. Likewise ALLVRE is said to be the very cusp between lunations. The Author of the Centiloquium chiefly uses that word, according to the Arabic version of Hali Rodoan, especially proposition 46, just as he also mentions the preceding in proposition 58. ALMAGSTVM. Thus is entitled the Book of the Great Construction of Ptolemy, from Arab. Al, which signifies order, and the Greek Megiston, or from the Egyptian Megasice, which sounds like maximum and perfect. A truly divine and singular work, in which the whole doctrine of the spheres is set forth and explained. ALMANACH among the Arabs has the same meaning as, in Latin, numeration or distribution: from the Hebrew root Mach, which signifies to distribute or to number. Hence among astronomers, annotations and computations of celestial motions for each day, which the Greeks called Ephemerides, are commonly known even to the vulgar by the name Almanach. And under that title especially are esteemed the books of astrologers, in which the motions of the stars, eclipses, aspects of the planets, and other such things are displayed to the eye. ALMANAR, in Arabic, has the same meaning as supereminence, and the preponderance of one planet over another: we say elevation, or altitude; the Arabs then say that a certain planet has Almanar over another, when it is in a position emi-B itij

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LEXICON 4 nentior in suo circulo breui, seu Epicyclo: & de hoc eleua- tionis modo loquutum fuisse contendunt Ptolomæum in pro- pos. 63 sui Centiloqui, vbi dixit. Cum Saturnus lupterque con- iunguntur, vter eorum sublimior sit, vide; ac secundum natu- ram illius pronunciato. Aliter id explicat Alkabitius in expo- sitione huius verbi. In quo autem vetè consistat hæc præro- gatiua & supereminentia, vide in Verbo eleuatio. 132. ALMANEM Arab. idem sonat ac refrenatio: estque, ait Al- kabitius, quando Planeta motu suo vadit ad coniunctionem alterius, sed antequam iungantur, accidit retrogradatio; & sic tollitur, seu refrenatur, quam moliebatur, coniunctio. Argolus verò ait tunc fieri, cum tres Planetæ fuerint intrà fines suorum otbium. 133. ALMAVERICH apud Alkabitium hereditates indicat mor- tuorum, significatas per tertium dominum triplicitatis Do- mus octauæ. 134. ALMEGRAMETH Arab. Latinè dicitur Ara, sidus ad austra- les plagam constans stellis septem, vel sanè octo, vt placet Ke- plero, & Baiero. 135. ALMICANCHARATH apud Arabes sunt circuli paralleli ad horizontem in superiori hæmispherio computati, donec per- ueniatur ad Zenith capitis nostri. Dicuntur etiam Corona quia efformant quasdam veluti coronas ad Zenith; vti videre est in tabulis Astrolabij: Item & circuli altitudinum quia eorum ope stellarum altitudines dimetimut. 136. ALMOGIZA Latinè dicitur Limbus in Astrolobio: Estque cit- culus latus, ac prominens in matte Astrolabij intra se habens tabulas, ac rete inclusa, quæ ipsi posse à cotrespondent: in eo enim descriptæ sunt horæ æquinoctiales post meridiem vna cum gradibus æquatoris, singulis horis in singulos quindenos gradus tributis, quoadvsque perficiatur numerus horarum 24. & graduum 360. 137. ALMVCEDEME Alacaf, seu Almucedic Alaraf Chaldaicè, dicitur stella fixa secundæ magnitudinis de natura Saturni, & Mercurij in ala Septemtrionali Virginis, Latinè Vinde- miator. 138. ALMVDHEBIR apud Arabes est dignitas, & præeminentia planetæ in aliquo loco vel per dispositionem, vel per aspectum beneficum. Eo verbo vtitur Ptolemæus in Versione Arab. propos. 17. Centiloqui, vbi ait, quòd si fortunæ fuerint in almudhebir ad locum timendum nempe octauum, hoc est, si fuerint intrino vel sextili octauæ domus, annullabunt dam- num, quod alioqui inferrent, si ei loco simpliciter præfue- rint.

Transcription: Translated (English)

LEXICON 4 They contend that Ptolemy was speaking of this mode of elevation in proposition 63 of his Centiloquium, where he said: When Saturn and Jupiter are conjoined, see which of them is higher, and pronounce according to the nature of that one. Alkabitius explains this differently in the exposition of this word. But in what this prerogative and preeminence properly consists, see under the word elevatio . 132. ALMANEM, in Arabic, has the same meaning as restraint: and it is, says Alkabitius, when a planet by its motion goes toward the conjunction of another, but before they unite, retrogradation occurs; and thus the conjunction it was attempting is removed, or restrained. Argolus, however, says that it happens when three planets are within the bounds of their orbits. 133. ALMAVERICH, according to Alkabitius, indicates the inheritances of the dead, signified by the third lord of the triplicity of the eighth house. 134. ALMEGRAMETH, in Arabic. In Latin it is called the Ara, a constellation toward the southern quarter, consisting of seven stars, or truly eight, as Kepler and Bayer prefer. 135. ALMICANCHARATH, among the Arabs, are circles parallel to the horizon, reckoned in the upper hemisphere, until the zenith of our head is reached. They are also called Corona because they form certain crowns, as it were, toward the zenith, as may be seen in the tables of the Astrolabe. They are also called circles of altitudes because by their help we measure the altitudes of the stars. 136. ALMOGIZA, in Latin, is called the Limbus in the Astrolabe: and it is a broad, projecting circle in the frame of the Astrolabe, within which are enclosed the tables and the rete, corresponding to it; for in it are described the equinoctial hours after noon together with the degrees of the equator, each hour being assigned fifteen degrees, until the number of 24 hours and 360 degrees is completed. 137. ALMVCEDEME Alacaf, or Almucedic Alaraf, in Chaldean, is called a fixed star of the second magnitude, of the nature of Saturn and Mercury, in the northern wing of Virgo; in Latin, Vindemiator. 138. ALMVDHEBIR, among the Arabs, is the dignity and pre-eminence of a planet in some place, either by disposition or by a benefic aspect. Ptolemy uses this word in the Arabic version of proposition 17 of the Centiloquium, where he says that if the fortunes are in almudhebir toward a place to be feared, namely the eighth, that is, if they are in trine or sextile of the eighth house, they will annul the harm which they would otherwise inflict, if they simply had authority over that place.

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MATHEMATICVM. 21 ALMVEA Chaldaicum nomen, Latinè idem sonat, ac 139. visio, & respondentia ad inuicem: & est configuratio reliquorum quinque planetarum ad Luminaria, talis, qualis est domorum ipsorum ad domos Luminarium, sintque proinde orientales à Sole, arque occidentales à Luna. Sic Saturnus v[erò] [e]n[im] erit in Almugea Solis, quando fuerit ab eo distans per quinque signa secundum eorum successionem: in Almugea vesò Lunæ, quando tantumdem ab eadem se elongauerit; verum contrà successionem signorum: quia profectò eius domus, quæ sunt Aquarius, & Capricornus tantumdem distant à Leone & Cancro, domibus videlicet Luminarium, progrediendo, & secundum, & contrà successionem signorum. Similiter Iupiter est in Almugea Solis quando est in eius trino sinistro, in Almugea Lunæ cum in dextro, quia sagittarius eius domus est in trino sinistro Leonis, Pisces verò in dextro Cancri domicilij Lunæ. Sic Mars quando est in quadrato; Venus, cum in sextili; & sic de singulis. Et hoc modo planetas ad Luminaria se habere, vocant Astrologi, suas personas gerere, quia videlicet eandem participationem à Luminaribus habent, quam eorum domicilia à domicilijs Luminarium. Cuius rei rationem affert Hali Rodoan super Cap. 23. libri 140. primi Quadrip. Quia, inquit, quilibet quinque erraticorum habet duas domos propter participationem quam habet de natura ipsorum luminarium, & propter hoc quod habeant vim maiorem, quando sciicet erit inter eorum aliquem, & aliquod Luminarium tanta longitudo quanta est inter domum suam, & domum Luminarium, in medietate cuius est domus ipsa. Vnde aquum est, vt per talem habitudinem planeta vires acquiras, ac stesset in domicilio suo. Hæc Hali. ALMVRT Arab. Latine Ostensor. Linea fiduciæ, seu index 141. in Astrolabio alio nomine Albidada. ALMVSECHELET Luna cum stellis configuratio interpretatur. 142. Eo vtritur verbo Ptolemæus in Centiloq[ue] propos 23. dicens, Almusecheles Iunæ ad stellas facere natos mobiles, vel inerres. ALMVSTEVLE, idem quod Almushen, de quo mox infia. ALMVTHEN Arab. dicitur Planeta dispositor alicuius loci, 143. hoc est vincens reliquos in numero, & efficacia dignitarum facto scrutinio ex quinque essentialibus, domicilio nempe exaltatione, Trigono, Terminis, & Facie; licèt hanc postremam vt satis imbecillem, vel sanè euanidam recentiores communiter non admittant, & eius loco accipiant configurationem, seu aspectum quemlibet ad dictum locum. Eligat quisque quod sibi magis attrider: Nobis sat est insinuasse. ALNISIGREF Arab. Latinè dicitur separatio: & est iuxta 144.

Transcription: Translated (English)

MATHEMATICVM. 21 ALMVEA, a Chaldean name, in Latin it means the same as visio and mutual response; and it is the configuration of the remaining five planets in relation to the Luminaries, such as the relation of their houses to the houses of the Luminaries, so that they are consequently eastern from the Sun and western from the Moon. Thus Saturn, indeed, will be in the Almugea of the Sun when it is distant from it by five signs according to their succession; in the Almugea of the Moon, when it has moved away from it by the same amount, but contrary to the succession of the signs; because, in truth, its houses, which are Aquarius and Capricorn, are just as far from Leo and Cancer, the houses of the Luminaries, proceeding both according to and contrary to the succession of the signs. Likewise Jupiter is in the Almugea of the Sun when it is in its left trine, in the Almugea of the Moon when in the right, because Sagittarius, its house, is in the left trine of Leo, while Pisces is in the right of Cancer, the domicile of the Moon. So Mars when in the square; Venus, when in the sextile; and so for the others. And in this way astrologers say that the planets relate to the Luminaries as if they were playing their own parts, because they have the same participation from the Luminaries that their domiciles have from the domiciles of the Luminaries. Hali Rodoan gives the reason for this on chapter 23 of the first book of the Quadripartitum: because, he says, each of the five wandering stars has two houses on account of the participation it has in the nature of the Luminaries, and because they have greater power when, namely, between one of them and one of the Luminaries, there is such a distance as is between its house and the house of the Luminaries, in the middle of which that house lies. Hence it is fitting that by such a relation the planet acquires strength, as if it stood in its own domicile. Thus Hali. ALMVRT, Arab. In Latin, Ostensor. The line of faith, or pointer, in the astrolabe, otherwise called Albidada. 141. ALMVSECHELET means the configuration of the Moon with the stars. 142. Ptolemy uses this word in the Centiloquium, proposition 23, saying that the Almusecheles of the Moon to the stars makes natively mobile or inert things. ALMVSTEVLE is the same as Almushen, of which below. ALMVTHEN, Arab., is said of the planet dispositor of a certain place, 143. that is, the one prevailing over the others in number and in the effectiveness of dignities, after scrutiny has been made from the five essential dignities, namely domicile, exaltation, trine, terms, and face; although the last, as being quite weak or indeed fleeting, modern writers commonly do not admit, and in its place accept a configuration, or any aspect whatsoever, to the said place. Let each choose what pleases him more: it is enough for us to have indicated it. ALNISIGREF, Arab., is called separation in Latin: and it is, according to 144.

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LEXICON expositionem Hali, cum Planeta leuis existens in coniunctione partili alterius qui sit eo ponderosior, per motum suum separatur ab eo; reperitur tamen adhuc platicè configuratus, hoc est intra quantitatem lucis illius orbis. 146. ALOSAIH Arab. idem ac Vindemiaror, Stella secundæ magnitudinis in Ala septemtrionali Virginis, teste Argolo in Pandosio Sphærico. 147. ALPHANTIA albansica Latinè Armilla suspensoria in Astrolabio. 148. ALPHARD seu Alpharad, dicitur item Arab. Cor Hydræ, Stella fixa primæ magnitudinis Ptolemeo, at secundum alios secundæ, de natuta Saturni & Venetis in medio Hydræ existens in longitudine gr. ferè 23. Leonis. Hæc vna est ex illis stellis, quas D. Thomas opus 28. art. 4. finereas dixit, ac monstruosam in icare vita terminationem, quippequæ cum sit natutæ mixtæ ex contrarijs qualitatibus, saturninis tamen prædominantibus, affert secum humorum corruptionem, si in horoscopo reperiatur, præsettim cum malo radio Veneris, aut Saturni, & si fuerit cum Anæreta statim eius qualitatibus imbutur, & portendit sæpè venenum, vt volunt Astrologi. Propterea antiqui illi obseruatores, ad eius naturam posteris explicandam, Hydræ, venenosi scilicet monstri, nomen, ac figuram illi dederunt. 149. ALPHECCA, siue Alphelta. Vide Alfecca. 150. ALPHERATZ, siue Alpharatz Arab. Latinè dicitur Muscida equi. Stella fixa tertiæ magnitudinis de natura complicata Martis, Louis, & Veneris, existens in gr. 27 Aquatij cum latitudine maxima boreali. Item & Ensj Alpharatz, & Marchab Alpharatz aliæ duæ stellæ secundæ magnitudinis de natura Martis, & Mercurij in scapulis, ac dextro humero Pegasi existentes, & circa grad. 20. Piscium. De ea in alicuius ortu occidente cum malefica, aut malo eius radio, sic cecinit Pontanus in Vrania. Excuss, aut currulacerum, aut è calce cruentum, Aut dorso eiectum stygras desurbas ad vndas. 151. ALPHEMA Arab. dicitur lucida Coronæ Gnossiæ stella fixa splendidissima secundæ magnitudinis de natura Veneris, & Mercurij existens nunc in gr. 7. Scorpij cum grad. 44. latitudinis borealis. Hæc ob sui venustatem, ac pulchritudinem dicitur Cæli pupilla, settum, flos, neque in Genethliacis ab hac significatione aberrat, facit enim natum delicijs deditum, mollem, flores, & vnguenta tractantem, vt propterea de ea in alicuius horoscopo reperta sic venustè cecinerit Pontanus in Vrania.

Transcription: Translated (English)

LEXICON expositionem Hali, when a light Planet, being in partile conjunction with another which is the heavier, is separated from it by its own motion; yet it is still found platicly configured, that is, within the light of that orb. 146. ALOSAIH, Arab. the same as Vindemiaror, a star of the second magnitude in the northern wing of Virgo, as testified by Argolus in the Pandosio Sphaerico. 147. ALPHANTIA, in Latin and Albanian, a suspensory armlet in the Astrolabe. 148. ALPHARD, or Alpharad, is likewise called in Arabic the Heart of Hydra, a fixed star of the first magnitude according to Ptolemy, though according to others of the second, of the nature of Saturn and Venus, existing in the middle of Hydra in the longitude of about 23 degrees of Leo. This is one of those stars which St. Thomas, in work 28, art. 4, called harmful, and a monstrous termination in a life’s course, because, since it is of a mixed nature from contrary qualities, though with Saturnine qualities predominant, it brings with it corruption of the humors, if it is found in the horoscope, especially with an evil ray of Venus or Saturn; and if it be with the Anareta, it is at once imbued with its qualities, and often portends poison, as the astrologers maintain. For this reason the ancient observers, in order to explain its nature to posterity, gave it the name and figure of Hydra, that is, of the poisonous monster. 149. ALPHECCA, or Alphelta. See Alfecca. 150. ALPHERATZ, or Alpharatz, Arab. in Latin it is called Muscida equi. A fixed star of the third magnitude, of the mixed nature of Mars, Jupiter, and Venus, existing at 27 degrees of Aquarius with the greatest northern latitude. Also Ensj Alpharatz and Marchab Alpharatz are two other stars of the second magnitude, of the nature of Mars and Mercury, situated in the shoulders and right shoulder of Pegasus, and around 20 degrees of Pisces. Concerning it, when in a nativity it is setting together with a malefic planet, or under its evil ray, Pontanus thus sang in Urania. Excuss, or broken by a chariot, or bloodied at the heel, Or cast from the back toward the Stygian waters. 151. ALPHEMA, Arab. is called the bright star of the Gnosian Crown, a fixed star most splendid, of the second magnitude, of the nature of Venus and Mercury, now existing at 7 degrees of Scorpio with 44 degrees of northern latitude. Because of its grace and beauty it is called the eye of heaven, the seat, the flower; nor does it fall short of this meaning in genethliac matters, for it makes one devoted to pleasures, soft, and engaged with flowers and ointments; wherefore, when found in someone’s horoscope, Pontanus thus beautifully sang of it in Urania.

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MATHEMATICVM. Stella sub hac natis studium manet dulcium odorum: Conficiunt vnguenta, & florea sarta coronant. Mundicres indigna viro, comptusque puella Persimilis: quaque & Veneris molle imperat Astrum. Inde etiam occulmi sub pectore pasciur ignis, In vetitumque ruunt, & amor noua vincula nectit. Quocirca Nate ardentes compesce furores, Et leges meditare, & honesti concipe formam. De ea verò in occasu reperta cum Saturno, aut malo eius ra- dio, mox subdit. Exponit Natum feris damnante senatu, Pro tumulo fauces canum, aut rabida ora leonum Accipient, tumulo Saturnus condet vbi ipse Insedit loca, primo sub flore iuuenta. Prætereà fidus hoc, vt author est Plinius, est valde tem- <152:> pestuosum, quo cum Sole occidente Venti excitantur, pluuiæ ingruunt, & ronitrua; similiter oriens cum eodem Sole facit aerem frigidum, turbidum ac ventosum, cum Saturno autem adducit adhuc nuius, pro temporis qualitate, aut ad minus tempus frigidum, ac nebulosum. Oritut autem Romæ cum gradu 16. Libræ, occiditque cum decimo nono gradu Ca- <153.> pricorni. ALRAMECH, siue Alkameluz Arab. Arcturus, hoc est gla- dius & pugio Bootis, stella fixa informis primæ magnitudinis prope clunes Bootis existens, atque in longirudine in gr. 19. Libræ cum gr. 31. latitudinis borealis: naturam habet mix- tam Iouis, & Martis. Plinius vocat hoc fidus horridum, eo- quia cum Sole occidens tempestates facit, & ventos australes inscitat. At verò in Generhliacis, inquit Pontanus in Vrania, quod addicit natos infami supplicio, vel etiam parat infelici carcere mortem, si occidat cum prauo radio Saturni, vel Mar- tis. At verò in exortu facit fidelem, veri amatorem, cui cre- dentur opes, & pretiosa regum supellex, vel etiam erit custos forium, inrimusque cubicularius. Addit Sadius, quod cum Ioue dat diuitiarum affluentiam, at cum Saturno earundem profligationem minatur. ALRVKABA Arab. Latinè stella polatis Cynosura in extremo <154.> caudæ Vrsæ minoris sita, secundæ magnirudinis de natura Ve- neris, & Saturni, existens nunc temporis in gr. 24. Geminorum cum latitudine boreali gr. 66. adeoque omnium vicinissima polo Arctico, cum ab eo non distet nisi tres gradus. Obidque & Phanice quoque appellata est, eoquod à Phænicibus nautis plurimum obseruabarur: eum enim non adhuc com- perta esset vitrus acus magneticæ, ideo ipsi ex hac stella nosce-

Transcription: Translated (English)

MATHEMATICVM. Under this star there remains a love of sweet scents in those born beneath it: they make perfumes, and weave garlands of flowers. Unfit for work, and like a girl in dress and adornment, very similar: and in every way the gentle star of Venus rules it. Hence also there is kindled beneath the heart a hidden fire, and they rush into forbidden things, and love weaves new bonds. Therefore, child, restrain the burning frenzy, and meditate on laws, and conceive the shape of what is honorable. But concerning that which is found in its setting together with Saturn, or under an evil ray of his, he adds at once: It exposes the native, condemned by a savage senate, to the jaws of dogs, or the ravenous mouths of lions, as a tomb; Saturn will place the tomb where he himself has settled, in places at the first bloom of youth. Moreover this fixed star, as Pliny is author, is very stormy: when the Sun sets with it, winds are stirred up, rains and thunderclouds set in; similarly when it rises with the same Sun it makes the air cold, troubled, and windy; but with Saturn it brings even snow, according to the condition of the season, or at least cold and cloudy weather. At Rome it rises with the 16th degree of Libra, and sets with the nineteenth degree of Ca- pricorn. ALRAMECH, or Alkameluz in Arabic, Arcturus, that is, the sword and dagger of Bootes, a fixed, shapeless star of the first magnitude situated near the loins of Bootes, and in longitude at 19 degrees of Libra with 31 degrees of northern latitude: it has a mixed nature of Jupiter and Mars. Pliny calls this star rough, because when it sets with the Sun it makes storms and stirs up southern winds. But in the Genethliacs, says Pontanus in Urania, it assigns to those born under it an infamous punishment, or even prepares death in a miserable prison, if it set with the evil ray of Saturn or Mars. But at its rising it makes one faithful, a lover of truth, to whom riches and the precious furnishings of kings may be entrusted, or else he will be a keeper of doors, and a faithful chamberlain. Sadius adds that with Jupiter it gives abundance of wealth, but with Saturn it threatens the ruin of the same. ALRVKABA, Arabic; in Latin, the star called Cynosura, placed at the very end of the tail of the Little Bear, of second magnitude, of the nature of Venus and Saturn, now being in the 24th degree of Gemini with 66 degrees of northern latitude, and therefore the nearest of all to the Arctic pole, since it is distant from it by only three degrees. And for this reason it is also called Phoenice, because it was very much observed by Phoenician sailors; for when the magnetic compass had not yet been discovered, they by means of this star knew how to find

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28 LEXICON bant, vbi consisterent, quò iter instituere deberent, quantumve a loco re nori essent. Hius influxus ab Astronomis minimè obseruantur, quippe qui si quos habeat, semper ijsdem sunt, cum semper eodem sere loco consistat, & nullius penè sit motus, vnde pro loci, & sirus qualitate in influendo varieratem <155> aliquam subire possit. Hæc stella, inquit Ioannes Christmannus in obseruationibus solaribus, aliquando in ipsum polum recidet cum singulis annis accedat ad polum arcticum, & declinationem acquirat secundoru[m] viginti: vnde cum tempore Hipparchi, hoc est annis abhinc retrò 1700. absuetit à polo gr. 12. & min. 24. & nunc currente anno à partu Virginis 1660. non distet nisi gr. 2. & min. 31. manifestum sit ipsam tandem anno ab incarnatione Domini 2125. debere in ipsum polum incidere. Ricciolus tamen tomo primo Almagesti novi lib. 6. cap. 19: probl 5. in ea est sententia, vt nunquam, neque ipsa stella polaris, neque vlla alia assequutura sit adamussim Mundi polum. Quia, inquit, vt hoc assequeretur, deberet habere tantum latitudinis, quantum est complementum distantiæ polorum ab initio Cancri, ratione obliquitatis Eclipticæ, quæ in sententia ipsius deberet esse gr. 66. min. 30 oporteret ergo stellam istam non habere latitudinem maiorem gr. 66 min. 31. nec minorem gr. 66. min. 8. Sed quandonam, subdit, hæ conditiones concurrent simul, vt stella hæc sit in principio Cancri, in ipso tempore, quo ob variationem obliquitatis Eclipticæ, latitudo stellæ sit æqualis præcisè complemento obliquitatis, seù distantiæ? Latitudo autem stellæ polaris nunc est gr. 66. min. 2. Numquam ergo fuit, vel erit in ipso Mundi polo, etiamsi maximè sit ad illum necessura, & peruentura ad Cancri initium iuxta Tychonicum calculum anno 2092. & tunc distabit à mundi polo secundis septem: postea ab illo recedere incipiet. Hæc Ricciolus, dicens se olim deceptum authoritate Regiomontani; putasse hanc stellam assecuturam ipsum Mundi polum, sed postea re melius considerata, sententiam in melius commutasse. <156.> ALTALISIM Arab. stella fixa secundæ magnitudinis de natura Iouis & Saturni posita in ipsa effusione aquæ Aquarij proximè Fomahand stellæ insigniori priuæ magnitudinis, cui contermina est alia stellula eiusdem natutæ & qualitatis ab Arabibus dicta Calbez. <157.> ALTANI dicuntur Venti subterranei altè à terra spirantes, qui si in mare (è cuius regione semper exsufflant) progrediantur, Apogæi; si verò è mari ad terram reuertantur, Tropæi appellantur; de quibus vide Plinium, lib. 2. cap. 43. <158.> ALTITVDO apud Astronomos idem significat, ac Exaltatio

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28 LEXICON bant, where they should come to rest, whither they ought to set out on their journey, and how far they were from the place of their return. This influx is scarcely observed by Astronomers, since if they have any, they are always the same, because they always remain almost in the same place, and have hardly any motion, whence they could undergo some variation in influencing, according to the quality of place and position. <155> This star, says Ioannes Christmannus in the Solar Observations, will at some time fall upon the very pole, since each year it approaches the arctic pole and acquires a declination of 20 seconds: whence, since in the time of Hipparchus, that is, 1700 years ago, it was 12 degrees and 24 minutes away from the pole, and now, in the current year from the birth of the Virgin 1660, it is not distant by more than 2 degrees and 31 minutes, it is manifest that it must finally, in the year of the Lord's Incarnation 2125, strike the pole itself. Ricciolus, however, in the first volume of the New Almagest, book 6, chapter 19, problem 5, holds the opinion that neither the pole star itself nor any other star will ever exactly attain the world’s pole. For, he says, in order to achieve this, it would need to have just as much latitude as is the complement of the distance of the poles from the beginning of Cancer, on account of the obliquity of the Ecliptic, which in his opinion ought to be 66 degrees 30 minutes; therefore the star would need not to have a latitude greater than 66 degrees 31 minutes nor less than 66 degrees 8 minutes. But when, he adds, will these conditions occur together, so that this star is at the beginning of Cancer, at the very time when, because of the variation of the obliquity of the Ecliptic, the latitude of the star is precisely equal to the complement of the obliquity, or distance? But the latitude of the pole star is now 66 degrees 2 minutes. Therefore it was never, nor will it be, at the very pole of the world, even if it should be nearest to it, and will reach the beginning of Cancer according to the Tychonic calculation in the year 2092, and then it will be seven seconds distant from the world’s pole; afterward it will begin to recede from it. Thus Ricciolus, saying that he once was deceived by the authority of Regiomontanus; he had thought that this star would attain the very world’s pole, but later, having considered the matter more carefully, he changed his opinion for the better. <156.> ALTALISIM, Arab. a fixed star of the second magnitude, of the nature of Jupiter and Saturn, situated in the very outflow of the water of Aquarius, near the more famous star Fomahand of the first magnitude, to which is adjacent another little star of the same nature and quality, called by the Arabs Calbez. <157.> ALTANI are called subterranean winds blowing high from the earth, which if they advance into the sea (from whose region they always blow) are called Apogaei; but if they return from the sea to land, they are called Tropaei; concerning which see Pliny, book 2, chapter 43. <158.> ALTITVDO among Astronomers signifies the same as Exaltation

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MATHEMATICVM. 29 accipitur pro vna ex quinque dignitatibus essentialibus, quas obtinent planetæ in signis, estque secunda in ordine post Domicilij prærogatiuam. Etenim in Zodiaco sunt quædam loca, in quibus constituri planetæ peculiares effectus, eosque potentiores, atque efficaciores in inferioribus hisce pro- ducunt. Huiusmodi autem præcipuè sunt Domus, & Altiru- dines: Cuius rei rationem rationabilemque distributionem ingeniosè affert Ptolemæus in primo Quadrip. cap. 17. Sol, in- quit, quia in Ariete incipit ad verticem nostrum accedere, at- que altior fieri, calor eius augescit, dies noctibus incipiunt præualere; ideo in Ariete exaltari oportet, atque aliquam di- gnitatem, quam alritudinem dicimus, obtinere. Luna cum Sol est in Ariete ipsi coniuncta, incipit è radijs eius emerge- re, atque aliquatenus apparere cum est in Tauro; vnde in Tauro conuenit exaltari. Similiter discurrendum in alijs Pla- netis: Nisi quod Ptolemæus ponit Planetam exaltari in toto signo, Arabes verò in certo gradu signi, vt verbi gratia Sol in gradu 19. Arietis, Saturnus in gr. 21. Libræ, Iupiter in gr. 15. Cancri, & sic de singulis. Cuius quidem placiti, neque vllam afferunt rationem, neque experimentum. Nihilominùs id obseruare, supervacaneum forte non erit. Ponò in quo signo potissimum quisque Planeta exaltetur, & signatè in quo gra- du iuxta Arabum placita dicemus in V Exaltatio. ALVEHEZIT Arab. idem sonat, ac stellacadentes: sunt enim < 159.> species quædam accensionum metheorologicarum in aere factæ, quæ significant siccos vapores. Hali Kodoan in Com- ment. ad Quadrip. Ptolemai. ALYNTHIÆ signum, teste Hali in Commentar. ad propos. < 160.> 31. Centiloquij est signum revolusionis anni, in quod videli- cercadunt Ascendens, alijque significatores in puncto annuæ Revolutionis. ALZIMON, quod interpretatur fusus corrupto apud Nubia- < 161.> nos, & Feczanos, vocabulo, dicitur spica Virginis, stella, de quas sæpè incidit sermo. AM AMBLYGONIVM apud Geometras est figura triangularis, < 162.> quæ habeangulum vnum obtusum; in quo differ ab Oxy- gonio, quod habere debet omnes tres angulos acutos. Differt etiam ab regulatere, quia cum istud habere debeat omnes an- gulos æquales, necessario deberet esse omni ex parte obtu- sangulum; quod ex Euclide propos. 17. & , 2. primis libro, fieri non potest. Benè tamen amblygonium potest esse vel Isosceles, vel scalemum; si aut duo æqualia habeat latera, modò terrium vtrouis æqualium maius sit; aut omnia latera iuxæqualia sint,

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MATHEMATICVM. 29 is taken as one of the five essential dignities that planets hold in the signs, and is second in order after the prerogative of Domicile. For there are certain places in the Zodiac in which planets, when established there, produce particular effects, and those more powerful and more efficacious in these lower regions. Of this kind are especially the Houses and Exaltations: the reason for this, and a rational distribution of it, Ptolemy ingeniously gives in the first Quadripartite, ch. 17. The Sun, he says, because in Aries it begins to approach our zenith and to become higher, its heat increases, and the days begin to prevail over the nights; therefore in Aries it ought to be exalted, and to obtain a certain dignity, which we call altitude. The Moon, when the Sun is in Aries and joined to it, begins to emerge from its rays and to appear somewhat when it is in Taurus; hence it is fitting that in Taurus it be exalted. Likewise one must reason through the other planets: except that Ptolemy places the planet as exalted in the whole sign, whereas the Arabs place it in a certain degree of the sign, as for example the Sun in the 19th degree of Aries, Saturn in the 21st degree of Libra, Jupiter in the 15th degree of Cancer, and so on for each. Of this opinion they bring forward neither any reason nor any experiment. Nevertheless, it will perhaps not be superfluous to observe it. Next, in which sign each planet is chiefly exalted, and specifically in which degree according to the Arabs’ opinion, we shall say in V Exaltatio. ALVEHEZIT, Arabic: it means the same as “falling stars”; for these are certain kinds of meteorological combustions made in the air, which signify dry vapors. Hali Kodoan in the Commentary on Ptolemy’s Quadripartite. ALYNTHIÆ sign, according to Hali in the Commentary on proposition 31 of the Centiloquium, is the sign of the year’s revolution, into which, as it were, the Ascendant and the other significators fall at the point of the annual Revolution. ALZIMON, which among the Nubians and Fezzans is said, by a corrupted word, to mean “spindle,” is called the ear of Virgo, the star about which there is often mention. AM AMBLYGONIUM among geometers is a triangular figure that has one obtuse angle; it differs from OXYGONIUM, which must have all three angles acute. It also differs from the regular figure, because since this must have all equal angles, it would necessarily have to be obtuse-angled in every part; which, by Euclid, proposition 17 and 2 of the first book, cannot be. Yet an amblygonius can be either isosceles or scalene; if it has two equal sides, provided that the third is greater than either of the equal ones; or if all its sides are unequal,

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LEXICON 32 modò angulorum inæqualium, quos efformare necessariò debet, v[er]nus sit obtusus, & reliquis omnibus maior. Sed de hac re vide sub Verbis Angulus, & Triangulus. 163. AMFROCKACIATOR Gtxcè, siue Arfocarazieutu Arabicè, apud Ptolem. lib. 3. Quadrip. cap. 8. ex versione Arab. Hali, significat hominem occulta penetrantem, hoc est, qui ex certa cælorum positione satidicum spiritum sortiatur, atque arcana patefaciat, & vera ptonuntiet. 164. AMNIMODAR apud Astronomos est Planeta rectificator Genitutæ, seù potiùs est via quædam rectificandi natalitium Thema, & inueniendi artificiosè gradum, præcisè Horoscopantem tempore editi foetus, à Ptolemæo inuenta, per constitutionem Planetæ obtinentis dominium in proximè præcedenti Luminarium coniunctione, vel oppositione. Cùm enim principale fundamentum in Genethliaca facultate, (quod artis sustentaculum iure nominat Ptolemæus) sit indagare quisnam gradus Zodiaci adamussim incidat in lineam orientalem in puncto, quo editur infans; idque difficile admodum sit obtinere siue ab hotologijs ob eotum varietatem, siue ab alijs instrumentis ob multas, quas inuoluunt difficultates, itavt vel minima variatio notabilem temporis differentiam importet, hæcque etiam multum iudicium Natiuitatis, quod totum ab gradu horoscopante p[er]pendet variare possit; ob id necessarium erat viam quandam certain, stabilem, ac naturæ principijs, rationi, atque experimentis consentaneam inuenire; qua ex Ascenstonu[m] doctrina ad datam proximè horam auspicari possimus, quisnam gradus reuera ascendat in Horoscopo cum foetus in lucem editur. Quam viam approbat etiam D. Thomas opusc. 28. art. 4 in responsione ad secundum, dum de hora natiuitatis sermonem iniens sic loquitur. Quia hora talis difficulter cognoscitur, ideò inuentum est remedium, vt accipiatur gradus ascendens circul, hoc est hora consunctionis Luminarium, cui adaquatur circulus; quia ille habet influentiam ad communem necessitatem quæ proximè sequitur, vel accipiatur ascendens ad natiuitatem ex vtero. Hæc autem Ptolemæo alijsque autiquis Astronomis melior non eluxit, quam considerando habitudinem Planetæ prædominantis ad præcipuos coeli cardines: siquidem iugi obseruatione compertum est, sidera quæ præsunt nouilunijs, ac plenilunijs, maximas semper vires obtinuisse in tota illa lunatione, ac potissimè in generationibus rerum, vt non complementum habeant nisi cum Planeta totius lunationis dispositor inuenitur in situ mundi sortis & efficax ad dandum tebus edendis impulsum. 165. Hic enimusèo definire cuinam Planetæ competat rectiùs.

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LEXICON 32 more of the unequal angles, which he must necessarily form, its true be obtuse, and greater than all the others. But on this matter see under the words Angulus and Triangulus. 163. AMFROCKACIATOR, in Greek Gtxcè, or Arfocarazieutu in Arabic, according to Ptolemy, book 3 of the Quadripartite, chap. 8, from the Arabic version of Haly, signifies a man who penetrates hidden things, that is, one who, from a certain position of the heavens, obtains a prophetic spirit, and reveals secrets, and pronounces what is true. 164. AMNIMODAR, among the astronomers, is the rectifying planet of the nativity, or rather it is a certain way of rectifying the nativity chart, and of artificially finding the degree that precisely horoscopes at the time of the birth of the child, invented by Ptolemy, through the constitution of the planet holding dominion in the nearest preceding conjunction or opposition of the luminaries. For since the principal foundation in the art of nativities, (which Ptolemy rightly calls the support of the art) is to investigate which degree of the zodiac exactly falls upon the eastern line at the point where the infant is born; and since this is very difficult to obtain either from horologies because of their variety, or from other instruments because of the many difficulties they involve, so that even the smallest variation would bring a notable difference of time, and this could also greatly alter the judgment of the nativity, which depends entirely on the horoscopic degree; for this reason it was necessary to find a certain, stable way, in agreement with the principles of nature, reason, and experience; by which, from the doctrine of the ascendants, we may proceed to the given nearest hour and know which degree truly ascends in the Horoscope when the child is brought into the light. This way is also approved by St. Thomas, opuscle 28, art. 4, in the response to the second, when, beginning to speak of the hour of nativity, he says as follows: Because such an hour is difficult to know, therefore a remedy was found, that the ascending degree of the circle be taken, that is, the hour of the conjunction of the luminaries, to which the circle is adjusted; because that has an influence on the common necessity which immediately follows, or let the ascendant be taken for the nativity from the womb. This, however, did not appear better to Ptolemy and the other ancient astronomers than by considering the relation of the predominant planet to the principal cardines of the heavens: for by continual observation it has been found that the stars which preside over new moons and full moons have always obtained the greatest powers throughout that whole lunation, and especially in the generation of things, so that they do not have their completion unless the planet dispositor of the whole lunation is found in a position of the world suited and effective for giving impetus to the things to be born. 165. Here, then, he defines to which planet it more rightly belongs.

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MATHEMATICVM. 31 dius, sicut etiam quomodo instituenda sit huiusmodi tificatio, non est res parui negorij, nec strictim prætenda, quippe quæ non æquè à Professoribus traditur. Alienim volunt ab hac prærogatiua excludenda esse lumina- vt pote ea, quæ sunt generales rerum significatores, ac inde in hac re passiuè se habeant, & subesse alijs debeant ùs, quam præesse. Excludunt etiam Planetas combustos, ogrados, aut quouis modo debiles, & impeditos. Alij c[on]limitationem non admittunt; sed vt in alijs rebus, ita in negotioeum absolutè præsiciunt; qui repetus sit in loco dicto plures prærogatiuas habere, aut sanè potiorem ex aque essentialibus dignitatibus, Trigono, videlicet, Do- ilio, Exaltatione, Terminis, & Facie, seu configuratione, eam ob rationem quod Ptolemæus huius rectificationis in- tor, illimitare loquitur, & neminem prorsus excludit. ræstat tamen hic apponere ingeniosissimam ratiocinatione præstantissimi cuiusdam Astronomi in re genethliaca satissimi; qui rem altiùs examinando, duodecim signa sedum triplicitatum rationem dispescit, vnicuique triplici- suos dominos cum vniuersa Astronomorum turba præsi- us. Verùm quia Luminaria, vt supra dictum est, sunt posubiectum in hac re, ptoindeque disponi magis ab alijs nt, quam disponere: & ex alia patre Mercurius vt pote pitis naturæ, sibique non constans neque alienum locum are posse videarur; iure ab hac prærogatiua excluduntur, vt iam soli quatuor planetæ super sint, quorum singuli ulis triplicitatibus ex integro dominantes hoc rectificandi ere potiantur: sicque si præcedens luminarium synodus, oppositio celebrata fuerit in signis triplicitatis igneæ, Ioui ummodo competat rectificatio: si in triplicitare terrea, eri: si in Aetea, Saturno: si demum in Aquea, soli Marti, irrendo in reliquis doctrinam Ptolemæi, vt si præcesserit sisto, accipiatur illud signum, quod tempore oppositio- ictæ existebat supra terram. Quod si ambo fuerint supra m, vnum videlicet in cardine orientali, alterum in occi- iure id accipiendum erit, quod lineam orientalem vt- potiorem possider. Quod etiam expressè monent alij, æsertim Cardanus in Commentarijs. reà modum etiam instituendæ huiusmodi rectificationis, ita conveniunt Professores: Vulgus enim Astronomorum r[ecipe] gradum Ascendentis, aut medij Coeli figuræ æstimati. 1æ- gendum esse per gradum Planetæ rectificantis, quem ob- tintali figura pro vicinitate graduum: V. si Ascendens, mpli gratia, sit pars 28. Libræ, medij verò Coeli 3. Leo-

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MATHEMATICVM. 31 ...as to how such a rectification is to be established, it is no small matter, nor is it to be lightly handled, since it is not taught equally by all Professors. Some are unwilling that the lights should be excluded from this prerogative, as being those which are the general significators of things, and therefore in this matter stand passively and ought to be subject to others rather than to preside over them. They also exclude combust planets, under the beams, or in any way weak and impeded. Others admit no limitation; but, as in other matters, so in this business they determine absolutely that the place in question shall have more prerogatives, or certainly the more worthy one, from among those essential dignities, namely Trine, Domus, Exaltation, Terms, and Face, or configuration, for the reason that Ptolemy, in treating of this rectification, speaks without limitation and excludes no one at all. It remains, however, to add here the most ingenious reasoning of a certain most excellent Astronomer in genethliacal matters, most learned in this point; who, examining the matter more deeply, divides the twelve signs according to the ratio of the triplicities, assigning to each triplicity its own lords, in agreement with the whole company of Astronomers. But because the Luminaries, as was said above, are the subject in this matter, and therefore are rather to be disposed by others than to dispose; and because on the other hand Mercury, as being of a changeable nature and not constant to itself, nor appearing able to occupy a place that is not its own, is rightly excluded from this prerogative, so that now only four planets remain, each of which, ruling entirely over their own triplicities, may enjoy this privilege of rectification: thus, if the preceding conjunction of the Luminaries, or the opposition, was celebrated in signs of the fiery triplicity, only Jupiter is to be assigned the rectification; if in the earthy triplicity, Venus; if in the airy, Saturn; if finally in the watery, Mars alone, following in the rest the doctrine of Ptolemy, so that if the conjunction preceded the opposition, that sign is to be taken which at the time of the opposition under consideration was above the earth. But if both were above the earth, namely one in the eastern angle and the other in the western, then by right that one is to be taken which possesses the eastern line as the stronger. This is also expressly noted by others, especially Cardanus in the Commentaries. Moreover, as to the method by which such a rectification is to be established, the Professors do not all agree: for the common run of Astronomers reckons the degree of the Ascendant, or of the Midheaven, as the point to be estimated. It should be considered by the degree of the rectifying planet, which is constituted in the natal figure according to the proximity of the degrees: for example, if the Ascendant be 28 degrees of Libra, and the Midheaven 3 degrees of Leo...

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LEXICON nis; Planeta autem rectificans sit Venus, quæ in Natiuitate reperiatur in gr. 10. Geminorum; tunc, quia 10. sunt propinquiores tribus, quam 28. corrigitur gradus medij Coeli, locando in eo 10. gr. Leonis, sicque ad rationem eius constructa sit more solito cælestis figura locando in Ascendente 29. gr. Libræ &c. Quodsi Venus habeat 24. Geminorum totidem gradus Libræ constituantur in Ascendente, & sic reliquæ domorum cuspides per signa & gradus his gradibus per ascensionum doctrinam respondentes. Addunt alij, quod quando Planeta rectificans in suis gradibus est nimium distans à gradibus medij Coeli, vel Ascendentis, tunc rectificatio instituenda est per gradum Antiscij sui intuentis, vel imperantis, aut obedientis, prodireque etiam exactam, atque accidentibus congruam rectificationem. 168. Verum hic rectificandi modus, nisi meliùs instituatur, nec rationi, neque experimentis accommodari potest. Nam primò sequeretur, vt quando Planeta rectificator est nimium ponderosus, (quales ferè semper sunt Saturnus, & Iupiter) aut fuerit stationarius, vel terrogradus, in quo statu insensibiliter mouetur in Zodiaco, ij omnes, qui in vna eademque lunatione nascerentur, deberent eundum gradum ascendentem habere, aut cælum culminans, si non in signo, saltem in numero graduum, quod est ridiculum. Deinde quæ proportio, quæ habitudo Planetæ rectificantis ad cardines, per hoc quod in numero tantum concordent, si non adsit alia congruentia, aut respectus? Quodsi dicas adesse in Antiscio, vel in aspectu in debita distantia, qui à numero ad numerum est partilis: ergò vbi saltem non erit familiaritas, & aspectus, (vt in signis inconjunctis) inanis prorsus cuader hæc sola numerorum proportio. Præterquamquod radij ad Cardines accepti in partibus Zodiaci inanes reperiuntur, vt eruditè probat Titus in Cælesti Philosophia. 169. Quapropter ex Ptolemæi mente (vt ipsemet Titus obseruat in Breuiarijs ad Quadrupart.) accipienda est proportio sideris rectificantis ad cardines per aspectus in mundo in partibus proportionalibus domorum; ita vt si dus rectificans constituatur in cælesti figura in tanta distantia à cardinibus mundi accepta in partibus proportionalibus sui arcus, vt eorum aliquem, præcipuè verò Ascendentem respiciat aliquo radio, aut etiam sit in eius centro. Tali enim modo consideratus forris inuenitur, & efficax ad dandum impulsum foetui, vt emergat ex vtero, sibique arroget partum. Quæ proinde rectificatio multis experimentis probata inuenitur exacta, atque accidentibus apprimè cougria: Sic enim in exemplo dato, si Venus planeta

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LEXICON nis; but let the rectifying planet be Venus, which in the Nativity is found in 10° Gemini; then, because 10 are nearer to 3 than 28, the degree of the Midheaven is corrected by placing there 10° Leo, and thus, according to its construction in the usual manner, let the celestial figure be set up by placing in the Ascendant 29° Libra, etc. But if Venus be at 24° Gemini, let as many degrees of Libra be placed in the Ascendant, and likewise the remaining cusps of the houses through the signs and degrees corresponding to these degrees by the doctrine of ascensions. Others add that when the rectifying planet is in its degrees too far distant from the degrees of the Midheaven or of the Ascendant, then the rectification is to be made by the degree of its Antiscion, looking to or ruling, or obedient, and it may even produce an exact rectification, and one congruent with the accidents. 168. But this manner of rectifying, unless it be established better, can be adapted neither to reason nor to experience. For first, it would follow that when the rectifying planet is too ponderous, (such as Saturn and Jupiter are almost always,) or should it be stationary, or retrograde, in which state it moves insensibly in the Zodiac, all those who were born in one and the same lunation ought to have the same degree rising, or the sky culminating, if not in sign, at least in the number of degrees, which is ridiculous. Then what proportion, what relation does the rectifying planet have to the angles, by this fact alone that they agree only in number, if no other congruence or respect is present? But if you say that it is present in the Antiscion, or in aspect at the proper distance, which from number to number is partial: therefore where at least there will not be familiarity and aspect (as in unconjoined signs), this proportion of numbers alone is utterly vain. Besides, the rays taken to the angles in the parts of the Zodiac are found to be vain, as Titus eruditely proves in Celestial Philosophy. 169. Wherefore, according to Ptolemy's mind, (as Titus himself observes in the Breviaries to the Quadripartite,) the proportion of the rectifying star to the angles is to be taken through aspects in the world in proportional parts of the houses; so that if the rectifying star be placed in the celestial figure at such a distance from the angles of the world, taken in proportional parts of its arc, that it may regard some one of them, especially the Ascendant, by some ray, or even be in its center. For in such a way, considered abroad, it is found, and effective for giving the impulse to the fetus, that it may emerge from the womb and claim the birth for itself. And therefore such rectification is found, by many experiments, to be exact and very congruent with the accidents: thus in the example given, if Venus the planet

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MATHEMATICVM. 15 aneta rectificans reperiatur in octaua domo cum ro. gradibus eminorum, debet ita constitui, vt vel sit in media distantia ter Octauam, & Nonam, vnde emittat radium sesqui qua- tum ad Ascendens, vel in cuspide nonæ domus, vnde ittit trinum, vel sanè in cuspide Octauæ, vnde emittit se a em ad Culmen; idque pro maiori vicinitate, aut congruen- cum accidentibus Nati, corrigendo videlicet gradum do- is, vnde emittitur radius per gradum & præsentiam parti- n ipsius Planetæ rectificantissicque ad rationem eius nouam uram erigendo. <170.> Quod si hac in re, vnde ars tota dependet meam quoque intentiam proferte non sit inuerecundum, eam submissè pro- am aliorum judicio examinandam, corrigendamque. Ita- e in hoc negotio rectificationis formam, non per gradum anetæ rectificantis (nisi fortè is angulum possideat) sed per proportionalem eius distantiam à cardinibus Mundi vnde ittat radium ad eorum aliquem instituerem. Deinde à mu- re rectificandi nullum Planetam excluderem, nisi fortè com- stum, aut ita sub Solis radiis existentem, vt jure censeatur ptus. Siquidem eius tunc vires à Sole sua potentia absumun- , qui proinde in eius locum subintrat, vt omnes communi- asserunt, in Planetarum combustione: in quo tantum casu em ipsum eius loco sufficerem, secundariò tamen, & per idens, per hoc quod gerit vices Planetæ predominantis, eius- veluti substiturus consideraretur. Cæterùm Luminaria ipsa se primò, & principaliter ad hoc munus assumere non pro- em ex communi ratione superiùs tacta, quòd ea sint gene- s rerum significatores. At verò quod aliàs Planeta rectifi- is sit dejectus, aut retrogradus, non videtur officere, quo nus in hanc rectificandi Prouinciam assumi possit. Nam, n hæc rectificatio, vt dictum est, per aspectum ad cardines ituenda sit retrogradatio Planetæ, esse in suo detrimentos casu, impertinens est ad hoc negotium: siquidem ea est io proprij motus in Zodiaco; aspectus autem ad cardines sit à partibus Zodiaci, sed à domibus per proportionalem antiam ab ipsis cardinibus acquisitam motu primi mobiliss- er partes sui arcus diurni, aut nocturni. Siue igitur sit velox Zodiaco, siue tardus, retrogradus, aut directus parum re- , cùm ad cardines Mundi æquè se habeat, vt possit probè orum aliquem suos radios proijcere. <171.> imiliter, quod sit in suo detrimento, vel casu, aut etiam nico radio ab aliis infestatus, facit solùm quòd is naturam m peruertat, ac malignetur; Minimè verò, quòd non dem efficientiam æquè benè habere possit ad cardines,

Transcription: Translated (English)

MATHEMATICVM. 15 if the rectifying planet be found in the eighth house, with degrees of the eminors, it ought to be so placed that it may either be in the middle distance between the Eighth and the Ninth, whence it may cast a ray sesquiquad- rate to the Ascendant; or in the cusp of the ninth house, whence it emits a trine; or indeed in the cusp of the Eighth, whence it emits itself to the Midheaven; and that for the greater proximity, or agree- ment with the accidents of the native, correcting, namely, the degree of the do- micile, whence the ray is emitted, through the degree and presence of the parti- cular planet rectified, and thus raising it to the reason of its new position. <170.> But if in this matter, on which the whole art depends, it should not be improper for me also to put forward my own intention, I would humbly pro- pose it to be examined and corrected by the judgment of others. Thus in this business of rectification I would establish the form, not by the degree of the rectifying planet (unless perhaps it possess an angle), but by its proportional distance from the cardinal points of the world, whence it may cast a ray to one of them. Then, in the matter of the planet to be rectified, I would exclude no planet, unless perhaps one that is com- bust, or so existing under the rays of the Sun that it may justly be deemed consumed. For then its powers are taken away by the Sun’s own potency, who therefore enters into its place, as all authors commonly assert in the combustion of planets: in which sole case I would substitute the Sun itself in its place, though secondarily, and by derivation, because it performs the office of the predominant planet, and would be considered as it were a substitute. Moreover, I do not propose that the Luminaries themselves should be assumed first and principally for this task, for the common reason noted above, namely, that they are general significators of things. But on the other hand, the fact that the planet to be rectified is debilitated, or retrograde, does not seem to hinder its being assumed into this province of rectification. For, since this rectification, as has been said, is to be taken by aspect to the cardines of the world, the planet’s retrogradation, being a detriment in its own case, is irrelevant to this business: for that is a condition of its own motion in the Zodiac; but aspect to the cardines comes not from the parts of the Zodiac, but from the houses by a proportional distance acquired from the cardines themselves by the motion of the first mobile, through the parts of its diurnal or nocturnal arc. Whether therefore it be swift in the Zodiac, or slow, retrograde, or direct, it matters little, since in relation to the cardines of the world it is equally situated, so that it may well cast its rays to one of them. <171.> Similarly, the fact that it is in its detriment, or fall, or even afflicted by the malign ray of others, only means that it perverts its nature and acts malignantly; by no means, however, that it cannot have its efficiency equally well in relation to the cardines,

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34 LEXICON eos exquisitè respiciat vnde, & det generationibus rerum impulsum. Quod sanè experimento liquet in aëris mutationibus, quæ Planeta dispositote præcedentis Lunationis (nisi fottè, vt dictum est, fuerit combustus) omninò pendent, atque ab eius bona, vel mala constitutione sumitur significatio. 172. Stet igitur, Genesis rectificationem instituendam esse per aspectum Planetæ dispositoris præcedentis Luminarium conjunctionis, aut oppositionis ad cardinas; præcipuè verò ad Ascendens. Atque ex concurrentibus eum præferendum esse, qui, ni sit combustus, aut sub radiis propè nimium constitutus, fuerit porissimum divisor terminorum, in quibus celebrata fuit conjunctio; vel oppositio; Aut sanè plures prærogatiuas ex quinque essentialibus supra dictum locum haberet. Quod si plures concurrant, & alter habeat v.g. Domicilium, alter Exaltationem, alius Trigonum, meritò videretur præferendus esse qui Trigoni prærogatiuam obtinebit, cùm in hac re Ptolemæus in dignitatum enumeratione primò Trigonum, deinde Domicilium, postea Exaltationem, mox Terminorum dispositionem, tandem faciem, seu configurationem commemoret. 173. AMPHICYRTOS Græcè proptè significat aliquid decliue, & gibbosum: Hinc ab Astronomis absolutè vsurpatur pro Luna adhuc gibbosa, & nondum perfecta ad Plenilunium, cùm videlicet est in Trino, aut Sesquicadrato Solis, circà decimum, aut duodecimum à conjunctione diem: Tunc enim quoddam decliue, & gibbosum nostris oculis exhibet, vt propterea jure Amphicyrtos appelletur. 174. AMPHISCII Græcè audiunt habitatores regionum, quæ subsunt perpendiculariter Æquatori; sic dicti ab Vmbra, eò quod vmbram suam ad omnem plagam, Orientalem nempe, Occidentalem, Borealem, atque Australem, pro temporum varietate conspiciant. Hi perpetuum experiuntur æquinoctium: duas Æstares, tempore vniuersalis æquinoctij, quo Sol existens in principio Arietis, & Libiæ, transit per eorum verticem; duas etiam Hyemes, quando Sol in tropicis existens maximam declinationem habet arque adeò maximè ab eorum vertice recedit: quæ profectò potius dicendæ sunt remissiones caloris, quæ Hyemes; cùm aliàs perpetuam experiantur æstatem, ni potius Ver appellare velimus. Siquidem cum Sol non plus supra terram consistat, quam infra; hinc est, vt aëream regionem, ac superius hæmispherium non nimium inflammare possit; & si, qui sunt diei seruores, mox noctis longitudine, ac temperie infringantur; itaue asseuerent habitatores, quique huc inde venerunt, iucundissimam ibi esse

Transcription: Translated (English)

34 LEXICON It thus looks most closely toward that point from which it gives an impulse to the generations of things. This is certainly made clear by experience in the changes of the air, which depend entirely on the dispositor of the preceding Lunation, unless perhaps, as was said, it has been combust; and the signification is taken from its good or bad condition. 172. Therefore let it stand that the rectification of the Genesis is to be undertaken by the aspect of the Planet dispositor of the preceding conjunction of the Luminaries, or of the opposition to the angles, especially to the Ascendant. And among the concurrent ones, preference is to be given to that one which, if it is not combust, or placed too near under the rays, was chiefly the divider of the terms in which the conjunction, or opposition, was celebrated; or certainly would have more prerogatives from the five essential dignities of the aforesaid place. But if several concur, and one has, for example, Domicile, another Exaltation, another a Trine, it would rightly seem that preference should be given to the one who obtains the prerogative of the Trine, since in this matter Ptolemy, in his enumeration of dignities, mentions first the Trine, then Domicile, afterward Exaltation, next the disposition of the Terms, and lastly face, or configuration. 173. AMPHICYRTOS in Greek properly signifies something sloping and humped: hence it is used by astronomers absolutely for the Moon while still gibbous, and not yet full, when, namely, it is in trine, or sesquiquadrate, with the Sun, about the tenth or twelfth day from conjunction: for then it shows our eyes something sloping and humped, so that it is rightly called Amphicyrtos. 174. AMPHISCII in Greek are the inhabitants of the regions lying directly beneath the Equator; so called from shadow, because they see their shadow toward every quarter, namely east, west, north, and south, according to the variation of the seasons. These people experience a perpetual equinox: two summers, at the time of the universal equinox, when the Sun, being at the beginning of Aries and Libra, passes through their zenith; and also two winters, when the Sun, being in the tropics, has the greatest declination and thus recedes most from their zenith: these indeed ought rather to be called remissions of heat than winters; since otherwise they experience a perpetual summer, or rather, if we wish, a spring. For since the Sun does not remain more above the earth than below, it is thus unable to inflame the airy region and the upper hemisphere too much; and if the heat of the day is soon broken by the length and tempering influence of the night, then those who dwell there, and those who have come from elsewhere, declare that it is most pleasant there

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MATHEMATICVM. 35 ommorationem, ac longè suauiorem, quam in toto Italiæ actu: tantum abest vt vera sint, quæ de ijs locis dixere Poëtæ is oras esse ex nimio æstu prorsus inhabitabiles. Huiusmodi nt Incolæ aureæ Chersonesi, Insula S. Thomæ medium In- læ S. Laurentij, Sumatra, Maldiuiæ, aliæque regiones, pro- videre est in mappis Mundi. Et hi cum Polos habeant hori- onti adjacentes, nec vnum altero elatiorem, inde est, vt nnes stellas conspiciant, atque istæ æqualiter semper orian- t, & occidant. AMPHORA dicitur vndecimum ab Ariete signum. Vide 176. quarum. AMPLITUDO Ortiua apud Astronomos (idem dic de occi- 177. na) est latitudo, seu differentia ortus, & occasus stellæ, aut iussibet partis coeli à Græcis ortus, & occasus æquatoris in prizonte, & vnde Sol oritur, & occidit initio Veris, & utumni. Quæ quidem semper æqualis est cum occidua, & uò maior fuerit hæc differentia ortus, & occasus, eò maior reitur Amplitudo, maiotque aut minor arcus diurnus. AMPOTIM Græcè vocat Ambrosius miram illam Maris 178. fundationem reciprocationemque motus, quam integro die : quatuor momenta variat, fluctuatque quod ideò hunc mo- m nos vulgò fluxum, & refluxum maris vocamus. Contin- t enim præsertim in Oceano Atlantico atque in Mari supe- , seu Adriatico, vt per ferè sex horas aquæ intumescant, ad tus decurrant, & augeantur: mox vicissim per sex alias horas ecrescant, retrocedant, ac minuantur. Huius motus recipro- tio vt omnium oculis obuia est, ita intellectus omnis aciem æstringit adeò, vt eius causam nemo adhuc Philosophorum muerit: Quinimò constans de eorum Principe fama est, quod am diu in huius abditissimi arcani speculatione fatigatus ma- is ac magis intricaretur, in morbum inciderit; ac tandem esperatione adactus in Euripum se præcipitem dedetit altiùs oc inclamans O Mare cum tecapere non possim, tu me exci- : Possidonius cum Trabone, Solino, Mela, & communiori philosophantium schola eam in Lunæ motum refundit. Quo im tempore (inquit Possidonius apud Setabonem) Luna Hori- mtem ascenderit, Mare ad terram ascendere incipit, quousqve l Cælo medium ipsa conscenderit: ubi verò declinare fidus ipsum perit, sensim rursùs à terra pelagus ad medium mare delabitur, nec ad Occidentis punctum Luna descenderit: postea mane rursus scendis quousque sub tellurem in medio, & imò coeli sit Luna: unde Mare à litore ad medium maris regreditur, quoad iterum una ad Orientea procedas, & eleuetur rursusque mare terras fluas. Hucusque Possidonius. Quod vel inde confirmari po- C ij

Transcription: Translated (English)

MATHEMATICVM. 35 ...a more pleasant dwelling, and far more agreeable than in all Italy: so far are those things from being true which the Poets have said of those regions, that because of the excessive heat their coasts are utterly uninhabitable. Of this kind are the inhabitants of the Golden Chersonese, the Island of St. Thomas, the middle of the Island of St. Lawrence, Sumatra, the Maldives, and other regions, as may be seen in maps of the world. And since these have poles adjoining the horizon, neither one more elevated than the other, it follows that they see all the stars, and that these always rise and set equally. AMPHORA is called the eleventh sign from Aries. See 176. AMPLITUDE of rising among astronomers (the same may be said of setting) is the latitude, or difference of the rising and setting of a star, or of any part of the heaven, from the Greeks, of the rising and setting of the equator on the horizon, and from where the Sun rises and sets at the beginning of Spring and Autumn. This is always equal to the setting amplitude; and the greater this difference of rising and setting is, the greater the Amplitude becomes, and the greater or smaller the diurnal arc. AMPHOTIM, in Greek, Ambrose calls that wonderful ebbing and flowing of the sea, that in the course of a whole day changes by four motions and fluctuates; and therefore we commonly call this motion the flux and reflux of the sea. It occurs especially in the Atlantic Ocean and in the upper sea, or Adriatic, so that for about six hours the waters swell, advance, and increase; then in turn for another six hours they diminish, recede, and lessen. Although the reciprocal movement of this motion is obvious to everyone’s eyes, it so constrains the sharpest intellect that no philosopher has yet discovered its cause. Indeed, there is a steady report about their chief, that after being long wearied in the contemplation of this most hidden mystery and becoming more and more entangled, he fell ill; and at last, driven to desperation, he threw himself into the Euripus, crying aloud, “O Sea, since I cannot understand you, you will understand me.” Posidonius, with Trabon, Solinus, Mela, and the more common school of philosophers, ascribes it to the motion of the Moon. “At the time,” says Posidonius in Strabo, “when the Moon has risen above the horizon, the sea begins to rise toward the land, until she herself has ascended halfway up the sky; but when the star begins to decline, the sea gradually again flows back from the land toward mid-sea, until the Moon has descended to the western point. Afterward in the morning it rises again, until the Moon is beneath the earth in the middle, and at the bottom of the sky; whence the sea returns from the shore to mid-sea, until the Moon again proceeds toward the east, and the sea is again lifted over the lands.” So far Posidonius. Which may even be confirmed from this...

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LEXICON test, quia rota ista reciprocario in quatuor, vt dixi momenti parres tribura, horarum quinque supra viginti spatio absolu- tur; vna videlicet hora supra integrum diem naturalem; quan- ta est Luna periodus, & circumuolutio, donec ad eam coeli positionem, in qua pridie erat, reuertatur: siquidem ipsa mo- tu proprio ex Occidente in Orientem quindecim circiter gra- dus contra motum primi mobilis nititur, & rerocedit in vno die: quæ retrocessio facit, vt ferè per horam circuitum suum retardet, donec idem punctum teneat, quod Sol sua revolutio- ne facit spatio 24. horarum. Plinius, alijque, præsertim recen- tiores non modo ad Lunam, sed & ad Solem hunc motum re- ferunt. Obseruatunt enim in eorum aspectibus quadratis, aquas penè immobiles permanere: at vetò in coniunctionibus, & oppositionibus maximos fieri, & citissimos fluxus refluxusque. Cuius rei causam affert Molerus lib. 2. Isag. 7. ad Ephemer. Quia, inquit, quando Luminaria fuerint coniuncta dum mouentur mo- tu primi mobilis per quartam fluxus, mare velocissimè fluit, dum mouentur per quartam refluxus mare citissimè refluit, dum Lumi- naria suns opposita; eo quia dum unum mouetur per quartam flu- xus, alterum etiam per quar:am oppositam huc fertur, ideò vele- cissimè aqua fluit, vel refluit. Dum Luminaria quadrata radiatio- ne se conspicunt, quia dum alterum est in Orient, reliquum in Meridie, vel sub, vel supra terram, & hac duo puncta sunt fluxus. & refluxus, quia ab aqualibus potentiis aqua ad contrarias partes fertur, ideò immobilis permanet, hac de causa in quadraturis Lu- minarium nullo ferè mouetur motu. Hæc ille, docens subinde quartas Orientalem diurnam, quæ est à puncto Orientis ad punctum Meridiei, & illi oppositam Occidentalem, quæ est à puncto occasus ad Lineam imi coeli esse quartas fluxus eò quia Luminaria elogantur à terra & properant ad Lineam Meridia- nam: sicur etiam reliquas duas esse refluxus, quia à Meridiano elonganrur, & terræ approximamur ad circulum horizontis. Verum & hic motus prolocorum diuersitare ac Marium positu ad Lunam, adhuc varius est in ipsis Luminarium quadraturis, aut coniunctionibus, vel oppositionibus; cum Mediterraneum, quod Italiam alluir, aut nullum, aut tam exiguum habeat flu- xum, & refluxum, vt minimè obseruari queat. Similiter Ocea- nus Australis, qui est proximus Mexico, Cubæ Insulæ, & aliis partibus Americæ nullum patitur æstum. E contra ma- gnus deprehenditur in Mari Siculo: adhuc maior versus Sep- tentrionem, vt in Anglia, Hollandia, & Noruegia, & ma- ximus in fræro Magellanico, aliisque regionibus Occidenta- lioribus: vt proinde difficile admodum sit huius diuersitatis ra- tionem reddere. Cæterum ex triplici capite euenire potest hæc

Transcription: Translated (English)

LEXICON test, because this wheel reciprocating in four, as I said, moments is distributed, is completed in a space of twenty-five hours; that is to say, one hour beyond the complete natural day; such is the period and revolution of the Moon, until it returns to that position of the heavens in which it was the day before: since it by its own motion from West to East advances about fifteen degrees against the motion of the primum mobile, and goes back in one day; and this retrocession causes it to delay its circuit by nearly an hour, until it holds the same point which the Sun by its revolution makes in the space of 24 hours. Pliny, and others, especially more recent writers, refer this motion not only to the Moon, but also to the Sun. For they observed that in their quadrate aspects the waters remain almost immobile: but in conjunctions and oppositions the greatest and swiftest ebb and flow occur. Molerus gives the cause of this matter in lib. 2. Isag. 7. ad Ephemer. Because, he says, when the luminaries are conjoined while moving by the motion of the primum mobile through the quarter of flood, the sea flows most rapidly; while moving through the quarter of ebb, the sea ebbs most swiftly; when the luminaries are opposite, because while one moves through the quarter of flood, the other also is carried through the opposite quarter, therefore the water flows or ebbs most rapidly. When the luminaries behold one another by quadrate radiation, because while one is in the East, the other is in the South, either under or above the earth, and these two points are those of flood and ebb, because by equal powers the water is carried toward contrary parts, therefore it remains motionless; for this cause at the quadratures of the luminaries there is scarcely any motion. Thus he, teaching afterward that the eastern daily quarters, which are from the point of the East to the point of the South, and the western opposite to them, which are from the point of the setting sun to the line of the lower heaven, are quarters of flood, because the luminaries are distant from the earth and hasten toward the meridian line; likewise that the other two are of ebb, because they are removed from the meridian and approach the earth toward the circle of the horizon. But even here this motion, because of the diversity of places and the position of the seas in relation to the Moon, is still variable in the very quadratures of the luminaries, or in conjunctions, or oppositions; since the Mediterranean, which washes Italy, has either no tide at all, or so small an ebb and flow that it can scarcely be observed. Likewise the Southern Ocean, which is nearest to Mexico, the island of Cuba, and other parts of America, suffers no tide. On the other hand, a large one is found in the Sicilian Sea; still greater toward the North, as in England, Holland, and Norway; and greatest in the Strait of Magellan and other more westerly regions: so that it is very difficult to give a reason for this diversity. Moreover, from a threefold source this may arise

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MATHEMATICVM. 37 aris vicissitudo, vt optimè obseruat Titus in Cælesti Philosofialib. 1. cap. 20. Primò per motum localem aquarum con- urrentium a locis vbi minuuntur ad loca, in quibus augentur: hoc modo contigeret, vt Luminaria attaherent aquas aris suis radiis tanquam bibulis; dum instar spongiiæ mira- li suetu eas secum attrahunt quousque ad lineam Meridianam rgunt: deficere verò cum ab ea elongantur, & ad horizon- m properant. Secundò, quod fiat in Mari vera augmentatio uarum, vel diminutio per veram productionem, & consum- ionem, quod nequit intelligi quomodo tam breui temporis atio in tanta aquarum copia fieri possit. Tertiò, quod im- aratâ substantia aquæ fiat rarefactio in accessu, & condensa- ex recessu luminarium ad Meridiem, siue ex calore, siue alia occulta qualitate: quemadmodum videmus in Ther- oscopiis instrumentis non ita pridem inuentis ad venandum locus, vel dies sit altero calidior, vel frigidior: posita enim qua in ampulla vitrea collo valde oblongo, & in superiori par- orificij bene obturato, si locus fuerit calidior, aqua magis cendit in collo vasis, eò quia calor ambiens illam rarefacit: si rò fuerit frigidior, aqua descendit, eò quia frigus ambiens am condensat. Et hoc modo existimauit ipse Titus accidere ne Maris fluxum, atque refluxum. Tandem Arabes quos < 180.> am sequuntur multi ex recentioribus Astronomis hunc flu- m, & refluxum Maris aliud non esse putant, quam simpli- n motum aquæ ad motum vniuersiratis, vt nos dicemus in Aqua, quo vniuersa supra ipsam motu primi mobilis rapiun- tab ortu ad occasum: qui tamen morus in aqua vtpote mo- lium omnium cæssiore atque à primo mobili remorissima dissimus est, quippe qu rarione distanriæ, & propriæ graui- is magis resistit dato impulsui, quàm aër; hic magis, quàm hæra ignis; hæc insuper magis quàm orbis Lunæ, & sic de iquis: Vnde maior est, & velocior aquæ motus sub æqua- e, quàm extra, quia eriam ipse æquator vtpote magis à lis distans plus itineris facit, quàm reliquæ pattes Cæli: sed hac re iterum recurret sermo. Interim hic præterite nolo od ex Arist. tradit Plinius; nullum nempe Animal, nisi in ris refluxu expirare: idque obseruatum ait in Oceano Gal- o, & solùm in homine. Quod tamen falsum arbitratur Bo- us. Verum Leuinus Lemnius de miraculis Natura lib. 4. c. 1. nij dictum improbare non audet, aitque solùm se obseruallie quos in Oceani accessu obiisse: & præsertim notat in mari- o Belgij tractu obæsos æstu accedente periclitari: contrà les, & macilentos in maris recessu faciliùs emori. Cuius rei sano aliam esse non arbitror, nisi quia cum Luna per acces- C iij

Transcription: Translated (English)

MATHEMATICUM. 37 The ebb and flow of the sea, as Titus observes very well in Cælesti Philosophia, book 1, chapter 20: first, by the local motion of waters flowing together from places where they diminish to places in which they increase; in this way it would happen that the luminaries would draw the waters to themselves by their rays, as if by suckers, while, like a sponge, they wonderfully attract them with themselves until they reach the Meridian line; but they fail when they move away from it and hasten toward the horizon. Secondly, that in the sea there is a true increase or diminution of the waters by a real production and consumption, which cannot be understood, how such a change could be made in so short a time and in such a great quantity of water. Thirdly, that in the substance of the water there is a rarefaction on the approach, and a condensation on the recession of the luminaries toward the south, whether from heat or from some other hidden quality; just as we see in thermoscopic instruments, recently invented, for observing whether a place or day is warmer or colder than another: for if water is placed in a glass bulb with a very long neck, and the upper part of the opening well stopped, if the place is warmer, the water rises more in the neck of the vessel, because the surrounding heat rarefies it; but if it is colder, the water descends, because the surrounding cold condenses it. And in this way Titus himself thought that the ebb and flow of the sea took place. Finally, the Arabs, whom many of the more recent astronomers follow, think that this flow and ebb of the sea is nothing other than a simple motion of the water in accordance with the motion of the universe, as we shall say in Aqua , by which all things above it are carried along by the motion of the first mobile from east to west; yet this motion in water, as being the slowest of all motions and the farthest from the first mobile, is very slow, since, by reason of distance and its own heaviness, it resists the given impulse more than air does; air more than the sphere of fire; that more than the sphere of the Moon, and so on: hence the motion of water is greater and swifter under the equator than outside it, because even the equator itself, as being farther from the pole, makes a longer journey than the other parts of the sky: but of this matter the discussion will return again. Meanwhile I do not wish to pass over here what Pliny relates from Aristotle, namely that no animal expires except at the ebb of the sea: and he says that this was observed in the Gallic Ocean, and only in man. This, however, Bonosius considers false. But Levinus Lemnius, in De Miraculis Naturae , book 4, chapter 1, does not dare to disapprove of Pliny’s statement, and says only that he observed some die at the incoming tide: and especially notes that in the seacoast tract of Belgium the obese are endangered as the tide comes in; on the contrary, the lean and emaciated die more easily at the ebb of the sea. I do not think the reason for this can be any other than that when the Moon, by its approach... C iij

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LEXICON 38 sum ad Meridianum humores augeat, & æstum faciat, per recessum minuat, consequenter vt in Mari, ita & in humano corpore idipsum præstat: qui fit, vt obæsi & pingues in accessu humoribus aucti deficiant, & suffocentur: exiles verò periclitentur, quia humidum radicale in iis alioqui valdè debile, ex Lunæ recessu minuitur; adeò vt sæpè etiam extinguantur Qua ratione etiam alibi adnotauimus, in occasu Solis qui est vitalis parentiæ fons, & caloris innati fotor, ægros vt plutimum ex defectu caloris naturalis extingui 181. AMVSIVM Instrumentum est Mathematicum colligendis ventis, discernendisque idoneum, cuius præcipuè mentionem facit Vitruvius. lib. 1. cap. 6. 182. AMVSSIS Perpendicularum, Libella, Norma, seu Regula ad quam Mathematici aliquid adæquant. AN 183. ANABIBAZON, teste Valla in Astronom. idem sonat apud aliquos, ac nodus austrinus, seu Cauda Draconis Lunæ: sicut è contra Casabibazon nodus boreus, & caput Draconis. Vide suis locis. 184. ANACAMPTICA pars est Opticæ, ac scientia, qua per radios objecti alicuius luminosi reflexos in superficie quadam plana partim obscura, partim diaphna, eius formam, affectiones, magnitudinem, distantiam, aliaque id genus considerat: dicitur etiam Casoprica. 185. ANACLATICA pars item est Opticæ, et scientia, qua per lineas siderum aliorumque obiectorum visualium refractas in medio diuersæ densitatis eorum figuras, magnitudines, distantias, aliaque demetimur. Vide in V. Optica. 186. ANÆRETA Græcè, Arabicè Ata; Latinè idem sonat, ac Abscissor: directè oppositus Aphetæ. Estque locus in Cælo, ad quem directione pertingens Apheta vitæ periculum in Nato adducit. Inter Anæretas communiter compurantur corpora Maleficarum Saturni & Martis, eorum radij hostiles, Anticia seu Paralelli quicumque tam in Mundo considerati, quàm in Zodiaco, Termini, nec non & stellæ fixæ participantes maleficarum naturam; præsertim, quæ cum Planetis aliquando congrediuntur, vt sunt Cor Leonis, Cor Scorpij, Hercules, Pallilitium, Lanx australis, &c. Cardo Occidentalis, quando Vitæ dator constituitur inter ipsum, & Calmen: sicut etiam Angulus imi Coeli, qui proptereà ab aliquibus dicitur Fouea Planetarum; ac demùm proprius quadrarus Aphetæ, qui ferè semper est vltimus vitæ terminus. Alij etiam admitunt inter Anæretas Dominum octauæ, vt potè domus mortis, etiamsi fuerit ex beneficis; sed sanè perperam: cum benefi-

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LEXICON 38 as it moves toward the Meridian it increases the humors and produces heat; as it recedes it diminishes them. Consequently, just as in the sea, so also in the human body it performs the same thing: so that the obese and fat, when the humors increase at the approach, fail and are suffocated; but the lean are endangered, because the radical moisture in them, otherwise very weak, is diminished by the retreat of the Moon; so much so that they are often even extinguished. For this reason we have also noted elsewhere that at the setting of the Sun, which is the vital fountain of parenthood and the nourisher of innate heat, the sick for the most part perish from a defect of natural heat. 181. AMVSIVM. It is a mathematical instrument suitable for collecting and discerning winds, mentioned especially by Vitruvius, book 1, chapter 6. 182. AMVSSIS. A plumb line, level, square, or rule by which mathematicians make something equal. AN 183. ANABIBAZON, according to Valla in Astronomy, means the same among some as the southern knot, or Dragon’s Tail of the Moon; just as, on the contrary, Casabibazon is the northern knot and the Dragon’s Head. See the respective places. 184. ANACAMPTICA is a part of Optics, and the science by which, through the reflected rays of some luminous object on a certain plane surface, partly dark and partly transparent, its form, properties, size, distance, and other such things are considered: it is also called Casoprica. 185. ANACLATICA is likewise a part of Optics, and the science by which, through the refracted lines of stars and other visible objects in a medium of diverse density, we measure their forms, sizes, distances, and other things. See under V. Optica. 186. ANÆRETA, in Greek; in Arabic Ata; in Latin it means the same as Abscissor: directly opposed to the Apheta. It is a place in the sky which, when reached by direction, brings danger to the life of the native. Among the Anæretæ are commonly counted the bodies of the malefics Saturn and Mars, their hostile rays, any Anticia or Parallels, whether considered in the World or in the Zodiac, the Terms, and also fixed stars sharing the nature of the malefics; especially those that at times come into conjunction with the planets, such as Cor Leonis, Cor Scorpij, Hercules, Pallilitium, Lanx australis, etc.; the Western angle, when the giver of life is placed between it and the Calmis; likewise the angle of the lower heaven, which for that reason is called by some the Pit of the Planets; and finally the proper square of the Apheta, which is almost always the last boundary of life. Others also admit among the Anæretæ the Lord of the eighth house, as being the house of death, even if he should be among the benefics; but certainly wrongly: since benefi-

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MATHEMATICVM. 39 orum non sit vitam abscindere, sed potiùs prorogare: Vnde us ad summum erit qualitatem Mortis decernere. Positâ unâ viæ Moderatrice Solis corpus dicitur interimere: sed id on facile admitterem, nisi forte eslet nimium natura & qualitibus malesicorum imbutus: sic nec Mercurium, cùm sit valde debilis ex eadem ratione qua Apheta esse non potest. Plura ud Argolum de diebus criticis. ANALEMMA apud Astronomos Instrumentum Gnomonium est ad Solis vmbras venandas accommodatum instar sphæræ, quod potissimùm inseruit ad horologia Solaria describendi. Bernard. Baldus. ANAPHORA Græcè audit secunda Domus, quasi Parta In- ni, quæ proximè succedit Primæ infra terram; eò quod pertis veluti folibus Solem, aliaque sidera ad lineam Orientam detrudat ac peruehat. Ex ea sumunt Astrologi iudicium de abstantia, ac bonis, quæ propria industria, non ex hæreditra- proueniunt: adeoque judicatur felix; estque qualitatis fri- idæ, & humidæ. ANAPHORÆ item vocantur ab aliquibus promiscuè domus accedentes, videlicet secunda, Quinta, Octava, & Vndecia; sicut è contra Casaphora cadentes ab angulis, quales sunt tertia, Sexta, Nona, & Duodecima. ANAPHORÆ etiam appellantur Ascensiones obliquæ signo- m per analogiam ad prædicta: sicut è contrario. ANAPHYSEMATA ex Apuleio in lib. de Mundo vocant ræci eos spiritus, qui de fundo vel hiatibus terræ expelli ad iperna Maris solent. Nos communiori vocabulo sed ex Græ- sis similiter derivato Apogæos vocitamus. ANATOLAS dicitur Cardo ipse Orientis, quasi superata nebrarum densitate, lucem tandem aperiat. De eo vide plura 1 V. Horoscopum. ANAVBARACH apud Arabes est inanis quædam ipsorum ob- ruatio super Nouenarias Planetarum, de qua multa habent Ichabitiùs, & eius Commentator Ioannes de Saxonia. Itaque spiciendum docent quantum inambulauerit Planeta ex gra- ibus, & minutis in signo, vel domo cuius inquiritur Noue- aria: deinde diuidendum præcipiunt totum signum in nouem artes, dando cuilibet parii tres gradus, & minuta viginti, & idendum in quamnam partem ex istis ceciderit gradus Plane- s, aut Domus, cuius ediscere voles Nouenarium. Quo præ- ito, volunt dandam esse primam diuisionis partem Domino gni mobilis eiusdem triplicitatis, & secundam partem Do- mino sequentis signi; & sic per ordinem procedendo, quous- ue peruenniatur ad illam partem, in qua est Planeta, cuius C iii

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MATHEMATICVM. 39 whose task is not to cut off life, but rather to prolong it: hence it will be at most to determine the quality of death. With one manner of the Sun as ruler, the body is said to be destroyed: but I would not easily admit that, unless perhaps it should be too much imbued by nature and by the qualities of evil influences: so neither Mercury, since it is very weak, for the same reason can it not be Apheta. See more on Argolus concerning critical days. ANALEMMA among astronomers is a Gnomonic instrument adapted for hunting the Sun’s shadows, in the likeness of a sphere, which has chiefly served for describing sundials. Bernard. Baldus. ANAPHORA in Greek is called the second House, as though the Parta- Inni, which next succeeds the First under the earth; because it, as it were, draws forward and carries toward the line of the East the planets and other stars through the portals. From it astrologers take judgment concerning substance and goods, which arise from one’s own industry, not from inheritance: and therefore it is judged fortunate; and of a cold and moist quality. ANAPHORÆ likewise are called by some indiscriminately the houses that follow, namely the second, fifth, eighth, and eleventh; just as, on the contrary, Casaphora are those falling away from the angles, such as the third, sixth, ninth, and twelfth. ANAPHORÆ are also called the oblique ascensions of the signs, by analogy to the aforesaid: just as, on the contrary. ANAPHYSEMATA, from Apuleius in the book On the World, the Greeks call those spirits which are accustomed to be expelled from the bottom or fissures of the earth up to the upper regions of the sea. We, by a more common term but likewise derived from Greek, call them Apogæi. ANATOLAS is called the very Cardinal point of the East, as though, after the density of darkness is overcome, it at last opens to the light. See more about this under Horoscopum. ANAVBARACH among the Arabs is a certain empty notion of theirs concerning the novenaries of the planets, of which much is found in Achabitius, and his commentator Johannes de Saxonia. Therefore they teach that one should observe how far the planet has traveled from the degrees and minutes in the sign or house whose novenary is being inquired into: then they prescribe that the whole sign be divided into nine parts, giving to each part three degrees and twenty minutes, and to see into which part among these the degree of the planet, or of the house whose novenary you wish to know, has fallen. When this has been done, they wish the first part of the division to be assigned to the Lord of the movable sign of the same triplicity, and the second part to the Lord of the following sign; and so proceeding in order, until one arrives at that part in which is the planet whose C iii

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40 LEXICON quæris Dominum Nouenariæ. Sic ponamus, quod Sol, exem- pli gratiâ, sit in gr. 24. Aquarij: ad sciendum, quisnam sit dominus Nouenariæ Solis, dandi sunt tres primi gradus, & 10. minuta Aquarij Domino signi Mobilis triplicitatis eiusdem quod est Libra, & Dominus eius est Venus (est enim Libra, Aquarius, Gemini Triplicitas aërea) ergo Venus est Domina primæ Nouenariæ: inde secundæ erit Mars, qui Scorpioni dominatur, proximè succedenti Libra: & sic de singulis, quousque perueniatur ad gradum Solis, qui incidit in Nouenariam Veneris Dominæ Tauri. Proindeque ipsa erit Domina Nouenariæ Solis. Quando igitur in libris Arabum sit sermo de Domino anaubarach Luminarium, si fuerit in die intelligitur de Domino Nouenariæ Solis, si de nocte, de Domino Nouenariæ gradus Lunæ. 194. ANDROCOMETES est species noui cuiusdam Phænomeni, seu Cometes habentis figuram quasi hominis, de quo plura vide in Plin. lib. 2. cap. 25. & alibi sæpè. 195. ANDROMEDA Arab. Marat Musa seleb hoc est Mulier catenata, sidus ad Borealem plagam propè Cæpheum constans stellis 13. secundùm Ptolem. at secundùm Baierum 17. omnibus ferè de natura Veneris, & Mercurij, quarum tres insigniores sunt secundæ magnitudinis, vna in capite dicta etiam vmbilicus Pegasi, quoniam in sidus illud transit; altera in Cingulo Arabice Mirach, seu Mizar; tertia in pede australi dicta Allamach. omnes in longitudine sub signo Arietis. Est sidus infaustum, vt ipsamet figuta præsefert destinans ad carceres, captiuitates, supplicia. De eo in alicuius horoscopo inuenta hæc venustè magis quàm verè habet Pontanus in Vrania. At contrà trux Andromeda noua funera, & atram. Molitur mortem, ac sauis cruciatibus instans Supplicia exquisit: neque enim aut lamenta parentum, Conjugis aut moveant lachryma, aut data munera flectant: Mors illi pretium: & tormenta immania cura: Vimclaque, Carcerque, & modoso ex are cathena. Vindictam Dea pro scopulis, quibus ipsa pependit Deposcens, studia hac nascentibus improba monstrat. Carus fiesque manus, & acutam in colla securim; Diuellisque artus truncos, & viscera mandis Sana impassa fame; vel cum minus improba savit Praficis effossis granida & tellure metalis. Hæc de hoc sidete horoscopante ludit Pontanus; sed & de eodem Occidente pejora pronunciat: sic enim subdit, Sanior obs, ciesque feris & corpora truncis affigens, animam extremis cruciatibus ausert.

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40 LEXICON you seek the Lord of the Decan. Thus let us suppose that the Sun, for example, is at 24° Aquarius: in order to know who is the lord of the Sun’s Decan, the first three degrees and 10 minutes of Aquarius are given to the lord of the movable sign of the same triplicity, which is Libra, and its lord is Venus (for Libra, Aquarius, Gemini are the airy triplicity); therefore Venus is the Lady of the first Decan: then of the second will be Mars, who rules Scorpio, next following Libra: and so on for each one, until one reaches the degree of the Sun, which falls in the Decan of Venus, Lady of Taurus. Therefore she herself will be the Lady of the Sun’s Decan. When therefore in the books of the Arabs there is mention of the Lord of the anaubarach Luminaries, if it is by day it is understood to mean the Lord of the Sun’s Decan; if by night, the Lord of the Decan of the Moon’s degree. 194. ANDROCOMETES is a kind of new Phenomenon, or a Comet having the figure of a man, concerning which see more in Pliny, book 2, chapter 25, and often elsewhere. 195. ANDROMEDA Arab. Marat Musa seleb, that is, Chained Woman, a constellation toward the north near Cepheus, consisting of 13 stars according to Ptolemy, but according to Bayer 17, almost all of the nature of Venus and Mercury, of which three are the most notable, of second magnitude: one in the head, also called the navel of Pegasus, because it passes into that constellation; another in the Girdle, Arabic Mirach, or Mizar; the third in the southern foot, called Allamach. All are in longitude under the sign Aries. It is an unlucky constellation, as its very figure suggests, denoting prisons, captivities, punishments. Concerning it, in someone’s horoscope, Pontanus in Urania has the following, more elegant than true. But on the contrary, the fierce Andromeda plots new funerals and black death, and, pressing on with savage torments, exacts punishments. For neither the lamentations of parents, nor the tears of a husband, nor gifts given, move her: death is her price, and monstrous torments her care: chains and prison, and a chain forged from a modest fire. The goddess, demanding revenge for the rocks on which she herself hung, displays these evil pursuits to those born under it. You will become dear to the hands, and a sharp axe to the neck; and you will tear apart the limbs, and feed upon the severed entrails, healthy but suffering hunger; or when she rages less evilly, you will preside over mines and metals, dug out from the earth. Thus Pontanus plays about this star when it is rising in a horoscope; but he also pronounces worse things concerning the same when it is setting: for thus he adds, A saner beast, fastening bodies and limbs to savage [torments], takes away the soul with extremest tortures.

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MATHEMATICVM. 41 Perpetuis etiam vinctis, & carceretetro Dammabit: si forte minax hinc inde benignum Sretsidus, dubio certans vtrinque sauore. Vtcumque sit, hoc vnum moneo hueusque dicta seu vera sint, u Poëtarum somnia à nostro hemisphetio ob sideris maxi- am alritudinem longè fieri neque enim vnquam aut oritur, t occidit nisi fortè quoad paucas admodum stellas infimæ : quare & effectus etiam si quos haber infaustos in nihi- m cedunt. 196. ANEPATROS apud Ptolem. lib. 3. cap. 7. iuxta versionem rab significat genituram trium Masculotum, in quam con- niant, Saturnus, Iupiter, & Mars. ANGETENAR Arab. dicitur fixa in corpore Ceri quartæ ma- 197. nitudinis de naruta Satutni: de qua in V. Cetus. ANGVLVS diciur id quod constat ex duabus lineis in vnum 198. unctum desinentibus: definitur enim ab Euclide quod sit dua- m linearum mutuus contactus . Vnde in ædificiis, vbi duo pa- teres in vnum coëunt, anguli appellanrrur. Hinc apud Astro- omos quatuor Coeli puncta, seu Cardines, vnde Ottus, & Occasus, Culmen & Imum incipiunt Anguli appellari solent. tangulus quidem Medij Coeli dicitur Meridianus superior, culmen, Cor coeli, & decima domus, in qua Sol constituius fficit Metidiem. Angulus Imi coeli Meridianus inferior, seu quarta domus. Angulus Orientis pars supra terram emergens scendens, Horosc. & Prima domus, ad quam cùm Sol per- enerit incipir diem: Angulus denique Occidentis dicitur pars la quæ à superiori ad inferius hemisphætium deptimitur, & unctum Occasus in qua Sol incipit noctem. Portò Angulus geneticè sumprus apud Geomerras diuiditur 199. n rectum, acutum, & obtusum. Angulus rectus est cum inea recta perpendiculariter cadit super aliam rectam in plano onsistentem, ita ut vtrinque æquale spatium liuquæ: vbi enim Iteram lineam tangit duos angulos rectos efformat. Acutus nior est Recto, hoc est minus spatium inter vtrumque latus clinquit, estque magis acuminatus: obtusus verò est recto nior, minusque acuminatus. Irem omnes isti anguli subdi- idi possunt in rectilineos, curuilineos & mixros. Rectilinei unt qui sub rectis lineis continentur: curu:linei, quorum traque linea curua est, & circularis: mixti denique quotum na linea curua est, altera recta. Ex tribus verò lineis se mutuo angentibus efficitur triangulum, quod dividitur in Rectan- gulum, Æquilaterum, Isoceles, Scalenum, Amblygonium, Oxygonium. Similiter ex quatuor lineis coëuntibus efforma- tur quadrangulum constans ex quatuor angulis: quod etiam di-

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MATHEMATICVM. 41 He also will condemn those perpetually bound and in the dark prison: if perhaps, threatening on this side and kindly on that, it is brightly fixed, disputing with doubtful favor on both sides. However it may be, I give this one warning: whether the things said so far be true or the dreams of poets, from our hemisphere, because of the great altitude of the star, they are far from being able to occur; for it never rises or sets, except perhaps with respect to a very few of the lowest stars. Therefore even if it should have any unlucky effects, they come to nothing. 196. ANEPATROS, in Ptolemy, book 3, chapter 7, according to the version, means the geniture of three males, in which Saturn, Jupiter, and Mars agree. ANGETENAR, in Arabic, is said of a fixed star in the body of Cetus, of the fourth magnitude, by nature of Saturn; concerning which see in V. Cetus. 197. ANGVLVS is said to be that which consists of two lines ending in one point: for Euclid defines it as the mutual contact of two lines. Hence in buildings, where two beams come together into one, they are called angles. Likewise among astronomers, the four points of the sky, or cardines, from which the East, West, Culmen, and Nadir begin, are usually called angles. The angle of the Midheaven is called the superior meridian, the Culmen, the Heart of the sky, and the tenth house, in which the Sun is placed at midday. The angle of the lower heaven is the inferior meridian, or fourth house. The angle of the East is the part rising above the earth, the Ascendant, and the first house; when the Sun has reached it, the day begins. The angle of the West is called that part which descends from the upper to the lower hemisphere, and the point of setting in which the Sun begins the night. Moreover, an angle taken in the geometric sense is divided into right, acute, and obtuse. A right angle is when a straight line falls perpendicularly upon another straight line lying in a plane, so that equal space remains on both sides; for where it touches the other line it forms two right angles. An acute angle is smaller than a right angle, that is, it leaves less space between the two sides, and is more pointed. An obtuse angle, however, is larger than a right angle and less pointed. Further, all these angles can be divided into rectilinear, curvilinear, and mixed. Rectilinear angles are those contained by straight lines; curvilinear, those whose lines are both curved and circular; mixed, finally, those of which one line is curved and the other straight. From three lines mutually touching one another a triangle is formed, which is divided into right-angled, equilateral, isosceles, scalene, obtuse-angled, and acute-angled. Similarly, from four lines coming together there is formed a quadrangle consisting of four angles, which also is di-

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42 LEXICON uiditur in perfectum quadratum, Rhombum, Rhomboidem, & Parallelogramma: Quorum singula, sicut & trianguli species suo loco sub propriis nominibus explicantur. 200. ANNAEL Arab. teste Hali, idem sonat, ac translatio lumi- nis quod contingit quandocumque fuerint tres Planetæ platicè coniuncti, quorum Medius superet alios in motu, & leuitates qui profecto ab vno ad alium transiens, dicitur transferre lu- men anterioris ad posteriorem. 201. ANNVLVS Astronomicus Instrumentum est Mathematicum pluribus annulis, seu circulis constans, ad siderum positus, altrudines, declinationes metiendas aptissimum: quippe quod totam Sphæram, descriptosque in ea circulos, & præcipuas fixas, non secus ac Planisphærium, proindeque totam coele- stem doctrinam velut in speculo coarctaram, exquisitissimè continet. De eo scripserunt abundè Gemma Frisius, Ioan. Tuisner, Bonerus, Io. Dryan. & alij. 202. ANNVS communirer dicirur circuitus quidam temporis, quo expleto reditur ad idem punctum. Vnde Seruius ab Annulo di- ctum putat, alij à Gæco verbo E' nce alij aliunde deriuarum contendunt. Antonomasticè & absque vlloadiuncto accipitur pro integra Solis revolutione in Zodiaco, incipiendo ab initio Arieris vsque ad finem Piscium quæ perficitur spario 365. die- rum, & fere sex horarum. Hinc Astronomi annum compu- tant ab æquinoctio verno, & eam ob rem Mundum eò potissi- mum tempore creatum tenent. 203. Datut etiam annus Lunatis constans duodecim Lunationi- bus, quarum siugulæ continent dies 29. hor. 12. & min. 44. itaut totus annus includat dies 354. hor. 8. min. 48. sitque 11. fere diebus minor anno solati. Vnde exorta ratio Epactæ, Pe- riodus Callipica & alia æquationes de quibus infra. 204. Porrò Annus solaris diuiditur in Tropicum, & Sidereum: Tropicus est sparium temporis, quo Sol recurrit ad punctum æquinoctium, vel solstitium, vnde initio anni discesserat, & eius magnitudo est semper æqualis dierum 365. hor. 5 min. 55. circiter, & solum variatio est in aliquibus secundis, & terriis. Dicitur autem Tropicus à Gæco verbo προπος, quod conuer- sio interpretatur. Sidereus ad sidera, hoc est fixas refertur, & est spatium illud temporis, quo Sol, integro Zodiaco peragra- to reuertitur ad stellam fixam in cornu Arietis, seu aliam quamlibet, in octavo orbe consistentem; vnde semper maior Tropico est annus sidereus, & continet secundùm Thebit (qui primus huius anni siderei inuentor fuisse creditur) dies 365. hor. 6. min 9. De qua re vide Ptolemæum lib. 3. sua magna constructionis.

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42 LEXICON is reduced into the perfect square, Rhombus, Rhomboid, & Parallelogram: each of which, like the species of a triangle, is explained in its place under its proper names. 200. ANNAEL in Arabic, according to Hali, means the same as the transference of light, which happens whenever three planets are platically conjoined, of which the middle one surpasses the others in motion and lightness, and which, passing from one to another, is said to transfer the light of the former to the latter. 201. ANNVLVS. The astronomical instrument is a mathematical instrument consisting of several rings or circles, most suitable for measuring the positions, heights, and declinations of the stars: indeed it contains the whole sphere, and the circles described in it, and the principal fixed stars, no less than a Planispherium, and thus the whole celestial doctrine, as it were compressed in a mirror, most exquisitely. On it have written abundantly Gemma Frisius, Ioan. Tuisner, Bonerus, Io. Dryan. & others. 202. ANNVS is commonly said to be a certain circuit of time, after which one returns to the same point. Hence Servius thinks it is called from Annulus; others contend from the Greek word E' nce, others derive it elsewhere. By antonomasia, and without any added term, it is taken for the complete revolution of the Sun in the Zodiac, beginning from the start of Aries to the end of Pisces, which is completed in the space of 365 days and nearly six hours. Hence astronomers compute the year from the vernal equinox, and for that reason hold that the world was created especially at that time. 203. There is also a lunar year, consisting of twelve lunations, each of which contains 29 days, 12 hours, and 44 minutes, so that the whole year includes 354 days, 8 hours, 48 minutes, and is thus almost 11 days shorter than the solar year. Whence arose the reckoning of the Epact, the Callippic Period, and other equations, of which below. 204. Moreover, the solar year is divided into tropical and sidereal: the tropical is the space of time in which the Sun returns to the equinoctial point or solstice from which it departed at the beginning of the year, and its magnitude is always equal to about 365 days, 5 hours, 55 minutes, with only slight variation in some seconds and thirds. It is called tropical from the Greek word προπος, which is interpreted as turning. The sidereal refers to the stars, that is, the fixed stars, and is that span of time in which the Sun, having traversed the entire Zodiac, returns to the fixed star in the horn of Aries, or any other, situated in the eighth sphere; hence the sidereal year is always greater than the tropical year, and according to Thebit (who is believed to have been the first inventor of this sidereal year) it contains 365 days, 6 hours, 9 minutes. On this matter see Ptolemy, book 3 of his great construction.

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MATHEMATICVM. 43 ANNVS Magnus simpliciter ab aliquibus dicitur reditus om- ium Stellarum ad idem punctum vnde discessetant ab initio lundi, cum primùm moueri coeptunt: quod fit ex Cicerone ratio 12954. annorum solatium. Astronomi verò rectiùs ap- pellant integram reuolutionem octauæ Sphæræ seu Firmamen- , quam Ptolemæus, alijque antiquiores statuebant in annis 000. Recensiores autem in annis 4900 quo etiam tempore seruatum est, omnes orbes cælestes redire ad idem punctum si erant initio Mundi, cum primum creari sunt. Vnde (vt id dixer dicam) non omninò inanis est opinatio illorum, qui plunt, totidem annis Mundum ipsum duraturum: eò quia et perfecta sunt opera, & dum tantum temporis spatium lin- ilis orbibus ad suum cursum perficiendum Diuina constituit cuidentia, æquum non esse, nec credibile, vt nolit postea rum motus absolui, atque ad idem punctum, vnde moueri reperant, non redite. Sed hæc imperfectabilia sunt, quæ Deus sua posuit potestate: vnde circa ea ludere quidem potest mana sapientia, collineare non potest. ANNVS Ægyptium, qui etiam Persicem dicebatur, constabat < 206.> uolutione dierum 360. quot videlicet sunt gradus in Zodia- , itaut singuli menses 30. dierum spatio constituerentur. uoniam autem hac reuolutione Sol non petueniebat ad lo- m suum, vnde discesserat; sed adhuc quinque dies desidera- ntur; hos quasi adiectitos, & supernumerarios extra men- s ipsos, antequam nouum exordientur annum computa- nt; neglecta intercalatione horarum sex, quæ singulis qua- iennis vnum diem constituunt: ideò absolutè hic annus erat ntum dierum 365. vt passim tradit Ptolemæus in Almagesto. At quia, vt modò diximus singulis annis prætermittebantur < 207.> oræ sex, quæ requirebantur, ad hoc vt Sol ad idem punctum diret, vnde discesserat; inde siebat, vt quarto quoque anno- nus Ægyptius integro die ante solstitij pristini diem absol- retur, & in annis 40. anteuetteret per decem dies, & in nis 1460. per dies 365. hoc est per vnum annum. Quare olutis annis cælestibus 1460. transierant iam anni Ægyptij 61 & initium anni Ægyptij, seu prima dies primi mensis, ii dicebatur Thoth redibat ad eandem diem, tempusque cælo ngruens. Hæc verò periodus annorum Iulianorum, ac ferè eclstium 1460. sed Ægyptiorum 164t. dicta est. ANNVS MAGNVS Canicularis, & Periodus Cynica, seu So- < 208.> iaca, à Canicula, quæ Græcè dicitur Cynos, & Sothis, eò iod hæc periodus inuenta fuerit à coniunctione, & ortu ma- tino Solis cum Canicula. ANNI MAGNI Luni-solares sunt quibus peractis Lunæ, Solis. < 209.>

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MATHEMATICVM. 43 The Great Year is simply called by some the return of all the stars to the same point from which they departed at the beginning of the world, when they first began to move: which, according to Cicero’s reckoning, is 12,954 years. Astronomers, however, more correctly call it the complete revolution of the eighth sphere, or firmament, which Ptolemy and other earlier writers placed at 36,000 years. More recent authors, however, at 4,900 years; and it was also held that by that time all the heavenly orbs had returned to the same point, if they were at the beginning of the world, when first created. Hence, if I may say so, the opinion of those is not altogether groundless who think that the world itself will endure for as many years; because its works are finished, and because, while Divine providence has appointed such a span of time to the celestial spheres for accomplishing their course, it is not fitting, nor credible, that afterwards their motions should not be completed and return to the same point from which they began to move. But these things are not within human power, since God has placed them beyond it; wherefore human wisdom may indeed play about them, but cannot strike the mark. The Egyptian year, which was also called the Persian, consisted of 360 days, namely the number of degrees in the Zodiac, so that the individual months were fixed at a span of 30 days. But because in this revolution the Sun did not return to the place from which it had departed, five days were still lacking; these, as it were, were added on and counted as supernumerary outside the months themselves, before they began the new year; the intercalation of six hours, which in four years make one day, being neglected. Therefore this year was absolutely only 365 days, as Ptolemy everywhere relates in the Almagest. But because, as we just said, six hours were omitted each year, which were required in order that the Sun might return to the same point from which it had departed, it came about that every fourth year the Egyptian year was completed one full day before the day of the former solstice, and in 40 years it had advanced by ten days, and in 1,460 years by 365 days, that is, by one year. Therefore, when 1,460 celestial years had elapsed, 1,461 Egyptian years had already passed, and the beginning of the Egyptian year, or the first day of the first month, which was called Thoth, returned to the same day, a time corresponding to the heavens. This period of 1,460 Julian years, and almost celestial years, but Egyptian 1,461, was called the year of the Great Canicular Period, or Cynic, or Sothic Period, from Canicula, which in Greek is called Cynos and Sothis, because this period was discovered from the conjunction and morning rising of the Sun with Canicula. The Great Lunisolar Years are those at the completion of which the Moon and the Sun.

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44 LEXICON < 109.> que syzigiæ ad idem diei momentum reuertebantur: inde ANNVS MAGNVS Metonicus dictus est à Metone Atheniensi eius inuentore. Cùm enim, vt supra dictum est, quilibet annus Solaris superer annum Lunarem (constantem duodecim perfectis Lunationibus, quarum singulæ compleatur diebus 29. hor. 12. min. 44.) vndecim ferè diebus; hinc est, vt singulis annis, Nouilunia totidem diebus anticipent, donec in annis 19. numerus compleatur, & Nouilunia redeant vt erant prius. Sicque annus iste Metonicus constat diebus 6939. cum horis 16. & diuidia, quot ferè diebus, & horis constant omninò vndeuiginti anni Solares, comprehendunt enim isti ad amussim dies 6939. & horas 18. itaut hæc periodus vna hora & semisse Lunarem superet, quam communem, & congruentem Luminarium periodum primus omnium inuenit Meton, vt diximus, à quo ei nomen est inditum: Et hic decemnouennalis recursus, Aurens numerus appellatus est, de quo suo loco. Porrò quoniam Luna, vt modò dicebamus, horâ vna, & semisse à Solis decemnouennali cursu, discrepat, ac præcedit, inde sit, vt in quatuor annis magnis Metonicis, hoc est in annis communibus 76. ipsa anticipet per horas 6. & in annis 312. & sex mensibus, integrum diem præcedat, & successiuè semper magis ac magis excrescat hæc deuiatio, quæ tandem tum ob Lunæ Embolismicam Lunationem quæ aliquando anno Lunari superadditur, (qui proinde Annus Embolismicus hoc est insititius dicitur constant ex re, decim Lunationibus) tum ob Solis inæqualem morum, in Zodiaco potest in ordinem reduci, arque exquisitissimè compleri; ita ut Annus lunaris ad amussim cum Solari conueniat. Qua de re consule librum nouæ rationis Kalendarj Romani restituendi jussu & authoritate Gregorij XIII editum. Cæterum hæc periodus communiter appellatur Callippica ab eius repertore Callippo, vt in loco dicemus. < 110.> ANNVS Periodicus apud Chronologos significat durationes & fata Imperiorum. Testantur enim Historiæ omnium temporum, si à prima sua origine repetantur Regna, & Respublicas potentiores quingentis tantummodo annis flotuisse; Plurima verò hunc terminum non attigisse; nulla aut pauca superasse. Annus ergò quingentesimus Imperiorum Periodicus dicitur, eò quia circa eius finem Imperia, & Monarchiæ, aut in torum cedere, aut mutationem aliquam considerabilem subire soleant. Id passim obseruare est in Imperio Græcorum, Medorum, Assyriorum, ac denique in Romano. Et mirum est, quomodo hebdomades septuaginta Danielis ad hanc etiam periodum apprimi respondeant, cum de aduentu Christi, & in-

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44 LEXICON < 109.> that syzygies returned to the same moment of the day: hence the GREAT YEAR is called Metonic, from Meton of Athens, its inventor. For since, as was said above, each Solar year exceeds the Lunar year (which consists of twelve complete lunations, each completed in 29 days, 12 hours, 44 minutes) by about eleven days; it follows that in each year the new moons anticipate by so many days, until in 19 years the number is completed, and the new moons return as they were before. Thus this Metonic year consists of 6939 days, with 16 hours and a half, by which number of days and hours there are altogether nineteen Solar years, for these exactly contain 6939 days and 18 hours; so that this period exceeds the Lunar one by one hour and a half, which common and fitting period of the luminaries was first of all found by Meton, as we said, from whom it takes its name: and this nineteen-year cycle is called the Golden Number, of which elsewhere. Moreover, since the Moon, as we were just saying, differs from the Solar nineteen-year course by one hour and a half, and goes ahead of it, it follows that in four great Metonic years, that is, in 76 common years, it anticipates by 6 hours, and in 312 years and six months, it goes ahead by a whole day, and successively this deviation always grows greater and greater, which finally both on account of the Moon’s embolismic lunation, which is sometimes added to the lunar year, (which therefore is called an embolismic, that is, an intercalary year, consisting in fact of 13 lunations) and on account of the Sun’s unequal motion in the zodiac, can be brought back into order and completed with the utmost exactness; so that the lunar year may agree exactly with the solar. On this matter consult the book of the new method for restoring the Roman Calendar, published by order and authority of Gregory XIII. Meanwhile this period is commonly called Callippic after its discoverer Callippus, as we shall say in its place. < 110.> PERIODIC YEAR among chronologists signifies the duration and fate of empires. For the histories of all times bear witness, if kingdoms and republics are traced back from their earliest origin, that the more powerful ones flourished only for five hundred years; most, however, did not reach this limit; none or few exceeded it. The five-hundredth year of empires is therefore called periodic, because around its end empires and monarchies either usually fall completely, or undergo some considerable change. This may be observed everywhere in the empire of the Greeks, Medes, Assyrians, and finally in the Roman. And it is remarkable how the seventy weeks of Daniel also correspond closely to this period, when concerning the coming of Christ, and in-

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MATHEMATICVM. 41 enti rerum mutatione sequuta post annum 490. quo hæc præxerat Gabriel Danieli, vt explicant passim Expositores super o Danielis caput. Cuius rei causam, alij in Coelorum mo- s, atque in aliquam fixam, quæ regionibus fiat Verticalis ferunt, alij in transitum Superiorum Planetarum ex vno in um Trigonum; alij, vt Plato in miram quandam numeri moniam, quia, inquit, sexquitertia radix juncta quinario as efficiat harmonias, vltrà quas, cum Natura posteà dete- res gignar, circumactam periodum necesse est finire Impe- t. Alij rectiùs in homiium, Principumque nequitiam vt pè diuina testantur eloquia, causam mutationum regnotum ijciendam censent: sæpè etenim propter populi peccata incipes, & Respublicæ puniuntur; Vnde cùm ad certam etam peruenerint, quæ diuinam concitat itam in eorum poe- m Respublicæ, quò nil tristius enertuntur. ANOMALIA Græcè, Latinè dicitur irregularitas motus ali- <211.> ius Planetæ: aliquando etiam sumitur pro ipso argumento regularitatis, & æquationis adhibendæ; quod argumentum tarcus inter lineam absidum, & lineam motus medij, seu est stantia loci medij Planetæ ab Apogæo. Atque id potissimùm renditur in Luna, vt vera eius cum Sole conjunctio dignosci eat. Cum enim compertum sit, Solem non vniformiter oueri in Zodiaco; quandoquidem in semicirculo Boreali oratur octo ferè diebus cum dimidio magis, quàm in Austra- hinc deductum est, ipsum inæqualiter moueri in quadrans Zodiaci: Nam tempore Hipparchi, & Ptolemæi plures <212.> es insumebat in primo quadrante, hoc est ab æquinoctio erno ad solstitium Æstiuale, quam in secundo: nostro autem mpore segnior est in secundo, quàm in primo; tardissimus item circa gradum sextum Cancri. Cuius irregularitatis cau- m saluat Blacanus in sphæra Mundi... Idipsum videre etiam in Luna: Proptereà inquiritur eorum Anomalia, vt per m habeatur æquatio, & verus motus, sicque punctum præci- m eorum veræ synodi haberi possit. ANSER, Olor, Gallina, sidus in Coelo ad Borealem pla- <213.> m de quo vide in Verbo Cignus. Item. ANSER Americanus nouum item sidus ad polum Antarcti- <214.> m non ita pridem ab Americæ repertoribus detectum, atque Aue quadam propria illarum regionum, vernaculo earum cabulo dicta Tonean , nominatum. Quare vide in V. To- am. ANTARCTICVS hoc est oppositus Arctico dicuntur tam Polus <215.> australis nobis inuisus, quàm circulus circà eum formatus à plo Zodiaci item australi nobis etiam in conspicuo.

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MATHEMATICVM. 41 the change of things that followed after the year 490, when Gabriel Daniel preceded this, as the Expositors on Daniel’s chapter explain everywhere. The cause of this matter some assign to the motions of the heavens, and to some fixed position that becomes vertical to the regions; others to the passage of the superior planets from one trigon to another; others, as Plato, to some marvelous harmony of number, because, he says, when the sesquitertian ratio is joined to five it produces harmonies, beyond which, when Nature afterward brings forth more unequal things, it is necessary for the completed period to end the impulse. Others more rightly judge that the cause of changes in kingdoms is to be laid to the wickedness of men and princes, as the divine oracles often testify: for often because of the sins of the people princes and republics are punished; whence, when they have reached a certain measure which stirs up divine anger, they are destroyed in punishment, and republics are overturned to the point that nothing is more sad. ANOMALIA, in Greek; in Latin it is called irregularity of the motion of another planet: sometimes it is also taken for the very argument of the irregularity and the equation to be applied; which argument is the distance of the planet’s mean place from the apogee between the line of apsides and the line of mean motion. And this is investigated especially in the Moon, so that her true conjunction with the Sun may be recognized. For since it is known that the Sun does not move uniformly in the zodiac—inasmuch as in the northern semicircle he spends about eight and a half days more than in the southern—it has been inferred from this that he moves unequally in the quarter of the zodiac. For in the time of Hipparchus and Ptolemy he spent more days in the first quarter, that is, from the vernal equinox to the summer solstice, than in the second; but in our time he is slower in the second than in the first; slowest also around the sixth degree of Cancer. Blacanus explains the cause of this irregularity in the sphere of the world... The same is seen also in the Moon: therefore their anomaly is investigated, so that by it the equation and true motion may be obtained, and thus the exact point of their true synod may be determined. ANSER, Olor, Gallina, a star in the heavens toward the north pole, concerning which see under the word Cignus. Likewise. ANSER Americanus, likewise a new star near the south pole, recently discovered by the explorers of America, and a bird peculiar to those regions, called in their vernacular tongue Tonean, so named. Therefore see under V. Tonean. ANTARCTICVS, that is, opposite to the Arctic: thus are called both the southern pole, hidden from us, and the circle formed around it, as well as the southern pole of the zodiac, likewise visible to us.

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46 LEXICON <216.> ANTARES Græcè dicitur Cor Scorpij, Stella fixa primæ magnitudinis de natura Marris, & Iouis vna ex stellis regiis, sed etiam ex violentis. Vnde cum Luminaribus reperta maximas dignitates pollicetur, sed non sine vitæ discrimine, ac violentia: Cum Venere inclinat ad Musicam, & Poësin: Cum Luna in bono aspectu beneficarum gratiam Principum comparat, facitque eorum intimum familiarem. Vide in V. Cor Scorpij. <217.> ANTASCONES, quasi sub contrario axe vocantur populi habitantes in locis diametraliter oppositis, à quorum videlicet plaga ad alteram correspondentem Linea imaginariè porrecta, necessariò transire debet per centrum Mundi, vnde etiam appellantur. <218.> ANTIGENÆ ab Alberto Magno, quasi contrarios omninò effectus experientes: & à Græcis. <219.> ANTICHTONES. Siquidem locorum diametraliter oppositorum incolæ ijsdem anni temporibus contrarios aliis effectus habent. Sic dum Sol in vna parte Meridiem facit, in altera Medium noctis inducit: dum vni diem longissimum, ac noctem breuissimam, alteri è contra noctem breuissimam, diem longissimum procreat: dum vni æstum, alteri frigus, dum vni Ver, alteri Autumnum parat, iis dempris, qui sub æquatore versantur, nam istis solum in diei noctisque alternatione est cum prædictis communicatio, cæterùm ibi vt alibi dictum est, semper & vbique æqvinoclitium: tam hic quàm illic eodem tempore hyems aut æstas: eadem caloris intensio, idem hominum color. Hi à nostris communiter sumpto à Græcis vocabulo appellantur. <220.> ANTIPODES quasi obuersis pedibus incedentes, ambo enim, vt ait Plinius aduersa suis oppositis premunt vestigia; itaut vulgus existimer, nostros Antipodas, capire deorsum verso incedere. Hos derider D. Augustinus lib. 16. de Ciuitate Dei cap. 9. Imò ex testimoniis sacræ Scripturæ contendit probare nulla ratione credendum esse Antipodas inueniri, proindeque esse hæreticum illos astruere: Quia, inquit, cùm diuina Scripturæ testetur homines ex vno Adam in hoc nostro hemisphario progenios, nimos absurdum est dicere, aliquos homines ex hoc in alud hemispharum, impertransibilis Oceani immensitate traietta, nauigare potuisse, vt etiam illic humanum genus propagarent. Id iplum lenfere etiam Lactantius Firmianus lib. 3. Diuin. Instit. c. 24. Bedæ de ratione temporum cap. 32. Procopius Gazæus, alijque Patres, adeò vt olim malè audirent qui eos ex congruentiis ac Mundi situ admittere compellebantur, suamque sententiam proferre minimè auderent. Cæterum nostris temporibus vsq[ue] adeò certum est dari Antipodas atque in regionibus nostris ter-

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46 LEXICON <216.> ANTARES is called in Greek the Heart of the Scorpion, a fixed star of the first magnitude, of the nature of Mars and Jupiter, one of the royal stars, but also of the violent ones. Hence, when found with the Luminaries, it promises the greatest dignities, but not without danger to life and violence. With Venus it inclines to Music and Poetry. With the Moon in a favorable aspect it gains the favor of princes, and makes one their intimate familiar. See under the Heart of the Scorpion. <217.> ANTASCONES, as if under the opposite axis, are called peoples inhabiting places diametrically opposite, from whose region, that is, to the corresponding opposite one, an imaginary line drawn must necessarily pass through the center of the world; from this they are also called so. <218.> ANTIGENÆ, by Albertus Magnus, as though experiencing altogether contrary effects; and from the Greeks. <219.> ANTICHTONES. For the inhabitants of places diametrically opposite have, in the same seasons of the year, effects contrary to others. Thus while the Sun makes noon in one part, in the other it brings on midnight; while to one it produces the longest day and the shortest night, to another, on the contrary, the shortest night and the longest day; while to one it prepares heat, to another cold; while to one spring, to another autumn, excepting those who dwell under the equator, for with them there is only communication with the aforesaid in the alternation of day and night; otherwise, there as elsewhere said, it is always and everywhere the equinox: both here and there at the same time winter or summer; the same intensity of heat, the same color of men. These are commonly called by our people, using a Greek word. <220.> ANTIPODES, as if walking on reversed feet; for both, as Pliny says, press their footsteps opposite to those opposite to them, so that the common people think that our Antipodes walk with their heads turned downward. St. Augustine derides them in book 16 of the City of God, chapter 9. Indeed, from the testimonies of Holy Scripture he strives to prove that on no account should it be believed that Antipodes are found, and therefore that it is heretical to assert them: because, he says, since divine Scripture bears witness that men are descended from one Adam in this our hemisphere, it is very absurd to say that certain men could have sailed from this hemisphere to another, having crossed the immeasurable vastness of the impassable Ocean, so as there also to propagate the human race. The same is held by Lactantius Firmianus, book 3 of the Divine Institutes, chapter 24, by Bede, On the Reckoning of Time, chapter 32, by Procopius of Gaza, and other Fathers, so much so that in former times those were ill spoken of who were compelled to admit them from the concordances and the situation of the world, and did not dare to put forward their opinion. But in our times it is now so certain that there are Antipodes as that in our regions ter-

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MATHEMATICVM. 47 oppositis, homines ex Adam vtique propagatos, vt illos gare modò, perinde ac delirare sit: Nauigant enim quo- lie ad eos Mercatores nostri, ac Religiosi homines ad Euan- lium prædicandum, indeque illi ad nostras Regiones, ac ui temporis spatio toto penè emenso, ac remenso Oceano, nos cum mercibus, & inuisi vulnus hominibus reuertuntur: de magna Catholico Regi, cuius auspiciis & impensis ristophorus Columbus eas oras detexit non tam regnorum, àm opum accessio facta est. Excusandi sunt tamen prædicti tres, ex zelo fidei, si aliter tam constanti animo censuere, si eos fortè ex Solis congruentijs admisissent, cogerentur eri, tales homines ex Adam non prædeatos, quandoqui- m constans omnium scriptorum fama esset, vel ab Clementis upore, quod inter hanc Borealem & illam Australem pla- m immensus interfunderetur Oceanus, quem nullus homi- m permeasset vnquam sed nec permeare potuisset. Nondum im prætergressæ erant Herculeæ illæ Columnæ in quibus talis inscriptio Non pluo vltra omnes ab vlterioris navigatio- s studio arcebat, absterrebatque. Porrò si quis vnius loci An- dodas exspicari velit, eius longitudini Geographicæ addat 180. additamenti postremo numero sistatur index, qui di- to Antipodarum Meridianum demonstret, in quo tot gra- s latitudinis enumerantur versus plagam vnam, quot lati- dinis habet in plaga altera data Ciuitas, & voti compos erit. : Malaca in Hispania diametraliter opposita est Capiti Corso Blanco in America non procul à Brasilia: sic Insulæ Borneo Taprobana Antigena est regioni Amazonum, & Lacui Pa- næ item in Americæ: sic Riuus argenteus dictus Rio de La ata extremis finibus Chinensium, vbi ad se tutandum ab in- sionibus Tartarorum murum 400. leucarum extruxerunt, sic de singulis: Et hæc de Antipodis seu Antichthonibus di- sint, qui etiam. ANTAZONES dicuntur teste Iosepho Laurentio in Amalthea, < 222.> quia sub contraria Zona vitam degunt. ANTICHTONES etiam vocat Macrobius habitatores quos < 223.> git in Luna, quasi in opposita terra habitantes, qua de re de in Verbo Luna. ANTECANIS vocatur ab Hippocrate, ac Tullio Canis minor < 224.> dycen, eò quia sit Canis maioris Prodromus, & paulò antè sum oriatur, hoc est circa octauum Kalendas Augusti, cum ta- en Canis maior oriatur Romæ circa ipsas Kalendas; quo mpore inquit Hippocrates, Poisiones mala. ANTICA Arabice dicitur interior, & caua pars Astrolabij < 215.> comprehendens tabulas ac retè, quod limbo intra quem ob-

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MATHEMATICVM. 47 opposites, men descended from Adam in any case, so that to deny that they are such now is much the same as to rave: for our Merchants and religious men sail thither to preach the Gospel, and from there they to our Regions; and after the whole space of time has almost been spent, and the Ocean crossed and recrossed, they return to us with merchandise, and to men an unwelcome wound: of great advantage to the Catholic King, under whose auspices and at whose expense Christopher Columbus discovered those shores, there was made not so much an addition of kingdoms as of wealth. Yet the aforesaid three are to be excused, if out of zeal for the faith they judged otherwise with so steadfast a mind, if perhaps they admitted from the congruities of the Sun that they were compelled to say that such men were not descended from Adam; since the constant report of all writers was that, by reason of the stupor of the climate, there flowed between this Northern and that Southern plain an immense Ocean, which no man had ever crossed, nor could ever cross. Nor indeed had those famous Pillars of Hercules been passed, on which the inscription Non plus ultra deterred and kept back all from the study of farther voyaging. Moreover, if anyone wishes to look for the Antipodes of one place, let him add 180 to its Geographical longitude; let the index be fixed at the last number of the addition, which will indicate the Meridian of the Antipodes, in which are reckoned so many degrees of latitude toward one quarter as the given city has of latitude in the other quarter, and he will have his wish. Thus Malaca is diametrically opposite Cape Corso Blanco in America not far from Brazil: so the island of Borneo is opposite to the region of the Amazons, and also to Lake Parana in America: thus the River called Rio de La Plata is at the extreme borders of the Chinese, where they have built a wall of 400 leagues to protect themselves from the incursions of the Tartars; and so in individual cases. And these things concerning the Antipodes or Antichthones be said, who also are called ANTAZONES, according to Joseph Laurentius in the Amalthea, < 222.> because they lead their life under the opposite Zone. ANTICHTONES Macrobius also calls the inhabitants whom < 223.> he places in the Moon, as though dwelling in the opposite earth; on which matter see also under the word Luna. ANTECANIS is called by Hippocrates and Tullius the Little Dog < 224.> or Canis minor, because it is the forerunner of the greater Dog, and rises a little earlier, that is, about the eighth day before the Kalends of August, whereas the greater Dog rises at Rome about the Kalends themselves; at which time, says Hippocrates, illnesses are bad. ANTICA in Arabic means the inner and hollow part of the Astrolabe < 215.> comprehending the tablets and the net, which within the rim, in which above...

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48 LEXICON uoluitur, circumscribitur. Dicitur etiam Maser, seu etiam Matrix quia perinde se habet, ac si tabulas quasi filios in vtero gerat. 216. ANTINOVS fidus in coelo propè æquatorem ad Australem plagam sub Capricorno situm formatum ex aliquibus stellis informibus; cum Ptolemæus ipsum inter 48. imagines non connumerauerit. Keplerus ei assignat stellas septem, at verò Baierus vndecim: dicitur etiam ab aliquibus Ganimedes. 217. ANTISCIA hoc est intuentia sunt partes signorum æquè distantes à Tropicis, aut ab Æquatore, quæ quidem si sint eiusdem potentia & eandem habeant declinationem tam numero quam regione dicunt absolutè intuentia, & primaria; si verò sint eiusdem quidem declinationis, sed denominationis diversæ, vocantur communiter contrantiscia seu Imperantia & obedientia, atque Antiscia secundaria: & sanè quod ad partem Borealem declinar, dicitur imperare ei, quod flectit ad Austrum. Porrò Vulgus Astrologorum computat planetarum Antiscia in Ecliptica ad numeros respondentes, etiamsi illi aliquam habeant latitudinem: quò sit vt sæpenumetò ea pro Antisciis accipiantur, quæ verè ex Ptolemæi mente Antiscia non sunt; cum non eosdem cum Planetis inueniantur describere parallelos, aut in eodem parallelo consistere. Notum quippe est variata sæpè latitudine variari etiam declinationem, variari, & parallelos. Vnde si Planeta latitudine præditus est, sicut in eius declinatione accipienda, latitudinis ratio habenda est, ita & in eorum Antiscijs supputandis, quæ profectò nihil aliud sunt, quàm idem vel æquales parallelli seu æquidistantia à Tropicis, aut ab æquatore. Quapropter meritò Placidus de Titis in sua Cælesti Philosophia relicto nomine antiquo propriore vocabulo, ea parallelos declinationis appellat. 218. Ad extrahenda igitur vera Planetarum Antiscia, accipienda est eorum declinatio, atque eadem prorsus in signis Antiscijs siue Intuentibus, siue Imperantibus & Obedientibus, siue in Ecliptica, siue extrà, inuenienda, & hic locus erit verum Planetæ illius Antiscium; ad quem postea deductus significator completur directio, perinde ac si pertingeret ad aliquem eius aspectum, & Intuentia æquiparantur coniunctioni, Imperantia vero, & Obedientia oppositioni. Ponamus casum, quod Sol verbi gratiâ, qui semper incedit per Eclipticam reperiatur in gr. 10. min 20. Leonis, eius Antiscium benè erit in gr. 19. min .... Tauri in Ecliptica item computatum (vt aliàs fieri solet) eo quia ambo ista loca conveniunt in eadem declinatione Boreali gr. 17. min. 43. At enim demus Lunam repetiri in alicuius Nauuitate in gr. 25. Cnacri, cum

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48 LEXICON is revolved, circumscribed. It is also called Maser, or also Matrix, because it is as though it bears the tablets like children in the womb. 216. ANTINOVS, a fixed one in the sky near the equator, situated toward the southern region under Capricorn, formed from some formless stars; although Ptolemy did not count it among the 48 images. Kepler assigns it seven stars, but Bayer eleven: it is also called by some Ganymede. 217. ANTISCIA, that is, “opposites,” are the parts of the signs equally distant from the Tropics or from the Equator, which if they are of the same power and have the same declination both in number and in region are called absolutely “opposites,” and primary; but if they are indeed of the same declination, yet of different denomination, they are commonly called contrantiscia, or “commanding” and “obedient,” and secondary Antiscia: and certainly, insofar as it declines to the North, it is said to rule that which bends toward the South. Moreover, the common run of astrologers compute the Antiscia of the planets on the ecliptic according to corresponding numbers, even if they have some latitude; so that very often those are taken as Antiscia which, in truth, according to Ptolemy’s mind, are not Antiscia; since they are not found to describe the same parallels with the planets, or to stand in the same parallel. For it is well known that, as latitude is often varied, declination is also varied, and the parallels as well. Hence, if a planet is endowed with latitude, just as account must be taken of latitude in determining its declination, so too in calculating its Antiscia, which are indeed nothing other than the same or equal parallels, or equidistant points from the Tropics or from the Equator. Wherefore Placido de Titis rightly, in his Celestial Philosophy, abandoning the ancient name, calls them by the more proper term “parallels of declination.” 218. Therefore, to extract the true Antiscia of the planets, their declination must be taken, and exactly the same declination must be found in the Antiscia signs, whether Opposites, or Commanding and Obedient, whether on the ecliptic or outside it; and this place will be the true Antiscium of that planet; to which, when the significator is afterward carried, the direction is completed, just as if it had reached some aspect of it, and Opposites are equated with conjunction, while Commanding and Obedient are equated with opposition. Let us suppose the case that the Sun, for example, which always moves along the ecliptic, is found at 10° 20' of Leo; its Antiscium will properly be at 19° ... of Taurus on the ecliptic likewise computed (as is usually done elsewhere), because both these places agree in the same northern declination of 17° 43'. But let us suppose the Moon to be repeated in someone’s nativity at 25° of Cancer, with

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MATHEMATICVM. 49 m latitudine meridiana gr. 5. verum eius Antiscium non erit gr. 5. Geminorum qui correspondet gradui 25. Cancri, vt garia tradunt præcepta, eò quia de iis minimè verificatur blemxi dictum, quod æquales temporis spatio oriuntur & aqua- vatio distent ab eodem vel ab veroque punctorum aquincetialium: id indagandum siue in Ecliptica, siue extra in eodem paral- leclinationis Lunæ, quæ cum data latitudine erit gr. 16. 1. 18. Igitur eius verum Antiscium erit grad. 14. min. 40. uri in Ecliptica; quia hic gradus sali præditus est declina- re, atque incidit in eundem parallelum cum Luna: ad quem teà gradum directus Sol, iure dicitur ad Lunæ Antiscium solutus. Accidit etiam, vt Planeta tanta sit præditus latitudine, vt < 229.> indoque eius Antiscium extra Eclipticam prorsus, imò im extra viam realem alicuius Planeræ significatoris cadat; proinde eius Antiscium planè vacuum effectu remaneat, ppe quod nunquam ab aliquo significatore per viam suam lem incedentem per directionem attingi potest: & ideò in casu eius ratio habenda non est. Sic ponamus Martem repe- in eodem gradu 25. Cancri, sed cum latitudine boreali, m sanè habere potest graduum nouem: tunc eius Antis- n extra Zodiacum cadit, cùm eius declinatio sit grad. 30. m neque Sol neque vllus significator vquam attingit, cùm ummum ea in Sole excedere non possit gr. 23. min. 31. & in ia quacumque latitudine prædita maior esse nequeat, quam 26. min. 7. Vnde cùm nunquam possint pertingere ince- do per viam suam realem, ad parallelum declinasionis rtis; nunquam etiam directione possunt ad eius Antiscium uci, benè verò ad eius Contrantiscium, seu parallelum di- sæ declinationis, quod secat Eclipticam, aut orbitam Lunæ quam realiter incedit; ita vt motu suo pergens, ad illud dem perueniat. adem ratione qua in Zodiaco per æquidistantiam à punctis < 230.> dinalibus considerantur Antiscix, quæ sunt eiusdem po- ix, & eiusdem penè actiuitaris, ac corpora ipsa Planeta- ; eadem inquam ratione fulia plurimis experimentis in- iosè admodum adinuenit P. de Titis in Calisti Philosophia, iscia in mundo per æquidistantiam videlicet à Cardini- mundi: quos, sicut illos parallelos declinationis, ita & in senti parallelos cosmicos placuit appellare, qui planè dem virtutis & efficaciæ atque Antiscia in Zodiaco, esse periuntur: sed de his iterum redibit sermo in V Paralleli. NTISCII apud Geographos appellantur populi habitantes in < 231.> s Antiscijs, sic dicti eò quod obuersas inuicem vmbras D

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MATHEMATICVM. 49 in southern latitude 5 degrees; but its true Antiscion will not be 5 degrees of Gemini, which corresponds to the 25th degree of Cancer, as the usual rules set forth, because of them the statement is by no means verified, namely that they arise at equal intervals of time and are separated from the same or from the true equinoctial points: this must be investigated either in the Ecliptic or outside it in the same parallel of the Moon’s declination, which with the given latitude will be 16 degrees. 1. 18. Therefore its true Antiscion will be at 14 degrees 40 minutes in the Ecliptic; because this degree is endowed with such declination, and falls on the same parallel with the Moon: to which degree, if the Sun is directed, it is rightly said to be carried to the Moon’s Antiscion. It also happens that a planet is endowed with so great a latitude that its Antiscion falls wholly outside the Ecliptic, indeed even outside the real path of some significator; therefore its Antiscion remains completely empty of effect, since it can never be reached by any significator proceeding by its own real path through direction: and therefore in such a case no account is to be taken of it. So let us suppose Mars to be found in the same 25th degree of Cancer, but with northern latitude, which indeed it can have of nine degrees: then its Antiscion falls outside the Zodiac, since its declination is 30 degrees; and neither the Sun nor any significator ever reaches it, since in the Sun it can at most exceed 23 degrees 31 minutes, and in any latitude whatever it may be endowed with, it cannot be greater than 26 minutes 7 seconds. Whence, since they can never arrive by proceeding along their own real path to the parallel of the planet’s declination, they can also never by direction be brought to its Antiscion; but indeed to its Contrantiscium, or the parallel of opposite declination, which cuts the Ecliptic, or the orbit in which the Moon actually travels; so that, proceeding by its motion, it arrives at that same point. In the same way as in the Zodiac, by means of equidistance from the cardinal points, Antiscions are considered, which are of the same position and almost the same activity as the planets themselves; in the same way, I say, Fulia, after many careful experiments, very ingeniously discovered in the Celestial Philosophy that there are antiscia in the world by equidistance, namely from the cardinal points of the world: which, like those parallels of declination, have been pleased to call cosmic parallels, and which are plainly found to be of the same power and efficacy as the antiscia in the Zodiac; but of these I shall speak again in Parallel V. ANTISCII among geographers are called peoples dwelling in the Antiscions, so named because they cast opposite shadows upon one another. D

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50 LEXICON habeant; sicut & Amploiscij, qui quadruplicet vmbra verberantur; & Periscij, qui eandem habent versatilem, & circularem. Similiter. 232. ANTIPATHIA Græcè dicitur naturalis ille rerum diffensus, & contrarietas, quam passim videmus, & admiramus, ad aliam causam id refundere non valentes, quam in dependentiam, & subordinationem quam habent inferiora ista ad suas causas superiores vniuocas, vel diuersas. Qua de re vide in V. Sympathia. 233. ANTOCCI dicuntur: quasi contrahabitabiles, populi in æqualibus, sed oppositis parallelis, hinc inde ad æquatorem constituti, ira vt habeant eandem latitudinem locorum, eandem numero Poli elevationem, sed non eiusdem, quantum enim attollitur his Polus boreus, tantum illis austrinus, vnde consequenter habent æquales, sed in oppositis signis ascensiones, æquales arcus diurnos, pariterque nocturnos; æquales demum temporum dispositiones, locorumque temperies, sed non æquè, hoc est non in eisdem mensibus, sed in oppositis: dum enim istis solstitium æstiuum accidit, & vndique æstu torrentur, illos è conttatio hyemis rigor corripit, & insolens frigus: quando istis floridum Ver arridet, illi Autumuale, tempus experiuntur, & magnam fructuum copiam colligunt. Tales sunt accolæ capitis bonæ spei, & habitatores Moreæ, Zacynthi, &c. Extremum insulæ sancti Laurentij dictæ vulgò Madagascar, & Mate rubrum: sicut è contra Perioeci vocantur qui habitant sub vno Meridiano, eodemque parallelo, sed in locis eiusdem paralleli oppositis, vt dicemus in suo loco. A P 234. APARCTIAS Græcè dicitur ventus Septentrionalis vnsus ex quatuor Cardinalibus, sic dictus ab Arcto, seu Polo Arctico, vnde exsustlat. Est generaliter frigidus, & siccus, niuosus, serenitatis auctor, corruptionis vindex, & omnium saluberrimus, licer ob nimiam frigiditarem sit floribus, & germinibus nouis infensus: ab Italis audit Tramontana. 235. APELIOTES, Græcè Eurus, Latinè dicirur, ac Subsolanus, Venrus spirans ab oriuæquinoctiali: sic dictus ab orenre Sole. Est item vns ex quatuor Cardinalibus, calidus, & siccus, sed tamen cum insigni temperie, ideoque à Ptolemao sanguineus dictus. Noctu plerumque silet, & incipit spirare oriente Sole. Hyeme producit gelu: æstate verò serenitatem adducit. Conseruat corpora, ac salubritatis est parens. In Italia vocatur Levante. 236. APERITIO Portarum apud Astrologos audiunt maximæ quædam atque euidentissimæ aëris, ac temporum mutationes quæ

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50 LEXICON have; as the Amphiscii, who are struck by a fourfold shadow; and the Perisci, who have the same shadow that is versatile and circular. Likewise. 232. ANTIPATHIA, in Greek, is called that natural mutual repulsion and contrariety of things which we see and admire everywhere, not being able to refer it to any other cause than the dependence and subordination which these lower things have to their superior causes, whether univocal or diverse. On this matter see under V. Sympathia. 233. ANTOCCI are called, as it were, co-inhabitants: peoples in equal but opposite parallels, situated on either side of the equator, so that they have the same latitude of places, the same number of degrees of elevation of the poles, but not the same one; for however much the north pole is raised for these, so much is the south for those. Hence, consequently, they have equal, but opposite, signs of ascension, equal diurnal arcs, and likewise nocturnal ones; and finally equal dispositions of seasons and climates, but not equally, that is, not in the same months, but in opposite ones: for when summer solstice occurs for these, and they are scorched everywhere by heat, for those the severity of winter seizes them, and unusual cold; when the flowery spring smiles upon these, they experience an autumnal time and gather a great abundance of fruits. Such are the inhabitants of the Cape of Good Hope, and the dwellers of Morea, Zacynthus, etc. The extremity of the island called St. Lawrence, commonly Madagascar, and the Red Sea: just as, on the contrary, Perioeci are called those who dwell under one and the same meridian, and the same parallel, but in places opposite to the same parallel, as we shall say in its proper place. A P 234. APARCTIAS, in Greek, is called the northern wind, one of the four cardinal winds, so named from Arctos, or the Arctic Pole, from which it blows. It is generally cold and dry, snowy, the author of clear weather, the enemy of corruption, and the most wholesome of all; though, because of excessive cold, it is hostile to flowers and new shoots. Among the Italians it is called Tramontana. 235. APELIOTES, in Greek, is called Eurus, in Latin also Subsolanus, the wind blowing from the equinoctial east: so named from the rising sun. It is likewise one of the four cardinal winds, hot and dry, yet with notable moderation, and therefore called by Ptolemy sanguineous. By night it usually is silent, and begins to blow at sunrise. In winter it produces frost; in summer, however, it brings clear weather. It preserves bodies and is the parent of health. In Italy it is called Levante. 236. APERTIO Portarum, among astrologers, means certain very great and obvious changes in the air and in the seasons, which

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MATHEMATICVM. 51 unquam ferè fallunt, experientia teste, sed certissimum sem- er sortiuntur effectum; idque sit in certis Planetarum con- ressibus, aut irradiationibus. Et potissimum hoc obseruatur 1 Planetis dominis oppositarum domotum, vt Saturni, & So- s (Aquarius enim Saturni domicilium opponitur Leoni, cu- is dominator est Sol, & sic de reliquis.) Saturni, & Lunæ, Iouis & Mercurij; Martis, & Venetis. Quandocumque igitur ti Planetæ, vel corpore iunguntur, vel de quadtato, aut de pposito se respiciunt, magni quidam effectus expectandi sunt rea aëris mutationem; præsertim si Luna sese immisceat, :que ab vno ad alterum defluat. Et Saturni quidem cum Sole ongressus adducit aëris turbulentiam, frigus maximum, si temporis tatio id petat, in signis tetters nebulas: in aqueis plu- ias, & congruenti tempore, niues; præsertim si Saturnus erit dispositor præcedentis luminarium conjunctionis, aut ppositionis. Iouis, & Mercurij congressus, quadratus, aut ppositio adducit ventos magnos, terræ motus, eradicationes ar- orum, ædisiciorum, & similium. Tandem Martis & Venetis onuenientia gignit imbres, grandines, coruscationes, toni- rua cum fructuum pernicie. Hæc, inquam, tria genera aperi- onis portarum semper sortiuntur suum effectum, minorem uidem quando inuicem conjunguntur, maiorem, quando pponuntur, & maximum, quando intercedit Luna, Venus, ut Mercurius, ita vt eorum aliquis defluat à leui ad pondero- am; vt si Luna defluerer à Sole ad Saturnum (aut Mercurius, ui ex se significator est pluuiæ) tunc enim magna imbrium opia expectanda erit, præsertim si eorum aliquis sit rettogra- us, aut si planeta retrogradus alteri portas aperientium cor- ore jungeretur. APHÆNETÆ Græcè dicuntur stellæ absconditæ synodicè ob < 237.> olem vicinum, cuius radijs earum fulgor extinguitur. APHETA, hoc est dimissor dicitur apud Græcos Vitæ dator < 238.> Arabibus Hileg, seu Hylech; estque apud Astrologos luminare, lanera, aut alius locus in Coelo, qui in genituris vitæ domi- gium sortiatur. Et benè quidem affectus, robustus, in bono- um aspectu, vitam robustam, diuturnam, validam, pau- isque ægritudinibus obnoxiam pollicetur: malè constitutus, ebilis, in malorum dignitatibus, seu eorum hostili radio in- :status, mala affert in vita, & quandoque interitum, si dire- tione perueniat ad locum Anæreticum, hoc est abscissorem. Quæ autem sint loca Anæretica, dictum est in V. anæreta. Por- ò quinque tantum significatores ponit Ptolemæus, qui sortirà possint virtutem Aphæticam: luminare conditionarium; So- :em nempè de die, Lunam de nocte: Planetam, qui plures D ij

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MATHEMATICVM. 51 Never, or almost never, do they fail, as experience bears witness, but they always obtain a most certain effect; and this is in the conjunctions or irradiations of the planets. And this is especially observed in the planets that are rulers of opposite houses, such as Saturn and the Sun (for Aquarius, the domicile of Saturn, is opposed to Leo, whose ruler is the Sun, and so of the rest), Saturn and the Moon, Jupiter and Mercury; Mars and Venus. Whenever, therefore, these planets either are joined bodily, or regard one another by square or opposition, some great effects are to be expected, especially concerning the change of the air; particularly if the Moon takes part in it, and passes from one to the other. And indeed the conjunction of Saturn with the Sun brings about turbulence of the air, very great cold, if the season of the year require it, in earthy signs fogs; in watery signs rains, and in suitable weather snow; especially if Saturn be the disposer of the preceding conjunction or opposition of the luminaries. The conjunction, square, or opposition of Jupiter and Mercury brings great winds, earthquakes, uprooting of trees, buildings, and the like. Lastly, the conjunction of Mars and Venus produces rains, hail, flashes of lightning, thunder, with destruction of fruits. These, I say, three kinds of opening of the gates always obtain their effect: a lesser one, indeed, when they are joined to one another; a greater, when they are opposed; and the greatest, when the Moon, Venus, or Mercury intervenes, so that one of them passes from light to weightiness; as if the Moon passed from the Sun to Saturn (or Mercury, who of himself is a significator of rain), then indeed a great abundance of showers is to be expected, especially if one of them be retrograde, or if a retrograde planet be joined in body to another of the gate-openers. APHÆNETÆ are called in Greek the hidden stars, when they are synodically concealed by reason of the neighboring Sun, by whose rays their brightness is extinguished. < 237.> APHETA, that is, dismissor, is called among the Greeks the giver of life; among the Arabians Hileg, or Hylech; and for astrologers it is a luminary, a planet, or some other place in the heaven which in nativities obtains dominion over life. When well placed, strong, and in a good aspect, it promises a robust, long, vigorous life, and one subject to few illnesses; when badly constituted, weak, in the dignities of malefics, or oppressed by their hostile ray, it brings evils in life, and sometimes death, if by direction it reaches the Anaretic place, that is, the cutting-off place. What places are Anaretic has been said in V. anæreta. Moreover, Ptolemy sets down only five significators that may obtain the virtue of Aphæta: the conditionary luminary; namely, the Sun by day, the Moon by night: the planet which has the greater number of...

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52 LEXICON prærogatiuas obtinet in locis luminarium, Ascendentis, partis fortunæ, & præcedentis luminarium conjunctionis, aut oppositionis, & ipsam partem fortunæ, seu horoscopum luna-rem de nocte: si modò reperiantur in locis idoneis, hoc est in Ascendente, decima, vndecima, nona & septima domibus videlicet, quæ aut sint ipse horoscopus, aut cum eo aliquam habent familiaritem, & aspectum. Hinc duodecima, & octa-ua, quia nullam cum horoscopo connexionem habent, & adhuc vaporibus è tertia emergentibus sunt implicatæ, ideò ab hoc negotio excluduntur: vnde si in iis reperiatur aliquis significator, ad quem aliàs de iure vitæ prorogatio pertine-ret, is præter mittitur, & sumitur alius ex ordine succedens; modò is etiam in locis aphæticis reperiatur: alioquin, si nullus ex quatuor supradictis idoneus fuerit repertus, assumendus est ipse horoscopus, & Linea orientalis in vitæ prorogationem; qui nihilominus semper, & vtcumque sit generalem habet vi-tæ, & valetudinis significationem. Quoad planetam potiores dignitates obtinentem in locis principalibus Genituræ modo enumeratis, aduertunt aliqui ipsum, præter idoneum cæli si-tum, debere esse insignitum optimis prærogatiuis, adhoc vt vice luminarium aphætica dignitate gaudere possit, nimirum vt sit in Angulis, plenus lumine, cursu velox, atque in suis dignitatibus essentialibus. Alij ab hac prærogatiua excludunt malesicos ob suam malignitatem, & Mercurium ob naturam eius versatilem, ac luminis imbecillitatem, & solos beneficos admittunt, eosque non absolutè, sed Iouem in Genituris viro-rum, Venerem autem in foeminarum, nec quidem frequenter, sed rarò admodum & cum sunt in genitura nimium potentes, luminaribus vice versa debilibus, & afflictis: Alioquin semper aut pars fortunæ de nocte, aut horoscopus de die sumendum præcipientes. 239. APHALIVM Græcè dicitur punctum illud in quo tellus, aut sidus aliquod maximè distar à Sole: sicut Perihelium punctum, in quo à Sole quam minimè distat. 240. APHERÆTÆ appellantur à Græcis planetæ minuti numero, quando videlicet efficiuntur tardiores, & eorum motus diurnus est minor motu medio: de qua re vide Maginum, aliosque in Isagog. 241. APHETES, teste Valla, dicitur planeta retrogradus, cum mouetur suo motu, proprio ab ortu ad occasum, hoc est à con-sequentibus in antecedentia signa. Posthetes autem, cùm est di-rectus, & mouetur ab occasu in ortum semper ad consequen-tia signa. 242. APHÆVIMIS Græcobarbar, dicitur in Sphæra barbarica pri-

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52 LEXICON pre-eminence is obtained in the places of the luminaries, of the Ascendant, of the Part of Fortune, and of the preceding conjunction or opposition of the luminaries, and the Part of Fortune itself, or the lunar horoscope by night: provided they are found in suitable places, that is, in the Ascendant, tenth, eleventh, ninth, and seventh houses, namely those which are either the horoscope itself, or have some familiarity and aspect with it. Hence the twelfth and eighth, because they have no connection with the horoscope, and are still involved with vapors emerging from the third, are excluded from this business: whence if in them some significator is found to which, by right, the prolongation of life would otherwise belong, it is passed over, and another succeeding in order is taken; provided that this one also is found in aphhetic places: otherwise, if none of the four aforesaid should be found suitable, the horoscope itself, and the eastern line, are to be taken for the prolongation of life; which nevertheless always, and in whatever way, has a general signification of life and health. As to the planet holding the higher dignities in the principal places of the nativity just enumerated, some note that it must, besides a suitable position in the heavens, be distinguished by the best prerogatives, so that it may be able to enjoy aphhetic dignity in place of the luminaries, namely, that it be in the angles, full of light, swift in course, and in its essential dignities. Others exclude the malefics from this prerogative because of their malignity, and Mercury because of its changeable nature and weakness of light, and admit only the benefics; and not absolutely so, but Jupiter in nativities of men, and Venus in those of women, nor even frequently, but very rarely, and when in the nativity they are too powerful, while the luminaries, on the other hand, are weak and afflicted: otherwise always prescribing either the Part of Fortune by night, or the horoscope by day, to be taken. 239. APHALIVM is said in Greek of that point at which the earth, or any star, is farthest from the Sun: as Perihelium is the point at which it is least distant from the Sun. 240. APHERÆTÆ are called by the Greeks the planets when they are lessened in number, namely, when they become slower and their daily motion is less than the mean motion: on this matter see Maginus and others in the Isagoge. 241. APHETES, according to Valla, is said of a retrograde planet, when it moves by its own motion from east to west, that is, from the following to the preceding signs. Posthetes, however, when it is direct, and moves from west to east, always toward the following signs. 242. APHÆVIMIS, Greco-barbarous, is said in the barbaric Sphere pri-

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MATHEMATICVM. 53 nus Decanus Leonis existens sub dispositione Saturni, atque deò habet significationem crudelitatis, violentiæ laboris, udaciæ, libidinis, &c. APHVT in Sphæra barbarica dicitur tertius Decanus Virgi- < 243.> is sub dominio Mercurij senecturis, pigritiæ, debilitatis embrotum ex morbo, arbores vellendi, ciuitates deuastandi. < 244.> APIS, seu Musca sidus in cælo ad polum Antarcticum non apridem detectum habens quatuor stellas sub signo Sagitta- < j. Item.> APVS dicitur aliud sidus nouum ad polum item Antarcticum, < 245.> instans stellis 12. insimæ notæ, alio nomine Manucodiata, & ud nos Paradisi auis. APLANES Græcè idem sonat ac non discurrens, & eo nomi- < 246.> significantur stellæ fixæ ob contrariam planetis conditio- em, quasi minimè errones, & discurrentes similiter ab iis. APLANE dicitur Firmamentum, & Orbis in quo stellæ hu- < 247.> smodi fixæ sunt. APOCASTAIS apud Cræcos idem sonat ac revolutio integra < 248.> leris, qua toto circulo confecto redit ad idem punctum vnde oueri coepit, quæ & periodus à nostris dicitur. At si post infectum circulum vlterius revoluatur donec conjungatur al- < 249.> ri astro, dicitur synodus: transitus autem ab arcu, aut puncto iquo insigni ad aliud dicitur Parados. APODEATE. Hoc vocabulo vtitur Ptolemæus cap. de Monst. < 250.> versione Arab. dicens, quod quando fortunæ fuerint apo- ate de luminatibus, & ipsa cadentia, vel ascendens non as- cientia, natus erit permutatæ figuræ. APOGÆVM Græcè dicitur pars summa Eccentrici, aut Epi- < 250.> cli Planetarum, Arabicè in qua constituti, eleuatiores, < 250.> riores, validioresque fiunt: vt Sol hoc tempore est in suo pogæo circa sextum gradum Cancri, in quo distat à terra < 250.> illariis 4588,60. cum tamen in Perigæo, hoc est in opposi- < 250.> Augis (in quo reperitur cùm est in Capricorno) non distet entro telluris, nisi milliar. 4272480. ita vt tota quantitas < 250.> ingationis Apogæi à Perigæo, sicque regionis circà quam < 250.> utiatur Sol cùm ab vno in aliud transit, per lineam rectam < 250.> milliar. 316480. Portò Apogæa, & Perigæa planetarum < 250.> n sunt semper fixa in eodem loco, sed successu temporis < 250.> iantur, cùm obseruatum sit ea secundù mordinem signorum, < 250.> iduo sed tamen lentissimo, & penè insensibili moru cieri, < 250.> æ omnia irregularitatem pariunt in plurimis, ac præcipuè in < 250.> o motu planerarum, qui in Apogæis euadunt tardiores, ve- < 250.> iores in perigæis, & maximè Sol: qua de re vide Magnum < 250.> Tabulis secundarum mobilium, & alibi sæpe. D iii

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MATHEMATICVM. 53 now the Decan of Leo, existing under the disposition of Saturn, and therefore has the signification of cruelty, violence, labor, boldness, lust, etc. APHVT in the barbaric Sphere is said to be the third Decan of Virgo under the dominion of Mercury, of old age, sloth, weakness, a miscarriage from illness, uprooting trees, devastating cities. APIS, or the star Musca in the sky near the Antarctic pole, lately discovered, having four stars under the sign Sagitta- APVS is said to be another new star also near the Antarctic pole, with 12 stars of the lowest magnitude, otherwise called Manucodiata, and with us, the bird of Paradise. APLANES in Greek means the same as non-discurrens, and by that name are signified the fixed stars, because of their condition contrary to the planets, as it were least wandering and moving likewise away from them. APLANE is called the Firmament, and the sphere in which such fixed stars are. APOCASTAIS among the Greeks means the complete revolution of the circle, by which, the whole circle having been completed, it returns to the same point from which it began to turn, which by our people is also called a period. But if, after the completed circle, it is revolved further until it joins another star, it is called a synod: the passage, however, from an arc or some notable point to another is called a Parados. APODEATE. Ptolemy uses this word in chap. de Monst. in the Arabic version, saying that when the fortunes have been apo- deate from the luminaries, and they themselves are descending, or the ascendant not ascending, the native will be of a changed figure. APOGÆVM in Greek is called the highest part of the eccentric, or epi- cycle of the planets, in Arabic in which, when placed, they become more elevated, stronger, and more powerful: as the Sun at this time is in its apogee around the sixth degree of Cancer, in which it is distant from the earth milliar. 4588,60. whereas in the perigæum, that is, in the opposite of the auge (in which it is found when it is in Capricorn) it is not distant from the center of the earth, except milliar. 4272480. so that the whole amount of the elongation of the Apogee from the Perigee, and thus of the region around which the Sun revolves when it passes from one to the other, in a straight line milliar. 316480. Moreover, the Apogees and Perigees of the planets are not always fixed in the same place, but are changed in the course of time, since it has been observed that according to the order of the signs, they are moved by a continuous yet very slow and almost imperceptible motion, and these cause irregularity in many things, and especially in the motion of the planets, which become slower at their Apogees, faster in their perigees, and especially the Sun: on which account see the Great Tables of the secondary mobiles, and elsewhere often. D iii

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54 LEXICON 251. APOGAE dicti sunt venti subterranei, seu è terra spirantes atque in mare præcipiti cursu ruentes, qui propterea impe- tuosi sunt, & tempestatum auctores: de his vide Plin. lib. 2. cap. 43. 252. APOLLO dicitur prior Geminorum, alio nomine Castor: si- dus in cælo olim in Geminis in primo mobili, nunc autem in Cancro constitutum. Cuius præcipua stella in capite Arabic. Rus Algense dicta secundi honoris de natura Martis & Mercu- rij, ac patum Saturni, est nimium procellosa, ventos suscitat, & aërem turbat. 253. APORRHÆA dicitur Luna cum à planetæ, vel stellæ alicuius conjunctione recedit, nullique alteri applicat: à Latinis dici- tur cursu vacua, & feralis. 254. APORROGAS Græcè audiunt coruscationes quædam, seu po- rius aërij quidam defluxus, atque accensi vapores, qui ad ter- ram labentes stellarum casus imitari videntur, vnde & vulgo stellæ cadentes vocitantur. 255. APOTELESMA Græcè idem sonat, ac effectus horoscopi, hoc est quicquid ex Astrorum conuenientia, & mutuo respectu in natali cuiusque efficitur boni, vel mali, ac coeli ipsius consti- turio indicant. Hac de re extant Apotelesmatum Ptolemæi libri. 256. APOTOME apud Geometras vocatur ea pars figuræ rationa- lis, à qua altera rationalis auferatur à potentia tantum com- mensurabilis existens ipsi toti, quæ proinde irrationalis erit vt docat Euclides lib. 10. Propos. 74. Hinc 257. APOTOME etiam dicitur in Musica semitonium maius, quod opponitur Diesis, & est toni reliqua pars, qua ipse tonus Die- sis, & semitonium minus superat. 258. APPARENTIÆ vulgò audiunt apud Astronomos, quæ apud Græcos Phanomena, appellantur ostenta videlicet, & insolita quæ in sublimi generantur ex accensis vaporibus, idque siue substantiam & corpus habeant, vt crinitæ, trabes, iacula, sidera, discutentia &c. siue nullam prorsus, sed ex collisione visus fiant, vt Iris, atex, halones, virgæ: de quibus omnibus suis in locis. 259. APPLICATIO apud Astronomos appellatur progressio plane- tæ leuioris, existentis tamen intra quantitatem orbis alterius ponderosi, quousque eidem corpore iungatur; ad differen- tiam defluxus, qui est separatio eiusdem à coniunctione partili cum planeta ponderoso, atque elongatio ab illo; ita tamen, vt adhuc maneat intra eius orbem: & in has species diuiditur as- pectus Platicus. 260. Quatuor autem modis contingere potest huiusmodi applica-

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54 LEXICON 251. APOGAE are called subterranean winds, or those blowing out of the earth and rushing with a headlong course into the sea; and therefore they are violent, and authors of storms: concerning these see Pliny, book 2, chap. 43. 252. APOLLO is said to be the first of the Twins, by another name Castor: a star in the heavens, once in Gemini in the first moving sphere, but now placed in Cancer. Its principal star in the head, called in Arabic Rus Algense, of the second honor, of the nature of Mars and Mercury, and partly of Saturn, is excessively stormy; it stirs up winds and disturbs the air. 253. APORRHÆA is said of the Moon when it withdraws from a conjunction with a planet, or with some star, and applies to none other: by the Latins it is called void of course, and feral. 254. APORROGAS in Greek denotes certain flashes, or rather certain airy outpourings and ignited vapors, which, falling toward the earth, seem to imitate the falling of stars, whence they are commonly called falling stars. 255. APOTELESMA in Greek means the same as the effect of the horoscope, that is, whatever is produced for good or evil from the agreement and mutual aspect of the stars in anyone’s nativity, and what the constitution of the sky itself indicates. On this subject there are the books of Ptolemy’s Apotelesmata. 256. APOTOME among geometers is called that part of a rational figure from which another rational part is taken away, being only commensurable by power with the whole itself, which therefore will be irrational, as Euclid teaches, book 10, proposition 74. Hence 257. APOTOME is also called in Music the greater semitone, which is opposed to the Diesis, and is the remaining part of the tone, by which the tone itself exceeds the Diesis and the lesser semitone. 258. APPARENTIÆ are commonly called by astronomers those things which among the Greeks are called Phanomena, namely portents and unusual things generated aloft from ignited vapors; and this whether they have substance and body, as comets, beams, lances, stars, darting lights, etc., or whether they have none at all, but arise from the collision of sight, as the rainbow, atex, halos, rays: concerning all of these in their proper places. 259. APPLICATIO among astronomers is the advance of a lighter planet, while still existing within the quantity of the orbit of another heavier one, until it is joined to it by bodily conjunction; in distinction from defluxus, which is the separation of the same from a partial conjunction with a heavy planet, and its elongation from it, yet still in such a way that it remains within its orbit: and the Platic aspect is divided into these species. 260. But this kind of application can occur in four ways.

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MATHEMATICVM. 55 cio. Primò, cùm vterque planeta est directus, sed tamen co- rum leuior, cùm sit motus velocioris existens in paucioribus gradibus vadit, & pertingit ad gradum, in quo est planeta pon- derosior. Secundò cùm vterque est retrogradus, & leuior, qui est in pluribus partibus, retrocedendo pertingit ad tardiorem. Tertio, quando planeta anterior motu directo applicat sub- sequenti retrogrado. Quarto tandem cum planeta leuior retro- gradus existens in pluribus gradibus retrogradiendo occurrit alteri tardiori, item retrogrado existenti in paucioribus. Toti- dem modis eriam contingere potest defluxus: de quo suo loco. APSIS Antiquis audiebat ima pars Eccentrici, seu Epicycli opposita Augi. Vide in V. Absis. APVLIN excorrupto vocabulo Græco dicitur ab aliquibus 261. caput præcedentis Geminorum Apollo. Arabicè Ras Algenze, vel potiùs Elgeanize. AQ 262. AQVA Elemenrum omnibus) si vnam Terram excipias) pon- derolius, ac vilius, natura sua frigida, & humida, sed, v[er]r aër ob suam fluxibilitatem facilè alrerabilis: sic dicta, quasi æqua æquat enim Tertæ rotunditatem; & cum ea vnum globum, qui est totius Mundi centrum constituit: Vel sanè quasi æqua subintelligitur, vnumus. Quandoquidem ex eius recessu in lo- cum vnumi apparuit arida, & tellus habitationi, & vitæ ani- mantium idonea facta est. Nam eius locus naturalis deberet esse supra terram, proindeque totam circumdare, at circum- plecti, eo modo, quo nunc aër totum terræ, aquarumque am- bitum circumplectitur; sicque ab initio, rerum id ordine po- stulanre à summo Opifice factum est; sed postea ad diuinum illud imperium: Congregentur aqua in locum vnum, & appareat arida. Mox scissa terra sinus dedit amplissimos in quos aquæ ptolaberentur, ac terrex partes, quæ sinus illos implebant, in vnum congestæ atque in montes elatæ, opportunam animan- tibus habitationem dedere Quod vel inde manifestum sit, quia communis Nautarum sensus est plurimis experimentis proba- tus, dicubi tantam esse Maris profunditatem, quanta Montium altitudo, quæ sibi inuicem correspondeant. Hoc tamen non officit, quin duo hæc elemenra vnum corpus sphæricum, & si rude, scabrumque constituant; nam perinde sunt in eo mon- tium prominentiæ, ac tuberculi illi qui obseruantur in Aurantij pomo, qui profectò eius rotunditati minimè officiunt, vt alias obseruauimus. Est autem aqua natura sua dulcissima seu potius insipida, 264. vetùm in mari continuo motu, & Solis radiis exurentibus, sit salsa, & amara, quandoquidem salsedo, vt docet Aristoteles, D iiij

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MATHEMATICVM. 55 cio. First, when both planets are direct, but the lighter one, since it has a swifter motion and moves through fewer degrees, reaches the degree at which the heavier planet is. Second, when both are retrograde, the lighter one, being in more parts, in retrograding reaches the slower one. Third, when the preceding planet, with direct motion, comes into conjunction with the following retrograde one. Fourth, finally, when the lighter planet, being retrograde and in more degrees, in retrograding meets the other, slower one, also retrograde, and existing in fewer degrees. In as many ways a defluxus can also happen, of which in its proper place. APSIS. Among the ancients, the lower part of the eccentric, or epicycle, opposite the auge, was called apsis. See under V. Absis. APVLIN, from a corrupted Greek word, is called by some 261, the head of the preceding Gemini, Apollo. In Arabic, Ras Algenze, or rather Elgeanize. AQ 262. AQVA. This element, surpassing all others in weight if you except one Earth, is by nature cold and moist, but water, because of its fluxibility, is easily alterable; it is so called as if from æqua, for it makes the roundness of the Earth equal; and with it it constitutes one globe, which is the center of the whole world: or indeed as if æqua were understood, one. For from its recession into one place the dry land appeared, and the earth became fit for the habitation and life of living creatures. For its natural place ought to be above the earth, and therefore to surround the whole earth and waters, embracing them in the manner in which now the air encloses the whole circuit of the earth and waters; and thus from the beginning, according to the order of things required by the Supreme Maker, it was done; but afterwards by that divine command: Let the waters be gathered into one place, and let the dry land appear. Soon the earth, split open, gave very wide hollows into which the waters flowed, and the parts of the earth that filled those hollows, being gathered together into one body and raised into mountains, provided a suitable dwelling for living creatures. This is even manifest from the common observation of sailors, confirmed by many experiments, that in some places there is such a depth of the sea as there is height of mountains, corresponding to one another. Yet this does not prevent these two elements from constituting one spherical body, though rough and uneven; for the prominences of mountains in it are no different from those little bumps observed on an orange, which certainly do not prevent its roundness, as we have noted elsewhere. Now water, by its nature, is sweetest, or rather tasteless; nevertheless, in the sea, through continual motion and the burning rays of the sun, it is salty and bitter, since saltiness, as Aristotle teaches, D iiij

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LEXICON fit per calorem, quo mediante in humoribus pars dulcis, & insipida separatur, & pars terrestris, quæ remanet aduritur & permiscetur cum humoribus aquosis, & quamuis mare continuo aquarum accessu ex imbibibus, ac fluuiis dulcissimis renouetur, semper tamen eadem salsedine gauder ob olis radios perpetuo exurentes, qui proinde successu temporis mare totum absumerent, ni perpetui sones, & alumina in mare continuo restagnantes, hanc aquarum diminutionem compensarent. Et hinc est etiam, cur ex tanto aquarum accessu nunquam mare redundet. 265. Verùm hic magna exurgit dubitatio, quamobrem etiam lacus etiam Solis radiis exposui, non sint falsi? ad quod respondemus, quod lacus non ià apicantur, neque tot motibus in proprio alueo agitantur, ac mare: quamuis etenim multi inueniantur lacus amplissimi, solaribus radiis perpetuò exposiri & maximè agitati, ac turbibi, quia tamen agnatio illa non est perpetua, vt in mari, ideò partes illæ terrestres aquis admixtæ illicò perunt fundum, & radij solij idcircò eas adurere, & per consequens salsas reddere pauco temporis interuallo non possunt. Non negauerim tamen vbi Solis radij maximè feruidi sunt, ac lacus amplissimi, vt sub Zona torrida, ibi eos etiam aliqua salsedine præditos esse, vt Historici passim testantur, verùm non tanta, vt mare, quippe non tot motibus quatiuntur. 266. Hinc in mari, seu Oceano, sex sunt motus omninò diuersi. Primus alterationis qui fit à radijs solaribus: secundus ventorum vi concitatus: tertius motus deorsum, & hi tres conveniunt etiam suo modo lacubus, & fluminibus: quartus Oceani proprius vniuersitatis ab Oriente in Occidentem, qui dicitur longitudinis: quintus in latitudine à Polis ad æquatorem: sextus tandem altitudinis, seu intumescentiæ, qui vocatur æstus, & est cæteris insignior, & euidentior, maximè in Oceano ubi, vt inqui Keplerus, spatiosa est reciprocationis libertas. 267. Porrò de motu vniuersitatis testantur omnes ferè Naucleri qui ex Hispania ad Americam, vicinasque insulas soluunt, vel inde in Palæstinam, aut ex Anglia in Hyberniam aliasque oras, siue Orientaliores, siue Occidentaliores pergunt. Constat enim illis etiam cessante quocumque vento, aut æquali vi impellente, citiùs ad Occidentales partes, seriùs ad Orientales navigari: ita vt ex Hispania in Mexicum nauigantes rectâ, perficiant iter vna, vel ad summum duobus circiter mensibus: remeantes verò insumant quatuor, modò quinque, modò etiam sex menses, quin vt impetum aquarum eos ad Occidentem impellentium deuitent, opus est illi obliquè iter instituere versus Septentrionem, indeque ventorum exsufflan-

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LEXICON caused by heat, by which means, in the humors, the sweet and insipid part is separated, and the earthy part, which remains, is burned and mixed with the watery humors, and although the sea is continually renewed by the access of waters from springs and sweetest rivers, it nevertheless always rejoices in the same saltness, because the rays of the sun are perpetually burning it, and would therefore in the course of time consume the whole sea, were it not that the perpetual sands and alumina continually resting in the sea compensate for this diminution of the waters. And hence also comes it that, from so great an influx of waters, the sea never overflows. 265. But here there arises a great doubt, why even lakes, even when exposed to the rays of the sun, are not made briny? To this we respond that lakes are not so agitated, nor stirred by so many motions in their own basin, as the sea is. For although there are found many very large lakes, perpetually exposed to solar rays and greatly agitated and disturbed, yet because that agitation is not perpetual, as in the sea, therefore those earthy parts mixed with the waters immediately sink to the bottom, and the sun’s rays on that account cannot burn them and consequently render them salty in a short interval of time. I would not deny, however, that where the sun’s rays are exceedingly fierce and the lakes very large, as under the Torrid Zone, they are there also endowed with some saltness, as historians everywhere testify, but not so much as the sea, since they are not shaken by so many motions. 266. Hence in the sea, or Ocean, there are six motions altogether different. The first is of alteration, which is caused by the rays of the sun; the second, stirred up by the force of the winds; the third, a downward motion; and these three also belong in their own way to lakes and rivers. The fourth is proper to the Ocean, a motion of universality from East to West, which is called lengthwise; the fifth, in latitude from the Poles to the equator; the sixth, finally, of height, or swelling, which is called the tide, and is more remarkable and evident than the others, especially in the Ocean where, as Kepler says, there is spacious freedom of reciprocity. 267. Moreover, all the shipmasters almost testify concerning the motion of universality who sail from Spain to America and the neighboring islands, or from there to Palestine, or from England to Ireland and other shores, whether more eastern or more western. For it is established that for them, even when any wind ceases, or an equal force impels them, one sails more quickly toward the western parts, more slowly toward the eastern: so that those sailing from Spain to Mexico, proceeding in a straight course, complete the journey in one, or at most about two months; but on returning they spend four, sometimes five, sometimes even six months, unless they wish to avoid the pressure of the waters driving them westward, in which case it is necessary to set the course obliquely toward the North, and thence by the blowing of the winds...

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MATHEMATICVM. 57 ium auxilium adipisci: Idipsum experiuntur Lusitani tendentes ad Indias Orientales etiamsi secundis alioqui ventis fruant. Cuius tei plurima afferunt experimenta Trimarchus lib. Moscor. disp. 1. sect. 6. Adrianus, Metius, & Furnerius lib. Hydrographia cap. 23. Caulam autem huius motus ascribit lem Turnerius Solis ardori; humores, atque halitus ad se erpetuò trahentis: vt etiam quintum, quem diximus mo- im, à polis ad æquatorem; & eo maximè intra tropicos, ib via scilicet Solis, vbi violentior apparet vterque motus eplerus eum refundit in Lunam, aquas, & humores omnes d se magnetica vi prolectantem. Sed Arabes, & cum illis vicomercatus longè verosimilius id tribuunt motui primi mo- nilis rapientis secum omnes inferiores sphæras: atque adeò non modò cælos inferiores, sed & Aërem, & Oceanum; li- et hic quia cæteris sphæris remorior, sua vi, & aquarum trafficie aliquantò magis resistat, quam aër: hic magis, quam cæli superiores, vt alias adnotauimus. Cui opinioni nec refra- gatur Resta de Meteoris lib. 3. tr. 1. cap. 16. nec Mastrius ibid. mast. 4. num. 248. Quoad quintum verò motum, qui dicitur latitudinis à polis < 268.> dæquatorem, eum jamptidem agnouit Arist. 1. Meteor. cap. text. 6. & sequuti sunt Alexander Aphrodisæus D. Thomas, Vicomercarius, Nyphus, & alij. Cuius causa alia sanè non est, vt benè discurrat Turnerius, quam Solis calor, qui dum sem- pet intra tropicos mouetur, aquas ad se allicit, & quæ sub llis sunt, paularim absumit: qui sit, vt ad earum libtamentum exæquandum, aquæ hincinde à Septentrione, & Austro versus æquatorem ruant; præsertim, si verum est quod ait idem Turnerius, Sole in Capricorno existente, aquas, quæ intrà tropicos sunt, transire æquatorem, & naturali impetu ver- sus tropicum fluere; quod ipsum experiri est Sole existente in Cancro, nam illuc aquæ omnes accurrunt. Aristoteles ta- men, loco citato, hunc motum tribuit Aluminum multitudi- ni, & magnitudini, in Mæotin, & in Euxiuum mare sese exonerantium. Sextus denique motus Oceani est qui dicitur fluxus & refluxus spatio vigintiqninque circiter hotarum omninò in Lunam refundendus: de quo vide in Verbo Ampotim. Ex aquæ continuo motu Plotinus Philosophus, alijque < 269.> eam animatam dixêre. Quod fortassè non omninò incredi- bile existimauetim, si non de anima rationali, neque de sen- sibili, aut vegetabili, sed de alia quadam alterius speciei, setmosit, quam jute dixetis locomotticem, & ea forsan cor- pora cælestia informantur, quæ illis intrinsecam vim sese

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MATHEMATICVM. 57 they may obtain the same help: the Portuguese experience this as they head toward the East Indies, even when they enjoy favorable winds otherwise. Very many experiments of this matter are brought forward by Trimarchus, lib. Moscor. disp. 1. sect. 6; Adrianus, Metius, and Furnerius, lib. Hydrographia, cap. 23. But Turnerius ascribes the cause of this motion to the ardor of the sun, which continually draws to itself the humors and vapors: thus also the fifth motion, which we have said is the motion from the poles to the equator, and especially within the tropics, that is, by the path of the sun, where both motions appear more violent. Kepler refers it to the moon, attracting the waters and all humors to itself by a magnetic force. But the Arabs, and with them Vicomercatus, attribute it much more probably to the motion of the first mobile, which draws along with it all the lower spheres; and thus not only the lower heavens, but also the air and the ocean: although here, because it is slower than the other spheres, it resists somewhat more by its own force and by the disturbance of the waters than the air does; and the air more than the higher heavens, as we have noted elsewhere. This opinion is not opposed by Resta de Meteoris, lib. 3, tr. 1, cap. 16, nor by Mastrius, ibid. mast. 4, num. 248. As to the fifth motion, however, which is called the latitude from the poles to the equator, Aristotle had long ago recognized it, 1 Meteor. cap. text. 6, and after him Alexander Aphrodisaeus, St. Thomas, Vicomercarius, Nyphus, and others. Its cause is in truth no other, as Turnerius rightly argues, than the heat of the sun, which, while it moves continually within the tropics, attracts the waters to itself and gradually consumes those beneath it; the result is that, in order to equalize the reduction of their level, waters from here and there, from the North and the South, rush toward the equator; especially if what the same Turnerius says is true, namely that when the sun is in Capricorn the waters that are within the tropics cross the equator and flow by natural impulse toward the tropic; this is what can be observed when the sun is in Cancer, for all the waters then rush there. Aristotle, however, in the passage cited, attributes this motion to the multitude and magnitude of the Alani discharging themselves into the Maeotic and the Euxine Sea. The sixth and final motion of the ocean is that which is called ebb and flow, in a space of about twenty-five hours; it must altogether be referred to the moon: see under the word Ampotim. From the continuous motion of the water, Plotinus the philosopher and others said that it was animated. Which perhaps would not be judged altogether incredible, if it were not spoken of a rational soul, nor of a sensitive or vegetative one, but of some other soul of a different species, which you would rightly call a locomotive soul, and with this perhaps the heavenly bodies are informed, which have in themselves that intrinsic power to move themselves.

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58 LEXICON inouendi tribuat; quemadmodum de spongia aliisque rebus in natura tertij ordinis multi senserunt. Vel sanè dictum referri potest ad animam quandam vniuersalem speciei item diuersæ vniuersum hoc informantem quod multi Philosophorum tum ex antiquis, tum ex recensioribus opinati sunt, comparatione facta Macrocosmi ad Microcosmum, in quo aqua perinde se habet ac sanguis in homine; qui proinde vt hanc cum aqua analogiam seruet, & ipse ad Lunæ motum augeatur, vt obseruauit inter cæteros Plinius, & mouetur circulariter circa cor, vt tradunt Anatomia peritiores. Quamquam id ne hoc quidem euincit in sententia eorum qui sanguinem minimè animatum volunt, sed aiunt, contineri in venis tanquam in vasis. Vtcumque sit (quod parum refert) certum est aquas siue ab intrinseco, siue ab extrinseca vi continenter moueri, motuque hoc suo terram, quæ in mundi centro quiescit paulatim corrodere, & complanare. Ita vt, postquam ad perfectam rotunditatem perduxerit sit ipsam vndique vallatura, ex quo demum sæculo huic finis paretur: vt notat Blancanus, vel ex hoc probans Mundum neque æternum fuisse, neque in æuum duraturum: Quod tamen non placet Ricciolo. 70. Cæterum aquam terra esse minorem multi Recensiores existimarunt. Inter hos Claius, Fernelius, Contarenus, Piccolomineus, & Auersa, aiuntque eandem proportionem habere ad terram, quam habet 1. ad 2190. additque Piccolomineus, se diligentissimè considerasse sphæras, quæ side- liores reperiri potuerunt in repræsentando terram & aquam, & comperisse, superficiem terræ discoopertæ longè maiorem esse superficie aquæ. Antiqui tamen majorem astruebant, quibus ego ex proportione tantum sphærarum motus, libenter adstipularer. 271. Aqvarius signum vndecimum in Zodiaco, domicilium Saturni, sic dictum ab Aquario sidere quod ei suberat tempore Prolemai, sed nunc ob motum proprium octauæ sphæræ præcessit, sicut & cæteri Asterismi, estque intra gr. 22. Aquarij primi mobilis, & gr. 15. Piscium. Est natura sua calidum, & humidum, triplicitatis aërea, quoad effectus autem frigidum, ventosum, aquosum maximè in eius parte Australi, quæ humores, & niues facit. 272. Aqvea signa sunt Cancer, Scorpio, Pisces, quæ constituunt trigonum aquem frigidum, & humidum, cuius Trigonocraatores sunt Mars, Venus, & Luna, quia signa foeminina sunt (Mars enim vt alibi obseruatum est foeminescit) &

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58 LEXICON should grant the power of setting in motion; just as many have thought concerning sponge and other things in the nature of the third order. Or else the said statement can be referred to a certain universal soul of the species, likewise of different species, informing this whole universe, as many philosophers, both among the ancients and among the more recent, have believed, by comparison of the Macrocosm with the Microcosm, in which water is related just as blood is in man; and therefore, so that it preserves this analogy with water, it too is increased according to the motion of the Moon, as Pliny noted among others, and is moved circularly around the heart, as those more skilled in anatomy report. Although even this does not prove the point in the opinion of those who want blood to be by no means animate, but say that it is contained in the veins as in vessels. However that may be (which matters little), it is certain that waters, whether by an intrinsic force or by an extrinsic one, are continually moved, and by this motion gradually corrode and level the earth, which rests at the center of the world. So that, after it has been brought to perfect roundness, it will everywhere surround it, after which at last an end will be made to this age: as Blancanus notes, thereby proving that the world has neither been eternal nor will last forever: which, however, does not please Ricciolo. 70. Moreover, many of the more recent writers have thought that water is smaller than earth. Among these are Claius, Fernelius, Contarenus, Piccolomineus, and Aversa, and they say that it has the same proportion to the earth as 1 has to 2190. Piccolomineus adds that he has considered most carefully the spheres, which could be found most faultlessly in representing earth and water, and has discovered that the surface of the uncovered earth is far greater than the surface of the water. The ancients, however, maintained the greater measure; to them I would gladly assent, if only on the basis of the proportion of the motion of the spheres. 271. Aquarius, the eleventh sign in the Zodiac, the domicile of Saturn, is so called from the star of Aquarius that was beneath it in the time of Ptolemy, but now, on account of the proper motion of the eighth sphere, it has moved ahead, as have the other asterisms. It lies within 22 degrees of Aquarius, the first movable sign, and 15 degrees of Pisces. By its own nature it is hot and humid, of the airy triplicity; in its effects, however, it is cold, windy, and watery, especially in its southern part, which produces vapors and snows. 272. The water signs are Cancer, Scorpio, and Pisces, which make up the cold and humid watery trigon, whose trigonocrators are Mars, Venus, and the Moon, because they are feminine signs (for Mars, as has been observed elsewhere, becomes feminine) and

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MATHEMATICVM. 39 hi tres planetæ in eis dignitates obtinent; & Mars quidem, & Luna de nocte, Venus autem interdiu; adeoque dicitur trigonus Occidentalis propter Martis, & Lunæ dominatum. Quæ aurem regiones, & oppida huic triplicitati subsunt: vide in Ptolemæo lib 2. cap 2. Aqvela, vultur volans sidus in cælo ad Borealem plagam < 273.> intra Galaxiam stellas habens iuxta Ptolemæum & antiquiores 3. At Keplero reste 11. licet Baierus ei tribuat stellas omninò 31. sed confundit cum eo Antinoum. Omnes autem hæ stellæ sunt de natura Martis, & Louis, inter quas splendida in scapulis secundæ magnitudinis Arabicè Alkastr. Hæc in Horoscopo dicit Pontanus quod facit feros, magnanimos, raptores, belligeros, mortis contemptores, sic enim canit; quibus Bella placem, & prada subacto ex hoste petita, Et spolijs vitam, & violenta agitare rapina: Nec dubiens etiam armatos incurrere in hostes, Nudi armos, morsemque velint pro lante pacisis. Quod si adhuc accesserit benignus radius Louis, subdit, quod erunt victores, & parriam decorabunt, ac defendent armis ac victorijs. At si Sarurnus, aur Mars quous modo astiterint, tunc facient quidem bellicosos, sed sub aliorum imperio. Idipsum confirmat Stadius. Oritur autem Romæ cum gradu ferè 24. Sagittarij. Aqvi lo Boreas ventus Septentrionalis lateralis Septenttioni < 274.> inclinans ad Ortum; sic dictus à vehementissimo, ac celerimo flatu, quasi aquilæ volarum imitati velis. Est de natura sua frigidus, & succus, salubris, aërem purgans, & pro ratione temporis grandinosus, ac niuosus. Accipirur sæpenumero pro ipso vento Septentrionali vno, ex quatuor Cardinalibus ob vicinitatem, atque effectuum similitudinem: de eo vide Plin. lib. 2. cap. 47. AR ARA Sacrarium, Thutibulum, Lar, sidus in cælo ad Au- < 275.> stralem plagam nobis inconspicuum: de quo Cicero de Na- tura deorum. Deinde Nepa cernes propter fulgens acumen Aram, quam flatu permulces spiritus Austri. Continet stellas seprem omnes de natura Veneris, & parum Mercurij, inter quas præcipua tertiæ magnitudinis in medio flammæ sita; quæ si in Horoscopo reperiatur (inquit Stadius) inclinat ad pietalem, ad sacerdoria capessenda, atque ad stu- dia sacrarum literarum, præsertim si bonum testimonium accesserit beneficarum: Ac verò in occasu cum malo radio

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MATHEMATICVM. 39 these three planets hold dignities in it; Mars indeed, and the Moon by night, Venus however by day; and therefore it is called the Western trigon because of the dominion of Mars and the Moon. What regions and towns are subject to this triplicity: see in Ptolemy, book 2, chapter 2. Aquila, the eagle, a flying constellation in the sky toward the northern quarter <273.> having stars within the Milky Way according to Ptolemy and the older writers, 3; but for Kepler 11, though Bayer assigns it altogether 31 stars, but he confuses Antinous with it. All these stars are of the nature of Mars and Jupiter, among which the bright one in the shoulders of the second magnitude is Arabicly called Alkastr. About this in the horoscope Pontanus says that it makes men fierce, magnanimous, plunderers, warlike, contemptuous of death; thus he sings: quibus Let me appease wars, and booty sought from a defeated enemy, And to live by spoils and to stir up violence by rapine: Nor do they hesitate even to rush against armed enemies, bare-armed, and they wish for death rather than peace with the lance. But if a benign ray of Jupiter should also be added, he says that they will be victors, and will adorn and defend their fatherland with arms and victories. But if Saturn, or Mars in some way, should be present, then they will indeed make men warlike, but under the power of others. Stadius confirms the same. It rises at Rome with a degree of about 24 Sagittarius. Aquilo, the north wind, a lateral northern wind inclining toward the east; so called from its most violent and swift blast, as if imitating the wings of an eagle by its sails. It is by nature cold and moist, wholesome, purifying the air, and according to the season hail-bearing and snowy. It is often taken for the north wind itself, one of the four cardinal winds, because of its nearness and similarity of effects: see Pliny on this, book 2, chapter 47. AR ARA, an altar, a shrine, a lar; a constellation in the sky toward the southern quarter, invisible to us: concerning which Cicero in On the Nature of the Gods. Then you will behold Nepa beside the shining point of the Altar, which the breath of the south wind caresses. It contains seven stars, all of the nature of Venus and somewhat of Mercury, among which the chief, of third magnitude, is situated in the middle of the flame; and if this should be found in the horoscope (says Stadius), it inclines toward piety, toward undertaking priestly offices, and toward the study of sacred letters, especially if there should be added a good testimony from benefics. But in the setting with an evil ray

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Martis, aut Saturni, affert periculum combustionis. 276. ARANEA Rete, Voluellum in Astrolabio representans in plano omnem rationem ptimi mobilis sese in orbem rotando spatio quatuor, & viginti hotarum. In ea videre est descriptos nedum polos, & omnes circulos, qui concipiuntur in primo mobili, sed etiam præcipuas stellas fixas suo loco secundùm longitudinem, & latitudinem, ascensionem rectam atque declinationem, quam habent, additis etiam ad earum plenam noritiam singularum nominibus. Eius inuentorem ferunt fuisse Eudoxum quemdam Samium, qui etiam nomen indidit sumptum à reticula Araneæ cui est valdè persimilis: Arabicè dicitur albacantabus. 277. ARATEA sphæra dicitur globus Astronomicus vulgò Cælestis, in quo omnes stellæ fixæ suis quæque Asterismis inclusæ atque interstinctæ conspiciuntur vna cum positu ad æquatorem atque habitudine ad Zodiacum tam in longum, quam in latum: ita vt facili iure, huius instrumenti ope, possit quis stellam quamuis addiscere, locum in Zodiaco inuestigare, ortum & occasum noscere, ascensiones eruere, atque ad eam significatorum quemlibet per motum directionis deducere. Dicitur Aratea ab Arato antiquissimo poëta Græco eius inuentore, qui etiam Græcè elegantissimo carmine descripsit & explicauit, appellauitque librum Phanomena hoc est Apparentia. Quem postè Germanicus Cæsar Augusti filius, Sextus Auienus Ruffus, & Marcus Tull. Cicero adhuc adolescens in latinum sermonem transtulerunt. 278. ARCHATAPIAS ex Græcobarb. dicitur in sphæra barbarica primus Decanus Piscium existens sub dispositione, ac dominatu Saturni, qui proinde dat ei significatum anxietatis, cogitationum profundarum, migrationis de loco ad locum, quærendi, & cumulandi opes &c. 279. ARCHITECTVRA ars est ex præceptis Geometricis comparata, qua traditur ratio extruendorum ritè quorumcunque ædificiorum humanæ vitæ commodis congruentium, ac penè ad vniuersi istius dispositionis idæam: Eius genera tria sunt ædificatio, Gnonomica, & Machinatio: Vide Vitruuium l.2.c.3. 280. ARCITENENS dictus est Sagittarius ab arcu, quem manibus gestat, vnde Sagittam ciaculare velle videtur, alio nomine Chyron, Centaurus &c. 281. ARCTOPHILAX Græcè hoc est Vrsacustos appellatur fidus in Cælo propè Vtsam constitutum, quasi ad eam constituendam alio nomine Vociferator, Bubulcus, Bootes. Stellas habet iuxta Ptolemæum 23. at secundùm Keplerum 28. & Baierum 34. qui tamen inter eas annumerat etiam informes circa consi-

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On Tuesday, or Saturday, it brings danger of burning. 276. ARANEA. A web, representing the Volvelle in the Astrolabe, in plane form, by rotating itself in a circle through the space of twenty-four hours. In it may be seen described not only the poles and all the circles which are conceived in the first mobile, but also the principal fixed stars in their places according to longitude and latitude, right ascension and declination, which they have, with the names of each also added for full knowledge of them. They say its inventor was a certain Eudoxus of Samos, who also gave it the name taken from the spider’s web to which it is very similar: in Arabic it is called albacantabus. 277. ARATEA. A sphere is called the astronomical globe, commonly the celestial one, in which all the fixed stars, each enclosed within and set among their asterisms, are seen together with their position in relation to the equator and their relation to the Zodiac, both in length and in breadth: so that by means of this instrument, one may easily learn any star, investigate its place in the Zodiac, know its rising and setting, work out its ascensions, and by motion of direction lead it to any one of the significators. It is called Aratea from Aratus, the most ancient Greek poet, its inventor, who also in very elegant Greek verse described and explained it, and called the book Phanomena, that is, Apparitions. This was later translated into Latin by Germanicus Caesar, son of Augustus, Sextus Avienus Rufus, and Marcus Tullius Cicero while still a young man. 278. ARCHATAPIAS. From barbarous Greek it is said in the barbaric sphere to be the first Decan of Pisces, existing under the disposition and dominion of Saturn, which therefore gives it the meaning of anxiety, deep thoughts, moving from place to place, seeking, and accumulating wealth, etc. 279. ARCHITECTURA. Architecture is an art formed from geometrical precepts, by which is taught the proper method of constructing any buildings whatsoever, suited to the conveniences of human life, and almost to the idea of the arrangement of the whole of this universe: its three kinds are building, gnomonics, and machinery: see Vitruvius, book 2, chapter 3. 280. ARCITENENS was the name given to Sagittarius, from the bow which he carries in his hands, as if wishing to shoot an arrow, otherwise called Chyron, Centaurus, etc. 281. ARCTOPHILAX. In Greek this is called the Bear-keeper, a faithful one stationed in the sky near the Bear, as though set there to guard it; otherwise called Vociferator, Bubulcus, Bootes. According to Ptolemy he has 23 stars, but according to Kepler 28, and according to Bayer 34, who however also counts among them the unformed ones around the constellation.

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MATHEMATICVM. 61 stentes: inter quas insignior est quæ inter crura primæ magnitudinis dicta Arcturus de qua mox infra. Plura vide in Verbo Bootes. < 281.> Arctos Græcè, Latinè Vrsa, apud Astronomos accipitur ad significandum promiscuè duo sidera in Cælo, quorum alterum Vrsa maior Græcis Elicem altera Cynosura nobis Vrsa minor dicitur. Vtrumque ad polum arcticum ira intra circulum arcticum clausæ, & complicatæ, vt vna resupinata alterius contegat caput, at quæ supina maior, quæ recta minor, ore alterius caudam arripere velle demonstrat: de vtraque sic cecinit Ouid. Esse duas Arctos, quarum Cynosura vocatur. Sedonijs: Esicem graia carina nosat. Verum, etsi olim Arctos nomine vtraque veniebat Vrsæ, modò tamen vsus obtinuit, vt solùm signetur minor, & Cynosura: Quinimò sæpissimè pro ipso Polo, qui ei proximè adjacet, & ab ea, denominationem sumit, accipitur; Vnde &c polus Arcticus, qui suprà nos artollitur, & circulus eum ambiens dictus: sicur etiam Septentrionalis à Septentrionibus, hoc est, stellis minorem Vrsam efformantibus; nec non Borealis à Borea vento inde exsufflante. < 283.> Arcturus ex Græco quasi Cauda Vrsæ dictus Isidoro Ar Euzona , Arabicè Alramec, vel Alkameluz, & Colanzæ, hoc est gladius, & pugio Bootis dicitur stella fixa primæ magnitudinis de natura Iouis, & Martis in Boote extrà formam existens inter eius crura. Eius ortus certissimas tempestates facit vt ait Plin. lib. 2. cap. 39. Arcturi fidus, inquir, non ferme sine procellosa grandine emergit. occasus cum Sole excitar venros Australes: Reliqua vide in Verbo Alramech. < 284.> Arcevs apud Astronomos est pars circuli intercepta ab vno ad aliud punctum, qua videlicet vel totius circuli quantitatem, vel aliud quid Geometricè, & proportionaliter auspicamur. Hinc arcum directionis dicimus quantitatem æquatoris intercepram inter duo puncta in cælo, quorum alterum ster loco significaroris, alterum promissoris, quam per certum tempus, explere debet vnus quousque ad alterum deuoluatur: Sed de hac re dicetur in V. Directio. < 285.> Area apud Geometras audit spatium vacuum, seu superficies plana intra latera alicuius figuræ, seu planæ, seu circularis comprehensa: quæ quidem in figuris planis mensuratur per quadrata earum linearum per quas latera, seu ambitus earundem figurarum mensurari solent; in figuris verò circularibus per semidiameum circuli multiplicatam in dimidiam parrem circumferentia: vt si circumferentia alicuius circuli sit 132.

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MATHEMATICVM. 61 …existing: among which the more notable is that which is called, between the thighs of the first magnitude Arcturus , of which below. See more in the word Bootes. <281.> Arctos, in Greek; Vrsa, in Latin, is taken by astronomers to signify indiscriminately two stars in the heavens, of which the one, the greater Bear, is called by the Greeks Elice, and the other, Cynosura, by us the Lesser Bear. Both, as it were, bound to the arctic pole within the arctic circle, and intertwined, so that one, lying on its back, covers the head of the other; the greater one lying supine, the smaller erect, seems with the mouth of one to be trying to seize the tail of the other. Of both Ovid sang thus: There are two Arctos, one of which is called Cynosura. Sedonijs: Esicem graia carina nosat. But although formerly both Bears came under the name Arctos, now usage has prevailed that only the lesser one be so designated, and Cynosura; indeed, very often it is taken for the pole itself, which lies nearest to it and takes its name from it. Hence also the arctic pole, which is raised above us, and the circle surrounding it, is so called; also the Septentrionalis, from the Septentriones, that is, from the stars forming the Lesser Bear; and likewise Borealis, from Boreas, the wind blowing from there. <283.> Arcturus , so called from the Greek as it were Cauda Vrsæ, by Isidore Ar Euzona , in Arabic Alramec or Alkameluz, and Colanzæ, that is, sword and dagger, is said to be a fixed star of the first magnitude, of the nature of Jupiter and Mars, existing in Bootes outside its form, between his thighs. Its rising produces very certain storms, as Pliny says, lib. 2, cap. 39. The star of Arcturus , he says, does not emerge without stormy hail; its setting with the Sun stirs up southern winds. See the rest in the word Alramech. <284.> Arcevs, among astronomers, is a part of a circle intercepted from one point to another, by which, namely, we infer geometrically and proportionally either the quantity of the whole circle or something else. Hence we call the arc of direction the portion of the equator intercepted between two points in the heavens, one of which signifies the place of the significator, the other of the promissor, which must be fulfilled in a certain time, until one is carried over to the other. But of this matter it will be spoken in V. Directio. <285.> Area, among geometers, denotes an empty space, or a flat surface enclosed within the sides of some figure, whether plane or circular: and indeed in plane figures it is measured by the squares of the lines by which the sides, or the bounds, of those figures are usually measured; but in circular figures by the semi-diameter of the circle multiplied by half the circumference: as if the circumference of a certain circle were 132.

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Sagittario constituit Trigonum igneum, cuius dominatores sunt Sol, & Iupiter. Tempore Ptolemæi sub hoc signo erat sidus, & constellatio Arietis in octaua sphæra continens stellas tredecim (exceptis quinque informibus circa ipsam) omnes ferè de natura Satutni, aut Martis, quarum prima in cornu borealì consistens immediatè incidebat in æquatorem; at nunc ob motum proprium octauæ sphæræ præcessit gr. ferè 18 Primæ eius partes ventos & imbres faciunt, mitiùs tamen quàm tempore Ptolemæi: mediæ sunt temperatæ: extemæ tandem calidæ; cumque Zodiacus præditus sit latitudine, pars eius borealis est calidior, & nocua ob plures stellas ibi consistentes de natura Martis & Mercurij: Australis verò frigida ob stellas de natura Saturni. ARIO, teste Kirchero, Chaldaicè dicitur Leo, quintum ab Ariete signum: apud Hebræos autem Arich. ARISTA, & Spica promiscuè appellatur fixa insignis in manu Vitginis, quæ triticeam spicam in manu gestare imagine præsefert: De ea satis dictum in Verbo Azimech, & alibi sæpè. ARITHMETICA vna est ex principalioribus Mathesis disciplinis, quæ versatur circa quantitatem discretam, seu mavis dicam, numeros (per quod contradistinguitur à Geometria, quæ considerat quantitatem continuam) tradens methodum supputandi, multiplicandi, & partiendi: proindeque omnes numetorum passiones, proportiones, & habitudines, quas adinuicem habent, considerat, atque aliis applicat, vt ex his tandem ad ignota deueniat. Sic positis tribus numeris notis, quartum numerum ignotum per proportionum regulam, quæ aliàs dicitur Aurea, præcipit inuenire: si videlicet secundus, & tertius multiplicentur ad inuicem, ac numerus ex multiplicatione productus diuidatur per primum: Nam numerus quotiens erit quartus quæsitus, hoc est cui tertius numerus correspondet, & ad quem eandem seruat proportionem, quam primus ad secundum. Hinc considerat in numeris additionem vnius ad alterum, quæ est duorum vel plurium numerorum in vnum collectio: substractionem, quæ est numeri minoris ab altero maiore subductio: multiplicationem, quæ est ductio vnius numeri in alium; sicque cum alter ipsorum augetur toties, quoties in altero continetur vnitas: ac tandem diuisionem quæ est partitio propositi alicuius numeri in partes ab altero numero denominatas. Ex ipsis autem numeris aliquem appellat partitorem, seu diuidentem, & est is qui denominat partes, in quas numerus diuidendus tribuitur; qui ob eam etiam causam denominator audit, quatenus denominat, & indicat partes, in quas vnum torum intelligitur esse diuisum: numeratorem

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Sagittarius constitutes the fiery Trigon, whose rulers are the Sun and Jupiter. In Ptolemy’s time, under this sign was the star, and the constellation of Aries in the eighth sphere, containing thirteen stars (except for five shapeless ones around it), all almost of the nature of Saturn or Mars; the first of which, standing in the northern horn, then immediately touched the equator; but now, by the proper motion of the eighth sphere, it has preceded by about 18 degrees. Its first parts produce winds and rains, though more mildly than in Ptolemy’s time; the middle are temperate; the outer parts are finally hot; and since the Zodiac is endowed with breadth, its northern part is hotter and harmful because of the many stars there, of the nature of Mars and Mercury: the southern part, however, is cold because of the stars of the nature of Saturn. ARIO, according to Kircher, in Chaldean means Leo, the fifth sign from Aries; among the Hebrews, however, Arich. ARISTA, and Spica, are used interchangeably for the notable fixed star in the hand of Virgo, which in image represents a wheat ear carried in the hand: enough has been said of it in the word Azimech, and elsewhere often. ARITHMETIC is one of the principal disciplines of mathematics, which deals with discrete quantity, or, if you prefer, with numbers (whereby it is distinguished from Geometry, which considers continuous quantity), and it teaches the method of calculating, multiplying, and dividing; and therefore it considers all the properties, proportions, and relations that numbers have among themselves, and applies them to other things, so that from these it may finally arrive at what is unknown. Thus, three known numbers being given, it teaches how to find a fourth unknown number by the rule of proportion, which is otherwise called the Golden Rule: namely, if the second and third are multiplied together, and the number produced by the multiplication is divided by the first, the quotient will be the fourth sought, that is, the number to which the third number corresponds, and toward which it preserves the same proportion as the first does to the second. Hence it considers in numbers addition of one to another, which is the combining of two or more numbers into one; subtraction, which is the taking away of a smaller number from a larger; multiplication, which is the bringing of one number into another, so that one of them is increased as many times as unity is contained in the other; and finally division, which is the partition of some proposed number into parts named by another number. Of these numbers it calls one the divisor, or divider, and this is the one that names the parts into which the number to be divided is assigned; for that reason it is also called the denominator, insofar as it names and indicates the parts into which one whole is understood to be divided: numerator

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us dominatorem ocsigno etat si- oninens stellas ipsam) omnes prima in corru torem; at nunc q[ui] ferè 28 Pri- s tamen quam tremæ tandem dine, pars eici bi consistentes rigida ob stellas o, quintum ab signis in manu i imagine prx- alibi sæpè. Mathesis disci- um, seu manu à Geometria, ns methodum deque omnes nes, quas ad- at, vt ex his umeris notis, egulam, quæ i secundus, & ex multipli- umerus quo- erus corres- , quam pri- : addit:onem umerorum eti minoris e est ductio um augetur em diuisio- rtes ab al- is aliquem eominat i ob eam t, & in- diuisum: eratorem MATHEMATICVM. 63 numeratorem , & est numerus, qui enumerat minutias, seu partes quas continet proposita fractio ex illis, in quas totum, cuius est fractio diuisum est; & quotientem, qui est numerus partium, in quas numerus diuidendus tribuitur, quique eo quociens denominatur, quia indicat quoties diuisor in nu- mero diuidendo continetur. Similiter in numeris considerat æqualitatem, vel inæqualitatem; primos, seu simplices, qui sunt quos sola vnitas metitur, quales sunt 2. 3. 5. 7. 11. 13. 17. 19. 23. 29. 31. &c. & compositos, quos non vnitas, sed nu- merus aliquis metitur, vt 4. 6. 8. 9. 10. 12. 14. 15. &c. vel enim eos metitur, & in partes æquales dispescit numerus binarius, vel ternarius, vel quartenarius, &c. de quibus fusè agit Eu- clides à lib. 7. vsque ad 9. inclusiùè, & luculenter explicat Claius in Arithmetica practica, nec non in commentar. super eiusdem Euclidis elementa. Porrò non ita opponuntur inter se istæ duæ præcipuæ Mathesis diuisiones, Geometria, inquam, & Arithmetica, vt non pari passu incedant, manus complicent, ac sibi mutuò opitulentur. Er quidem, vt benè obseruat Alexander de Ales, in primo Meteor. ea est Geometriæ ad Arithmeticam propor- tio, quæ est puncti ad vnitatem, linæ ad numerum simplicem, corporis quanti ad numerum compositum. Hinc est, vt Geo- metria ad quantum suum continuum artificiosè dimetien- dum, Arithmeticis fractionibus opus habet, & ipsa vicissim Arithmetiæ, vt munus suum rectiùs, & expeditiùs exequa- tur è promptuario suo auxiliares confert suppetias. Quapro- pter ei & planos & cubos, & quadratos, & solidos, & angu- los, & latera mutuat (vt haber Proclus in Euclid.) datque vt iisdem præceptis in numeris dimetiendis vtatur, quibus ipsa in figuris Geometricis, seu planis, seu solidis vsa est, eandem- que illa proportionem inueniat in quantitate discera, quam ipsa in suo quanto continuo. Sic anguli, seu termini, & radi- ces proportionis dicuntur duo numeri, quibus minores in ea- dem proportione assumi nequeunt: latera appellantur duo numeri sese mutuò complicantes, aut multiplicantes ad fa- ciendum vnum tertium numerum seu aggregatum, seu multi- plicatum: qui verò ab ipsis prosilit, si è duobus tantum late- ribus, dicerur planum, si è pluribus, solidum. Similiter qua- dratus numerus is est, qui æqualiter æqualis est, siue qui sub duobus æqualibus numeris continetur; vt est 16. existens ex multiplicatione mutua 4. & 4. Cubus qui sub tribus æqua- libus numeris continetur; vt est numerus 27. ex multipli- catione 3. 3. 3 quippe ex 3. in 3. deducto sit 9. & ex 9. in 3. pro- ducto sit 27. & alia huiusmodi quæ fusiùs videre est in Euclides integro lib. 7. E

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us the ruler with sign, and it is— containing the stars itself) all things first into a fall er; but now which nearly 28 Pri- s however at last the severest finally dine, part eici standing by rigid because of the stars o, the fifth from signs in the hand in the image prx- elsewhere often. Mathesis is taught um, or hand from Geometry, ns method and all things which ad- at, so that from these numbers known, rule, which is second, and from multipli- number what- number corres- , than the first : addition numbers even of the smaller there is the reduction when it is increased division by means of— parts from another some number he names because on that account t, and in- undivided: ator MATHEMATICAL. 63 numerator , and is the number which counts the small parts, or parts which the proposed fraction contains from those into which the whole, of which it is a fraction, is divided; and the quotient, which is the number of parts into which the number to be divided is distributed, and which is so called because it indicates how many times the divisor is contained in the number to be divided. Likewise in numbers it considers equality, or inequality; prime, or simple numbers, which are those measured only by unity, such as 2. 3. 5. 7. 11. 13. 17. 19. 23. 29. 31. &c. and composite numbers, which are measured not by unity but by some number, as 4. 6. 8. 9. 10. 12. 14. 15. &c. For either they are measured by, and divided into equal parts by, the binary number, or the ternary, or the quaternary, &c.; concerning which Euclid treats at length from Book 7 to Book 9 inclusive, and Clavius explains them clearly in the Practical Arithmetic, as well as in his commentaries on the elements of the same Euclid. Moreover, these two principal divisions of Mathesis are not so opposed to each other, Geometry, I mean, and Arithmetic, that they do not advance at the same pace, join hands, and aid one another. Indeed, as Alexander de Ales observes well, in the first book of the Meteorology, such is the proportion of Geometry to Arithmetic as is that of the point to unity, of line to the simple number, of a body of quantity to the composite number. Hence it is that Geometry, in order to measure its continuous quantity artfully, has need of arithmetic fractions, and it in turn contributes from its store auxiliary help to Arithmetic, so that it may perform its task more rightly and more expeditiously. Wherefore it borrows for it both planes and cubes, and squares, and solids, and angles, and sides (as Proclus has in Euclid), and gives it that it may use the same precepts in measuring numbers which it itself has used in geometric figures, whether plane or solid, and that it may find the same proportion in discrete quantity which it itself found in its own continuous quantity. Thus angles, or terms, and roots of proportion are called two numbers by which smaller ones in the same proportion cannot be assumed: sides are called two numbers mutually combining, or multiplying, to make one third number, whether aggregate or multi- plied: but what springs from them, if from only two sides, is called a plane, if from more, solid. Similarly qua- dratus numerus it is that which is equally equal, or which is contained under two equal numbers; as is 16, existing from the mutual multiplication of 4 and 4. A cube is that which is contained under three equal numbers; as is the number 27, from the multiplication of 3, 3, 3, since from 3 multiplied by 3 it is 9, and from 9 multiplied by 3 it is produced as 27; and other things of this kind are to be seen more fully in the entire Book 7 of Euclid. E

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LEXICON Denique ea est Arithmeticæ facultatis dignitas, vt quemadmoduni obseruauit Philosophus in primo Physicorum, ipsa necessariò omnes Mathematicas scientias præcedat, ad earumque notitiam nos manducat, atque vt Platonis verbis vtar. Arithmeticam si quis auferet, omnes artes auferuntur & nullamant, & omnes in totum peribunt. Verum si quis diuinam, & mortalem originem inspexerit, in qua pietas erga deos, & numerus cognoscitur, cognoscit, quantum numero opus sit: nam & tota Musica numeris opus habet in motibus, & sonis: & quod maximum est, numeri omnium bonorum causa sunt, ex quo cognosci possit, quod omne malum, & omnis motus rationis expers, & indecorus sine rythmo est, & inconcinus: & omnia quæ cum malo communionem habent esse absque numero oportet tandem statuete eum qui felix futurus est, & qui justum, & bonum, & pulchrum, & omnia huiuscemodi ignorat. A Plato: De Arithmeticæ inuentione vide Polydor. Virgil. lib 1. c. 18 & Rhodigin. lib 18 c. 34 302. ARMILLA olim dicebatur ornamentum militare, ad modum circuli, quo milnes ex bello victores honoris causa ab Imperatoribus munerabantur, vt eo armum (sic enim audiebat antiquis simistrum brachium) ad fortitudinis indicium decorarent. Inde ad omne circulorum genus significandum hoc nomen translatum est: præcipuè verò apud Astronomos, apud quos circuli materiales sphææ, sed potissimum suspensorium Astrolabij, vel alterius consimilis instrumenti possum ad illud perpendiculatiter statuendum, quod Arabes Abalantica vocuere, Armilla antonomasticè dicta est: Inde etiam. 303. ARMILLARIS sphæra appellatur quæ pluribus circulis ex solidiori aliqua materia factis interstincta totam primi mobilis doctrinam continet, atque oculis exhibet ad differentiam Araeæ non ita pridem memoratæ, quæ vndequaque solida est, atque in ea circuli, & sidera fixa tantum delineata propriis quæque locis apparent. 304. ARNIG. Arab. Musicale dicitur instrumentum, quod ideò apud Astronomos Arabes sumitur pro ridicula, Lyra, seu Vulture cadente, cælesti sidere, de quo alibi sermo. 305. AROLABVM instrumentum Mathematicum ad venandas siderum affectiones. 306. ARPEEN Græcobarbat. dicitur tertius Decanus Libræ in sphæra barbarica sub dominatu Louis, habens significationem gulositatis, hilaritatis, carminum malorum saporum, &c. 307. ARTVRVS. Vide Arcturus. AS 308. ASANGES Chaldaicè, vel potius Mesanguo dicitur astrum

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LEXICON Finally, such is the dignity of the art of Arithmetic, that, as the Philosopher observed in the first book of the Physics, it necessarily precedes all mathematical sciences and leads us to knowledge of them; and, to use Plato’s words, if anyone takes away Arithmetic, all arts are taken away and have no existence, and all will utterly perish. But if anyone considers its divine and mortal origin, in which piety toward the gods and number are recognized, he understands how much number is needed: for all Music has need of numbers in motions and sounds; and, what is greatest, numbers are the cause of all good things, from which it may be known that every evil, and every motion devoid of reason and indecorous, is without rhythm and discordant; and all things that have communion with evil ought finally to be established without number, if he who is to be happy, and who knows nothing of the just, the good, the beautiful, and all such things. By Plato. On the invention of Arithmetic see Polydore Virgil, book 1, c. 18, and Rhodiginus, book 18, c. 34. 302. ARMILLA was formerly the name for a military ornament, in the form of a circle, with which soldiers victorious in war were rewarded by emperors as a mark of honor, so that they might decorate the arm (for thus the left arm was called by the ancients) as a sign of bravery. Hence the name was transferred to signify every kind of circle: especially among astronomers, among whom the material circles of the sphere, but chiefly the suspensory part of the Astrolabe or of another similar instrument, by which it could be set upright perpendicularly, which the Arabs called Abalantica, was antonomastically called Armilla. Hence also. 303. ARMILLARY sphere is the name given to that which is interspersed with many circles made of some more solid material and contains, and displays to the eye, the entire doctrine of the first mover, in distinction from the aforementioned Araea, which is solid throughout, and in which the circles and fixed stars appear only drawn in their proper places. 304. ARNIG. In Arabic, this musical instrument is so called, and therefore among the Arabic astronomers it is taken for the Lyre, or the Falling Vulture, the heavenly star, of which elsewhere there is mention. 305. AROLABVM, a mathematical instrument for hunting the affections of the stars. 306. ARPEEN, in Greco-Barbarous usage, is called the third decan of Libra in the barbaric sphere under the dominion of Louis, having the signification of gluttony, cheerfulness, bad flavors in songs, etc. 307. ARTVRVS. See Arcturus. AS 308. ASANGES in Chaldean, or rather Mesanguo, is called a star

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MATHEMATICVM. Accem stellis (quot videlicet chordæ sunt in Psalterio decachordo, quod per id nominis significatur) constans; apud nos Lyra, seu Fidicula. Keplerus autem in eo siderè considerat stellas vndecim, & Baierus in sua Vranometria tredecim. ASBIA Græcè, Latinè dicitur Hydra. Vide suo loco. < 309.> ASCENDENS, horoscopus, horizon, finitor Orientalis est linea illa in Oriente, vnde emergunt sidera, quæque diuidit hemisphærium superius nobis conspicuum ab inferiori, quod latet sub terra. Dicitur etiam angulus Orientis, & prima domus in cælesti figura Estque apud Astrologos significator vitæ, & corporis affectionum, morum itinerum &c. Significar etiam initia rerum, eo quod est domus initatiua cælestis motus. ASCENDENS etiam appellarur illa pars cæli, quæ incipit à li- < 310.> nea Meridiana Imi cæli, & per viaru Orientis incedens, vsq; ad Meridianum superius extenditur (sicque includit tertiam, secundam, primam, duodecimam, vndecimam, ac decimam domum) vel inde dicta, quod per eam incedentes planetæ & partes primi mobilis semper ascendunt: sicut è contra descendens vocatur pars opposita, à linea Meridiana supra terram ad lineam Imi cæli per Occidentem gradiens, quia per eam planetæ semper descendunt. Hinc. ASCENSIONES, & d[er]scensiones signorum sunt partes æquatoris, quæ cum rali signo, aut Zodiaci parte coascendunt, & simul descendunt; adeoque etiam planearum, quos in eisdem partibus repetiri contingit. Portò ascensiones ac descensiones, aliæ rectæ, aliæ obliquæ. Ascensiones rectæ sunt partes æquatoris, quæ ascendunt per lineam rectam, adeoque comprehendunt omnes illas cæli parres, quæ sub linea recta ducta per polos muudi, & parres æquatoris opposiras continentur, quod accidit in sphæra recta, atque in sphæra obliqua tantum in circulo recto, seu Meridiano. Ascensiones, & descensiones obliquæ sunt partes æquatoris, quæ obliquè ascendunt, aut descendunt in sphæra obliqua vbi alter polorum attollitur: quoque obliquior erit sphæra, eò obliquior erit ascensio æquatoris, sicque minor portio eius ascendit cum signis Zodiaci borealibus, maiorum Australibus. E contrà maior arcus descendit in borealibus, quàm in australibus. Arcus verò differentiæ ascensionum, aut descensionum, qui intercipitur inter ascensionem rectam, & obliquam, vocatur DIFFERENTIA Ascensionalis, cuius ope extrahuntur ascensiones, < 313.> ac descensiones obliquæ ad omnem poli elevationem. Data enim elevatione poli alicuius regionis, ac declinatione sideris, statim apparet differentia ascensionalis, quæ pro ratione declinationis borealis, aut australis, addenda, vel subterahenda E ij

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MATHEMATICVM. Consisting of stars, namely as many as there are strings in the ten-stringed Psaltery, which is signified by that name; with us, Lyra, or Fidicula. Kepler, however, considers in it eleven stars, and Bayer in his Uranometria thirteen. ASBIA, in Greek, is called Hydra in Latin. See in its proper place. < 309.> ASCENDENS, horoscopus, horizon, the eastern finitor is that line in the East from which the stars emerge, and which divides the upper hemisphere visible to us from the lower one, which lies hidden under the earth. It is also called the angle of the East, and the first house in the celestial figure. Among astrologers it is the significator of life, and of the affections of the body, of manners, of journeys, etc. It also signifies the beginnings of things, because it is the initiatory house of celestial motion. ASCENDENS is also called that part of the sky which begins from the < 310.> meridian line of the lowest heaven, and proceeding by the path of the East, extends to the upper meridian (and thus includes the third, second, first, twelfth, eleventh, and tenth houses), or so called because through it the planets and parts of the primum mobile, moving through it, always ascend: just as, on the contrary, the descending part is called the opposite part, moving from the meridian line above the earth to the line of the lowest heaven by way of the West, because through it the planets always descend. Hence. ASCENSIONS and descensions of the signs are the parts of the equator which, together with a given sign, or part of the Zodiac, ascend coascend and descend together; and likewise also those of the planets, which happen to be repeated in the same parts. Moreover, ascensions and descensions are of two kinds, right and oblique. Right ascensions are the parts of the equator which ascend by a straight line, and thus comprise all those parts of the sky which are contained beneath a straight line drawn through the poles of the world, and the opposite parts of the equator, which happens in the right sphere, and in the oblique sphere only in the right circle, or Meridian. Oblique ascensions and descensions are the parts of the equator which ascend or descend obliquely in an oblique sphere where one of the poles is raised: and the more oblique the sphere is, the more oblique will be the ascension of the equator, and thus a smaller portion of it ascends with the northern signs of the Zodiac, a greater one with the southern. Conversely, a larger arc descends in the northern signs than in the southern. But the arc of the difference of ascensions, or descensions, which is intercepted between the ascension right and oblique, is called the DIFFERENCE of Ascension, by means of which oblique ascensions and < 313.> descensions are drawn out for every elevation of the pole. For a given elevation of the pole of any region, and the declination of a star, the difference of ascension immediately appears, which, according to the amount of northern or southern declination, is to be added or subtracted. E ij

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LEXICON est ab ascensione recta eiusdem sideris; statimque prosilis ascensio, aut descensio obliqua ad datam poli eleuarionem di- et x regionis; quibus mediis postea directiones perficiuntur. Atque ascensionibus rectis vtimur in sphæra recta, & in cir- culo recto; obliquis in sphæra obliqua à primo gradu eleua- tionis poli vsq[ue] ad grad. 90. Extant ad hoc Tabulæ differentiæ ascensionalis, ascensionum rectarum, necnon obliquarum ad quamcumque poli eluationem: Qui volet videat apud Magi- num, & Argolum. 314. ASCHER Ais:mini Arab. alio nomine Alhabor dicitur stella fixa fulgentissima micans in ore canis Maioris: de qua abundè dictum in V. Alhabor. 315. ASCONES, siue dominus Ascone dicitur species quædam Co- metæ de natura Mercurij parui quidem corpore, & coloris cæ- rulei, sed cum cauda oblonga, qui apparens porrendit bella, & mortes Principum vitorum, necnon etiam morbos acutos, tyrannides, & similia. 316. ASELLI à Manilio dicti etiam lugula (quamuis hæ commu- niter pro cingulo Orionis accipiantur, vt suo loco dicemus) sunt stellæ paruæ quidem quippequæ quartæ magnitudinis, sed magnæ potentiæ, & plusquam credi possit, infensissimæ in pectore Cancri vna cum Præsepi stella nebulosa consisten- tes, de natura Martis, & Solis in gradu 2. Leonis, ferè in ipsa Ecliptica, ideoque tantæ actiuitaris. Hæ cum Sole exorientes turbant aërem, impetuosis imbribus ingruunt, fulgure, & to- nitruis. Naturum faciunt agrellem, irreligiosum, terricum, ad studia venationis applicitum: si verò in occasu fuerint cum Martis iniquo radio, acerbam mortem, ait Firmicus, dum adhuc dormiet ministrant. 317. ASICATH Græcobar. significat in sphæra barbarica pri- mum Decanum Tauri, cuius dispositio est penes Mercurium, & est indicium arationis, sationis, structuræ, deductionis co- loniarum, scientiarum ciuilium, Geometriæ &c. Item 318. ASICCAN ibidem dictui Primus decanus Arietis competens Martis, proindeque est signum audaciæ, fortitudinis, elatio- nis, inuerecundiæ &c. 319. ASIDA Arab Latinè Lupus astrum: de quo suo loco. 320. ASPECTVS est mutua quædam habitudo, seu familiaritas duorum siderum sese aliquo radio harmonicè considerato, in- tuentium, quo eorum virtus augescit, aut deprauatur, per mutuam efficientiam, prout fuerint in actiuis, passuisve qua- litatibus natura conformia, aut difformia. Hoc autem fit, vel per circuli medietatem, cum planetæ sunt in locis diametrali- ser oppositis, & vocatur Oppositio: vel per tertiam circuli

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LEXICON is from the right ascension of the same star; and at once there follows ascension, or oblique descension according to the given elevation of the pole, di- et x of the region; by which means directions are afterwards completed. And we use right ascensions in the right sphere, and in the right circle; oblique ones in the oblique sphere, from the first degree of the elevation of the pole up to 90 degrees. For this there exist Tables of ascensional difference, of right ascensions, and also of oblique ones for whatever elevation of the pole: whoever wishes may see Maginus and Argolus. 314. ASCHER Ais:mini in Arabic is also called Alhabor, a fixed star most brilliantly shining and twinkling in the mouth of the Greater Dog: concerning which enough has been said under V. Alhabor. 315. ASCONES, or dominus Ascone, is said to be a certain kind of comet, of the nature of Mercury, small indeed in body, and of a blue color, but with an oblong tail; and when it appears it portends wars, and the deaths of princes and rulers, as well as acute diseases, tyrannies, and the like. 316. ASELLI, called by Manilius also lugula (although these are commonly taken for the belt of Orion, as we shall say in its place), are stars indeed small, being of the fourth magnitude, but of great power, and more hostile than can be believed, situated in the breast of Cancer together with the nebulous star Praesepe, of the nature of Mars and the Sun, in the 2nd degree of Leo, almost on the very Ecliptic, and therefore of such activity. When these rise with the Sun they disturb the air, rush in with violent rains, lightning, and thunder. They make one rustic, irreligious, stubborn, inclined to the pursuits of hunting; but if they be in setting with an unfavorable ray of Mars, Firmicus says they administer a bitter death while one is still asleep. 317. ASICATH, in Greco-Barbarous speech, signifies in the barbaric sphere the first decan of Taurus, whose disposition is under Mercury, and it is an indication of plowing, sowing, founding, the leading out of colonies, civic sciences, Geometry, etc. Likewise 318. ASICCAN, mentioned there, is the first decan of Aries, belonging to Mars, and therefore is a sign of audacity, fortitude, elevation, shamelessness, etc. 319. ASIDA, in Arabic, in Latin means a star of the Wolf: concerning which, in its place. 320. ASPECT is a certain mutual relation, or familiarity, of two stars looking at one another by some harmonically considered ray, by which their power is increased or diminished, through mutual action, according as they are, in active or passive qualities, naturally alike or unlike. This happens either by half the circle, when the planets are in diametrically opposite places, and it is called Opposition: or by the third part of the circle

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MATHEMATICVM. 69 partem, & appellatur Trinus: vel per quarram partem, & di- citur Quadratus: vel denique per sextam partem, & audit Sex- tillis. Conjunctio verò, qua duo planetæ conueniunt in eo- dem signo, eodemque gradu, licet impropriè dicatur aspe- ctus, nihilominus inter aspectus computatur, cum fit vera fa- miliaritas, eaque omnium potentissima. Addunt alij ex Ke- plero, sumpta proportione ad modos musicos, alios aspectus minores, & sunt sesquiquadratus qui est distantia per quar- tam partem circuli & insuper per alterius quartæ dimidium hoc est per grad. 135. Quintilem, qui est distantia per quintam partem, & Biquintilem, qui est distantia duarum ex quinque partibus. Atque huiusmodi radios compurant nedum in Zo- diaco, sed etiam in mundo à domibus, per partes propor- tionales arcus diurni, aut nocturni cuiuscunque sidetis. Poriò aspectus alius platicus, alius partilis Partilis est, cum præcisè, aut in eodem gradu consistunt duo planetæ (& est in conjun- ctione) aut tot partibus ad vnguem distant, ad inuicem, quot requiruntur ad talem aspectum efformandum: hicque platico est longè perfectior, qui solùm est ad orbem, hoc est, cum non quidem ad amussim, distant, neque radius proijcitut ad corpus planetæ, sed solum incidit in orbem, seu sphæram lucis ipsius: De quo, sicut & de eius diuisione in applicationem, & defluxum plura vide in V. Platicus, nec non sub propriis no- minibus singulorum aspectuum. ASSABE Arab. Latinè Eurus. Ventus subsolanus vnsus ex < 3> quatuor cardinalibus, spirans ab ortu æquinoctiali: Vide in V. Græco Apeliotes. ASSANGE Armig. Arab. seu potiùs Chaldaicè, Latinè Fidi- < 3> cula vultur cadens, sidus in cælo: de quo vide alibi. ASSV apud Metheorologicos est genus quoddam aërearum < 3> impressionum, quod est in duplici differentia, aliud ascendens, constatum ex partibus exhalationis accensæ in suprema aëris < 3> regione, & videtur ascendere, sicut si euolarent scintillæ de < 3> fornace: aliud verò descendens, & est ignis reiensus in nube, qui tamen expellitur obuiante nube frigida, & cadit continuò, < 3> propter quod videtur quod stella cadens sit longa, quia relin- < 3> quit vestigia casus post se. 10. de Combis in compend. Theo- < 3> logicæ veritatis lib. 2. 1. 9. Vide in V. idera discurrentia. ASTACVS, Nepa, Cammarus Vide Cancer. < 3> ASTER nomen gericum stellæ singularis, prout præscindit à < 3> fixa, vel erratica. Verum aster, mus, & astrum significant multitudinem, & congregationem plutium stellarum iuetran- < 3> tium; quæ conueniunt ad formandum vnum integrum sidus, < 3> aut figuram, vt est Vela, Leo, Lyra, &c. E iii

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MATHEMATICVM. 69 by the third part, and is called Trine; or by the fourth part, and is called Quadrate; or finally by the sixth part, and is called Sextile. Conjunction, however, by which two planets meet in the same sign and the same degree, though improperly called an aspect, is nevertheless counted among the aspects, since it makes a true familiarity, and that the most powerful of all. Others add, following Kepler and taking proportion according to musical modes, other minor aspects, namely the sesquiquadrate, which is the distance by a fourth part of the circle and moreover by half of another fourth, that is, by 135 degrees; the quintile, which is the distance by a fifth part; and the biquintile, which is the distance of two out of five parts. And they compute such rays not only in the Zodiac, but also in the world by houses, through proportional parts of the diurnal or nocturnal arc of any star. Moreover, one aspect is platic, another partile. It is partile when two planets are exactly, or in the same degree, in conjunction, or are at the precise number of parts from one another required for such an aspect to be formed; and this platic one is far more perfect, which is only in orb, that is, when they are not exactly distant, nor is the ray projected to the body of the planet, but only falls within the orb, or sphere of its light. On this, as also on its division into application and defluxion, see more in V. Platicus, and likewise under the proper names of the individual aspects. ASSABE. In Arabic, in Latin Eurus. The east-south-east wind, one of the four cardinal winds, blowing from the vernal east: see in the Greek V. Apeliotes. ASSANGE. In Armig., Arabic, or rather Chaldean, in Latin Ficulida; a falling vulture, a star in the heavens: see elsewhere. ASSV among meteorologists is a certain kind of aerial impression, which is of two kinds: one ascending, consisting of parts of ignited exhalation in the upper region of the air, and it seems to ascend, as if sparks were flying out of a furnace; the other descending, and is fire retained in a cloud, which nevertheless is driven out by an opposing cold cloud, and falls continually, for which reason it seems that a falling star is long, because it leaves traces of its fall behind it. 10. de Combis in compend. Theologicae veritatis lib. 2. 1. 9. See in the V. moving matter. ASTACVS, Nepa, Cammarus. See Cancer. ASTER is the Greek name for a single star, insofar as it is distinguished from a fixed star or a wandering one. But aster, mus, and astrum signify a multitude and congregation of many stars joining together to form one complete constellation or figure, such as Vela, Leo, Lyra, etc. E iii

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70 LEXICON 326. ASTRO, ex Græcobarbaro dicitur secundus decanus Aqvarij, sub dominatu Mercurij in sphæra barbarica, significator bonorum morum, formæ, intellectus, mansuetudinis cum modestia, liberalitatis, &c. 327. ASTRABISTER dictum est instrumentum quoddam Geometricum ad mensutandas altitudines, & profunditates, instar radij Latini 328. ASTRAA dicta est ab Arato Virgo, cæleste sidus inter Leonem & Libram, mutuato ex fabulis nomine, fingunt enim Poëtæ ipsam justitiæ antistitem aureo illo sæculo è cælo in terras migrasse, sed mortalium sceleribus offensam cælos repetiisse, vbi in cæleste illud sidus conuersa eorum facta de longè perpendit, & aqua lance dijudicat: hinc illi lances applicitæ: alio nomine dicitur trigone, Aurono, Isis; eius sideris qualitatem, numerum stellarum, quibus constat, naturam & alia: Vide in V. Virgo 329. ASTROCYNOS, & ASTROCYON Græcè appellatur Canis sidereus major, alio nomine Sirius qui inter multas stellas quibus integratur duas peculiari consideratione dignas habet, alteram in capite quæ vocatur Isis, alteram in ore seu lingua apud Arabes Alhabor: de vtrisque suo loco. 330. ASTROLABIVM instrumentum Mathematicum, totam ferè cælestem doctrinam in plano rep[er]æsentans, vnde & planisphærsum dictum est quasi sphæram in plano demonstret, ex eo enim perquam bellè astrorum motus colliguntur, distantiæ mensurantur, ascensiones, descensiones, declinationes, & alia id genus intuitiue noscuntur. Fertur à primo parente Adam inuentum, vel saue ab Abraham: licet postea successu temporis perfectiùs semper, & perfectiùs elaboratum prodierit. De eius fabrica, & vsu multi scripsêre, imprimisque Egnatius Dantes, & Ioannes Stoferinus egregiis voluminibus. 331. ASTROLOGIA Græcè, Latinè Astrorum sermo seu scientia interpretatur, quæ & Astronomia promiscuè dicta est: Nisi quod vsus postea obtinunt, vt Astrologia vsurparetur pronotitia quadam coniecturali ex astrorum positu comparata, qua de rerum mutationibus, alijsque effectibus qui à cælorum positu ottum habent, pronunciatur. Astronomia verò pro ipsa astrorum scientia sumitur, quæ in eorum præcisa consideratione sistit, stellarum motus, naturas, magnitudines, affectiones scrutatur, ac dimetitur: vnde Astrologia supponit Astronomiam, atque in ea fundatur. Hæc enim pars est nobilior Geometriæ, quantitatem continuam, sed solùm altioris ordinis, & cæleltem considerans; illa scientia experimentalis longo vsu a posteriori, & ex effectibus comparata, quæ nec scien-

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70 LEXICON 326. ASTRO, from Græcobarbaro, is said to be the second decan of Aquarius, under the rule of Mercury in the barbaric sphere, a significator of good morals, beauty, intellect, gentleness with modesty, generosity, etc. 327. ASTRABISTER was the name given to a certain geometrical instrument for measuring heights and depths, in the manner of the Latin radius 328. ASTRAA was called by Aratus Virgo, a celestial star between Leo and Libra, the name borrowed from fables; for the poets imagine that Justice herself, the chief of all in that golden age, migrated from heaven to earth, but, offended by the crimes of mortals, returned to heaven, where, turned into that celestial star, she from afar weighs their deeds and judges with the scales of water: hence the scales are applied to her: by another name she is called trigone, Aurono, Isis; the quality of that star, the number of the stars of which it consists, its nature, and other things: See under V. Virgo 329. ASTROCYNOS, and ASTROCYON, is the Greek name for the greater sidereal Dog, otherwise called Sirius, which among the many stars of which it is made up has two worthy of special consideration, one in the head, called Isis, the other in the mouth or tongue, among the Arabs Alhabor: of both in their proper place. 330. ASTROLABIVM, a Mathematical instrument, representing almost the whole of celestial doctrine on a plane, whence it is also called a planisphere, as if it showed a sphere on a plane; for by means of it the motions of the stars are very cleverly gathered, distances are measured, ascents, descents, declinations, and other things of this kind are known intuitively. It is said to have been invented by the first parent Adam, or perhaps by Abraham: although afterward, over the course of time, it came forth ever more perfectly and perfectly worked out. Many have written about its construction and use, especially Egnatius Dantes and Ioannes Stoferinus in excellent volumes. 331. ASTROLOGIA, in Greek, in Latin is interpreted as the discourse or science of the stars, and this has also been promiscuously called Astronomy: except that usage later prevailed, so that Astrology was employed for a certain conjectural foreknowledge drawn from the position of the stars, by which one pronounces on changes in things and other effects that depend on the position of the heavens. Astronomy, however, is taken for the science of the stars itself, which rests in their precise consideration, investigating and measuring the motions, natures, magnitudes, and affections of the stars: whence Astrology supposes Astronomy, and is founded upon it. For this is the nobler part of Geometry, considering continuous quantity, but only of a higher order, and celestial; that science is experimental, acquired by long use a posteriori, and from effects, which neither scien-

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tiæ quidem nomen meretur, quandoquidem neque rem per causam scrutatur, neque certitudinem habet, quæ scientiæ animæ est, sed per conjecturas, & experimenta procedit. Hæc propriissimè, ac strictissimè scientia in summo certitudinis apicè sita. Quamobrem, etsi in nomine, seu potius nominis notione conueniant, in re tamen longissimè differunt. <332.> Porrò Astrologiæ objectum sunt naturales effectus à causis exlestitibus producibiles, quatenus perspectâ rerum naturâ, corporumque exlestitium inter se habitudine, ex iis, quæ alias experientia duce pluries euenisse Astrologus noscit, prudens colligit similes effectus ex simili causarum congressu etiam prodituros. Verum, quia inter naturales effectus alij sunt, qui merè à natura proueniunt, & quidem necessariò (posito diuino, & vniuersali concursu, & causarum secundarum connexione) qualis est calor, qui ab igne naturaliter prouenit, nutritio Animalis naturaliter præstita per alimenta &c. alij, qui etsi naturaliter prodeant, originatiè tamen sunt à causa libera, liberè media, proportionata, & causas subordinatas ad talium effectuum productionem applicante; qualis est occasio hominis abs se, vel ab alio præstita, domus ædificatio, liberorum procreatio &c. alij, qui à causa libera liberè etiam secundùm substantiam proueniunt, vt studium, pietas, amor, odium, virtutes denique & vitia, quæ à natura non nisi valdè remotè ex qualitate temperamenti dependent; alij demum qui mixti ordinis sunt, pendent enim ex natura simul, & libera hominis voluntate, ita vt fiat ex iis quædam causarum confusio, atque mixtio, in qua effectus naturales sæpè humano artificio peruertuntur, sæpè etiam adjuuantur, quales sunt plantarum insitio, terræ quantumuis rudis, & asperæ (idem, pro sui ratione, dic de ingenio) excolatio &c. idcircò varia est astrorum circa huiusmodi effectus actiuitas, varia etiam Astrologiæ de eorum productione diuinatio. Cum profectò quæ à natura purè, & absque vll vel sanè paruo hominis artificio prouenint, necessariò etiam producantur, atque adeò certò per Astrologiæ præcepta prædici possint; quæ purè à libertate humana pendent, siue secundùm se tota, siue originatiuè, aut per sui magnam partem omninò liberè prodeant, sicque etiam ab Astrologo vel nullo modo, vel posita conditione, vel sanè valdè remotè ex debili quadam conjectura desumpta ex temperamento possint prædici; Quæ verò mixta sunt, possunt quidem ex parte prævideri, quâ videlicet ex naturali causarum connexione pendent, cum ea certitudine, aut probabilitate, quam causæ liberæ cum natura simul concurrentis maior, aut minor actiuitas, diligentia, obsistentia dat posse fieri. Hinc fallaces, E iiij

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Indeed, it deserves the name only in a certain sense, since it investigates neither the thing through its cause, nor has the certainty that belongs to science in the soul, but proceeds by conjectures and experiments. This, most properly and most strictly, is science placed at the highest summit of certainty. Wherefore, although they agree in the name, or rather in the notion of the name, in reality they differ very greatly. <332.> Moreover, the object of Astrology is natural effects producible from celestial causes, insofar as, by a knowledge of the nature of things and of the relationship of celestial bodies among themselves, the astrologer prudently gathers from those things which experience has shown many times to have happened that similar effects will also proceed from a similar conjunction of causes. But because among natural effects there are some which arise purely from nature, and indeed necessarily (given the divine and universal concurrence and the connection of secondary causes), such as heat, which naturally proceeds from fire, and the nourishment of an animal naturally supplied through food, etc.; others, which although they arise naturally, are nevertheless originally from a free cause, freely mediating, proportionate, and applying subordinate causes to the production of such effects; such as an occasion provided by oneself or by another, the building of a house, the procreation of children, etc.; others, which proceed from a free cause freely even as to substance, such as study, piety, love, hatred, and finally virtues and vices, which depend on nature only very remotely, from the quality of temperament; others finally which are of a mixed order, for they depend at once on nature and on the free will of man, so that a certain confusion and mixture of causes arises from them, in which natural effects are often corrupted by human artifice, and often also aided, such as the grafting of plants, the cultivation of land however rough and rugged (the same, according to its own nature, may be said of intellect), etc.; therefore the activity of the stars with regard to such effects is various, and so too is Astrology’s divination concerning their production. For certainly those things which arise purely from nature, and without any, or at least very little, human artifice, are also necessarily produced, and thus can be predicted with certainty by the precepts of Astrology; but those which depend purely on human freedom, whether wholly in themselves, or originatively, or by the greater part of their being entirely free, can thus either not be predicted by the astrologer at all, or only conditionally, or indeed very remotely from a weak conjecture drawn from temperament; whereas mixed things can indeed be foreseen in part, namely insofar as they depend on the natural connection of causes, with that certainty or probability which the greater or lesser activity, diligence, or resistance of the free causes concurrently acting with nature allows to be possible. Hence deceptive, E iiij

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60 LEXICON Martis, aut Saturni, affert periculum combustionis. 276. ARANEA Rete, Voluellum in Asstolabio representans in plano omnem rationem primi mobilis sese in orbem rotando spatio quatuor, & viginti horarum. In ea videre est descriptos nedum polos, & omnes circulos, qui concipiuntur in primo mobili, sed etiam præcipuas stellas fixas suo loco secundùm longitudinem, & latitudinem, ascensionem rectam atque declinationem, quam habent, additis etiam ad earum plenam noritiam singularum nominibus. Eius inuentorem ferunt fuisse Eudoxum quemdam Samium, qui etiam nomen indidit sumptum à reticula Araneæ cui est valdè persimilis: Arabicè dicitur albacantabat. 277. ARATEA sphæra dicitur globus Astronomicus vulgò Cælestis, in quo omnes stellæ fixæ suis quæque Asterismis inclusæ atque interstinctæ conspiciuntur vna cum positu ad æquatorem atque habitudine ad Zodiacum tam in longum, quam in latum: ita vt facili iure, huius instrumenti ope, possit quis stellam quamuis addiscere, locum in Zodiaco inuestigare, ortum & occasum noscere, ascensiones eruere, atque ad eam significatotum quemlibet per morum directionis deducere. Dicitur Arataa ab Arato antiquissimo poëta Græco eius inuentore, qui etiam Græcè elegantissimo carmine descripsit & explicauit, appellauitque librum Phanomena hoc est Apparentia. Quem posteà Germanicus Cæsar Augusti filius, Sextus Auienus Ruffus, & Marcus Tull. Cicero adhuc adolescens in latinum sermonem transtulerunt. 278. ARCHATAPIAS ex Græcobarb. dicitur in sphæra barbatica primus Decanus Piscium existens sub dispositione, ac dominatu Saturni, qui proinde dat ei significatum anxietatis, cogitationum profundarum, migrationis de loco ad locum, quærendi, & cumulandi opes &c. 279. ARCHITECTVRA ars est ex præceptis Geometricis comparata, qua traditur ratio extruendotum ritè quorumcunque ædificiorum humanæ vitæ commodis congruentium, ac penè ad vniuersi istius dispositionis idæam: Eius genera tia sunt ædificatio, Gnonomica, & Machinatio: Vide Vittuuium l.2.c.3. 280. ARCITENENS dictu est Sagittarius ab arcu, quem manibus gestat, vnde Sagittam eiaculare velle videtur, alio nomine Chyron, Centaurus &c. 281. ARCTOPHILAX Græcè hoc est Vrsacustos appellatur sidus in Cælo propè Vrsam constitutum, quasi ad eam constituendam alio nomine Vociferator, Bubulcus, Bootes. Stellas habet iuxta Ptolemæum 23. at secundùm Keplerum 28. & Baierum 34. qui tamen inter eas annumerat etiam informes circa consi-

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60 LEXICON A burning hazard is brought by Mars or Saturn. 276. ARANEA: a web, representing the Voluellum in the Asstolabium, in a plane showing the whole operation of the first mobile by rotating itself through the space of twenty-four hours. In it may be seen described not only the poles and all the circles which are conceived in the first mobile, but also the principal fixed stars in their place according to longitude and latitude, right ascension and declination, which they have, with the individual names of each also added for their full knowledge. They say its inventor was a certain Eudoxus of Samos, who also gave it the name taken from the spider’s little net to which it is very similar: in Arabic it is called albacantabat. 277. ARATEA is the name given to the astronomical sphere, commonly the celestial globe, in which all the fixed stars, each enclosed and separated by their own asterisms, are seen together with their position relative to the equator and their relation to the Zodiac, both in length and in breadth: so that, with this instrument’s help, one may easily learn any star, investigate its place in the Zodiac, know its rising and setting, determine its ascensions, and deduce from it any sign by way of direction. It is called Arataa from Aratus, the most ancient Greek poet, its inventor, who also described and explained it in very elegant Greek verse, and named the book Phanomena, that is, Apparitions. This was later translated into Latin by Germanicus Caesar, son of Augustus, Sextus Avienus Rufus, and Marcus Tullius Cicero while still a youth. 278. ARCHATAPIAS, from Graeco-barbarous usage, is said in the barbatical sphere to be the first Decan of Pisces, existing under the disposition and dominion of Saturn, who therefore gives it the meaning of anxiety, deep thoughts, migration from place to place, seeking and accumulating wealth, etc. 279. ARCHITECTVRA is an art formed from geometric precepts, by which the method of properly constructing any buildings congruent with the conveniences of human life, and nearly to the idea of the disposition of the whole universe, is taught: its kinds are three, namely building, gnomonics, and machinery: see Vitruvius, book 2, chapter 3. 280. ARCITENENS is called Sagittarius, from the bow which he carries in his hands, as though he wished to shoot an arrow; by another name Chyron, Centaurus, etc. 281. ARCTOPHILAX, in Greek meaning Bear-keeper, is the constellation in the sky situated near the Bear, as if set there to guard it; by another name Vociferator, Bubulcus, Bootes. It has, according to Ptolemy, 23 stars; but according to Kepler, 28, and according to Bayer, 34, who nevertheless also counts among them the unformed ones around the constel-

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MATHEMATICVM. 61 stentes: inter quas insignior est quæ inter cruta primæ magni- tudinis dicta arcturum de qua mox infra. Pluta vide in Verbo Bootes. ARCTOS Græcè, Latinè Vrsa, apud Astronomos accipitur ad significandum promiscuè duo sidera in Cælo, quorum alte- < 181.> rum Vrsa maior Græcis Elicem altera Cynosura nobis Vrsa mi- nor dicitur. Vtrumque ad polum arcticum ita intra circulum arcticum clausæ, & complicatæ, vt vna resupinata alterius contegat caput, at quæ supina maior, quæ recta minor, ore alterius caudam arripere velle demonstrat: de vtraque sic ceci- nit Ouid. Esse duas Arctos, quarum Cynosura vocatur. Sedonijs: Esicem graia carina notas. Verum, etsi olim Arctos nomine vtraque veniebat Vrsæ; modò tamen vsus obtinuit, vt solùm signetur minor, & Cyno- sura: Quinimò sæpissimè pro ipso Polo, qui ei proximè adjacet, & ab ea, denominationem sumit, accipitur; Vnde &c polus Arcticus, qui suprà nos attollitur, & circulus eum am- biens dictus: sicut etiam Septentrionalis à Septentrionibus, hoc est, stellis minorem Vrsam efformantibus; nec non Bo- realis à Borea vento inde exsufflante. ARCTVRVS ex Græco quasi Cauda Vrsæ dictus Isidoro Ar- < 183.> Euzona, Arabicè Alramec, vel Aikameluz, & Colanza, hoc est gladius, & pugio Bootis dicitur stella fixa primæ magnitu- dinis de natura Louis, & Martis in Boote extrà formam exi- stens inter eius crura. Eius ortus certissimas tempestates facit vt ait Plin. lib. 2. cap. 39. Arcturi sidus, inquit, non ferme sine procellosa grandine emergit. occalus cum Sole excitat ventos Australes: Reliqua vide in Verbo Alramech. Arcvs apud Astronomos est pars circuli intercepta ab vno < 184.> ad aliud punctum, qua videlicet vel totius circuli quantita- tem, vel aliud quid Geometricè, & proportionaliter auspica- mur. Hinc arcum directionis dicimus quantitatem æquatoris interceptam inter duo puncta in cælo, quorum alterum stet lo- co significatoris, alterum promissoris, quam per certum tem- pus explere debet vnus quousque ad alterum deuoluatur: Sed de hac re dicetur in V. Directio. AREA apud Geometras audit spatium vacuum, seu superfi- < 185.> cies planæ intra latera alicuius figuræ, seu planæ, seu circularis comprehensa: quæ quidem in figuris planis mensuratur per quadrata earum linearum per quas latera, seu ambitus earum- dem figurarum mensurari solent; in figuris verò circularibus per semidiametum circuli multiplicatam in dimidiam partem circumferentiæ: vt si circumferentia alicuius circuli sit 132.

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remaining: among which the most notable is that among the fixed stars of first magnitude called Arcturus, of which more below. See more in the word Bootes. ARCTOS, in Greek, Vrsa in Latin, is taken by astronomers to signify indifferently the two stars in the sky, of which the greater is called by the Greeks Helice, the lesser by us Cynosura, or the Greater Bear and the Lesser Bear. Both, around the arctic pole, are so enclosed within the arctic circle and so intertwined that one, lying on its back, covers the head of the other; but the greater, being supine, and the lesser, upright, seems with the mouth of one to be trying to seize the tail of the other. Of both Ovid sang thus: There are two Bears, one of which is called Cynosura. Sedonii: with Greek keel, the signs of Esic. Yet although in former times both Bears went by the name Arctos, now usage has prevailed so that only the lesser Bear is so designated, and Cynosura. Indeed it is very often taken for the Pole itself, which lies nearest to it and from it takes its name; hence also the arctic pole, which rises above us, and the circle surrounding it, are so called; just as also the septentrional from the Septentrions, that is, the stars forming the Lesser Bear; and likewise boreal from Boreas, the wind blowing from there. ARCTURUS, from the Greek, as it were “the tail of the Bear,” called by Isidore Arctos Euzona, in Arabic Alramec or Aikameluz, and Colanza, that is, “sword” and “dagger” of Bootes, is a fixed star of first magnitude, of the nature of Jupiter and Mars, situated in Bootes outside the figure, between his legs. Its rising brings certain weather conditions, as Pliny says, book 2, chapter 39: “The star of Arcturus,” he says, “does not rise without stormy hail. When it sets with the Sun it stirs southern winds.” See the rest in the word Alramech. Arc, among astronomers, is the part of a circle intercepted from one point to another, by which, namely, we estimate either the quantity of the whole circle or something else geometrically and proportionally. Hence we call the arc of direction the quantity of the equator intercepted between two points in the sky, one of which stands in the place of the significator, the other of the promissor, which the one must complete over a certain time until it is carried over to the other. But this matter will be discussed under V. Direction. AREA, among geometers, denotes empty space, or the plane surface enclosed within the sides of some figure, whether plane or circular: and this is measured in plane figures by the squares of those lines by which the sides, or boundaries, of those figures are ordinarily measured; in circular figures, by the radius of the circle multiplied by half the circumference: thus, if the circumference of a circle be 132.

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62 LEXICON diameter verò 41. Si 21. quæ est quantitas semidiametri multi- plicetur per 66. Dimidium circumferentiæ producetur nume- rus areæ circuli prædicti 1386. Rectangulum enim compre- hensum sub semidiametro cuiusuis circuli, & dimidiara parre circumferentiæ eiusdem æquale est eidem circulo. 286. AREA item appellari solet circulus ille qui sub Sole, Luna alijsque astris efficitur ex haliruum copia ibi adunatorum, in quos eorum radij incidenres, quandam veluti coronam circa ipsum sidus efformare videntur: Qua de re vide quæ dicentur in V. Coronæ, nec non in V. Halones. 287. AREDIR Arab idem est ac pulsatio dispositionis & naturæ alicuius planetæ; quod tunc sit, cum aliquis Planeta repertus in alterius dignitatibus illum respicit aliquo radio: nam tunc ille dicetur transmittere suam dispositionem, & virtutem ei, in cuius dignitatibus reperitur. Et hæc transmissio à Latinis di- citur pulsatio. Aliter explicatum fuit in V. Aikia Dapha quod interpretatur pulsatio virtutis. 288. ARGENTVM, seu Argenticomus dicitur apud Astronomos species quædam noui Phænomeni, seu comætes de natura lo- uis, qui est adeò fulgidus vt vix in eum oculorum acies inten- di possit, vt proinde argenti, vnde nomen hausit, fulgorem & puritatem imitari videatur. Hic de nouo apparens Principibus indicat mutationem vitæ, ac regni, quæ, licet fiat in melius, non tamen erit absque perturbationibus, & animi angore. Si- gnificat etiam in vniuersum copiam frugum, bonamque aëris constitutionem, ac salubritatem. De hoc hæc habet Plin. Fit etiam candidus cometes argenteo crinesta refugens vt vix contueri liceat specieque humana Dei effigiem in se ostendens. Quæ verba suspicatur Fromendus spectare ad stellam Magorum, ac de ea voluisse Plinium loqui, quia fama percrebuerat in ludea visum Cometem fulgentissimum in cuius medio imago erat cuiusdam pueruli expressa. 289. ARGESTES Græcè dicitur ventus Occidentalis collateralis Fauonio spirans ab occasu æstuiali à nostris dictus Corus, ab aliis Scoron, & Olympias est natura frigidus, & humidus; licet ab initio siccus, vnde & procellas adducit (vnde ei nomen à Græcis) & niues & grandines facit. Per flat potissimum in æquinoctio autumnali. 290. ARGETENAR Arab. dicitur stella fixa quartæ magnirudinis in flexu Eridani propè Acarnar. 291. ARGION Græcè idem, quod Bootes: de quo suo loco. Hic in Horoscopo repertus, inquit Firmicus, facit hominem ab omni venationis studio alienum, sed qui tamen venationis fructu gaudat, canes ad hoc nuntiat, arma, setia, ac sagittas

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62 LEXICON diameter, however, 41. If 21, which is the quantity of the semidiameter, is multiplied by 66, half the circumference is produced: the number of the area of the aforesaid circle, 1386. For the rectangle contained under the semidiameter of any circle and half the circumference of the same is equal to that circle. 286. AREA is also commonly called that circle which is formed under the Sun, Moon, and other stars from the abundance of vapors gathered there, into which their rays, striking, seem to fashion as it were a certain crown around the star itself. On this matter see what will be said in V. Coronæ, and also in V. Halones. 287. AREDIR in Arabic means the pulsation of the disposition and nature of some planet; and this occurs when a planet found in the dignities of another looks upon it with some ray. For then it is said to transmit its disposition and power to that in whose dignities it is found. And this transmission is called by the Latins pulsatio. It was otherwise explained under V. Aikia Dapha, which is interpreted as pulsation of power. 288. ARGENTVM, or Argenticomus, is said by astronomers to be a certain kind of new phenomenon, or comet, of a luminous nature, so bright that the sharpness of the eyes can scarcely be directed toward it; and thus it seems to imitate the brilliance and purity of silver, from which it takes its name. When it appears newly, it indicates to princes a change of life and of kingdom, which, though it may be for the better, will nevertheless not be without disturbances and anguish of mind. It also signifies in general an abundance of crops, a good condition of the air, and healthfulness. Of this Pliny says the following: “There is also a white comet, with silver hair falling back, so that it can scarcely be looked at, and showing in itself the image of a god in human form.” Fromendus suspects that these words refer to the star of the Magi, and that Pliny wanted to speak of it, because rumor had spread that in Judea a most brilliant comet had been seen, in the middle of which there was an image of a certain little boy depicted. 289. ARGESTES in Greek is called the western collateral wind, blowing from the summer sunset; by our writers it is called Corus, by others Scoron, and Olympias. By nature it is cold and humid, though at first dry, and therefore it brings storms, whence its name among the Greeks, and it makes snow and hail. It blows especially at the autumnal equinox. 290. ARGETENAR in Arabic is called a fixed star of the fourth magnitude in the bend of Eridanus, near Acarnar. 291. ARGION in Greek means the same as Bootes; of which elsewhere. Found in the horoscope, says Firmicus, it makes a man alien to all pursuit of hunting, but one who nevertheless delights in the fruits of hunting; it signifies dogs for this purpose, weapons, nets, and arrows

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MATHEMATICVM. 63 ad feras insectandas venatoribus tradar. In occasu verò inuentus cum Martis iniquo radio, facit periculum moriendi ex bide canis, aut ferarum dilaceratione. ARGONAVIS sidus in cælo ad Australem plagam stellas contineus secundùm communem, numero 45. at secundùm Baier. 63 omnes ferè de natura Saturni, & parum louis, inter quas vna fulgentissima in Canopo existens primæ magnitudinis Arabicè Rubael. Hæc in hotoscopo, inquit Pontanus in Vrania, facit Nauclerum, & præstat fortunam in navigationibus, præsertim si Veneris benigno radio fulciatur: At in occasu cum Saturno partiliter repeita, portendit mortem in aquis. ARGUMENTVM nil aliud audit apud Matheseos professores quàm arcus, per quem alium arcum quærimus, dicitur argumentum analogicè ad Logicam argumentationem. Nam sicut argumentum apud Logicos ducit nos in cognitionem rei vsque adhuc ignotæ; ita arcus iste habet nobis notificare alium arcum proportionalem ignorum. Duplex est, æquatum quod dicitur etiam verum, & medium. Medium est arcus Zodiaci incipiens à linea Augis planetæ, & terminans ad lineam medij moruseiusdem. Æquatum verò est cui adjacet æquatio, proindeque terminatur ad lineam veri motus: De hac re fúse in tabulis secundorum mobilium, præsertim apud Maginum. ARGUMENTVM latitudinis Luna dicitur distantia eiusdem à capite vel cauda Draconis, vbi scilicet in duobus punctis diametraliter opposiris intersecatur orbita Lunæ ab Ecliptica, secundùm successionem signorum progrediendo; cuius ope quanritatem realis obscurationis tam corporis solaris, quàm disci lunaris in eclipsibus venamur, hoc est, quor digiti eclipptici obscurentur. ARIADNÆ corona. Vide corona Gnoosia. ARIAMECH, siue Alramech Arab. idem quod Arcturus, aut Bootes. ARIDED, vel Hierezim. Arab quasi rosa, vel lilium redolens dicitur cauda Cygni stella fixa secundæ magnitudinis de natura Veneris, & Mercurij in extremo caudæ Cygni sideris ad borealem plagam inra Galaxiam constituti, corrupto vocabulo adigege: de qua satis alibi dictum. ARTES signum cæleste, & primum in ordine in Zodiaco, domicilium Martis, & exalrario Solis, vnde incipit calores intendere; & vbi noctes antea præualebant diebus, mox Sole primum eius gradum ingresso, vtpote in æquatore, illis æquantur, ac tandem cedere incipiunt, & fieri breuiores. Est siguum mobile, igneum, calidum, & siccum, quod cum Leone &

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MATHEMATICVM. 63 to be handed over to hunters for the pursuit of wild beasts. When found in the setting, under the hostile ray of Mars, it threatens death from the bite of a dog, or from being torn by wild beasts. ARGONAVIS is a constellation in the sky toward the southern region, containing according to the common reckoning 45 stars, but according to Baier 63, almost all of the nature of Saturn and a little of Jupiter, among which one most brilliant, situated in Canopus, of first magnitude, is called in Arabic Rubael. Pontanus in Urania says that in the horoscope this makes a sailor and grants good fortune in navigation, especially if supported by the benign ray of Venus; but in the setting, when partile with Saturn, it portends death in the waters. ARGUMENTVM means nothing other, among teachers of mathematics, than the arc by which we seek another arc; it is called “argument” by analogy with logical argumentation. For just as an argument among logicians leads us to knowledge of a thing still unknown, so this arc has to make known to us another proportional arc of the unknown. It is of two kinds: equated, which is also called true, and mean. The mean is the arc of the zodiac beginning from the line of the planet’s apogee and ending at the line of the planet’s mean motion. The equated, however, is that to which the equation is attached, and therefore it ends at the line of true motion. On this matter see at length in the tables of secondary motions, especially in Maginus. ARGUMENTVM of lunar latitude is called the distance of the Moon from the head or tail of Draco, where, in two diametrically opposite points, the orbit of the Moon is intersected by the ecliptic, proceeding according to the succession of the signs; by means of this we seek the quantity of the real obscuration both of the solar body and of the lunar disk in eclipses, that is, how many ecliptic digits are obscured. ARIADNÆ corona. See the Gnoosian crown. ARIAMECH, or Alramech in Arabic, the same as Arcturus, or Bootes. ARIDED, or Hierezim. In Arabic, meaning as it were “smelling of rose or lily,” it is said of the fixed star in the tail of Cygnus, of second magnitude, of the nature of Venus and Mercury, at the extreme end of the tail of the constellation Cygnus, situated toward the northern region in the Milky Way, corrupted in pronunciation to adigege; enough has been said elsewhere about it. ARTES is a celestial sign, and the first in order in the Zodiac, the domicile of Mars and the exaltation of the Sun, from which the heats begin to increase; and where nights formerly prevailed over days, as soon as the Sun enters its first degree, namely in the equator, they are made equal, and finally begin to give way and become shorter. It is a movable, fiery, hot, and dry sign, which with Leo and

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64 LEXICON Sagittario constituit Trigonum igneum, cuius dominatores sunt Sol, & Iupiter. Tempore Ptolemæi sub hoc signo erat si- dus, & constellatio Arietis in octaua sphæra continens stellas tredecim (exceptis quinque informibus circa ipsam) omnes ferè de natura Saturni, aut Martis, quarum prima in cornu borealì consistens immediatè incidebat in æquatorem; at nunc ob motum proprium octauæ sphæræ præcessit gr. ferè 28 Pri- mæ eius partes ventos & imbres faciunt, mitiùs tamen quàm tempore Ptolemæi: mediæ sunt temperatæ: extremæ tandem calidæ; cumque Zodiacus præditus sit latitudine, pars eius borealis est calidior, & nocua ob plures stellas ibi consistentes de natura Martis & Mercurij: Australis verò frigida ob stellas de natura Saturni. 299. ARIO, teste Kirchero, Chaldaicè dicitur Leo, quintum ab Ariete signum: apud Hebræos autem Arich. 300. ARISTA, & Spica promiscuè appellatur fixa insignis in manu Virginis, quæ triticeam spicam in manu gestare imagine præ- sefert: De ea satis dictum in Verbo Alimech, & alibi sæpè. 301. ARITHMETICA vna est ex principalioribus Mathesis disci- plinis, quæ versatur circa quantitatem discretam, seu mavis dicam, numeros (per quod contradistinguitur à Geometria, quæ considerat quantitatem continuam) tradens methodum supputandi, multiplicandi, & partiendi: proindeque omnes numerorum passiones, proportiones, & habitudines, quas ad- inuicem habent, considerat, atque aliis applicat, vt ex his tandem ad ignota deueniat. Sic positis tribus numeris notis, quartum numerum ignotum per proportionum regulam, quæ aliàs dicitur Aurea, præcipit inuenire: si videlicet secundus, & tertius multiplicentur ad inuicem, ac numerus ex multipli- catione productus diuidatur per primum: Nam numerus quo- tiens erit quartus quæsitus, hoc est cui tertius numerus corres- pondet, & ad quem eandem seruat proportionem, quam pri- mus ad secundum. Hinc considerat in numeris additionem vnius ad alterum, quæ est duorum vel plurium numerorum in vnum collectio: substractionem, quæ est numeri minoris ab altero maiore subductio: multiplicationem, quæ est ductio vnius numeri in alium; sitque cum alter ipsorum augetur toties, quoties in altero continetur vniras: ac tandem diuisio- nem quæ est partitio propositi alicuius numeri in partes ab al- tero numero denominatas. Ex ipsis autem numeris aliquem appellat partitorem, seu diuidentem, & est is qui denominat partes, in quas numerus diuidendus tribuitur; qui ob eam etiam causam denominator audit, quatenus denominat, & in- dicat partes, in quas vnum totum intelligitur esse diuisum: numeratorem

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64 LEXICON Sagittarius constitutes the fire Trigon, whose rulers are the Sun and Jupiter. In the time of Ptolemy, under this sign was the star and constellation of Aries in the eighth sphere, containing thirteen stars (apart from five shapeless ones around it), all nearly of the nature of Saturn or Mars, the first of which, standing in the northern horn, fell immediately upon the equator; but now, because of the proper motion of the eighth sphere, it has precessed about 28 degrees. Its first parts cause winds and rains, though more mildly than in the time of Ptolemy; the middle parts are temperate; the extreme parts are hot. And since the Zodiac is endowed with latitude, its northern part is hotter and harmful because of the many stars there standing of the nature of Mars and Mercury; the southern part, however, is cold because of stars of the nature of Saturn. 299. ARIO, according to Kircher, in Chaldaic is called Leo, the fifth sign from Aries; among the Hebrews, however, Arich. 300. ARISTA, and Spica, are used interchangeably to name the notable fixed star in the hand of Virgo, who is represented in image as bearing a wheat ear in her hand: enough has been said of it in the word Alimech, and elsewhere often. 301. ARITHMETICA is one of the principal disciplines of Mathematics, dealing with discrete quantity, or, if you prefer, with numbers (by which it is distinguished from Geometry, which considers continuous quantity), teaching the method of calculating, multiplying, and dividing; and therefore it considers all the properties, proportions, and relations of numbers which they have among themselves, and applies them to other things, so that from these it may finally arrive at the unknown. Thus, three known numbers having been posited, it teaches how to find the fourth unknown number by the rule of proportions, which is otherwise called the Golden Rule: namely, if the second and third are multiplied together, and the number produced by the multiplication is divided by the first. For the number sought will be the fourth term, that is, the one to which the third number corresponds, and with which it preserves the same proportion as the first does to the second. Hence it considers in numbers the addition of one to another, which is the collection of two or more numbers into one; subtraction, which is the taking away of a smaller number from a larger; multiplication, which is the carrying of one number into another, and is when either of them is increased as many times as there are units contained in the other; and finally division, which is the partition of some proposed number into parts denominated by another number. Now from the numbers themselves it calls one a partitor, or divider, and this is the one that names the parts into which the number to be divided is distributed; for this reason it is also called the denominator, insofar as it names and indicates the parts into which one whole is understood to be divided: numerator

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MATHEMATICVM. numeratorem , & est numerus, qui enumerat minutias, seu partes quas continet proposita fractio ex illis, in quas totum, cuius est fractio diuisum est; & quotientem, qui est numerus partium, in quas numerus diuidendus tribuitur, quique eo quoriens denominatur, quia indicat quoties diuisor in numero diuidendo continetur. Similiter in numeris considerat æqualitatem, vel inæqualitatem; primos, seu simplices, qui sunt quos sola vnitas meritur, quales sunt 2. 3. 5. 7. 11. 13. 17. 19. 23. 29. 31. &c. & compositos, quos non vnitas, sed numerus aliquis meritur, vt 4. 6. 8. 9. 10. 12. 14. 15. &c. vel enim eos meritur, & in partes æquales dispescit numerus binarius, vel ternarius, vel quartenarius, &c. de quibus fusè agit Euclides à lib. 7. vsque ad 9. inclusiùè, & luculenter explicat Clauius in Arithmetica practica, nec non in commentar. super eiusdem Euclidis elementa. Porrò non ita opponuntur inter se istæ duæ præcipuæ Mathesis diuisiones, Geometria, inquam, & Arithmetica, vt non pari passu incedant, manus complicant, ac sibi mutuò opitulentur. Er quidem, vt benè obseruar Alexander de Ales, in primo Meteor. ea est Geometriæ ad Arithmeticam proportio, quæ est puncti ad vnitatem, lineæ ad numerum simplicem, corporis quanti ad numerum compositum. Hinc est, vt Geometria ad quantum suum continuum artificiosè dimetendum, Arithmeticis fractionibus opus habet, & ipsa vicissim Arithmeticæ, vt munus suum rectiùs, & expeditiùs exequatur è promptuario suo auxiliates confert superias. Quapropter ei & planos & cubos, & quadratos, & solidos, & angulos, & latera mutuar (vt haber Proclus in Euclid.) darque vt iisdem præceptis in numeris dimeriendis vratur, quibus ipsa in figuris Geometricis, seu planis, seu solidis visa est, eandemque illa proportionem inueniat in quantitate discera, quam ipsa in suo quauro continuo. Sic anguli, seu termini, & radices proportionis dicuntur duo numeri, quibus minores in eadem proportione assumi nequeunt: latera appellantur duo numeri sese mutuò complicantes, aut multiplicantes ad faciendum vnum tertium numerum seu aggregatum, seu multiplicatum: qui verò ab ipsis prosilir, si è duobus tantum lateribus, dicerur planum, si è pluribus, solidum. Similiter quadratus numerus is est, qui æqualiter æqualis est, siue qui sub duobus æqualibus numeris continetur; vt est 16. existens ex multiplicatione mutua 4. & 4. Cubus qui sub rtibus æqualibus numeris continetur; vt est numerus 27. ex multiplicatione 3. 3. 3. quippe ex 3. in 3. deducto sit 9. & ex 9. in 3. producto sit 27. & alia huiusmodi quæ fusiùs videre est in Euclide integro lib. 7. E

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MATHEMATICS. numerator , and it is the number that counts the small parts, or the parts contained in the proposed fraction out of those into which the whole, of which it is a fraction, is divided; and the quotient, which is the number of parts into which the dividend is divided, and is so called because it indicates how many times the divisor is contained in the dividend. Likewise, in numbers it considers equality or inequality; the prime, or simple, which are those that unity alone measures, such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.; and composite numbers, which unity does not measure, but some number does, such as 4, 6, 8, 9, 10, 12, 14, 15, etc.; for either the binary number, or the ternary, or the quaternary, etc., measures them and divides them into equal parts, concerning which Euclid treats at length from book 7 up to 9 inclusive, and Clavius explains it clearly in the Practica Arithmetica, as well as in the commentary on the Elements of the same Euclid. Moreover, these two chief divisions of Mathematics, Geometry, I say, and Arithmetic, are not so opposed to one another that they do not advance at the same pace, join hands, and aid one another. Indeed, as Alexander of Hales observes well, in the first book of the Meteorologica, such is the proportion of Geometry to Arithmetic as that of the point to unity, of the line to the simple number, of the bodily magnitude to the composite number. Hence it is that Geometry, in order to measure its own continuous quantity artfully, needs arithmetic fractions, and in turn Arithmetic, in order to carry out its function more rightly and more expeditiously, draws assistance from its storehouse above. Wherefore it borrows from it both planes and cubes, and squares, and solids, and angles, and sides (as Proclus says in Euclid), and gives so that it may use the same precepts in measuring numbers as it is seen to use in geometric figures, whether plane or solid, and that it may find the same proportion in discrete quantity as it does in its own continuous quantity. Thus angles, or terms, and roots of proportion are called the two numbers by which smaller ones cannot be taken in the same proportion: the sides are called the two numbers mutually combining or multiplying themselves to make one third number, either summed or multiplied: but what springs from them, if from only two sides, is called plane; if from several, solid. Likewise a square number is one that is equally equal, or which is contained under two equal numbers; such as 16, arising from the mutual multiplication of 4 and 4. A cube is that which is contained under three equal numbers; such as the number 27 from the multiplication of 3, 3, 3; for from 3 by 3 is obtained 9, and from 9 by 3 the product is 27, and other such things can be seen more fully in the whole of Euclid, book 7. E

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LEXICON Denique ea est Arithmeticæ facultatis dignitas, vt quemadmoduni obseruauit Philosophus in primo Physicorum, ipsa necessariò omnes Mathematicas scientias præcedat, ad earumque notitiam nos manducat, atque vt Platonis verbis vtar, Arithmeticam si quis auferet, omnes attes aufetuntur & nullæ manent, & omnes in totum peribunt. Verum si quis diuinam, & mortalem originem inspexerit, in qua pietas erga deos, & numerus cognoscitur, cognoscit, quantum numero opus sit: nam & tota Musica numeris opus habet in motibus, & sonis: & quod maximum est, numeri omnium bonorum causa sunt, ex quo cognosci possit, quod omne malum, & omnis motus rationis expers, & indecorus sine rythmo est, & inconcinnus: & omnia quæ cum malo communionem habent esse absque numero oportet tandem statuere eum qui felix futurus est, & qui justum, & bonum, & pulchrum, & omnia huiusce modi ignorat. A Plato: De Arithmeticæ inuentione vide Polydor. Virgil. lib 1. c. 18 & Rhodigin. lib 18 c. 34 302. ARMILLA olim dicebatur ornamentum militare, ad modum circuli, quo milites ex bello victores honoris causa ab Imperatoribus munerabantur, vt eo armum (sic enim audiebat antiquis simistrum brachium) ad fortitudinis indicium decorarent. Inde ad omne circulorum genus significandum hoc nomen translatum est: præcipuè verò apud Astronomos, apud quos circuli materiales sphæræ, sed potissimum suspensorium Astrolabij, vel alterius consimilis instrumenti positum ad illud perpendiculariter statuendum, quod Arabes Abalantica voca- uere, Armilla antonomasticè dicta est: Inde etiam. 303. ARMILLARIS sphæra appellatur quæ pluribus circulis ex solidiori aliqua materia factis interstincta totam primi inobilis doctrinam continet, atque oculis exhibet ad differentiam Arataæ non ita pridem memoratæ, quæ vndequaque solida est, atque in ea circuli, & sidera fixa tantum delineata propriis quæque locis apparent. 304. ARNIG. Arab. Musicale dicitur instrumentum, quod ideò apud Astronomos Arabes sumitur pro ridicula, Lyra, seu Vulture cadente, cælesti sidere, de quo alibi sermo. 305. AROLABVM instrumentum Mathematicum ad venandas siderum affectiones. 306. ARPEEN Græcobarbar. dicitur tertius Decanus Libræ in sphæra barbarica sub dominatu Louis, habens significationem gulositatis, hilaritatis, carminum malorum saporum, &c. 307. ARTVRVS. Vide Arcturus. AS 308. ASANGES Chaldaicè, vel potius Mesanguo dicitur astrum

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LEXICON Finally, such is the dignity of the art of Arithmetic that, as the Philosopher observed in the first book of the Physics, it necessarily precedes all mathematical sciences and leads us to the knowledge of them; and, to use Plato’s words, if one removes Arithmetic, all the arts are taken away, none remain, and all perish utterly. But if one considers its divine and mortal origin, in which reverence toward the gods and number are recognized, one sees how necessary number is: for all Music also requires number in its movements and sounds; and what is greatest, numbers are the cause of all goods, from which it may be known that all evil, and every motion devoid of reason and indecorous, is without rhythm and out of tune; and that all things which have communion with evil must at last be determined to be without number by him who is to be happy, and who is ignorant of the just, the good, the beautiful, and all things of this kind. From Plato: on the invention of Arithmetic, see Polydor. Virgil, book 1, ch. 18, and Rhodiginus, book 18, ch. 34 302. ARMILLA was formerly called a military ornament, in the form of a circle, with which soldiers victorious in war were honored by Emperors as a reward, so that with it they might adorn the arm (for thus the left arm among the ancients was called) as a sign of bravery. Hence the name was transferred to signify every kind of circle, especially among Astronomers, among whom the material circles of the sphere, but chiefly the suspensory part of the Astrolabe or some similar instrument placed to set it perpendicularly, which the Arabs called Abalantica, was by antonomasia called Armilla. Hence also. 303. ARMILLARIS is the name given to a sphere interlaced with several circles made of some solid material, which contains and displays to the eyes the whole doctrine of the first movable sphere, in distinction from the Arataea, mentioned not long ago, which is solid throughout, and in which the circles and fixed stars alone appear drawn in their proper places. 304. ARNIG. In Arabic it is called a musical instrument, which therefore among Arab astronomers is taken for the Ridiculous, the Lyre, or the Falling Vulture, a celestial star, of which elsewhere there is discussion. 305. AROLABVM a mathematical instrument for hunting the affections of the stars. 306. ARPEEN in Greek-barbarous usage is called the third Decan of Libra in the barbaric sphere under the dominion of Louis, having the signification of gluttony, merriment, bad songs, flavors, etc. 307. ARTVRVS. See Arcturus. AS 308. ASANGES in Chaldean, or rather Mesanguo, is called a star

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MATHEMATICVM. < 309.> decem stellis (quot videlicet chordæ sunt in Psalterio decachor- lo, quod per id nominis significatur) constans; apud nos Lyra, eu Fidicula. Keplerus autem in eo sidere considerat stellas vn- ecim, & Baierus in sua Vranometria tredecim. ASBIA Græcè, Latinè dicitur Hydra. Vide suo loco. < 310.> ASCENDENS, horoscopus, horizon, finitor Orientalis est nea illa in Oriente, vnde emergunt sidera, quæque diuidit hemisphærium superius nobis conspicuum ab inferiori, quod met sub terra. Dicitur etiam angulus Orientis, & prima do- mus in cælesti figura Estque apud Astrologos significator vitæ, corporis affectionum, morum itinerum &c. Significat etiam niria rerum, eo quod est domus initatiua cælestis motus. < 311.> ASCENDENS etiam appellatur illa pars cæli, quæ incipit à li- nea Meridiana Imi cæli, & per viam Orientis incedens, vsq[ue] d Meridianum superius extenditur (sicque includit tertiam, ecundam, primam, duodecimam, vndecimam, ac decimam lomum) vel inde dicta, quod per eam incedentes planetæ & partes primi mobilis semper ascendunt: sicut è contra descen- dens vocatur pars opposita, à linea Meridiana supra terram ad ineam Imi cæli per Occidentem gradiens, quia per eam pla- netæ semper descendunt. Hinc. < 312.> ASCENSIONES, & descensiones signorum sunt partes æquato- ris, quæ cum tali signo, aut Zodiaci parte coascendunt, & imul descendunt; adeoque etiam planerarum, quos in eisdem partibus reperiri contingit. Postò ascensiones ac descensiones, aliæ rectæ, aliæ obliquæ. Ascensiones rectæ sunt partes æqua- toris, quæ ascendunt per lineam rectam, adeoque compre- tendunt omnes illas cæli partes, quæ sub linea recta ducta per polos muudi, & partes æquatoris oppositas continentur, quod iccidit in sphæra recta, atque in sphæra obliqua tantum in circu- o recto, seu Meridiano. Ascensiones, & descensiones obliquæ unt partes æquatoris, quæ obliquè ascendunt, aut descendunt n sphæra obliqua vbialter polorum attollitur: quoque obli- quior erit sphæra, eò obliquior erit ascensio æquatoris, sicquo nior postio eius ascendit cum signis Zodiaci borealibus, ma- or cum Australibus. E contrà maior arcus descendit in borea- ibus, quàm in australibus. Arcus verò differentiæ ascensio- rum, aut descensionum, qui intercipitur inter ascensionem ectam, & obliquam, vocatur < 313.> DIFFERENTIA Ascensionalis, cuius ope extrahuntur ascensio- nes, ac descensiones obliquæ ad omnem poli elevationem. Da- caenim eleuatione poli alicuius regionis, ac declinatione side- ris, statim apparet differentia ascensionalis, quæ pro rarione declinationis borealis, aut australis, addenda, vel subtrahenda E i

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MATHEMATICUM. < 309.> consisting of ten stars (namely, as many strings as there are in the ten-stringed psaltery, which is signified by that name); among us, Lyra, or Fidicula. Kepler, however, considers there to be eleven stars in that constellation, and Bayer in his Uranometria thirteen. ASBIA in Greek, in Latin is called Hydra. See it in its proper place. < 310.> ASCENDENS, horoscopus, horizon, the eastern boundary is that line in the east from which the stars emerge, and which divides the upper hemisphere visible to us from the lower, which is under the earth. It is also called the angle of the east, and the first house in a celestial figure. Among astrologers it is a significator of life, the state of the body, habits, journeys, etc. It also signifies the beginning of things, because it is the initiating house of celestial motion. < 311.> ASCENDENS is also called that part of the sky which begins from the southern line of the lower heaven, and, proceeding through the way of the east, extends up to the upper meridian (and thus includes the third, second, first, twelfth, eleventh, and tenth houses), or so called because through it the planets and parts of the prime mobile, passing along, always ascend; just as, on the contrary, the descending is called the opposite part, from the southern line above the earth moving through the west to the line of the lower heaven, because through it the planets always descend. Hence. < 312.> ASCENSIONS and descensions of the signs are parts of the equator which ascend and at the same time descend together with such a sign, or part of the zodiac; and likewise also of the planets, which happen to be found in the same parts. Moreover, ascensions and descensions are some right, others oblique. Right ascensions are parts of the equator which ascend in a straight line, and therefore comprise all those parts of the sky that are contained under a straight line drawn through the poles of the world and opposite parts of the equator, which occurs in a right sphere, and in an oblique sphere only in the great circle, or Meridian. Oblique ascensions and descensions are parts of the equator which ascend or descend obliquely in an oblique sphere where one of the poles is elevated: and the more oblique the sphere is, the more oblique will be the ascension of the equator; thus a smaller arc rises with the northern signs of the zodiac, a greater with the southern. On the other hand, a greater arc descends in the northern than in the southern. But the arc of the difference of ascensions or descensions, which is intercepted between the right and the oblique ascension, is called < 313.> DIFFERENTIA Ascensionalis, by means of which oblique ascensions and descensions are extracted for any elevation of the pole. For given the elevation of the pole of some region and the declination of a star, the ascensional difference immediately appears, which, according to whether the declination is northern or southern, is to be added or subtracted. E i

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LEXICON est ab ascensione recta eiusdem sideris; statimque profili r ascensio, aut descensio obliqua ad datam poli elevationem di- etæ regionis; quibus mediis postea directiones perficiuntur. Atque ascensionibus rectis vtrimur in sphæra recta, & in cir- culo recto; obliquis in sphæra obliqua à primo gradu eleua- tionis poli vsq[ue] ad grad. 90. Extant ad hoc Tabulæ differentiæ ascensionalis, ascensionum rectarum, necnon obliquarum ad quamcumque poli elevationem: Qui volet videat apud Magi- num, & Argolum. 314. ASCHER Ali:mini Arab. alio nomine Alhabor dicitur stella fixa fulgentissima micans in ore canis Maioris: de qua abundè dictum in V. Alhabor. 315. ASCONES, siue dominus Ascone dicitur species quædam Co- meræ de natura Mercurij parui quidem corpore, & coloris cæ- rulei, sed cum cauda oblonga, qui apparens portendit bella, & monies Principum virorum, necnon etiam morbos acutos, tyrannides, & similia. 316. ASELLI à Manilio dicti etiam lugula (quamuis hæ commu- niter pro cingulo Orionis accipiantur, vt suo loco dicemus) sunt stellæ paræ quidem quippequæ quartæ magnitudinis, sed magnæ potentiæ, & plusquam credi possit, infensissimæ in pectore Cancri vna cum Præsepi stella nebulosa consisten- tes, de natura Martis, & Solis in gradu 2. Leonis, ferè in ipsa Ecliptica, ideoque iamæ actiuiatis. Hæ cum Sole exorientes turbant aërem, imperuosis imbribus ingruunt, sulfure, & to- nitruis. Natum faciunt agrestem, irreligiosum, iettricum, ad studia venationis applicitum: si verò in occasu fuerint cum Martis iniquo: radio. acerbam mortem, ait Firmicus, dum adhuc dormiet min. tantur. 317. ASICATH Græcobar. significat in sphæra barbarica pri- mum Decanum Tauri, cuius dispositio est penes Mercurium, & est indicium arationis, sationis, structuræ, deductionis co- loniarum, scientiarum ciuilium, Geometriæ &c. Item 318. ASCECAN ibidem dicitur Primus decanus Arieris competens Martii, proindeque est signum audaciæ, fortitudinis, elatio- nis, inuerecundiæ &c. 319. ASIDA Arab Carinè l upus astrum: de quo suo loco. 320. ASPECTVS est mutua quædam habitudo, seu familiaritas duorum siderum sese aliquo radio harmonicè considerato, in- tuentium, quo eorum virtus augescit, aut deprauatur, per mutuam efficientiam, prout fuerint in actiuis, passiuisve qua- litatibus natura conformia, aut difformia. Hoc autem sit, vel per circuli medietatem, cum planetæ sunt in locis diametrali- ter oppositis, & vocatur Oppositio: vel per tertiam circuli

Transcription: Translated (English)

LEXICON is from the right ascension of the same star; and immediately from the ascension, or oblique descension, according to the given elevation of the pole of the region; by these means directions are afterward accomplished. And we use right ascensions in the right sphere, and in the right circle; oblique ones in the oblique sphere, from the first degree of elevation of the pole up to the 90th degree. For this there are extant tables of ascensional difference, of right ascensions, and likewise of oblique ones for whatever elevation of the pole: whoever wishes may see them in Maginus and Argolus. 314. ASCHER Ali:mini in Arabic is called by another name Alhabor, a most brilliant fixed star, shining in the mouth of the Greater Dog; of which it has been amply said in V. Alhabor. 315. ASCONES, or Lord Ascone, is said to be a certain species of comet of the nature of Mercury, small indeed in body, and of a blue color, but with an elongated tail, which, when appearing, portends wars, and the deaths of leading men, as well as acute diseases, tyrannies, and the like. 316. ASELLI, called by Manilius also lugula (although these are commonly taken for the Belt of Orion, as we shall say in its proper place), are stars indeed small, since they are of the fourth magnitude, but of great power, and more hostile than can be believed, situated in the breast of Cancer together with the nebulous star Praesepe, of the nature of Mars and the Sun, in the 2nd degree of Leo, almost in the very Ecliptic, and therefore of great activity. These, when rising with the Sun, disturb the air, they come on with violent rains, with sulfur and thunder. They make the native born rustic, irreligious, gloomy, inclined to the study of hunting; but if they are setting with the evil ray of Mars, Firmicus says they bring bitter death, while still he will sleep much. 317. ASICATH, in Greek and Arabic, signifies in the barbarous sphere the first decan of Taurus, whose disposition is under Mercury, and it is an indication of plowing, sowing, building, colonization, civil sciences, geometry, etc. Also 318. ASCECAN is there called the first decan of Aries, belonging to Mars, and therefore it is a sign of audacity, strength, exaltation, shamelessness, etc. 319. ASIDA, Arabic, Carinè, the star of the wolf: concerning which in its proper place. 320. ASPECT is a certain mutual relation, or familiarity, of two stars beholding one another by some harmonically considered ray, by which their power is increased or corrupted, through mutual efficiency, according as they are by nature conformable or differing in active or passive qualities. And this takes place either by the half of the circle, when the planets are in diametrically opposite places, and it is called Opposition: or by the third part of the circle

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MATHEMATICVM. 69 partem, & appellatur Trinus: vel per quattam partem, & dicitur Quadratus: vel denique per sextam partem, & audit Sextillis. Conjunctio verò, qua duo planetæ conveniunt in eodem signo, eodemque gradu, licet imptoptiè dicatur aspectus, nihilominus inter aspectus computatur, cum sit vera familiaritas, eaque omnium potentissima. Addunt alij ex Keplero, sumpta proportione ad modos musicos, alios aspectus minores, & sunt sesquiquadratus qui est distantia per quartam partem circuli & insuper per alterius quattæ dimidium hoc est per grad. 135. Quintilem, qui est distantia per quintam partem, & Biquintilem, qui est distantia duarum ex quinquo partibus. Arque huiusmodi radios computant nedum in Zodiaco, sed etiam in mundo à domibus, per partes proporsionales arcus diutni, aut nocturni cuiuscunque sideris. Portò aspectus alius platicus, alius partilis Partilis est, cum præcisè, aut in eodem gradu consistunt duo planetæ (& est in conjunctione) aut tot partibus ad vnguem distant, ad inuicem, quot requituntur ad talem aspectum efformandum: hicque platico est longè perfectior, qui solùm est ad orbem, hoc est, cum non quidem ad amussim, distant, neque radius proijcitur ad corpus planetæ, sed solum incidit in orbem, seu sphæram lucis p[er]sùs: De quo, sicut & de eius diuisione in applicationem, & lefluxum plura vide in V. Platicus, nec non sub propriiis noninibus singulotum aspectuum. ASSABE Arab. Latinè Eutus. Ventus subsolanus vnnus ex < 321.> quatuor cardinalibus, spirans ab ortu æquinoctiali: Vide in V. Græco Apeliores. ASSANGE Armig. Arab. seu potiùs Chaldaicè, Latinè Fidicula vultur cadens, sidus in coelo: de quo vide alibi. < 322.> Assvapud Metheorologicos est genus quoddam aëtearum < 323.> impressionum, quod est in duplici differentia, aliud ascendens, onflatum ex partibus exhalationis accensæ in suprema aëris egione, & viderur ascendere, sicut si euolarent scintillæ de ornace: aliud verò descendens, & est ignis reventus in nube, qui tamen expellitur obuiare nube frigida, & cadit continuè, ropter quod videtur quod stella cadens sit longa, quia relinquit vestigia casus post se. Io. de Combis in compend. Theologicæ veritatis lib. 2. 1. 9. Vide in V. idera discurrentia. ASTACVS, Nepa, Camniarus Vide Cancer. < 324.> ASTER nomen gericum stellæ singularis, prout præscindit à < 325.> axa, vel erratica. Verum astermus, & astrum significant multitudinem, & congregationem plusium stellarum inextrarium; quæ conveniunt ad formandum vnum integrum sidus ut figuram, vt est Vela, Leo, Lyra, &c. E iii

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MATHEMATICVM. 69 by a third part, and it is called Trinus; or by a fourth part, and it is called Quadratus; or finally by a sixth part, and it is called Sextilis. Conjunction, moreover, when two planets come together in the same sign and the same degree, although improperly called an aspect, is nevertheless counted among the aspects, since it is a true familiarity, and the strongest of all. Others add, following Kepler and taking proportion according to musical modes, other minor aspects, and these are the sesquiquadratus, which is the distance by a fourth part of the circle and moreover by half of another fourth, that is by 135 degrees; the quintile, which is the distance by a fifth part; and the biquintile, which is the distance of two fifth parts. And they reckon such rays not only in the Zodiac, but also in the world from houses, by proportional parts of the daily or night arc of any star. Moreover, one aspect is platick, another partile. Partile is when two planets precisely, or in the same degree (and this is in conjunction), or are distant from one another by exactly as many parts as are required to form such an aspect; and this platick is far more perfect, which is only ad orbem, that is, when they are not indeed exactly distant, nor is the ray projected to the body of the planet, but only falls within the orb, or sphere of light itself: concerning which, as also concerning its division into application and recession, see more in V. Platicus, as well as under the proper names of the several aspects. ASSABE Arab. In Latin, Eutus. The east wind, one of the four cardinal winds, blowing from the equinoctial east: see in V. In Greek, Apeliores. ASSANGE Armig. Arab., or rather Chaldaic, in Latin Fidicula vultur cadens, a star in the heavens: see elsewhere. < 322.> Assva among the meteorologists is a certain kind of aerial impressions, which is of a twofold difference: one ascending, inflamed from parts of burning exhalation in the upper region of the air, and it seems to ascend, as if sparks were flying out of a furnace; the other descending, and it is fire returned in a cloud, which nevertheless is driven out by meeting a cold cloud, and falls continuously, for which reason a shooting star seems long, because it leaves traces of its fall behind it. Jo. de Combis in Compendium Theologicae Veritatis, book 2, 1. 9. See in V. idem discurrentia. ASTACVS, Nepa, Camniarus. See Cancer. < 324.> ASTER is the Greek name for a single star, insofar as it is distinguished from a fixed star, or a wandering one. But astermus and astrum signify a multitude and congregation of several stars inextricably joined together, which agree to form one complete constellation as a figure, as is Vela, Leo, Lyra, etc. E iii

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70 LEXICON 326. ASTRO, ex Græcobarbaro dieitur secundus decanus Aquarij, sub dominatu Mercurij in sphæra barbarica, significator bonorum morum, formæ, intellectus, mansuerudinis cum modestia, liberalitatis, &c. 327. ASTRABISTER dictum est instrumentum quoddam Geometricum ad mensutandas altitudines, & profunditates, instar radij Latini 328. ASTRÆA dicta est ab Arato Virgo, exælete sidus inter Leonem & Libram, mutuato ex fabulis nomine, fingunt enim Poëtæ ipsam justitiæ antistitem aureo illo sæculo è cælo in teitas migrasse, sed mortalium seeleribus offensam cælos repetisse, vbi in cæleste illud sidus conuersa eorum facta de longè perpendit, & æqua lance dijudicat: hinc illi lances applicitæ: alio nomine dicitur trigone, Auseno, Isis; eius sideris qualitatem, numerum stellarum, quibus constat, naturam & alia: Vide in V. Virgo 329. ASTROCYNOS, & Astrocyon Græcè appellatur Canis sidereus major, alio nomine Sirius qui inter multas stellas quibus integratur duas peculiari consideratione dignas habet, alteram in capite quæ vocatur Isis, alteram in ore seu lingua apud Arabes Alhabor: de vtrisque suo loco. 330. ASTROLABIVM instrumentum Mathematicum, totam ferè exælestem doctrinam in plano repæsentans, vnde & planispharum dictum est quasi sphæram in plano demonstret, ex eo enim perquam bellè astrorum motus colliguntur, distantiæ mensurantur, aleensiones, descensiones, declinationes, & alia id genus intuitiue noscuntur. Fertur à primo parente Adam inuentum, vel sane ab Abraham: licet postea successu temporis perfectiùs semper, & perfectiùs elaboratum prodierit. De eius fabriea, & vsu multi scripsêre, imprimisque Ægnarius Dantes, & Ioannes Stroflerinus egregiis voluminibus. 331. ASTROLOGIA Græcè, Latinè Astrorum sermo seu scientia interpretatur, quæ & Astronomia promiscuè dicta est: Nisi quod vsus postea obtinuit, vt Astrologia vsurparetur pronotitia quadam coniecturali ex astrorum positu comparata, qua de rerum mutationibus, alijsque effectibus qui à exlotum positu ortum habent, pronunciatur. Astronomia verò pro ipsa astrorum scientia sumitur, quæ in eorum præcisa consideratione sistit, stellarum motus, naturas, magnitudines, affectiones serutatur, ac dimetitur: vnde Astrologia supponit Astronomiam, arque in ea fundatur. Hæc enim pars est nobilior Geometriæ, quantitatem continuam, sed solum altioris ordinis, & cælestem considerans; illa scientia experimentalis longo vsu a posteriori, & ex effectibus comparata, quæ nec scien-

Transcription: Translated (English)

70 LEXICON 326. ASTRO, from Græco-barbarous usage, is called the second decan of Aquarius, under the dominion of Mercury in the barbaric sphere, a significator of good morals, beauty, intellect, gentleness, together with modesty, liberality, etc. 327. ASTRABISTER is the name given to a certain Geometric instrument for measuring heights and depths, in the manner of the Latin radius 328. ASTRAEA is called Virgo by Aratus, the bright star among Leo and Libra, taking its name from the fables; for the poets imagine that she herself, the minister of justice, in that golden age had migrated from heaven to earth, but offended by the crimes of mortals had returned to heaven, where, changed into that celestial star, she from afar surveys their deeds and judges them with equal scales: hence scales are attached to her: by another name she is called Trigone, Auseno, Isis; the qualities of that star, the number of stars of which it consists, its nature, and other things: See under V. Virgo 329. ASTROCYNOS, and Astrocyon in Greek, is called the greater sidereal Dog-star, otherwise Sirius, which among the many stars of which it is composed has two worthy of particular consideration, one on the head, called Isis, the other in the mouth or tongue, among the Arabs Alhabor: of both in their proper place. 330. ASTROLABIVM, a Mathematical instrument, representing almost the whole of celestial doctrine on a plane, whence it is also called planisphæra, as if it showed the sphere on a plane; for by means of it the motions of the stars are very neatly gathered, distances are measured, ascensions, descensions, declinations, and other things of that kind are intuitively known. It is said to have been invented by the first parent Adam, or indeed by Abraham: although later, as time passed, it came forth ever more perfectly and more perfectly elaborated. Many have written on its construction and use, especially Ægnarius, Dante, and Ioannes Stroflerinus in excellent volumes. 331. ASTROLOGIA, in Greek, is interpreted in Latin as discourse or science of the stars, and it has also been promiscuously called Astronomia: unless later usage prevailed, so that Astrologia was employed for a certain conjectural foreknowledge derived from the position of the stars, by means of which one pronounces on changes in things and other effects which arise from the position of the stars. Astronomia, however, is taken for the science itself of the stars, which rests in their precise consideration, examines and measures the motions, natures, magnitudes, and affections of the stars: whence Astrologia presupposes Astronomia, and is founded upon it. For this is the nobler part of Geometry, considering continuous quantity, but only of a higher order, and celestial; that other is an experimental science, acquired a long time a posteriori, and from effects, which neither scien-

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MATHEMATICVM. 71. iræ quidem nomen meretur, quandoquidem neque rem per causam scrutatur, neque certitudinem habet, quæ scientiæ unima est, sed per conjecturas, & experimenta procedit. Hæc propriissimè, ac strictissimè scientia in summo certitudinis picè sita. Quamobrem, etsi in nomine, seu potius nominis otione conueniant, in te tamen longissimè differunt. < 332.> Porrò Astrologiæ objectum sunt naturales effectus à causis ælestibus producibiles, quatenus perspectâ rerum naturâ, orporumque cælestium inter se habitudine, ex iis, quæ alias experientia duce pluries euenisse Astrologus noscit, prudens olligit similes effectus ex simili causarum congressu etiam prolituros. Verum, quia inter naturales effectus alij sunt, qui nerè à natura proueniunt, & quidem necessatiò (posito diuino, & vniuersali concursu, & causarum secundarum connetione) qualis est calor, qui ab igne naturaliter proueuit, nutritio Animalis naturaliter præstita per alimenta &c. alij, qui uti naturaliter prodeant, originariè tamen sunt à causa libera, iberè media, proportionata, & causas subordinatas ad talium effectuum productionem applicante; qualis est occisio hominis abs se, vel ab alio præstita, domus ædificatio, liberorum procreatio &c. alij, qui à causa libera liberè etiam secundùm substantiam proueniunt, vt studium, pietas, amor, odium, irtutes denique & vitia, quæ à natura non nisi valdè remotè ex qualitate tempetamenti dependent; alij demum qui mixti ordinis sunt, pendent enim ex natura simul, & libera hominis voluntate, ita vt fiat ex iis quædam causarum confusio, atque nixtio, in qua effectus naturales sæpè humano artificio perpertuntur, sæpè etiam adjuuantur, quales sunt plantarum initio, terræ quantumuis rudis, & asperæ (idem, pro sui ratiore, dic de ingenio) excolatio &c. idcircò varia est astrorum irea huiusmodi effectus actiuitas, varia etiam Astrologiæ de orum productione diuinatio. Cum profectò quæ à natura puerè, & absque vllò vel sanè paruo hominis artificio proueniunt, necessariò etiam producantur, atque adeò certò per Astrologiæ præcepta prædici possint; quæ putè à libertate humana penent, siue secundùm se tota, siue originatuiè, aut per sui manam partem omninò liberè prodeant, sicque etiam ab Astrologo vel nullo modo, vel posita conditione, vel sanè valdè emotè ex debili quadam conjectura desumpta ex temperamento possint prædici; Quæ verò mixta sunt, possunt quidem ex parte præuideri, quà videlicet ex naturali causarum connetione pendent, cum ea certitudine, aut probabilitate, quam causæ liberæ cum natura simul concurrentis maior, aut minor actiuitas, diligentia, obsistentia dat posse fieri. Hinc fallaces, E iiij

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MATHEMATICVM. 71. It truly deserves the name of an art of conjecture, since it neither investigates things through their causes, nor has the certainty which is the sole mark of science, but proceeds by conjectures and experiments. This is most properly, and most strictly, science placed at the height of certainty. Wherefore, although they agree in the name, or rather in the use of the name, yet in reality they differ very greatly. <332.> Moreover, the object of Astrology is natural effects producible by celestial causes, in so far as, having perceived the nature of things and the relations of the heavenly bodies among themselves, the astrologer, from what he knows by experience to have often happened in like cases, prudently infers that similar effects will also follow from a similar concurrence of causes. But because among natural effects some are such as arise simply from nature, and indeed necessarily (given the divine and universal concurrence, and the connection of secondary causes), such as heat, which naturally proceeds from fire, the nourishment of an animal naturally provided through food, etc.; some are such as, although they seem to proceed naturally, are nevertheless originally from a free cause, which freely mediates, proportionately applies, and sets subordinate causes in motion for the production of such effects; such as the killing of a man by oneself or by another, the building of a house, the procreation of children, etc.; some are such as proceed from a free cause even according to their substance, as study, piety, love, hatred, and finally virtues and vices, which depend on nature only very remotely, through the quality of temperament; others at last are of a mixed order, for they depend both on nature and on man’s free will, so that a certain confusion and mixture of causes arises from them, in which natural effects are often brought to completion, and often also assisted, by human art, such as the cultivation of plants, the tilling of land however rough and harsh it may be (the same, according to its own nature, may be said of genius), etc. Therefore the efficacy of the stars concerning such effects is various, and so too is Astrology’s divination of their production. For things that proceed simply from nature, and without any, or certainly with very little, human artifice, are necessarily also produced, and thus can be foretold with certainty by the precepts of Astrology; but those which depend on human freedom, whether wholly in themselves, or originally, or through some part of themselves entirely free, can also by the astrologer be predicted either not at all, or only conditionally, or certainly very remotely, from some weak conjecture drawn from temperament; while those which are mixed can indeed be foreseen in part, namely insofar as they depend on the natural connection of causes, with whatever certainty or probability the greater or lesser activity, diligence, or resistance of the free causes acting together with nature makes possible. Hence fallacious, E iiij

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LEXICON hinc temerariæ sæpè sunt Astrologorum prædictiones, quæ non ad hanc ratam causarum amussim librantur. Hinc jure proscripta fuit ab Ecclesia ea Astrologiæ pars, quæ de rebus vtcunque liberis, certò vel etiam probabiliter agit, arque dijudicat; cum enim huiusmodi effectus, qua liberi sunt, sint etiam contingentes, & qua tales æquè incerti sint; inde fit, vt nequeant certò pronunciari, sed neque probabiliter, nisi ex debili quadam conjectura, & posita conditione, vt ad eos quis se liberè determinauerit. Accedit quod, cum hæc actuum humanorum prædictio, etsi alias cum [con]tano salis, & accuratè fiat, possit in Reipublicæ damnum vergere (nescit enim indoctum vulgus discernere ea, quæ à natura sunt ab iis quæ ab hominis voluntate; nescit Astrologicis prædictionibus vti ad sibi cauendum, aut consulendum, sed quæ dicta fuerint, tanquam ex tripode pronunciata auidè excipit, & inconsideratè exequitur) idcircò eius vsus meritò interdictus, vtpote Reipublicæ vniuersim perniciosus, & solùm in iis, quæ sine noxa publico bono consulere possunt, permissus. Talis est circa agricolatinem, nauigatoriam, & rem medicam; qua quidem in re non, magis cærræ sunt Astrologorum prædictiones, quam quæ de hominis vita naturaliter producenda, perspecta eius Genesi pronuntiantur, sed ideò illæ prohibentur, & istæ fieri permittuntur, quia hæ non adeò animum turbant, & hominem sollicitum reddunt, vt illæ; proindeque euadunt innocuæ, & aliquando proficuæ. Cæterum ad hominis natuitatis momentum erigere natalitium thema, coelestis siderum positus, ex eoquo ritè confecto colligere temperamentum, naturales animi affectiones, corporis constitutionem, morbos naturaliter prouenieutes, vitam debilem, vel robustam, aliaque huiusmodi, non est extra veram Naturæ aleam, neque vlla lege prohibitum vt ex Theologis obseruant Azor. lib. 9. cap. 13. Suar de Relig. 10. 1. lib. 2. cap. 11. Trullench. lib. 2. cap. 10. dub. 4. Tancredi de Relig. lib. 2. cap. 2. quæst. 3. & alij passim. Quod etiam probant Principum figuræ, Ecclesiæ authoritate impressæ, & ab omnibus legi permisæ; quandoquidem isti effectus naturales sunt, à natura necessariò prouenientes, licet fortè quandoque educatione, studio, & arte præuerti possint, & impediri, eo prorsus pacto, quo annonæ caritas, & abundantia, pecudum productio, perniciosorum animalium ingruentia, & alia huiusmodi quæ humano artificio præueniri possunt, & adjuuari. Qua de re vide Titum in Quast. Physiomathemat. cap. ultimo. Astron Græcè dicitur genericè fidus in cælo. Sed tamen aliquando Antonomasticè accipitur pro cane Maiore Sirio, seu

Transcription: Translated (English)

LEXICON Hence the predictions of astrologers are often rash, since they are not measured by this fixed rule of causes. Hence that part of astrology was rightly proscribed by the Church which treats and judges certainly, or even probably, of things that are in some sense free; for since effects of this kind, insofar as they are free, are also contingent, and as such equally uncertain, it follows that they cannot be pronounced upon with certainty, nor even probably, except from a weak kind of conjecture and with the condition added that a person has freely determined himself toward them. Moreover, since this prediction of human actions, even if otherwise made with due reserve and accuracy, may turn to the harm of the commonwealth—for the ignorant crowd does not know how to distinguish those things that come from nature from those that come from the will of man; it does not know how to use astrological predictions to guard itself or to take counsel, but greedily seizes upon whatever has been said, as though spoken from the tripod, and carries it out inconsiderately—therefore its use has deservedly been forbidden, as harmful to the commonwealth as a whole, and permitted only in those matters in which one may consult without harm to the public good. Such are agriculture, navigation, and medicine; and in these matters the predictions of astrologers are no more certain than those uttered concerning the natural course of a man’s life, once his Genesi has been examined. But the former are prohibited and the latter allowed, because the latter do not so disturb the mind and render a man anxious as the former do; and thus they become harmless and sometimes useful. However, to erect the natal theme to the moment of a man’s birth, to take the heavenly positions of the stars from it, and from a duly prepared chart to infer temperament, natural affections of the soul, the constitution of the body, diseases naturally arising, a weak or robust life, and other things of this kind, is not beyond the true scope of nature, nor is it forbidden by any law, as theologians note: Azor, lib. 9, cap. 13; Suar. de Relig. 10.1, lib. 2, cap. 11; Trullench, lib. 2, cap. 10, dub. 4; Tancredi de Relig. lib. 2, cap. 2, quæst. 3; and others everywhere. This is also proved by the figures of princes, printed with ecclesiastical authority and permitted to be read by all; since these effects are natural, necessarily proceeding from nature, though perhaps at times they may be forestalled and prevented by upbringing, study, and art, exactly in the same way as the dearness and abundance of grain, the increase of livestock, the inrush of harmful animals, and other such things that can be anticipated and aided by human skill. On this matter see Titus in Quast. Physiomathemat., cap. ultimo. Astron, in Greek, is used generically for a star in the heavens. But sometimes, by antonomasia, it is taken for the Greater Dog, Sirius, or

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MATHEMATICVM. 73 otius lucida in eius ore, quæ est omnium stellarum maxima, ab aliquibus ipso Sole grandior pethiberur. ASTROTHEMATA stellarum positus in cælesti figura; sicut iam ASTROTHESIA dicitur constellatio, & imago cælestis pluriis stellis constans. Irem &c. ASTRVM Asterismus, sidus, congeries stellarum; Aster rò vt alibi dictum est, vnicam tanùm stellam significat. ASYMETRIA apud Geometras accipirur pro chorda in cirilo, quæ eum diuidit in duas parres, & est veluri Diamerer, uæ tamen per eius centrum non transit. Vide in V. Chorda. AT. ATABVLVS ventus est provincialis Apulix, illique maxi- operè infensus, vnde & nomen sumpsit ex Græco Atinbalin, uod noxam, & detrimentum significat. Est enim frigidissimus, & valdè siccus, vt restarut Plin. lib. 17. cap. 24. eri circa rumam exsufflat omnia aresacit, & adurit. De eo pluta habet eneca in quasi natural. lib. 5. cap. 17. ATAZIR Arab. Latinè interpretarut Directio: estque arrifiosè deductio promissoris in locum significatoris. Sæpissimè ecipirur pro ipso loco Anærerico, seu directione peculiari itæ Moderatoris ad locum inreremptorum: Qua de re vide dali super Quadrip. Prolem, tra. 3 cap. 10. & super Centiloquium epissimè. ATEMBVI ex Græcobarb. dicitur in sphæta barbarica tertius decanus Piscium, sub dominatu Martis, significans scorrationes, amplexationes, oblectationes cum mulieribus, orium &c. rem ATERECHINIS ibidem dicitur secundus decanus Libræ cuius dispositorio spectat ad Saturnum, ac significare habet quietem, ibertarem, vitam bonam, & securam. ATIN Eltaur, hoc est oculus Tauri dicitur Arabicè Palilium alio nomine Aldebaran stella fixa vna Hyadum, eaque nsignior p[er]tine[m] magnitudinis de natura Martis in oculo Au- trali Tauri consistens, quæ etiam vna cum sociis promiscuè ATHLANTIDES appellanrur, & suculæ stellæ inquam pluuio- æ in capire Tauti: de quibus Virgilius Geotg. 1. Ante tibi Eoa Athlantides abscendantur, Debica quam sucis committas semina... De iis plura vide in V. V. Hyades & Suculæ. ATHALE apud Alkabitium idem sonat, ac ascendens. ATHORAIGE Arab. (licet malè vt obseruat Ricciol. sed po- tius Altorsch, vel etiam Benat Einasch.) dicuntur Pleiades Ver- giliæ septem videlicet stellæ de natura Martis; & Lunæ in

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MATHEMATICUM. 73 the brighter one in its mouth, which is the largest of all the stars, by some is said to be larger than the Sun itself. ASTROTHEMATA, the positions of stars in a celestial figure; as now ASTROTHESIA means a constellation, and a celestial image consisting of several stars. Item, etc. ASTRUM, an asterism, a star, a gathering of stars; Aster, however, as has been said elsewhere, signifies only a single star. ASYMMETRIA, among geometers, is taken for a chord in a circle which divides it into two parts, and is as it were a diameter, yet does not pass through its center. See under V. Chorda. AT. ATABULUS is a provincial wind of Apulia, and greatly hostile to it, whence it also took its name from the Greek Atinbalin, which signifies harm and damage. For it is very cold and very dry, so that, as Pliny relates, lib. 17. cap. 24, around Rome it blows everything dry and scorches and burns it. More on this is found in Seneca, Quaest. Natur. lib. 5. cap. 17. ATAZIR, Arabic; in Latin interpreted as Direction: and it is an astrological deduction of the promissor to the place of the significator. Very often it is taken for the place itself, whether anaretic, or for the special direction of the Lord to the place of the slain. On this matter see Cardanus on Quadripartitum Ptolemaei, tr. 3 cap. 10, and on the Centiloquium often. ATEMBUI, from Greek-barbarous usage, is said in the barbaric sphere to be the third decan of Pisces, under the dominion of Mars, signifying fornications, embraces, pleasures with women, and such like. ATERECHINIS, there is said to be the second decan of Libra, whose dispositor is assigned to Saturn, and it is said to signify quiet, freedom, a good and secure life. ATIN Eltaur, that is, the eye of Taurus, is called in Arabic Palilium, otherwise Aldebaran, a fixed star, one of the Hyades, and the most notable in magnitude, of the nature of Mars, situated in the southern eye of Taurus, which also together with its companions is commonly called ATHLANTIDES, and is one of the rainy stars in the head of Taurus; concerning which Virgil, Georg. 1. Before you shall set the Eoan Athlantides, before you commit the seeds to the furrows... See more on these in V. V. Hyades and Suculae. ATHALE, among Alkabitius, means the same as ascendant. ATHORAIGE, Arabic (though badly so, as Ricciolus observes; but rather Altorsch, or also Benat Einasch.) are called the Pleiades, the Vergiliae, namely seven stars of the nature of Mars; and of the Moon in

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74 LEXICON Teuri pectore consistentes, licet septima, vt aliàs obseruatum est, aliquando conspicua sit, aliquando non. Earum ortus cum Sole sereno coelo, hyemis asperitatem, si nubilo, eandem pluuiosam præsignat: occasus autem pluuias niuelque adducit; ar si cum Saturno occiderint, aur Mercutio turbant aërem, nebulas & ventos producunt. Occidunt autem Romæ cum grad. ferè 27. Tauri: Plura sub V. Pleiades. 346. ATTESTATIONES vocant quandoque Astrologi, teste Vallastellarum adiniuicem irradiationes, quas vulgari nomine appellamus aspectus, nempe trinos, sextiles, quadritos, oppositiones; licet attestatio, vt ex etymo nominis patet, aliquid amplius vltra irradiationem dicat, hoc est testimonium rei significatæ, & effectum talis irradiationis. 347. ATMOSPHERA, hoc est halituum sphera dicitur pars illa aëris terræ vicinior, quæ ob terrestres halitus, qui ei perpetuò admiscentur, crassior, & impurior est cæteris aëris regionibus; quî fit, vt per eius crassitiem radij solares immissi ex parte retineantur, atque in eius opacitate reflectantur, qui ad terram vsque peruenerunt, vnde originem habuit lux illa crepera, & suboscura, quam nos manè & ferò in aëre propè horizontem tam ortiuum, quam occiduum videmus, & vulgari nomine crepusculum vocitamus. AV 348. AVERVS Lumine dicitur planeta, cùm recedit à Sole, vel Sol ab eo à conjunctione ad oppositionem; quò enim magis à Sole discedit, eò magis lumine, quod à Sole muruatur abundat, vt vel lippis oculis videre est in Luna, & in Venere. E contra minutus lumine dicitur, cum accedit ad Solem, vel Sol ad ipsum ab oppositione ad conjunctionem. Esse autem lumine plenum, vel auctum, computatur inter maximas dignitates accidentales, planetis, conuenientes: quippe cælestia corpora (vt erudirissimè probar Tirus in Ca esti philosophus) lumine potissimum operentur. 348. AVERVS numero vocatur planeta, quando moru suo proprio supetar suum motum medium, & idem sonat, de motu velox. Quod item inter præcipuas planetarum fortitudines numeratur; tunc enim euadit viribus præualens, ac validior, eò quod moru suo proprio contrà motum primi mobilis gradiens, quò velocior est, eò magis supra nostrum hemisphærium moratur; non enim rapimur exquisitè à primo mobili, vt esset si foret stationarius, aut rerrogradus, sed aliquantulum tesistir, & contrà niritut, adeoque plus temporis habet ad inferiora hæc alreanda. E contra minutus numero dicitur, cum tardi motus est, nec exæquat medium motum: vnde fit vt citiùs cursum suum

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74 LEXICON The stars standing together in the heart, although the seventh, as has elsewhere been observed, is sometimes visible and sometimes not. Their rising, with the Sun in a clear sky, foretells the severity of winter; if the sky is cloudy, the same foretells rain. Their setting, however, brings rain and snow; but if they set with Saturn or Mercury, they disturb the air and produce mists and winds. They set at Rome when, from the beginning of Taurus, about 27 degrees remain. See more under V. Pleiades. 346. ASTATATIONS the Astrologers sometimes call, as Vallastellarum testifies, those mutual irradiations which we commonly call aspects, namely trines, sextiles, squares, oppositions; although attestation, as the etymology of the word shows, means something more than irradiation, that is, it signifies the testimony of the thing signified and the effect of such irradiation. 347. ATMOSPHERE, that is, the sphere of vapors, is the name given to that part of the air nearest the earth, which, because of the earthly vapors perpetually mingled with it, is thicker and more impure than the other regions of the air; whence it comes about that by its thickness the incoming solar rays are partly retained and in its opacity reflected, those rays having reached as far as the earth, from which that dim and somewhat obscure light takes its origin, which we see in the morning and evening in the air near the horizon, both rising and setting, and which we commonly call twilight. AV 348. A VERUS in light is said of a planet when it recedes from the Sun, or the Sun from it, from conjunction to opposition; for the more it departs from the Sun, the more it abounds in light, which it borrows from the Sun, as can easily be seen even by half-blind eyes in the Moon and in Venus. On the contrary, it is said to be diminished in light when it approaches the Sun, or the Sun approaches it, from opposition to conjunction. To be full of light, or increased, is reckoned among the greatest accidental dignities proper to the planets; for celestial bodies (as the most learned Tyrus proves in the Celestial Philosopher) operate chiefly through light. 348. A VERUS in number is said of a planet when by its own motion it exceeds its mean motion; and it has the same meaning as swift in motion. This too is numbered among the principal strengths of the planets; for then it becomes more powerful and stronger, because by moving by its own motion against the motion of the first mover, the faster it is, the more it remains above our hemisphere; for we are not drawn along exactly by the first mover, as we would be if it were stationary or retrograde, but it resists somewhat, and runs contrary to it, and thus has more time to attend to these lower things. On the contrary, it is said to be diminished in number when its motion is slow and does not equal the mean motion; whence it happens that it completes its course more quickly

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MATHEMATICVM. 75 rnum perficiat, sicque minus agere possit in isthæc inferiora. incum Luna moru suo proprio sit omnium planetarum citis- na pergit enim quandoque secundum successionem signo- m quindecim gradus, adeoque procedendo ab Oriente in cidentem, rotidem gradibus remaner retro: consequenter is omnibus supra teriam consistit, plus temporis haber ad in- iora hæc alteranda, quod sæpè est horar. 20 & eò plus, de etiam est vt ista maximè ab ea repatiantur, vt vel ob id, eius efficientia, sublunarium nomen sortita sint. AVELLAR Græcè, vel potius Chaldaicè dicitur Stella fixa < 349.> cundæ magnitudinis de natura mixta Marris, & Mercurij, & rurni in capite præcedentis Gemiuorum consistens, qui Ca- bor, seu Apollo dicitur. Arabicè Ras Algeuze. AVGENTES fortunam gradus vocantur apud antiquos Arabes < 350.> tri quidam signorum gradus, in quibus repertæ fortunæ, aut guli plurimum augerur eorum virtus: qua de re vide in V. radus. AVIS, Gallina Olor, Cignus, fidus in Cæload borealem pla- < 351.> tim, ad Galaxiam: de quo alibi satis dictum. Item AVIS Paradisiaca dicitur aliud fidus ad polum Antarcticum < 352.> nouo detectum à Nautis Hilpanis ad Australes plagas appul- i. Vide in V. Manucodiata. AVLAX in tabulis Persicis dicitur extrema Eridani, hoc est < 353.> Icus, Stella fixa primæ magnitudinis de natura louis, & Ve- ceris existens in gr. 21. Arietis Arabicè Acarnar. AVRA lenis est ventus suauiter perflans, non omninò absimi- < 354.> is Zephiro, & aliquibus Apogæis. AVREA regula Encomiasticè nominatur apud Arithmeticos < 355.> signis quædam numerorum proportio, qua, datis tribus nu- meris notis, quartus ignotus emergit: multiplicatur enim ter- us numerus (cuius proportionalem partem volumus indagare) er secundum numerum, & productum postea diuiditur per rimum datum; nam quotiens est quartus numerus proportio- < 356.> alis, quem quærimus. Visitatissima, & peincessaria regula mnibus non tam Arithmeticis, quàm vniuersæ Mathesis professoribus. AVREVS numerus sic dictus, quod Athenis aureis literis scri- < 357.> tus repetiebatur, est mensura motus capitis Diaconis Lunæ, quæ completur in annis solatibus 19. cuius ope omnis ferè inæ- qualitas motus lunaris adæquatur, indeque eruitur Epacta cui- jue anno conueniens, ac Lunæ ætas. Sic igitur definiri potest. Est artificiosa Cyclo decennouennalis revolu 10 per annos sequentes distributa ab vnsatæ ad numerum 19. quo expleto sierum reditur ad vnsatem. Eius inuentor fuit Meton quidam Atheniensis à

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MATHEMATICUM. 75 rnum it accomplishes, and so it can act less in these lower things. Since the Moon, by its own motion, is the swiftest of all the planets; for it sometimes advances according to the succession of the signs fifteen degrees, and thus, proceeding from the East to the West, remains behind by the same number of degrees: consequently, since it is placed above all things on earth, it has more time to work upon these lower things, which is often 20 hours and even more; and also because these things are most affected by it, so that for this reason its influence has received the name of sublunary. AVELLAR is said in Greek, or rather in Chaldaic, to be a fixed star <349.> of the second magnitude, of a mixed nature of Mars and Mercury, and of Saturn, situated in the head of the preceding Gemini, which is called Cabar, or Apollo. In Arabic, Ras Algeuze. AUGENTES fortunae gradus are called among the ancient Arabs <350.> certain degrees of the signs, in which fortunes are found, or rather their virtue is greatly increased; on this matter see in V. Gradus. AVIS, Hen, Swan, Cygnus, a fixed star <351.> in the northern sky, near the Galaxy: enough has been said about it elsewhere. Likewise AVIS Paradisiaca is said to be another fixed star <352.> near the Antarctic pole newly discovered by Spanish sailors when they arrived at the southern lands. See in V. Manucodiata. AVLAX in the Persian tables is called the extreme of Eridanus, that is, Canopus, a fixed star of the first magnitude of the nature of Jupiter and Venus, existing at 21° of Aries. In Arabic, Acarnar. AVRA is a gentle wind, softly blowing, not altogether unlike Zephyr, and some Apogæi. AVREA rule is honorifically named among arithmeticians <355.> a certain proportion of numbers, by which, given three known numbers, a fourth unknown emerges: for the third number (whose proportional part we wish to find) is multiplied by the second number, and the product is then divided by the first given number; for the quotient is the fourth proportional number <356.> that we seek. A very common and necessary rule for all, not so much for arithmeticians as for professors of the whole of mathematics. AVREVS numerus is so called because, written in golden letters at Athens, it was repeated; it is the measure of the motion of the Moon’s head of the diaconis, which is completed in 19 solar years, by whose aid nearly all inequality of the lunar motion is adjusted, and from which the Epact appropriate to each year and the age of the Moon are derived. Thus it can be defined: it is an artificial revolution of the nineteen-year cycle distributed through the following years from 1 to the number 19, after which being completed it returns again to 1. Its inventor was a certain Meton of Athens.

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76 LEXICON quo & Metonicus annus dictus is, in quem anni Lunisolarè[m] conueniunt, vt dictum est suo loco. Nunc si quis innenire vo- luerit aureum numerum currentem, addat anni mille simi cur- rentis vnitatem, & summam diuidat per 19. quod post diuisio- nem remanet erit aureus numerus illius anni: Quod si integra prodeat diuisio, ita vt nullus supersit numerus minor 19. tunc aureus numerus erit 17. talisque erit etiam Epacta; vnde No- uilunia redeunt vt erant ptiùs, & annus lunaris conuenit cum solar: sic anno currenti 1660. addita vnitate fiunt 1661. qui- bus diuisis per 17. remanent adhuc 8. talis igitur erit aureus nu- merus præsentis anni: De ea re vide fusiùs Maurolycum, & Robertum Lyngoniensem in suo Compto Ecclesiastico. 357. AURIGA, Eniochus, Eriethonius, Arabibus Memesciast[us], hoc est mulus clitellatus, sidus in coelo ad Borealem plagam constans stellis quatuordecim secundùm antiquos, at secundùm Keplerum 27. & per Baierum 31. omnibus ferè de natura Martis & Mercurij; quarum præcipua primæ magnitudinis in sinistro humero dicitur Capella, Hircus. Is in horoscopo, in- quit Stadius, facit Aurigas, Equites, Speculatores, Medicos, & qui mediis herbis aliis medeantur. In occasu verò adducit periculum mottis violentiæ. vel ob casum è curru, vel calce equorum, vel sanè artuum laceratione. 358. AVRORA vulgò dicitur Crepusculum maturinum, seu pri- ma diei lux subolcura ad Orientem, ante Solis aduentum matu- tino tempore apparens: inde dicta, quod ante Solis ortum ab eius aureis spiculis illustratus aër quasi aurescit, vel potius vt alij volunt, quasi aurororans quia eo tempore lenis aura per- flans rorem de coelo pluit: Vide in Verbo Crepusculum. 359. AVRORA item, seu Masurina dicitur apud Astronomos spe- cies quædam cometæ matutino tempore, & in aurora apparen- tis, colore ruso cum longa cauda. Is participat naturam Mar- tis, & cum apparuerit ex parte Orientali habens caput depres- sum inferiùs, portendit prælia, & combustiones ignis, æstus, ariditates, famem, pestilentiam, incendia &c. maximè in re- gionibus calidioribus. 360. AYSTER, Græcè notus ventus Meridionalis vnus ex qua- tuor cardinalibus, qui à puncto Meridiei exoritur: ab aqua- rum haustu, quem apud nos habet, sic dictus, calidus, & hu- midus in nostris hisce regionibus Septentrionalibus, at in Au- stralibus trans Oceanum Atlanticum frigidus, & siccus, eius- dem prorsus qualitatis, ac in nostris Boreas & Septentrio: si- cur isti in illis regionibus mutant qualitates, & inducunt na- turam Austri, & Norapelioris, vt præ cæteris testatur Alon- sus de Ouaglie in descriptione Regni Chilensis. Nec id sanè

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76 LEXICON which is also called the Metonic year, into which the lunar-solar years agree, as was said in its place. Now if anyone wishes to find the current golden number, let him add the unit to the thousandth year currently running, and divide the sum by 19. What remains after the division will be the golden number of that year; but if the division comes out exact, so that no number less than 19 remains, then the golden number will be 17. And such will also be the Epact; whence the new moons return as they were before, and the lunar year agrees with the solar one. Thus in the current year 1660, when the unit is added, there become 1661, which divided by 17 leave still 8; therefore such will be the golden number of the present year. On this matter see more fully Maurolycus and Robert Lyngonensis in his Ecclesiastical Computation. 357. AURIGA, Eniochus, Eriethonius, called by the Arabs Memesciastus, that is, a harnessed mule, a constellation in the sky standing toward the north, consisting of fourteen stars according to the ancients, but according to Kepler 27, and according to Bayer 31, all of a rather Martian and Mercurial nature; the chief of which, of the first magnitude on the left shoulder, is called Capella, Hircus. In the horoscope, says Stadius, it produces charioteers, horsemen, scouts, physicians, and those who heal others with herbs. At setting, however, it brings the danger of violent death, either by a fall from a chariot, or by a horse’s kick, or indeed by the tearing of the limbs. 358. AURORA is commonly called the morning twilight, or the first dim light of day in the east, appearing in the morning before the arrival of the sun: so called because before the sun rises the air, illuminated by his golden rays, seems to turn golden, or rather, as others hold, because it is as though “aurorating,” since at that time a gentle breeze blowing scatters dew from the sky: see under the word Crepusculum. 359. AURORA likewise, or Masurina, is called among astronomers a certain kind of comet appearing in the morning and at dawn, reddish in color with a long tail. It shares the nature of Mars, and when it appears on the eastern side with its head lowered downward, it portends battles and fiery burnings, heat, dryness, famine, pestilence, conflagrations, etc., especially in hotter regions. 360. AYSTER, in Greek, is the well-known southern wind, one of the four cardinal winds, which rises from the point of south; so called from the drinking of waters which it has among us. It is warm and humid in these our northern regions, but in the southern regions beyond the Atlantic Ocean it is cold and dry, of exactly the same quality as Boreas and Septentrio are in our regions. Just as these in those regions change qualities and assume the nature of Auster and Norapelior, as Alonso de Ouaglie testifies above all in the description of the Kingdom of Chile. Nor is this indeed

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MATHEMATICVM. 77 ratione vacat; cùm enim Auster, quò ad nostras regiones commigiet, nostrique Boreas ad Australes transire debeat tum per mare Oceanum, tum per Zonam torridam, nil mirum est, si & humores ab vno, calorem ab altera mutuetur, secumque ad loca quò perflans tendit asportet. At verò & Auster in regionibus Metidionalibus, & Septentrio in Borealibus spirant immediatè à Polis, transeuntque per Zonas vtrinque frigidas, nec per maria sed per montes asperrimos, vnde priusquam ad mare pertingant, aut per æquatorem transeant, frigidas, & siccas qualitates locorum vnde originem trahunt, retineant necesse est. Simili etiam ratione Notapeliotes vulgò Siroccus in Sicilia, atque in certo Ital[i]æ tractu calidus, & siccus dignoscitur, non vt alibi vniuersim calidus, & humidus. E contra Boreas ibi est quidem frigidus, non autem siccus, vt Romæ, sed humidus, quia videlicet & hic à frigida regione spitans transit per mare vnde humores trahit, ille autem ab Austro exsufflans transit per Zonam torridam, & non quidem per mare, sed per mediam Africam, quæ longo tractu interponitur; vnde esse quidem calidus potest, humidus autem, cum non habeat, vnde humores ehibat, esse non potest. Hæc ex occasione sint dicta. Cæretùm, cum de ventorum scut & de signorum natura, & qualitatibus loquimur, semper loquimur habito respectu ad plagam Borealem quam nos inhabitamus; cum certum sit, si trans mare Atlanticum, vltraque æquatorem pergeremus, oppositum ex asse ijs, quæ hic dici- mus experturos. Sed enim nobis loquimur, nostrisque regionibus morem gerimus, quarum passioues experimur, affectiones patimur, aërem respiramus. Hinc de Austro scriptum reliquit Hippocrates quod visum hebetat, caput humoribus replet, pigritiam adducit, membra dissoluit, morbos generat, febres putridas, pestilentias, pleuritidas, aliasque ægritudines contagiosas. Idem infensissimus hortis dicitur à Theophrasto lib. 2. cap. 4. AVTOMATA instrumenta quædam mechanica sunt, iuxta 361. Geometriæ præcepta tam subtiliter, & concinnè elaborata, vt sponte sua nullaque apparentè extrinsecus impellente vi, moueantur, atque in orbem statis temporibus ordinatè notentur à , quod Græcè vltroneum interpretatur. Inter hæc celeberrima illa Archimedis vitrea sphæra, quæ omnes cælestes motus exquisitissimè imitabatur: in quam lepidè Iust Claudianus. Iupiter in paruo cùm cerneret Æthera vitro, Risit & ad superostalia dicta dedit. Huccine morzalis progressa potentiæ cura:

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MATHEMATICUM. 77 it lacks proportion; for since the Auster, as it comes to our regions, and our Boreas must pass over to the southern regions, both by the Ocean Sea and by the Torrid Zone, it is no wonder if it draws moisture from the one and heat from the other, and carries them with it to the places toward which it blows. But indeed both the Auster in the southern regions and the Septentrio in the northern regions blow immediately from the poles, and pass through zones cold on both sides, and not through seas but through very rugged mountains; wherefore, before they reach the sea or cross the equator, they must retain the cold and dry qualities of the places from which they take their origin. In a similar manner also the Notapeliotes, commonly called the Scirocco in Sicily and in a certain region of Italy, is recognized as hot and dry, not, as elsewhere, universally hot and humid. On the contrary, Boreas there is indeed cold, but not dry, as at Rome, but humid; because here too, blowing from a cold region, it passes over the sea, from which it draws moisture, whereas the other, blowing from the Auster, passes through the Torrid Zone, and not indeed over the sea, but through the middle of Africa, which lies interposed over a long stretch; whence it can indeed be hot, but humid it cannot be, since it has no source from which it may draw moisture. Let these things have been said by way of occasion. Moreover, when we speak of the face of the winds and of the nature and qualities of the signs, we always speak with respect to the northern quarter which we inhabit; since it is certain that if we were to travel across the Atlantic Sea beyond the equator, we would experience exactly the opposite of what is said here. But we speak for ourselves and accommodate ourselves to our own regions, whose conditions we experience, whose affections we suffer, whose air we breathe. Hence Hippocrates wrote concerning the Auster that it dulls the sight, fills the head with humors, brings on sluggishness, relaxes the limbs, generates diseases, putrid fevers, pestilences, pleurisy, and other contagious illnesses. The same is said by Theophrastus, book 2, chapter 4, to be most hostile to gardens. AUTOMATA are certain mechanical instruments, elaborated according to the precepts of geometry with such subtlety and elegance that, of their own accord and with no apparently external force impelling them, they move, and at fixed times are regularly made to turn in a circle, from what in Greek is interpreted as spontaneous. Among these the most celebrated was that glass sphere of Archimedes, which most exquisitely imitated all the motions of the heavens; concerning which Claudian wrote charmingly: When Jupiter beheld heaven in a small glass, he laughed and gave utterance to words above the stars. Has the care of mortal power thus advanced?

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MATHEMATICVM. 79 temporis esse inueniuntur, Saturni initio Capricorni cum min. 35. Louis in grad. 7. minut. 27. Libræ: Martis in grad. 29. min. 29. Leonis: Solis in grad. 11. min. 4. Cancri. Veneris in grad 16 minut. 50. Geminorum: Mercutij tandem (cum in Luna eam assignare non sit) in grad. 1. min. 39 Sagittarij. Similiter oppositum Augis est in partibus signorum oppositis. Plura habes apud extractores Tabularum secundorum mo-bilium. AX <356.> Axis apud Astronomos audit linea quædam imaginaria, quæ ab uno Mundi cardine, seu polo per centrum telluris tran-siens, in alterum terminatur; circa quam totam Cælorum machinam intelligimus circumvolui. Et quoniam plures po-los, pro ratione motuum atque orbitarum secundorum mo-bilium, circa quos singula agitentur, conamur astruere, vt diceamus, cum fiet termo de polis; ideò plures axes ab vno in alterum, ex dictis polis protensos concipi necesse est, qui omnes, per centrum telluris transite debeant, seque mutuò intersecare: ita vt nihil aliud axis sit, quàm mundi dia-meter, circa quam sphæiæ voluantur. Antonomasticè tamen accipitur pro insigniore, hoc est axe mundi ad eiusdem polos Arcticum, & Antarcticum terminante. AZ <366.> AZELFAGE Arab. dicitur cauda Cigni, stella fixa secundæ magnirudinis de natura Veneris, & Mercurij, existens nunc temporis in primo gradu Pitcium cum latitudine boreali gr. ferè 60. intrà Galaxiam. Hæc in horoscopo aut cum Luna maximè inclinare dicitur ad Venerea, quippe quæ habet natu-ra sua corpus humoribus replere, ac spetina producere. Est nunc Verticalis Florentiæ, Bononiæ, Placentiæ, aliisque Galliæ Cisalpinæ vrbibus, quæ sunt in eleuatione poli grad. 44. cum ipsa totidem ferè habeat declinationis borealis. Alio nomine, sed corrupto, vt notat Ricciolus, dicitur Deneb. Adigege. AZEMENA Arab. idem sonat, ac corporis debilitas: Vnde <367.> pars Azemena apud Arabes Generhiacos audit ea pars quæ dirigitur pro corporis infirmiratibus. Absolutè autem sumpta sunt cerri quidam gradus signorum, in quibus reperta Luna, aut maleficus, adducit morbum aliquem incurabilem, seu inseparabilem, vt sunt cæcitas, surditas, membri debilitas, & similia; idque pro ratione signorum, & planetarum tam ibi existentium, quam eundem locum respicientium, habito etiam respectu ad situm mundi, in quem incidit talis gradus Por-ro gradus Azemene quos Arabes omnes, & nonnulli ex

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MATHEMATICVM. 79 At the beginning of Saturn, they are found to be in Capricorn with min. 35. Louis in degree 7, minute 27, Libra: Mars in degree 29, minute 29, Leo: the Sun in degree 11, minute 4, Cancer. Venus in degree 16, minute 50, Gemini: Mercury at last (since in the Moon it is not assigned there) in degree 1, minute 39, Sagittarius. Likewise the opposite of the Augis is in the opposite parts of the signs. You have more in the extractors of the Tables of secondary mobiles. AX <356.> Axis among astronomers is called a certain imaginary line, which, passing through the center of the earth from one cardinal point of the world, or pole, ends in the other; around which we understand the whole machine of the heavens to revolve. And because we strive to establish several po-les, according to the relation of the motions and orbits of the secondary mobiles, around which each thing is stirred, so that, as we shall say when the discussion of the poles comes, we must conceive several axes extended from one to the other of the said poles, all of which must pass through the center of the earth, and mutually intersect one another: so that an axis is nothing else than the diameter of the world, around which the spheres revolve. Yet in an antonomastic sense it is taken for the more eminent one, that is, the axis of the world, terminating at its poles, the Arctic and Antarctic. AZ <366.> AZELFAGE in Arabic is said to be the tail of Cygnus, a fixed star of the second magnitude, of the nature of Venus and Mercury, now at present existing in the first degree of Pisces, with northern latitude of about 60 degrees, within the Galaxy. This in a horoscope, or when the Moon is especially inclined toward Venusian matters, because by its nature it has the power to fill the body with humors and produce the spine. It is now vertical at Florence, Bologna, Piacenza, and other cities of Cisalpine Gaul, which are at the elevation of the pole 44 degrees, since it itself has about the same amount of northern declination. By another name, but corrupted, as Ricciolus notes, it is called Deneb. Adigege. AZEMENA in Arabic has the same meaning as bodily weakness: hence <367.> the part Azemena among the Arabs, Generhiacos, is called that part which is directed toward bodily infirmities. Taken absolutely, however, they are certain degrees of the signs in which the Moon found, or an evil planet, brings about some incurable or inseparable disease, such as blindness, deafness, weakness of a limb, and the like; and this according to the nature of the signs and of the planets both existing there and regarding that same place, also taking account of the position of the world into which such a degree falls. Moreover the degrees of Azemene, which all the Arabs, and some of

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40 LEXICON antiquioribus admittunt, tales commuiter circumferuntur. In Tauro gradus sextus, seprimus, octauus, nonus, & decimus (in Ariete enim nullum est assignare, neque in Geminis, neque in Virgine, neque in Libra, neque in Piscibus) In Cancro 9. 10. 11. 12. 13. 14. 15. In Leone grad. 18. 27. 28. In Scorpione grad. 19. & 19 In Sagittario grad 1. 7. 8. 18 & 19. In Capricorno grad. 26. 27. 28. 29. In Aquario randem grad. 18. & 19. Qua autem ratione ij adinuenti sint, vel potius efficti, non satis constant apud ipsos: ideoque communi suffragio à Recensioribus omnibus vanitatis arguuntur. Hoc vnum tamen monuerim, quod si fortè isti gradus ab antiquis huiusmodi qualitatis esse comperti sunt, id certè non aliunde, quam ab stellis fixis, quæ in eosdem gradus incidebant, credendum est, collegisse; cum nulla appareat ratio conuincens: quare hi potius gradus Eclipticæ (quæ sanè imaginatia est) & non alij hanc infortunam sorriti sint At enim, etiam si fixis hanc qualitatem moribiscam velimus appingere; jam nunc ob eorum præcessionem, recessit prædicta qualitas à signatis gradibus & transiuit ad alios, sub quibus modo eædem stellæ reperiuntur. 369. Hac occasione placet hic nouam, atque ingeniosam Adriani Negusanrij viri eruditissimi, ac mihi cum paucis arctissima familiaritate conjuncti, obseruationem attexere, dignam sanè quæ opus isthuc nobilitet. At enim gradus medios signorum fixorum, hoc est grad. 15. Tauri, Leonis, Scorpij, & Aquarij esse infortunatos, ac debiles: quippe qui ibi consistunt, vbi contrariæ qualitates æqualibus viribus pugnant, succedente mox victoria vuius super aliam, à qua fit transitus: inde fit, vt hæc pugna, & contrarietas plurimum labefactet planetam ibi repertum Quapropter idem testatur, sæpissimè se expertum fuisse, Aphætam constitutum intrà fines horum graduum intulisse naso valdè debilem complexionem, nec non eiusdem directiones ad Anxretas, etsi alioqui debiles ibi consistentes, vitam etiam abscidisse. 370. AZIMECH apud Arabes non vnam tantum fixam designat (vt malè aliqui opinantur) sed modò vnam, modò aliam, de natura tamen Veneris, & Mercurij & non promiscuè sed tantum insigniores: vnde semper ponitur cum adjuncto, quod signatam stellam discernat, vt in proptiis locis dictum est. Non negauerim tamen hoc nomen absolutè prolatum apud multos Antonomastice accipi pro spica Virginis stella omnium, quæ sunt de natura Veneris, & Mercurij, nobilissima

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40 LEXICON those found in the earlier ones are commonly circulated. In Taurus: the 6th, 7th, 8th, 9th, and 10th degrees; in Aries, however, none can be assigned; nor in Gemini, nor in Virgo, nor in Libra, nor in Pisces. In Cancer: degrees 9, 10, 11, 12, 13, 14, 15. In Leo: degrees 18, 27, 28. In Scorpio: degrees 19 and 29. In Sagittarius: degrees 1, 7, 8, 18, and 19. In Capricorn: degrees 26, 27, 28, 29. In Aquarius, likewise, degrees 18 and 19. By what reasoning these were devised, or rather fabricated, is not sufficiently clear even to their own advocates; and therefore by the common judgment of all later writers they are accused of vanity. This one thing, however, I would note: that if perchance the ancients found these degrees to possess such a quality, it must certainly be believed that they collected it not from any other source than from the fixed stars that fell upon those same degrees; since no convincing reason appears why these degrees of the Ecliptic (which surely is imaginary) and not others should have obtained this misfortune. But even if we wish to ascribe this harmful quality to the fixed stars, now because of their precession, the aforesaid quality has receded from the marked degrees and passed to others, under which the same stars are now found. 369. On this occasion it seems fitting to append here a new and ingenious observation of Adrianus Negusanius, a most learned man and one with whom I am joined in very close familiarity among a few, an observation certainly worthy to ennoble that work. Namely, the middle degrees of the fixed signs, that is, the 15th degrees of Taurus, Leo, Scorpio, and Aquarius, are unfortunate and weak: namely because there they stand where contrary qualities contend with equal force, the victory of one over the other soon following, from which there is a transition. Hence it comes about that this struggle and contrariety greatly weaken the planet found there. For this reason the same author testifies that he has very often experienced that an Aphēta placed within the bounds of these degrees brought a very weak complexion into the native, and also that his directions to Anxretae, though otherwise weak, standing there, have even cut off life. 370. AZIMECH among the Arabs does not designate just one fixed star (as some wrongly think), but now one, now another, from the nature of Venus and Mercury; and not indiscriminately, but only the more notable ones: hence it is always used with an adjunct that distinguishes the star indicated, as has been said in the proper places. I would not deny, however, that this name, when used absolutely, is taken by many as a proper name, namely for the star Spica Virginis, the noblest of all the stars that are of the nature of Venus and Mercury.

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MATHEMATICVM. 11 Ama, quæ alias, & plures notiones habet, vt dicemus in locis, vbi sermo recurrent. AZIMUTH. Arabicè appellantur circuli Verticales, seu Meridiani transeuntes per verticem locorum, atque ipsum verticalem primarium intersecantes in puncto Vetricis, indeque ad Horizontis pattes oppositas desinentes, aut etiam vlterius vsque ad Nadir protensi. Concipiuntur autem in cælo, ac circà tellurem descripti; iique propè infiniti, sicut & infiniti possunt concipi Horizontes. Eorum ope venamur, tum stellarum positus, ac distantiam adinuicem, tam longitudinem, ac distantiam ab Insulis Canariis sitis in Occidente, à quibus placuit Prolemæo, & antiquis Cosmographis hanc longitudinem computare. Est autem longitudo, vt in loco diceitur, arcus æquatoris interceptus inter duos Meridianos, primum scilicet dictarum Insularum, & loci, cuius longitudinem quærimus; quot enim gradus æquatoris inter prædictos Meridianos intercipiuntur, tanta dicitur esse longitudo, ciuitatis, aut regionis: & quantus est arcus interceptus inter Meridianum duorum locorum, tanta est distantia eorumdem. Vt proinde Azimutha, seu circuli verticales per gradus æquatoris distribuantur, sicque concipiantur tantum esse 180. Cum quilibet Meridianus comprehendat duos gradus oppositos. Id magis magisque explicabitur in Verbo Meridianum, atque in Verbo Longitudo quoad Geographos. AZONI, & AZones dicti sunt populi extrà Zonam habitantes, qui, cùm reuerà dari non possunt, omnis enim terræ tractus in quinque Zonas diuiditur, in quarum aliqua quicunque in orbe degit, degat necesse est, vt magis explicabitur in V. Zonæ Ideò cum Iosepho Laurentio in Amathea Onomast. eos credidetim Azones appellatos fuisse, qui extrà fasciam Zodiaci habitant, quos inter & nos comprehendimur, & quicunque extra Zonam, quam vocant torridam commorantur. Si quidem Zodiacus ab vno in alterum tropicum semel, & iterum transiens protenditur, nec extrà tropicos, qui sunt eius limites diuagatur. Quapropter ijs tantùm, qui in Zona torrida degunt, Sol aliquando sit verticalis, secus autem iis qui extrà Zonam, hoc est Zodiaci amplitudinem sunt, qui proptereà Azones vocantur. AZORVM Insula in Occidente cum latitudine graduum 40. versus polum Antarcticum celebres sunt apud nouos noui orbis hoc est Indiarum Occidentalium detectores: quippe quæ, inquiunt, sitæ sunt ad verum Occidentis Meridianum; vnde ab illis computandam esse autumant longitudinem Ciuitatum, non ab Insulis Canarijs seu fortunatis, vt cum voluit Prole- F

Transcription: Translated (English)

MATHEMATICVM. 11 Ama, which has other and many notions, as we shall say in the places where the discussion will recur. AZIMUTH. In Arabic are called the Vertical circles, or Meridians passing through the zenith of places, and intersecting the primary vertical at the point of the vertex, and then ending at the opposite parts of the Horizon, or also extended farther as far as the Nadir. They are conceived, moreover, in the heavens and described around the earth; and these are almost infinite, just as infinite Horizons may also be conceived. By their help we track both the positions of stars and their mutual distance, as well as longitude and distance from the Canary Islands lying in the West, from which Ptolemy and the ancient Cosmographers were pleased to compute this longitude. Now longitude is, as is said in its place, the arc of the equator intercepted between two meridians, namely the first of the said Islands, and of the place whose longitude we seek; for however many degrees of the equator are intercepted between the aforesaid meridians, that much is said to be the longitude of a city, or region; and as great as is the arc intercepted between the meridian of two places, so great is their distance. Thus therefore the Azimuths, or vertical circles, are distributed by degrees of the equator, and are conceived to be only 180. Since each meridian contains two opposite degrees. This will be explained more and more in the word Meridian, and in the word Longitude as regards Geographers. AZONI, and AZONES were called peoples dwelling outside the Zone, who, since they cannot in fact exist, for every tract of the earth is divided into five Zones, in some one of which whoever dwells in the world must of necessity dwell, as will be explained more fully in V. Zonæ. Therefore with Josephus Laurentius in Amathea Onomast. I think those were called Azones who dwell outside the belt of the Zodiac, among whom we are included, and whoever lives outside the Zone that they call the torrid one. For indeed the Zodiac, passing once and again from one tropic to the other, extends onward, nor does it wander outside the tropics, which are its boundaries. Wherefore only to those who dwell in the torrid Zone is the Sun sometimes vertical; otherwise to those who are outside the Zone, that is, outside the breadth of the Zodiac, who for that reason are called Azones. AZORVM The Islands in the West, with latitude of 40 degrees toward the Antarctic pole, are celebrated among the recent discoverers of the new world, that is, of the West Indies: for, they say, they are situated at the true Meridian of the West; whence they judge that the longitude of cities ought to be computed from them, not from the Canary or Fortunate Islands, as Ptole-

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LEXICON mæus, neque à Gadibus Insula, vt placuit Straboni, Artemidoro, & Proclo: qui proptereà ab istis locis numerare incipiebant longitudines Ciuitatum, quia ignorabant verum Occidens, quod præcedenti tantum sæculo, tanto cum Christianæ Reipublicæ bono, ac detegenium laude repertum est. Siquidem, vt benè aduertit Iunctinus in sphæram Io. de Sacrobosco, cum verum Occidens constitui debeari in fine tetræ habitabilis ex opposito Orientis, atque ad angulos rectos polorum Mundi; consequenter ibi erit, vbi linea quædam concipiarur, diuidens æquatorem ad angulos rectos, & Colurum solstiriorum intersecans; qvæ à nauigantibus linea diametri, seu diametet Mundi appellatur. < 374.> Porrò hæc linea comprehendit immediatè laudatas Insulas, parum vltia Promontorium Hieron, ad quinque gradus: vbi etiam acus nautica, seu sagitta magnetica se rectè vertit ad polos mundi, diuidens æquatorem ad angulos rectos. Quod etiam oculatus testis probat à se expertum Gonzalus de Ouido in summario de itineribus ad partes Indiæ Occidentalis cap. 84. qui regiones illas quatuor vicibus peragruit. Ait enim se, quoriscumque peruenit ad istud Meridianum, semper vidisse magnetis sagittam rectè se vertere diametraliter ad polos mundi. Et nactat lepidam historiam memoratu dignam, quod quoriscunque ei coniigit cum suis locijs per hanc lineam pertransire, omnes pediculi, quos ipsi habebant in capitibus, in vestimentis, aut vbiuis in nauibus, confestim tanquam mortui deueniebant, atque ipsi ab eorum molestia libetabantur: verum cùm posteà discederent ab illis partibus Occidentalibus ac suo itinere Hispaniæ viam adorienies cum suis nauibus, redirent ad hanc lineam diametri, mox pediculi reuiuiscebant, vt priùs, ac semper multiplicabantur quò magis parribus nostris apptopiabant. Ex quo portento atque ex rotaru recto acus magneticæ ad polos mundi comprehenderunt, ipsum esse verum Occidentis Meridianum; cum nullibi in alio Meridiano contingat id videre, quod in isto, qui nunc vulgò appellatur sancta Maria. Quapropter non abs re foret nouum catalogum Ciuitatum construere, atque earum longitudinem non ab Canariis, vt olim, sed ab Azorum Insulis compusare. Quem laude dignum laborem vtinam sapiens quis aggrederetur. < 375.> Azvbene Arab Latinè Cheles, leu Gla[n]iæ Cancri stellæ fixæ sunt quartæ magnitudinis de natura Saturni, & Martis, quæ reuerà informes sunt circa constellationem Cancri, at reperiuniur nunc remporis in grad. 11. & 12. Leonis cum grad 3 & 6. latitudinis borealis: Sunt stellæ infensæ præsertim oculis, nec quicquam boni, sive in cardinibus genituræ,

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LEXICON mæus, not from the island of Gades, as Strabo, Artemidorus, and Proclus pleased to say: for for this reason they began to count the longitudes of cities from those places, because they were ignorant of the true Occident, which only in the preceding century, with so much benefit to the Christian commonwealth and with the praise of discovery, was found. Indeed, as well observed by Iunctinus in the sphere of Io. de Sacrobosco, since the true Occident ought to be established in the end of the habitable earth opposite the Orient, and at right angles to the poles of the world; consequently it will be there where a certain line is imagined, dividing the equator at right angles and intersecting the colures of the solstices; which by sailors is called the diameter line, or diameter of the world. < 374.> Moreover, this line immediately includes the aforementioned islands, a little beyond Cape Hieron, at five degrees: where also the nautical needle, or magnetic arrow, turns correctly toward the poles of the world, dividing the equator at right angles. This is also proved by the eyewitness Gonzalus de Ouido, who experienced it himself in the summary of journeys to the parts of the West Indies, chap. 84, who traversed those regions four times. For he says that whenever he came to that meridian, he always saw the magnetic arrow turn straightly and diametrically toward the poles of the world. And he tells a witty story worth remembering, that whenever it happened that he and his men passed through this line with their places, all the lice which they had in their heads, in their garments, or anywhere on the ships, at once fell down as though dead, and they were freed from their annoyance; but when afterwards they departed from those western parts and, on their voyage toward Spain, approached again with their ships to this diameter line, the lice immediately came back to life as before, and always multiplied the more they approached our parts. From this prodigy, and from the right turning of the magnetic needle toward the poles of the world, they concluded that this is the true meridian of the Occident; since nowhere else on any other meridian does it happen to see that which occurs in this one, which is now commonly called Santa Maria. Wherefore it would not be amiss to construct a new catalog of cities, and to compute their longitude not from the Canaries, as formerly, but from the Azores Islands. Would that some wise man would undertake this praiseworthy labor. < 375.> Azvbene Arab. In Latin Cheles, or Gla[n]iæ, are fixed stars of the fourth magnitude, of the nature of Saturn and Mars, which are in truth unformed around the constellation of Cancer, but are now found in the 11th and 12th degree of Leo, with 3 and 6 degrees of northern latitude: they are hostile stars, especially to the eyes, and of no good whatever, whether in the angles of the nativity,

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MATHEMATICVM. 83 siue cum Luminaribus reperiantur adducunt. Item < 376.> AZVBENE confusè vocatur ab aliquibus Libræ sidus à che- lis Scorpij, propterea quod Libra, & Scorplus olim vnicum signum erat: vnde Hyginus, Scorpio, inquit, hæc propter magnitudinem membrorum in duo signa diuiditur, quorum vnius effigiem nostri Libram dixerunt, & Marianus Capeila lib. 8. de nupt. philosop. cap. de sixis signis. Zodiacus quidem, ait, æquales duodecim signorum integras portiones, sed vndecim habet signa: Scorpius enim tam suum spatium occupat corpore, quam Chelis occupat Libra. BA < 1.> BACVLVS Astronomicus vulgò dictus D. Iacobi, est instru- mentum Mathematicum ad altitudinem, latitudinem, rerum distantias, aliaque dimetienda: qua de re vide Clauium in Geometria practica. < 2.> BALANA, cetus, Pistrix Arabibus Akaitos, vel Elkaitos sidus in Cælo ad australem plagam continens stellas 22. secundùm Prolemaeum, at secundùm Baierum 27. (cum tamen Keple- rus ei assignat tantum 21) omnes ferè de natura Saturni, in- ter quas præcipua, quam vocant alij Narem, alij Mandibu- lam ceti Arabicè Menchar secundæ magnitudinis: proxima huic accedit quæ in Cauda, terria quæ in corpore. Ferunt Fabulatores fuisse belluam illam, quæ deuoratura Androme- dam, victa fuit, atque interempta à Perseo. Caput haber sub constellatione Arietis, & extendir caudam vsque ad effusio- nem aquæ Aquarij. Est sidus turbidum, procellosum. Cum Sole exoriens inducir tempus turbidum, & humidum: Occi- dens, frigus, niues, & imbres, sicut etiam cum Saturno. Alias eius significationes vide in V. Cetus. < 3.> BALTHEVS, cingulus Orionis constans tribus fulgentissi- mis stellis in linea recta secundæ magnitudinis de natura Io- uis, & Saturni, quacum prima existit ferè in æquatore; aliæ dux ad gradus duos declinant ad Austrum; in longitudine sub grad. 19 Geminorum. Porrò cui ascendit Baltheus, inquir Cardanus, is erit studiosissimus, ac doctissimus. Quo- ad temporis qualitatem obnunciar aërem turbidum spirante Fauonio: quandocumque cum Sole cong editur. < 4.> BASILISCVS, Regulus, cor Leonis, Stella fixa regia secun- dæ quidem magnitudinis, sed ob sui præstantiam, miram efficientiam, atque in Ecliptica consistentiam inter primæ magnitudinis computata. Est de natura Mariis, & louis; adeoque etiam inter abscindentes stellas ab aliquibus con- numetata. Hanc solam obseruauit Titus, vt habet in sua F ij

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MATHEMATICUM. 83 whether they are found together with the luminaries, they bring forward. Likewise < 376.> AZVBENE is confusedly called by some the star of the Balance from the claws of Scorpio, because Libra and Scorpio were once a single sign; hence Hyginus says, “Scorpio is divided into two signs because of the size of its limbs, the appearance of one of which our people have called Libra,” and Marcellus Capella, book 8 of De nuptiis philosophiae , chapter on the fixed signs: “The Zodiac indeed,” he says, “has twelve equal portions of the signs, but it has only eleven signs; for Scorpio occupies as much space with its body as Libra occupies with its claws.” BA < 1.> BACVLVS, commonly called Astronomical Staff of St. James, is a mathematical instrument for measuring altitude, latitude, distances of things, and other matters: on this see Clavius in practical geometry. < 2.> BALANA, cetus, Pistrix; to the Arabs Akaitos, or Elkaitos; a star sign in the sky toward the southern region, containing 22 stars according to Ptolemy, but according to Bayer 27 (though Kepler assigns it only 21), almost all of the nature of Saturn, among which the chief one, which others call the Nostril, others the Jaw of the whale, in Arabic Menchar, is of the second magnitude: next to this comes the one in the Tail, and the third in the body. The mythographers report that it was that beast which, about to devour Andromeda, was overcome and slain by Perseus. It has its head under the constellation of Aries and extends its tail as far as the pouring out of Aquarius. It is a turbulent, stormy star. When rising with the Sun it brings unsettled and humid weather; when setting, cold, snow, and rain, as also when with Saturn. See its other significations under V. Cetus. < 3.> BALTHEVS, the belt of Orion, consisting of three very bright stars in a straight line, of the second magnitude, of the nature of Jupiter and Saturn, with the first of them lying almost on the equator; the other two decline two degrees to the south; in longitude under 19 degrees of Gemini. Moreover, whoever has the Belt ascending, says Cardanus, will be most studious and most learned. As for the quality of the time, it foretells a turbulent air when the Favonius blows: whenever it comes into conjunction with the Sun. < 4.> BASILISCVS, Regulus, the heart of Leo, a royal fixed star indeed of the second magnitude, but because of its excellence, wonderful efficacy, and position in the Ecliptic, counted among those of the first magnitude. It is of the nature of Mars and Jupiter; and therefore by some it is also numbered among the stars that cut off. Titus alone observed this, as he has in his F ij

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84 LEXICON Cælesti Philosophia, ex stellis fixis proijcere radios ad planetas, eosque esse non minoris efficaciæ, quam ipsos radios planetarum: idque ob situm suum in Ecliptica, vbi cum omnibus planetis aliquando congreditur. Est nunc in gradu 21. Leonis. Ea in horoscopo, aut culmine Cæli, præsertim cum Ioue aut Venere, vel eorum benigno radio magnam tribuit felicitatem, gloriam, & honores, atque ab statu humili ad eminentem, ac sublimem euebit. 5. BATA-KAITOS Arab Venter ceti, Stella fixa tertiæ magnitudinis de natura Saturni, existens nunc in gradu 13 Arietis, cum latitudine australi grad. 15. de qua vide in V. Cetus, Balena. 6. BED-ALGENSE seu etiam Belde-ensis Arab. dicitur dexter humerus Orionis, Stella fixa sub usa primæ magnitudinis de natura Martis, & Mercurij: Vide etiam in V. Orion. 7. BELLATRIX altera Stella item subrufa, & valde iutilans secundæ tamen magnitudinis in sinistro humero eiusdem Orionis. Nomen accepit à bello, ad quod mirè propellit, & si quidem fuerit in horoscopo cum bono aspectu Martis, aut Iouis, facit Duces strenuos, magnanimos, periculorum contemptores. Observatione cautum est, Lunæ directiones ad hanc stellam rixam aliquam semper inducere, aut iter repentinum. Porrò hæ duæ stellæ Beldegensis, inquam & Bellatrix cum Marte exorientes maxime colores intendunt, vt notat Argolus in Astronomicis lib. 2. cap. 10 8. Beibenix sunt stellæ fixæ principaliores, quæ in singulis imaginibus cælestibus considerantur; præcipue verò corda iplarum, & quæ sunt primæ magnitudinis: vt regulus in Leone, Antares in Scorpio, Spica in Virgine, Alpharad in Hydra, &c. Vsus tamen obtinuit, vt omnes stellæ primæ magnitudinis in singulis Asterismis dispositæ vocentur corda ipsorum, & consequenter Beibenix: teste Hali super proposit. 29. Centiloquij, licet ego inter stellas Beibenias alias etiam secundi ordinis, & minoris conditionis apud alios connumeratas inuenierim. De stellis Beibeniis extat insignis tractarus Hermetis apud Iunctinum in fine commentar. in spharam loamis de Sacrobosco. 9. BENNENAX ELKERD, vel Benenaim, id est Ncturnum dicitur apud Arabes Stella fixa secundæ magnitudinis posita in extremo caudæ Vrsæ majoris, de natura Martis in longitud. grad. 22 Virginis cum latitudine grad. 54. boreali. Aliàs dicitur primus equus Planetri BERENICES Cima dicta etiam spicarum manipulus, fidus in Cælo prope caudam Leonis, & apud antiquos cum ea confu-

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84 LEXICON Celestial Philosophy: to cast rays from the fixed stars to the planets, and for those rays to be no less efficacious than the rays of the planets themselves; and this because of their position in the Ecliptic, where they at times come into conjunction with all the planets. It is now in 21 degrees of Leo. It in the horoscope, or at the summit of the heavens, especially when joined with Jupiter or Venus, or with their benign aspect, bestows great happiness, glory, and honors, and raises a person from a low estate to an eminent and sublime one. 5. BATA-KAITOS, Arab. “belly of the whale,” a fixed star of the third magnitude, of the nature of Saturn, now located at 13 degrees of Aries, with southern latitude 15 degrees; concerning which see in V. Cetus, Whale. 6. BED-ALGENSE, or also Belde-ensis, Arab., is called the right shoulder of Orion, a fixed star, about of the first magnitude, of the nature of Mars and Mercury; see also in V. Orion. 7. BELLATRIX, another star likewise reddish, and very shining, of the second magnitude, on the left shoulder of the same Orion. It received its name from war, to which it wonderfully impels, and if indeed it should be in the horoscope with a favorable aspect of Mars or Jupiter, it makes leaders energetic, magnanimous, and contemptuous of dangers. By observation it has been noted that the Moon’s directions to this star always bring about some quarrel, or a sudden journey. Moreover, these two stars, namely Bedegensis and Bellatrix, rising with Mars, greatly intensify colors, as Argolus notes in his Astronomical Works, book 2, chapter 10. 8. Beibenix are the principal fixed stars, which are considered in each celestial image; especially, however, the hearts of those figures, and those of the first magnitude: such as Regulus in Leo, Antares in Scorpio, Spica in Virgo, Alpharad in Hydra, etc. Yet usage has prevailed, so that all stars of the first magnitude placed in each asterism are called the hearts of those asterisms, and consequently Beibenix: as Haly testifies in proposition 29 of the Centiloquium, though I myself have found among the Beibenian stars others also of the second rank, and of lesser condition, counted by others. There is an important treatise on the Beibenian stars by Hermes in Junctinus at the end of the commentary on Sacrobosco’s Sphere by Ioannes. 9. BENNENAX ELKERD, or Benenaim, that is, “the Night One,” is called among the Arabs a fixed star of the second magnitude placed in the extremity of the tail of Ursa Major, of the nature of Mars, in longitude 22 degrees Virgo, with latitude 54 degrees north. Otherwise it is called the first horse of the planets. BERENICES, called also a cluster of spikes, a faithful star in the sky near the tail of Leo, and among the ancients together with it co-

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MATHEMATICVM. 85 sum, constat stellis septem: at si Keplero credamus 11. ple- rumque obscuris, aur nebulosis de natura Lunæ, & Veneris, effoimanibus fere triangulum incidens in ipsum colurum æquinoctio[n]um. A Ptolemæo dicitur Triches hoc est Crines ab aliis Piocamos id est Cincen us. Hæc cum Sole, aut Luna in eodem circulo posicionis mala adducit in oculis, ac potentiæ visuæ, quemadmodum reliquæ stellæ nebulosæ. BERTHAS fixa secundæ magnitudinis, de natura Louis, & 11. Mercurij, quæ tempore Hermetis (qui eius mentionem facit) erat in gr 27. lib æ, dune autem præcessit, & repetitur in Scorpione Hæc in ho oscopo, aut culmine Cæli inclinat ad pietarem, iustitiam, beneficentiam: facit etiam Poetam, Rhetorem, ac Physicarum rerum studiosum. BESTRA Censauriue lupus apud Persas Bridemif: sidus in 12. coelo ad australem plugam sub signo Libræ constans 19 stellis Ptolemæo, & Kepleio, at Barero 20. omnibus fere de natura Saturni, & parum Marris, quarum duæ tantum in nostro he- mispherio conspiciuntur, in extremo pedis sinistri positæ, cæteris perpetuò latentibus. Vide in V. Fera, Lupus. BICORPOREA signa, sunt quæ, vt nominis etymon præse- 13. fert, bina corpora habent, binasque figuras, Eiusmodi sunt signa communia, Gemini, quod per binos pueros sese mu- tuò amplexantes repræsentatur: Virgo habens spicam in ma- nu: Sagittarius non modò quia habet arcum, & sagittam in manibus, verùm etiam quia componitur ex duplici corpore hominis videlicet, & equi: vnde & humanum dicitur quoad primam medietatem, ferinum quoad secundam: & Pisces duos repræsentans lino illigatos. His annumerari possunt Ophiucus habens serpentem in manibus, Perseus cum Medu- sa, Centaurus, &c. quæ in ascendente conceptionis reperta duplicatum sætum præsignant. BIOTHANATOS Græce proprie significar eos, qui violenta 14. morte tolluntur. Apud Astronomos verò pressius accipitur pro iis tantùm, qui sibi mortem conciscunt. Freqvens eius vsus est apud Ptolemæum capite de Morte, qui tamen re- ctiùs audirent Authothanatos. Vide authorem Thesauri linguæ Græcæ. BIQVINTILIS radius, est nouus aspectus à Keplero, & aliis 15. recensoribus consideratus constans duabus è quinque parti- bus circuli, hoc est grad. 140 vnde se mutuò respicientes planetæ contrahunt familiaritatem. Est natura sua faustus, & ben gnus aspectus, quemadmodum Quintilis, Sextilis, & Trinus: sicut è contrà Quadratus, Sesqui quadratus, & Op- positio infausti sunt, & imperfectæ familiaritatis. Poriò k iij

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MATHEMATICVM. 85 are so; it consists of seven stars: but if we trust Kepler, the 11th is for the most part obscure, or nebulous, of the nature of the Moon and Venus, making with the latter almost a triangular figure, falling upon the very colure of the equinoxes. By Ptolemy it is called Triches, that is, Hair; by others Piocamos, that is, Cincenus. This, when with the Sun or Moon in the same circle of position, brings evils upon the eyes and upon the power of sight, as do the other nebulous stars. BERTHAS, a fixed star of the second magnitude, of the nature of Louis, and of Mercury. In the time of Hermes (who makes mention of it) it was in gr. 27. lib. æ, but now it has advanced and is found in Scorpio. This in the horoscope, or at the culmination of the heavens, inclines to piety, justice, benevolence; it also makes a Poet, a Rhetorician, and one devoted to physical studies. BESTRA, the wolf of Centaurus among the Persians, Bridemif: a star in the 12th heaven toward the southern wing under the sign Libra, consisting of 19 stars according to Ptolemy and Kepler, but 20 according to Barero, almost all of the nature of Saturn, and a little of Mars, of which only two are seen in our hemisphere, placed at the extreme of the left foot, the others being perpetually hidden. See under V. Fera, Lupus. BICORPOREAL signs are those which, as the etymology of the name indicates, have two bodies and two figures. Such are the common signs: Gemini, represented by two boys embracing one another; Virgo, having an ear of grain in the hand; Sagittarius, not only because it has bow and arrow in its hands, but also because it is composed of a double body, namely of man and horse; whence it is called human as to the first half, bestial as to the second; and Pisces, representing two fish tied together with a line. To these may be added Ophiucus, holding a serpent in his hands, Perseus with Medusa, Centaurus, etc., which, when found in the ascendant of conception, signify a doubled birth. BIOTHANATOS, in Greek, properly signifies those who are taken away by violent death. Among Astrologers, however, it is taken more strictly for those only who take their own life. Its use is frequent in Ptolemy in the chapter on Death, though they would more correctly be called Authothanatos. See the author of the Thesaurus of the Greek language. BIQVINTILIS radius is a new aspect, considered by Kepler and other revisers, consisting of two-fifths of a circle, that is, 140 degrees; wherefore planets beholding one another mutually contract familiarity. By its nature it is a fortunate and good aspect, as are Quintilis, Sextilis, and Trinus; just as, on the contrary, Quadratus, Sesquiquadratus, and Opposition are inauspicious and of imperfect familiarity. Moreover k iij

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86 LEXICON Quintilis, Biquintilis, & Sesquiquadrati radix, vti dicebam apud antiquos ratio habita non est, ideò ab ipsis prætermisssi. Verùm Keplerus rem altiùs refodiendo, ex consonantiis harmonicis subtili ratione inuenit, arque experientia probauit non minus aliis esse efficaces. Cui subscribit Tirus in Cælesti Philosophia: Vide quæ dicta sunt in Verb. Aspectus. 16. Bissextus, & Bissextilis dicitur Annus ille intercalaris constans diebus 366. quarto quoque anno adueniens, vna vide- licet die superaddita ad Februarium: sic dictus ab ipsa die superaddita, quæ cum præcedente pro vna integra die computabatur: atque adeò bis dicitur sexto Kalend. Martij. Eius inuentio tribuitur Cæsari Dictatori: Cùm enim anim- aduertisset Solem cursum suum perficere in signifero spatio dierum 365 & sex circiter horarum; ideò statuit, quarto quoque anno adijciendum essediem vnum, quantum scilicet constituunt sex horæ quater ductæ. Verum enim uerò Anni tropici magnitudo (vt in loco admonuimus) reuera non est dierum 365. & horarum sex, sed horarum quinque & minuto- rum ferè 49. ita vt quolibet anno vndecim minuta deficiant ad sex integras horas: quî fit, vt singulis quadrienniis, ad- dito etiam die intercalari, non respondeant ad amussim inte- græ Solis revolutiones in Zodiaco: ita vt reuertatur ad idem punctum, vnde initio anni discesserat, sed inueniatur in inte- grô quadriennio præcessisse ad min. ferè 44 quæ longo tem- poris tractu ita excreuerunt, vt decem integros dies comple- uerint. Adeò vt æquinoctium vernum (vti Autumnale, & solstitia) sedem suam mutauerit, & jam non ampliùs recide- ret in 12. Kalendar. Aprilis, vt erat in principio, sed in ter- tio Idus Martij; atque insuper successu temporis, eò res de- uenire poterat, vt solstitium Hyemale in Æstatem recideret, æquinoctium Vernum in tempus solstitij, cum maxima re- rum, Ecclesiasticorumque rituum perturbatione. Cui malo occutrere volens Gregorius XIII. non sine cælesti numine, detractis prius ab anno correctionis 1582. decem integris die- bus, quibus præcesserant æquinoctia, & solstitia ea in mo- mento in suas sedes restituit. Et ne in posterum ob eandem paucorum minurorum negligentiam à suis sedibus mutaren- tur, statuit, vt Bissextus singulis quidem annis celebraretur, addito, vt priùs erat in vsu, die illo intercalari quarto quo- libet anno, exceptis tamen Centensimis, qui nisi Bissextiles anteâ semper fuerint, in posterum tamen non omnes cente- simi Bissextiles forent, sed in quadringentis quibusque an- nis, primi quique tres centesimi sine additione diei illius in-

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86 LEXICON Quintilis, Biquintilis, and Sesquiquadrati radix, as I said, were not regarded by the ancients, and therefore were omitted by them. But Kepler, by digging the matter more deeply, found by a subtle reasoning from harmonic consonances, and proved by experience, that they are no less effective than the others. To this subscribes Tirus in the Cælestial Philosophy: See what is said in the word Aspectus. 16. Bissextus, and Bissextilis, is the name given to that intercalary year consisting of 366 days, occurring every fourth year, with one day added to February; so called from that very added day, which, together with the preceding one, was reckoned as one whole day: and thus it is called twice the sixth day before the Kalends of March. Its invention is attributed to Caesar the Dictator: for when he had observed that the Sun completed its course in the zodiacal space of 365 days and about six hours, he therefore decreed that every fourth year one day should be added, namely the amount constituted by six hours multiplied by four. But in truth the magnitude of the tropical year, as we have noted elsewhere, is not really 365 days and six hours, but five hours and about 49 minutes; so that each year there is a deficiency of eleven minutes from the full six hours. Hence it comes about that in each period of four years, even with the added intercalary day, the full revolutions of the Sun in the Zodiac do not correspond exactly, so that it does not return to the same point from which it departed at the beginning of the year, but is found in the full four-year period to have advanced by about 44 minutes, which in the long course of time have grown so much that they have completed ten full days. So much so that the vernal equinox, like the autumnal one and the solstices, had changed its position, and no longer fell on the 12th day before the Kalends of April, as it did at the beginning, but on the third Ides of March; and furthermore, with the passage of time, matters could have come to such a pass that the winter solstice would fall in summer, the vernal equinox in the time of the solstice, with the greatest disturbance of affairs and of ecclesiastical rites. Gregory XIII, wishing to remedy this evil, not without heavenly inspiration, first removed from the year of correction 1582 ten full days, by which the equinoxes and solstices had gone before, and at that moment restored them to their places. And lest in future, because of the same negligence of a few minutes, they should again be moved from their seats, he decreed that the Bissextus should indeed be observed in each year, with the intercalary day added, as had previously been the custom, every fourth year, except for the centesimal years, which, unless they had always been Bissextile before, should nevertheless not all be Bissextile in future, but in each four hundred years the first three centesimal years should be without the addition of that day in

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MATHEMATICVM. 37. tercalaris transigerentur; quarius verò quicque centesimus esset Bissextilis Ita vt annus 1600. sit, vt antea Bissextilis; anni verò 1700. 1800. 1900. Bissextiles non essent, bene verò centesimus sequens hoc est 2000. Idque in perpetuum obser- uando, nunquam Æquinoctia, & Solilitia à suis sedibus de- turbarentur: Qua de te plura apud Clauium in Kalendario Gregoriano. 17. BIVMBRES hoc est binas habentes vmbras dicuntur populi habitantes in Zoua torrida citrà Tropicos ad æquatorem, vbi pro temporum varietate binam experiuntur vmbram, alte- ram ad Meridiem, alteram ad Septentrionem: Vide in V. Amphisej. 18. BOLIDES apud Plinium, lib. 2. cap. 26. sunt species Co- metarum Quale, inquit, Mucinensibus malis visum est. Quæ distant à facibus per hoc, quod istæ vestigia longa faciunt, priore ardente parte: Boles verò perpetua ardens longiorem trahit limitem: Hæc Plinius. 19. BOOTES, Bubulcus, Arctophilax Plaustri ductor dicitur si- dus in Cælo prope Elicen, seu Vrsam maiorem continens stellas 23. iuxta Ptolemæum, Keplerum autem 28. & ex Baiero 34. omnes ferè de natura Louis, & Saturni, inter cuius femora adest vna infornis clara, & rutilans primæ magnitudinis de natura Martis, & Louis nomine Arcturus Arabicè Alramech quasi Vociferator, vel Theguins, hoc est plorans, de qua satis dictum suo loco. Ea cum Ioue, inquit Stadius, magnas diui- tias cum dignitate pollicerur: sicut è contrà cum Saturno earum profligationem protendit: Vide etiam in V. Arcto- philax. 20. BOREAS, ventus Septentrionali vicinus, ac lateralis spi- rans, ex parte ortus Solstitialis, sic dictus vel à nutrimento, quia sementem, fructus, & animantia valdè nutrit, vel cettè à boaru, quod flatus eius sit violentus reboans, ac sonorus. Est frigidus, & siccus, aërem purgans, & corruptioni resi- stens, sicut & reliqui Septentrionales venti. Aliquando acci- pitur etiam pro ipso vento cardinali, qui immediatè à Septen- trione exsufflat; dicto à Græcis Aparctia, ob eius vicinirem, & similitudinem naturæ. Quid Borea flante, aggrediendum, quidue cauendum sit: Vide apud Plin lib. 18. cap. 33. Dictus est etiam Aquila ab Aquilæ volaru, quem æmulari videtur, vt suo loco admonuimus. 21. BORRHAPELIOTES, ventus vnsus ex quatuor inter- medijs medio loco exsufflans inter Septentrionem & Æqui- noctialem ortum: à Nostris dictus est Græcus, cò quod per mediam Græciam transeat; Estque frigidus, & siccus, 111j

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MATHEMATICVM. 37. the intercalary days should be carried through; and every hundredth year should be bissextile, so that the year 1600 should be, as before, bissextile; but the years 1700, 1800, 1900 should not be bissextile, and the following centenary, that is 2000, should be so. And if this were observed forever, the Equinoxes and Solstices would never be displaced from their seats: concerning which, see more in Clavius on the Gregorian Calendar. 17. BIVMBRES, that is, those having two shadows, are called the peoples inhabiting the torrid zone this side the Tropics toward the equator, where, according to the variety of seasons, they experience a double shadow, one to the South, the other to the North: see under V. Amphisej. 18. BOLIDES in Pliny, book 2, chap. 26, are species of comets, as, he says, appeared to the people of Mucinum in bad omens. They differ from torches in this, that the latter make a long trail with the burning part in front; but a bolis, always burning, draws a longer line: thus Pliny. 19. BOOTES, Bubulcus, Arctophilax, driver of the wagon, is the star in the sky near Elicen, or the Greater Bear, containing 23 stars according to Ptolemy, 28 according to Kepler, and 34 according to Bayer; nearly all are of the nature of Jupiter and Saturn, among whose thighs there is one very bright and reddish star of the first magnitude, of the nature of Mars and Jupiter, called Arcturus; in Arabic Alramech, as it were “the Shouter,” or Theguins, that is, “the weeping one,” concerning which enough has been said in its place. With Jupiter, says Stadius, it promises great riches with dignity; on the contrary, with Saturn it extends their ruin: see also under V. Arctophilax. 20. BOREAS, a wind neighboring on the North, and blowing sideways from the part of the solstitial rising of the sun, is so called either from nourishment, because it greatly nourishes seed, fruits, and living creatures, or certainly from boaru, because its blast is violent, roaring, and noisy. It is cold and dry, purging the air and resisting corruption, like the other northern winds. Sometimes it is also taken for the cardinal wind itself, which blows directly from the North; by the Greeks called Aparctia, on account of its nearness and similarity in nature. What ought to be undertaken, and what avoided, when Boreas is blowing: see in Pliny, book 18, chap. 33. It is also called Aquila from the flight of the eagle, which it seems to emulate, as we have noted in its place. 21. BORRHAPELIOTES, a single wind, blowing from one of the four intermediate places in the middle position between the North and the Equinoctial rising; by ours it is called Greek, because it passes through the middle of Greece; and it is cold and dry, 111j

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LEXICON 88 nubes generans, & aliquando nives 23. BORRHOLYS. CVS, ventus est item principalis, vnus ex quauior intermediis, qui à loco æquè inter Septentrionem & Occasum interiecto perflat, à Noltris dicitur Magistralis quasi nauigationis Magister existat in mari Mediterraneo, vbi primum obseruatus fuit. Est natura sua humidus, nimbosus, procellosus, & in Æstate tonitruosus: in Autumno verò, aut vere violentus, repentinus, ac turbulenius. 23. BRIDEMIF, in tabulis Persicis dicitur Lupus, Fera, Bestia Centauri sidus videlicet ad australem plagam fere nobis inconspicum: de quo paulò ante dictum in V. Bestia. 24. BRINEK, frue Brineti apud Hermetem dicitur stella lucida Lyræ, primi honoris, alio nomine Vvega. 25. BRVMA ex Græco quasi breuis dies appellatur tempus solstitij hyemalis, quando dies sunt breuissimi, & noctes è contrà longissimæ in introitu Solis, ad primum gradum Capricorni: quod accidit post Gregorianam anni correctionem circa duodecimum kalendar. Ianuarij. Ipso brumali tempore Origanum aridum, & suspensum domi repene efflorescere, & murium jecora adaugeri testatur Cicero 2. de D minat. ac reipsa vel rustici experiuntur Democritus apud Plinium, talem futuram esse hyemem arbitrarur, qualis fuerit Brumæ dies, & circa eum terni. Portò Brumæ tempore quid Agricolis faciendum, vide apud ipsum Plinium lib. 18. cap. 26. 26. BVLTHO, Chaldaicè dicitur Virgo, sextum ab Ariete signum, Hebraicè autem Betulah, prout testatur kircherus in Oedipo Ægyptiaco. Vide in V. Virgo. 27. BVBVLCVS vide Bootes. CA 1. CABALLVS Barbarè dictus est vectisteres premens ac ligans rete, ac tympana in Astrolabio circa Clauum ex specie quam vtecumque oculis exhibet. Arabicè Alpheras Z. 2. CACODÆMON Græcè, Latinè malus genius dicta est duodecima domus ab horoscopo cadens ab angulo Medij Cæli, sic dicta à tristium, & exitialium rerum significatione: est enim significatrix carcerum, hostium occuliorum, aliarumque tribulationum, ac difficultatum. Consignificatus eius est Venus, & in ea gaudet Saturnus: qua ratione vide in V. Gaudium 3. CADENS apud Astronomos appellatur planeta quotiescunque in Cælesti figura reperitur in domibus cadentibus ab Angulis, quales sunt tertia, sexta, nona, & duodecima, quas Iulius Firmicus pigra, & abiecta figura loca nominat, eò quod in illis constituti planetæ plurimum debilitentur: licet reuerà

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LEXICON 88 generating clouds, and sometimes snow 23. BORRHOLYS. CVS, is also a principal wind, one of the four intermediate ones, which blows from a place lying equally between the North and the West; by us it is called Magistralis, as though it were the Master of navigation in the Mediterranean Sea, where it was first observed. By nature it is humid, rainy, stormy, and in summer thunderous; in autumn however, or in spring, violent, sudden, and turbulent. 23. BRIDEMIF, in Persian tables is called Lupus, Fera, Bestia, namely the constellation of Centaurus, situated toward the southern part, and almost invisible to us; of which something was said a little before under V. Bestia. 24. BRINEK, from Brineti with Hermes is called the bright star of Lyra, of the first honor, by another name Vega. 25. BRUMA, from the Greek, as it were “short day,” is the name for the time of the winter solstice, when the days are very short and the nights, on the contrary, are longest, at the entrance of the Sun into the first degree of Capricorn: which occurs after the Gregorian correction of the year around the twelfth day before the Kalends of January. At the very time of bruma, Cicero testifies in 2. de D minat. that dry oregano, suspended at home, almost flowers again, and that mice’s livers increase; and in fact even rustics experience it. Democritus, quoted by Pliny, thinks that such a winter will be as was the day of Bruma and the three days around it. Moreover, what should be done by farmers at the time of Bruma, see in Pliny himself, book 18, chapter 26. 26. BVLTHO, in Chaldean is called Virgo, the sixth sign from Aries; in Hebrew, however, Betulah, as Kircher testifies in the Oedipus Aegyptiacus. See under V. Virgo. 27. BVBVLCVS see Bootes. CA 1. CABALLVS, in the barbarous tongue, is called a supporting strap pressing and binding the net, and the drums in the Astrolabe around the Clavus, by whatever appearance it shows itself to the eyes. In Arabic, Alpheras Z. 2. CACODÆMON, in Greek, in Latin “evil spirit,” is the twelfth house falling away from the horoscope from the angle of the Midheaven, so called from the signification of sad and disastrous things: for it signifies prisons, hidden enemies, and other troubles and difficulties. Its co-significator is Venus, and in it Saturn rejoices: for which reason see under V. Gaudium 3. CADENS, among astronomers, is called a planet whenever it is found in the celestial figure in the cadent houses from the angles, such as the third, sixth, ninth, and twelfth, which Julius Firmicus calls sluggish and abject places in the figure, because the planets placed in them are greatly weakened; although in truth

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MATHEMATICVM. 89 nona, & tertia illis non officiant, immò potiùs prosint, cum nonæ communiter tribuantur duæ fortitudinis partes, terræ verò vna. Ratio autem quare in istis planetæ non infortunentur; hæc, meo judicio esse potest, quia videlicet benigno aspectu aspiciunt horoscopum: nona quidem de Trino, tertia de Sextili: & insuper nona est in magna altitudine à terra proxima decimæ, vbi planetæ puriores sunt, validiores ac liberi à terrenis vaporibus; & idcircò nona licet cadens euadit nihilominus fortunata; estque exceptis cardinibus potissimus locus vbi constituta Luminaria, aur pars fortunæ vim obtinent hilegialem, melius quam in vndecima, ob radij nempe fortitudinem, ac præcellenriam, quo horoscopum intuetur. CADENS item dicitur planeta, quando in Zodiaco reperitur in signo opposiro suæ exaltationis: qua de re vide in V. Casus. CACIAS ventus Orientalis spirans ab exortu solstiriali: sic dictus à Caci flumine Hellesponti per quod transit vnde & Hellespontium ab aliquibus appellatur. Est frigidior, & inconstantior Subsolano ob participarionem cum ventis Septentrionalibus, arque adeò flaru suo subinde molestus, nubifer ac pluuiosus. De eo notar Aristoteles, quod contrà naturam aliorum ventorum nubes non abs se propellit, sed ad se attrahit: Plura apud Erasimum in Adagijs. CÆNACVLVM, alijs Tenaculum, est species quædam Come- ræ criniti, magni, oblongi, ac lati instar Cænaculi, seu mensæ quadrilareræ, vnde & nomen hausit. Est de natura Lunæ, portendisque afflictionem populi sine discrimine, seditiones, bella, legum innouationes, &c. ex morbis inducir catarahos, paralises, hydropas, epylepsias, scabies, dolores colicos, obstructiones, & alios huius generis morbos. CALBEZ Arab. est stella fixa secundæ magnitudinis in effusione aquæ Aquarij proxima Fomahand de natura Louis, & Saturni. Eius conreimina est altera stella nomine Alcalism eiusdem naturæ. CALCULATOR dicitur Latinè Regula, Dioptra, Alhida[n]da in medio Astrolabij collocata, ab officio, quo fungitur calculandi gradus altitudinis stellarum, quam per Astrolabium venamur: prorenditur enim vsque ad limbum Astrabij in quo circulus descriptus est in 360. partes dislectus. CALLIPICA Periodus dicta est Lunaris Anni magni cum Cyclo Solis decennouennali conuenientia, ab eius inuentore Callippo, qui floriit Olympiade 162. annis ferè 128. ante Christum: In ea enim 940 Lunares menses explentur, & dies 13878. ferè, quot ferè comprehendunt Cycli Solares decenno-

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MATHEMATICVM. 89 The ninth and third do not hinder them, but rather help them, since the ninth commonly grants two parts of fortitude and the earth one. The reason why in these places the planets are not unfortunate, may, in my judgment, be this: namely, because they behold the horoscope with a benign aspect; the ninth indeed by a trine, the third by a sextile; and moreover the ninth is in great altitude, near the tenth house from the earth, where the planets are purer, stronger, and free from earthly vapors; and therefore the ninth, though cadent, nevertheless turns out fortunate; and excepting the angles, it is the chief place where, if the Luminaries or the Part of Fortune are placed, they possess hilegial force, better than in the eleventh, because of the strength and excellence of the rays with which it looks upon the horoscope. CADENS is likewise said of a planet when in the Zodiac it is found in the sign opposite to its exaltation: on this see under the Fifth Case. CACIAS, an eastern wind blowing from the solstitial rising: so called from the river Cacus of the Hellespont, through which it passes, whence by some it is also called Hellespontius. It is colder and more changeable than the Subsolanus, by participation with the northern winds, and therefore by its blast at times troublesome, cloud-bringing, and rainy. Aristotle notes of it that, contrary to the nature of other winds, it does not drive the clouds away from itself, but draws them to itself. More in Erasmus in the Adages. CÆNACVLVM, by others Tenaculum, is a certain kind of comet, hairy, large, oblong, and broad, like a cœnaculum, or square table, from which it also took its name. It is of the nature of the Moon, and portends affliction of the people without distinction, seditions, wars, innovations of laws, etc.; from diseases it induces catarrhs, paralyses, dropsies, epilepsies, scabies, colic pains, obstructions, and other diseases of this kind. CALBEZ, Arab., is a fixed star of the second magnitude in the pouring of the water of Aquarius, near Fomahand, of the nature of Venus and Saturn. Its companion is another star named Alcalism of the same nature. CALCULATOR is called in Latin the Regula, Dioptra, Alhida[n]da placed in the middle of the Astrolabe, from the office which it performs in calculating the degrees of the heights of the stars, which we pursue through the Astrolabe; for it is extended as far as the rim of the Astrolabe, in which a circle is described, divided into 360 parts. CALLIPICA Period was named the agreement of the Lunar Great Year with the nineteen-year cycle of the Sun, from its inventor Callippus, who flourished in the 162nd Olympiad, about 128 years before Christ. For in it 940 lunar months are completed, and about 13,878 days, as many as are almost comprehended by the nineteen-year Solar cycles.

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90 LEXICON. uennales quatuor, seu quatuor anni Metonici, in quorum singulis contingunt quidem Nouilunia ijsdem diebus mensium, in quibus contingebant ante annos 19. Solates, at non ijsdem horis, sed aliquantò priùs, nempe per horam, & semis, vt dictum est in V. annus Metonicus . In annis verò 76. Luna anticipat easdem sedes, quas ante illos obtinebat hor. 5. min. 50. secund. 10. tert. 44. ac tandem in annis 312. & sex mensibus, die fermè toto, qui tandem per dies bissextiles superaddditos, & septem Lunationes embolismicas exquisitissimè compensari potest, ita vt annus Lunaris ad amussim cum Solari conveniat: Quade re vide quæ haber 10 Lucidus Samotheus in libro quem Chronicon, seu de emendatione temporum inscriptit in Epitome emendationis Calendarij ad finem adjecta, vbi ex Paulo Episcopo Forosempioniensi, & Ioanne Stofflerino duplicem methodumtradit temporis ita instituendi, vt deinceps Lunationes ne in minuto quidem anticipent, sed ad amussim conveniant cum tecursu Solis. Hæc igitur convenientia in anno Lunisolari ab eius inventore Callippo Periodus Callapica dicta est. Plura apud Clauium in Restitut. Kalendadarij II. CAMMARVS corrupto vocabulo ab aliquibus dicitur signum cæleste, & sidus in Zodiaco quartum ab Ariete, dictum etiam Nepa, vel Astacus, Arabicè Elsartan à Latinis verò communiter. II. CANCER domicilium Lunæ, & exaltatio Louis signum mobile aqueum, frigidum, & humidum, sic dictum à similitudine Cancri piscis, quia sicut iste super pectus suum graditur retrocedendo; ita Sol in hoc signo incipit quasi retrocedere à nobis, atque ad æquatorem accedere. Dispositio quoque stellarum, quæ Cancri sidus constituunt, videntur etiam non ineptè hoc ei nomen inferre: Quandoquidem in eo tres stellæ hinc inde ad latus dispositæ, quasi Cancri brachia repræsentant: & cum Cancer sit veluti totum pectus, hominesque è contrà qui sub hac constellatione nascuntur, corpore breues, sed ampli pectore prodire perhibeantur, vt testis est Iunctinus, ideò Cancri est ei nomen inditum: idcircò etiam ex membris humanis habet pectus, pulmonem, hepar, & costas. 13. Porrò Cancri sidus in octava sphæra, vt alibi in aliis signis obseruatum est, jam recessit à Tropico, & signo Cancri in primo mobili; estque nunc totum in Leone. Constat stellis 13. iuxta Proleniæum, computantem inter eas quarior etiam informes, at iuxta Keplerum 17 & Baierum 35 ex quibus vna in chelis dicta ab Arabibus Azubene præterea tres in pectore consistentes, infensissimæ vna Prasepe dicta, Nebulosa

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The four Gregorian cycles, or four Metonic years, in each of which New Moons occur on the same days of the months on which they occurred 19 years before, and in the same hours, but a little earlier, namely by one hour and a half, as was said in V. Metonic year . But in 76 years the Moon anticipates the same positions which it occupied before by 5 hours, 50 minutes, 10 seconds, 44 thirds; and finally in 312 years and six months, almost a whole day, which can at last be most exactly compensated by the additional leap days and the seven embolismic lunations, so that the lunar year may agree exactly with the solar year. On this matter see what Lucidus Samotheus has in the book which he entitled Chronicon, or On the Correction of Time , added at the end of the Epitome of the Correction of the Calendar , where, from Paul, Bishop of Forojuliensis, and Ioannes Stofflerinus, he gives a double method of arranging time so that in future the lunations do not anticipate even by a minute, but agree exactly with the course of the Sun. This harmony, therefore, in the lunisolar year was called by its inventor Callippus the Callippic Period. More on this in Clavius, Restitutio Calendarii . II. CAMMARVS, a corrupted word, is said by some to be a heavenly sign and the fourth star in the Zodiac from Aries, also called Nepa, or Astacus; in Arabic Elsartan, but commonly by the Latins. II. CANCER, the domicile of the Moon and the exaltation of Jupiter, a movable watery, cold, and moist sign, so called from the likeness to the crab, because just as this creature walks backward upon its breast, so the Sun in this sign begins, as it were, to move backward from us and to approach the equator. The arrangement of the stars that make up the constellation of Cancer also seems not inaptly to have given it this name: since in it three stars, arranged on either side, represent, as it were, the crab’s claws; and since Cancer is, as it were, the whole breast, and men born under this constellation are said to be short in body but broad in chest, as Juntinus attests, the name Cancer was given to it for that reason. Therefore, from the human members it has the breast, lungs, liver, and ribs. 13. Moreover, the constellation of Cancer in the eighth sphere, as has been noted elsewhere in the other signs, has now receded from the Tropic and the sign of Cancer in the prime mobile; and it is now entirely in Leo. According to Ptolemy it consists of 13 stars, counting among them four also faint ones; but according to Kepler 17 and Bayer 35, of which one in the claws, called by the Arabs Azubene, and furthermore three in the breast, the most conspicuous of which is called Praesepe, the Nebulous one.

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MATHEMATICVM. 91 de natura Martis & Lunæ, secunda & tertia Aselli, quartæ magnitudinis, de natura Martis, & Louis, de quibus alibi sermo. Et ideò primæ huius sideris partes vbi stellæ istæ consistunt, siccissimæ sunt, mediæ, & vliimæ præditæ etiam magna caliditate, & siccitate: sed Australiores magis æstuosæ, ac noxix. CANIS Maior Sirius, Canicula, sidus in cælo ad australem < 14.> plagam sub signo Cancri constans stellis decem & octo secundùm Ptolemæum, omnibus ferè de natura Louis, & Veneris, quarum potissima Arabicè Albor in ore fulgens, ab aliquibus Sole ipso grandior perhibetur. Nec dubium a quin omnium saltem stellarum, tam errantium, quam inenarrantium sit maxima, vt oculis ipsis conspici potest, & ex effectuum magnitudine coniectari. Eius exorientis cum Sole patentes vires recitat Plin. lib. 3. cap 4 cuius rei rationem reddit Alexander Aphrodizus problem. 74. Occasus ipsius cum Sole commouet Austrum, inducit calorem serenum cum sonitruis, & fulmine. Cum Saturno addit & pluuias, cum Marte facit æstum magnum, cum Mercurio ventos. De eo horoscopante in Genituris hominum sic cecinit Pontanus in Vrania. Exoriens: Incendi flammis, & pectora concitat astu. Iræ ingens, dolor atque ingens ingentibus ausis, Ingentesque tument animi: imperiosa cupido Nil æquum patitur: feruet sisus arida habendi: In faci usque vocat, violentaque tela ministrat. Non pietas mouet, aut amor, aut reverentia Diuum, Præsertim si Trescimus sese addidit Heros. At si in occasu reperiatur, de eo mox subdit. Infelix nato exitium paras, vnde serarum Dente lacer cadat in simus, vrsive, lusive Prada, vel audaci per:at lansatus ab Vimbo Si Manors va idem aspici ns concusserit hastam. Porrò circa Canem maiorem sunt, & aliæ stellæ informes omninò vndecim, nondum in certum Asteriscum redactæ, quæ sunt de natura Veneris, & omnes ferè quartæ magnitudinis; & easdem significationes habent ac reliquæ stellæ Veneræ, & Louiales CANIS Minor, Procyon, Antecanis Arabicè Algomeysali- < 15.> dus in Cælo propè canem maiorem, sed illo borealius: constat duabus tantùm stellis, alterâ in ceruice quartæ magnitudinis de natura Mercurij, alterâ in femore, cui signatè nomen Procyon primæ magnitudinis, de natura Martis. Et ipsum cum Sole, vel Marte exoriens vehementissimum inducit æstum, atq; ab eo tempore incipiunt dies Caniculares. Plura in V. Procyon.

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MATHEMATICVM. 91 concerning the nature of Mars and the Moon, the second and third of Asellus, of fourth magnitude, concerning the nature of Mars and of Jupiter, about which there is discussion elsewhere. And therefore the first parts of this star, where these stars are situated, are very dry; the middle and last parts are also endowed with great heat and dryness: but the more southern parts are more scorching and harmful. CANIS Maior Sirius, Canicula, a star in the sky in the southern <14.> quarter under the sign of Cancer, consisting, according to Ptolemy, of eighteen stars, almost all of the nature of Jupiter and Venus, the chief of which, Arabicly Albor, shining in the mouth, by some is said to be greater even than the Sun itself. Nor is there any doubt that it is the largest of all the stars, both wandering and fixed, as can be seen with the eyes themselves, and inferred from the greatness of its effects. Pliny recounts in lib. 3, cap. 4 the powers of its rising together with the Sun, for which reason Alexander Aphrodisias gives an explanation in problem. 74. Its setting together with the Sun stirs up the south wind, brings calm heat with thunder, and lightning. With Saturn it adds rains; with Mars it produces great heat; with Mercury, winds. Concerning it, when horoscoped in the nativities of men, Pontanus sang thus in Urania. Rising: I burn with flames, and stir the heart with ardor. Great wrath, and great grief for great undertakings, and great spirits swell: an imperious desire permits nothing fair: the thirst for possessing grows hot: it calls to deeds, and furnishes violent weapons. Neither piety, nor love, nor reverence for the gods moves me, especially if the Thrice-Great Hero has joined himself. But if found in setting, he adds this soon after: You prepare ruin for the unhappy child; whence, torn by a ferocious tooth, he may fall as prey into the jaws of a bear or lion, or, wounded, perish by a bold blow from a spear if Mars, looking upon the same thing, has shaken the spear. Moreover, around Canis Major there are also eleven other shapeless stars altogether, not yet reduced to a certain asterism, which are of the nature of Venus, and almost all of fourth magnitude; and they have the same significations as the other stars of Venus and Jupiter. CANIS Minor, Procyon, Antecanis, Arabicly Algomeysalis, a star in the sky near Canis Major, but farther north than it: it consists of only two stars, one in the neck of fourth magnitude, of the nature of Mercury, the other in the thigh, which is specifically named Procyon, of first magnitude, of the nature of Mars. And it too, when rising with the Sun or Mars, brings about a most violent heat, and from that time the Dog Days begin. More in V. Procyon.

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92 LEXICON 16. CANOPVS Arabicè Rubayl stella fixa fulgentissima primæ magnitudinis de natura Iouis & Saturni, in tenione Nauis Aigo consistens; Romæ nunquam exoriens, sed vanum Melitæ, vix horizontem radens, quippequæ existit nunc in grad. 9. Cancri cum latitudine australi grad. ferè 40 Cui nihilominus incidit in horoscopum, is erit magni nominis, ac nauagationibus intenuis: Verùm in occasu cum malo radio Saturni portendit naufragium. 17. CAPELLA, seu Capra, alio nomine Hercus Arabicè Alioth. sidus in coelo, seu potiùs stella vna primæ magnitudinis de natura Martis, & Mercurij, existens in sinistio humero Aurigæ quàm Nauis infensam canir Germanicus in expositione Arabi Ph nomenon. Hæc in horoscopo, inquit Pontanus in Vrania facit timidum, curiosum nouarum rerum, amatorem &c. In occasu verò irreligiosum, sacrorum prophanatorem 18. CAPER dicitur etiam Capricornus signum cæleste decimum ab Ariete mobile, terreum, siccum, & frigidum, domus Saturni, & exaltatio Martis; sic dictus, quia sicut illud animal ad frondes, & arbores se erigit, ita & Sol in eius introitu incipit elevari, atque ad nos accedere, cùm priùs recederet: Vnde etiam dicitur Tropicum, & Solstiuale. Quique sub eo nascuntur faciem habent oblongam, mentio acuto. capillis asperis, moribus denique ac voce Caprum imitari videntur. Erus constellatio in octavo orbe incipit à gradu 28. Capticorni primi 19. mobilis, atque extenditur vsque ad grad. 2t Aquarij Stellas habet 28 quarum præcipuæ duæ in Cauda tertiæ magnitudinis de natura Iouis & Saturni, Arab. Elgæda, vel Alcanta-rus reliquæ de natura Martis, & Mercurij. Primæ eius patres calidæ sunt, atque noxia; mediæ temperatæ; vltimæ pluuiosæ. 20. CAPVT Draconis, stella fixa tertiæ magnitudinis de natura mixta Iouis, Martis, & Saturni, Arabicè Ras Abem siue etiam Eltanin: de ea vide suffùs in V. Draco. CAPVT, & Cauda Draconis etiam audiunt apud Astronomos Nodi, seu intersectiones planetarum, præsertim verò Lunares: quæ sunt puncta vbi orbita Lunæ (idem dic de orbitis aliorum) intersecat orbitam Solis, & eclipsam, quorum quidem alterum tendit ad Boream, inde incipiente Luna habere latitudinem borealem; alterum ad Austrum, vbi Luna incipit gaudere latitudine australi. Vbi autem obtinet maximam latitudinem, dicitur Venter, siue Australis, siue Borealis, pro ratione latitudinis, quam habet: & jure quidem, nam sicut Draco corpore magnus, ac latus est, prope caput verò, & caudam exilis, & subtilior, ita spatium intercepium inter

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92 LEXICON 16. CANOPUS, in Arabic Rubayl, a fixed star of the first magnitude, of the nature of Jupiter and Saturn, situated in the keel of the Ship; never rising at Rome, but visible at Malta, scarcely grazing the horizon, since it is now in 9 degrees of Cancer, with southern latitude of about 40 degrees. Whoever has this in the horoscope will be of great name and favored in voyages; but in the setting, with the evil ray of Saturn, it portends shipwreck. 17. CAPELLA, or Capra, otherwise called Hercus, in Arabic Alioth, a star in the sky, or rather a single star of the first magnitude, of the nature of Mars and Mercury, located on the left shoulder of Auriga, which Germanicus in his exposition of the Arabic phenomenon calls hostile to the Ship. This, in the horoscope, says Pontanus in Urania, makes one timid, curious about new things, a lover, etc. In the setting, however, irreligious, a profaner of sacred things. 18. CAPER is also called Capricorn, the tenth celestial sign, movable from Aries, earthy, dry, and cold, the house of Saturn, and the exaltation of Mars; so called because, just as that animal raises itself toward foliage and trees, so the Sun, on entering it, begins to rise and to come toward us, whereas before it had been retreating. Hence it is also called the Tropic and the Solstitial sign. Those born under it have an oblong face, a narrow chin, rough hair, and in manners and even voice seem to imitate the goat. The constellation in the eighth sphere begins at the 28th degree of Capricorn, the first of the movable signs, and extends to the 2nd degree of Aquarius. It has 28 stars, of which the chief two in the Tail are of the third magnitude, of the nature of Jupiter and Saturn, Arabic Elgæda, or Alcantarus; the others are of the nature of Mars and Mercury. The first stars of it are hot and harmful; the middle ones temperate; the last rainy. 20. CAPUT DRACONIS, a fixed star of the third magnitude, of the mixed nature of Jupiter, Mars, and Saturn, in Arabic Ras Abem or also Eltanin: see more fully in V. Draco. CAPUT and Cauda Draconis are also called by astronomers the Nodes, or intersections of the planets, especially of the Moon: these are the points where the orbit of the Moon (the same may be said of the orbits of the others) intersects the orbit of the Sun, and the eclipse, one of which tends toward the North, where the Moon begins to have northern latitude; the other toward the South, where the Moon begins to enjoy southern latitude. But where it attains its greatest latitude, it is called the Belly, whether southern or northern, according to the latitude it has: and rightly so, for just as the Dragon’s body is large and broad, but near the head and tail slender and thinner, so the space intercepted between

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MATHEMATICVM. 93 duos semicirculos, & deferentis Lunam, & æquantis, vide- tur quendam velui Draconem efformare, cuius pars lata Dra- conis ventrem repræsentat; intersectiones verò Caput, & Caudam. Postò huiusmodi intersectiones non semper loco < 22.> consistunt, sed mouentur, & ipsæ motu proprio in Zodiaco, retrogradè tamen non directè: in superioribus insensibiliter, ita vt nodus boreus Saturni nunc temporis sit in grad. 3. min. 20. Cancri, Louis similiter in grad. 3. min 7. Cancri; Martis in grad. 1. min. 17. Tauri: Nodus verò Austinus in locis oppositis: In reliquis autem tribus nodi sunt perpetuò varia- biles, ac præcipuè in Luna, cum ad dies singulos isti ferè tribus minutis retrocedant. Obseruant Astronomi nodos planetarum, præsertim Luna- < 23.> res, eorumque naturam considerant, & boreum quidem aiunt imitari naturam Louis, & Veneris; Austrinum verò naturam Saturni, & Martis; ad eosque dirigunt significatores non se- cus ac ad ipsa corpora planetarum: quod tamen improbat Titus in Cæsti philosophia. Ego re bene perpensa, non ne- < *> garem ipsas aliquam efficientiam saltem indirectam, vt cum Luna repetitur al cui maleficæ iuncta in nodis, æque in augu- lis, facit natum gibbosum, claudum, aut vrcunque contor- tum, vt habet Proleminus lib. 3. cap. 17. Sed id prouenit eò quia in Ecliptica radius, aut coniunctio est validior, proinde- que Luna magis à malefica infestatur, quod & in Sole accidit, qui tamen semper est in Ecliptica. Et ideò caput dicitur esse de natura Mercurij, cum bonis bonum, cum malis malum, quia in Ecliptica planetæ fortiores sunt, & dum relicta austra- li parte, incipiunt accedere ad boream, boni bonitatem auges- cunt, mali malitiam: è contrà in nodo austrino planetæ des- cendunt à boreali plaga, æque accedunt ad Austrum, vbi debiliores euadunt; meritò igitur cauda Draconis cum bonis mala dicitur, cum malis bona, quia cum illis eorum bonita- tem minuit, cum istis eorumdem labefactat malitiam. Caput perhibetur esse Masculinum, Cauda ex minina: Hæc Arabicè appellatur Amabibazon illud autem Casabibazon, vt in loco diximus. CAPVT Apollo fixa in capite præcedentis Geminorum Ara- < 24.> bicè Ras Algense, vel etiam Elgieutze de natura Martis & Mercurij: de qua alijs in locis dictum. CAPVT Herculis stella fixa in capite Herculis fulgens, non < 25.> quidem eius, qui & Hercules dicitur, & est alter etiam Gemi- norum dictus etiam Pollux, sed eius qui alio nomine Engo- nasis appellatur propè Ophiaccum: de qua vide in V. Ras Al- gest.

Transcription: Translated (English)

MATHEMATICVM. 93 the two semicircles, that is, the one carrying the Moon and the one equating it, seem to form something like a Dragon, whose broad part represents the Dragon’s belly; the intersections, however, the Head and the Tail. Moreover, such intersections do not always remain fixed in the same place <22.>, but move, and move by their own motion in the Zodiac, retrograde indeed, but not directly: in the superior planets imperceptibly, so that the north node of Saturn is now at 3 degrees 20 minutes of Cancer, that of Venus likewise at 3 degrees 7 minutes of Cancer; Mars’s at 1 degree 17 minutes of Taurus: the southern node, however, in opposite places. In the remaining three, the nodes are perpetually variable, and especially in the Moon, since in each day these move back by nearly three minutes. Astronomers observe the nodes of the planets, especially the lunar ones, and consider their nature; and they say that the northern one imitates the nature of Venus and Mars, and the southern one the nature of Saturn and Mars; and to them they direct significators no differently than to the planets’ own bodies: which, however, Titus rejects in Cæstius’s philosophy. I, after the matter has been well weighed, would not deny that they have some efficacy at least indirectly, as when the Moon is joined to a malefic in the nodes, or likewise in the angles, it makes the native hunchbacked, lame, or somehow distorted, as Proleminus has in book 3, chapter 17. But this happens because in the ecliptic the ray, or conjunction, is stronger, and therefore the Moon is more afflicted by the malefic, which also happens in the Sun, who nevertheless is always in the ecliptic. And therefore the head is said to be of the nature of Mercury, doing good with the good, evil with the evil, because in the ecliptic planets are stronger, and when, having left the southern part, they begin to approach the north, the good increase goodness, the bad wickedness; on the contrary, at the southern node the planets descend from the northern region, likewise they approach the south, where they become weaker; therefore the Dragon’s tail is rightly said to be evil with the good, good with the evil, because with the former it diminishes their goodness, with the latter it weakens their wickedness. The Head is said to be masculine, the Tail feminine: this is called in Arabic Amabibazon, but that Casabibazon, as we said in the place. CAPUT Apollo, a fixed star in the head of the preceding Gemini, in Arabic Ras Algense, or also Elgieutze, of the nature of Mars and Mercury: concerning which something has been said elsewhere. CAPUT Herculis, a fixed star shining in the head of Hercules, not indeed that one who is also called Hercules and is the other of the Gemini, also called Pollux, but the one who by another name is called Engonasis near Ophiuchus: see concerning this at V. Ras Algest.

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94 LEXICON 16. CAPVT seu sectio equi. Vide in V. Equiculus. 27. CAPVT Medusa vide Algon, Gorgonis caput. 28. CAPVT Ophimi Arab. Ras Alangue stella fixa secundæ magnitudinis, de natuta Veneris, & Saturni, existens nunc temporis in gr. 18. Sagittarij cum gr. 13. declinationis borealis. Vide in Verbo Ophimus. 29. CARC[ON] NOS apud poëras Græcos dicitur Cancer sidus, de quo paulò antè fuit sermo. 30. CARPENTVM, Solium, Thronus, est dignitas, seu prærogatiua planetæ consistentis in loco, vbi plures obtiner dignitates: sic Carpentum Saturni est Aquatius, quia in eo obtinet Domicilium, & Trigonum: Iouis solium est Sagittarius ob eandem rationem: similiter Mars habet thronum in Scorpio ne, Sol in Leone, Venus in Tauro, Luna in Cancro: quia ibi habent domicilium, & trigonum: ac tandem Mercurius in Virgine, vbi obtinet dominium, & exaltationem. Hæc dignitas ab aliquibus dicitur gaudium: quia in istis locis planetæ videntur gaudere, & maximè extolli. 31. CASMON, & Cozimon apud Ægyptios appellantur nodi, seu intersectiones Orbitæ singulorum planetarum cum Ecliptica in duobus punctis oppositis: & primum quidem nodum austrinum, secundùm verò boreum, quos nos ex forma caudam, & caput Draconis vocamus, vt paulò antè dictum est. 32. CASSIOPEA Arab. Dach Elkarsi hoc est Cath dra, vel sedes regia sidus in cælo ad borealem plagam intrà Galaxiam constans stellis tredecim clarè conspicuis, sed longè plures obseruauit in eo Tycho, nec non Baetus, & Galilæus. Et anno quidem 1572. ad Cathedram propè eam, quam vocant Schedir apparuit in hoc sidere insignis stella, quæ & ipsum Iouem, & Sirium, splendore, candore lucis, & corporis magnitudine superans, ita omnium Astronomorum illius temporis, oculos animosque præstrinxit, atque in sui contemplationem conuertit, vt nemo planè fuerit, qui de ea non scripserit, disceptarit, vt vel ob id dubium esse possit, nùm cælo, an terris potiùs illustrior fuerit, clariorque. De ea integrum volumen edidit Tycho Brahe verus Astronomiæ instaurator; multa Keplerus, Michael Moestlinus, Abbas Maurolycus, Fortunius Licetus, Theodorus Gramineus, alijque scripsere. 33. Sed & Theodorus Beza apud Tychonem pag. 327. non minus imperitè, quàm petulanter opinatus est hanc stellam fuisse de genere Cometarum, quinimò illum eundem, qui in ortu Christi Magos Hierosolimam destinauit, atque perduxit; aitque quod sicut tunc primi aduentus prodromus, ita & nunc finem mundi, & secundum Christi aduentum prænunciare,

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94 LEXICON 16. CAPVT, or the head of the horse. See in V. Equiculus. 27. CAPVT Medusa, see Algon, the head of Gorgon. 28. CAPVT Ophimi. Arab. Ras Alangue, a fixed star of the second magnitude, of the nature of Venus and Saturn, now being at 18° of Sagittarius with 13° of north declination. See in the word Ophimus. 29. CARC[ON] NOS, among the Greek poets, is called the sign Cancer, concerning which mention was made a little before. 30. CARPENTVM, Solium, Thronus, is the dignity, or prerogative, of a planet residing in a place where it obtains several dignities: thus Saturn’s Carpentum is Aquarius, because in it he has domicile and trine; Jupiter’s throne is Sagittarius for the same reason; likewise Mars has a throne in Scorpio, the Sun in Leo, Venus in Taurus, the Moon in Cancer, because there they have domicile and trine; and finally Mercury in Virgo, where he obtains rulership and exaltation. This dignity is called by some joy, because in these places the planets seem to rejoice and to be most highly exalted. 31. CASMON and Cozimon are called by the Egyptians the nodes, or intersections, of the orbit of each planet with the ecliptic at two opposite points: the first indeed the southern node, the second the northern, which we, from their form, call the Dragon’s tail and head, as was said a little before. 32. CASSIOPEA. Arab. Dach Elkarsi, that is, the chair or royal seat, a constellation in the heavens on the northern side within the Galaxy, consisting of thirteen clearly visible stars, but Tycho, as well as Baetus and Galileus, observed far more in it. And in the year 1572, near the chair which they call Schedir, there appeared in this constellation a remarkable star which, surpassing both Jupiter and Sirius in brilliance, whiteness of light, and size of body, so struck the eyes and minds of all the astronomers of that time and turned them to its contemplation that there was absolutely no one who did not write or dispute about it, so that on that account one might even doubt whether it was more splendid and brighter in the heavens or on earth. Tycho Brahe, the true restorer of astronomy, published a complete volume on it; Kepler, Michael Moestlinus, Abbot Maurolycus, Fortunius Licetus, Theodorus Gramineus, and others wrote much about it. 33. But Theodorus Beza, in Tycho, p. 327, no less ignorantly than impertinently, held that this star was of the race of comets, indeed the very same one which at the birth of Christ directed the Magi to Jerusalem and brought them there; and he says that just as then it was the forerunner of the first coming, so now also it foretells the end of the world and the second coming of Christ,

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MATHEMATICVM. 95 Quod tamen Tycho, illum ait non seriò affirmasse, sed ex poëtica festiuitare lusisse: Etenim sic Beza audacter, impudens Vaticinator eceinit. Iste nouus, nullo furiali crine, cemetes, Et radians puro, cui noster igne imbar, Et quid portendat terris, Deus ille deo. um Nousit, & ostendens tempore fatæ suo. Quod si humana a quid possuns presciscere mentes, I alta scrutari, nec mihi signa nefas. Hic ille est olim paruam Dausdis ad urbem Duxit ab Eoo, qui priùs orbe Magos. Et qui nascensi præluxit, nuncrat idem: Ecce redux reducem rursus adesse Deum. Huic igitur felix o turba applaudè piorum. Tu verò Herodes sanguinolente time. Lanegrauius Hassix Beza cautior, & minus audax eam cum <34.> stella Magorum comparat, ac dicit esse diuersam: in hoc tamen vtramque conuenire ait, quod vtraque Christi aduentum significare habent: sic enim haber in epistola ad Peucerum relata à Tychone som 1. pag. 600. Cometam esse concludere non possumus propter magnam ipsius claritudinem, & quod motus sic expers; in uno enim puncto octaua sphara hactenus persistit; tum quod ità sublimis extrà elementarem regionem sit constituta. Neque facilè possumus asseuerare, condidisse Deum stellam aliquam recentem, cum tale aliquid à Mundo condito non sit auditum. Posteà verò de fine, ad quem Deus ipsam præluxisse voluit sic ait. Quantum isaque nos judicare valemus, censetur nobis insigne quoddam miraculum, & quidem unum eorum, qua nouissimum diem præcessura sunt. Ex quo enim domus Deus primum filij sui Domini nostri esu Christi aduentum antè per stellam significare, Magisque annunciari voluit, speramus, illum per hanc quoque vltimum aduentum Domini nostri Christi prænunciaturum. Hæc ille. Andreas Rosa apud eundem Tychonem obseruat singulis <55.> bismille annis circiter miracula eiusmodi cælitus edi, & cum ætatibus mundi ex dicto Eliæ Talmudistæ tripartito concludere; iraque ante diluuium tale quid apparuisse, vel saltem ante exitum Israëlitarum de Ægypto, columnam scilicet igneam: Tum post annos item bis mille apparuisse stellam Magorum in Oriente, hoc est iuxta terræ initium, vt salutis exordium demonstraret: Tandem anno 1572 apparuisse stellam hanc nouam propè potum arcticum, vt mundi finem ostenderet, quasi cælorum motus qui circa polos fiunt, non multo post sint desituri.

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MATHEMATICVM. 95 Yet Tycho says that he did not affirm this seriously, but was merely playing with poetic levity. For thus Beza sang, boldly, the shameless prophet: That new one, with no frenzied hair, bright with pure fire, And what he portends for the lands, that god learned from God, And by showing in its own appointed time. For if human minds can in any way foresee these things, It is not impious for me to investigate the heights, nor are the signs unknown to me. This is he who once brought to the small city of Dausdis from the East The Magi, who had first been before the world. And he who shone at his birth then was the same: Behold, the returning God is again present to the returning one. Therefore, happy crowd of the pious, applaud him. But you, bloody Herod, fear. Langengravius Hassia, Beza more cautious and less bold, compares it with the star of the Magi and says that it is different; yet he says that both agree in this, that each is to signify the coming of Christ: for so he writes in the letter to Peucer, quoted by Tycho, Som. 1, p. 600: “We cannot conclude that it is a comet, because of its great brightness and because it is without motion; for it has remained so far in one point of the eighth sphere. Then too, because it is placed so exalted outside the elemental region. Nor can we easily assert that God has created some recent star, since no such thing has been heard of since the creation of the world.” Afterwards, however, concerning the end to which God wished it to shine forth, he says thus: “As far as we are able to judge, it seems to us to be a certain remarkable miracle, and indeed one of those things that are to precede the last day. For since God first willed to signify the coming of his Son, our Lord Jesus Christ, by a star, and to announce it more fully, we hope that by this also he will foretell the final coming of our Lord Christ.” Thus he. Andreas Rosa, in Tycho himself, observes that miracles of this kind are produced from heaven about every two thousand years, and concludes from the threefold ages of the world, according to the saying of Elias the Talmudist, that something of this sort appeared before the Flood, or at least before the خروج of the Israelites from Egypt, namely the pillar of fire; then, after another two thousand years, the star of the Magi appeared in the East, that is, near the beginning of the earth, in order to show the beginning of salvation; finally, in the year 1572 this new star appeared near the Arctic Pole, in order to show the end of the world, as if the motions of the heavens which take place around the poles were soon to cease.

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96 LEXICON 36. Denique Tycho ipse postquam de huius stellæ situ, specie[m] materia, productione multa disseruit, prædicit magnam per eam religionis alterarionem portendi, cuius mutationis tempus ex directionum regulis vsque ad annum 1592. protendit, & tunc dicit initia mutationum, & semina jacienda; inde dirigendo stellam ad locum maximæ conjunctionis, quæ proximè p[er]cessit in grad. 21. Piscium air directionem complendam in annis 48 à prima fulsione stellæ, hoc est anno 1632. Et quia stella hæc fuit verticalis Moscouiæ, idcirco existimat ex Moscouia primas occasiones rubarum, ac mutationum orituras, & affert nescio quod vaticinium Sybillæ Iubutinæ, quod refert etiam Cornelius Gemmæ lib. de divinæ natura characte ismis in eius rei comprobationem Verum jam sumus ad ann. 1662. & ab termino directionis transacti sunt adhuc triginta anni, nec quicquam huius muraionis comminaræ præsertim ex Moscouia vidimus: sed nec visuros speramus. Et hæc obiter dicta sint de hac stella ex occasione Cassiopæ in cuius Asterismo apparuit: de eius tamen efformatione, loco, materia, aliisque ad nostrum institutum spectantibus iterum redibit sermo in V. Phanomenon. 37. CATABIBAZON, teste Valla, apud Arabes, seu Ægyptios idem sonar ac caput Draconis, seu nodus boreus Lunæ, sicuti Anabibazon idem, ac Cauda. 38. CATAEGIS ventus est ex genere procellarum, quem (inquit Apuleius in lib. de Mundo) præfractum possumus dicere, qui de eas parte submissus inferiora repentinis impulsibus quæstis Per quod opponitur Vortici, qui ex intimo alidæ humi exiliens ad suprema erigitur. 39. CATAPHORÆ dicuntur Græcè in Cælesti figura Domus cadentes ab Angulis, tertia, sexta, nona & duodecima; quemadmodum Anaphora quæ proximè succedunt Angulis, secunda, quinta, octava, & vndecima. 40. CATHALZE Arabicè vocatur linea meridiana subterranea descripta in Planisphærio, quæ constituit angulum Imi Cæli, qui etiam 41. CATOGEVM, hoc est domus subterranea apud Græcos aliquando audit, sumpta analogia ad Catogæum, quod propriè, & vniuersaliter domicilium subterraneum significat. 42. CATHETVS incidentia apud Astronomos dicitur linea recta ducta ex quous puncto radij incidentis ad planum speculum, seu reflexium perpendiculariter. 43. CATHETVS vero reflexionis est linea recta ducta ex quous puncto radij reflexi perpendiculariter ad planum speculum vsque ad occursum cum radio incidente per imaginationem. Eius

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96 LEXICON 36. Finally Tycho himself, after he had discoursed at length concerning this star’s position, appearance, matter, and production, predicts that by it a great alteration of religion is portended, the time of which change he extends, according to the rules of directions, as far as the year 1592, and then says that the beginnings of changes and the seeds are to be sown; from there, by directing the star to the place of the greatest conjunction, which had recently passed into the 21st degree of Pisces, he would complete the direction in 48 years from the first shining of the star, that is, in the year 1632. And because this star was vertical to Moscow, he therefore thinks that from Moscow the first occasions of tumults and changes would arise, and he brings forward some sort of prophecy of the Sibyl Iubutina, which Cornelius Gemma also cites in lib. de divina natura characte ismis in confirmation of this matter. But now we are already at the year 1662, and from the term of the direction thirty years have still passed, yet we have seen nothing of this threatened upheaval, especially from Moscow; nor do we hope to see it. And let these things have been said in passing about this star, on the occasion of Cassiopeia in whose asterism it appeared: but concerning its formation, place, matter, and other things pertaining to our purpose, discourse will return again in V. Phanomenon. 37. CATABIBAZON, according to Valla, among the Arabs, or Egyptians, sounds the same as the head of the Dragon, or the northern node of the Moon, just as Anabibazon is the same as the Tail. 38. CATAEGIS is a wind of the kind of storms, which, says Apuleius in the book De Mundo, we may call broken, which, from above, being driven downward, seeks the lower parts with sudden impulses. Whereby it is opposed to the Vortex, which, springing up from the innermost depths of the ground, rises to the highest parts. 39. CATAPHORÆ are called in Greek, in the celestial figure, the Houses falling away from the angles, the third, sixth, ninth, and twelfth; just as Anaphora are those that follow next to the angles, the second, fifth, eighth, and eleventh. 40. CATHALZE is the Arabic name for the subterranean meridian line drawn on the planisphere, which constitutes the angle of the lower heaven, which also 41. CATOGEUM, that is, a subterranean house, is sometimes called among the Greeks, by analogy with Catogæum, which properly, and universally, signifies a subterranean dwelling. 42. CATHETUS of incidence is called by astronomers the straight line drawn from any point of the incident ray to the plane mirror, or reflective surface, perpendicularly. 43. CATHETUS of reflection, however, is the straight line drawn from any point of the reflected ray perpendicularly to the plane mirror up to the meeting with the incident ray in imagination. Its

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MATHEMATICVM. 97 Eius explicationem fusè tradit Ricciolus in Almagesto novo lib. 80. sect. 6. cap. 2. CATOPTRICE est pars Opticæ, reflexiones coelestium cor- <44.> porum deprehendens, atque exinde eorum magnitudinem, ac longinquitatem dimetiens: alio nomine dicitur Anacamprica. CASVS est genus quoddam deteriorationis planetæ; quod <45.> accidit, quando reperitur in signo quod est oppositum alteri, in quo ipse haber suam Exaltationem. Vt Libra est locus casus Solis, quia ille in Ariete exalratur. Ptolemæus ponit totum signum pro casu: Arabes verò cærum quendam gradum, sicut & in exaltatione, vt alibi obseruarum est. Sic pro exemplo Sol deprimitur in Libra, sed præcipuè in gr. 19. Qua de re vide in V. Exaltatio. CASTOR, alio nomine Apollo dicitur prior Geminorum, <46.> Arabicè Bedalgense. CAVDA Capricorni, Arab. Deneb Algedi dicitur fixa tertia <47.> magnitudinis de natura louis, & Saturni existens nunc tem- poris in gr. 17. Aquarij, cum gradu ferè 3. latitudinis meridio- nalis. Ea in Oriente dar morum grauitatem, fortunam in diui- tiis, sed amoris illecebras, ac zelorypiæ cruciatus. Oritur Romæ cum gradu 22. Aquarij, occidit cum 16. CAVDA Cygni, Arab. Deneb Adigege seu potiùs Eldegiagicho, <48.> stella fixa secundæ magnitudinis de natura Veneris, & Mercu- rij existens nunc in gradu primo Piscium, cum gradu ferè 60. latitudinis borealis. Oritur Romæ cum gr. 23. Scorpij: occi- dit cum gr. 6. Arietis. Eius naturam vide in V. Adigege. CAVDA Ceti, Arab. Deneb. Kaitos stella fixa secundæ ma- <49.> gnitudinis de natura Saturni existens nunc in grad. 28. Piscium, <9> cum latitudine meridiana grad. 21. Ea in Horoscopo facit multis ægritudinibus obnoxium: dat periculum submer- <50.> sionis, præsertim, si Saturnus, aut Luna adstipuletur, vi- tam laboriosam, multisque ærumnis oppressam: quod etiam præstare. CAVDA Delphini fixa, tertia magnitudinis de natura Sa- <51.> turni, & Martis existens in gr. 9 Aquarij cum gr. ferè 30. la- titudinis borealis quæ oritur Romæ cum gr. 2. Capricornis, & occidit cum 23. Aquarij. CAVDA Draconis Sideris. Vide in V. Draco. <52.> CAVDA Draconis Lunæ: Vide in V. Caput Draconis. <53.> CAVDA Leonis, Arab. Deneb. Eleced. fixa primæ magnitudi-

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MATHEMATICVM. 97 Its explanation is given at length by Ricciolus in the New Almagest, book 80, sect. 6, ch. 2. CATOPTRICE is a part of Optics, which detects the reflections of celestial bodies, and thereby measures their size and distance: by another name it is called Anacamprica. <44.> CASVS is a certain kind of deterioration of a planet; which occurs when it is found in the sign opposite to another in which it has its Exaltation. Thus Libra is the place of the fall of the Sun, because it is exalted in Aries. Ptolemy assigns the whole sign for the fall; the Arabs, however, a certain degree, as also in exaltation, as has been observed elsewhere. Thus, for example, the Sun is depressed in Libra, but especially in degree 19. On this matter see under V. Exaltatio. <45.> CASTOR, also called Apollo, is the first of the Twins, in Arabic Bedalgense. <46.> CAVDA Capricorni, in Arabic Deneb Algedi, is called the third fixed star of the second magnitude, of the nature of Jupiter and Saturn, now at 17 degrees of Aquarius, with almost 3 degrees of southern latitude. In the East it gives seriousness of manners, fortune in wealth, but enticements of love and the torments of jealousy. It rises at Rome with 22 degrees of Aquarius, and sets with 16. <47.> CAVDA Cygni, in Arabic Deneb Adigege, or rather Eldegiagicho, is a fixed star of the second magnitude, of the nature of Venus and Mercury, now at the first degree of Pisces, with almost 60 degrees of northern latitude. It rises at Rome with 23 degrees of Scorpio; it sets with 6 degrees of Aries. Its nature may be seen under V. Adigege. <48.> CAVDA Ceti, in Arabic Deneb Kaitos, a fixed star of the second magnitude, of the nature of Saturn, now at 28 degrees of Pisces, with 21 degrees of southern latitude. In a horoscope it makes one subject to many illnesses; it gives danger of drowning, especially if Saturn or the Moon is in conjunction; a laborious life, oppressed by many hardships: which also can be seen. <49.><50.> CAVDA Delphini, fixed star of the third magnitude, of the nature of Saturn and Mars, now at 9 degrees of Aquarius with almost 30 degrees of northern latitude, which rises at Rome with 2 degrees of Capricorn, and sets with 23 degrees of Aquarius. <51.> CAVDA Draconis Sideris. See under V. Draco. <52.> CAVDA Draconis Lunæ: See under V. Caput Draconis. <53.> CAVDA Leonis, in Arabic Deneb Eleced, a fixed star of the first magnitude

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LEXICON 98 lucre, honores, ac dignitates amplas, præsertim, si cum Luminari conditionatio fuerit, aut cum beneficis, vel horum radijs fulva. Otitur Romæ cum glad. 4. Virginis: Occidit cum 27. Scorpij. 54. CAVDA Vrsa majoris belicis, fixa secundæ magnitudinis de natura Martis, Arabicè alalieth, seu Benenash quæ Romæ nunquam infà horizontem deptimitur. Nihilominus, si circa lineam Orientalem in alicuius natiuitate deprehendatur, multa, inquit Stadius, infortunia, multas calamitates adducit: propellit ad libidinis vitia; quo sit, vt natus multas ignominiae notas incurrat. 55. CAVDA Vrsa minoris, Arab. Alrukabah id est plaustrum, est stella polaris in extremo caudæ Vrsæ minoris sita, secundæ magnitudinis, ab ipso polo nunc temporis minus tribus gradibus distans, & aliquando ferè ad ipsum polum accessura: de qua multa diximus suo loco. 56. CAVRVS ventus: Vide CORUS. 57. CAZIMI, Arab. idem importat, quam centrum Solis. Hinc apud Astronomos aliquem planetam esse in Cazimi, nihil aliud significat, quàm esse in corde Solis, hoc est, vt non distet ab eo, siue in longitudine, siue in latitudine plus minutis 17. quanta videlicet est vtiusque semidiameter, & disci Solaris, & corporis singulorum planetarum. 58. Est digniras, ac fortitudo planetæ perinde habita, ac si esset in domo sua: cum aliàs conjunctio planetæ cum Sole sit illi noxia, & inter eius detrimenta annumeretur. Et si quidem ea sit minus medietate sui otbis est illi pessima, & vocatur combustio Sol enim sua potentia totam illius virtutem absorbet, remanente illo, vt ita dicam, combusto, viribus spoliato, & atefacto: & quò maior erit cum Sole approximatio, eò vires illius debilitantur, & ad Solem redundant. Nihilominus vt dixi, esse in corde Solis reputatur inter fortunas, & incrementa planetæ; non quia verè ipse acquitat quidquam virium; sed quia existens perfectè cum Sole coniunctus, iste exquisire imbibitur eius qualitatibus, illo nullatenus resistente; ac proinde Sole ipsius vices subintrante, ac potentiùs exerente dicitur planeta ipse numeris, & viribus auctus vice ipsius, siue bonus sit, siue malus potentiùs agar, ac dicatur in eius naturam mutatus. At verò combustus, aut sub radiis existens, etsi potentiâ Solis vires eius ad rationem vicinitatis aliquatenus infringantur, non ita tamen, vt omninò deperant, atque à Sole absumantur; sed magna pars apud ipsum remanet, quibus Soli magis, aut minus resistit, & suam activitatem demonstrat, quam non potest à Sole exquisitè posses-

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LEXICON 98 wealth, honors, and great dignities, especially if there has been an association with a luminary, or with benefics, or with rays from them. It is used in Rome with the 4th of Virgo: it sets with the 27th of Scorpio. 54. CAUDA of Ursa Major, fixed star of the second magnitude, of the nature of Mars, in Arabic alalieth, or Benenash, which in Rome is never depressed below the horizon. Nevertheless, if it is found near the eastern line in a nativity, it brings, says Stadius, many misfortunes, many calamities: it drives toward the vices of lust; so that the native incurs many marks of disgrace. 55. CAUDA of Ursa Minor, Arabic Alrukabah, that is, the wagon, is the polar star situated at the end of the tail of Ursa Minor, of the second magnitude, now less than three degrees distant from the pole itself, and at times almost approaching the pole itself: of which we have spoken at length in its proper place. 56. CAVRUS, a wind: see CORUS. 57. CAZIMI, in Arabic, signifies the same as the center of the Sun. Hence among astronomers for a planet to be in Cazimi means nothing else than to be in the heart of the Sun, that is, not to be farther from it, either in longitude or latitude, than 17 minutes, which is the semidiameter of both the Sun’s disc and the bodies of the individual planets. 58. It is the dignity and strength of a planet, regarded as if it were in its own house: whereas otherwise the conjunction of a planet with the Sun is harmful to it, and is counted among its detriments. And if indeed it is within less than half its orbit, it is worst for it, and is called combustion; for the Sun, by its power, absorbs all its force, leaving it, so to speak, burned up, stripped of strength, and blinded: and the greater the approximation to the Sun, the more its powers are weakened and flow back to the Sun. Nevertheless, as I said, to be in the heart of the Sun is reckoned among the fortunes and increases of a planet; not because it truly acquires any force, but because, being perfectly joined with the Sun, it is keenly imbibed by his qualities, offering no resistance; and therefore, the Sun taking over its office and exercising it more powerfully, the planet itself is said to be increased in number and strength in place of the Sun, whether it be good or bad, acting more powerfully, and said to be changed into his nature. But a combust planet, or one existing under the rays, although by the power of the Sun its forces are somewhat impaired in proportion to proximity, are not so completely lost as to be wholly destroyed and consumed by the Sun; rather, a large part remains in it, by which it resists the Sun more or less and shows its activity, which it cannot be exquisitely possessed by the Sun.

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MATHEMATICVM. 99 tus, & cum eo vnumquid factus. Qui fit, vt in Cazimi existens, fortis, & vivibus auctus. combultus autem, aut sub radiis, infirmus, ac debilis habeatur. CE CEGINVS dicitur apud quosdam sinister humerns Bootis stella videlicet fixa tertiæ magnitudinis, de natura Marris, & 59. Saturni existens in grad. 4. Libræ cum maxima latitudine boreali: quæ nunc, cum habeat declinationis grad. ferè 40. consequenter fit verticalis Regno Neapolis, quod valdè ob- seruandum CEGINVS etiam audit apud quosdam Cepheus, vt testis est 60. Ricciolus in Almagesto: de quo mox insia suo loco. CENTAURVS, qui & Typhon sidus in cælo ad australem plagam 61. nobis perpetuò laiens; constans stellis 36 omnibus ferè de natura Marris, & Veneris: Ex quibus insignior est fulgens in summirare prioris pedis dexri primæ magnitudinis de natura Iouis, & Veneris. Is in horoscopo, inquir Maternus, facit 62. aurigam equorum cultorem, nutritorem, vel etiam domitorem: & si Mars benigno radio affulgeat, faciet inter fortissimos equires militare. Si verò in occalu repertus fuerit, & hunc locum maleuolæ stellæ irradiauerint, natus, aut ex alio proiectus morierit, aut quadrupedis imperu, vel equi calce percussus, aut ab aliquo equo pojectus peribit: vel euerso curiu hentibus aquis misera morie lacerabitur. Hæc ille. In longitudine rorus est sub signo Libræ. CENTILOQUIVM Anthonomasticè apud Astronomos audit 63. insignis tractarus complectens centum sententias in breues aphorismos redactas, ac Prolemæo Astrologorum facilè principi ascriptus: qui & fructus librorum juorum hoc est Quadripartiri, & Almagesti indigitatur. Verùm magna controuersia est inter Astronomos, an is reuerà sit Prolemæi opus, an potiùs Hermetis Trismegisti, cuius aliera Aphorismorum Centuriacircumfertur. Hali Heben Rodoam Prolemæi Commentator in Commentar. super Quadrip. affirmar, illud non esse Polemæi, sed Hermetis: sed tamen aggressus Centiloquij commentationem, seu fuerit affectus magnificandi operis, quod explicandum suscipiebat, seu fuerit maior veri noritia comparata, Ptolemæi genuinum opus esse farerur. Secundò Hieronymus Cardanus post hæc rem benè considerans, ac dicta dictis obijciens, sententiæ vnitatem in ijs non esse comperijt. Ac tandem Argolus, alijque nostri temporis doctissimi viri pro liquidò habent, id Ptolemæi opus non esse, sed dicti G ij

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MATHEMATICUM. 99 Thus, and with it made one. Which is why, when it is in Cazimi, it is strong and increased in vitality. But when combusta, or under the rays, it is held to be weak and feeble. CE CEGINUS is called by some the left shoulder of Bootes, namely a fixed star of the third magnitude, of the nature of Mars and Saturn, located at 4 degrees Libra, with the greatest northern latitude: which now, since it has a declination of nearly 40 degrees, consequently becomes vertical to the Kingdom of Naples, which is greatly to be observed. CEGINUS is also called by some Cepheus, as Ricciolus testifies in the Almagest; about whom more in his own place shortly. CENTAURUS, which is also the constellation Typhon in the heavens, lying perpetually to our southern quarter, consists of 36 stars, all of them almost of the nature of Mars and Venus: among these the most notable is the brilliant star at the summit of the forward right foot, of the first magnitude, of the nature of Jupiter and Venus. This, in the horoscope, says Maternus, makes a driver of horses, a groom, a keeper, or even a tamer; and if Mars shines upon it with a favorable ray, it will make one to serve in war among the strongest horsemen. But if it is found in setting, and malignant stars have shone upon this place, the native, or one cast out from somewhere else, will die, or perish struck by the kick of a beast of burden or of a horse, or thrown by some horse; or, overturned in the wagon, he will be torn miserably by the rushing waters. Thus he. In longitude it is under the sign of Libra. CENTILOQUIUM is called, by way of eminence, among astronomers, a notable treatise comprising one hundred sentences reduced to brief aphorisms, and easily attributed to Ptolemy, prince of astrologers; and it is also designated as the fruit of his books, that is, of the Quadripartitum and the Almagest. But there is great controversy among astronomers whether it is truly Ptolemy’s work, or rather that of Hermes Trismegistus, whose other Century of Aphorisms is circulated. Hali Heben Rodoam, Ptolemy’s commentator in his commentary on the Quadripartitum, affirms that it is not Ptolemy’s, but Hermes’s. Yet, having undertaken a commentary on the Centiloquium, whether from a desire to magnify the work he was explaining, or from having acquired greater knowledge of the truth, he declared it to be a genuine work of Ptolemy. Secondly, Hieronymus Cardanus, after considering the matter carefully and comparing statement with statement, found that there is no unity of doctrine in them. And finally Argolus and other most learned men of our time hold it for certain that it is not a work of Ptolemy, but of the said G ij

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toe LEXICON Hermetis, aliàs Trutinæ ad indagandum verum conceptionis tempus inuentoris, quam postea in Centiloquio aphor. 51. expressam, & confirmatam videmus in hæc verba. In quo signo Luna est Gensura tempore, illud fac Ascendens, in conceptu; & in quo signo inuenta fuerit in conceptu, illud aut eius oppositum fac Ascendens in partu. Ex quo liquet vt tantum absit, quod hic fructus librorum Ptolemæi sit, vt is ne verbo quidem id explicet siue in Quadripartito, vbi de rectificatione Genituræ < 54.> agit, siue in alio librorum suorum loco. Vtcumque se res habeat, certum est, dictum Centiloquium magnæ esse auctoritatis, magnique nominis, idque siue à Ptolemæo ipso à suis operibus excerptum sit, siue à quous alio Ptolemæi gloriam affectante, cæteris omnibus id genus operibus antecellere. Quod etiam Angelicus Doctor 3. contra Gentes cap. 84. suo testimonio confirmauit. Sic enim ait: Verum est, quod Ptolemaus in Centiloquio dicit; Cum fuerit Mercurius in natiustate alicuius in aliqua domorum Satu mi, & ipse fortis in esse suo, dat bonitatem intelligentia fundiùs in rebus. Et hæc obier dicta sint de Auctore, & auctoritate Centiloquij, quod nos D. Thomam sequuti semper sub Ptolemæi nomine citabimus. < 55.> CENTRVM Græcè, Latinè punctum significat in medio sphæræ vel Circuli collocatum, ad quod ductæ lineæ à superficie, aut peripheria, omnes inueniantur æquales. Differt autem à puncto præcisè sumpto, quia hoc definitur ab Euclide cuius pars nulla est, ac præscindit ab eo, quod sit principium figuræ mediatum, vel non; Centrum autem semper appellat cujusuis rei medium, quod concipiatur indivisibile, licet subinde punctum ferè semper pro centro accipiatur, ac pro centro nil aliud veniat, quàm punctum in medio sphæræ aut circuli constitutum. Hinc terra in Mundi meditullio collocata, atque ad cælorum immensitatem relara, instar puncti cum sit, Mundi centrum vocatur. Vnde Cicero 1. Tusculan. Persuadens, inquit, Mathematico terram in medio Mundi situm ad vniversi Cals complexum quasi puncto instar obserere, quod Centrum alij vocant. Porrò quandocumque Mathematici stellarum motus, situs, distantias, apparentias, aliaque id genus supputare volunt, semper id à centro stellæ ad centrum alterius corporis aggrediuntur: sicque veras lumina-rium defectiones, quas, & Eclipses vocant, à centris lumina-rium computant, ac rationem habent vtriusque semidia-metri, nec non telluris, ad cuius centrum, non ad superficiem rectè ciacularus à sidere radius terminatur. Hinc patallaxes, hinc differentia illa veri motus, & apparentis: de quibus om-nibus suo loco.

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to the LEXICON Hermes, otherwise called the Balance, for investigating the true time of conception of the inventor, which we later see expressed and confirmed in the Centiloquium, aphorism 51, in these words. In which sign the Moon is at the time, make that the Ascendant in conception; and in which sign she is found in conception, make that or its opposite the Ascendant in birth. From this it is clear how far this is from being a product of the books of Ptolemy, since he does not explain it even by a word, whether in the Quadripartitum, where he treats of the rectification of a nativity, <54.> or in any other place in his books. However the matter may stand, it is certain that the said Centiloquium is of great authority and of great name, whether it was excerpted from Ptolemy himself from his works, or by some other person seeking the glory of Ptolemy; it surpasses all other works of that kind. This also the Angelic Doctor confirmed by his testimony in 3 Contra Gentiles, chapter 84. For thus he says: It is true, as Ptolemy says in the Centiloquium: When Mercury shall be in the nativity of someone in some house of Saturn, and he himself strong in his own being, he gives goodness of intelligence more deeply in things. And these words having been set forth, let this be said concerning the author and authority of the Centiloquium, which we, following St. Thomas, shall always cite under the name of Ptolemy. <55.> CENTRUM in Greek, in Latin punctum, signifies a point placed in the middle of a sphere or circle, to which lines drawn from the surface or periphery are all found equal. It differs, however, from a point taken precisely, because this is defined by Euclid as having no part, and it excludes whether it is the principle of a figure, mediate or not; but center always calls the middle of any thing, which is conceived as indivisible, although afterward the point is almost always taken for the center, and by center nothing else is meant than a point established in the middle of a sphere or circle. Hence the earth, placed in the middle of the world, and compared with the immensity of the heavens, since it is like a point, is called the center of the world. Whence Cicero, in the 1st Tusculan Disputation, says, persuading the mathematician to regard the earth as situated in the middle of the world, enclosed by the whole embrace of the universe, as it were like a point, which others call the center. Moreover, whenever mathematicians wish to calculate the motions, positions, distances, appearances, and other matters of that kind of the stars, they always proceed from the center of one star to the center of another body; and thus they compute the true eclipses of the luminaries, which they also call eclipses, from the centers of the luminaries, and take account of both semi-diameters, as well as that of the earth, to whose center, and not to the surface, the ray cast from the star is rightly terminated. Hence parallax, hence that difference between true motion and apparent motion, of all which in their proper place.

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MATHEMATICVM. 101 CENTRA domorum apud Astronomos dicuntur cuspides, 66. seu lineæ diuidentes domos à domibus, estque præcisè gradus ille Zodiaci qui in dictam lineam diuisionis incidit; cùm aliàs domus rotum illud spatium, quod inter vtramque lineam in- terponitur appelletur. Vide in V. Cuspis. CEPHEVS dictus eriam Ceginus, lasides, host est dominus 67. Solis, Arabicè ex Græco vocabulo corrupro Keiphus: sidus in cælo ad borealem plagam propè Andromedam, continens stellas vndecim cum duabus informibus, sed apud Baierum 17. omnes de natura louis, & Saturni, inter quas, tres luci- diores testatur Kircherus in Oedipo vocari Arabicè Kaar, Keds, & San, hoc est Pastorem, Canem, & Ouem; quæ autem est in sinistro humero vocatur Aderaimin: De hoc si- dere horoscopante, sic cecinit Pontanus in sua Vrania. Regales illum vestes, rutilantisq; auro Scepta de ent R gem, ac gentis imperitasse subacta: Inde venit nato frontis sua uga feuera, Et dura imperia, & vultu mens aspera duro, Et post pauca Nec fiet mores............ Forsitan & populi mores describet, & artes Liberiore, oco ludem, risumque mouebit Personam simulans, teget & sub melle venenum Spiculaque in salibus tinget der. sor amaris. De eo autem in occasu reperto, sic ludit. Occumbens satum, in scopulis crudele minatur, Aut primo saus nascentem extinguit in ortu, Aut vnco in castum trahit, atque euiscerat artus. CERATIAS ex Græco dicitur genus quoddam Cometæ, quod 68. cornu speciem repræseniare videtur; Cornu enim Græcè rò dicitur. Eiusmodi fuit qui apparuit anno 1618. quem posteà tot mala subsequuta sunt. De eo Plinius lib. 3. cap. 35. CERADOS Græcè, teste Hali super Ptolemæi quadrup. sunt 69. signa infirmantia, seu mutilata, quæ enumerar, Arierem, videlicet, Taurum, Cancrum, Scorpium, & Capricornum: sed ego potiùs crediderim voluisse dicere Corniculata: Conso- nar & Græcum etymon. CERV, sidus in cælo ad Australem plagam, in longitudine 70. implectens signum Arietis, & medium Tauri. Habet apud Ptolemæum stellas 22. apud Keplerum 21. & apud Baier. 27. quarum præcipuæ tres, vna in naribus dicta mandibula Ceti, Arab Menchar altera in cauda lucidior, & australior dicta Demeb, terria in ventre, quam Batem appellant, omnes de natura Saturni. Hoc sidus in horoscopo alicuius inuenium, inquit Firmicus, facit, piscationi addictum, sed maiorum G ii)

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MATHEMATICVM. 101 CENTRA of houses among astronomers are called cusps, 66. or the lines dividing houses from houses, and it is precisely that degree of the Zodiac which falls upon the said line of division; whereas otherwise the house is called that whole space which is placed between the two lines. See under V. Cuspis. CEPHEVS, also called Ceginus, Iasides, that is, lord 67. of the Sun, in Arabic from the corrupted Greek word Keiphus: a star in the sky toward the northern region near Andromeda, containing eleven stars with two formless ones, but according to Bayer 17, all of them of the nature of Jupiter and Saturn; among these, Kircher testifies in Oedipus that three brighter ones are called in Arabic Kaar, Keds, and San, that is, Shepherd, Dog, and Sheep; the one which is in the left shoulder is called Aderaimin: Of this star in the horoscope, Pontanus thus sang in his Urania. Royal garments upon him, and a scepter gleaming with gold the kingdom, and that he had ruled a subdued people: Then from the birth came the fire of his brow, and harsh commands, and a mind with stern face, harsh, and after a few lines: He will also describe the character of peoples and the arts, with freer amusement, he will move laughter and sport, while feigning a person, and he will hide poison under honey, and he will dip his darts in playful jests of bitter words. But about him, found in the setting, he thus plays. As he sets, he cruelly threatens from the rocks, or at first extinguishes the newborn in its rise, or with a hook drags and disembowels the limbs. CERATIAS is said in Greek of a certain kind of Comet, which 68. seems to represent the shape of a horn; for horn in Greek is called ro. Such was the one that appeared in the year 1618. many evils afterward followed. Of it Pliny, book 3, chapter 35. CERADOS in Greek, as Hali testifies in Ptolemy’s quadrupeds, are 69. the weakened, or mutilated, signs, which he enumerates: Aries, namely Taurus, Cancer, Scorpio, and Capricorn; but I would rather believe that he meant to say horned ones: the Greek etymon agrees as well. CERV, a star in the sky toward the southern region, in longitude 70. extending through the sign of Aries and the middle of Taurus. It has, according to Ptolemy, 22 stars; according to Kepler, 21; and according to Bayer, 27, of which the principal three, one in the nostrils called the jawbone of the Whale, Arabic Menchar; another on the tail, brighter and more southern, called Demeb; the third in the belly, which they call Batem, all of the nature of Saturn. This star, found in someone’s horoscope, says Firmicus, makes him addicted to fishing, but of the greater

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LEXICON piscium, aut sanè ijs mercandis, ac sale, alijsque liquamini- bus, vt fieri assolet, condendis, ac vendendis. In occasu verò periculum facit, quo natantes, vel in fluvio, vel in mari à Cracodilis, vel alijs huiusmodi bestiis lacerentur. CH 71. CHAKITIEHI Græcè dicitur in cælesti figura sexta domus ab horoscopo cadens, ab angulo imi cæli, hoc est mala for- suna: eò quod est significatrix malorum, atque infumita- tum, & nullam cum horoscopo societatem haber. Ascribitur ei color niger, ex membris humanis venter cum intestinis. Consignificatorem habet Mercurium, & gaudet in ea Mars, qui inibi repertus, experientia teste, Medicinæ studijs facit intentum. 72. CHAMALSON sidus in cælo ad polum Antarcticum nobis innisum constans stellis nouem infimæ conditionis, à nouis Astronomis detectum atque alijs imaginibus recens adjun- ctum. Eius caput incidit in colurum æquinoctiorum. Totum verò sidus est in longitudine sub signis Scorpij, & Sagittarij, ac ferunt esse directè oppositum Vræ minori. 73. CHASMA, teste Plinio, lib. 3. cap 26. est Cæli quidam hiatus statis temporibus apparens, qualis est, quem nunc satis conspicuè videmus in pectore Cigni, in loco vbi noua stel- la apparuit anno 1600. ac tandem post aliquot menses eua- nuit. Hunc idem Plinius falco in genere Cometarum col- locat. 74. CHELA sunt Scorpionum, & Cancrorum brachia, quæ postea ab Astronomis acceptæ sunt ad significandas chelas Scorpij sideris, seu versùs Lances australem, & borealem: (quandoquidem antiqui vt in loco dicemus pro vno tantùm sidere computabant & Libram, & Scorpium, & insuper istæ dux stellæ modo in longitudine sunt in Scorpionis signo) vtraque autem est secundæ magnitudiuis de natura Martis, & Saturni, quarum prior nempe lanx australis est vna ex stel- lis regijs; & ideò in horoscopo reperta, aut cum luminaribus, præsertim si bono beneficium radio fulciatur, ad magna euehit, atque honores, & diuitias pollicetur. 75. CHELISERIAM dicta est ab aliquibus Lyra, Fidicula, Vul- tur cadens sidus ad borealem plagam: de quo fusè in suo loco. 76. CHELEVB, seu Chelub. Arab. dicitur Perseus, Inachides & Cyllenius: de quo vide suo loco. CHELIDONIVS ventus est anniuersarius spirans verno tem-

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LEXICON of fish, or rather for trading in them, and in salt and other liquors, as is usually done, for preserving and selling them. But in the west it signifies danger, whereby those swimming, either in a river or in the sea, may be torn by crocodiles or other such beasts. CH 71. CHAKITIEHI is called in Greek, in the celestial figure, the sixth house falling from the horoscope, from the angle of the lower heaven, that is, bad fortune: because it is a significator of evils and of things not to be spoken of, and has no partnership with the horoscope. Black is assigned to it as its color, and from the human members, the belly with the intestines. It has Mercury as a co-significator, and Mars rejoices in it, who, when found therein, experience testifies, makes one intent on the studies of Medicine. 72. CHAMALSON is a star in the sky near the Antarctic pole, resting upon us, consisting of nine stars of the lowest condition, discovered by the new Astronomers and recently added to other figures. Its head falls on the equinoctial colure. The whole star lies in longitude under the signs of Scorpio and Sagittarius, and they say it is directly opposite Ursa Minor. 73. CHASMA, according to Pliny, book 3, chapter 26, is a certain opening in the sky appearing at fixed times, such as that which we now clearly see in the breast of Cygnus, in the place where a new star appeared in the year 1600 and at length vanished after some months. The same Pliny places this among the kind of comets called falcon. 74. CHELA are the arms of the Scorpion and of Cancer, which were afterward adopted by astronomers to signify the claws of the star of Scorpio, or toward the southern and northern scales: (for the ancients, as we shall say in its place, counted both Libra and Scorpio as only one star, and moreover these two stars are now in longitude in the sign of Scorpio) but each is of the second magnitude, of the nature of Mars and Saturn, of which the former, namely the southern scale, is one of the royal stars; and therefore, if found in the horoscope, or with the luminaries, especially if supported by a favorable benefic ray, it lifts one to great things, and promises honors and riches. 75. CHELESIERIA was called by some Lyra, Fidicula, and Vultur cadens, a star toward the northern quarter: of which more fully in its place. 76. CHELEVB, or Chelub. In Arabic, Perseus is so called, Inachides and Cyllenius: see of this in its place. CHELIDONIUS is a yearly wind blowing in the spring time

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MATHEMATICVM. 101 pore ab exortu vespertino Arcturi, omnium ventorum minissimus, ac suauissimus, qui postea conueritur in Fauonium, nomen hausit ab aduentu hyrundinum, quæ eò potissimum tempore ad nos adueniunt: quamobrem & dictus est. CHENEN, in sphæra barbarica dicitur tertius decanus, Sagittarij manus sub dominatu Saturni, obstinationis in proposito, contradictionis, dexteritatis in malo Rixarum, & factorum abominabilium. CHIRON, Centaurus, Typhon, fidus in exlo ad australem plagam, de quo non multo antè dictum est in Verbo Centaurus. Ab aliquibus etiam accipitur de Sagittarij signo, vno ex duobus Zodiaci, cuius in loco mentio erit. CHORDA apud Geometras est linea recta arcui subtensa, quæ diuidat circulum in duas partes inæquales, sicque per centrum minimè transeat (in quo differt à diametro) sed vel supra, vel infra sit, relinquens in circulo æquabilia spatia, seu portiones ipsius, quarum maior sit quæ centrum complectitur, minor verò quæ comprehenditur sub ipsa chorda. Nomen sortita est à similiudine quam habet ad chordam arcui venatorio subiensam, vnde Sagitta per arcum ejaculatur. Porrò dimidium chordæ sinus rectus appellatur, & semilles rectarum, prout in loco dicemus. Huius ope, ac tabularum sinuum tangentium, & secantium tota triangulorum doctrina resoluitur: per eam enim venamur quantitatem arcus, cui subtenditur, atque alterius ad alteram proportionem. Vide fusiùs in V. Simùs. CHOREYTE, teste Hygino, appellantur à Græcis duæ stellæ Vrsæ minoris, quæ polari æquales in magnitudine, ac splendore, eam circumdant, & circumdantes, choceas veluti ducere, eique gestire, ac subfamulati videntur. CHOROGRAPHIA pais est Geographiæ, quæ particularium tanrum prouinciarum, aut regnorum descriptionem tradit, cum tamen Geographia sit vniuersalis descriptio totius terræ habitabilis. CHRISEVS COMETES. Vide Rosa. CHRONICVS idem sonat ac Temporalis, quid importet. Vide in V. Achronicus. CRONOCRATOR Græcè, Latinè interpretatur temporis dominus. Apud Astronomos Chronocratores dicuntur planeæ, qui fuerint temporum dispositores. Rhodiginus Chronocratorem appellat luminare temporis, vt Solem de die, Lunam de nocte. Aben Ragel, alijque Astrologi diuidunt ætatem hominis in septem partes pro singulis eius statibus, ac singu- G iii

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MATHEMATICVM. 101 before sunrise from the rising of Arcturus, the least of all the winds, and the sweetest, which afterward turns into the Zephyr, took its name from the arrival of swallows, which especially at that time come to us: wherefore it is so called. CHENEN, in the barbaric sphere, is said to be the third decan, the hand of Sagittarius, under the dominion of Saturn, of obstinacy in purpose, contradiction, skill in evil, quarrels, and abominable deeds. CHIRON, Centaur, Typhon, fixed in the sky toward the southern quarter, of which not long before mention was made under the word Centaurus. By some it is also taken for the sign of Sagittarius, one of the two of the Zodiac, of which place mention will be made. CHORDA among geometers is a straight line subtending an arc, which divides a circle into two unequal parts, and thus does not pass through the center at all (in which it differs from the diameter), but is either above or below it, leaving in the circle equal spaces, or portions of it, of which the greater is that which contains the center, the lesser however that which is contained under the chord itself. It took its name from the similarity which it has to the string stretched under a hunting bow, from which the arrow is shot through the arc. Moreover, half of the chord is called the right sine, and the sines of lines, as we shall say in its place. By its aid, and that of tables of sines, tangents, and secants, the whole doctrine of triangles is resolved: for by it we hunt out the quantity of the arc, to which it is subtended, and the proportion of one to another. See more fully under V. Simùs. CHOREYTE, according to Hyginus, are called by the Greeks two stars of the Lesser Bear, which, equal to the polar one in magnitude and brightness, surround it, and, while surrounding it, seem as though to lead it about, to rejoice over it, and to be in service to it. CHOROGRAPHIA is a part of Geography, which gives the description of particular provinces or kingdoms only, whereas Geography is the universal description of the whole inhabited earth. CHRISEVS COMETES. See Rosa. CHRONICVS means the same as Temporal, what it imports. See under V. Achronicus. CRONOCRATOR in Greek, in Latin it is interpreted lord of time. Among astronomers Chronocrators are called the planets, which have been the regulators of times. Rhodiginus calls the luminaires chronocrators of time, as the Sun by day, the Moon by night. Aben Ragel, and other astrologers, divide the age of man into seven parts according to each of his states, and singu- G iii

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104 LEXICON gulis planetis per ordinem attribuunt: sicque infantiam, quæ amplectitur quatuor priinos ætatis annos tribuunt Lunæ: pueritiam ab quarto vsque ad quartum decimum annum, Mercurio: Adolescentiam à quarto decimo vsque ad vigesimum secundum, Veneri: Iuuentutem à vigesimo secundo vsque ad quadragesimum primum, Soli: Virilitatem à quadragesimo primo vsque ad quinquagesimum sextum, Marti: Senectutem à quinquagesimo sexto vsque ad sexagesimum octauum, Iouis: Decripitatem à sexagesimo octauo vsque ad nonagesimum octauum saturno: Denique reliquum tempus à nonagesimo octauo vsque ad centesimum secundum annum, quod est genus quoddam Infantiæ, itetum Lunæ. Horumque annorum dispositores vocant Græci Ghtonocratores. De qua re abundè <86.> satis discurrit Ptolemæus in Qadrip. cap. ultimo. Alij item ex Ptolemæi mente temporum arbitros, vt plurimum esse dicunt duos planetas, quorum vns principalis est qui vel corpore vel radio proximè occurrit Aphetæ, & cuius dominium tandiu durat, quandiu significator ad alium promissorem pertingat. Alter verò sit minus principalis, & particeps domini, qui sit dominus termini constitutus in eodem circulo positionis significatoris. Sic enim subdit Ptolemæus, loco citato. Primum quidem danda sunt tempora cujuslibet prorogatoris illis planetæ, qui tenet gradum loci Aphetici, aut alteri illum aspiciensi. Si autem deest, demus es planeta, qui proximè antecessit, donec peruensamus ad alium, qui applicatur ad sequentem gradum, juxta ordinem signorum Deinde huic tribuemus tempora vsque ad sequentem, & in cæteris similiter: & simul assumantur planetæ, vt sint dispositores, qui sunt in suis finibus. Hucusque Ptolemæus tradens aliam inueniendorum Chronocratorum rationem. Et hi quidem generales dicuutur. Cæterum particulares Chronocratores vide in Verbo dominus temporis. CI <87.> CINGVLVS Orionis. Vide in V. Baltheso: item in lugula. <88.> CIGNVS. Vide in V. Cygnus. <89.> CIRCVS ventus lateralis Septentrioni ad occasum, oppositus directè Phæniciæ, seu Euro Astro, sic dictus ob sui violentiam qua obliquè cum turbine, ac vertigine spirans, omnia turbar, & circumuertit: Alij Cercium vocant, alij Thraciscum quia per Thraciam exsufflando transit. Frigidus est, & siccus, ventorum gyros, & niuum congelationes facit, & grandines: vnde etiam est maximè procellosus, impetu vehementi

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104 LEXICON they assign to the planets in order: thus infancy, which embraces the first four years of age, they attribute to the Moon: boyhood from the fourth to the fourteenth year, to Mercury: adolescence from the fourteenth to the twenty-second, to Venus: youth from the twenty-second to the forty-first, to the Sun: manhood from the forty-first to the fifty-sixth, to Mars: old age from the fifty-sixth to the sixty-eighth, to Jupiter: decrepitude from the sixty-eighth to the ninety-eighth, to Saturn: finally, the remaining time from the ninety-eighth to the one-hundred-and-second year, which is a certain kind of infancy, again to the Moon. And the arrangers of these years the Greeks call Ghtonocrators. On this matter Ptolemy discourses at sufficient length in the Quadrip. last chapter. Others likewise, from Ptolemy’s view, say that the arbiters of times are, for the most part, two planets, of which the principal one is the one that either by body or by ray comes nearest to the Apheta, and whose dominion lasts as long as the significator reaches another promissor. The other, however, is less principal and a sharer in the dominion, and is the lord of the term established in the same circle of the significator’s position. For thus Ptolemy adds, in the cited place. First indeed the times must be given to whichever planet holds the degree of the Aphetic place, or to another looking upon it. But if it is lacking, let us give them to the planet that came just before, until we arrive at another that is applying to the following degree, according to the order of the signs. Then to this one we shall assign the times up to the next, and similarly in the rest; and at the same time let the planets be taken as disposers, which are in their own bounds. Thus far Ptolemy, transmitting another method of finding Chronocrators. And these indeed are called general. But see the particular Chronocrators under the word lord of time. CI 87. CINGULUS of Orion. See under V. Baltheso: also under Iugula. 88. CYGNUS. See under V. Cygnus. 89. CIRCIUS, a lateral wind from the north toward the west, directly opposite Phoenicias, or Euro-Astrus, so called because of its violence, by which, blowing obliquely with a whirlwind and a whirling motion, it disturbs and overturns everything. Others call it Cercius, others Thraciscus, because it blows through Thrace. It is cold and dry; it produces the whirlings of winds and the freezing of snow, and hail; whence also it is especially stormy, with a violent blast

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MATHEMATICVM. 103 tissimo ruens. Eo potissimum infestatur Gallia Narbonensis, vt auctor est Gellius, & in Italia v[er]bs nomine Beneuentum olim ab ipso Maleuentum dicta, vt explicar Procopius lib. 1. sic inquiens Quondam Prisci Maleuentum dixere: id namque 90. Oppidum, Dalmatia ex aduerso oppositum est, in continentione situm in quod spiritus violentior quidam, & acerbs simus (Circus nempe ventus) ingruere consueust: quis vstque vbi flare caperet, non feris iter agere, sed domi se quisque conservare laborat. Nem vento huius est violentia, vt vel equissem cum equo simul arreptum sublimem mox deferat, dixque per aerem circumactum, & quocumque tulerit c[on]sus projectum interimat: vnde & Maleuentum, & in edito positum ex eo vento toleratu difficili fortitum est nomen. Hueusque Procopius de ea vrbe, quæ postea boni ominis ergo Beneuentum appellari exp[er]it. CIRCITORES & Vigiles dictæ sunt duæ stellæ secundæ magnitudinis in V[er]sæ minoris corpore extremæ, quæ polarem circumstant, & quasi custodes ambiunt, vnde a Græcis, vt habet Hyginus Choreata etiam appellatæ sunt, quasi choreas circâ eam ducentes. CIRCULVS, & Circus à Mathematicis sic definitur. Est figura 92. plana, unà tantùm lineâ contenta, in cuius medio punctus sit, à quo omnes lineæ ad circumferentiam ducta aqua es sint. Differt à sphæra, quæ non est figura plana, sed perfectè rotunda, neque vnica linea terminatur, & circumscribitur, sed lata quædam superficie vndequaque concluditur. Differt etiam ab Ellipsi, quæ, quamuis figura plana sit, vnaque linea circumscribitur (in quo conuenit cum circulo) quia tamen in ea non datur punctum, à quo duci possint æquales lineæ ad ipsam circumferentiam, seu linearu terminantem, ideò circulus dici non porest, neque orbicularem formam retinet, sed oualem. CIRCULVS rectus in sphæra dicitur Meridianus, v[er]nus ex sex 93. circulis majoribus, ad differentiam horizontis, qui (præterquam in sphæra recta, & sub æquatore) semper est obliquus atque obliquè ex ea emergunt sidera; cum alias ad Meridianum, vbiuis locorum semper ascendant rectè. Complectitur autem hic circulus in cælesti figura decimam, & quartam domum: quæ proinde constituuntur per ascensiones rectas: atque hic circulus consideratur immobilis in situ Mundi. CIRCULVS rectus etiam dicitur æquator æquè distans à polismundi, 94. hoc est grad. 90. hinc inde, atque adeò in medio sphætæ collocatus: de quo plura diximus suo loco, sicut è contià. CIRCULVS obliquus appellatur Zodiacus ad differentiam circ. 95.

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MATHEMATICVM. 103 tumbling down with the greatest force. For this reason Gallia Narbonensis is especially exposed to it, as Gellius relates; and in Italy the city now called Beneventum, formerly named Maleventum by that very wind, as Procopius explains in book 1. Thus he says: “Once the Prisci called it Maleventum: for that town, opposite Dalmatia, is situated on a plain, into which some very violent and exceedingly sharp wind is accustomed to burst forth (namely the Circius wind); and as often as it begins to blow there, men do not make a journey on foot, but each labors to remain at home. Such is the violence of this wind that it will even seize a rider together with his horse, lift him aloft at once, whirl him about through the air, and cast him wherever it carries him, destroying him as he is thrown down. Hence the name Maleventum, and for a city set on high, hard to endure because of that wind, the name was given.” So far Procopius concerning that city, which afterward, for the sake of a good omen, came to be called Beneventum. CIRCITORES and Vigiles were the names given to two stars of the second magnitude at the ends of the body of Ursa Minor, which surround the pole and, as it were, guard it; whence among the Greeks, as Hyginus has it, they were also called Choreata, as though conducting dances around it. CIRCULUS, and Circus, is defined by mathematicians thus. It is a plane figure contained by a single line, in the middle of which there is a point from which all lines drawn to the circumference are equal. It differs from a sphere, which is not a plane figure but perfectly round, and is not bounded and described by a single line, but enclosed on every side by a certain broad surface. It differs also from an ellipse, which, although it is a plane figure and is bounded by one line (in which respect it agrees with the circle), nevertheless does not have within it a point from which equal lines can be drawn to the circumference, or boundary line; therefore it cannot be called a circle, nor does it retain a circular form, but an oval one. CIRCULUS rectus in the sphere is called the Meridian, one of the six greater circles, in distinction from the horizon, which (except in a right sphere and under the equator) is always oblique, and the stars rise obliquely from it; whereas to the Meridian, in whatever place, they always rise directly. This circle includes in the celestial figure the tenth and fourth houses, which are therefore determined by right ascensions; and this circle is considered fixed in the position of the world. CIRCULUS rectus is also called the equator, equally distant from the poles of the world, that is, 90 degrees on either side, and thus placed in the middle of the sphere; of which we have said more in its proper place, as well as the contrary. CIRCULUS obliquus is called the Zodiac, in distinction from circ. 95.

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106 LEXICON culi recti, cùm is semper obliquè ascendat, tam in sphæra recta quàm in obliqua, cùm alias æquator in sphæra recta, æqualiter semper ascendat, & in obliqua, si non rectè saltem æqualiter, & Zodiaco rectiùs. 96. CIRCULI altitudinum vocantur circuli paralleli ad horizontem vsque ad summum verticem, eò quia eorum ope venamur altitudines siderum, & elevationem suprà horizontem. Arabicè dicuntur Almscantharath: vide quæ sub hoc vocabulo fusè diximus. 97. CIRCULI horarij sunt circuli ducti per polos mundi, ac partes oppositas horizontis, quibus venamur quantitatem diei ac noctis, horas planetarias, arcus semidiurnos, ac seminocturnos planetarum, atque elevationem policuiuscumque sideris ad mentem Ptolemæi ad verum circulum positionis habendum. 98. CIRCULI positionum sunt circuli transeuntes per communes intersectiones horizontis, & Meridiani, atque per centrum stellæ, quibus potissimum vtuntur Rationales ad eius situm in mundo venandum, ad quos reducuntur etiam circula domorum. 99. CIRCULI verticales sunt circuli transeuntes per verticem alicuius loci, sese ibi mutuò intersecantes, ac tandem ad oppositas horizontis partes terminantes, quibus iuquirimus locorum longitudines, ac distantiam siderum à quacumque horizontis parte, nec non ab inuicem per latum. Arabicè Azimutha: de quibus suo loco dictum. 100. CIRCUMFERENTIA. Vide Peripheria. 101. CIRCVMVALLATIO, teste Valla, idem valet apud Astronomos, ac Obsessio; estque cum planeta medius inter duos, ita circumdatur, ac vallo quasi obsiderur, vt vim suam exerere minimè valeat, neque aliorum aspectus recipere. Hæc obsessio ab infortunis alicui benefico, aut promiscuæ naturæ intentata, pessimæ est: à beneficis verò erga maleficum optima: quippe quæ ita eius vires debilitat, vt nil ferè operari valeat planeta obsessus, sed tota eius actiuitas ab illis absumatur, aut sanè labefactatur. 102. CIRNECIR apud Hermetem in lib. de judicijs & significationibus stellarum Beibeniarum, audit stella fixa lucida lancis borealis, secundæ magnirudinis de natura Louis, & Mercurij, existens nunc temporis in grad. 15 Scorpij cum tot ferè grad. latitudinis borealis. Hæc in horoscopo (inquit idem Hermes) facit fortunatum Regem, amatorem aliaris Dei, malorum persecutorem, magni nominis apud exteros, ac poësis cultorem.

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106 LEXICON The circles of ascension are called circles parallel to the horizon up to the highest vertex, because by their aid we observe the altitudes of the stars and their elevation above the horizon. In Arabic they are called Almscantharath: see what we have said at length under that word. 97. The hour circles are circles drawn through the poles of the world and the opposite parts of the horizon, by which we observe the length of day and night, the planetary hours, the semidiurnal and seminocturnal arcs of the planets, and the elevation of any star according to Ptolemy's view, if it is to be taken as the true circle of position. 98. The circles of position are circles passing through the common intersections of the horizon and the meridian, and through the center of the star, which the Rationalists chiefly use to observe its place in the world; to these are also referred the circles of houses. 99. Vertical circles are circles passing through the zenith of some place, mutually intersecting there, and finally ending at the opposite parts of the horizon, by which we inquire into the longitudes of places and the distance of stars from any part of the horizon, as well as from one another at large. In Arabic, Azimutha: concerning which something has been said in its proper place. 100. CIRCUMFERENCE. See Peripheria. 101. CIRCVMVALLATIO, according to Valla, has the same meaning among astronomers as Obsessio; and it is when a planet, placed between two others, is so surrounded and, as it were, besieged by a wall that it can scarcely exercise its force, nor receive the aspect of the others. This siege, when inflicted by infortunes upon some benefic or one of mixed nature, is the worst; but from benefics against a malefic it is the best: for it so weakens its powers that the besieged planet can do almost nothing, but all its activity is consumed by them, or indeed is much impaired. 102. CIRNECIR, in Hermes's book on the judgments and significations of the fixed stars called Beibeniæ, is the name of a bright fixed star in the northern scale, of the second magnitude, of the nature of Jupiter and Mercury, now situated in the 15th degree of Scorpio with almost so many degrees of northern latitude. In the horoscope, says the same Hermes, it makes a fortunate king, a lover of the altar of God, a persecutor of evils, of great renown among foreigners, and a cultivator of poetry.

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MATHEMATICVM. 107 CL CLIMA Græcè, Latinè audit spatium siue in cælo, siue in 103. terra contentum inter duos parallelos, quod quia semper minor, ac minor concipi potest, ideò & plura Climata in infinitum. Nihilominus tamen nunc tempotis accipitur pro tanto terræ, aut cæli, cui terra subest, spatio, per quantum sensibiliter variari potest ortus, & occasus signorum, nec non diesum, ac noctium artificialium quantitas, & longitudo. Differentia igitur semihoræ, qua augeatur maximi diei artificialis, aut maximæ noctis quantitas, visa est veteribus condigna portio, ac sensibilis assignanda cuilibet Climatis Et quoniam non omnem tertam habitabilem existimabant, sed solùm sub Zonis temperatis, quæ sunt inter tropicos, & circulum seu Arcticum, seu Antartcticum (partes enim æquatori vicinas propter nimium calorem, & quæ sub circulis Arctico, & Antartico continentur, ob nimium frigus inhabitabiles ctedidetunt) ideò vniuersam Zonam temperatam, quæ est ad botealem plagam in septem climata diuisetunt incipiendo à primo parallelo versus æquatorem, seu Tropico Cancri, vbi maximus dies est horarum 15. vsque ad circulum Arcticum, singulis sua nomina, à celebri aliquo loco, quem pettansit parallelus, qui per medium climatis describitur, tribuentes. Sed quoniam Recensiores, expetientia duce, comprobauere, totam ferè terræ molem habitabilem esse, & adhuc, si vlla pars inhabitabilis poter, satis esset ad rationem climatum, vt maximorum dierum quantitas augeatur, ant minuarur; ideò rem meliùs auspicati, ac Ptolemæum sequuti, describunt in superficie terræ circulos parallelos ab æquatore versus Polum, tanta inter se distantia, quanta requiritur, vt vniuscuiusque maximus dies differat horæ quadrante ab die maximo alterius parallelis ita vt vnumquodque clima tribus parallelis definiatur. Atque hac ratione constituunt viginti t[em]pia climata, hinc citra æquatorem ad Polum boreum (totidem consequenter trans illum ad Austrum) atque intra quadrangintanouem parallelos includunt, singulis parallelis horæ, vt dictum est, quadrantem assignantes. Primùm clima includit Insulam Taprobanam, & sinus 104. Aualicum, & Aduliticum, ac definitut tertio parallelo ab æquatote, vbi Polus attollitur gr. 8. min 34. ac maximus dies artificialis est hor. 12. min. 30. latitudo eius est grad. 8. min. 34.

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MATHEMATICVM. 107 CL CLIMATE, in Greek and in Latin, signifies a space either in the heavens or on earth contained between two parallels, which, because it can always be conceived smaller and smaller, therefore there are also more and more climates without end. Nevertheless, nowadays it is taken to mean so much of the earth, or of the sky under which the earth lies, as the rising and setting of the signs, and likewise the quantity and length of artificial days and nights, can sensibly vary. Therefore the difference of a half-hour, by which the quantity of the longest artificial day, or of the longest night, is increased, seemed to the ancients a suitable and perceptible portion to be assigned to each climate. And since they considered not all the earth habitable, but only that under the temperate zones, which are between the tropics and the circle, either Arctic or Antarctic (for the regions near the equator, because of the excessive heat, and those contained under the Arctic and Antarctic circles, because of excessive cold, they judged uninhabitable), therefore they divided the whole temperate zone, which is toward the northern quarter, into seven climates, beginning from the first parallel toward the equator, or Tropic of Cancer, where the longest day is 15 hours, as far as the Arctic circle, assigning to each its own name from some famous place which the parallel, drawn through the middle of the climate, passes. But since the more recent writers, guided by experience, have proved that almost the whole mass of the earth is habitable, and that even if there were any uninhabitable part, it would be enough for the purpose of climates that the quantity of the longest days should increase or diminish; therefore, taking a better course and following Ptolemy, they describe on the surface of the earth circles parallel from the equator toward the pole, at such distance from one another as is required so that the longest day of each may differ by a quarter of an hour from the longest day of another parallel, so that each climate is defined by three parallels. And in this way they establish twenty climates, from here this side of the equator to the boreal pole (and correspondingly as many beyond it toward the south), and include within forty-nine parallels, assigning to each parallel, as has been said, a quarter of an hour. The first climate includes the island of Taprobana, and the Avalic and Adulitic gulfs, and is defined by the third parallel from the equator, where the pole is elevated 8 degrees 34 minutes, and the longest artificial day is 12 hours 30 minutes; its latitude is 8 degrees 34 minutes.

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108. LEXICON 105. Secundùm elima (quod est primum antiquorum) amplectitur quartum, quinrum, & sexrum parallelum; ita tamen vt hic definiat maximum diem hor. 13. min 15. ac loca illi subjecta deprimantur infra polum grad 20. min. 33. eiusque medium transit per Meroen Insulam, à qua, muiuaro nomine, à Græcis Diameros dictum est, sub hoc elimare continenrur Insulæ fortunatæ, pars Arabiæ, Nubi populi, Goa celeberrima Vrbs, arque Indiarum Emportum, Insula sancti Thomæ, & plurimæ aliæ prouinciæ, latitudo eius est grad. 7. min. 50. 106. Tertium elima dictum Diasynoës quia eius principium est ab Synoë, & complectitur Prolemaidam, Ægyptrum, maioremque partem Regni Chinensis, ac terminarut octauo parallelo, vbi altitudo Poli est grad. 27. min. 36. & dies maxima est hor. 13 min. 45 est larum gr. 7. min 3. 107. Quartum elima definitur decimo parallelo, & amplectitur Persidem, & reliquam pattem Ægypti, & quia transit per mediam Alexandriam Dialexandros est appellatum, eius finis habet diem maximam hor. 14. min. 15. Polusque super loca illi subjecta, eleuatur gr. 33. min. 45. amplitudo eius est grad. 6. min. 9. 108. Quintum elima dictum Diarhodos quia transit per Rhodum Insulam, continet Phæniciam Cyprum, Cretam, Smyrnam, & Hellespontum, definiturque duodecimo parallelo, sub quo dies maxima est hor 14. min. 45 & altitudo Poli est gr. 39. minut. 2. hora eius latitudo est grad. 5. min. 17. 109. Sextum elima appellatur Diaromes quia transit per Romam, & sub se habet Bizantiam, Massiliam, Hispaniam, Regnumque Neapolis, est latum gr. 4. min 30. atque extenditur vsq[ue] ad quartumdecimum parallelo, vbi eleuatio Poli est g ad. 43. min. 32. & dies maxima est hor. 15. min. 15. Seprimum elima, quod dicitur Diapontos quia transit per Pontum continet intrà se Venerias, Mediolanum, finitimasque vrbes Vngariam, & Galliæ magnam parrem & clauditur parallelo 16. in latitudine grad. 3 min. 48 sub eleuarione Poli gr. 47. min. 20. vbi maxima dies artificialis est hor. 15. minut. 45. Octauum elima nomine Diaborystenes quia transit per Botystenis ostia amplectitur Podoliam, Germaniam supetiolem, Poloniam, aliasque plures Seprentrionis prouincias; estque larum gr. 3. min. 13. vlrimus eius terminus claudiur parallelo 18. vbi dies maximus est hor. 16. min. 15. sub eleuatione Poli gr. 50. min. 49. 110. Nonum elima incipit à Martide palude (vbi climatum ter-

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108. LEXICON 105. According to the sixth clime (which among the ancients is the first), it includes the fourth, fifth, and sixth parallels; yet so that here it determines the maximum day at 13 hr. 15 min., and the places subject to it are depressed below the pole by 20 deg. 33 min., and its middle passes through the Island of Meroe, from which, by a common name, it was called by the Greeks Diameros; under this clime are contained the Fortunate Islands, part of Arabia, the peoples of Nubia, Goa, the most famous city and emporium of the Indies, the Island of Saint Thomas, and many other provinces; its latitude is 7 deg. 50 min. 106. The third clime, called Diasynoës, because its beginning is from Synoë, includes Prolemaida, Egypt, and the greater part of the Chinese kingdom, and ends at the eighth parallel, where the height of the Pole is 27 deg. 36 min. and the longest day is 13 hr. 45 min.; its breadth is 7 deg. 3 min. 107. The fourth clime is defined by the tenth parallel, and includes Persia and the remaining part of Egypt, and because it passes through the middle of Alexandria it is called Dialexandros; its end has the maximum day of 14 hr. 15 min., and the Pole above the places subject to it is elevated 33 deg. 45 min.; its breadth is 6 deg. 9 min. 108. The fifth clime, called Diarhodos because it passes through the Island of Rhodes, contains Phoenicia, Cyprus, Crete, Smyrna, and the Hellespont, and is defined by the twelfth parallel, under which the maximum day is 14 hr. 45 min. and the height of the Pole is 39 deg. 2 min.; its latitude is 5 deg. 17 min. 109. The sixth clime is called Diaromes because it passes through Rome, and beneath it are Byzantium, Marseilles, Spain, and the Kingdom of Naples; it is 4 deg. 30 min. wide and extends up to the fourteenth parallel, where the elevation of the Pole is 43 deg. 32 min. and the maximum day is 15 hr. 15 min. The seventh clime, which is called Diapontos because it passes through Pontus, contains within it Venice, Milan, and the neighboring cities, Hungary, and a large part of Gaul, and is bounded by the parallel 16, in latitude 3 deg. 48 min., under the elevation of the Pole of 47 deg. 20 min., where the greatest artificial day is 15 hr. 45 min. The eighth clime, by the name Diaborystenes because it passes through the mouths of the Borysthenes, includes Podolia, Upper Germany, Poland, and many other provinces of the North; and it is 3 deg. 13 min. broad. Its last boundary is closed by the eighteenth parallel, where the greatest day is 16 hr. 15 min., under the elevation of the Pole of 50 deg. 49 min. 110. The ninth clime begins from the Marsh of Maeotis (where climatum ter-

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MATHEMATICVM. 109 minus est veteribus) ac terminatur parallelo 20. sub eleuatione Poli gr 53 min. 17. vbi dies maximus est hor. 16 min. 45. sub se habet Vvittembergam, & reliquam Saxoniam: ipsum verò est latum gr. 2. min. 44. Decimum clima est latum grad. 2 min. 17. comprehensum 113. intra fines 20. & 22 paralleli, cuius medium transit per Rostochium, & Rhenum, habet diem maximam hor. 17. min. 15. sub eleuatione Poli gr. 55. min. 34. Vndecimum clima terminatur, & clauditur parallelo 24. sub 114. eleuatione Poli gr. 57. min. 34. vbi dies maxima est hor. 17. min. 45. habetque sub se Moscouiam, & Hyberniam, amplitudine sua comprehendit gr. 2. Duodec num clima amplectitur Noruegiam, & vltimam 115. partem Britannæ, estque latum grad. 1. min. 40. terminatur autem parallelo 26. in altitudine Poli gr. 59. min. 14 vbi dies maxima est hor. 18. min. 15. Decimum-tertium clima extenditur ad parallelum 18. in 116. altitudine Poli grad. ferè 61 vbi dies maxima est grad. 1. min. 26. comprehendit totam Gothiam, in amplitudine grad. 1. min. 26. Decimum-quartum clima transit per medias Bergas Noruegix, 117. completuique parallelo 30. vbi dies maxima est hor. 19. min. 15. in eleuatione Poli grad. 62. tota eius amplitudo est gr. 1. min. 13. Decimum-quintum clima transit per Vviburgum Filandix, 118. habetque latitudinis gr. 1 sub parallelis 30. 31. & 32. cuius medium, hoc est sub parallelo 31. dies maxima est hor. 19. min. 30. in altitudine Poli gr. 62. min. 25. vbi accolæ experiuntur diem maximam hor. 19. 30. extenii autem sub parallelo 32. hor. 19. min. 45. Decimum-sextum clima est latum min. 52. & transit per 119. Arontiam Sueciæ ciuitatem, sub eleuacione Poli gr. 63. min. 22. cuius finis habet diem maximam hor. 20. min. 15. Decimum-septimum clima continetur sub parallelis 34. 35. 120 & 36. in altitudine Poli gr. 64. min. 30. estque latum min. 44. cuius medium transit per ostia fluuij Dalenxanlij, vbi dies maxima est hor. 20. min. 45. Decimum-octauum clima est latum min. 36. clauditurque 121. parallelo 38. in altitudine Poli gr. ferè 65. vbi dies maxima est hor. 21. min. 15. Decimum-nonum clima protenditur à parallelo 38. vsque ad 122. 40. atque amplitudine sua complectitur min. 29. in cuius fine dies maxima constat horis 21. min. 45. in eleuatione Poli grad. 65. min. 35.

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MATHEMATICVM. 109 less than the ancient ones) and it is terminated by the 20th parallel, at the elevation of the pole 53 degrees 17 minutes, where the longest day is 16 hours 45 minutes. Under it lies Wittenberg and the rest of Saxony; its breadth itself is 2 degrees 44 minutes. The tenth climate is 2 degrees 17 minutes in breadth, contained between the 20th and 22nd parallels, the middle of which passes through Rostock and the Rhine; it has the longest day of 17 hours 15 minutes, at the elevation of the pole 55 degrees 34 minutes. The eleventh climate is bounded and enclosed by the 24th parallel, at the elevation of the pole 57 degrees 34 minutes, where the longest day is 17 hours 45 minutes; and it has under it Moscow and Ireland, and in its breadth it comprises 2 degrees. The twelfth climate includes Norway and the farthest part of Britain, and is 1 degree 40 minutes broad; it is terminated by the 26th parallel, at the altitude of the pole 59 degrees 14 minutes, where the longest day is 18 hours 15 minutes. The thirteenth climate extends to the 18th parallel, at an altitude of the pole of nearly 61 degrees, where the longest day is 1 degree 26 minutes; it includes all of Gothia, in a breadth of 1 degree 26 minutes. The fourteenth climate passes through the middle of Bergen in Norway, and is completed by the 30th parallel, where the longest day is 19 hours 15 minutes, at the elevation of the pole 62 degrees; its entire breadth is 1 degree 13 minutes. The fifteenth climate passes through Viborg in Finland, and has a latitude of 1 degree under parallels 30, 31, and 32, the middle of which, that is, under the 31st parallel, the longest day is 19 hours 30 minutes; at the altitude of the pole 62 degrees 25 minutes, where the inhabitants experience the longest day of 19 hours 30 minutes; but at the extreme under the 32nd parallel, 19 hours 45 minutes. The sixteenth climate is 52 minutes broad and passes through the Swedish city of Arontia, at the elevation of the pole 63 degrees 22 minutes, the end of which has the longest day of 20 hours 15 minutes. The seventeenth climate is contained under the 34th, 35th, and 36th parallels, at the altitude of the pole 64 degrees 30 minutes, and is 44 minutes broad; its middle passes through the mouths of the river Dalenxanlij, where the longest day is 20 hours 45 minutes. The eighteenth climate is 36 minutes broad and is bounded by the 38th parallel, at an altitude of the pole of nearly 65 degrees, where the longest day is 21 hours 15 minutes. The nineteenth climate extends from the 38th parallel as far as the 40th, and in its breadth comprises 29 minutes, at the end of which the longest day amounts to 21 hours 45 minutes, at the elevation of the pole 65 degrees 35 minutes.

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110 LEXICON 123. Vigesimum clima latum min. 12. amplectitur extrema Nor- uegia loca, siniturque parallelo 42. sub quo dies maxima est hor. 22. min. 15. in altitudine Poli gr. 66. 124. Vigesimum-primum climat transit per Sueciam, & conrine- tur intra parallelum 42 & 44. cuius medium habet diem ma- ximam hor. 22. min. 30. estque in altitudine Poli. gr. 66. min. 6. amplitudo eius est min. 17. 125. Vigesimum-secundum clima transit per mediam Albam, Russiam; estque in altitudine Poli gr. 66. & min à 14. vsque ad 25. cuius medium habet diem maximam constantem hor. 23. finis verò cadit sub parallelo 46. vbi dies maxima est hor. 23. min. 15. tota eius latitudo est min. 11. 126. Vigesimum-tertium clima, quod est vltimum complectitur partem Islandiæ, & vicinas Insulas sub parallelis 46. 47. & 48. cuius principium habet diem maximam hor. 23. min. 15. me- dium hor 23. min. 30. finis hor. 23. min 45 in altitudine Poli grad 66 min 28. estque latum solis min. 5. 127. Tandem parallelo 49. terminantur omnia climata vbi dies maximus est hor 24. ita vt ibi Sol incipiat non occidere, sed circulariter ferri; vt propterea populi ea loca inhabitantes vo- centur Perisc 1, hoc est Circumbrasiles quia vmbra illorum est versatilis, & circum circà se vertit, quod accidit ab hoc pa- rallelo vsque ad polum, sub quo dies vnius naturalis integra- tur ex integro anno, sex enim mensibus Sol nunquam occi- dit, cùm reperiatur in semicirculo boreali, qui nunquam sub terra sit, & è contrà dum est in semicirculo australi, qui semper sub terra latet, spatio item sex mensium facit longis- simam noctem: quæ tamen, neque nox dici potest, cùm ha- beat ferè semper lucem crepusculinam valdè claram ob Solis vicinitatem. 128. Postò quæ diximus de parallelis ad æquatorem constituen- tibus diuersa climata in nostra plaga Septentrionali conci- pienda sunt etiam in altero Hemisphætio versus polum An- tarcticum, vbi totidem climata constituenda sunt in eadem amplitudine, arque in eadem poli Antarcticci eleuatione, cum eadem prorsus quantitate dierum ac de nostris regioni- bus diximus, quæ vtique climata nominari possunt vel à præcipuis locis, per quæ transeunt, vel sanè (vt de Polo sit) ab oppositis. 129. Hic autem, etsi obiter, non erit fortè injucundum dis- quirere quod clima ex modo numeratis sit temperatius, atque habitationi hominum accommodatius. Auicennas lib. 1. Fen. cap. 1. opinatur quod sub æquatore vbi incipit primum clima sit locus habitationis omnium temperatissimus, quia, inquit,

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110 LEXICON 123. The twentieth climate, extending 12 minutes, embraces the farthest places of Norway, and is bounded by the parallel 42, under which the longest day is 22 hours 15 minutes, at the elevation of the Pole 66 degrees. 124. The twenty-first climate passes through Sweden, and is contained within parallels 42 and 44; its middle has the longest day, 22 hours 30 minutes, and it is at the elevation of the Pole 66 degrees 6 minutes. Its breadth is 17 minutes. 125. The twenty-second climate passes through the middle of White Russia, and is at the elevation of the Pole 66 degrees, and 14 minutes up to 25; its middle has a constant longest day of 23 hours. Its end falls under parallel 46, where the longest day is 23 hours 15 minutes. Its whole breadth is 11 minutes. 126. The twenty-third climate, which is the last, includes part of Iceland and the neighboring islands under parallels 46, 47, and 48; its beginning has the longest day 23 hours 15 minutes, the middle 23 hours 30 minutes, the end 23 hours 45 minutes, at the elevation of the Pole 66 degrees 28 minutes, and it is 5 minutes wide in terms of the sun. 127. Finally, all climates are terminated by parallel 49, where the longest day is 24 hours, so that there the sun begins not to set, but to move in a circle; and therefore the peoples inhabiting those regions are called Periscioi, that is, “Circumshadowed,” because their shadow is movable and turns round about them. This happens from this parallel up to the pole, under which one natural day is made up of a whole year: for six months the sun never sets, when it is found in the northern semicircle, which is never beneath the earth; and on the contrary, while it is in the southern semicircle, which always lies hidden under the earth, it makes the longest night over the space of six months. Yet this can hardly be called night, since it has almost always a very bright crepuscular light because of the sun’s nearness. 128. After what we have said about the parallels to the equator constituting different climates in our northern region, it must also be understood in the other hemisphere toward the Antarctic pole, where an equal number of climates must be constituted with the same breadth, and with the same elevation of the Antarctic pole, and with exactly the same quantity of days as we have said of our regions; these climates may indeed be named either from the principal places through which they pass, or, quite properly, as to the Pole, from the opposites. 129. Here, though incidentally, it will perhaps not be unpleasant to inquire which climate among those now numbered is the most temperate and most suitable for human habitation. Avicenna, book 1, Fen. cap. 1, thinks that under the equator, where the first climate begins, is the most temperate place of habitation for all, because, he says,

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MATHEMATICVM. 118 rectitudo Solis supra verticem minus malum operatur, & minus mutat aërem, quam Solis propinquitas apud nos, qui suumus in majori latitudine, ibi enim non tantùm temporis consistit in hemisphærio, vt illud possit æquè, ac nostrum nimium ex eius radijs incalescere: & prætereà id probat experientia, & ex nostris qui illuc appuli, ad nos postea remearunt, testimonia dicentium sub æquatore esse temperatum aërem, fæcundissimam terram, iucundissimamque habitationem. Auerroës putat quintum clima, sub quo ipse erat, esse omnium temperatissimum. Manardus Ferrariensis epist. 7. sextum sub quo terrariam laudat. Albertus Magnus è contrà septimum, vbi Ratisbona, cuius ipse erat accola, & Episcopus, cæteris omnibus anteponit: quia, inquit, homines hic pulcherrimi, proceri corporis, justæ staturæ, & venusti coloris. Reuerà vnusquisq[ue] sibi plaudit, & patriæ amore illectus, atque aëri assuefactus, in ea plus jucunditatis inspicit, quàm in reliquis regionibus: vnde meritò ille cecinit: Nescio, qua natale solum dulcedine cunctos Ducit, & immemores non sinit esse sui. <130.> Sed enim dicendum est vnum quemque veritate coactum suum clima laudasse, idque illis cæteris omnibus temperatius esse; non absolutè, vt optimè obseruauit Galenus, sed respectu suorum habitatorum qui ibi nati, ibi assuefacti, ibi aërem sibi naturalem respirant, ibi etiam suæ temperiei accommodam quisque trahit moram, inuenit similitudinem. Sola igitur habitatio à primordijs constitutionis acquisita, vel longo vsu facta jam connaturalis est animantibus accommodata; alienæ verò incommodæ, & intemperatæ. Sic Lusitani, olim qui, <131.> acquisitis à suo Rege in India Orientali postubus, & castis præsediarij milites mittebantur vix tres aut quatuor menses ibi moram trahentes, cum climatis contrarietatem ferre non possent, miserè extinguebantur, vt postea cautum sit, non nisi pueros, & adolescentes eò mittere, quò aëri assueti, rem patriam, suaque iura in alienis regionibus tutarentur. Idipsum videre est in reliquis animantibus cuique regioni proprijs, quæ in alias asportata, aut vim generatiuam, amittunt, aut in totum etiam extinguuntur. Vt in elephantis, qui in Africa sunt in loco sibi connaturali, si in Italiam ducuntur, viuunt quidem, sed generare non possunt; si vlteriùs in Germaniam, aut alias Septentrionis prouincias, non modò non speciem propagare, sed & ne vita quidem diù frui possunt: & hæc de climatum ratione satis sint dicta. <132.> CLIMACTERICVS, ex etymo Græco, petinde est, ac Latinè scalars: Apud Astronomos verò, Physicos, aliosque passum

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MATHEMATICVM. 118 the straightness of the Sun above the zenith works less harm, and changes the air less than the Sun’s nearness with us, who are in a greater latitude; for there the time does not remain so long in the hemisphere that it can become, as ours does, too much heated by its rays; and moreover experience proves this, and also the testimony of those of ours who sailed there and later returned to us, saying that under the equator the air is temperate, the earth most fertile, and habitation most pleasant. Auerroës thinks the fifth climate, under which he himself was, to be the most temperate of all. Manardus of Ferrara in epist. 7 praises the sixth climate. Albertus Magnus, on the contrary, the seventh, where Regensburg, of which he was himself an inhabitant and bishop, he prefers to all the others: because, he says, the men here are most beautiful, of tall body, of proper stature, and of pleasing complexion. Truly each one applauds himself, and, drawn by love of country and accustomed to the air, sees more delight in it than in the other regions: whence he rightly sang: I know not what sweetness of native soil draws all men, and does not allow them to be forgetful of themselves. <130.> But indeed it must be said that each one, compelled by the truth, has praised his own climate, and that it is more temperate than all the others; not absolutely so, as Galen observed most rightly, but in relation to its inhabitants, who were born there, accustomed there, breathing there the air natural to them, and there too each one draws for himself a dwelling suitable to his own temperament, and finds a likeness. Thus a habitation acquired from the first beginnings of life, or made by long use, is now connatural and suited to living creatures; but foreign habitations are uncomfortable and intemperate. Thus the Portuguese, who once, <131.> when posts and garrisons had been acquired by their king in the East Indies, sent soldiers who, remaining there scarcely three or four months, since they could not bear the contrariety of the climate, were miserably destroyed; so it was later decreed that only boys and adolescents should be sent there, so that, accustomed to the air, they might defend the fatherland and their own rights in foreign regions. The same is seen in the other animals proper to each region, which, when carried into others, either lose their generative power, or are even completely extinguished. As in elephants, which are in Africa in a place connatural to them: if they are led into Italy, they indeed live, but cannot breed; if farther into Germany, or other provinces of the North, they are not only unable to propagate their kind, but cannot even enjoy life for long: and let enough have been said on this matter of climates. <132.> CLIMACTERICVS, from the Greek etymology, is just as if in Latin it were scalars: but among astronomers, physicists, and others, a step

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112 LEXICON scriptores pro quoque anno vitæ humanæ decretorio, & scalari, qui certo numerosum rythmo recurrens, mortis periculum, grauem morbum, aut ingens aliquod infortunium importare, constans semper probauit experientia. Porrò id obseruate, neque superstitiosum esse, neque inutile docent communiter Theologi, & ex Partibus Ambrosius, Augustinus, Beda, Boëhius, alijque. At verò eius rei rationem reddere, difficile admodum est, & quæ intellectum compleat: impossibile. De eadem multa scripserunt Plato, Cicero, Macrobius, Gellius, & ex Recensoribus Petrus Bongus, Maginus, Argolus, ac nouissimè doctè nimis, & etuditè Claudius Salmasius. Communior tamen sententia est, planetas singulos assumere dominium supra corpus humanum secundùm ordinem, quemadmodum singulis annis: ita vt primo anno dominetur Luna, secundo Mercurius, tertio Venus, quarto Sol, quinto Mars, sexto Lupiter, septimo Saturnus: Cumque singulis septenis annis dominetur Saturnus, idcircò illos nominant climactericos, judicarios, ominosos, vt rectos à planeta nimis infenso, & vitæ hominis inimico; sed audiamus Ficinum hujus sententiæ principem: sic enim scribit lib. 2. cap. 20 de vita producenda. Cum Astronomi singulas deinceps dies horas planetas ordine singulis distribuerint, similiterque septem bebdomade dies, atque ipso fatu per menses digesserint officia planetarum, cur non etiam per annos eadem disponamus? Vt quemadmodum infantem in aluo latentem rexit primo mense Saturnus: ultimo Luna, sic statim natum, ordine jam conuerso, primo ipsius anno ducat Luna, secundo si vis Mercurius, tertio Venus, quarto Sol, quinto Mars, sexto Lupiter, septimo verò Saturnus, atque deinceps ordo per vi am similis repetatur. Itaque in septimo quolibet vita annis in corpore mutatio maxima, ideoque periculosissima: quandoquidem & Saturnus nobis communiter est peregrinus, & ab eo tunc planetarum summo ad Lunam è vestigio planetarum infimam gubernatior dis. Cæterùm præter climactericos constantes ex septenarijs obseruant alij annos Enneaticos <133.> constantes ex nouenarijs, qua ratione nescimus: sicut etiam ex ipsis Climactericis, quare aliqui periculosiores, alij minus periculosi, semper tamen secum afferant aliquam corporis discretiam: alij etiam quod magis mirere, impunè transeant. Augustus apud Suetonium, Caium nepotem suum gaudere jussit, transgressus sum enim, inquit, annum sexagesimum tertium, quo anno, plusquam alijs mori conspicuus. Periculosissimum quoque perhibeunnum 49 & 56. Sed de hac re non incongruam, neque hactenus excogitatam rationem, fortè alibi afferemus. Pronunc satis. COELVM

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112 LEXICON writers assign to each year of human life a decisive and climacteric influence, and by a certain recurring numerical rhythm it has always been constantly proved by experience that it brings danger of death, serious illness, or some great misfortune. Moreover, that this should be observed is taught by theologians generally, and among others by Ambrose, Augustine, Bede, Boethius, and others. But indeed to give a reason for this matter is very difficult, and impossible to make fully intelligible. Many have written on the same subject: Plato, Cicero, Macrobius, Gellius, and among later writers Petrus Bongus, Maginus, Argolus, and most recently, with great learning and erudition, Claudius Salmasius. The more common opinion, however, is that each of the planets takes dominion over the human body in order, just as in each year: so that in the first year the Moon rules, in the second Mercury, in the third Venus, in the fourth the Sun, in the fifth Mars, in the sixth Jupiter, in the seventh Saturn. And since Saturn rules in every seventh year, they therefore call those years climacteric, judgment years, ominous years, as being marked by a planet excessively hostile and an enemy to human life; but let us hear Ficino, the chief authority for this opinion: for thus he writes, book 2, chapter 20, de vita producenda . Since astronomers have distributed the planets in order to the individual hours of the successive days, and likewise have arranged the seven days of the week, and even by fate have assigned the offices of the planets through the months, why should we not also arrange the same by years? Thus, just as Saturn governed the infant hidden in the womb in the first month, and the Moon in the last, so immediately after birth, with the order now reversed, let the Moon guide him in his first year, Mercury in the second if you wish, Venus in the third, the Sun in the fourth, Mars in the fifth, Jupiter in the sixth, and Saturn in the seventh; and thereafter let the same order be repeated by the same route. Therefore in every seventh year of life there is a very great change in the body, and therefore a very dangerous one: since Saturn is commonly a stranger to us, and at that time from the highest of the planets he governs, by a direct course, down to the Moon, the lowest of the planets. Moreover, besides the climacteric years computed from sevens, others observe enneatic years, computed from nines, for what reason we do not know; just as also among the climacteric years themselves, some are more dangerous and others less dangerous, though always they bring some change in the body; others, too, which you may wonder at more, pass by unharmed. Augustus, according to Suetonius, told his grandson Gaius to rejoice: “for I have passed,” he said, “my sixty-third year,” in which year, more than in others, death is conspicuous. The forty-ninth and fifty-sixth years are also said to be most dangerous. But on this matter we shall perhaps elsewhere offer a not inappropriate and as yet unworked-out explanation. Enough for the present. COELVM

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COELVM dicitur pars illa, & potior Vniuersi, quæ est super omnia elementa, substantiæ, vt fert communior Philosophorum sententia, ab hac sublunari diuersæ, formæ, vt creditur, incorruptibilis, quamque communiter Ætheta appellarunt, amplectiturque corpora ipsa cælestia, astra, planetas, atque orbes deferentes in quibus ista fixa esse intelliguntur. Dicitur cælum à cælando, vt habet Ambrosius lib. 2 examiner. eò quod impressa stellarum lumina habeat, quasi cælarum varijs imaginibus opus. Quinque autem cæli proprietates communiter enumerantur. Lumen, situs, incommutabilitas motus, & natura, quæ à Philosophis quinta nuncupatur essentia. Quod ad lumen attinet, id manifestum est esse præcipuam cæli proprietatem, qua in hæc inferiora influit per motum localem qui lumen ipsum applicat, & pro siderum adinuicem habitudine aut intendit, aut remittit. Non quod omnes cæli partes sint luce præditæ (cum hac prærogatiua sola fulgeant astra) sed quod sit sua natura pellucidum, & astrorum lumen in se recipiat, & transfundat. Quoad situm is est cæteris omnibus præcellentior: quò enim magis aliquid rem ouetur à terra, eò est purius, & nobilius. De incommutabilitate verò nemo est qui dubitet, quandoquidem sola corpora cælestia neque alterari, neque corrumpi queunt; vt notat Philosophus in libris de cælo. Quoad morum, is circularis est, continuus ac perpetuus; motus autem elementorum rectus est, irregularis, & citò finem habet. Tandem natura cæli, siue ea simplex sit, siue composita, longè ab omni sublunarium rerum natura discedit, & est cæteris omnibus præstantior, ac diuinior. Porrò cælorum numerum pio motuum diuersitate constituebant antiqui, cum enim viderent omnia astra rapidissimo motu ferri ab Oriente in Occidentem, ac insuper aliqua ex ipsis contrario motu, & quidem singulis proprio versus Orientem cieri, seu potius ab motu vniuersitatis retardari; ideò & plures motus, & plures cælos admisertunt: Et quidem Ionstonus de adm. cal. cap. 2. hæc habet: In orbis variè distinxere astronomi, placuere Eudoxo XXIII Callippo XXX. Prolemao XXX. Regiomontano XXX. II. Aristoteli XVII D. cum esse commun: est opinso At enim Fracastorius LXX. cælos poluit omnes terræ concentricos: septem in Luna, in Mercurio vndecim, totidem in Venere, in Sole quatuor, in Marte nouem, in Ioue vndecim, in Saturno decem, supra Firmamentum sex, & Firmamentum, quod Aplanem vocat ex septem orbibus constans. H

Transcription: Translated (English)

HEAVEN is said to be that part, and the nobler part of the Universe, which is above all the elements, a substance, as the more common opinion of the Philosophers holds, different from this sublunary world in form, incorruptible, as it is believed, and commonly called Ætheta ; and it comprehends the heavenly bodies themselves, the stars, the planets, and the carrying spheres in which these are understood to be fixed. Heaven is said to be from cælando , as Ambrose has in lib. 2 examer. , because it has the shining lights of the stars impressed upon it, as if the work of various images had been done in the sky. Five properties of heaven are commonly enumerated: light, position, immutability, motion, and nature, which by the Philosophers is called the fifth essence. As for light, it is manifest that this is the principal property of heaven, by which it flows into these lower things through local motion, which applies the light itself, and either increases or diminishes it according to the relation of the stars to one another. Not that all parts of heaven are endowed with light (since only the stars shine with this prerogative), but because by nature it is transparent, and receives and transmits the light of the stars within itself. As to position, it is more excellent than all the rest; for the more a thing is removed from the earth, the purer and nobler it is. As for immutability, no one doubts it, since the heavenly bodies alone can neither be altered nor corrupted, as the Philosopher notes in the books De cælo . As for motion, it is circular, continuous, and perpetual; but the motion of the elements is straight, irregular, and quickly comes to an end. Finally, the nature of heaven, whether it be simple or composed, departs far from all the nature of sublunary things, and is superior to all the rest and more divine. Moreover, the ancients established the number of the heavens by the diversity of motions; for when they saw all the stars carried by the swiftest motion from East to West, and besides this some of them moved in a contrary motion, and indeed each by its own proper motion toward the East, or rather were retarded by the motion of the universe, they therefore admitted both more motions and more heavens. And indeed Iohnstonus, de adm. cal. cap. 2, has these words: “Astronomers distinguished the spheres in various ways; Eudoxus approved 23, Callippus 30, Ptolemy 30, Regiomontanus 30, 2, Aristotle 17, D. with the common opinion being that…” But Fracastorius, however, posited 70 heavens, all concentric with the earth: seven in the Moon, eleven in Mercury, as many in Venus, four in the Sun, nine in Mars, eleven in Jupiter, ten in Saturn, six above the Firmament, and the Firmament itself, which he calls the Aplane , consisting of seven spheres. H

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134 LEXICON Verùm hæc omnia gratis & absque vllor fundamento conficta ni cælorum nomine orbis, concentricos, & epicyclos velimus intelligere. Decem igitur omninò sunt cæli mobiles si ij solidi sunt (vt taceam de Empyteo, quod fides docet omninò immobile ac firum, quippe quod sedes Beatorum est) ex quibus septem totidem planeris assignarunt; octauum Firmamentum seu Cælum stellarum in quo fixa constituuntur: Nonum verò cùm non nisi per motum dignoscerent, essetque prætereà pellucidum ac transparens, Christallinum dixerunt, ac tandem decimum primum mobile, quod secum reliquos rapit, atque ab Oriente in Occidentem spatio vigintiquatuor horarum circumvoluitur, & rotatur. 136. At enim si physicè loquamur (vt bene ostendit Titus in cælesti Philosophia) omnia quæcumque sidera vno tantùm motu, qui est raptus & primi mobilis agitantur ab Oriente in Occidentem; neque alius proprius cuique motus vlterius admittendus. Quod autem singula non quotidie cum ijsdem partibus primi mobilis occidant, sed vicissim loca permutent, atque in præcedentibus semper conspiciantur, quæ successiuè occidunt, ac proinde videantur motu proprio, & contrario præcedentes partes acquirere; id non à vero motu, sed potiùs à motus morositate, ac mobilium resistentia, & ponderositate procedit. Quod vel ex eo patet, quia propius est, ac contiguus primo mobili stellarius Orbis validiùs ab eo trahitur, ac citiùs quàm cæleri inferiores motum diuturnum vniuersitatis absoluit. Inde Saturnus; mox Iupiter, & sic per ordinem progrediendo, omnes quò magis à primo mobili remouentur eò magis eius impulsui resistunt, ita vt Luna quæ postrema omnium est, ac teriæ vicinior, tantùm resistat, vt singulis diebus modò vndecim, modò quindecim gradus retrò remaneat, quod nos proprium motum in Zodiaco vocitamus; reuerà tamen est quædam retardatio, & motositas, qua impulsui primi mobilis resistit. Igitur hac ratione Luna non est dicenda omnium planetarum velocissima, sed tardissima: Saturnus non sequis, ac piger, sed longè plus alijs expeditior: ac tandem Firmamentum velocitate proximè accedit ad primum mobile, eò quia non remanet retrò nisi quatuor tantum minutis; ac motum suum circularem ab Oriente in Occidentem circà tellurem (prærer quem alium reuerà non habent) citiùs compleat: inde Saturnus, mox Iupiter: denique serius omnibus Luna. Quia verò id non officit communi v sui loquendi, ac verè sidera hac morositate permutant loca, situm suum, & consistentiam in Zodiaco; ideò admittitur, dici posse duplex huiusmodi motus, quo post inueteratam consuerudinem

Transcription: Translated (English)

134 LEXICON But all these things are fabricated for nothing and without any foundation, unless by the name of the heavens we wish to understand the spheres, concentric and epicycles. Therefore there are altogether ten movable heavens, if they are solid (to say nothing of the Empyrean, which faith teaches is altogether immovable and firm, since it is the seat of the Blessed). Of these they assigned seven to the same number of planets; the eighth, the Firmament or Heaven of the stars, in which the fixed stars are set; the ninth, however, since they recognized it only by its motion, and since it was moreover transparent and pellucid, they called the crystalline; and finally the tenth, the first mobile, which carries the rest with it and revolves and turns from East to West in the span of twenty-four hours. 136. But if, in truth, we speak physically, as Titus well shows in Celestial Philosophy, all the stars whatever are driven by only one motion, that is, the carrying along of the first mobile, from East to West; and no other proper motion is to be admitted for each individual star. As for the fact that the individual stars do not every day set with the same parts of the first mobile, but in turn exchange places, and are always seen in advance, while those that set successively, and therefore seem to acquire prior and contrary parts by their own motion, this proceeds not from a true motion, but rather from the slowness of the motion, and from the resistance and heaviness of the moving bodies. This is clear even from the fact that the stellar sphere, being nearer to and contiguous with the first mobile, is drawn more strongly by it, and more quickly than the lower spheres completes the long motion of the universe. Then Saturn; next Jupiter; and thus proceeding in order, all the more they are removed from the first mobile, the more they resist its impulse, so that the Moon, which is last of all and nearest to the earth, resists so much that each day it remains behind by now eleven, now fifteen degrees, which we are accustomed to call its proper motion in the Zodiac; yet in truth it is a certain retardation and slowness, by which it resists the impulse of the first mobile. Therefore, for this reason, the Moon must not be called the fastest of all the planets, but the slowest; Saturn not sluggish and lazy, but far more swift than the others; and finally the Firmament comes closest in speed to the first mobile, because it remains behind by only four minutes, and completes its circular motion from East to West around the earth, apart from which they truly have no other; therefore Saturn, next Jupiter; finally, later than all, the Moon. But because this does not interfere with common usage of speech, and the stars truly by this slowness exchange places, their position, and their state in the Zodiac; therefore it is accepted that such a twofold motion can be said to exist, by which after long-established custom

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MATHEMATICVM. 115 res Astronomicæ faciliùs explicantur. Quemadmodum eam ob rem admittuntur plures orbis, Eccentrici, Epicycli, &c. ad saluandas apparentias, atque ad comparandam probam re- rum cælestium agnitionem; cum tamen post Tychonem qui primus omnium stabiliuit, ac ferè extra controuersiam posuit Cælum fluidum, id jam necessarium non sit, & possint optimè sine illis intelligi: atque adeò non plures cæli, sed vnum tap- tum vastissimum per quod stellæ non secus ac pisces in mari discuriant, jam modò videarur procul omni dubio asserendum. Quod autem huic cælorum fluxibilitati nil penius refragetur, imò potius faueat illud lobi cap. 35. vbi cæli solidissimi appel- lantur tanquam ære fundati: dicemus in V. Firmamentum. Ex hoc cælorum motu Philo Iudæus lib. de somnijs opinatus < 138.> est suauissimum sonum fieti, atque ad hoc respicere sacras pa- ginas, semper cum cælos laudare Deum asserunt, & illud lobi 38. Quis enarrabis calorum rationem, & concentum cali quis dormire jacies? Quem ob loci distantiam nos non sentimus, sed id diuina prouidentia factum, quia si posset, inquit, hæc suauissima harmonia, quam cælum suo motu edit ad aures nostras peruenire, in nobis excitaret impotentes amores, & insanum desiderium, quo stimulati rerum ad victum necessariarum obli- uisceremur, non passi cibo, potuque per fauces demisso, sed quemadmodum immortalitatis Candidati diuinis consumma- tæ musicæ cantibus. Huic opinioni adstipulatur etiam D. An- selmus lib. 1. de Imagine mundi, sic inquiens. Sep[er]em calorum orbis cum dulcisona harmonia voluuntur, ac suauissimi concentus eorum circuitione efficiuntur: qui sonus ideò ad nostras aures non peruenit, quia vltra aerem fit, & eius magnitudo nostrum angustum auditum excedit: nullus enim à nobis sonus percipitur nisi qui in aëre efficitur: à terra autem vsque ad Firmamentum cælestis musica mensuratur, ad cuius exemplar nostra musica inuenta est. Sequuti sunt Ambros. in præfat. ad Psalm. Boëth. lib. 1. de Mu- sica cap. 2. Isidorus lib. 3. Esymol cap. 16. & multi alij. Ad hoc etiam alludere visus est Licentius Presbiter, cùm ad Augusti- num præceptorem suum scribens, sic cecinit: apiauit numeros calis, sussitque sonoros, Exercere modos, parilesque agitare choreas. Quæ quidem opinio, etsi communiter reijciatur, atque ab < 139.> Irenæo nimis rigidè lib. aduers. hæreses, inter damnata Mar- cosiorum dogmata annumeretur; non tamen nunc temporis probabilitate cæter, præsertim posita cæli fluxibilitate, quæ eius- dem ferè rationis est ac ipse aër, quinimò non desunt qui dicant (& mihi maximè arridet) vnum continuum cum cælo con- stituere, eiusdem substantiæ, quæ tamen semper subtilior, &c H ij

Transcription: Translated (English)

MATHEMATICVM. 115 Astronomical matters are more easily explained. For that reason, more spheres, eccentrics, epicycles, and the like are admitted, to save the appearances and to attain a sound knowledge of heavenly things; although after Tycho, who was the first of all to establish, and almost beyond dispute to set forth, the fluid heaven, this is no longer necessary, and they can be understood quite well without them: and thus, it now seems that not many heavens, but one only, a vast one through which the stars range about no otherwise than fishes in the sea, ought to be asserted beyond all doubt. Moreover, that nothing at all opposes this fluxibility of the heavens, and rather that it is supported by it, is that passage of Job, chapter 35, where the heavens are called most solid, as if founded in brass: we shall speak of this under V. Firmament. From this motion of the heavens Philo Judaeus, in book On Dreams, thought that the sweetest sound was produced, and that the sacred pages refer to this when they always say that the heavens praise God, and likewise that passage of Job 38: Who can declare the order of the heavens, and who shall put to sleep the harmony of heaven? Because of the distance of place we do not perceive it; but this has been done by divine providence, because if, he says, this most sweet harmony, which heaven gives forth by its motion, could reach our ears, it would stir up in us unruly loves and a mad desire, by which we would be driven to forget the things necessary for life, not being restrained by food and drink passed down through the throat, but as candidates for immortality by the divine songs of consummate music. To this opinion also agrees St. Anselm, in book 1 of On the Image of the World, speaking thus: The spheres of the seven heavens are turned with sweet-sounding harmony, and by their circuit most delightful concords are produced; which sound does not reach our ears because it is made beyond the air, and its greatness exceeds our narrow hearing: for no sound is perceived by us except that which is made in the air; but from the earth up to the Firmament celestial music is measured, according to whose exemplar our music was invented. They were followed by Ambrose in the preface to the Psalms, Boethius in book 1 of On Music, chapter 2, Isidore in book 3 of the Etymologies, chapter 16, and many others. To this also Licentius the presbyter seems to have alluded when, writing to his teacher Augustine, he thus sang: He fashioned the numbers of the heavens, and commanded them to sound, To practice modes, and to move in equal dances. This opinion, although commonly rejected, and by Irenaeus too severely, in book Against Heresies, numbered among the condemned dogmas of the Marcosians, is not without probability in our own time, especially if the fluidity of the heaven be assumed, which is of almost the same nature as the air itself; indeed there are not wanting those who say (and I especially like it) that it constitutes one continuous thing with the heaven, of the same substance, though always subtler, etc. H ij

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116 LEXICON subtilior vsque ad Empyreum est, licet aër noster infinitè propemodum dictet ab ea substantia per quam discutiunt sideras nihilominus, sicut motus violentius corporum per aërem quò est concitanior eò vocaliorem sonum edit ex allisione: sic fieri potest in motu siderum per vastissimum illud expansum, vt ex allisione corporum dulcissimus concentus fiat, qui ad nostras aures ob magnam dictan iam non peruenit. Quod autem Irenæus, Epiphanius, Basilius, & alij Paires, eam opinionem reiiciant, atque hæresis suspectam habeant dicendum est, cum Sixto Senenisi . de Quæstion. Physicis in diuinam Scripturam, ipsos potiùs inuehi, non in ipsam cælestium sonorum assertionem, sed potiùs in hiuolas rationes, quibus aliqui eam tueri annitebantur, & maximè in prodigiosa quædam figmenta, quæ impiè ex hoc concentu hæreticorum turba, præsertim Maecoliorum inferebant. 140. Denique, an ex hoc cælestium corporum motu colligi possit ipsa esse animata quemadmodum credidit ipse Philo, Origenes ac Hieronymus, & an id asserere sit contrarium sacra Scripturæ, dicemus in V Mundus, cùm hic satis superque pro nostra instituta ratione fuerimus immorati. 141. CORRVS, congressus, conjunctio, & si qui alij sunt dicendi modi apud Astronomos significant conuenientiam, & aduationem duorum, vel plurium planetarum in vnum eundemq; gradum Zodiaci, aut in eundem circulum positionis coincidentiam, qua sibi mutuò agunt, lumen conferunt, atque ad influendum tanquam vnum principium vniuntur. Quæ quidem conjunctio si fuerit exquisita & in eodem gradu, dicitur partilis: si verò fuerit ad Orbem, ita vt sphæra lucis vnius alterum comprehendat, dicitur platica: Qua de re fusè loquuti sumus in V. Aspectus. 142. COLVBRAMET, corrupto vocabulo apud Arabes ex Latinis sumpto, dicitur corpus serpentis, seu etiam manus serpentarij, quæ in ipsum corpus serpentis incidit; Stella videlicet fixa terriæ magnitudinis de natura Saturni, & Veneris parvæ qualitatis, ac venenosa alio nomine Ted; quæ nunc temporis existit in gr 28 Scorpii, cum latitudine boreali ferè gr 18 Orietur Romæ cum gr. 18. eiusdem Scorpii, occidit cum 20. Sagittarij. 143. COLUMBA sidus in cælo ad polum Antarcticum atque adeò nobis inuisum constans stellis vndecim, quatum duæ præcipuæ sunt in dorso, quatuor inferioris conditionis in oliuæ ramo quem gestat in ore; reliquæ infimæ notæ sparsim per torum corpus. Hoc sidus est vnum de duodecim quæ non ita pridem à Nautis Hispanis ad terram australem nauigantibus dete-

Transcription: Translated (English)

116 LEXICON is subtler all the way to the Empyrean, although our air is almost infinitely different from that substance through which they are illuminated; nevertheless, just as the motion of bodies, the more violently they are driven through the air, the louder a sound they produce from their collision, so too it can happen in the motion of the stars through that vast expanse that, from the collision of bodies, a most sweet harmony is made, which does not reach our ears because of the great distance. But that Irenaeus, Epiphanius, Basil, and other Fathers reject that opinion, and hold it suspect of heresy, must be said, according to Sixtus Senensis de Quaestione Physicis in divine Scripture, that they attack not so much the assertion of celestial sounds itself, but rather the flimsy reasons by which some strove to defend it, and especially certain monstrous fictions, which an impious crowd of heretics, especially the Maecolians, introduced from this harmony. 140. Finally, whether from this motion of the heavenly bodies it can be inferred that they themselves are animated, as Philo himself, Origen, and Jerome believed, and whether to assert this is contrary to sacred Scripture, we shall say in V Mundus, since here we have remained enough and more than enough for our intended purpose. 141. CORRVS, congressus, conjunctio, and if there are any other modes of speaking among astronomers, signify the agreement and conjunction of two or more planets in one and the same degree of the Zodiac, or coincidence in the same circle of position, by which they act upon one another, confer light, and are united for influencing as though one principle. And this conjunction, if it be exact and in the same degree, is called partile; but if it be to the Orb, so that the sphere of one light encompasses the other, it is called platic: on which matter we have spoken at length in V. Aspectus. 142. COLVBRAMET, a corrupted word among the Arabs taken from Latin, is said of the body of the serpent, or also of the hand of the Serpent-bearer, which falls upon the serpent's own body; namely, a fixed star of the size of the earth, of the nature of Saturn, and of the small quality of Venus, and venomous, by another name Ted; which at present is in 28 degrees of Scorpio, with northern latitude of nearly 18 degrees. It rises at Rome with 18 degrees of the same Scorpio, and sets with 20 degrees of Sagittarius. 143. COLUMBA, a constellation in the sky near the Antarctic pole and therefore invisible to us, consisting of eleven stars, of which two are the chief in the back, four of lesser condition in the olive branch it carries in its beak; the rest of lower note are scattered throughout the whole body. This constellation is one of the twelve which not long ago, by Spanish sailors sailing to the southern land, were discove-

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MATHEMATICVM. 117. sunt, arque alijs 48 imaginibus ab antiquis constitutis, ad- juncta. Est nunc sub signo Geminorum cum declinatione au- strali ad gr. 40. COLVRI dicunuur duo circuli maximè, quos imaginamur in < 144.> cælo, trans untes per Polos mundi, ac se mutuò ad angulos rectos secantes; quorum alter transit per puncta æquinoctialia Arietis, & Lib:æ, & dicitur Colurus æquinoctiorum, alter verò per puncta solstitialia Caneri, & Capricorni, & polos Zo- diaci, & vocatur Colurus solstitiorum. Nominis etymon va- riè & ægrè nimis deducitur à plerisque, præsertim ab Hipparcho & Ioanne de Sacrobosco: quod ideò lubens prætereo. Porrò eorum officium est, primò ostendere quatuor principalia Zodiaci puncta, in quæ perueniens Sol, causat quatuor anni tempora, in quibus maximè mutationes fiunt. Secundò diuidere Æquatorem, Zodiacum, proindeque totum cælum in quatuor partes æquales: & Colurus quidem æquinoctiorum signat puncta æquinoctialia, ac diuidere Zodiacum in duas medietates, quarum altera sit meridionalis, in qua Sol exi- stens efficit dies breuiores, altera Septentrionalis, vbi Sol fa- cit dies longiores, Colurus autem solstitiorum ostendit pun- cta solstitialia, ac metitur maximas Solis declinationes, quas habet in tropicis, vbi efficit diem longissimum, aut breuissi- mum. Ostendunt etiam Coluti siderum se mutuò intuentium, aut obedieutium ad imperantia habitudinem per eorum æqui- distantiam hinc inde ab eodem Coluro, vnde est, quod eos- dem, aut pares describunt parallelos, & æquali temporis spatio orientur, & occidant, & insuper in ijsdem partibus horizon- tis. Quæ omnia ægrè concipi possent, ni coluri in cælo conci- perentur, quorum ope hæc omnia intelligamus. COMA Berenices, sedus in cælo à Ptolemæo non considera- < 145.> tum, sed cum extremo caudæ Leonis confusum, constans stellis vndecim ad colurum æquinoctiorum, eius cum luminaribus congressus oculis est infensus. Vide sub V. Berenices. COMBVSTVS dicitur planeta, quando est junctus Soli, non < 146> distans ab eo plus medietate suorum Orbium, tam ante quàm post: Hinc Saturnus erit combustus, quoties à Sole non disti- terit plus gradibus quinque, Iupiter gr. sex &c. Atgolus verò contendit, combustionem non ex parte recipienris oriri, sed à luce Solis, qui intrà sphæram suam omnia aresfacit, & exsic- car; ac proinde quodcumque astrum reperiatur intrà semidia- metrum suæ lucis quæ est gr. 8. min. 30. dicendum esse com- bustum. Vtcunque sit, parum refert: siue enim planeræ sint intrà semidiametrum lucis Solis, siue intrà totam illius sphæ- ram, semper magis, ac magis deteriorantur, pro majore, ac H uij

Transcription: Translated (English)

MATHEMATICVM. 117. are, and are added to the other 48 figures established by the ancients. It is now under the sign of Gemini, with a southern declination of 40 degrees. COLVRI are said to be the two greatest circles, which we imagine in the sky, passing through the poles of the world and cutting one another at right angles; one of which passes through the equinoctial points of Aries and Libra, and is called the Colure of the Equinoxes; the other through the solstitial points of Cancer and Capricorn, and the poles of the Zodiac, and is called the Colure of the Solstices. The etymology of the name is drawn variously and too laboriously by many, especially by Hipparchus and Ioannes de Sacrobosco: which I therefore gladly pass over. Moreover, their function is, first, to show the four principal points of the Zodiac, on reaching which the Sun causes the four seasons of the year, in which the changes are especially made. Second, to divide the Equator, the Zodiac, and therefore the whole sky into four equal parts: and the colure of the equinoxes indeed marks the equinoctial points, and divides the Zodiac into two halves, one of which is southern, in which the Sun, when it is there, makes the days shorter, the other northern, where the Sun makes the days longer; but the colure of the solstices shows the solstitial points, and measures the greatest declinations of the Sun, which it has at the tropics, where it makes the longest day or the shortest. The colures also show the relationship of the stars gazing upon or obeying one another to the ruling ones through their equal distance on this side and that from the same colure; hence it is that they are described as the same, or as parallel pairs, and rise and set in equal spans of time, and moreover in the same parts of the horizon. All these things could hardly be conceived unless the colures were conceived in the sky, by whose aid we understand all these matters. COMA Berenices, a constellation in the sky not considered by Ptolemy, but confused with the end of the tail of Leo, consisting of eleven stars near the colure of the equinoxes; its conjunction with the luminaries is offensive to the eyes. See under V. Berenices. COMBVSTVS is said of a planet when it is joined to the Sun, not being distant from it by more than half of its orbits, both before and after: hence Saturn will be combust whenever it is not farther from the Sun than five degrees, Jupiter six degrees, etc. But Atgolus maintains that combustion does not arise on the part of the receiver, but from the light of the Sun, which within its sphere dries up and withers everything; and therefore that whatever star is found within the semidiameter of its light, which is 8 degrees 30 minutes, ought to be called combust. However that may be, it matters little: for whether the planets are within the semidiameter of the Sun’s light, or within its whole sphere, they are always more and more impaired, in proportion to the greater and

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118 LEXICON majore propinquitate: eorum enim virrus à Sole absumitur, & eneruarur. H ac qui à combustione sit liber, adhuc tamen manere dicitur sub radijs Solis, quia hæc vicinitas, licet non tantum, quantum combustio, nihilominus semper affert aliquale detrimentum Et quidem combustionem dicunt communiter importare sex parres debilitaris, quauor verò esse sub radijs: quod tamen ego haud ità absolutè contenderem, sed potius gradus hosce debilitatis computarem à majori vicinitate ad Solem Cæterùm planeta combustus semper debilis est, siue <147.> bonus, siue malus, ita vt in beneficis minuatur bonitas per combustionem, in maleficis autem malitia (quod malè aliqui non admirtunt) dicentes pessimam esse combustionem maleficarum, ni fortè dicere voluerint pessimam esse ipsis maleficis, non autem nobis, cum per eam minus lædant, quando tota earum virtus eneruatur à potentia Solis, & si quam reliquam habeant, ea à Sole attrahitur; qui proinde earum qualitatibus imburus euadit in fortuna, vel è contrà fortuna per combustionem beneficatam, inratque ipse vices planeræ, qui intra fines illius Orbis existens comburitur. <148.> COMBUSTA via (nescitur qua ratione) dicitur in Zodiaco totum illud spatium, quod est ab initio Libræ vsque ad dimidium Scorpij, seu potius vt volunt Recensiores consideratur in secunda medietare Libræ, ac robo Scorpionis signo: fortassè ob stellas fixas, maleficæ, & adurentis naturæ, quæ intrà id spatium reperiantur, quæ cum jam recesserint à loco suo quod habebant tempore Ptolemæi, consequenter benè jam & ipsa via combusta priorem sedem mutasse dicitur, & vlteriùs processisse. Hoc igitur spatium longitudinis 45. ferè graduum reputatur maximè infortunatum, ac debilirat valdè planetam ibi repetum, & præcipuè Lunam: quod ideò in ratione detrimenti, & malitiæ, esse in via combusta, Lunam, proximè accedit ad eius Eclipsin. <149.> COMETA, seu Cometes dicuntur noua Phænomena in cælo, siue in aëris regione genita quasi Coma, quam specie præsefert: Vnde Plinius lib. 2. cap. 25. Cometas, inquit, Græci, nostri Crinitas, horrendes crine sanguineo, & comarum modo in vertice hispidas. Cicero illud vocat Cincinnatum sidus, quia habet circumfusos vndique radios, tanquam crines: quod licet proprium sit certæ cuiusdam speciei, quæ repentè in cælo apparet, & dicitur Rosa, vsus tamen obtinuit, vt Cometes genestè accipiatur pro quocunque nouo ostento, ac Phænomeno, saltem ex ijs quæ infrà Lunam apparent. <150.> Et quidem hæc Phænomena non modò in aëris regione, sed & in Cælo, atque in ipso Firmamento gigni, jam modò apud

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118 LEXICON by greater proximity: for their force is taken away by the Sun and weakened. And he who is free from combustion is nevertheless said to remain under the Sun’s rays, because this nearness, though not to the same extent as combustion, nevertheless always brings some detriment. Indeed, they commonly say that combustion implies six parts of debility, but that four are being under the Sun’s rays; I would not, however, contend this so absolutely, but rather reckon these degrees of weakness from greater proximity to the Sun. Furthermore, a combust planet is always weak, whether good or bad, so that in benefics their goodness is diminished by combustion, but in malefics their malice is diminished (which some wrongly do not admit), saying that combustion is worst for the malefics, unless perhaps they mean that it is worst for the malefics themselves, but not for us, since by it they do us less harm, when all their power is weakened by the strength of the Sun, and if they have any remaining, that too is drawn away by the Sun; wherefore he is made poor in fortune by their qualities, or conversely fortune benefits through combustion, and he himself undergoes the role of the planet, who, existing within the bounds of that orbit, is combust. 148. COMBUSTA via (it is not known for what reason) is said in the Zodiac to be all that space which extends from the beginning of Libra to the middle of Scorpio, or rather, as the more recent writers wish, it is considered to be the second half of Libra and the head of Scorpio’s sign: perhaps because of fixed stars of a malefic and scorching nature that are found within that space; and since these have now moved away from the place they occupied in Ptolemy’s time, consequently the burnt way itself is now rightly said to have changed its former seat and moved farther on. Therefore this span of longitude, of about 45 degrees, is reckoned very unfortunate and greatly weakens the planet found there, especially the Moon: which is why, in terms of detriment and malice, being in the burnt way for the Moon comes nearest to its eclipse. 149. COMET, or Cometes, are called new phenomena in the sky, or generated in the region of the air, almost like a coma, which they resemble in appearance. Hence Pliny, book 2, chapter 25: “Comets,” he says, “the Greeks call them; we, Criniti; horrid with blood-red hair, and shaggy on the summit like locks.” Cicero calls it a “curled star,” because it has rays spread around on all sides, like hair. Although this properly belongs to a certain species which suddenly appears in the sky and is called a Rose, usage has nevertheless prevailed so that Cometes is generally taken for any new portent and phenomenon, at least among those that appear below the Moon. 150. And indeed that these phenomena are generated not only in the region of the air, but also in the heavens and even in the Firmament itself, has now among

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MATHEMATICVM. 119 omnes Astronomos est ferè indubitatum, cum plurima visa sint omni prorsus parallaxi carere, ac fixarum ad vnguem mo- tum, lumen, aliasque passiones habere: sed de his peculiatis consideratio erit in V. Phenomenon. Hic autem comatæ nomi- ne nos intelligimus, atque intelligi volumus ea tantum ostenta, quæ in sublimi aëre infra Æthera generantur ex accensis va- poribus, quos & trajectiones, & repentinos ignes, & volantia sidera, & incensas stellas appellant, ac Problemæus omnes sub vnico Ctinitarum nomine comprehendit lib. 2. cap. 9. Sic igiur acceptus Cometes definitur à Leopoldo, quod sit < 151.> vapor terrenus habens grossas partes fortiter conjacentes, ascenden- ses per virtutem alicujus astri ad superiorem partem, astus, regno- rum, &c aliarum rerum magnam alterationem significans in hoc mundo Ex qua definitione, seu potiùs descriptione liquer, causam efficientem Cometarum esse Solem, & astra attrahen- tia in sublime vapores eosque accendentia: qui proinde tandiù durant, quoad vsque tota eorum materia ardendo absumatur. Quapropter semper cum apparuerit Cometa, signum est ma- gnæ siccitatis, atque caliditatis: aliàs non possent astra è terra materiem tantam resoluere, sursumque euehere: & ideò nil mirum si semper infausta portendat, sterilitatem terræ, famem, pestilentiam, inundationes, & similia. Vnde merito Claudian. cecinit: Et nunquam terris spectatum impunè Cometem. Potiò plurima ostentotum genera expendit Plinius lib. 2. < 152.> cap. 25. quæ tamen omnia possunt ad tres classes reduci, vel enim hæc nullam substantiam habent, sed ex collisione visus apparent, vt sunt Virgæ, Areæ, Halones, Iris; vel substan- tiam habent, vt Trabes, lacula, &c. Vel denique sunt medium quid mixtum vero corpore, & apparentijs, & hi retinent com- munæ vocabulum Cometæ. Rurlius isti subdiuiduntur in Cau- datos, Barbatos, & Crinitos. Caudati sunt, cum materia exha- lationis protrahitur in longum, & partes longius deorsum protenduntur. Barbati sunt, quando maretiâ exhalationis est subtilis, & continua, & demittitur inferius. Criniti verò qui & Cincinnati dicuntur, sunt quando materia exhalationis in medio est crassioris substantiæ, & per circuitum subtilioris: tunc enim in medio apparet lumen magis densum & in circuitu magis rarum, velut quidam cincinni. Ex his nouem præcipui enumerantur, Veru, Cænaculum, Pertica, Miles, Asconas, Aurora, Argentum, Nigra, & Rosa. Quorum omnium na- turam, causas, portenta, sub proprio cujusque nomine expli- cabimus. Existimauit Democritus Cometas esse illorum He- roum mentes, qui postquam diù vixerunt in terris, tandem obituri extremos peragunt triumphos, aut in cælum stellarum H iiij

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MATHEMATICVM. 119 it is almost beyond doubt among all astronomers, since very many have been seen to lack all parallax whatsoever and to have the motion, light, and other properties of fixed stars: but consideration of these peculiarities will be given in the fifth phenomenon. Here, however, by the name of comets we understand, and wish to be understood, only those portents which are generated in the upper air beneath the Ether from kindled vapors, which they call asterisms, as well as shooting stars, sudden fires, wandering stars, and burning stars; and Ptolemy comprehends all of them under the single name of xitinitæ in book 2, chapter 9. Thus, then, a comet being thus accepted is defined by Leopold as being < 151.> a terrestrial vapor having coarse parts strongly adhering together, rising by the power of some star to a higher region, signifying a great alteration of cities, kingdoms, and other things in this world. From this definition, or rather description, it appears that the efficient cause of comets is the Sun and the stars attracting vapors upward and kindling them: and therefore they last only so long as all their matter is consumed by burning. Wherefore whenever a comet has appeared, it is a sign of great dryness and heat; otherwise the stars could not draw so much material out of the earth and carry it upward. And therefore it is no wonder if it always portends ill fortune, barrenness of the earth, famine, pestilence, floods, and the like. Hence Claudian rightly sang: And never has a comet been seen on earth with impunity. Pliny more fully examines the many kinds of portents, book 2, < 152.> chapter 25, all of which, however, can be reduced to three classes: either these have no substance at all, but appear by an illusion of sight, as are rays, halos, circles, and rainbows; or they have substance, as beams, javelins, and so on; or finally they are some middle thing mixed of true body and appearances, and these retain the common name comet. These are further divided into Tailed, Bearded, and Hairy. Tailed are those when the matter of the exhalation is drawn out into length, and the parts extend farther downward. Bearded are those when the matter of the exhalation is subtle and continuous, and is let down below. Hairy, however, also called Cincinnati, are those when the matter of the exhalation is of denser substance in the middle and finer around the circuit: then in the middle a denser light appears and around it a more rarefied one, like certain curls. Among these, nine principal kinds are enumerated: Veru, Cænaculum, Pertica, Miles, Asconas, Aurora, Argentum, Nigra, and Rosa. We shall explain the nature, causes, and portents of all these under the proper name of each. Democritus thought that comets were the spirits of those heroes who, after living long on earth, at last, about to die, perform their final triumphs, or ascend into the sky of the stars. H iiij

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120 LEXICON quasi splendida sidera reuocantur, ac proptereà, inquit, se- quuntur fames, morbi populares, & ciuitia bella, quasi ciui- tates & populi ducibus illis optimis, & gubernatoribus, qui diuisos furores placabant desererentur. Sed hæc inter Poëta- rum figmenta censenda sunt. Cæterùm de Cometis egregiè multi scripserunt; imprimisque Fortunius Licetus, Antonius Gattus, Io. Baptista Venantius, & Io. Camillus Gloriosus. 153. COMMIXTIO, ex Abraham ludæo, inter Astrologos est, cum duo planetæ præsertim diuetsæ naturæ, quales sunt Mars, & Luna, Saturnus, & Sol, junguntur corpote: tunc enim sit quæ- dam commixtio, & confusio qualitatum, & resultat tertia quædam veluti natura, quæ vt plurimum non bona est (nisi sint conformis naturæ) tunc enim alter alterius vim retundit, confundit, minuitque opus. 154. COMMUNTA signa dicuntur, quæ duplici figura notantur, qualia sunt Gemini, Virgo, Sagittarius, Pisces, eò quia cùm sint in extremis sinibus quatuor anui temporum, in quibus mu- tationes fiunt, participant de subsequentibus: sic Pisces exem- pli gratiâ non tam hyemis finis sunt, quàm Veris initium. Sub signis communibus affirmant Astrologi nasci Gemellos, aut bicorporea Monstra. 155. COMPETENTES gradus, secundùm Alcabitium, audiunt duæ partes signorum, quæ fuerint vnius longitudinis, ac distantiæ à punctis tropicis, aut æquinoctialibus, quod idem est ac si dicamus duo gradus se mutuò intuentes, aut verbi gratiâ 20. gradus Arietis cum 10. grad. Virgiuis: habent enim eandem declinationem, proindeque idem robur, ac fortitudinem: Qua de re abundè satis diximus in V. Antiscia. 156. COMPLEMENTVM arcu apud Geometras dicitur excessus ille, quo gradans arcum ipsum superet, si is quadrante sit mi- nor, sin minus, & ipse quadrante sit maior, jam reliquum illud, quo ipse quadrantem superat dicitur complementum ar- cus. Vid. Clau. in spharum Procl. 157. CONCAVVM dicitur quod intrinsecus habet regularem ali- quam curvitatem; qualis est linea, & superficies alicujus or- bis, seu circuli, quæ intrinsecus, & ex parte quam suo ambi- tu includunt, sunt curvæ. Hinc omnes orbis cælestes hanc du- plicem curvitatem habentes, & extrinsecus, & intrinsecus, di- cuntur concaui, & conuexi: conuexi quidem in superficie exte- riori, quà orbes superiores tanguit; concaui verò quoad super- ficiem interiorem, qua tanguit, & includunt orbes minores. Corpora autem planetarum, & globi quicumq[ue] non possunt di- ci concaui, quia non habent superficiem interiorem; bene verò conuexi, quia habent extimam, qua clauduntur & terminan-

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120 LEXICON quasi bright stars are recalled, and therefore, he says, there follow famines, public diseases, and civil wars, as though cities and peoples were being abandoned by those best leaders and governors who calmed divided madness. But these things are to be counted among the inventions of the Poets. Moreover, many have written excellently about Comets; especially Fortunius Licetus, Antonius Gattus, Io. Baptista Venantius, and Io. Camillus Gloriosus. 153. COMMIXTIO, from Abraham the Jew, among Astrologers is when two planets, especially of diverse nature, such as Mars and the Moon, Saturn and the Sun, are joined bodily: then there is a certain mingling and confusion of qualities, and there results a third kind of nature, as it were, which for the most part is not good (unless they are of a conformable nature); then one restrains, confuses, and diminishes the force and operation of the other. 154. COMMON signs are called those which are marked by a double figure, such as Gemini, Virgo, Sagittarius, Pisces, because when they are at the extreme ends of the four seasons of the year, in which changes occur, they partake of what follows: thus Pisces, for example, are not so much the end of winter as the beginning of spring. Under common signs Astrologers affirm that twins, or bicorporeal monsters, are born. 155. COMPETENT degrees, according to Alcabitius, are understood as the two parts of signs which are of one longitude and of the same distance from the tropical or equinoctial points, which is the same as if we were to say two degrees mutually facing one another, or, for example, 20 degrees of Aries with 10 degrees of Virgo: for they have the same declination, and therefore the same strength and force. On this matter we have spoken sufficiently in V. Antiscia. 156. COMPLEMENT of an arc, among Geometers, is called that excess by which the degrees surpass the arc itself, if it is less than a quadrant; but if it is not less, and itself is greater than a quadrant, then that remaining part by which it exceeds the quadrant is called the complement of the arc. See Clau. in spharum Procl. 157. CONCAVE is said of that which inwardly has some regular curvature; such as the line and surface of some orb, or circle, which inwardly, and on that side which they enclose by their circumference, are curved. Hence all the celestial orbs, having this double curvature, both outward and inward, are called concave and convex: convex indeed with respect to the outer surface, by which they touch the higher orbs; but concave with respect to the inner surface, by which they touch and include the smaller orbs. But the bodies of the planets, and all globes whatsoever, cannot be said to be concave, because they do not have an inner surface; but they are truly convex, because they have an outermost surface, by which they are enclosed and terminated.

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MATHEMATICVM. 121 tur. Vide Vitellion in Opt. lib. 1. CONCENTRICVM appellatur etiam omne id quod habet 158. idem centrum cum alio: sicut è contrà Eccentricum, quod habet diuersum centrum. Hinc apud Astronomos concentrici vocantur illi orbis cælestes, quorum centrum idem est cum centro mundi: Eccentrici verò ij, qui licet terram circumdent, eorum tamen centrum diuersum est à centro mundi: Vtrumque autem diuiditur in Concentricum, & Eccentricum simpliciter, & Concentricum & Eccentricum secundum quid. Concentricum simpliciter est quando vtraque superficies orbis, & concaus, & conuexa est cumcentrica cum centro mundi: similiter Eccentricum simpliciter, quando neutra superficies habet centrum mundi pro suo centro. Eccentricum secundum quid est, quando Orbis secundum vnam tantùm superficiem, scilicet concauam, aut conueam est concentricus mundo, secundùm alteram verò est Eccentricus: cuiusmodi est Orbis augem deferens, qui proinde partim Concentricus, partim Eccentricus est. CONDITIONARIVS apud Astronomos dicitur planeta sequens 159. conditionem temporis: vt si diurnus de die sit supra terram, nocturnus verò de nocte lustret superius hemisphærium. Præcipuè autem id in luminaribus vsurpatur: vnde & luminare conditionarium absolurè dicitur illud, cui competit prærogariua hylegij, & cæteris omnibus antefertur, vt Luna de nocte post Solis occasum: Sol in spatijs cirepusculinis, aut interdiu, &c. CONFINIVM, teste Valla, idem importat, ac fines, seu termini planerarum: est que cum plures planetæ fuerint in ijsdem, aut in aliorum terminis constituti. CONGRESSVS Coniunctio. Vide in V. Coitus 160. COODROMVS, Græcè dicitur planeta, præsertim Luna solitaria, cùm nulli alij applicat, siue corpore, siue radio. Quod est ratio quædam notabilis detrimenti in planetis maximè promiscuis, quales sunt Luna, & Mercurius, qui aliorum semper radio, & subsidio gaudent. Hæc autem passio à Latinis dicitur Feralissas. CONSTELLATIO est congeries plurium stellarum in certam 162. quandam formam, & imaginem redacta, quales sunt omnes Asterismi, atque Imagines octauæ sphæræ. Antiqui enim Astronomi ad fixarum naturam explicandam, earumque numerum distinguendum, ac memoriâ retinendum, colligarunt eas in plures imagines, quarum singulæ, sui consideratione, nos prudenter ad earum naturæ noriam manuducerent: Qua de re vide quæ fusiùs dicemus in V. Imagines Cælestes. CONTACTVS, teste Valla, est conjunctio partilis duorum

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MATHEMATICVM. 121 tur. See Vitellio in Opt. lib. 1. CONCENTRICUM is also called everything that has the same 158. center as another; just as, on the contrary, Eccentricum is that which has a different center. Hence among astronomers the concentric are called those heavenly spheres whose center is the same as the center of the world: but the eccentric are those which, although they surround the earth, yet have a center different from the center of the world. Both, however, are divided into Concentricum and Eccentricum simply, and Concentricum and Eccentricum in a qualified sense. Concentricum simply is when both surfaces of the sphere, both the concave and the convex, are concentric with the center of the world; similarly, Eccentricum simply, when neither surface has the center of the world as its center. Eccentricum in a qualified sense is when the sphere, according to only one surface, namely the concave or the convex, is concentric with the world, but according to the other it is eccentric: of this kind is the sphere carrying the apogee, which therefore is partly concentric and partly eccentric. CONDITIONARIVS is the name given by astronomers to a planet following 159. the condition of the time: as if a diurnal planet by day were above the earth, but a nocturnal one by night traversed the upper hemisphere. It is used especially of the luminaries: hence a conditionary luminary is absolutely called that to which the prerogative of hyleg belongs, and which is preferred before all the others, as the Moon by night after the setting of the Sun: the Sun in the twilight hours, or by day, etc. CONFINIVM, according to Valla, means the same as the bounds or termini of the planets: and this is when several planets are situated in the same ones, or in the termini of others. CONGRESSVS, conjunction. See in V. Coitus 160. COODROMVS is the Greek name for a planet, especially a solitary Moon, when it applies to no other, whether by body or by ray. This is a certain notable cause of detriment in planets, especially those that are mixed, such as the Moon and Mercury, who always enjoy the ray and support of others. This condition is called by the Latins Feralissas. CONSTELLATIO is a collection of several stars reduced into a certain 162. form and image, such as all Asterisms and the Images of the eighth sphere. For the ancient astronomers, in order to explain the nature of the fixed stars, and to distinguish their number, and to keep it in memory, gathered them into several images, each of which, by its own consideration, would prudently lead us to the knowledge of their nature: on this matter see what we shall explain more fully in V. Celestial Images. CONTACTVS, according to Valla, is the partial conjunction of two

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122 LEXICON planetarum, qui se corpore tangant[ur], quæ, alio nomine, dicitur Agglutinatio, Synodus, &c. Verum Contactus dicit aliquid aliud quàm Synodus, & Conjunctio: Nam hæc tantum dicit, vt planetæ conueniant in vno eodemque gradu Zodiaci, aut in eodem circulo positionis, etiamsi corpore distent, & in latum: Contactus verò importat[ur] talem corporum conuenientiam, qua se inuicem tangant; & adhuc agglutinatio talem contactum, qui sit ad vnguem, ac propemodum penetratio. 164. CONTRATRATOS, & Micros Contratatos aliquibus, teste Kirchero in Oedipo Ægyptiaco, audiunt duæ stellæ valdè præsignes, sibi in rectum angulum respondentes, nec longè ab inuicem dissitæ; Arcturus videlicet, & spica Virginis: Et ille quidem, quia corpore aliquatenus grandior, simpliciter Contratatos appellatur; hæc verò quia minor aliquantò, & situ apparet inferior, Micros, hoc est paruus, Contratatos dicitur. 165. CONTRANTISCIA vulgò audiunt paralleli declinationis secundarij, quos Imperantes, & Obedientes vocitamus: suntq[ue] duæ partes signorum, quæ æqualiter hinc inde distant ab Æquatore; ita vt habeant eandem numero declinationem, regione tamen diuersam: hoc est vna tot gradus declinationis borealis; altera totidem australis. Atque in partibus Eclipticæ extrahuntur à signo opposito eius Antiscij, & gradibus, qui ad triginta supersint. Sic ponamus, Solem exempli gratiâ, teperiri in gt. 12. Arietis; eius Antiscium erit in gt. 18. Virginis. Contrantiscium etiam in gt. 18. Piscium: habent enim eandem numero declinationem, sed denominatione diuersam. Porrò Contrantiscia planetarum reputantur non secùs, ac eorum oppositiones; sicut Antiscia intuentia speciem habent conjunctionis: Qua de re fusè diximus in V. Antiscia. 166. CONVERSA directio est deductio significatoris ad locum promissoris motu primi mobilis facta, contra successionem signorum. Hujusmodi directionem apertè admittit Ptolemæus lib. 3. c. 14. docetque imptimis per eam dirigendum esse Aphætam ad Cardinem Occidentis, quia, inquit, Dominum vise abscendit, stellas verò interjectas, eorumque radios non occidere, sed tantùm addete, vel demere aliquot annos ijs, qui generaliter per prorogatorem collecti sunt, quia, subdit, non ipsa vadunt ad prorogatorem, sed prorogatos ad eas. Quare non est audiendus 167. Argolus, qui vult, Ptolemæum non majorem vim in hac directione conuersa agnouisse, quam, quæ importat directionem ascendentis ad oppositum Aphætæ. Cæterùm longè diuersum esse hunc motum à motu directo, luculentissimè probat Titus in cælesti Philosophia lib. 3. cap. 6. vbi benè aduettit Cardines, qui semper fixi consistunt, non posse dirigi hoc motu, sed tan-

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122 LEXICON of the planets, which touch each other by their bodies; this, by another name, is called Agglutination, Synodus, etc. But Contactus says something other than Synodus and Conjunctio: for these only say that the planets agree in one and the same degree of the Zodiac, or in the same circle of position, even if they are distant in body and in breadth: but Contactus imports such an agreement of bodies, by which they touch one another; and still more, agglutination, such a contact as is exact to a hair’s breadth, and almost a penetration. 164. CONTRATRATOS, and Micros Contratatos, according to some, as Kircher testifies in the Oedipus Aegyptiacus, are the names given to two very notable stars, answering each other at a right angle, and not far distant from one another; namely Arcturus and the Spica Virginis: and the former, because it is somewhat larger in body, is simply called Contratatos; but the latter, because it is somewhat smaller and appears lower in position, is called Micros, that is, little Contratatos. 165. CONTRANTISCIA are commonly called the secondary parallels of declination, which we call Imperantes and Obedientes: and they are two parts of the signs, which are equally distant this way and that from the Equator; so that they have the same declination by number, but different in region: that is, one has so many degrees of northern declination; the other as many of southern. And in the parts of the Ecliptic they are reckoned from the opposite sign of its Antiscia, and from the degrees that remain above thirty. Thus let us suppose, for example, the Sun to be in 12° Aries; its Antiscium will be in 18° Virgo. The Contrantiscium also in 18° Pisces: for they have the same declination by number, but different in denomination. Moreover, the Contrantiscia of the planets are accounted no otherwise than their oppositions; just as the Antiscia, when viewed, have the appearance of conjunction. On which matter we have spoken at length in V. Antiscia. 166. CONVERSA direction is the bringing down of the significator to the place of the promissor, made by the motion of the primum mobile, against the succession of the signs. A direction of this kind Ptolemy plainly admits, book 3, ch. 14, and especially teaches that by it Aphæta is to be directed to the angle of the West, because, he says, the lord of the path rises, but the intervening stars and their rays do not fall, but only add or take away some years from those which are generally collected by the prorogator, because, he adds, they themselves do not go to the prorogator, but the prorogated to them. Wherefore one should not listen to 167. Argolus, who wants Ptolemy to have acknowledged no greater force in this converse direction than what imports the direction of the ascendant to the opposite point of the Aphæta. Moreover, that this motion is very different from the direct motion Titus most clearly proves in Celestial Philosophy book 3, ch. 6, where he well notes that the Angles, which always remain fixed, cannot be directed by this motion, but can-

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MATHEMATICVM. 125 tum moderatores, hoc est planeras, & Fortunæ partem, qui moru primi mobilis rapiuntur, arque ad loca promissorum deduci possunt, sed tamen addit, hoc motu dirigi solum posse prædictos moderatores ad siderum radios accepros in siru mundi, non autem in Zodiaco: Sed de hac re vide quæ fusiùs diximus in V. Directio. Vocat autem Prolemæus hunc dirigendi modum Horinaum, sicut & rectum Actinobolum, de quibus etiam suo loco. 168. CONVEXVM, ex Virellione lib. 1. opt. defin. 3. dicitur corpus seu superficies, aut linea, quæ extrinsecus regularem aliquam curuitarem habeat: Qua ratione omnia corpora solida, & rotunda dicuntur conuexa: Similiter omnes orbis, & Sphæræ secundum superficiem extimam, qua junguntur orbibus superioribus; si ut & isti ex parte, qua illis junguntur, dicuntur etiam secundùm interiorum superficiem, concaui. Circulus autem secundùm eandem lineam, qua efformetur, dici poterit concauus, & conuexus: Concauus quidem in ordine ad aream, quam circumambit, quia respectu illius haber intinsecus curuitatem; conuexus autem extra illam, quia haber extrinsecus curuitatem. Vide quæ paulò antè diximus in V. Concauus. 169. CONVS propriè dicitur nux pinea, quæ ex lato in acutum definit. Hinc apud Geometras sumitur pro figura solida quæ turbini contraria sit, & ex acuto ampliatur in latum. Est igitur basis Coni circulus, cujus centrum per lineam rectam conceptam in ejus medio conjungarur cum apice ejusdem coni, qui terminarur in puncto. Ad ipsum autem concipiendum præcipit Euclides, menti obijciendum esse triangulum, cujus manente vno latere eorum, quæ circa rectum angulum, circumductum triangulum in seipsum seuoluitur, vnde moueri cæperat circum allumptam figuram. Arque si quiescens recta linea æqualis sit alteri, quæ circa rectum angulum conuestitur; Conus ille sit Orthogonius: si minor, sit Amblygonius: si verò major, Oxygonius. Quorum differentiam in triangulis planis tradidimus suis in locis. Porrò axis Coni intelligitur esse linea illa quiescens, circà quam triangulum voluitur, ac terminarur ad apicem Coni, & centrum basis; cui Conus innititur. Vid. plura apud Clauium in Euclid lib. 11. defin. 18. & seq. 170. COR Cæli dicitur gradus Zodiaci incidens in angulum me- dijcæli, hoc est, in lineam meridianam. Potissimùm id attenditur apud Arabes, aliosque seruantes modum æqualem in cælesti Themare erigendo. Quandoquidem diuidebant Zodiacum in duodecim partes æquales, singulis domibus triginta gradus Zodiaci tribuendo, neglecto proisùs æquatore. Qui debat, vt singulis domibus singula correspondeant signa, &

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MATHEMATICVM. 125 then the directors, that is, the planets, and the part of Fortune, which are carried by the motion of the primum mobile, and can be led to the places of promises; but he adds that by this motion the aforesaid directors can be directed only to the rays of the stars received in the situation of the world, not however in the Zodiac: but on this matter see what we have said more fully in V. Directio. Ptolemy, however, calls this mode of directing Horinaum, just as he also calls the straight one Actinobolum, concerning which also in its proper place. 168. CONVEX is said, from Virellion, lib. 1. opt. defin. 3, of a body or surface, or line, which on the outside has some regular curvature: for which reason all solid bodies and round bodies are called convex. Likewise all spheres and globes, according to the outer surface by which they are joined to the superior spheres; and if also on that part by which they are joined to them, they are likewise called concave according to the surface of the interior. A circle, however, according to the same line by which it is formed, can be called concave and convex: concave indeed in relation to the area which it surrounds, because with respect to that it has an inward curvature; convex however outside that, because it has an outward curvature. See what we said a little before in V. Concauus. 169. A CONE is properly called a pine nut, which ends from broad to sharp. Hence among geometers it is taken for a solid figure contrary to a top, and widening from sharp to broad. The base of the cone is therefore a circle, the center of which, by a straight line conceived through its middle, is joined with the apex of the same cone, which ends in a point. But in order to conceive it, Euclid prescribes that a triangle be set before the mind, one side of which remaining fixed, the triangle drawn around the others, about a right angle, rolls itself back into itself, whence it had begun to move about the assumed figure. And if the resting straight line be equal to another which is drawn around a right angle, that cone is Orthogonius; if smaller, Amblygonius; if larger, Oxygonius. We have given the difference of these in plane triangles in their proper places. Moreover, the axis of the cone is understood to be that resting line around which the triangle revolves, and it terminates at the apex of the cone and the center of the base upon which the cone rests. See more in Clavius on Euclid, book 11, definition 18, and following. 170. The HEART OF THE HEAVEN is called the degree of the Zodiac falling on the angle of the midheaven, that is, on the meridian line. This is chiefly observed among the Arabs and others who preserve the equal method in erecting the celestial scheme. For they divided the Zodiac into twelve equal parts, assigning thirty degrees of the Zodiac to each house, the equator being entirely neglected. Which should be, so that to each house a sign may correspond, and

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124 LEXICON cum numerò gradum, quem obtinebat horoscopus, tenerent etiam domus succedentes in consequentibus signis; ac proinde gradus, qui incidebat in cuspidem domus decimæ non semper erat idem, ac qui ex amussi cadebat in lineam meridianam (qui solus dirigendus erat per ascensiones rectas) sed quandoq[ue] longè diuersus, ac distans. Vnde ad eum dignoscendum, seorsim signabant in decima, hoc vocabulo prænotantes: Cor cæli. 171. COR Hydræ. Arab Aipherad, stella fixa primæ (alijs secundæ) magnitudinis de natura Saturni, & Venetis, existens in gr. ferè 23. Leonis cum latitud ne australi totidem ferè graduum. Hæc cum sit naturæ mixtæ ex contrarijs qualitatibus, Saturninis tamen prædominantibus, affect humorum insitam in ipsa natura corruptionem, præsertim cum malo radio Venetis, aut Saturni: Et si in alienjus ortu cum Anæreta fuerit, portendit venenum. Oritur Romæ cum gr. 2 Virginis. 172. COR Leonis, Regulus, Basiliscus. Arabicè Kalb eleced, stella fixi, seu primæ, seu secundæ magnitudinis, sed tamen ob sui præstantiam inter primas, & præcipuas computata, de natura Martis, & louis consistens in Ecliptica, atque in longirudine in gr. 25. Leonis priuni mobilis. Est princeps, & potissima inter stellas regias, quæ in horoscopo, medio Cæli, aur cum luminaribus reperia, amplam fortunam, magnosque semper honores pollicetur. Nihilominus est etiam abscindentis naturæ ob participationem cum Marte, vt proinde in horoscopo, aliquam semper afferat corporis discretiam. Oritur Romæ atque in cæteris Orbis partibus (cùm enim consistat ferè in Ecliptica, paruam differentiam importat) cum gr. 25. Leonis, cum eodemque mediat Cælum, & occidit: Vide amplius in V. V. Basiliscus, & Regulus. 173. COR Scorpij, Græcè Antares, stella fixa Regia, sed tamen violenta primæ magnitudinis de natura Martis, & louis, existens nunc temporis in gr. 5. Sagittarij, cum totidem ferè latitudinis meridionalis. Est item venenosæ naturæ, abscindens & humorum corruptrix. Ea tamen in horoscopo reperta cum Luna, inquit Stadius, immensas tribuit diuitias, facit ductorem milium, atque ad magnos honores euehit Si verò cum Marte, aut cum Saturno fuerit, bella, & labores portendit, grauesque causas irarum. Est opposita ex diametro Pallilitio, seu oculo australi Tauti, primæ item magnitudinis, ac regiæ; vt proinde mirum non sit, si in præcipuis figuræ cardinibus reperta magna promittat, quippe quæ significationes cum illa commiscet. Oritur Romæ cum gr. 8. Sagittar. occidit verò cum 28 Scorpij. IN COR DE SOLIS dicitur esse planeta, cùm non distiterit ab eo

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124 LEXICON and the subsequent houses in the following signs also held the degree occupied by the horoscope; and therefore the degree that fell on the cusp of the tenth house was not always the same as that which, from the rule, fell on the meridian line (which alone was to be directed by right ascensions), but sometimes very different and distant. Hence, in order to distinguish it, they marked it separately in the tenth, prefixing this term: Cor cæli . 171. Cor Hydræ . Arabic Aipherad , a fixed star of the first magnitude (by others of the second), of the nature of Saturn and Venus, situated at about 23 degrees of Leo, with southern latitude of about the same number of degrees. Since it is of a mixed nature from contrary qualities, though with Saturnian qualities predominant, it affects the humors, and the corruption inherent in its own nature, especially when under an evil ray of Venus or Saturn. And if, in someone’s nativity, it should be with the Anaretic point, it portends poison. It rises at Rome with 2 degrees of Virgo. 172. Cor Leonis , Regulus, Basiliscus. In Arabic Kalb eleced , a fixed star, of either first or second magnitude, but nevertheless, because of its excellence, counted among the first and principal ones, of the nature of Mars and Jupiter, lying on the Ecliptic, and in longitude at 25 degrees of Leo, the first mobile. It is the chief and most powerful among the royal stars, which, when found in the horoscope, Midheaven, or with the luminaries, promises great fortune and always great honors. Nevertheless, because of its participation with Mars, it is also of a cutting nature, so that in the horoscope it always brings some bodily disfigurement. It rises at Rome and in the other parts of the world (for since it lies almost on the Ecliptic, it brings little difference) with 25 degrees of Leo, and with the same it culminates and sets: see more in V.V. Basiliscus and Regulus . 173. Cor Scorpij , in Greek Antares , a royal fixed star, but nevertheless violent, of the first magnitude, of the nature of Mars and Jupiter, now situated at 5 degrees of Sagittarius, with about the same amount of southern latitude. It is also of poisonous nature, cutting and corrupting the humors. Yet when found in the horoscope with the Moon, Stadius says, it grants immense riches, makes a leader of thousands, and raises one to great honors. But if it be with Mars or with Saturn, it portends wars and labors, and grievous causes of anger. It is exactly opposite to Pallilitius, or the southern eye of Taut, likewise of the first magnitude and royal; so it should not be surprising if, found in the principal angles of a figure, it promises great things, since it mixes its significations with that star. It rises at Rome with 8 degrees of Sagittarius; it sets with 28 degrees of Scorpio. IN COR DE SOLIS a planet is said to be, when it has not been separated from it

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MATHEMATICVM. 115 plus min. 19 quantum videlicet importat aggregatum semidiametrorum disci solaris, & ipsius Planetæ. Apud Arabes dicitur esse in Cazimi. Vide sibi. CORONA Austr. na sidus est in cælo ad australem plagam (sic < 175.> dicta ad differentiam Septentrionalis) alio nomine Rota Ixionis, constans stellis tredecim, omnibus ferè de natura Saturni, & Martis, atque existens nunc temporis in longitudine in principio Libræ. Ea in horoscopo ob stellarum inibi consistentium malignitatem tantumdem malorum affert, quantum boni deceiunt stellæ de natura louis, & Veneris, oppositis vtique rationibus. CORONA Septentrionalis dicta Gnossia, Ariadnes &c. Sidus < 176.> in cælo ad borealem plagam propè Bootem constans stellis 8. at Keplero, & Baiero oculatorioribus omninò 10 ob sui pulchritudinem, splendorem, varietatem, ferè omnium quæ sunt in cælo siderum celeberrimum, atque omnium ferè nationum summis laudibus decantatum. Quippe quæ apud Perlas dicitur Piramis, hoc est sertum pupilla, apud Arabes Alphecca seu alphesal id est aperitio, aperit enim suo exortu iucunditatem Veris, & prata floribus cælum ipsum tribuit æmulari: ad quod fortè allusisse visus est bellè Muretus, cùm cecinit: Esse rosas cali merisò quis dixeris Astra? Astra, sed & terra dixeris esse Rosas. Inter præcipuas stellas est quæ Arabicè dicitur Mumir, id est pupilla secundæ magnitudinis de natura Veneris, & Mercurij existens nunc temporis in gr. 28. Scorpij cum latitudine boreali gr. ferè 41. De ea horoscopante ita eleganter cecinit Manilius lib. 5. Astronom. Clara Ariadnea quondam monumenta corona Et molles tribuent arces, hinc dona puella. Namque nisent: illic oriens est ipsa puella. Ille colet nitidis gemmantem floribus hortum, Pallentes violas, & purpureos byacinibus, Vernantisque rosæ rubicundo sangue florem; Aut varios nectet flores, sertisque locabit. Effingetque suum similes: in mutua pressos Incoquet, atque Arabum siluis mulcebit odoreo Et medios vnguenta dabit referentia status Vt sis adulserio succorum gratia maior. Hæc ille; quibus olim ego ipse piè ludens in Diui Stephani < 177.> Protomartyris adornandis laudibus vsus sum: dictaque est Panegyris, editaque Patauij anno 1657. Porro corona hæc non adeò innocens atque amabilis, vt non aliquid mali afferat, pam producit ventos, & pluuias, & tempestates in mari faciti

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MATHEMATICUM. 115 plus or minus 19, namely, as much as the sum of the semidiameters of the solar disk and of the planet itself amounts to. Among the Arabs it is said to be in Cazimi. See there for itself. CORONA Australis is a star in the sky on the southern side (so called, , in distinction from the Northern) otherwise named the Wheel of Ixion, consisting of thirteen stars, all almost of the nature of Saturn and Mars, and now at this time being in longitude at the beginning of Libra. In a horoscope, because of the malignity of the stars there placed, it brings as much evil as beneficent stars of the nature of Jupiter and Venus bring good, by opposite reasons. CORONA Borealis, called Gnossian, of Ariadne, etc., is a star in the sky on the northern side, near Bootes, consisting of 8 stars, or, according to Kepler and Bayer, of 10 at the most, because of its beauty, splendor, and variety, celebrated above almost all the stars that are in the heavens, and extolled with the highest praises by almost all nations. Indeed, among the Persians it is called Piramis, that is, the crown of the pupil; among the Arabs, Alphecca or alphesal, that is, opening, for by its rising it opens the delight of spring, and makes the meadows, with flowers, seem to rival the heavens themselves: to which Muretus perhaps seemed to allude elegantly when he sang: Who would say the stars are roses of the sky? They are stars, but you would also say that the stars are roses of the earth. Among the chief stars is one which in Arabic is called Mumir, that is, the pupil, of second magnitude, of the nature of Venus and Mercury, now being at 28 degrees of Scorpio, with northern latitude of about 41 degrees. Concerning this star when horoscoping, Manilius sang elegantly in book 5 of the Astronomica: The famous memorials of Ariadne’s crown will once grant gentle citadels, whence gifts to the maiden. For there they will shine; there the maiden herself is rising. He will cultivate a garden sparkling with bright flowers, pale violets, and purple hyacinths, and the blossom of springing roses with reddish blood; or he will weave various flowers and place them in garlands. And he will fashion his own likenesses: pressed together in mutual embrace he will prepare them, and will soothe with Arab perfumes the woods, and he will give the middle places ointments bringing back their appearance, so that by sweetening the juices your grace may be greater. Thus he; with which words long ago I myself, playfully and piously, made use in the adornment of the praises of Saint Stephen, the Protomartyr; and it was called a Panegyric, and published at Padua in the year 1657. Moreover, this crown is not so innocent and lovable that it does not bring some evil; it often produces winds, and rains, and storms at sea.

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126 LEXICON atque eius ortus matutinus cum Sole facit aërem frigidum, tu bidum, & ventosum. 178. CORONÆ in plural dicuntur ab aliquibus circuli altitudinem, Arabicè Almicantharath. Paralleli nempè ad horizontem atque ad verticem terminantes, quorum ope siderum altitudines dimenimur, cò quia singuli instar coronæ circumdare videntur verticem, aut horoscopum. Vide in V. Almicantharath. 179. CORONÆ etiam Latinè dicuntur, quæ à Græcis Halones, species quæ tam acensionum, quæ in sublimi videntur circà corpora p[er]ta stellarum, præcipuè verò circà luminaria: eas fieri inquit Vitellion in vapore leviter condensato. Vapor enim iste à sidere attractus in ea aëris regione, quæ sideri immediatè subest ab incidentibus eius radijs illustratur, & fulgorem illum facit, si nilem prorsus ei, quem videmus in Atmosphæra circà horizonem in aurora, & post Solis occasum, & vocamus lucem crepusculinam H s affine est parelium, quod est Solis reuerberatio in nube rotida; ita vt alium Solem repræsentet. Porrò coronæ hujusmodi circà Solem semper ventorum præsagia sunt, ex ea parte spirantium: vnde ipsæ dissipari coeperint. 180. CORPVS Geometricè definitur, quod sit magnitudo, quæ potest tribus diametris sese ad angulos rectos intersecantibus mensurari: per quod explicatur tria dimensio, qua constituitur corpus in suo esse longum, latum, & profundum. 181. CORVS, siue Cæurus ventus est Occidentalis, lateralis, Fauonio spirans ab oriu solstitiali, Aquiloni directè oppositus, sic dictus à siccitate: est enim ab initio siccus, licet posteà euadat frigidus, & humidus: Plate solet in æquinoctio autumnali cum maxima violentia, adducens procellas niues, grandines, atque interdum fulgura. Eò potissimùm infestatur Apulia: nisi spirauerit sereno cælo, nubila plerumque spectantur in Oriente. A Græcis Argestes diciunt à procellis, quas excitat, item & Sciron à rupe quadam vnde spirat, nec-non & Olympias à monte Olympo. 182. CORVS sidus in cælo ad australem plagam circà Colurum æquinoctiorum sub signo Libræ continens stellas septem de natura Veneris, & Saturni, quarum præcipua est quæ in ala dextra malignantis natutæ Arabicè Algorab 1ertiæ magnitudinis, quæ Romæ oriùr cum gr 13. Libræ, occidit verò cum 7 Virgin. 183. COSMICS idipsum sonat Græcè, ac Latine Mundanus: sed potissimùm vsurpatur de oriu, & occasu siderum matuino. Et ortus quidem cosmicus est, quando signum, aut stella mane vnà cum Sole suprà horizontem ascendit: vt Romæ canis major Sirus, verbi gratiâ diciùs oriti cosmicè; quia mane circà Kalendas Augusti cum Sole emergit ex horizonte. Impropriè

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126 LEXICON and its morning rising with the Sun makes the air cold, dark, and windy. 178. CORONÆ are said in the plural by some to mean circles of altitude, Arabic, Almicantharath. Namely, the parallels terminating toward the horizon and the zenith, by whose aid we measure the altitudes of the stars, because each seems to encircle the zenith, or the horoscopic point, like a crown. See in V. Almicantharath. 179. CORONÆ are also called in Latin those which the Greeks call Halones, kinds which are seen as halos in the heights around the bodies of the stars, especially around the luminaries: Vitellio says that these are formed in a vapor lightly condensed. For this vapor, drawn by the star into that region of the air which lies immediately beneath the star, is illuminated by the incident rays, and makes that gleam, if not exactly the same as that which we see in the atmosphere around the horizon at dawn, and after sunset, and which we call the twilight light. It is akin to the parhelion, which is the reflection of the sun in a round cloud; so that it represents another sun. Moreover, such crowns around the Sun are always omens of winds, from that quarter from which they are blowing: whence they begin to be dispersed. 180. CORPUS is defined geometrically as a magnitude that can be measured by three diameters intersecting one another at right angles: by which is explained the threefold dimension, by which a body is constituted in its being as long, broad, and deep. 181. CORVS, or Cæurus, is a western wind, lateral, blowing as Fauonius from the summer rising, directly opposite the Aquilo, so called from dryness: for it is dry at the beginning, although afterward it becomes cold and humid: it usually blows in the autumnal equinox with the greatest violence, bringing storms, snow, hail, and sometimes lightning. Apulia is especially afflicted by it: unless it blows in a clear sky, clouds are usually seen in the East. By the Greeks it is called Argestes from the storms it excites, also Sciron from a certain rock from which it blows, and likewise Olympias from Mount Olympus. 182. CORVS, a constellation in the sky in the southern part around the Equinoctial Colure, under the sign of Libra, containing seven stars of the nature of Venus and Saturn, of which the principal is the one in the right wing of the malignant nature, Arabic Algorab, of third magnitude, which at Rome rises with 13 degrees of Libra, but sets with 7 degrees of Virgo. 183. COSMICS means the same in Greek as Mundanus in Latin: but it is especially used of the morning rising and setting of the stars. And a cosmic rising is when a sign, or a star, in the morning ascends above the horizon together with the Sun: as, for example, at Rome Canis Major, Sirius, is said to rise cosmically; because in the morning around the Kalends of August it emerges from the horizon together with the Sun. Improperly

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MATHEMATICVM. 127 vero dicuntur oriri cosmicè omnia astra, quæ interdiu suprà nostrum liemisphærium ascendunt, Sole adhuc ipsum tenente. Occasus autem cosmoscus propriè, & rigorose dicitur quando stella aut signum aliquod manè occidit, atque infra horizontem deprimitur, dum Sol eodem tempore in cardine Orientali oritur, & emergit: At enim improptè dicuntur etiam occidere cosmicè ea omnia sidera, quæ de die subter occiduum cardinem labuntur. Hujusmodi ortus, & occasus siderum passim mentionem faciunt Poëtæ, ac præsertim Virgil. in Georg. COSMOGRAPHIA dicitur artificiosa mundi descriprio, seu 184. delineatio cælorum simul, terræque rationem continens, & connectens. Eius quippe munus est indicare, quorum cæli spatium quibusvis terræ extantis partibus correspondeat, & è contra: Regiones & oppida, amnes & maria, montes & valles enumerare, locorum terminos constituere, quæ longitudo, quæ latitudo Geographica, quæ item Gnomonum differentia, vmbrarumque pro laricudine locorum projectio, vude longitudo, vel dierum breuitas, horarumque interualla expiscari possint, statuere & explicare. Docet insuper quæ sidera sint Polis sinitima, quæve in Arcton, quæve in Meridiem sectant: eorumdem ortus & occasus pro diuersis locorum positionibus censet: Denique, vt vno verbo dicam, est Astronomiæ, Geometriæque summa ad praxim redacta, & complanata. Ei adeò affinis est Geographia, vt sæpenumero tum ab scriptoribus exteris, tum etiam ab ipsis Professoribus vna alterius nomine appelleitur, ac sæpissimè confundantur. Reuerà tamen Cosmographia est scientia abstractior, atque vniuersalior: procedit enim certioribus, & vniuersalioribus principijs per certa quædam principia ab Geometria desumpta: Geographia vero, quia magis ad praxim tendit, estque rebus vti de facto sunt, & mutationi subjacent alligata, est etiam cum ipsis rebus, de quibus agit, mutationi obnoxia, & Cosmographia inconstantior. Nam sæculorum decursu, multifariaque illustrium scriptorum traditione, nec semper consona sibi, nec certa est, cum locorum enumerationi historiam attexat, atque vt plurimum, quæ Cuiitatum, quæ Gentium, quæ Nationum, quæ populorum origo fuerit, vndeque rebus indita nomina sint explicat: tum & insignia quæque naturæ opera enarrat, atque in terræ situ describendo vberior esse solet quàm sua parens Geographia: Vt profectò hæc differentia inter has nobilissimas scientias dignoscatur, vt quemadmodum Geographia rerum vsui, ac prudentibus, ita Cosmographia accommodatior sit earumdem peritix, atque hominibus sapientibus. COZIMON, & Casmon apud Ægyptios appellantur nodi luna- 185.

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MATHEMATICVM. 127 But all the stars are said to rise cosmically which by day ascend above our hemisphere while the Sun still holds its course. Cosmical setting, however, is properly and strictly said when some star or sign sets in the morning and is depressed below the horizon, while at the same time the Sun rises and appears in the eastern quarter. But improperly there are also said to set cosmically all those stars which by day sink below the western quarter. Poets frequently make mention of such risings and settings of the stars, and especially Virgil in the Georgics. COSMOGRAPHY is the artificial description of the world, or the delineation of the heavens together with the earth, containing and connecting the proportions of both. Its office is to indicate to which parts of the expanse of the heavens any projecting parts of the earth correspond, and vice versa; to enumerate regions and towns, rivers and seas, mountains and valleys; to establish the boundaries of places; to determine what longitude, what geographical latitude, what difference of gnomons, and what projection of shadows according to the latitude of places, whereby the length of days or their brevity, and the intervals of the hours, may be investigated; to set forth and explain these things. It also teaches what stars are near the poles, which incline toward the North, and which toward the South; it judges their risings and settings according to the different positions of places. Finally, to put it in a word, it is Astronomy and Geometry reduced to practice and made plain. Geography is so closely related to it that very often, both by foreign writers and by the Professors themselves, one is called by the name of the other, and they are very often confused. Yet in truth Cosmography is a more abstract and more universal science: for it proceeds from more certain and more universal principles, drawn from Geometry by certain principles. Geography, however, because it tends more to practice and is tied to things as they are in fact and subject to change, is also mutable along with the things of which it treats, and more inconsistent than Cosmography. For over the course of centuries, and through the varied tradition of distinguished writers, not always consistent with itself nor certain, it joins history to the enumeration of places, and for the most part explains what was the origin of cities, peoples, nations, and peoples, and from where names were given to things; then it recounts every notable work of nature, and is usually more abundant than its parent Geography in describing the situation of the earth. So indeed this difference between these most noble sciences is to be recognized: just as Geography is suited to practical matters and to prudent men, so Cosmography is more fitted to the skill of those same subjects, and to wise men. COZIMON, and Casmon are called by the Egyptians the knots of the moon- 185.

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128 LEXICON res, caput videlicet, & cauda Draconis: de quibus abundè di- ximus suo loco. CR 186. CRATER, Patera, Vena, Vas, &c. dicitur fidus ad austra- lem plagam supra corpus Hydræ, Arabicè Pharmaz vel Elkis, seu etiam Eluarad, constans stellis septem secundùm Prole- mæum; at juxtà Keplerum octo, & ex Baieri obseruarionibus vndecim, quæ omnes ferè sunt de natura Saturni, & Veneris. Earum præcipua est, quæ in fundo vasis terriæ magnitudinis; quæ in horoscopo alicujus reperta (inquit Firmicus) faciet, vt ille campos colat, & fontes, aut riuos, seu fluuios ab alueo suo ad alia loca deducat. Is etit quoque vinearum amator, & qui infæcundis arboribus fæcundos inserat surculos. Inde meri genialis amor, studiumque bidendi. Subdit perbelle Pontanus in sua Vrania. Quod si reperta fue- rit in occasu, sine vllo maleficarum aspectu, portendit mor- tem inter epulas, & ebrietates: cum malo vero radio malefi- carum, præsettim Saturni, præfocationem in aquis, aut in dolio vinario: Hæc Firmicus. 187. CREPUSCULVM dicitur dubia illa, & suboscuta lux, quæ mane ante Solis ortum, & vespere post illius occasum conspi- citur in partibus horizontis ad Orientem, & Ocidentem (cre- perum enim Antiquis idem sonabat, ac dubium) Vnde & ma- tutinum, & vespertinum Crepusculum appellatur. Absolutè tamen sumitur p[otes]t vespertino, quoniam matutinum proprio nomine Aurora postmodum dicta est: de qua suo loco dictum. Causa huius suboscuræ lucis est interfusa circà tellutem vapo- rum congeries, quam rectè Atmosphæram vocamus, quæ cum aëtem crassiorem suis halitibus reddat, inde est, vt is solares radios non exquisitè transmittat, sed aliquatenus deti- neat, ac reflectat; proindeque conspicuus reddatur, ac lucem Solis acceptam vniuersæ reræ communicet. Porro quoniam æstra non influunt, nisi per lumen, & juxtà majorem, aut mi- norem lucis intentionem, & extensionem diuersimodè agunt in hæc inferiora, vt luculenter in loco probarum est; ideò acutissime P. Titus in Cælesti Philosophia demonstrat, Solem 188. in spatijs crepusculorum repertum dirigendum esse non in circulis horarijs, seu positionis, in quibus fiunt proporrio- nales distantiæ à cardinibus, sed in circulis parallelis ad hori- zontem, in quibus jugiter, & successiue magis, ac magis sem- per intenditur aut remirtitur gradus lucis v[er]sque ad primum pa- rallelum, seu ipsum finitorem, in quo Sol constitutus clarissi- me micat; vel vlrimum parallelum depressionis gr. 18. sub fini- tore, vbi desinit illa lux, & incipit spatium noctis obscurum; disi

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128 LEXICON res, namely the head and tail of the Dragon: of which we have spoken sufficiently in their place. CR 186. CRATER, Patera, Vena, Vas, etc., is called the figure on the southern side above the body of Hydra, in Arabic Pharmaz or Elkis, or also Eluarad, consisting of seven stars according to Ptolemy; but according to Kepler, eight, and from Bayer’s observations eleven, which are almost all of the nature of Saturn and Venus. Its principal star is the one in the bottom of the vessel, of the size of the Earth; which, if found in someone’s horoscope (says Firmicus), will make him cultivate fields, and lead springs or rivers, or streams from their channel to other places. He will also be a lover of vines, and one who grafts fruitful shoots into infertile trees. Hence the genial love of wine, and the study of drinking. Pontanus very neatly adds in his Urania. But if it is found setting, without any aspect of the malefics, it portends death amid feasts and drunkenness; but with an evil ray of the malefics, especially Saturn, drowning in waters, or in a wine barrel: thus Firmicus. 187. CREPUSCULVM is called that doubtful and dim light which is seen in the morning before sunrise, and in the evening after sunset in the parts of the horizon toward the East and the West (for creperum among the Ancients signified the same as doubtful). Hence there is both morning and evening twilight. Yet it may be taken absolutely for the evening, since the morning twilight was afterward called by the proper name Aurora: about which something has been said in its place. The cause of this dim light is a mass of vapors interposed around the earth, which we rightly call the Atmosphere; since, by its exhalations, it makes the air thicker, and therefore does not transmit the sun’s rays exactly, but somewhat detains and reflects them; and consequently it becomes visible, and communicates the light received from the Sun to the whole earth. Moreover, since the stars exert influence only through light, and according to the greater or lesser intensity and extension of light act differently upon these lower things, as has been clearly proved in its place; therefore P. Titus very acutely demonstrates in Celestial Philosophy that the Sun, 188. when found in the spaces of twilight, must be directed not in the hour circles, or circles of position, in which proportional distances from the cardines are made, but in the circles parallel to the horizon, in which the degree of light is continually and successively more and more either increased or diminished, up to the first parallel, or the very horizon, in which the Sun, being situated, shines most brightly; or the lowest parallel of depression, 18 degrees below the horizon, where that light ceases and the dark space of night begins; thus

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MATHEMATICVM. 119 nisi fortè ob nimiam sphæræ obliquitatem, & Poli altitudinem, vt accidit in Noruegia, & reliquis locis borealibus circà Polum, in æstate Sole existente in Cancro tota nox sit crepusculina luce perfusa. In quo casu ingeniosè adueitir Adrianus < 189:> Negusantius Solem semper euadere vitæ moderatorem, etiamsi in Zodiaco, & æquatore triginta & plus gradus ab gradu horoscopante distiterit: nunquam enim tantum subtus horizontem deprimitur vt à linea ascendente distet plus gr. 18. vnde jure optimo in situ mundi computari debet in ascendente, atque adeo in loco prorogatorio. Nam in crepusculo vespertino non est idoneus, nisi intrà quinque tantum gradus subtus occasum, ijsque cosmicè non in Zodiaco, aut in æquatore computatis. Porro quomodo dirigendus sit Sol existens in spatijs crepusculorum tradit ipsemer Titus lib. 3 cap. 14. can. 5. & clarius in primo Mobili, can. 20. adjecta ad finem tabula crepusculorum ab gradu 38. eleuationis Poli vsque ad grad. 60. Sed enim, vt ad suboscuram illam lucem, quam diximus in Atmosphæra fieri ob solares radios interceptos, reuerramur; præstat hic curiosam nec omnino injucundam quæstionem exponere: Quî, inquam fiat, vt post crepusculum vespertinum, quando lux illa suboscura deficit, Sole decem & octo gradibus infrà horizontem depresso, ac mane etiam antelucanis horis immediatè ante quam Sol lineam crepusculinam attingat, tenebræ magis magisque intendantur; aërque per semicirciter horam obscurior fiat, quam in reliquo noctis spatio; cum potiùs ratio expostulare videatur, id circà medium noctis, quo tempore Sol minus valet aërem circumfusum suis radijs illustrare ob terreni corporis interpositionem, debere maximè euenire. Quænam igitur causa est, cur non id media nocte accidat, sed immediatè post crepusculum vespertinum, & manè ane auroram; vt vel hoc vnum vbi alia signa desint, euidentissimum sit aduenrantis Auroræ? Hoc autem certissime euenire, quius pro suo libitu experire potest, sereno exlo, & luna silente, quando ipsa sua luce non valer tenebras istas discutere, proure ego sæpiùs obseruari. Huius arcanæ obscuritatis obscurissimæ quæstioni non obscure respondet eruditissimus Cabxus in Meteoris tono primo super textum Arist. 50. Quia, inquit, Cum Sol circà terram rotari intelligitur, intelligimus etiam terram vtpote corpus opacum, projere conum umbrosum in partem obuersam Soli; dumque Sol moueri intelligitur infrà terram, intelligimus etiam conum umbrosum circumferri, vt nova pars aeris terra circumfusa semper obscuretur, & nova illuminatur. Dum igitur Solis radius partem aeris ferire incipit, rare= I

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MATHEMATICUM. 119 unless perhaps because of the excessive obliquity of the sphere and the height of the Pole, as happens in Norway and the other northern places around the Pole, where in summer, when the Sun is in Cancer, the whole night is filled with twilight light. In which case Adrianus Negusantius cleverly notes that the Sun always escapes being the governor of life, even if in the zodiac and at the equator it has departed thirty or more degrees from the degree of the horoscope: for it is never depressed so far below the horizon that it is more than 18 degrees distant from the ascending line. Hence by the best right it ought to be reckoned in the position of the world as in the ascendant, and therefore in the prorogatory place. For in evening twilight it is not suitable, unless only within five degrees below the setting, and those in the cosmic sense, not reckoned in the zodiac or at the equator. Moreover, how the Sun, existing in the spaces of twilight, is to be directed is taught by Titus himself in book 3, chapter 14, canon 5, and more clearly in the Primum Mobile, canon 20, with a table of twilights appended at the end, from the 38th degree of elevation of the Pole up to the 60th degree. But since we are returning to that dim light, which we said is produced in the atmosphere because of intercepted solar rays, it is better here to set forth a curious and not altogether unpleasant question: how, I say, does it come about that after evening twilight, when that dim light fails, with the Sun depressed eighteen degrees below the horizon, and also in the morning, in the pre-dawn hours immediately before the Sun reaches the twilight line, the darkness becomes more and more intense, and the air becomes for about half an hour darker than during the rest of the night? Whereas reason rather seems to require that this should happen around midnight, at which time the Sun is less able to illuminate the surrounding air with its rays because of the interposition of the earthly body. What then is the cause that it does not happen at midnight, but immediately after evening twilight and in the morning before dawn, so that even by this one sign, where all others are lacking, the arrival of dawn is most evident? This certainly happens, and anyone may experience it at will, in a clear sky and with the moon silent, when its own light is unable to dispel these shadows, as I have often observed. To the question of this most hidden obscurity, the most learned Cabxus responds not obscurely in the Meteora, first treatise, on the text of Aristotle 50. For, he says, when the Sun is understood to revolve around the earth, we also understand that the earth, as an opaque body, projects a shadowy cone on the side facing the Sun; and when the Sun is understood to move below the earth, we also understand the shadowy cone to be carried around, so that a new part of the air surrounding the earth is always darkened and a new part illuminated. Therefore, while the Sun’s ray begins to strike a part of the air, it rare- I

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130 LEXICON facit etiam: rarefactus aer maiorem requirit locum, & consequenter partes vicina versus vmbram terra densantur; ex alia enim parte semper magis rarefiunt ex maiori lumine, vaporesque ex speciali instinctu refugiums illam lucem, vspote qua illos magis assenuas, & à densitate, ad quam natura impetu tendunt, retardat, & se trahunt ad conum umbrosum, & hinc intenduntur tenebra antelucana dum lucis radij accedunt ad vapores, qui nobis auroram creant: immò ex hoc rationem habebis trium effectuum, quos quisque experitur: Primus effectus est roris antelucani: ex ulla enim condensatione aeris, & fuga vaporum, ex vicini aeris rarefactione, & illuminatione consurgente, fit corpus illud grauius, & consequenter ima petit, & decidit roa aere quieto. Secundus effectus est manus frigus semper quacumque anni tempestate sub auroram, quam qualibet à ia noctis hora; hoc autem oritur ex ulla condensatione aeris ad confinium coni tenebrosi propter rarefactionem illuminati in proximo aeris. Tertiò communiter solet ventus seu aeris commasso sentiri sub auroram; quæ commotio oritur ex ulla condensatione, & rarefactione aeris. Hucusque Cabeus satis ingeniosè: sed de roris efformatione, vide quæ infrà dicemus suo loco. 190. CRITICI dies à Græco verbo Crisis (quod Latinè judicium sonat) ij appellantur, in quibus de morbis adueniantibus judicium aliquod fieri potest, quem finem, seu bonum, seu malum sortiri debeant. Nos decretorios vocamus, eò quod his præsertim diebus accidit extraordinarius quidam conflictus naturæ cum morbo, & acrior pugna, vt vel exinde appareat, quisnam sit de altero reportaturus victoriam. Tales sunt, in quibus Luna peruenit ad suos quadratos, oppositum, & locum radicalem, quem tenuit initio morbi. Hinc Medici omnes obseruant septimum quemque diem 14. 21. 27. quia totidem ferè dierum spatio Luna peruenit ad suum quadratum sinistrum, oppositum, quadratum dextrum, ac tandem ad suum locum radicalem. Verum, quoniam Lunæ motus in Zodiaco non est æqualis, aliquando enim citiùs aliquando tardius peruenit ad huiusmodi radios; ideò alij peritiores, id non ex numero dierum ausplicantur (licet vt plurimum huiusmodi configurationes septimo quoque die accidant) sed à reali, ac verò Lunæ motu; ita vt prima crisis quandoque præcedat, & sexto die accidat, quandoque etiam retardetur ex tardo motu Lunæ, & cadat in octauum diem: & sic de singulis. Quare soleriem Medicum expedit semper Ephemeridas præmanibus habere, & siderum motus, præsertim Lunæ, in dies singulos obseruare, vt probè suo munere fungi valeat, & ex astrorum positu discat medicamenta ægtis, congruis temporibus sub-

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130 LEXICON it also makes this point: rarefied air requires a larger place, and consequently the neighboring parts toward the earth’s shadow become denser; for on the other side they are always more rarefied by the greater light, and the vapors, by a special instinct, flee that light, since it more strongly thins them and, by the density toward which nature tends by impulse, delays them; and they draw themselves toward the shadowy cone, and hence the dawn-like darkness becomes more intense as the rays of light approach the vapors, which create the dawn for us: indeed, from this you will have the explanation of three effects that anyone experiences. The first effect is the morning dew; for from any condensation of the air, and the flight of the vapors, arising from the rarefaction and illumination of the neighboring air, that body becomes heavier and consequently moves downward and falls as dew in calm air. The second effect is the cold of the hand, which is always felt at dawn in whatever season of the year, more than at any hour of the night; this, however, arises from the condensation of the air at the boundary of the shadowy cone because of the rarefaction of the illuminated air nearby. Thirdly, a wind, or movement of the air, is commonly felt at dawn; this motion arises from condensation and rarefaction of the air. So far Cabeus, with sufficient ingenuity; but concerning the formation of dew, see what we shall say below in its proper place. 190. CRITICAL days are so called from the Greek word Crisis (which in Latin means judgment), because on those days some judgment can be made regarding approaching illnesses, to determine what end, whether good or bad, they are to have. We call them decisive, because on these days especially there occurs a certain extraordinary conflict of nature with the illness, and a sharper struggle, so that it may even become apparent which of the two will carry off the victory. Such are those days on which the Moon reaches its quadratures, opposition, and radical place, which it held at the beginning of the illness. Hence all physicians observe every seventh day, 14, 21, 27, because in roughly the same span of days the Moon reaches its left quadrature, opposition, right quadrature, and finally its radical place. But since the Moon’s motion in the Zodiac is not equal—for sometimes it reaches these aspects sooner, sometimes later—therefore others, more experienced, do not infer this from the number of days (although for the most part these configurations occur every seventh day), but from the real and actual motion of the Moon; so that the first crisis may sometimes come earlier and occur on the sixth day, and sometimes also be delayed by the Moon’s slow motion and fall on the eighth day; and so for each of the others. Therefore it is useful for the careful physician always to have ephemerides at hand and to observe the motions of the stars, especially the Moon, day by day, so that he may duly carry out his office and learn from the position of the stars the medicines for the sick, at suitable times sub-

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MATHEMATICVM. 131 ministrare. Prætereà extrà dies criticos, sunt & alij, quos vocant indicatiuos, in quibus accidit indicium aliquod, & initium fututæ crisis. Huiusmodi sunt quartus à die morbi, vel circà, qui est septemi indicatiuus, quo tempore Luna peruenit ad suum semiquadratum: (est enim aspectus iste licet aliàs imperfectus in hoc casu minimè negligendus, cum sic quadrati prodromus) item vndecimus, aut circà, qui est quartidecimi indicatiuus, in quo Luna suum sesquiquadratum tenet, & est oppositionis inchoatio, & indicium: tandem reliqui duo dies intermedij inter oppositionem, & reditum ad locum suum radicalem, in quibus Luna permeat secundum sesquiquadratum, quod est indicium futuræ crisis insecunda dichotoma, & in quo peruenit ad vltimum semiquadratum, quod est indicium eius, quæ fiet, mutationis cum Luna erit in suo loco radicali initio morbi. Denique non prætereundi < 192.> sunt reliqui dies in quibus Luna transit per omnes alios radios, præter modò enumeratos, quales sunt Sextiles, Trini, Quintiles, & Biquintiles ad locum suum radicalem, qui cùm sint natura sua boni, faciunt; vt natura in ijs roboretur, & vires acquirat ad resistendum morbo, sicut è contrà in alijs ptiùs enumeratis, cum sint natura mali, morbus augescit, atque iisdem armis, quibus naturam aggressus fuerat, denuò viribus potens factus, oppugnat. Et ideò Ptolemæus (siue quicumque alius sic Centiloquij anctor) in proposis. 60. præcipit inspiciendam esse in morbis Lunæ peragrationem in figura sexdecim laterum, sic inquiens. Super ægrosis criticos dies inspice, ac Lunæ peragrationem in angulis figura sexdecim laterum: Vbi enim eos angulos benè affectos smuenerss, benè erit languentis contrà malè si afflictos smuener s. Vbi per figuram sexdecim laterum omnes Lunæ positus ad locum suum radicalem significare voluit (vt nos in loco explicabimus) qui omninò sexdecim sunt, vt Keplerus acutè docet, ac felici omine discooperuit ex chordatum ad inuicem consonantia: duo videlicet Sextiles; duo semiquadrati; totidem Quintiles, bini etiam quadrati, bini tetragoni ac tandem bini sesquiquadrati, qui omnes vnà cum oppositione & redituad locum suum, sexdecim angulos irradiationis seu familiaritatis constituunt. Qua de re plura in Verbo Figura sexdecim laterum. Scripsit de diebus Criticis insigne volumen Andreas Argolus, qui lib. 1. cap. 21. aliquorum, ex his radijs mentionem facit (etsi alias non admittat, nisi communiter vsitatos) & vocat indicatiuos. CROTVS idem quod Centaurus sidus in cælo ad Australem < 193.> plagam nobis inuisum, de quo alibi dictum. Eo vtitur verbo I ij

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MATHEMATICVM. 131 ministering. Moreover, outside the critical days, there are also others, which are called indicative, in which some indication occurs, and the beginning of the future crisis. Of this kind are the fourth day from the day of the illness, or thereabouts, which is the indicative of the seventh day, at which time the Moon reaches its semiquadrate: (for although this aspect is otherwise imperfect, in this case it must by no means be neglected, since it is the forerunner of the square) likewise the eleventh, or thereabouts, which is the indicative of the fourteenth day, in which the Moon holds its sesquiquadrate, and is the beginning and indication of opposition; lastly, the remaining two intermediate days between the opposition and the return to its radical place, in which the Moon passes through the second sesquiquadrate, which is the indication of a future crisis in the second dichotomy, and in which it reaches the final semiquadrate, which is the indication of that change that will occur when the Moon is in its radical place at the beginning of the illness. Finally, the remaining < 192.> days are not to be passed over, in which the Moon passes through all the other aspects, except those just enumerated, such as the Sextiles, Trines, Quintiles, and Biquintiles to its radical place, which, since they are good by nature, cause that nature may be strengthened in them and gain strength to resist the illness, just as, on the contrary, in the others already enumerated, since they are evil by nature, the disease increases and, made powerful again by the same weapons with which it had attacked nature, it assaults nature anew. And therefore Ptolemy (or whoever else is the author of the Centiloquium) in proposition 60. commands that in illnesses the Moon's passage through a figure of sixteen sides is to be observed, saying thus: In the sick, observe the critical days, and the Moon's passage through the angles of the figure of sixteen sides: For where you shall find those angles well affected, it will be well for the sufferer; but badly if you find them afflicted. By the figure of sixteen sides he meant all the Moon's positions with respect to its radical place to signify (as we shall explain in the proper place), which are altogether sixteen, as Kepler sharply teaches, and under a lucky omen discovered from the consonance of chords with one another: namely two Sextiles; two semiquadrates; two Quintiles likewise, two squares, two tetragons, and finally two sesquiquadrates, which all together with the opposition and the return to its place, constitute sixteen angles of irradiation or familiarity. On this matter more in the Word Figure of sixteen sides. Andreas Argolus wrote an outstanding volume on the critical days, who in book 1. chapter 21. makes mention of some of these rays (though otherwise he admits none except the commonly used ones) and calls them indicative. CROTUS is the same as the constellation Centaurus in the sky in the southern < 193.> region, invisible to us, concerning which something has been said elsewhere. He uses that word I ij

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132 LEXICON Iosephus Scaliger ad Manilium. 194. CRVX Hispanicè elCruesero, fidus de nouo ab noui Orbis detectoribus discoopertum, sub ventre Centauri ad australem plagam, habens stellas quatuor in formam Crucis, quæ anti- quitùs erant informes, vna cum alia quaræ magnitudinis cir- ca ipsas. Nunc autem felici Crucis imagine insignita nauigantibus ad Austri oras in bonum omen cedii, quippe qui ex eius conspectu iter instituunt, sicut nostri antequam acus magnetica repetitetur ex aspectu stellæ polaris. CV 195. CVBVS apud Geometras est figura solida ex omni latere qua- dra, proindeque sex quadratis æqualibus comprehensa, quales sunt taxilli, & tesseræ, quibus in alueolo luditur. Dicitur 196. etiam Cubus apud Arithmeticos numerus æqualiter vtrinque æqualis, hoc est, qui sub duobus æqualibus numeris continetur: de quo alibi dictum est. 197. CVLEMEN apud Astronomos antonomasticè audii Medium Cæli, linea metidiana, & angulus decimæ domus; eò quod ad eum peruenientes planetæ, atque alia sidera summam alitudinem habeant, ac veluti in cæli fastigio collocentur. Significat apud Geneshliacos imperia, dignitates, officia publica, 198. opificium, maërem. Ratio autem, quare culmen sit naturalis actionum significator, atque inde dignitatum, officij Regni &c. est quam ingeniosè tangii P. Titus in Cælesti Philosophia lib i. cap. 17. conclus. 8. Quia, inquit, Luminaria, quæ sunt principales rerum omnium moderatores, ibi producunt qualitates maximè actiua: etenim propè sunt nobis, quam possint esse. Sed ex propè esse, sequitur ins: n[ost]ro qualitatis actiua, quia ex intensione actiuitas Quare eodem prorsus modo, quo Luminaria influunt qualitates vstales ab ortu; influunt etiam qualitates actiua à culmine. Atqui ex maiori actiuitate actionum claritas: ex hac, gloria, & laus: ex his tandem honores, & dignitates proueniunt, vt benè aduertit eruditissimus Pater Auersa in declarationibus factis ex decreto sacræ Congregationis ad eadem opera Titi. Qualitas enim actiua, inquit, ex ipsa actione se manifestat. 199. CVRSV vacuus dicitur planeta, apud Astronomos, quando documque fuerit ab alio separatus, nec prætereà applicat alteri, siue corpore, siue radio, sed est veluti solitatius & mærens aliorum auxilio destiturus, adeoque hæc passio inter majora detrimenta computatur, quæ à Latinis dicitur feraltas, & ea maximè in Luna attenditur. 200. CVRSV velox. Vide directus, Auclus numero. 201. CVRVILINEVM dicitur apud Geometras omne id, quod con-

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132 LEXICON Josephus Scaliger to Manilius. 194. CROSS in Spanish, el Cruesero, a faithful sign recently uncovered by the discoverers of the New World, beneath the belly of the Centaur toward the southern region, having four stars in the form of a Cross, which in ancient times were shapeless, together with others of various magnitude around them. But now marked with the fortunate image of the Cross, it serves as a good omen to sailors bound for the coasts of the South, since they set out on their journey from its sight, just as our people did before the magnetic needle was discovered, from the sight of the polar star. CV 195. CUBE among geometers is a solid figure equal on every side, and therefore enclosed by six equal squares, such as dice and gaming pieces, with which one plays in a small tray. It is also called 196. a Cube among arithmeticians, a number equally equal on both sides, that is, one contained under two equal numbers: about which something has been said elsewhere. 197. CULMEN among astronomers is, by antonomasia, the Midheaven, the meridian line, and the angle of the tenth house; because planets, and other stars, when they reach it, have their greatest altitude, and are placed, as it were, on the summit of the heavens. Among genethliacs it signifies powers, dignities, public offices, 198. craftsmanship, the mother. The reason, however, why the midheaven is the natural significator of actions, and hence of dignities, offices of state, and so forth, is very ingeniously touched on by Father Titus in Celestial Philosophy, book I, chapter 17, conclusion 8. Because, he says, the luminaries, which are the principal rulers of all things, there produce qualities most active; for they are as near to us as they can be. But from being near follows greater intensity in our active quality, because activity arises from intensity. Therefore in precisely the same way in which the luminaries influence vital qualities from the ascendant, they also influence active qualities from the midheaven. And from greater activity of actions comes distinction; from this, glory and praise; and from these at last honors and dignities arise, as the most learned Father Aversa wisely notes in the declarations made by decree of the Sacred Congregation concerning the same works of Titus. For the active quality, he says, manifests itself through the action itself. 199. COURSE vacuous is the planet, among astronomers, when, after it has been separated from another, it does not further apply to another, whether by body or by ray, but is as if solitary and sad, deprived of the help of others; and therefore this condition is reckoned among the greater detriments, which by the Latins is called ferality, and this is especially considered in the Moon. 200. COURSE swift. See direct, Node number. 201. CURVILINEAR is said among geometers of everything that con-

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MATHEMATICVM. 193 stat lineis curuis, vt sunt trianguli, & quadranguli considerati in cælestibus, qui omnes sunt curuilinei, cum efformentur, ex arcubus circulorum: Qua de re vide in V. Angulus. CVSIS Latinè dicitur quidquid in acumen desinit. Hinc 202. quia Cæli diuisio in duodecim domicilia ratione atcuum circulorum, ea in quasdam veluti cuspides terminat, hinc factum est, vt apud Astronomos singularum domotum initia Cuspides appellarentur. Et quatuor quidem puncta ottus, & occasus, Medij Cæli, & Imi, Cardines seu Anguli dicentur, reliqua verò domorum initia simplex cuspidum vocabulum retinerent. Porro singulatum domorum spatium triginta æquatoris gradibus mensuratur, facta ex æquo diuisione: quæque Zodiaci pars intercipitur intrà singularum domorum spatia, constituere dicitur talem domum, quæ etsi, vt modo dixi comprehendat spatium interjectum inter vnam & alteram cuspidem, eius tamen initium computatur à quinque præcedentibus gradibus æquatoris, & protenditur vsque ad grad. 25. eiusdem domus: ita vt planera, qui reperitur in grad. 20. Leonis verbi gratiâ in Zodiaco, habeatque præterea ascensionis rectæ grad. 142. atque in angulum Medij Cæli incidant grad. 24. eiusdem Leonis, etsi non peruenerit ad lineam meridianam, atque ad cuspidem domus decimæ, nihilominus dicetur, & reputabitur esse in decima domo. CY CYCLVS Græcè, Latinè circulus absolutè dicitur: magis 203. tamen pressè accipi solet pro integra revolutione certi cujusdam numeri annorum per orbem, donec ad initium redeat: vnde & Cyclus solaris, & Cyclus lunaris, & Cyclus decennouemmalis aurei numeri, quorum vsus, & sermo frequens in Kalendarijs. CYCLVS SOLARIS est revolutio annorum 28. ad inueniendam 204. literam Dominicalem; eò quod istæ post 28. annos eodem ptorsus ordine, ac priùs, redeunt. Hoc Cyclo vtebatur Ecclesia ante correctionem Gregorianam ad inueniendam literam Dominicalem: sed postea longè facilius, & expeditius inuenitur, vt videri potest apud Clauium in Computed Ecclesiastico. Nihilominus si quis hoc cyclo solari voluerit vti ad literam Dominicalem reperiendam, facili negotio id poterit. Siquidem anno Domini exhibito adijciantur nouem, & numerus inde compositus diuidatur per 28. nam numerus, qui ex diuisione relinquirur, erit numerus Cycli solaris. Quod si nihil ex quotiente remaneat; signum est, quod tunc numerus 1 iij

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in curved lines, as are triangles and quadrangles considered in the heavens, which are all curvilinear, since they are formed from arcs of circles. On this matter see under V. Angle. CUSIS in Latin is said of whatever ends in a point. Hence 202. because the division of the heavens into twelve houses, by reason of the arcs of the circles, terminates them into certain as it were points, it came about that among Astronomers the beginnings of the several houses were called Cusps. And indeed the four points, rising, setting, the Midheaven, and the Imum Coeli, will be called Angles or Cardinal Points, but the beginnings of the remaining houses will retain the simple name of cusps. Moreover, the space of each house is measured by thirty degrees of the equator, by an equal division being made; and whatever part of the Zodiac is intercepted within the spaces of the several houses is said to constitute such a house, which, although, as I have just said, it comprehends the space lying between one cusp and another, nevertheless its beginning is reckoned from five preceding degrees of the equator, and it extends as far as the 25th degree of the same house: so that a planet which is found, for example, at the 20th degree of Leo in the Zodiac, and moreover has 142 degrees of right ascension, and the 24th degree of the same Leo falls in the angle of the Midheaven, although it has not reached the meridian line and the cusp of the tenth house, nevertheless it will be said, and reckoned, to be in the tenth house. CY CYCLUS in Greek, in Latin circles absolutely so called: 203. however, it is usually taken more specifically for the complete revolution of a certain number of years around the cycle, until it returns to the beginning: whence also the solar cycle, and the lunar cycle, and the nineteen-year cycle of the golden number, whose use and mention are frequent in calendars. CYCLUS SOLARIS is the revolution of 28 years for finding the Dominical Letter; because these return after 28 years in exactly the same order as before. The Church used this cycle before the Gregorian correction for finding the Dominical Letter: but afterward it is found much more easily and conveniently, as may be seen in Clavius on the Ecclesiastical Computation. Nevertheless, if anyone should wish to use this solar cycle to discover the Dominical Letter, he can do so with ease. For if to the given year of Our Lord nine be added, and the number thus formed be divided by 28, then the number remaining from the division will be the number of the solar cycle. But if nothing remains from the quotient, it is a sign that then the number 1 iij

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Lexicon Cycli erit integra reuolutio annorum 18. Numerus autem quotiens, indicat quot reuolutiones Cycli solaris à Christi ortu, vsque ad annum propositum, excursæ sint. Alium item modum inueniendi huius Cycli solaris in digitis manus: vide apud eundem Clauium in restitutione Kalendarij. 205. CYCLVS lunaris est reuolutio, & successio 19. annorum, quibus expletis, redeunt lunationes ad pristinam in Kalendario sedem, hoc est ad locum vbi erant prius, & concordat annus lunaris cum solari: qua de re fusè diximus in V. Annus Metonicus. 206. CYCLVS Aurei Numeri. Vide in V. Aureus Numerus. 207. CYCLVS Epactarum. Vide in V. Epacta. 208. CYGNVS, vel rectiùs Cygnus olor Gallina, Ouidio Miluus, sidus in cælo ad borealem plagam secùs Aquilam intrà Galaxiam continens stellas septemdecim iuxta Ptolemæum, & duas informes circa alas, at Keplero sunt 27. & Baiero omninò 37. omnes de natura Veneris, & Mercurij; inter quas præcipua est Cauda, Arabicè Azelfage, vel corruptè Deneb Adigege: de qua alibi dictum. Totum verò sidus, dicitur Eldegiagich hoc est gallina, sicut etiam HiereZim, id est Rosa, vel lilium redolens. In huius pectore anno 1600. apparuit noua stella, quæ diù manens; tandem anno 1621. senùm euanuit, relinquens in suo loco quemdam hiatum, qui ad hæc vsque tempora cernitur. De ea multi scripser, & nos non nihil dicemus, in V. Phanomenon. Porrò Cygnus in horoscopo; inquit Pontanus in Vrania, inclinat ad aucupium, ad insidias auibus parandas, nec non etiam ad cantus eorumque voces imitandas. 210. CYLINDER, seu Cylindrus est figura Geomettica solidà, oblonga quidem, sed ad latus vndequaque rotunda; ita vt circulis æquè distantibus, & circulari superficie contineatur: Vnde est, quod cylindri bases sint circuli ipsi in extremis cylindri positi. Hinc quæuis columna cylindrica dici potest. Nomen hausit ex Græco ἀπὸ τεῦ ἀυλιθρεῖν, quod Latinè voluere interpretatur. 211. CYNOSVRA Græcè, quasi cauda Canis dicitur sidus in cælo Polo mundi arctico proximè adjacens, quod nos Vrsam minorem vocamus ad differentiam maioris, quæ non multò post sequitur, & capite versus huius minoris caudam voluitur. Constat stellis conspicuis omninò septem, vnde & Septentrionis nomen sortitum est, idque etiam toti plagæ, quæ ab æquatore vsque ad Polum protenditur, impertiuit.

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Lexicon The Cycle is a complete revolution of 18 years. The number, however, how many times, indicates how many revolutions of the Solar Cycle, from the birth of Christ up to the year proposed, have run their course. Another method of finding this Solar Cycle on the fingers of the hand may also be seen in the same Clavius, in the restoration of the Calendar. 205. CYCLE. It is the revolution and succession of 19 years, after which the lunations return to their former place in the Calendar, that is, to the place where they were before, and the lunar year agrees with the solar: on this matter we have spoken at length in V. Metonic Year. 206. Cycle of the Golden Number. See V. Golden Number. 207. Cycle of Epacts. See V. Epact. 208. CYGNUS, or more correctly Cygnus olor, the Hen, in Ovid the Kite, a star in the sky toward the northern part, next to Aquila, within the Galaxy, containing seventeen stars according to Ptolemy, and two shapeless ones around the wings; but for Kepler there are 27, and for Bayer altogether 37, all of the nature of Venus and Mercury. Among them the principal is the Tail, in Arabic Azelfage, or corruptly Deneb Adigege, of which elsewhere mention has been made. The whole constellation, however, is called Eldegiagich, that is, hen; as also HiereZim, that is, rose, or fragrant lily. In its breast, in the year 1600, there appeared a new star, which, remaining for a long time, finally vanished in the year 1621, leaving in its place a certain gap, which is seen even to these times. Many have written about it, and we too shall say something in V. Phanomenon. Moreover, Cygnus in the horoscope, says Pontanus in Urania, inclines one to fowling, to setting snares for birds, and also to singing and imitating their voices. 210. CYLINDER, or Cylindrus, is a solid geometric figure, indeed oblong, but round on every side; so that it is contained by equally distant circles and by a circular surface. Hence it is that the bases of cylinders are the circles themselves placed at the ends of the cylinder. Therefore any column may be called cylindrical. The name is taken from the Greek ἀπὸ τεῦ ἀυλιθρεῖν, which in Latin means “to roll.” 211. CYNOSURA, in Greek, as it were “the dog’s tail,” is called the star lying nearest the Arctic Pole of the world, which we call the Lesser Bear, by distinction from the Greater, which follows not long after, and revolves with its head toward the tail of this lesser one. It consists altogether of seven conspicuous stars, whence it also received the name of the North, and it has bestowed that name also on the whole region which extends from the equator to the Pole.

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DA DAPHA Alchia, Arab. idem sonat, ac pulsatio vittutis, estq[ue] cum Planeta alioqui impeditus committit alteri suam virtutem quod, qua ratione fiat, dictum est in V: Alchia. DAPHA Aredir è contrà interpretatur pulsatio dispositionis, & naturæ alterius planeta, quod etiam satis explicatum est in V. Aredir, & in V. Pulsatio. DÆMON Meridianus, sic ab aliquibus ob eius malignitatem dicta est Sagitta, telum, & iaculum, Arab. Schaam, vel Alham- ce, fidus videlicet propè aquilam, vel potiùs cum ipsa aquila vnum astrum constituens ad Galaxiam, constat se solo stellis quinque secundùm Prolæmeum, ac juxta Keplerum, & Baierum, octo. In horoscopo repertum portendit cædes, & strages virorum, idque siue bonæ siue malæ stellæ affulserint. Vi- de amplius in V. Sagitta. DAGIM Hebraicè, apud Chaldæos autem Dagiacho dicitur signum, & constellatio Piscium; vt habet Kircherus in Oedi- po Ægyptiaco. DATH Ellearsi, Arab. hoc est sedes regia dicta est cathedra Cassiopeæ sideris in Cælo celeberrimi: de quo satis dictum est suo loco. DAVLO, apud Chaldæos teste Kirchero appellatur Aquarius, vndecimum ab Ariete signum, Hebraicè autem Delli, id est situla. DECANI, apud Astronomos dicuntur tertæ partes signorum, quas & Facies appellarunt Antiq[ui]mi, singulis planetis per ordinem distributas: ita vt prima facies Arietis continens decem priores gradus, conueniat Marti domino signi: secunda Solì, qui proximè succedit Marti per ordinem planetarum, tertia Veneri, quæ illi substernitur. Dein prima facies Tauri competat Mercurio, secunda Lunæ, tertia Saturno: & sic per ordinem procedendo. Hotum inuentor creditur fuisse Nicèpso Rex & insignis Astrologus Arabs. Et hæc quidem Decanorum prærogatiua computatur inter quinque genera dignitatum essentialium, quas obtinent planetæ in signis; adeò vt absolutè pronunciet Firmicus, quod si planeta repertus fuerit in terminis sui Decanatus; perinde sit, ac si in suo domicilio constitueretur. Verùm in hoc cæteri Astronomi Firmico nullo pacto adstipulantur: quinimò Recensiores communter tam parui faciunt huiusmodi decanatus, vt in Tabella dignitatum essentialium jam modò eos describere (vt moris fuit antiquitùs) dedignentur. Nihilominus eorum mentionem facit I iii)

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DA DAPHA Alchia, in Arabic, has the same meaning as pulsatio virtutis, and it is when a planet otherwise impeded conveys its virtue to another; the way in which this happens has been explained in V. Alchia. DAPHA Aredir, on the contrary, is interpreted as pulsatio dispositionis, and of the nature of another planet, which has likewise been sufficiently explained in V. Aredir, and in V. Pulsatio. DÆMON Meridianus, the name given by some to Sagitta, telum, and iaculum, because of its malignity; in Arabic Schaam, or Alhamce, namely the faithful one near the eagle, or rather forming one star with the eagle itself toward the Milky Way. According to Ptolemy it consists of five stars alone, and according to Kepler and Bayer, of eight. Found in the horoscope, it portends slaughter and the destruction of men, whether good or bad stars are shining upon it. See more in V. Sagitta. DAGIM, in Hebrew, but among the Chaldeans called Dagiacho, is the sign and constellation of Pisces, as Kircher has in his Oedipus Ægyptiacus. DATH Ellearsi, in Arabic, that is, the royal seat, was the name given to the chair of the star Cassiopeia, most celebrated in the sky; enough has been said about it in its proper place. DAVLO, among the Chaldeans, as Kircher testifies, is called Aquarius, the eleventh sign from Aries; in Hebrew, however, Delli, that is, a bucket. DECANI, among astronomers, are called the third parts of the signs, which the ancients also called Faces, distributed in order to the individual planets: so that the first face of Aries, containing the first ten degrees, belongs to Mars, the ruler of the sign; the second to the Sun, who follows Mars next in the order of the planets; the third to Venus, who is placed beneath him. Then the first face of Taurus belongs to Mercury, the second to the Moon, the third to Saturn: and so proceeding in order. Their inventor is believed to have been Nicæpso, king and eminent Arab astrologer. And this prerogative of the decans is counted among the five kinds of essential dignities which planets hold in the signs; so much so that Firmicus flatly declares that if a planet is found within the bounds of its decanate, it is as though it were established in its own domicile. But on this point the other astronomers by no means agree with Firmicus; indeed, more recent writers commonly make so little of these decanates that they disdain even to describe them in the table of essential dignities, as used to be done in antiquity. Nevertheless, he mentions them I iii)

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116 LEXICON Ptolemæus in 2. Quadrip. cap. 18. diuidens vnumquodque si- gnum in tres partes æquales, vbi earumdem explicat qualita- tes, non tamen singulis planetis assignat; sed potius id fecisse videtur ratione fixarum in ea parte existentium, quam quod peculiare in ipsis præcisis fixis intelligat. Sed quidquid sit de istorum decanorum vi, ac potentia certum est Ptolemæum, cum de facie sermonem habet primo Quadrip. cap. 20; non de planetarum decanis intelligete, sed de ea configuratione ipso- rum ad Luminaria, quam habent domus istorum, ad illorum domicilia, & nos supra Almugeam diximus appellari. Cæterum quemadmodum decani dicuntur tertia queque partes signorum singulis planetis per ordinem attributæ, ita etiam 8. DECVRIONES vocantur ipsi Planetæ prædictis partibus, seu signorum decanis præsidentes. 9. DECLINATIO apud Astronomos dicitur deuiatio stellæ, siue cuiuslibet pariis cæli ab æquatore versus polorum alterutrum, quæ proinde ab eo denominationem sumit: ita vt si ad polum arcticum deflectat, eius declinatio borealis dicatur, si ad au- strum, australis. Hinc prima puncta Arietis, & Libræ nullam habent declinationem, quia immediatè incidunt in æquato- rem: puncta verò tropica maximam quam possit Zodiacus habere, hoc est gr. 23. cum dimidio, quia tantumdem etiam ab æquatore huiusmodi puncta elongantur. Planetæ maiore. declinationem habere nequeunt, quam gradus Zodiaci, quem perlustrare possunt, computata etiam latitudine: sic Sol qui semper est in Ecliptica, maiorem declinationem habere nequit, quam ipsa puncta tropica quæ maximè ab æquatore deuiant; hoc est gr. 23. min. 30. E contra fixa, quæ extra Eclipticam diuagantur, tantam declinationem habere possunt, quanta est paralleli, sub quo degunt; ita vt ea pertingere possit ad gr. 90 si ad ipsum polum immediatè accedant, & recidant, vt sot- tassè accider in stella polari proximè succedente sæculo, quæ nunc temporis est in declinatione gr. 87. min. 20. Ex declina- <10.> tione sideris colligitur quantitas eius arcus diurni, ac noctur- ni, eleuatio supra horizontem, distantia à vertice, circulus positionis, & alia huiusmodi, quæ valdè necessaria sunt ad res Astronomicas perficiendas. 11. DECVITVS figura, est Cæli constitutio inspecta tempore accedentis morbi vt volut aliqui, vel sanè ingrauescentis; cum profectò natura reluctans, viribus impar, tandem consterni- tur, atque in lecto petit decumbere. Vt proinde non momentum accedentis morbi, qui sensum, & ferè impercibiliter in- trat, sed tempus consternationis & decubitus præcipiat Hippo- crates Medicorum facilè princeps obseruandum esse, atque

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116 LEXICON Ptolemy in Quadripartitum 2, chapter 18, dividing each sign into three equal parts, where he explains their qualities, does not, however, assign them to the individual planets; but rather seems to have done this by reason of the fixed stars existing in that part, rather than because he understands something peculiar in those precise fixed stars themselves. But whatever may be the force and power of these decans, it is certain that Ptolemy, when he speaks of the face in Quadripartitum 1, chapter 20, does not mean the planetary decans, but that configuration of the planets themselves in relation to the Luminaries, which they have in the houses of those, in relation to those domiciles, and which we above said is called Almugeam. Otherwise, just as the decans are called the third parts of the signs, assigned in order to the individual planets, so also 8. DECURIONS are called the planets themselves presiding over the aforesaid parts, or decans of the signs. 9. DECLINATION, among astronomers, is called the deviation of a star, or of any part of the sky, from the equator toward either pole, and therefore takes its name from it: so that if it inclines toward the arctic pole, its declination is called northern; if toward the south, southern. Hence the first points of Aries and Libra have no declination, because they fall directly upon the equator; but the tropical points have the greatest declination that the Zodiac can have, that is, 23 degrees and a half, because these points are also removed by that amount from the equator. The planets cannot have a greater declination than the degree of the Zodiac which they can traverse, latitude being counted as well: thus the Sun, which is always in the Ecliptic, cannot have a greater declination than the tropical points themselves, which deviate most from the equator; that is, 23 degrees, 30 minutes. On the other hand, fixed stars, which wander outside the Ecliptic, can have as much declination as the parallel under which they dwell; so that it may reach 90 degrees if they approach the pole itself directly and fall upon it, as would perhaps happen in the coming century to the polar star, which at present is in declination 87 degrees, 20 minutes. From the declination of a star is gathered the size of its diurnal and nocturnal arc, its elevation above the horizon, its distance from the zenith, the circle of position, and other such things, which are very necessary for carrying out astronomical matters. 11. DECUBITUS, or figure, is the constitution of the heavens observed at the time of an approaching illness, as some say, or rather of one growing severe; when indeed nature, resisting and unable with her strength to cope, is at last overwhelmed and seeks to lie down in bed. Therefore Hippocrates, easily the prince of physicians, observed that not the moment of the approaching illness, which enters imperceptibly and almost without sensation, but the time of prostration and decubitus, should be considered, and also

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MATHEMATICVM. 137 adeò ad tale instans erigendum figuram morbi ingrauescentis. Quod sanè non sine fructu sit, sed magno cum ægrotantium bono. Quandoquidem astia ex mutua dependentia, ac relatione ad subjectum passibile, in quo jam pridem suas qualitates (in eius videlicet ortu) impresserunt, sunt veræ causæ alterationis rerum: & quemadmodum ortus, ita & conseruationis, defectionis, ac motus; cum hoc tamen vt non statim eliciant omnes effectus, sed dependenter à dispositionibus ægrorum pendentibus ab eorum Natali, & subsequentibus inde motibus. Hinc est, vt morbi, alterationes humorum, temperamentum, & cætera huiusmodi rectè prædici possunt ab Astrologis, nec proinde eorum prædictiones ab Ecclesia interdicantur, cùm hæc naturaliter à causis suis promanent. Et licet quandoque ex libero hominis albittio pendeant mors, morbi, mutatio tem- petamenti &c. idque ex irregulari viuendi ordine, vulnere, &c. tamen hic loquimur de morbis naturaliter prouenientibus, aut etiam de violentis, qui naturaliter ex ipsa constitutione naturæ Medico probè nora curari possunt, secùs de ijs, qui aut miraculosè adueniunt, aut etiam miraculosè curantur. Quandoquidem si bona est Cæli constitutio, inde sit, vt natura terrenis medicamentis adjuta morbo resistat, sin secus natura prosternatur, & illa inutiliter operentur. Quare vtiliter, & prudenter cæleste Thema ad tempus decubitus erectum à Medicis consultur, vt inde natura morbi innotescat, quibus-ve medijs illi sit occurrendum. DEFERENS ex Ricciolo lib. 3. cap. 20. in Cælestibus est cir- <13.> culus seu orbis non tam Epicyclum gestans, quàm ipsum cor- pus planetæ in eo infixum, & faciens illud siue in Epicyclo, siue in sua orbita circà mundum rotari. Atque adeò Eccentricus, & orbis deferens idem sunt in Theorica Eccentrici, & dicitur etiam ab Alfragano, & Albategnio Circulus egressæ cuspidis. DELAPSVS, Gixcè Ecptosis, reste Valla est cum ab Horoscopo <14.> deductus annus, in illud signum inciderit, in quo antecedens conjunctio fuit in Genesi. Quod plurimi sit ab Astrologis. DELPHIN, & Delphinus apud Arabes mutuato à Græcis no- <15.> mine Dalphin, dicitur fidus in cælo ad borealem plagam propè Aquilam constans stellis decem procellosis de natura Saturni, & Martis, quarum præcipua est cauda tertia magnitudinis, exi- stens nunc in gr. 9. Aquarij cum latitudine boreali ferè gr. 30. Cicero in Arasi Phenom. vocat eum Currum. Plinius Hermip- <15.> pum. est fidus procellosum cum Sole exoriens, adducit ventos, cum Saturno tempus nebulosum, & humidum: Occidens verò mane producit & niues. DELTETON Græcè, Latinè Triangulum fidus in cælo ad bo- <16.>

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MATHEMATICUM. 137 so as to raise the figure of the worsening disease to such a point. This is certainly not without benefit, but with great advantage to the sick. For since these things, by mutual dependence and relation to the passible subject, in which they have already long before impressed their qualities (in its very birth), are true causes of the alteration of things; and just as of birth, so also of preservation, failure, and motion; yet in such a way that they do not immediately produce all effects, but depend on the dispositions of the sick, depending on their Nativity, and on the motions following from it. Hence it is that diseases, alterations of humors, temperament, and other things of this kind can rightly be foretold by Astrologers, nor are their predictions therefore forbidden by the Church, since these naturally proceed from their causes. And although sometimes death, diseases, change of temper- ament, etc., depend on a man's free will, and this from an irregular order of living, a wound, etc., still here we speak of diseases arising naturally, or even of violent ones, which can be well treated by a physician according to nature itself; otherwise of those which either come by miracle, or are also cured by miracle. For if the constitution of the heavens is good, it follows that nature, assisted by earthly medicines, resists the disease; but if otherwise, nature is overthrown, and those remedies work uselessly. Therefore, usefully and prudently, the celestial Theme cast for the time of illness is consulted by physicians, so that from it the nature of the disease may be known, and by what remedies it should be met. DEFERENS, from Ricciolus, book 3, chapter 20. in the heavenly spheres is a cir- cle or orb carrying not so much an Epicycle, as the very body of the planet fixed in it, and making it rotate either in an Epicycle or in its own orbit around the world. And thus the Eccentric, and the deferent orb are the same in the theory of the Eccentric, and it is also called by Alfraganus and Albategnius the Circle of the departing cusp. DELAPSUS, or, in Greek, Ecptosis, according to Valla, is when a year, reckoned from the Horoscopus, has come to that sign into which the preceding conjunction was in the Genesi. This is highly valued by astrologers. DELPHIN, and Delphinus among the Arabs, borrowing the name Dalphin from the Greeks, is called a constellation in the sky toward the northern region, near Aquila, consisting of ten stormy stars of the nature of Saturn and Mars, the chief of which is the third magnitude tail, now being at gr. 9 of Aquarius with northern latitude of nearly gr. 30. Cicero in Aratus' Phenomena calls it the Chariot. Pliny calls it Hermippus. It is a stormy constellation; rising with the Sun, it brings winds; with Saturn, a cloudy and humid time; setting, however, it brings about morning and snow. DELTETON, in Greek, in Latin Triangulum, a constellation in the sky toward the north. <16.>

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138 LEXICON realem plagam in trianguli formam: Arabicè Mutlatum. Ptolemæus ei assignat stellas quatuor, Keplerus verò, & Baierus quinque omnes de natura Mercurij: vnde in horoscopo reper tum nato sublime tribuit ingenium. Romæ oritur cum grad. 21. Piscium: occidit cum 10. Tauri. 17. Deneb, Arabicè idem sonat, ac cauda: vnde Deneb Adigege dicitur cauda Cygni: Deneb Algedi, cauda Capricorni: Deneb Elecer, cauda Leonis, Deneb Kaytos, cauda Ceti, &c. Vide de singulis suo loco. 18. Descensio: Vide in V. Ascensio. 19. Detrimentum est genus quoddam debilitatis planetæ, quando reperitur in signo, quod diametraliter opponitur ei, in quo ipse obtinet domicilium, vt Sol in Aquario, Luna in Capricorno, & sicut domicilium est potissima inter dignitates essentiales, ita & detrimentum inter debilitates essentiales est maxima. DI 20. Diagoni vs, apud Græcos significat lineam ab angulo in angulum rectà producta. Hinc septem climata vetetum, quas certis lineis parallelis definiebant, ex composito Dia, & loci per cuius medium pertransibat ducta linea, nomine denominabant, sic primum clima quod per Meroen pertransibat Diameroes; secundum quia per Syenen, Diasyenen; tertium quia per Alexandriam Dialexandros; quartum, quia per Rhodum, Diabodos; quintum quia per Romam, Diaromes; sextum quia per Pontum, Diapontos; septimum quia per Borysthenen Diaborysthenes dicta sunt. De quibus omnibus, nec non de alijs à recensioribus adjectis: vide in V. Cl ma. 21. Diagramma, apud Geometras significat figuram vtcumque lineis efformatam, siue ea triangularis sit, siue quadrangularis, siue recti-linea, siue curui- linea, siue mixta, cuiusmodi sunt omnes figuræ quæ in sex libris elementorum Euclidis ob oculos exhibentur. 22. Diameter Græcè, Latinè dimetiens dicitur linea ab vno extremo in alterum protensa, qua eotum distantiam dimetimur. Eam præcipuè venamur in circulo, quem in duas partes æquales secat, ac necessario transire debet per eius centrum. Vnde & definitur ab Euclide. Est recta quadam linea per centrum ducta, & ex vtraque parte in circulo peripheriam terminata, qua circulum bifariam secat. Sicut è contà linea à centro ad peripheriam ducta semidiameter dicitur: Vide fusiùs in V. Dimetiens. 23. Diasaccora Arab. Græcè Discora apud Ptolemæum in Quadrip. ex versione Arabica Hali significat Genituram duorum masculorum, & vnius femellæ, cuius significatores sint Saturnus, Iupiter, & Venus.

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138 LEXICON the real side in the form of a triangle: Arabic, Mutlatum. Ptolemy assigns four stars to it, but Kepler and Bayer five, all of the nature of Mercury: hence, when found in the horoscope of one born, it grants a lofty intellect. In Rome it rises with 21 degrees of Pisces; it sets with 10 degrees of Taurus. 17. Deneb, in Arabic means the same as “tail”: hence Deneb Adigege is called the tail of Cygnus; Deneb Algedi, the tail of Capricorn; Deneb Elecer, the tail of Leo; Deneb Kaytos, the tail of Cetus, etc. See each under its own place. 18. Descensio: See under Ascensio, V. 19. Detriment is a certain kind of weakening of a planet, when it is found in a sign that is diametrically opposite to that in which it has its domicile, as the Sun in Aquarius, the Moon in Capricorn; and just as domicile is the chief among the essential dignities, so detriment among the essential debilities is the greatest. DI 20. Diagonius, among the Greeks, signifies a line drawn straight from angle to angle. Hence the seven climates of the ancients, which they defined by certain parallel lines, were named by a compound of Dia and the place through whose middle the line passed; thus the first climate, which passed through Meroe, was called Diameroes; the second, because through Syene, Diasyenen; the third, because through Alexandria, Dialexandros; the fourth, because through Rhodes, Diabodos; the fifth, because through Rome, Diaromes; the sixth, because through Pontus, Diapontos; the seventh, because through the Borysthenes, Diaborysthenes. Concerning all these, as well as others added by later writers: see under V. Cl ma. 21. Diagramma, among geometers, signifies a figure formed in whatever way by lines, whether triangular, quadrangular, rectilinear, curvilinear, or mixed, such as all the figures shown before our eyes in the six books of Euclid’s Elements. 22. Diameter, in Greek, in Latin dimetiens, is called the line extended from one end to the other, by which we measure the distance of things. We especially seek it in the circle, which it divides into two equal parts and must necessarily pass through its center. Hence it is also defined by Euclid: a straight line drawn through the center and terminated on either side at the circumference of the circle, by which it divides the circle into two equal parts. Likewise the line drawn from the center to the circumference is called the semidiameter: see more fully under Dimetiens, V. 23. Diasaccora, Arab.; in Greek Discora, in Ptolemy’s Quadripartite according to the Arabic version of Hali, signifies a nativity of two males and one female, whose significators are Saturn, Jupiter, and Venus.

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MATHEMATICVM. 139 < 24.> DICHOROMOS propriè significat ex Græca origine, id quod dimidiarum est, atque in duas partes sectum. Hinc apud Astronomos absolutè accipitur pro Lunæ quadraturis, cum septimo quoque die à conjunctione, vel oppositione cum Sole apparet dimidiata. < 25.> DIEPON, teste Valla, apud Arabes significat horæ dominum: pro cuius rei intelligentia sciendum est, antiquos Astronomos (nam Recensiores meritò hanc vanam Arabum obseruationem derident) diem, ac noctem artificialem diuisisse in duodecim partes æquales, quas & horas planetatias, & inæquales vocabant, ad differentiam horarum æqualium, quod est tempus respondens singulis quindecim gradibus æquatoris ascendentibus. Harum dominium planetis per ordinem attribuebant; ita vt primæ horæ diei ab exortu Solis, dominium assumeret is, à quo dies illa denominatur; secundæ horæ dominarerur qui proximè huic succederet: sic per ordinem descendendo vsque ad Solis occasum. Similiter primæ horæ noctis dominium habebit qui proximè succedit ei qui vltimæ horæ diei dominabatur; ita vt per ordinem procedendo, semper is iu primæ horæ diei sequentis dominium recidat, qui & ipsum diem suo nomine signat: Ita enim res ab initio ordinata fuit, vt ab eo dies denominaretur, qui per ordinem procedendo succederet ei, qui vltimæ horæ noctis dominium obtinebat. Sed vt exemplis res fiat clarior: ponamus hodie esse diem Dominicum: vtique cùm is sit ab initio Soli dicatus, primæ horæ exorientis Solis ipsemet Sol sibi dominium vendicauit: quia autem Soli succedit Venus, ideò hæc ei succedit in dominium secundæ horæ: mox tertia, Mercurius, inde Luna, postmodum Saturnus, ita vt nunquam turbato ordine, prima hora noctis incidat in Iouem, postrema quæ est duodecima, in Mercurium; cui immediatè succedit Luna, quæ proinde sequentem, proximè Dominico diei denominat diem, & primæ exorientis Solis horæ dominium sortietur: Inde Saturnus: mox Lupiter &c. Extat apud Auctores tabula harum horarum inæqualium singulis planetis per ordinem respondentium, quæ ab tradita methodo nullatenùs deuiat: ita vt eam quivis proprio Marte sibi queat construere. Tempore Æquinoctij horæ planetariæ sunt eædem ac horæ horologij, seu æquinoctiales, non sic reliquo tempore; præsertim in solstitijs. Quocircà qui voluerit facilè quantitatem horæ planetariæ competentem singulis diebus ac noctibus anni dignoscere, diuidat arcum semidiurnum vel seminocturnum in sex partes æquales; & quotiens erit hora inæqualis cuiusuis diei, vel noctis, atque adeò portio competens vnicuique planetæ in eiusdem dominium successuro.

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MATHEMATICVM. 139 < 24.> DICHOROMOS properly signifies, from its Greek origin, that which is half, and cut into two parts. Hence among Astronomers it is taken absolutely for the quadratures of the Moon, when every seventh day from conjunction, or opposition with the Sun, it appears half. < 25.> DIEPON, as Valla testifies, among the Arabs signifies the lord of the hour: for the understanding of which thing it must be known that the ancient Astronomers (for the more recent with good reason mock this vain observation of the Arabs) divided the artificial day and night into twelve equal parts, which they called both planetary hours and unequal hours, as distinct from equal hours, which is the time corresponding to each fifteen degrees of the equator rising. They assigned the rulership of these to the planets in order; so that the first hour of the day, from the rising of the Sun, would be ruled by the one from whom that day is named; the second hour by the one who succeeds him next: and so in order descending until sunset. Likewise the first hour of the night will be ruled by the one who immediately follows him who ruled the last hour of the day; so that proceeding in order, always the rulership of the first hour of the following day falls to that planet which also marks that day by its name: thus the matter was ordered from the beginning, so that the day would be named from the one who, proceeding in order, succeeded the one who held the rulership of the last hour of the night. But to make the matter clearer by examples: let us suppose that today is Sunday: indeed, since it is dedicated from the beginning to the Sun, the Sun itself claims rulership of the first hour of the rising Sun; and because Venus succeeds the Sun, therefore she succeeds him in the rulership of the second hour: then Mercury the third, then the Moon, afterwards Saturn, so that, the order never being disturbed, the first hour of the night falls to Jupiter, the last, which is the twelfth, to Mercury; whom the Moon immediately follows, and therefore she gives the following day, which is next called Sunday, its name, and will obtain the rulership of the first hour of the rising Sun: then Saturn; then Jupiter, etc. There exists among authors a table of these unequal hours corresponding in order to each planet, which in no way departs from the method given: so that anyone may construct it for himself by his own effort. At the time of the equinox the planetary hours are the same as the hours of the clock, or equinoctial hours; not so at the rest of the year, especially at the solstices. Wherefore whoever wishes easily to know the quantity of the planetary hour fitting each day and night of the year, let him divide the semidiurnal or seminocturnal arc into six equal parts; and so much will be the unequal hour of any day or night, and therefore the portion belonging to each planet in succession to its rulership.

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140 LEXICON 26. Dies apud Astronomos est mensura temporis, quo Sol motu primi mobilis raptus integrè circà tellurem voluitur; hoc est Spatium viginti-quatuor horarum: tantùm enim temporis insumit, quousque redeat ad idem punctum, seu circulum positionis, vnde discesserat, additâ ea parte, quam ipse motu suo in Zodiaco acquiesuit. Nam ptimum mobile citiùs revolutionem suam absoluit, nempè spatio 21 horarum, ac ferè 56. minutorum, itaut integra primi mobilis revolutio præcedat singulis diebus revolutionem Solis quatuor ferè minutis. Et hic est dies naturalis complectens diem, ac noctem artificialem, quod est temporis spatium, quo Sol vtrumque hemisphætium, & superius, & inferius perlustrat. Dies naturalis semper, & vbique æqualis est: non sic artificialis, qui solum sub æquatore seruat æqualitatem, & cum nocte etiam æquè pottionem diei naturalis diuidit: At extrà illum quò magis accedit ad tropicos, ac polus super regionem attollitur, eò inæqualior est, & longior quidem nocte, si Sol ad eum polum decliner, breuior, si ad oppositum Vnde & sub Polo immediatè degentibus, Sole in siguis borealibus existente, accidit dies longissima sex mensium tantumdemq; noctis, eo alteram Zodiaci partem perlustrante: ita vt in his regionibus integra Solis revolutio in Zodiaco duret vna die naturali, & vns dies naturalis sit integer annus. Porrò diei naturalis initium Astronomi computant à Metidie in Meridiem. Similiter Hispani & Galli, aliæque Nationes. Itali à Solis occasu. Chaldæi; atque Ægyptij à Solis ortu. Tandem Ecclesia in jejunijs, ritibus, festitque seruandis à media nocte. Sed de hac re satis pro nostro instituto. 27. DIFFERENTIA Ascensionalis est arcus æquatoris interceptus inter ascensionem, vel descensionem rectam, & obliquam eiusdem sideris aut cuiuscumque partis Zodiaci. Cùm enim diuersimodè ascendant in sphæra recta, & in obliqua (quæ enim habent declinationem borealem citius oriuntur, & serius occidunt; & è conttâ quæ australem serius ascendunt, citiusque descendunt ijs qui habent horizontem obliquum, quam qui habent tectum) ideò hæc diuersitas in gradibus æquatoris coascendentibus, vel condescendentibus computata vocatur differentia Ascensionalis: Vide in V. Ascensio. 28. DIGITVS Eclipticus apud Astronomos est duodecima pars disci Solaris, vel Lunaris, quem ideò in tot partes diuiserunt (quas alij Vncias appellant) vt innotesceret, quota pars alterius Luminarium eclipsum patientis obscuretur. Si enim tres digitis disci Lunaris in telluris vmbram immerguntur, dicere tur quarta pars Lunæ obscurata; si sex, dimidium; si duodecim, signum est quod totum corpus lunare obscuretur. Sed enim hic

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140 LEXICON 26. A day, among Astronomers, is a measure of time, in which the Sun, carried by the motion of the primum mobile, is completely revolved around the earth; that is, the space of twenty-four hours: for it takes so much time until it returns to the same point, or circle of position, from which it had departed, adding that part which it itself has traversed by its own motion in the Zodiac. For the primum mobile completes its revolution more quickly, namely in a space of 21 hours and nearly 56 minutes, so that the complete revolution of the primum mobile precedes the revolution of the Sun each day by nearly four minutes. And this is the natural day, comprising the artificial day and night, which is that space of time in which the Sun traverses both hemispheres, upper and lower. The natural day is always and everywhere equal: not so the artificial one, which preserves equality only under the equator, and together with the night divides an equal portion of the natural day; but outside that, the more it approaches the tropics and the pole is raised above the region, the more unequal it is, and indeed longer than the night if the Sun inclines toward that pole, shorter if toward the opposite. Hence also for those dwelling immediately under the pole, when the Sun is in the northern signs, there occurs a day of the greatest length of only six months, and as much night, while the Sun traverses the other part of the Zodiac: so that in these regions the complete revolution of the Sun in the Zodiac lasts one natural day, and one natural day is a whole year. Moreover, Astronomers compute the beginning of the natural day from noon to noon. Likewise the Spanish and the French, and other nations. The Italians from sunset. The Chaldeans and Egyptians from sunrise. Finally the Church, in fasts, rites, and observance of feasts, from midnight. But enough on this matter for our purpose. 27. The Ascensional difference is the arc of the equator intercepted between the right and oblique ascension or descension of the same star, or of any part of the Zodiac. For since they ascend differently in the right sphere and in the oblique one (for those that have northern declination rise sooner and set later; and conversely those that have southern declination rise later and descend sooner to those who have an oblique horizon than to those who have a direct one), therefore this diversity, computed in the degrees of the equator co-ascending or co-descending, is called the Ascensional difference: see under Ascension. 28. The Ecliptic digit, among Astronomers, is the twelfth part of the solar or lunar disc, which they therefore divided into so many parts (which others call unciae, or inches) so that it might be known what fraction of one of the luminaries suffering eclipse is darkened. For if three digits of the lunar disc are immersed in the earth’s shadow, it may be said that a quarter of the moon is obscured; if six, half; if twelve, it is a sign that the whole lunar body is obscured. But here

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MATHEMATICVM. 141 aduertendum, quod quando Luna totaliter eclipsatur, cum aliqua mora in tenebris, quia vmbra terræ, vel, vt volunt Astronomi recensiores penumbra Atmosphere incidens in cor- pus Lunare est maior ipso disco Lunari, ideò ad dignoscendam Eclipsis magnitudinem vltà duodecim digitos, dicuntur eclipsati tot digiti, quor sunt inter circumferentiam Disci ecli- psati & vmbræ, penumbraue eclipsantis, vt si post totalem obscurationem Luna tam profundè vmbram subintret, vt si forte eius diameter foret quindecim digitorum, adhuc tota obscurearetur, & intraret totam vmbram telluris, tunc dicerentur quindecim digiti eclipsati. Ar quoniam Lunæ corpus Solem eclipsantis per interpositionem inter ipsum, & nos vel non adæquat vel sanè non superat corpus Solare, ideò in Solis ecli- < 29.> psi ad mensurandam eius magnitudinem, non considerantur nisi duodecim tantum digiti, qui si fortè obscurentur omnes, tunc nulla pars disci Solaris erit conspicua, sed torum erit in tenebris. Eiusmodi erit mira, & portentosa Solis eclipsis, quæ accidet anno 1684. die 12. Iulij, hora circiter tertia post Me- ridiem. Portò hanc diametri obscurandæ tam in Sole, quàm in Luna quantitatem Astronomi venantur ab distantia Lunæ à capite, vel cauda Draconis, quam ideò argumentum verum latitudinis Lunæ appellant: quò enim propiùs ipsa accedit ad suos nodos, eò maior erit obscuratio in Eclipsi; etsi tempore veræ conjunctionis, aut oppositionis cum Sole, ipsa fuerit in eodem puncto cum suis nodis, hoc est omnis latitudinis expers, & in Ecliptica, tunc sanè totalis erit obscuratio, vel Solis, vel Lunæ, prou ea fuerit conjunctio, vel oppositio. DIGNITAS, apud Astronomos est quædam prærogatiua pla- < 30.> netæ qua ex eius habitudine ad Solem, loco in Zodiaco, aut in Mundi situ, motu, & configuratione ad alios, viribus auge- rur, & plurimùm roboratur. Ea multiplex est, & in duplici differentia. Aliæ sunt essentiales dictæ, non quia sint exteris potiores, sed quia conveniunt planetis ratione essentia, & na- turæ ipsorum, eo quia confortmentur cum dictis locis in primis qualitatibus passiuis, & actiuis, & hæc conformitas non ex accidente, sed ab intrinseco semper illis, & primariò insit. Aliæ accidentales, quæ non pet se, & primariò illis compe- tunt, sed extrinsecus & veluti ex accidente, vt ex situ Mundi aut ex accidentalibus passionibus, vt mox dicemus. Dignitates essentiales quinque statuit Ptolemæus 1. Quadrip. c. 15. Domi- cilium nempe, altitudinem, seu exaltationem, trigonum, ter- minum, & personam: de quibus suis in locis recurrerfermo. Accidentales etiam plures enumerantur: potissima verò est situs Muudi, hoc est quod sit in Angulo, vel succedente domo;

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MATHEMATICUM. 141 it is to be noted that when the Moon is totally eclipsed, and there is some delay in the darkness, because the shadow of the earth, or, as more recent Astronomers will have it, the penumbra of the atmosphere falling upon the lunar body is larger than the Moon’s own disc, therefore, in order to ascertain the magnitude of the eclipse beyond twelve digits, as many digits are said to be eclipsed as there are between the circumference of the eclipsed disc and the shadow, or penumbra, of the eclipsing body; as if, after total obscuration, the Moon should enter so deeply into the shadow that, if by chance its diameter were fifteen digits, it would still be wholly darkened, and would enter the whole shadow of the earth, then fifteen digits would be said to be eclipsed. But since the body of the Moon eclipsing the Sun by interposition between it and us either does not equal or certainly does not exceed the solar body, therefore in a solar eclipse, for measuring its magnitude, only twelve digits are considered; if perhaps all of these should be obscured, then no part of the solar disc will be visible, but the whole will be in darkness. Such will be the wonderful and portentous solar eclipse that will occur in the year 1684, on the 12th day of July, at about the third hour after noon. Moreover, astronomers seek this quantity of the diameter to be darkened, both in the Sun and in the Moon, from the distance of the Moon from the head or tail of the Dragon, which they therefore call the true argument of the Moon’s latitude; for the more closely it approaches its nodes, the greater will be the obscuration in the eclipse; and if at the time of the true conjunction, or opposition with the Sun, it should be in the same point with its nodes, that is, wholly without latitude and in the ecliptic, then certainly the obscuration will be total, either of the Sun or of the Moon, according as there is conjunction or opposition. DIGNITY, among Astronomers, is a certain prerogative of a planet, by which, from its relation to the Sun, place in the Zodiac, or position in the World, motion, and configuration with respect to the others, its powers are increased and greatly strengthened. It is manifold, and of a twofold difference. Some are called essential, not because they are superior to the others, but because they belong to the planets by reason of their essence and nature, since they are conformed with the said places in the primary passive and active qualities, and this conformity is not by accident, but is always inherent in them from within, and primarily. Others are accidental, which do not belong to them per se and primarily, but extrinsically and, as it were, by accident, as from the situation of the World or from accidental passions, as we shall soon say. Ptolemy, in Quadrip. c. 15, sets down five essential dignities: namely domicile, altitude or exaltation, trigon, term, and person; concerning which we shall treat in their proper places. More accidental dignities are also enumerated: the chief of them, however, is the situation of the World, that is, whether it is in an angle, or in a succedent house;

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142 LEXICON proximè accedit lumen, vt videlicet sit lumine auctus, non combustus, neque sub radijs Solis: inde, quod sit directus, & motu velox: mox quod sit Orientalis à Sole, si fuerit ex tribus superioribus, Occidentalis verò, si ex inferioribus. Postremò vt sit benè configuratus cum alijs: de quibus omnibus vide sub proprijs titulis. 31. DIMANTARCORIS Arab. Græcè Dunnata riferitas apud Pro- lemæum in textu Arabico ex versione Hali 3. Quadrip. cap. 7. significat Genituram duarum foeminarum, & vnius masculi, in quam conveniant Venus, Mars, & Luna. 32. DIMETIENS apud Mathematicos idem est quod Græcè Dia- meter, sic dicta, eò quod per eam metimur quantitatem rotius circuli per partes proporcionalis ipsius. Quandoquidem, cum ea sit mensura maioris distantiæ, quæ inter duo puncta circuli opposita dari possit; meritò per eius partes proporcionalis quantitatem arcus, seu certæ cuiusdam partis circuli, quem ipsa æqualiter diuidit, internoscimus; quod per tabulas sinuum rangentium, & secantium ad vltimas quasque minutias exqui- sitissimè obtineretur. 33. DIOPTRA Græcè, Latinè Ostensor interpretari potest, estq[ue] regula quædam in medio Astrolabij vel alterius consimilis in- strumenti collocata, repræsentans lineam rectam, seu dime- tientem totius circuli, quæ in gyrum voluitur per partes circuli interstinctas in limbo, signatque gradus oppositos. Alicubi in eius extemiratibus, duæ pinnæ, & spicilla sunt, per quæ tran- sire debeat radius visualis, atque in corpus, quod metiti volu- mus, terminetur. Dicitur etiam Linea fiducia, Arabicè verò Albidada. Hinc 34. DIOPTICA, dicitur ea Astronomiæ pars, quæ Solis, Lunæ, aliorumque siderum corpora speculatur, ac distantias, altitu- dines, declinationes, per dioptram, aliaque id genus instru- menta metitur. 35. DIRECTIO est realis motus in cælo, motu primi mobilis ab- solutus, quo Sol, Luna, Astra, vel quæuis alia Cæli pars, quæ in alicuius rei inceptione subintrat munus aliquid significandi aut efficiendi circa rem illam, feruntur ad situm alterius astri vel partis cæli aliquid similiter significantis, atque illa ad effe- ctum complendum quodammodo expectantis: quo itinere ex- pleto perficitur quidquid in radice, seu in prima positione astrorum ad inuicem in inceptione illius rei innuebatur pro tempore deuolutionis vnius ad alterum. Dicitur Directio, ab itineris directione, quod alterum ad alterum instituit: Hinc 36. DIRIGERE, apud Astronomos aliud non est, quam venari, & artificiosè inquirere arcum æquatoris interceptum inter præ-

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142 LEXICON comes nearest to light, namely, so that it is increased by light, not burned up, nor under the rays of the Sun: hence, that it is direct, and swift in motion: next, that it is Oriental from the Sun, if it be from the three superior bodies, but Occidental if from the inferior. Lastly, that it be well configured with the others: concerning all of which see under their proper titles. 31. DIMANTARCORIS, Arabic. In Greek, Dunnata riferitas, found apud Pro- lemaeus in the Arabic text from the version of Hali, Quadrip. 3, chap. 7, signifies the geniture of two females and one male, in which Venus, Mars, and the Moon agree. 32. DIMETIENS among mathematicians is the same as the Greek Dia- meter, so called because through it we measure the quantity of the whole circle by its proportional parts. For, since it is the measure of the greatest distance that can be given between two opposite points of a circle, we rightly by its proportional parts discern the quantity of the arc, or of a certain part of the circle, which it divides equally; which by tables of sines, tangents, and secants to the last minute would be most exactly obtained. 33. DIOPTRA in Greek, in Latin Ostensor, may be interpreted, and is a certain rule placed in the middle of an Astrolabe or other similar in- strument, representing a straight line, or diameter of the whole circle, which turns around in a circuit through the parts of the circle marked on the limb, and points out opposite degrees. In some places at its extremities there are two sights and pinnules, through which the visual ray ought to pass, and be terminated upon the body which we wish to measure. It is also called Linea fiducia, and in Arabic Albidada. Hence 34. DIOPTICS is called that part of Astronomy which observes the bodies of the Sun, Moon, and other stars, and measures distances, altitudes, declinations, by the dioptra and other instruments of that kind. 35. DIRECTION is a real motion in the heavens, completed by the motion of the primum mobile, by which the Sun, Moon, Stars, or any other part of the Heaven, which at the beginning of some thing enters in to signify or effect something concerning that thing, are carried to the position of another star or part of the heaven likewise signifying something, and as it were awaiting the completion of that effect: when this course is finished, whatever in the radix, or in the first position of the stars among themselves at the beginning of that matter, was indicated for the time of the unfolding of one to the other, is accomplished. It is called Direction, from the directing of the journey, which sets one toward another: Hence 36. TO DIRECT, among Astronomers is nothing other than to hunt for, and artfully investigate, the arc of the equator intercepted between the pre-

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MATHEMATICVM. 143 dicta loca, ac proinde metiri tempus quod requiritur quoad- vsque alter ad alterum deuoluatur. Cuius motus auctor & regu- lator est Sol per suum realem motum, non quidem illum annu[m], quo integro circulo Zodiaci peragrato regreditur ad idem pun- ctum, vnde discesserat, sed singulas illas lationes diurnas sin- gulis annis competentes, quibus adæquat morum primi mobi- lis; eo pacto, ac progressionum suo motu regulatrix est Luna: Et sicut hæc per suum motum progressuum ordinat, disponit, ac regit in viuentibus humidum radicale; ita Sol motu isto di- rectionis regit calorem vitalem; qui proinde aliud principium naturalem non habet quàm Solem ipsum omnis caloris, & vitæ fontem, vt propterea mirum non sit, si eo male affecto in cælestibus per concursum cum astris prauis, malè etiam habeat in terrestribus vita, quæ in calore innato consistit; hicque à motu Solis directorio totam suam virtutem, ac subsistendi potentiam recipit. Sed quia vt aliàs ex Prolemæo meminimus, non modò Sol, & Luna, sed etiam vtiusque horoscopus, & cæli culmen se habent vt subjectum passibile respectu aliorum siderum occursantium, quibus malè vel benè affectis ea eriam, quæ ab ipsis pendent benè vel malè habeant necesse est, inde sit, vt quandocumque hæc in sideta occursantia impingunt motu directionis, noui effectus in viuentibus exerantur circà eorum significata. Itaque duo loca concipienda sunt in cælo in quacumque directione: quorum alter dicatur significator, & se habeat vt subjectum passibile, eò quia significat in genere aliquid, vt vitam, morbos, fortunas &c. & recipiat in se im- pressiones siderum occursantium, alter se habeat vt causa effi- ciens, & dicatur Promissor, qui decernat, & promittat bona vel mala in illa re quam denotauerit significator, implenda pro reimpore, quo ipse ad eumdem locum peruenerir: & ab hoc munere, ne ipsa quidem luminaria excludenda sunt, quibus non repugnat pro diuersa consideratione, & habitudine diuersa- rum etiam causarum vices subire, idque ex eminenti eorum virtute. Sic igitur significator, & locus passibilis in hoc casu gerit vicem creditoris recepturi aliquid à Promissore, & loco occursante; qui se habet vt causa efficiens, statis temporibus, quibus expletis promissio adimpleatur, arque effectus in lucem exear per realem causarum congressum. Hæc itaque tempora nos directione metimur: & hæc temporis inquisitio vocatur, directio. Quomodo autem fiat huiusmodi causarum congressus, & quonam pacto expleto tempore directionis locus vns intelligarut realiter ad alterum deuolurus eo videlicet tempore, quo prodit effectus, paulò fusiùs explicandum est, eò maximè, quia diximus omnem directionis motum à Sole pendere, ac perfici

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MATHEMATICVM. 143 said places, and therefore to measure the time that is required until one is brought down to the other. The author and regulator of this motion is the Sun through its real motion, not indeed that annual one by which, after traversing the whole circle of the Zodiac, it returns to the same point from which it had departed, but those individual daily movements appropriate to each year, by which it matches the motion of the first mobile; in just the same way as the Moon, by its motion, regulates the progressions. And as the Moon by its motion of progressions orders, disposes, and governs the radical moisture in living beings, so the Sun by this motion of direction governs vital heat; which therefore has no other natural principle than the Sun itself, the source of all heat and life. Hence it is no wonder if, when the Sun is ill affected in the heavens through conjunction with evil stars, life also fares badly on earth, since life consists in innate heat; and from the Sun’s directing motion it receives its whole virtue and power of subsisting. But because, as elsewhere we have noted from Ptolemy, not only the Sun and Moon, but also the horoscope of each and the zenith of the heaven stand as a passible subject with respect to the other encountered stars, which, when ill or well affected, must likewise make good or bad that which depends on them, it follows that whenever these strike the encountered stars by the motion of direction, new effects are produced in living beings concerning their significations. Therefore two places must be conceived in the heaven in any direction: one of which is called the significator, and stands as a passible subject, because it signifies in general something, such as life, illnesses, fortunes, and so on, and receives into itself the impressions of the encountered stars; the other stands as the efficient cause, and is called the Promissor, who decrees and promises good or evil in that thing which the significator has denoted, to be fulfilled at the time when he himself shall have come to the same place. And even the luminaries themselves are not to be excluded from this office, since it does not conflict with them, under different considerations and the diverse relation of causes, to undergo these roles also, and this by reason of their eminent virtue. Thus, then, the significator and the passible place in this case play the role of a creditor about to receive something from the Promissor and the encountered place; the latter behaves as the efficient cause, at the fixed times, when these are completed, that the promise may be fulfilled, and the effect may come to light through the real conjunction of the causes. These times therefore we measure by direction: and this inquiry into time is called direction. But how such a conjunction of causes takes place, and in what manner, after the time of direction has been completed, one place is truly understood to be brought down to the other at that very time when the effect appears, must be explained somewhat more fully, especially because we have said that every motion of direction depends on the Sun and is accomplished

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144 LEXICON per motum primi mobilis, qui cùm sit rapidissimus, ac spatio vnius dici integre circà tellurem roterur, ac proinde videatur ad paucas horas singulas eius partes fer i ad situm significatorum: vt propterea non absuerint qui cixerint omnes motus directionis statim post natalem motu horatio minore spatio quam vna die compleri: In quo profecto casu non apparet ratio mensuræ ad annos, neque vlla similitudo causarum ad suos effectus, vt benè aduettit Titus lib. 3. cap. 3. Quapropter ipse aliam rationem diluendæ huius difficultatis excogitauit. ait enim: Dum Sol circà Mundum fertur latione diurna, seu motu raptus; Primum mobile vna cum omnibus astris, qua tanquam fixa sub ipso censentur esse, quia velocius monetur hoc motu, quam Sol, successuè non nihil præcurrit ipsum Solem; ita vt in fine vnius integra dies repersatur præcessisse uno gradu ferè, quantum scilicet decimus esse motum Solem contra ipsum primum Mobile. Dum ergo Sollatione vnius integra dies præordinat ex eo rem vitalem ad unum annum, astris præcurrendo appropriquans sitibus positionum prorogatorum, per gradem ferè, & sim iter su cessiue sequentibus diebus: dum autem appropinquunt, applicant etiam ad jam iaritates quibus præordinant naturales effectus ad actum sturos vna cum ipsi vita principiis: Vt exempli gratiâ, si in aliqua Gevesi, sit Sol in Meridie, dum circumfertur ad Occasum, Imum, & Orsum, primum Mobile successuè paulatim antecedit, ita vt vbi Sol ad Meridiem exquisitè peruenerir, inueniatur primum Mobile cum omnibus astris præcessisse per gradum ferè; quantum decimus Solem fuisse motum contra ipsum. Dico igitur tali modo fieri mo um directionis. Hæc Titus, quibus innuere videtur, motum directionis expleri non quidem, vt illi volebant minori spatio vnius dici ad singula momenta, quibus loca occursantia attingunt situm significatorum, sed ad singulos dies post natalem ratione præcessionis primi mobilis ad motum Solis, vnde in eius sententia, si locus occursans ver. gra. distet à loco prorogatorio per quindecim fere gradus, quia primum mobile vt dictum est præcedit Sol vno ferè gradu ad dies singulos, ideò ad hoc vt quindecim isti gradus adæquentur, & Sol reperiatur in eodem signo cum primo mobili requiri adhuc quindecim dies, quibus expleris intelligatur completa directio, & deuolutus occursans ad situm Prorogatoris. Tunc autem, subdit, præordinantur potentia naturales effectus ad singulos annos. Per morum istum qui sit ad singulos dies, ita vt singulæ diurnæ lationes singulis annis respondeant. Quod ideò directionem prius definierat, quod sit velox quidam mo'us, quo in nato cælestes causa breui tempore præordinant potentia effectus naturales ad actum ituros, in diuturno vita decursu. Verum

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144 LEXICON by the motion of the first mover, which, since it is most rapid and in the space of one day is wholly turned around the earth, and therefore seems to carry its parts to the positions of the significators within a few hours; wherefore those were not lacking who said that all motions of direction are completed immediately after birth by a motion of less than one day. In which case, indeed, there appears no proportion of measure to years, nor any likeness of causes to their effects, as Titus rightly notes, lib. 3, cap. 3. For this reason he himself devised another way of removing this difficulty. For he says: While the Sun is carried around the world by a diurnal motion, or motion of rapture, the First Mover, together with all the stars, which are thought to be fixed beneath it, because it is moved by this motion more swiftly than the Sun, gradually outstrips the Sun itself a little; so that at the end of one whole day it is found to have gone ahead by about one degree, as much as, namely, the tenth sphere moves the Sun against the First Mover itself. Therefore, while the Sun by the motion of one whole day preordains the vital outcome to one year, by advancing ahead of the stars and bringing them nearer to the positions of the prorogated places, by about one degree, and likewise successively in the following days; but while they are approaching, they also apply themselves to those degrees by which they preordain natural effects to be brought into act together with the very principles of life: as, for example, if in some revolution the Sun is at midheaven, while it is carried toward the West, the Nadir, and the East, the First Mover successively and gradually precedes, so that when the Sun has arrived exactly at midheaven, the First Mover, with all the stars, is found to have gone ahead by about one degree; as much as the tenth sphere is said to have moved the Sun against it. I therefore say that the motion of direction is accomplished in this way. Thus Titus, by which words he seems to indicate that the motion of direction is not completed, as they wanted, in less than one day, in the individual moments by which the encountering places reach the position of the significators, but on each day after birth by reason of the precession of the first mover relative to the motion of the Sun; whence, in his opinion, if the encountering place is, for example, distant from the prorogatory place by about fifteen degrees, because the first mover, as has been said, precedes the Sun by about one degree each day, therefore in order that these fifteen degrees may be equated and the Sun be found in the same sign with the first mover, fifteen days are still required, after which, when they have elapsed, the completed direction is understood, and the encountering place is turned toward the position of the Prorogator. Then, he adds, natural effects are preordained in potency for each year. By this motion, which is for each day, so that the individual daily motions correspond to the individual years. He had therefore defined direction previously as a certain swift motion by which, in the native, celestial causes in a short time preordain in potency natural effects that are to be brought into act, throughout the course of a long life. But

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MATHEMATICVM. 149 Verùm hæc explicatio, etsi alioqui ingeniosa, & quæ, fateor, mihi aditum præbuit ad huius arcani, ni fallor, uotitiam comparandam, non euacuat difficultatem: non enim tradit, quo- nam pacto fiat huiusmodi præordinatio, & qui fiat, vt cum causæ omnes post quindecim v.g. dies congrediantur, & com- pletæ reducantur ad actum, effectus nihilominus non nisi post quindecim annos elucescat, & eius vix vmbra quædam, tunc temporis quando causæ suam virtutem promunt, appareat? Plus enim, vt ille ait, nocet præsens musca, quàm ab sens leo. Ergò si post quindecim dies expletur motus directionis, & causæ ponuntur in actu proximo ad agendum, tunc quidem, & non post tantum temporis interuallum prodire debet effectus. Sciendum igitur est, Solem, qui vt diximus est regula om- nis motus directionis, spatio 24. horarum conficere integtam, ac perfectam reuolutionem circà tellurem: ita vt ea expleta ponatur in eodem circulo positionis, ac situ mundi, in quo, pridie erat, cùm primum ab eodem puncto moueri expit, motu primi mobilis ductus: At enim, cum ipse interim motu proprio, eoque contrario moueatur in Zodiaco, & conse- quenter etiam in æquatore singulis diebus ferè gradum vnum, indè est, vt etiamsi expleta vnicæ reuolutione spatio 24. hor. redeat ad eundem circulum positionis, non tamen ibi ponitur cum eodem gradu æquatoris, cum quo pridie erat, sed cum alijs, & alijs successiuè, quos ipse acquirit in dies singulos per proprium motum progrediendo secundùm successionem signorum. Similiter etsi ponatur in eodem circulo positionis, non tamen ponitur in eodem puncto eiusdem circuli, cum motus eius diurnus ratione sui motus proprij non sit circularis, sed spiralis, vnde ratione declinationis, quam successiuè ac- quirit vel deperdit, modò ponitur infra, modò suprà, sed in eodem circulo. Interim primum mobile, & æquator perfi- cit suam reuolutionem circà tellurem minori temporis spatio quàm ipse Sol; nempè in horis 23. & minutis ferè 56. ex quo sit, vt dum Sol ponitur in eodem circulo positionis, in quo pridie erat, ipse vlterius præcesserit ferè integro gradu, vt su- pra explicatum est, cuius situm Sol, vt ad amussim acquirat, requiritur spatium ferè quatuor minutorum temporis; quæ singulis diebus competentia inferunt in vno anno diem vnum naturalem præcessionis: ita vt dum æquator in vno anno facit 366. reuolutiones circà tellurem, eodem tempore Sol inue- niatur perfecisse tantùm 365. circuitiones, vna videlicet mi- nus. Vt igitur & ipse acquirat hoc quod acquisiuit æquator, ponaturque non modo in eodem circulo positionis, sed in eodem puncto præcisè, accum eodem gradu æquatoris, opor- K

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MATHEMATICVM. 149 But this explanation, although ingenious enough in other respects, and which, I confess, has given me access to acquiring, if I am not mistaken, some knowledge of this secret, does not remove the difficulty: for it does not explain by what means such a preordination is made, and how it comes about that, when all the causes come together after, say, fifteen days, and are fully reduced to act, the effect nevertheless does not appear until after fifteen years, and that scarcely some shadow of it appears at that time when the causes display their power? For, as he says, a present fly does more harm than a lion absent. Therefore, if the motion of direction is completed after fifteen days, and the causes are placed in actual readiness to act, then indeed, and not after so long an interval of time, the effect ought to emerge. It must therefore be known that the Sun, which, as we said, is the rule of all motion of direction, completes in the space of 24 hours one whole, and perfect revolution around the earth: so that, when this is completed, it is placed in the same circle of position, and in the same situation of the world, in which it was the day before, when it first began to move from the same point, being carried by the motion of the first movable; but in the meantime, since it moves by its own motion, and that in the opposite direction, in the Zodiac, and consequently also in the equator, by almost one degree each day, this is why, even if, having completed a single revolution in the space of 24 hours, it returns to the same circle of position, it is nevertheless not placed there with the same degree of the equator with which it was the day before, but with different and different ones successively, which it itself acquires day by day by advancing through its own motion according to the succession of the signs. Likewise, although it is placed in the same circle of position, it is nevertheless not placed in the same point of that same circle, since its daily motion, by reason of its own proper motion, is not circular, but spiral; whence, by reason of the declination which it successively acquires or loses, it is sometimes placed below, sometimes above, but in the same circle. Meanwhile the first movable, and the equator, complete their revolution around the earth in a smaller span of time than the Sun itself; namely in 23 hours and about 56 minutes, from which it follows that, while the Sun is placed in the same circle of position in which it was the day before, it has already advanced farther by almost an entire degree, as has been explained above; and to acquire exactly the same position of the Sun requires a space of about four minutes of time; which each day duly add up to in one year one natural day of precession: so that while the equator in one year makes 366 revolutions around the earth, in the same time the Sun is found to have completed only 365 circuits, one fewer, namely. Therefore, in order that it too may acquire what the equator has acquired, and may be placed not only in the same circle of position, but precisely in the same point, together with the same degree of the equator, it is neces- K

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146 LEXICON tet, vt integer annus voluatur, quo interim motu suo paulatim incedens, atque ad dies singulos gradum vnum acquirens perficiat integrum circulum, ponaturque cum ijsdem partibus æquatoris in eodem circulo, atque in eodem puncto positionis, in quo erat cùm primum moueri coepit. Hic igitur est motus directorius, & realis deuolutio Solis ad locum præfixum: qui singulis promissoribus adaptatus ad hoc vt ferantur ad loca moderatorum, tantum temporis sibi vendicat, quantus est arcus æquatoris inter vtrumque interceptus, tribuendo singulis gradibus vnum annum solarem is enim totus requiritur, vt modò diximus, ad hoc, vt Sol paulatim assequatur vnum æquatoris gradum, sitque cum eo in eodem non modo circulo, sed etiam in eodem puncto præciso positionis. Licet enim per vnam integram diem Sol gradum vnum æquatoris præcedat, sitque in eodem circulo positionis in quo pridie erat, integro spatio viginti-quatuor horarum, tamen ibi non est cum eodem gradu æquatoris, neque in eodem puncto eiusdem circuli, sed per quatuor minuta temporis gradus æquatoris, in quo pridie erat Sol, contingit circulu eumdem positionis quam ipse Sol, qui demum ersi mox illum attingat, non ramen in eodem puncto, sed vt id assequatur oportet vt integer annus voluatur, & exæquet circulationem illam qua æquator supergreditur Solis integras, hoc est 365, in anno revolutiones; quo expleto optimè intelligetur deuolutus ad priorem locum, proindeque etiam Promissor ad locum significatoris; sicque effectus tunc tandem prodeat, cum causæ realiter congrediuntur, ac ponuntur in actu secundo ad illum extrà se mittendum. Quod clarius explicari nequit, nisi res omnis in planisphærio oculis spectanda objiciatur. 39. Quoniam autem, vt diximus, Sol motu suo proprio in singulos dies acquirit fere gradum vnum in æquatore, & insuper motu raptus facit integram circulationem, & ponitur in eodem circulo positionis, licet non cum eodem gradu æquatoris, sed ille per quatuor minuta temporis præcessit, atque eumdem positionis circulu attigit quæ tépotis præcessio singulis æquatoris gradibus adaptata, constituunt integrum diem naturalem, inde sit, vt integer dies naturalis sit mensura vnius anni (hoc est totius temporis, quod requiritur vt Sol denuò attingat eumdem gradum æquatoris, & cum eo ponatur in eodem circulo positionis) & aux horæ æquinoctiales sint mensura peragrationis Solis in vno mense, ac demum quatuor minuta temporis sint mensura vnius dici, quo tempore sit præordinatio eorum, quæ futura sunt tempore expletæ directionis: nempe post vnum diem eorum quæ futura sunt post

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146 LEXICON that, in the course of one year, while meanwhile advancing little by little by its own motion, and acquiring one degree each day, it may complete a whole circle, and be placed with the same parts of the equator in the same circle, and in the same point of position, in which it was when it first began to move. This, therefore, is the directorial motion, and the real revolution of the Sun to the appointed place: which, being adapted in each of the promissors for this purpose, that they may be carried to the places of the moderators, claims for itself so much time as is the arc of the equator intercepted between the two, assigning to each degree one solar year; for the whole of it is required, as we said just now, for this end, that the Sun may gradually reach one degree of the equator, and be with it not only in the same circle, but also in the same precise point of position. For although in one entire day the Sun precedes one degree of the equator, and is in the same circle of position in which it was the day before, over a full space of twenty-four hours, yet there it is not with the same degree of the equator, nor in the same point of the same circle, but within four minutes of time the degree of the equator, in which the Sun was the day before, meets that same circle of position which the Sun itself occupies; and although it then at last reaches it, nevertheless not in the same point, but in order to attain that it is necessary that a whole year should elapse, and that the revolution by which the equator overtakes the Sun should be made equal, that is, 365 revolutions in a year; which being completed, it will be clearly understood to have returned to its former place, and therefore also the Promissor to the place of the significator; and thus the effect then at last comes forth, when the causes truly come together, and are placed in second act for the purpose of being sent outward to it. This cannot be explained more clearly unless the whole matter is presented to the eyes to be viewed in a planisphere. 39. Since, however, as we have said, the Sun by its own motion in each day acquires almost one degree in the equator, and besides this, by its carried motion makes a complete revolution, and is placed in the same circle of position, though not with the same degree of the equator, but that degree has passed on by four minutes of time, and it has attained the same circle of position, which temporal advancement, adapted to each degree of the equator, constitutes one whole natural day, hence it comes about that one whole natural day is the measure of one year (that is, of the whole time which is required for the Sun again to reach the same degree of the equator, and to be placed with it in the same circle of position) and that the equinoctial hours are the measure of the Sun’s course in one month, and finally that four minutes of time are the measure of one day, during which time there is the preordination of those things which are to come at the time of the completed direction: namely, after one day those things which are to come after

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MATHEMATICVM. 147 annum, & post duos dies, eorum quæ futura sunt post duos annos &c. Qui sit vt hæc diurna circulatio vocari possit anticipata quædam directio, &, vt eam vocat Titus, Directio secundaria (licet ipse aliter eam explicet) in qua ob similitudinem motus apparet vmbrasilis quædam inceptio directionis. Et hinc originem trahunt dies, & anni climacterici, in quibus Prorogator ponitur in loco respondente per aliquem radium ad locum directionis, ac Luna in morbis ponitur ad loca respondentia loco sui natalis, vel ab initio morbi vt post septem dies in quadrato, post 11. in oppositione loci radicalis &c. Verùm de his latiùs in V. Figura sexdecim laterum, & in V. Climactericus. < 40.> Porrò duplex est motus directionis, vt aliàs diximus, alter rectus à Ptolemaeo Actinobolus dictus, hoc est projectio radio- rum, qui sit in consequentiam signorum; & intelligitur fieri, vt Moderator existens immoblis in situ mundi, dirigatur ad astra, quæ sunt in locis orientalioribus secundùm successionem signorum: non quod ipse verè vadat ad illa, cùm vt dixi, constituar immobilis in suo circulo positionis, sed quod eo immobili permanente in suo situ, astra interim motu primi mobilis rapiantur, versus occidentaliores partes, adeoque impingant in situm Moderatoris. Alter est conuersus dictus Horinxus, qui sit contrà successionem signorum, & est cum ipse Moderator motu primi mobilis rapitur ad loca promissorum, qui in eo casu considerantur immobiles in suo situ mundi, seu circulo positionis, vbi expectant aduentum Moderatoris motu primi mobilis procedentem: duplex enim virtus tam promissoris quàm prorogatoris imprimitur, seu constituitur immobilis in duplici loco, altera in gradibus signorum, & in primo mobili, altera in situ mundi, & circulo positionis in, quibus reperiuntur tempore inceptionis alicujus rei: vt benè aduertit Titus cap. 4. & alibi sæpè: ergo necesse est, vt quæ in primo mobili constituta est, moueatur cum ipsa, & feratur ad loca in mundo qualitatibus contrariorum affecta, quod est conuersè dirigi: quæ verò in mundo imprimitur ster immobiliis, & expectet aduentum astrorum, seu radiorum infixorum in primo mobili, quæ ad ipsam ferantur; quod est dirigi recte. Quod ideò monet idem Titus, cardines non posse dirigi nisi rectè: non enim ipsi vadunt ad aliquem, cum considerentur tantum in mundo, sed astra, & partes primi mobilis ad ipsos feruntur, ergo tantùm accipiunt familiaritates in mundo, minimè verò in Zodiaco. < 41.> Quomodo autem instituenda sit praxis huiusmodi directionis supputandæ, non est nostri instituti explicare, præsertim K ij

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MATHEMATICVM. 147 a year, and after two days, of those things which are to happen after two years, and so forth. So that this daily circulation may be called a kind of anticipated directing, and, as Titus calls it, a secondary Direction (though he explains it otherwise), in which, by reason of the likeness of the motion, there appears a shadowy kind of beginning of direction. And hence take their origin the climacteric days and years, in which the Prorogator is placed in a place corresponding by some ray to the place of direction, and the Moon in diseases is placed at places corresponding to the place of her nativity, or from the beginning of the disease, as after seven days in square, after 11 in opposition of the radical place and so forth. But concerning these things more at length in V. Figure of sixteen sides, and in V. Climacteric. < 40.> Moreover, the motion of direction is twofold, as we have said elsewhere: one straight, called by Ptolemy Actinobolus, that is, the projection of the rays, which is in the succession of the signs; and it is understood to be done as the Moderator, remaining immobile in the position of the world, is directed toward the stars which are in the more eastern places according to the succession of the signs: not that he truly goes to them, since, as I said, he is constituted immobile in his circle of position, but because, while he remains immobile in his place, the stars in the meantime are carried by the motion of the first mover toward the more western parts, and thus strike against the place of the Moderator. The other is called reversed, Horinxus, which goes contrary to the succession of the signs, and is when the same Moderator is carried by the motion of the first mover to the places of the promissors, who in that case are considered immobile in their place in the world, or circle of position, where they await the coming of the Moderator proceeding by the motion of the first mover: for a double power, both of the promissor and of the prorogator, is impressed, or is constituted immobile in a double place, one in the degrees of the signs, and in the first mover, the other in the place of the world, and the circle of position in which they are found at the time of the beginning of some thing: as well noted by Titus, cap. 4, and elsewhere often: therefore it is necessary that what is constituted in the first mover be moved with it, and be carried to places in the world affected by the qualities of contraries, which is to be directed in reverse; but what is impressed in the world remains immobile, and waits for the arrival of the stars, or of the rays fixed in the first mover, which are carried toward it; which is to be directed rightly. For this reason the same Titus warns that the angles cannot be directed except rightly: for they do not go toward anyone, since they are considered only in the world, but the stars and parts of the first mover are carried toward them; therefore they receive familiarities only in the world, least of all in the Zodiac. < 41.> But how, moreover, the practice of this kind of computed direction is to be established, it is not our purpose to explain, especially K ij

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148 LEXICON cum apud omnes Professores passim obuia sit: sit enim aut per ascensoria tempora & distantiam à meridiano vtriusque tam significatoris, quam promissoris, aut per ascensiones seu rectas, seu obliquas vtriusque, sumptas ad rationem eius, ad quem sit deductio. De qua re fusè agit Titus lib. 3. caesesis Philosophia, à cap. 14. vsque ad cap 16. & fusiùs adhuc, atque ex professo in primo mobis, tradens etiam quomodo Sol in spatijs crepusculinis non sit dirigendus in circulis hotarijs, in quibus fiunt proportionales distantiæ à cardinibus, sed in circulis parallelis ad horizontem, in quibus quamcumque declinationem habeat servat semper eumdem erga nos gradum intensionis lucis, secundùm quam omnem suam actiuitatem exerit. Solum hic ex eodem Tito, ac doctrina superiùs tradita, quæ non nihil à communi discrepat, exponere volo modum adæquandi arcum directionis ad expiscandos præcisè annos, & menses effectuum. Igitur arcus directionis elicitus addatur ascensioni rectæ Solis, ac deinde in tabula ascensionum rectarum requirendus gradus Eclipticæ huic summæ competens: posteà computandi dies, & horæ, quas Sol insumpsit à puncto natiuitatis quousque ad dictum gradum peruenerit; nam dies qui præcessetunt, annos, singulæ binæ horæ, menses denotant, post quos apparebit effectus promisses per directionem. DIRECTVS dicitur planeta, cum motu suo proprio in Zodiaco sertur in consequentiam signorum: sicut è contrà Rettogradus, cùm mouetur à consequentibus in antecedentia signa. Esse autem directum, est species quædam dignitatis ex accidente planetæ aduenientis. Nam cum motu suo perductur contrà motum primi mobilis ab Occidente in Orientem nitatur; inde sit, vt seriùs occidat quàm ipsæ primi mobilis partes, ac proinde diutiùs supra terram consistat, plus temporis consequenter habeat ad illam suis qualitatibus imbuendam. Vide in V Auctus numero. DISCORA Græcè apud Ptoleimæum 3. Quadrip. cap. 7. ex Versione Arabica Hali, significat Genituram duorum masculorum, & vnius femellæ, in quam conueniant Saturnus, Iupiter, & Venus. DISCVS Græcè propriè patinam rotundam exprimit: inde hoc vocabulum ad omnem figuram rotundam, & planam significandam aptarum est: Quamobrem, & corpora luminarium, quæ quamuis perfectè sphætica, & rotunda, tamen ob nimiam distantiam plana videntur, & referunt quandam disci figuram, discus Solatis, & discus Lunatis sunt appellata; in quorum visa planitie diametrum Astronomi concipiunt, quam in æquales partes diuidunt omninò duodecim, quas & vncias,

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148 LEXICON since it is commonly found everywhere among Professors: for it is either by ascensional times and the distance from the meridian of both, both of the significator and the promissor, or by ascensions, whether right or oblique, of both, taken in proportion to the one to which the deduction is made. Titus discusses this matter at length in book 3 of Caesesis Philosophia, from chapter 14 to chapter 16, and even more fully, and expressly, in the first Mobile, also showing how the Sun in crepuscular spaces is not to be directed in the horizon circles, in which proportional distances are made from the cardines, but in circles parallel to the horizon, in which, whatever declination it may have, it always preserves the same degree of light’s intensity toward us, according to which it exerts all its activity. Here I wish only, from the same Titus and the doctrine set out above, which differs somewhat from the common view, to explain the method of adjusting the arc of direction in order to determine exactly the years and months of the effects. Therefore, let the arc of direction obtained be added to the Sun’s right ascension, and then in the table of right ascensions the degree of the Ecliptic corresponding to this sum is to be sought; afterward, compute the days and hours which the Sun has used from the point of nativity until it has reached the said degree; for the days which precede denote years, and each two hours denote months, after which the promised effect through direction will appear. DIRECT is said of a planet when by its own motion in the Zodiac it is carried in the order of the signs; as, on the contrary, RETROGRADE, when it moves from the succeeding signs into the preceding ones. To be direct, however, is a certain kind of dignity arising from an accident that comes to the planet. For since, by its own motion, it is carried contrary to the motion of the primum mobile, striving from West to East; it follows that it sets later than the parts of the primum mobile itself, and therefore remains above the earth longer, and consequently has more time to be imbued with its qualities. See in V Auctus, number. DISCORA, in Greek, in Ptolemy’s Tetrabiblos, book 3, chapter 7, from the Arabic version of Haly, means the nativity of two males and one female, in which Saturn, Jupiter, and Venus agree. DISCUS, in Greek, properly expresses a round plate: hence this word has been suited to signify every round and flat figure. For this reason, too, the bodies of the luminaries, which although perfectly spherical and round, nevertheless appear flat because of their great distance, and present a certain figure of a disc, have been called the disc of the Sun and the disc of the Moon; in whose apparent flatness astronomers conceive the diameter, which they divide into equal parts, namely twelve, which are also called ounces,

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MATHEMATICVM. 149 & digitos eclipticos vocauere, quorum posteà ope quantitatem obscurationis eorum in eclipsibus metiuntur. Hinc etiam DISCEVS à figura disci quam præsèfert, dicitur quidam Cometa, lata rotunditate refulgens, colo se electrino, vt habet Plinius, & raris in margine radijs circumseptus, qui habet naturam Veneris. DISPOSITOR apud Astronomos audit planeta, qui super aliquem locum dispositionem habet, dominatum, & curam: Vnde & Dispositio aliud non est, quàm cura, & munus decernendi de eo loco in quo planeta potiores habet prærogatiuas ex quinque essentialibus, Domicilio nempe, Exaltatione, Trigono, Terminis, & Persona. Qui ergo, facto scrutinio, super aliquem locum Eclipticæ plura habet dignitatum suffragia, is dicetur eiusdem loc[us] dispositor. Sic ponamus casum, quod celebranda sit luminatium synodus in grad. 2. Virginis; eius dispositio, ac jus decernendi pertinet ad Mercurium, eò quia in dicto loco Mercurius cæteris antecellit in dignitatum cumulo: haber enim ibi jus Domicilij, Exaltationem, & Fines. Is ergo erit dictæ conjunctionis dispositor: ad quem proinde spectabit decernere de qualitatibus aëris, aliisque quæ ex tali conjunctione prouenient. DIVISOR apud Arabes (qui eum lingua sua propria nominarun[us]) est planeta, qui habet prærogatiuam sinium, seu terminorum, in quibus incidit directio, aut rei alicuius significatio: Planeta autem, qui respicit eundem gradum siue in eo repertus fuerit, dicitur compar, & particeps diuisionis. Quomodo autem is eliciatur, dictum est supra in Verbo Algebusar. DIVISOR, etiam apud Arithmeticos dicitur numerus qui partes diuidendas denominat, seu in quas numerus diuidendus assumitur, vt est verbi gratiâ 9. respectu numeri 36. DIVRNVS, & Nocturnus denominatur. Planeta, aut signum, quod vincit in qualitatibus actiuis & passiuis. Etenim si vincant in eo qualitates actiæ dicetur diurnum, si præpolleant passiux, nocturnum Qualitates actiæ ex Philosopho sunt calor, & frigus; passiæ humiditas, & siccitas: Hinc cum Saturnus, exempli gratiâ, sit magis frigidus, quàm siccus; Iupiter magis calidus, quàm humidus. Sol magis calidus, quàm siccus, &c. dicuntur planetæ diurni. E contra quia Mars est magis siccus, quàm calidus, Luna magis humida quàm frigida, dicuntur passiui, & nocturni. Similiter in signis discurrendum: quorum ratio à respectu ad puncta Cardinalia, vnde sidera incipiunt influere primas qualitates, auspicanda est, vt benè discurrit Titus in Cælesti Philosophia. K iij

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MATHEMATICVM. 149 and they have called them the ecliptic digits, by means of which afterward they measure the quantity of their obscuration in eclipses. Hence also DISCEVS, from the shape of the disc that it bears, is called a certain comet, shining with broad roundness, like an electrinum pole, as Pliny has it, and surrounded by sparse rays on the margin, which has the nature of Venus. DISPOSITOR, among astronomers, is the planet that has disposition, dominion, and care over some place. Whence also Dispositio is nothing other than care, and the office of deciding concerning that place in which a planet has the greater prerogatives from the five essential dignities, namely Domicile, Exaltation, Trine, Terms, and Face. Therefore, whoever, after scrutiny, has more votes of dignities over some place of the Ecliptic, will be called the dispositor of that place. Thus let us suppose the case that a conjunction of the luminaries is to be celebrated in the 2nd degree of Virgo; its disposition, and the right of deciding, pertains to Mercury, because in that place Mercury surpasses the others in the accumulation of dignities: for there he has the right of Domicile, Exaltation, and Terms. He therefore will be the dispositor of the said conjunction; and it will therefore be his part to decide concerning the qualities of the air, and other things which will arise from such a conjunction. DIVISOR, among the Arabs (who named him in their own language), is the planet that has the prerogative of the bounds, or terms, in which a direction, or the signification of some matter, falls: but the planet that regards the same degree, whether it be found in it or not, is called the companion and partner of the division. How this is to be drawn out has been said above under the word Algebusar. DIVISOR is also called, among arithmeticians, the number that denominates the parts to be divided, or those into which the number to be divided is taken, as, for example, 9 with respect to the number 36. DIVRNVS, and Nocturnus, is the name given to a planet or sign that prevails in active and passive qualities. For if active qualities prevail in it, it is said to be diurnal; if passive qualities are predominant, nocturnal. According to the Philosopher, active qualities are heat and cold; passive, humidity and dryness. Hence when Saturn, for example, is more cold than dry; Jupiter more warm than humid. The Sun more warm than dry, and so forth, they are called diurnal planets. On the contrary, because Mars is more dry than warm, and the Moon more humid than cold, they are called passive and nocturnal. Likewise this is to be applied to the signs: the reason for this, drawn from the relation to the Cardinal points, from which the stars begin to influence the primary qualities, must be taken as the starting point, as Titus discusses well in Celestial Philosophy. K iij

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150 LEXICON DO 49. Docvs apud Geometras est figura, quæ latitudine, & crassisitie caret, tamen habet longitudinem. Hinc ignite quædam aëris impressiones oblongæ, & trabis similitudinem referentes, teste Plinio lib. 2. cap. 24. Docos Græci appellauêre. 50. DODECARDRVM de[n]n[it]it Euclides, quod sic figura solida sub duodecim pentagonis æqualibus, & æquilateris, & æquiangulis contenta: sicut Tetraedrum est figura quatuor triangulis constans, Octaedrum octo triangulis; Icoedrum figura sub viginti triangulis æqualibus, & æquilateris comprehensa. 51. DODECATEMORION communiter accipitur ab Astronomis pto duodecima quaque parte signiferi, quæ triginta gradus comprehendit, siue vnum integrum signum. Vnde dicitur Dodecatemotion Arietis, Dodecatemorion Tauri &c. Aliquando etiam sumitur pro domibus cælestibus in siru Mundi consideratis, quæ constituuntur per æqualem æquatoris diuisionem in duodecim partes. Singulis gradus triginta attribuendo. Scaliger verò ad Manilium ait Dodecatemorion esse duodecimam signi vnius partem, hoc est gr. duo cum dimidio. Certè visitarius sumitur pro integro signo. 52. DOMICILIVM est dignitas planetæ in signo, in quo ob conformitatem naturæ ita reperitur, ac si esset homo in domo sua. Et hæc est vna, immò & potissima ex quinque dignitatibus essentialibus, cui Astronomi, præsertim antiquiores tribuebant quinque suffragia fortitudinis; cum alias Exaltationi quatuor, Trigono tria, Terminis duo, Faciei, seu Decanatui tribuerent vnum: Vnde & Versus. Quinque suis domibus clares fortitur honores: Quattuor in solio quisque planeta suo: Finibus inque suis binos sibi aure triumphos, Tres autem in propria triplicitate capit. Vnam dumtaxat, fuerit si forte Decana Quisque suo, vases quod decuere boni. Neque hæc fortitudo planetæ in suo domicilio inanis est, vt non ratione, atque experimentis pateat conuenientissimè excogitata. Nam duo signa Cancri, & Leonis, quæ proximiùs ad nostrum verticem accedunt, reliquis validiora esse, nemo est, qui non videat: Iure igitur duobus luminaribus, quæ cæteris planetis actiuitate præcellunt, & à quibus omnium vira dependet assignata sunt; & Soli quidem planetæ calido, & sicco, calidi innati in viuentibus auctori atque fotori, signum Leonis, calidum item & siccum, in quo ipse existens mirificè calores suos impertit, vires suas adauget. Lunæ verò planetæ

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150 LEXICON DO 49. Docvs among geometers is a figure which lacks breadth and thickness, yet has length. Hence certain fiery impressions of the air, oblong and resembling beams, as Pliny witnesses, lib. 2, cap. 24, the Greeks called Docoi . 50. DODECARDRVM Euclid defines as that solid figure contained under twelve equal, equilateral, and equiangular pentagons: just as the tetrahedron is a figure consisting of four triangles, the octahedron of eight triangles, the icosaedrum of a figure comprehended under twenty equal and equilateral triangles. 51. DODECATEMORION is commonly taken by astronomers for the twelfth part of the zodiac, which comprehends thirty degrees, that is, one whole sign. Hence there is the Dodecatemorion of Aries, the Dodecatemorion of Taurus, etc. Sometimes also it is taken for the heavenly houses considered in the system of the world, which are constituted by the equal division of the equator into twelve parts, assigning thirty degrees to each. Scaliger, however, in his remarks on Manilius says that Dodecatemorion is the twelfth part of one sign, that is, 2 degrees 30 minutes. Certainly it is more commonly taken for a whole sign. 52. DOMICILIVM is the dignity of a planet in a sign, in which, because of conformity of nature, it is found as though a man were in his own house. And this is one, indeed the principal, of the five essential dignities, to which astronomers, especially the older ones, assigned five votes of strength; since to Exaltation they assigned four, to Trine three, to Terms two, to Face, or Decan, one: Whence also these verses. By his own houses he shines, winning honors: Four upon his own throne does each planet receive: In his own bounds he takes twin golden triumphs, Three also in his proper triplicity gains. Only one, if by chance he be in his Decan, Each one gets, which good vessels adorned him. Nor is this strength of a planet in its own domicile empty, so that it may not be shown by reason and experience to have been most suitably devised. For the two signs Cancer and Leo, which approach our zenith more closely, are stronger than the rest; no one, indeed, can fail to see it. Therefore by right they were assigned to the two luminaries, which surpass the other planets in activity and upon which the life of all things depends; and to the Sun, a planet hot and dry, the sign Leo, likewise hot and dry, in which, when it is placed, it wonderfully imparts its heat and increases its powers. But for the Moon, the planet

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MATHEMATICVM. 117 natura sua humido, & frigido, humidi radicalis origini, si- gnum quoque humidum & frigidum, quale est Cancer, tri- buendum erat. E contrà Saturnus omnis interius author, cali- di innari, radicalisque humoris destructor, & inimicus oppo- sitas hisce luminarium sedes occupare debebar, nempe Capri- cornum, & Aquarium cæteris humidiores, & quæ maxime di- stant à nostro vertice, sicut longe distar Saturnus à terra. Ex quibus Capricornus ob conformitatem naturæ (est enim vt ille natura frigidus & siccus) prima sedes foret. Mars etiam na- tura maleficus, cum vitam à luminaribus originatam sua ma- lignitate concutiat, eas domos sibi vendicare debebar, quæ hostili radio domos luminarium infestarent; idcircò attributa sunt ei signa Arietis, & Scorpij, quæ de quadraro signa lumi- narium intuerentur: E contrà benefici, ea loca haberent, quæ amicitiæ vinculo locis luminarium nectorentur: ideò Ioui fortunæ maiori ex domus assignandæ erant, quæ amicitiæ per- fectæ nexu, nempe radio trino cum locis luminarium vniren- tur, Sagirrarius, inquam, & Pisces. Veneri autem fortunæ minori Taurus, & Libra, quæ easdem domos respiciunt de Sextili. Tandem Mercurio, qui est omnium planeratum pro- ximior luminaribus; quippe à Sole nunquam corpore elon- garur plus gr. 28. Lunæ verò est contiguus ratione orbis, ex domus daræ sunt, quæ proxime accedunt ad luminarium do- mos, videlicet Gemini, & Virgo: Et hæc est ratio domicilio- rum, ac distributionis conuenienter factæ pro singulis pla- netis. DOMVS item vocatur duodecima quæque Cæli pars in situ < 53.> mundi considerata: diuidunt enim Astronomi superius, atque inferius hemisphærium in quatuor quadrantes, duos quos vo- cant Orientales, à linea videlicet horizontali ad lineam meri- dianam supra terram, & ab occasu ad lineam Imi cæli; reli- quos duos, quos Occidentales appellant à linea Meridiana ad occasum; atque ab Imo cæli ad Ortum. Hos autem quadrantes in ternas partes dispescunt: Ptolemæus quidem per binas horas temporales, rationales verò per duos circulos magnos tran- seuntes per communes intersectiones horizontis, & Meridiani, quorum ope diuiditur æquatuor in duodecim partes æquales, singulis domibus triginta æquatoris gradus attribuentes, nulla Zodiaci habita ratione, sed eo, vt jacer sub æquatore in partes siue æquales, siue inæquales, quæ videlicet intercipiuntur intrà fines horum circulorum, tributo. Et has intercapedines Dodecatemorias, domos, angulos succedentes, & cadentes ab angulis Astronomi appellarunt; quasum ordo esset inuer- sus, & contrà motum primi mobilis ordinatus: ita vt prima K iiiij

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MATHEMATICVM. 117 Since by its own nature it is moist and cold, to the origin of radical moisture there ought also to be assigned a sign likewise moist and cold, such as Cancer. On the contrary, Saturn, the author of all inward heat, and the destroyer and enemy of radical moisture, ought to occupy the opposite seats of these luminaries, namely Capricorn and Aquarius, which are moister than the others, and which are farthest from our zenith, just as Saturn is far distant from the earth. Of these, Capricorn, on account of conformity of nature—for it is by nature cold and dry like that planet—would be the first seat. Mars also, by nature malefic, since by his malignity he shakes the life originating from the luminaries, ought to claim those houses for himself which would harass the houses of the luminaries with a hostile ray; therefore the signs of Aries and Scorpio were assigned to him, which by square aspect look toward the houses of the luminaries. On the contrary, the benefics should have those places which are joined to the places of the luminaries by a bond of friendship; therefore for Jupiter, the greater fortune, houses were to be assigned which unite by the bond of perfect friendship, namely by the trine ray, with the places of the luminaries: Sagittarius, I say, and Pisces. For Venus, the lesser fortune, Taurus and Libra, which regard the same houses by sextile. Finally Mercury, who is nearest of all the planets to the luminaries—for in body he never departs from the Sun by more than 28 degrees, and in respect of orbit he is contiguous to the Moon—should have houses given to him which approach most closely to the houses of the luminaries, namely Gemini and Virgo. And this is the reason for the domiciles, and for the distribution suitably made for each planet. A house is also called each twelfth part of the heaven considered in the situation of the world. The astronomers divide the upper and lower hemisphere into four quadrants, two of which they call Oriental, namely from the horizontal line to the meridian line above the earth, and from the west to the line of the lower heaven; the other two, which they call Occidental, from the meridian line to the west, and from the lower heaven to the east. But they divide these quadrants into three parts: Ptolemy indeed by means of two temporal hours, but the rational astronomers by means of two great circles passing through the common intersections of the horizon and the meridian, by whose means it is divided into twelve equal parts, assigning to each house thirty degrees of the equator, no regard being had to the Zodiac, but only to that which lies beneath the equator, in parts either equal or unequal, which are intercepted within the bounds of these circles. And these intervals the astronomers have called dodecatemories, houses, succedent and cadent angles; whose order would be inverted, and arranged contrary to the motion of the first mobile: so that the first K iiiij

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152 LEXICON domus esset horoscopus, quæ comprehenderet quinque gradus æquatoris supra terram, & vigintiquinque sub terra: secunda domus diceretur non quam mox acquirunt sidera motu diurno lara, sed quæ proximè succederet Orienti sub terra: inde tertia, quæ propè esset Meridiano subterraneo, post quarta, Meridianus ipse subterraneus, & Imum cæli, & sic de singulis, incipiendo à quinque gradibus æquatoris præcedentibus cuspidem vsque ad triginta secundùm successionis ordinem, hoc est 25. à cuspide. Quare autem totum cælum, seu mundi ambitus in duodecim non plus, nec minus partes, seu domicilia sit dissectus, variæ suppetunt rationes, quarum potissima desumitur ratione aspectuum, & ex dignitate duodenarij numeri. Cùm enim is solus præ cæteris diuidi possit in duas, tres, quatuor, sex, ac duodecim partes æquales jure is erat præ cæteris eligendus, qui commodè omnes aspectus ad cardines exhibere posset, cæteris numeris ad eam rem minimè congruentibus. Porro duodecim cæli domorum significata, proprietates, & accidentia, si quis ediscere volet, proprias cuiusque dictiones suis in locis consulat. 54. DOMINVS anni , secundùm Arabes dicitur is planeta, qui in signo profectionali horoscopi dominium obtinet, ac jus domicilij: Vt si horoscopus, exempli gratia, hoc anno profectione transeat in signum Arietis, Mars dicetur anni dominus; sequenti verò anno erit Venus, quia signum profectione horoscopi est Taurus, in quo jus domicilij habet ipsa Venus, &c. Hunc plurimi faciunt in anni revolutionibus antiquiores Arabes, contendentes suis nugis eum esse maximæ auctoritatis, atque efficaciæ in rebus illo anno euenientibus decernendis; quæ prorsus delitamenta sunt. Ea in præsenti refellere, neque instituti mei est, neque rei dignitatis. Id vnum moneo, quoderiamsi è re foret illum admittere in profectionibus annuis colligendis, id faciendum esse, non per æqualem illum motum, ac profectionem locorum hylegialium per singula Zodiaci signa, tribuendo cuilibet anno solari signum vnum, quemadmodum hucusque Astronomi omnes tradiderunt, sed eo modo, quem nuper ex veris philosophiæ principijs inuenit ingeniosissimus, atque amicissimus P. Titus; nosque in loco vbi profectionum sermo inciderit, explicabimus. 55. DOMINVS genitura , apud Genethliacos dicitur is planeta, qui totius genitutæ sibi arrogat vniuersale dominium, quique alijs præstat in judicio temperamenti, morum (quantum naturales animi propensiones appellant) affectionum corporis, & similium, vnde natus in vniuersum, nomen Iouialis, Satur-

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152 LEXICON The first house would be the horoscopus, which would comprise five degrees of the equator above the earth, and twenty-five below the earth; the second house would be called not that which the stars immediately acquire by the daily motion, but that which would next succeed the Ascendant under the earth; then the third, which would be near the subterranean Meridian; after that the fourth, the subterranean Meridian itself, and the Imum cæli, and so of each in turn, beginning from the five preceding degrees of the equator up to thirty according to the order of succession, that is 25 from the cusp. But why the whole heaven, or the circuit of the world, is divided into twelve, neither more nor less, parts, or domiciles, there are various reasons, the chief of which is drawn from the aspects and from the dignity of the number twelve. For since this alone, more than the others, can be divided into two, three, four, six, and twelve equal parts, it was rightly to be chosen above the others, as one that could conveniently exhibit all aspects to the angles, the other numbers being least suited to that purpose. Moreover, if anyone wishes to learn the significations, properties, and accidents of the twelve houses of heaven, let him consult the proper terms of each in their own places. 54. DOMINVS of the year , according to the Arabs, is called that planet which in the profectional sign of the horoscopus obtains dominion and the right of domicile: thus if the horoscopus, for example, in this year by profection passes into the sign of Aries, Mars will be called lord of the year; the following year, however, Venus will be, because the profectional sign of the horoscopus is Taurus, in which Venus herself has the right of domicile, &c. The older Arabs make much of this in revolutions of the year, contending in their follies that it is of the greatest authority and efficacy in determining the events that happen in that year; these are altogether trifles. To refute them at present is neither my purpose nor consistent with the dignity of the subject. This alone I note, that even if it were useful to admit it in annual profections being calculated, it should be done not by that equal motion, and profection of the hylegial places through each sign of the Zodiac, assigning to each solar year one sign, as all astronomers have hitherto handed down, but in that way which recently, from the true principles of philosophy, the most ingenious and very dear Father Titus has discovered; and we shall explain it in the place where discourse on profections comes up. 55. DOMINVS nativity , among genethliacs is called that planet which arrogates to itself universal dominion over the whole nativity, and which surpasses the others in judgment of temperament, of manners (so far as the natural inclinations of the mind are called) of bodily affections, and the like, whence the native in general is named Jovial, Satur-

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MATHEMATICVM. 155. nimi, Mercurialis, sortitur. Ad quem præcisè pertineat hoc jus, non adhuc benè compertum. Iulius Firmicus magni no- minis author, quique floruit circà annos Christi 310. eum planetam huic dominio præficit, qui præest signo, in quod proximè ingreditur Luna post editum færum: exceptis ta- men ab hac prærogatiua luminatibus, vtpote vniuersalibus te- rum significatotibus. Sic exempli gratiâ posito, quod Luna genituræ tempore in Ariese reperiatur, genituræ domina erit Venus, eò quod Tauri signo, in quod proximè ingrediitur Luna post natiuitatem, Venus dominatur: Sed demus Lunam Geminos possidere; tunc profectò prætermisssis Cancro, & Leone luminarium domicilijs, transiit ad Virginem, cui præest Mercurius, qui propterea totius genituræ vniuersale dominium sortietur. Hæc Firmæmens, cui subscribit Pontanus, & non pauci ex recentioribus. Reuera tamen id nec vali- da ratione deductum, nec cum effectibus consonat. Et scimus Firmicum Latinè magis, quàm Philosophicè scripsisse, vt aduertiteriam Iunctinus; vnde & eius scripta propter sermo- nis elegantiam ab Ecclesia permissa sunt, cum aliàs multa ibi absona, Arabum superstitionibus inuoluta confarcinauerit: sicut & Pontanum, Poëtam magis, quàm Astrologum egisse. Alij absolutè eum huic dispositioni præficiunt, qui fuerit dominus ascendentis, vel in ascendente partiliter repetius. Et sanè, nulli dubium, ascendentis dominum, siue Almurhem, ac Planetam in eo repertum plurimùm posse in decernenda complexionenati: at in alijs, non ita clarè. Alij cum statuunt genituræ dominum, in cujus finibus tempore natiuitatis Sol reperiatur in geniura diurna, Luna verò in nocturna. Com- munior tamen sentencia insistens Ptolemæi præceptis, in ijs quæ habet lib. 3. Qu. drip. cap. 11. (vbi agit de Aphææ ele- ctione, quando luminaria vitæ moderationem fortuii ne- queunt) docenus, vt is eligatur in Aphetam, ex quinque erraticis, qui cum sit in locis idoneis, plures prærogatiuas habuerit in locis luminarium, ascendentis, medij cæli, & partis fortunæ (alij pro parte fortunæ ponunt locum præcedentis lu- minarium conjunctionis, aut oppositionis) ita & ipsi illum planetam præficiunt vniuersali rerum dominio, qui in omni- bus hisce locis plures prærogatiuas habens, cæteris anteibit; atque eum qui, facto scrutinio, proximus illi erit in numero dignitatum, in huius dominij participationem admittunt, exclusis semper luminaribus. Ego sanè, omnibus perpensis, ratione, & experientia du- ctus, ijs assentiri cogot, qui existimant eum planetam in hoc negotio præficiendum esse, qui cæteros vincet in fortitudine;

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MATHEMATICVM. 155. Mercurialis is assigned by them. To whom precisely this right belongs has not yet been well established. Julius Firmicus, an author of great name, who flourished around the year of Christ 310, assigns this planet to this rulership, which presides over the sign into which the Moon next enters after the birth: excepting, however, the luminaries from this prerogative, as universal significators of things. Thus, for example, if the Moon at the time of nativity is found in Aries, Venus will be the ruler of the nativity, because Venus rules Taurus, the sign into which the Moon next enters after birth. But let us suppose the Moon to occupy Gemini; then, passing over Cancer and Leo, the domiciles of the luminaries, it comes to Virgo, over which Mercury presides, and he will therefore obtain the universal dominion of the whole nativity. This is Firmicus, to whom Pontanus subscribes, as do not a few of the more recent writers. Yet in truth this is neither deduced by sound reasoning nor consonant with the effects. And we know that Firmicus wrote more in Latin than philosophically, as Iunctinus observes; hence his writings were permitted by the Church on account of the elegance of the language, although elsewhere he had stuffed them with many absurdities, wrapped up in Arabic superstitions; just as Pontanus acted more as a poet than as an astrologer. Others absolutely assign to this disposition the ruler of the ascendant, or the planet found partilely in the ascendant. And indeed, no one doubts that the lord of the ascendant, or Almurhem, and the planet found in it, can do very much in determining the complexion of the native; but in other matters, not so clearly. Others, again, set as ruler of the nativity that in whose boundaries the Sun is found at the time of birth in a diurnal nativity, but the Moon in a nocturnal one. The more common opinion, however, adhering to Ptolemy’s precepts in those matters which he treats in book 3, Qu. drip. chapter 11, where he discusses the election of the Aphæa, when the luminaries cannot govern the moderation of life, teaches that the Aphæa is to be chosen from among the five wandering stars, namely that one which, while being in suitable places, has the greater number of prerogatives in the places of the luminaries, of the ascendant, of the midheaven, and of the part of fortune (others, in place of the part of fortune, put the place of the preceding conjunction or opposition of the luminaries). Thus they also assign universal dominion over things to that planet which, having the greater number of prerogatives in all these places, will surpass the others; and they admit into participation in this dominion that one which, after examination, is nearest to it in the number of dignities, the luminaries always excluded. For my part, considering everything, led by reason and experience, I am compelled to agree with those who think that the planet to be set over this matter is the one that will surpass the others in strength;

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154 LEXICON sirque ideò in angulis, aut succedentibus (alijs in locis vilioribus existentibus) cursu velox, lumine plenus, atque in suis dignitatibus essentialibus. Ratio, quæ me mouer, hæc est: quia hic agitur de majori actiuitate, & concurrentia ad operandum in omnibus; cum semper, qui viribus præualet, maiores exerat in agendo. Sic plus præstabit in prælio generosus miles optimis armis munitus, viribus potens, situ eminens, amicorum patrocinio sultus, & numeris omnibus absolutus, quàm Dux, qui cæteris quidem præsit, verùm grauiter vulneratus, viribus impotens, in hostium finibus, vndique oppugnatus, atque in loco, vbi vires suas exerere, arma tractare, auctoritate sua vti minimè poterit: Non illi sua fortitudo proderit, non sua prudentia, non sua virtus, ac dignitas, ni cætera consequantur. Ita planè in easu nostro: parum refert planetam, aut dominium ascendentis habere, aut locis potioribus dominari, aut etiam signo in quod proximè intrabit Luna, si cæteroqui viribus debilis, impeditus, combustus, cadens, in maleficarum radijs, aut dignitatibus constitutus suas partes obire, suaque fortuna vri non possit. Præualebit equidem, qui facto scrutinio cæteris valentior in vniuersum inueniatur, quique vires suas exerere, tum ob loci situm, tum ob numerum dignitatum, seu fortitudinem, tum ob alia accidentia plus alijs poterit. Igitur ab hoc munere excludendi primò sunt, qui combusti, qui à maleficis sunt obsessi, qui retrogradi; mox qui aliàs debiles, peregrini, tardi motus, sub Solis radijs existentes; ac tandem qui in cadentibus reperiuntur. E contra is præficiendus, qui in angulo, ac (cæteris adhuc in angulo existentibus) qui fuerit in nobiliore, seu eiusdem anguli situ eminentiore; qui lumine plenus, qui in suis dignitatibus, qui beneficarum radijs fulciatur; qui demum, facto scrutinio, tam fortitudinum quàm debilitatum cæteris omnibus fuerit potentior, & validior: potissimè vetò in situ mundi sit optimè constitutus; ita vt cæli culmen cæteris angulis præferatur, mox linea Orientalis ac primadomus: inde cardo Oceidentis, & septima, post limum cæli, ac tandem succedentes per ordinem: postremo si nullus in his locis reperiatur, inspiciantur cadentes, primò nona, secundò tertia, deinde sexta, vltimo duodecima: atque in ijs locis is præ omnibus eligatur, qui magis ad Meridianum accedit. <17.> Neque ab hoc munere excludenda sunt luminaria, per hoc quod retum generalem significationem sibi vendicant, si &c ipsa cæteris paribus alijs antecellant tam quoad mundi situm, quàm quoad reliquas forrtitudines. Semper enim verum est, vt qui virtutibus præualet, præualeat & actiuitate; quique in

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154 LEXICON therefore in the angles, or in the succedent houses (others being in lower places), swift in course, full of light, and in its essential dignities. The reason that moved me is this: because here the question concerns greater activity and concurrence in acting in all things; since always, he who prevails in strength exercises greater power in action. Thus a noble soldier, equipped with the best arms, powerful in strength, eminent in position, supported by the patronage of friends, and complete in all things, will do more in battle than a Commander, who indeed is set over the rest, but is gravely wounded, powerless in strength, in the enemy’s territories, attacked on all sides, and in a place where he can by no means exert his powers, handle weapons, or make use of his authority: his bravery will not help him, nor his prudence, nor his virtue and dignity, unless the rest concur. So plainly in our case: it matters little to have the planet, or the rulership of the ascendant, or to dominate in the better places, or even the sign into which the Moon will next enter, if otherwise weak in strength, impeded, combust, falling, in the rays of the malefics, or placed in dignities, and cannot perform its parts or make use of its fortune. Rather, he will prevail who, after the scrutiny has been made, is found in general to be stronger than the rest, and who, both because of the position of the place and because of the number of dignities, or strength, and because of other accidental factors, can act more than the others. Therefore, from this office must first be excluded those who are combust, those beset by malefics, and those retrograde; next those who are otherwise weak, peregrine, slow in motion, and under the rays of the Sun; and lastly those found in cadent houses. On the contrary, he must be appointed who is in an angle, and, when others are still in the angle, who is in the more noble or more elevated position of that same angle; who is full of light, who is in his dignities, who is supported by the rays of the benefics; and finally, after scrutiny has been made, who is stronger and more powerful than all the others, both in strengths and in weaknesses: especially if he is best placed in the situ of the world; so that the Midheaven of the sky is preferred to the other angles, then the Oriental line and the first house; next the Western angle and the seventh, after the end of heaven, and lastly the succedent houses in order: finally, if none is found in these places, let the cadent houses be examined, first the ninth, second the third, then the sixth, and lastly the twelfth: and in these places let him be chosen above all who approaches the Meridian most. <17.> Nor are the luminaries to be excluded from this office simply because they claim for themselves the general signification of the thing, if they themselves, all else being equal, excel the others both as regards their position in the world and as regards the remaining strengths. For it is always true that he who prevails in virtues prevails also in activity; and he who in

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MATHEMATICVM. 119 radice potentior fuerit, atque optimè constitutus, potentiùs exerat suas vires, quàm qui debilis, & minus potens. Sic sæpenumerò videmus plurimos apertè natuiam Solis referre: aliis Lunam plurimum dominari, in ijsque Lunæ effectus clarissimè elucere; quod irrefragabili argumento est, alterum luminarium in eius efformatione plurimùm contulisse, proindeque totius genituræ dominium extunc sibi vendicasse: Et hæc satis de genituræ domino. DOMINVS Orbis, secundùm Arabes est dominus horæ planetariæ in qua quisque editus est in lucem, & successiuè qui secundæ horæ in dominium succedit per ordinem. Hunc profectò suis nugis, ac philaterijs gestiunt assumere in annorum subsequentium gubernationem, ac dominium: ita vt domino primæ horæ competat dispositio primi anni, & per eum significetur in eo anno esse nati, quantum ad sanitatem, & infirmitates corporis, sicut per dominum ascendentis: per dominum secundæ horæ significetur secundo anno esse substantiæ, sicut significatur per dominum secundæ domus: per tertium dominum horæ significetur esse fratrum in tertio anno, sicut per dominum terriæ domus, & sic prosequendo in dominis horarum subsequentium per ordinem domorum, & per annos subseqvetes vsque ad sinem vitæ. Res planè ridicula, & vanitatis plena. Sic etiam DOMINVS hora est dominus duodecimæ cuiusque partis diei, ac noctis, ijs in duodecim æquales partes tributis, quas ideò inæquales, ac horas planetarias appellamus. Qua de re vide jam dicta in V. Diepon, quod Arabicè dominum horæ significat. Porrò in electionibus rerum, huiusmodi horas planetarias obseruare, etsi fortè superuacaneum foret, non per hoc tamen erit vituperabile aut superstitiosum. Præstat hic apponere quæ circa hanc horæ electionem habet Albertus Magnus in speculo. Non enim libertas, inquit, arbitrij ex electione hora laudabilis coërcetur, sed potiùs in magnarum rerum inceptionibus electionem hora contemnere est arbitrij præcipitatio, non libertas. Quod etiam ex Ptolemæo confirmat Marsilius Fecinus lib. 3. de Vita, cap. 12. DOMINVS radiorum juxtà Arabum placita, seu potiùs deliramenta, est planeta aliquo radio respiciens signum profectionis horoscopi alicuius anni. Vt si progressio ascendentis istius anni, exempli gratiâ fuerit ad signum Arietis deuoluta, Mars erit dominus profectionis annuæ, vt supra dictum est, quia est dominator Arietis: si verò aliquis planeta Arietem quacunque irradiatione respexerit, is radiorum dominus appella-bitur: vt puta Iupiter ex 6. Leonis gradu illum trigono radio

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MATHEMATICUM. 119 if it were stronger in the root, and well constituted, it would exert its forces more powerfully than one that is weak and less potent. Thus we very often see many plainly reflect the nature of the Sun: others have the Moon ruling them most strongly, and in them the effects of the Moon shine most clearly; which is an irrefutable argument that one of the luminaries contributed very much to their formation, and therefore from the outset claimed for itself dominion over the whole geniture: and enough has been said about the lord of the geniture. LORD of the World, according to the Arabs, is the lord of the planetary hour in which each person is brought forth into the light, and successively the one who succeeds into rulership of the second hour in order. These men, indeed, with their trifles and philter-like follies are eager to take this as governing and ruling the subsequent years: so that the lord of the first hour is assigned the disposition of the first year, and by it it is signified that in that year the native is to be, as regards health and bodily infirmities, just as through the lord of the ascendant; through the lord of the second hour it is signified that in the second year there is to be property, just as is signified through the lord of the second house; through the third lord of the hour it is signified that there are to be brothers in the third year, just as through the lord of the third house, and so proceeding through the lords of the subsequent hours in the order of the houses, and through the subsequent years up to the end of life. A thing plainly ridiculous, and full of vanity. Likewise LORD of the hour is the lord of the twelfth part of each day and night, when these are divided into twelve equal parts, which for that reason we call unequal, and planetary hours. On this matter see what has already been said in V. Diepon, which in Arabic means lord of the hour. Moreover, in elections of things, to observe hours of this kind, although perhaps it would be superfluous, will not for that reason be blameworthy or superstitious. Here it is better to set down what Albertus Magnus has in the Speculum concerning this election of the hour. For not, he says, is the freedom of choice restrained by the election of a praiseworthy hour, but rather in the beginnings of great matters to despise the election of the hour is the rashness of choice, not freedom. This also Marsilius Ficinus confirms from Ptolemy, book 3 On Life, chapter 12. LORD of the rays, according to the opinion of the Arabs, or rather their deliriums, is the planet that looks upon by some ray the sign of the annual profection of the horoscope of someone in a given year. Thus if the progression of the ascendant of that year, for example, should have been brought to the sign of Aries, Mars will be the lord of the annual profection, as was said above, because he is the ruler of Aries; but if some planet should have looked upon Aries by any irradiation whatsoever, it will be called the lord of the rays: as for instance Jupiter from the 6th degree of Leo by a trine ray had it

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156 LEXICON intueatur: Venus è 18. Libræ, opposito: Saturnus è 28. Cancri Quadraro: ij omnes erunt domini radiorum. Quamobrem Mars anni dominus 73. diebus gubernia moderabitur, donec planetæ suos radios in eas Arietis partes jaculentur, quas Iupiter respicit. Itaque Martis Collega, nati patrocinia assumet spatio 146. dierum, qui æquipollent 12 gradibus interjectis è Veneris ad Iouis radios. Deinde succedit Venus moderatrix spatio vsque dietum 121. cum horis 17. qui respondent gradibus 10. residuis ad quadratum Saturni aspectum. Qui tandem radijs natum pulsabit iniquis, octonas horas, sex, quater atque dies, æquialenres nempè duobus gradibus residuis ad calcem vsque eius sideris. Hæc de radiorum dominis Arabes suis nugamentis abunde. 61. DOMINVS temporis, Græcis Chronocrator (de quo plura diximus suo loco) est ille planeta, qui in temporum distributione dominium temporis sortietur. Is pluribus modis intelligi potest: primò ratione totius ætatis hominis, vt ibi explicatum est; secundò ad certum tempus à luminaribus exordiendo. In diutnis igitur genituris initium temporum à Sole accipitur, & cæteris planetis impertitur: in nocturnis verò à Luna. Ergo cum Sol dominus temporum extiterit, vendicat sibi dominatum, siue decernendi potestatem ann. 1. mens. 7. hoc est vndeviginti menses. Luna ann. 2. cum vno mense, hoc est mens. omninò 5. Inde is planeta, qui in natalitio themate secundùm ordinem signorum in secundo loco fuerit supputarustertium, qui post secundum, & simili modo de cæteris. Sed quicumque suum decennium fuetit sortitus; licet ipse sit principalis totius temporis Chronocrator, cæteris tamen planetis per ordinem succedentibus portionem sui decennij distribuit, qui fuerint per ordinem immediatè positi in schemate natalitio, à seipso tamen primum incipiens, & post se illis portionem ttibuens, qui subsequentur. Itaque Saturnus habet menses 30. Iupiter 12. Mars 15. Sol, vt dictum est, 19. Venus 8. Mercurius 20. Luna tandem menses habet 25. In nocturnis verò genituris primum decennium habet Luna, inde qui per ordinem secundùm successionem signorum succedit, vt dictum est de Sole. Potro Tabulam Chronocratorum, nec non singulorum particulares significationes habes apud Firmicum lib 6. cap. 34. & sequentiibus. 62. DORADO, Indorum vocabulo, dicitur nouum sidus in cælo ad polum ararcticum nobis inuisum, à modetnis Astronomis detectum, vna cum alijs vndecim. Stellas habet omninò septem insimæ notæ sub Capricorno. Vocatur & Græco nomine Xiphias.

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156 LEXICON if Venus looks at 18 Libra, opposite: Saturn at 28 Cancer In square: all these will be lords of the rays. Therefore Mars, lord of the year, will govern for 73 days, until the planets cast their rays into those parts of Aries which Jupiter regards. Thus Mars’ associate will take up the protection of the nativity for a span of 146 days, which are equivalent to 12 intervening degrees from Venus to the rays of Jupiter. Then Venus succeeds as ruler for the span up to the said 121 with 17 hours, which correspond to the remaining 10 degrees to the square aspect of Saturn. He will finally strike the native with adverse rays, for eight hours, six, four, and even days, that is, equivalent to the two remaining degrees up to the end of that star. The Arabs have said enough of this about the lords of the rays in their trifles. 61. LORD OF TIME, called by the Greeks Chronocrator (of whom we have spoken more at its proper place) is that planet which, in the distribution of times, will obtain dominion over time. This can be understood in several ways: first, with regard to the whole age of a person, as explained there; second, with reference to a specific time, beginning from the luminaries. In day charts, therefore, the beginning of the times is taken from the Sun and assigned to the other planets; in nocturnal charts, however, from the Moon. Therefore, when the Sun has been the lord of times, it claims for itself dominion, or the power of deciding, for 1 year, 7 months, that is, 19 months in all. The Moon for 2 years with one month, that is, altogether 5 months. Then the planet which in the natal figure, according to the order of the signs, is in the second place is counted as third; the one after the second, and similarly with the rest. But whichever planet has obtained its own decade; although it is the principal Chronocrator of the whole period, it nevertheless distributes to the other planets in succession a share of its decade, to those which are placed in order immediately in the natal figure, beginning first from itself, and then after itself distributing a share to those which follow. Thus Saturn has 30 months. Jupiter 12. Mars 15. The Sun, as said, 19. Venus 8. Mercury 20. The Moon finally has 25 months. In nocturnal nativities, however, the first decade belongs to the Moon; then to the one who in the order of the succession of signs follows, as has been said of the Sun. Moreover, you have the Table of Chronocrators, as well as the particular significations of each, in Firmicus book 6, chapter 34 and the following chapters. 62. DORADO, in the Indian language, is called a new star in the sky near the arctic pole, invisible to us, discovered by modern astronomers, together with eleven others. It has seven stars in all, of the lowest magnitude beneath Capricorn. It is also called by the Greek name Xiphias.

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MATHEMATICVM. 157 DORYPHORIA Græcè idem sonat, ac Latinè securitas, & comitatus 1 (Arabes Ductoriam vocant) quod nos exemplo à Principibus sumpto, qui multo satellitum famulatu comitati incedunt, Satellitum planetarum ad luminaria cælestium luminum principes, nominamus. Et quemadmodum Regem famulatus præcedit, Reginam verò subsequitur, ita ad hoc satellitium luminaribus adornandum, debent quinque erraticæ Solem præcedere, sicque esse ab illo Orientales, Lunam verò subsequi, atque esse ab illa Occidentales. Quomodo autem fiat hic famulatus, satellitium, ac Doryphoria, aliter explicant Arabes, aliter Græci. Hi enim docent, tunc planetam facere Doryphoriam Soli, quando fuerit separatus ab illo, & extrà eius radios ad triginta gradus, quando mane apparuetit; in qua re valdè dissentiunt, & confunduntur. Aliqui enim inquiunt planetam infra 16. gradus nullo pacto facere Doryphoriam, quia vel est sub radijs, vel combustus. Alij verò id non attendunt, sed vbique sit intrà triginta gradus, etiamsi combustus, docent ipsum facere satellirium. Alchabitius tenet, quod infra 60. gradus intelligi debeat hæc distantia, cum planetæ fuerint extrà radios; eo modo, quo dictum est, & figura sexangula inueniatur: sed in alio capite dicit, quod quando planetæ fuerit in angulo, seu in sua similitudine, & Sol in sua similitudine in altero angulorum, tunc fiat Doryphoria. Arabes verò docent, quod non tantum ex præsentia, sed etiam ex radio cum luminaribus fiat Doryphoria: ita quod Sol verbi gratiâ sit in aliquo angulorum, & respiciatur ab erraticis per sextilem, trigonum, aut quadratum, nihiloseciùs fiat Doryphoria. Quid in tanta controversia determinandum sit, non est animus pro nunc explicare. Est enim res magni momenti, & à multis inftà explicandis dependet; quibus traditis liquidò apparebit, quid requiratur, quidue sufficiat ad verum satellitium luminaribus adornandum. Vnde cum iterum redibit sermo in V. Satellitium jactis jam fundamentis, facile erit ædificium struere, nouamque hanc doctrinam mentibus ingererè, ac tenacius implantare. Pro nunc sufficiat præmittere tanquam dicendorum basim, idque pro certo supponere, ad satellitium requiri, vnionem, & familiaritatem erraticarum cum Sole aut Luna (vt optimè probat Titus in Cæleste Philosophia) Cùm enim id sit accessus virium ad luminaria, ac veluti vectigal mutuari luminis, quod à lateronibus ipsis soluatur; nisi in ea distantia fuerint, qua eorum virtus vniri possit, atque ad luminaria transmitti, Satellitium facere, ac Doryphoriam minimè poterunt. Porrò quanta sit cælestis hæc constitutio, quantius momenti ad dignitates, & imperia decer-

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MATHEMATICVM. 157 DORYPHORIA in Greek means the same as in Latin security and escort 1 (the Arabs call it Ductoriam), because, taking our example from princes, who proceed accompanied by a great retinue of attendants, satellites we call the planets, as the princes of the celestial lights, by that name. And just as the retinue goes before a king, but follows a queen, so, for this escort to adorn the luminaries, the five wandering stars ought to go before the Sun, and thus be oriental from him, while the Moon ought to follow him, and thus be occidental from her. But how this retinue, escort, and Doryphoria come about, the Arabs explain one way, the Greeks another. For the latter teach that a planet then makes Doryphoria to the Sun when it has been separated from him and is beyond his rays by thirty degrees, when it appears in the morning; in which matter they differ greatly and are confused. For some say that a planet within 16 degrees in no way makes Doryphoria, because it is either under the rays or combust. Others, however, do not consider this, but wherever it is within thirty degrees, even if combust, teach that it makes a retinue. Alchabitius holds that this distance should be understood within 60 degrees, when the planets have gone beyond the rays, in the manner said, and the hexagonal figure is found; but in another chapter he says that when a planet is in an angle, or in its own dignity, and the Sun is in its dignity in another of the angles, then Doryphoria is made. The Arabs, however, teach that Doryphoria is made not only by presence, but also by aspect with the luminaries, so that if the Sun, for example, is in one of the angles and is aspected by the wandering stars by sextile, trine, or square, nevertheless Doryphoria is made. What should be determined in so great a controversy, I do not intend to explain for the present. For it is a matter of great importance, and depends on many things to be explained later; once these have been laid out, it will clearly appear what is required, and what suffices, for truly adorning the luminaries with a retinue. Hence, when the discussion returns again in V. retinue once the foundations have now been laid, it will be easy to build the edifice and to impress this new doctrine on minds, and implant it more firmly. For the present it will be enough to set forth as the basis of what is to be said, and to assume for certain, that retinue requires union and familiarity of the wandering stars with the Sun or Moon (as Titus proves best in Celestial Philosophy) For since this is an access of powers to the luminaries, and as it were the borrowing of a tribute of light, which is paid by those very ones on the side; unless they are in that distance in which their power can be united and transmitted to the luminaries, they will by no means be able to make a retinue or Doryphoria. Moreover, how great this celestial constitution is, how important for dignities and empires to be decr-

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LEXICON nenda, non satis explicari potest: Sed de ea re fusè loco cirato. 64. Doza almogiza, Arabicè idem significat ac Latinè Limbus in Astrolabio, qui est circulus prominens in eius extremitate, in cuius plano descripræ sunt horæ æquinoctiales distriburæ per singulos quidem gradus æquatoris, incipiendo à prima post Meridiem, vsque ad vigesimam quartam. Item & ventorum descripta nomina à partibus, vnde spirant: aliaque ad id spectantia. Vide in V. Limbus. DR 65. DRACO, sidus in exlo circa polum Zodiaci arcticum, Arabicè Eltanim continet secundum Prolemæum stellas 31. at ex testimonio Kepleri 32. & Baieri 33. omnes ferè de natura Saturni, & Iouis, inter quas præcipua est, quæ micat in capite Arabicè Ras abem, tertia magnitudinis, nec non altera quæ in lingua, habentes naturam mixtam ex Ioue, Sarurno, & Marte. In longirudine amplectitur omnia signa Zodiaci, quoniam, vt dixi, circumdat polum Zodiaci, vbi ea restringuntur, atque in ipsum polum desinunt. Is in horoscopo, inquit Firmicus, facit Marsos, & qui venenis ex herbarum succo paratis antidotis occurrant, ac serpentum istibus medeantur. In occasu verò adducit periculum veneni, vel ictus serpentis, maximè si Saturnus dictum locum maligno radio infestauerit. 66. DRACONS Luna capus, & cauda sunt nodi Lunares, seu intersectiones Eclipricæ, & orbitæ Lunæ in duobus locis oppositis, vnde sumitur argumentum latitudinis Lunæ, & à capite quidem borealis, à cauda verò australis. Quare aurem huiusmodi intersectiones à Dracone nomen sortitæ sint, dictum est alibi. 67. DRACO volans est genus quoddam ignitarum accensionum in aëre apparentium, cui materiam præbet exhalatio quædam viscosa, nec valdè calida, nec valdè densa, quæ à nubibus, dum ab illarum frigore truditur, exilire videtur recurruo tractu ad modum colubri, vel draconis, & quia ex altera parte nititur sursum ascendere, videtur quasi ardentes scintillas de ore vomere: ex alia verò parte, vbi est nubes illam constringens, præsefert quasi dorsum at caudam Draconis. DV 68. DVBHE, seu Dubbhelachar, Arab dicitur Vrsa maior, Helice quasi Vrsæ plantarum, vtramque enim imaginem refert, sidus ad polum Arcticum constans stellis 27. & octo informibus apud Ptolemæum, secundùm Baierum verò 32. ar iuxta Keplerum 36, ex quibus quæ in humero, secundæ magnitudinis, de

Transcription: Translated (English)

LEXICON nenda, cannot be explained sufficiently; but this matter has been treated at length in the place cited. 64. Doza almogiza, in Arabic signifies the same as the Latin Limbus in the astrolabe, which is the projecting circle on its edge, in whose plane are drawn the equinoctial hours divided through each degree of the equator, beginning from the first after midday up to the twenty-fourth. Likewise the names of the winds are drawn, according to the parts from which they blow, and other things pertaining to this. See also under V. Limbus. DR 65. DRACO, a constellation in the sky around the north pole of the zodiac, in Arabic Eltanim, contains according to Ptolemy 31 stars, but according to Kepler 32, and according to Bayer 33; almost all are of the nature of Saturn and Jupiter, among which the chief is that which shines in the head, in Arabic Ras abem, of third magnitude, as well as another in the tongue, having a mixed nature from Jupiter, Saturn, and Mars. In longitude it embraces all the signs of the zodiac, since, as I said, it surrounds the pole of the zodiac, where they are confined and end at that very pole. In the horoscope, says Firmicus, it makes healers, and those who meet poisons prepared from the juice of herbs with antidotes, and who cure serpent bites. In the setting, however, it brings danger of poison or of a serpent’s strike, especially if Saturn has afflicted the said place with a malignant ray. 66. DRACONS Head and Tail are the Lunar nodes, or intersections of the ecliptic and the Moon’s orbit in two opposite places, from which is taken the argument of the Moon’s latitude, the head indeed being northern and the tail southern. Why such intersections have received the name from the Dragon has been said elsewhere. 67. DRACO volans is a certain kind of fiery exhalation appearing in the air, to which provides matter a certain viscous exhalation, neither very hot nor very dense, which seems to spring from the clouds, being driven by their cold, with a winding course like a serpent or dragon, and because on one side it seems to strive to ascend upward, it appears as though it vomits burning sparks from its mouth; on the other hand, where there is a cloud constraining it, it presents as it were the back and tail of a Dragon. DV 68. DVBHE, or Dubbhelachar, is what the Arabs call Ursa Major, Helice, as it were the feet of the Bear; for it resembles both figures, a constellation around the Arctic pole consisting of 27 stars and eight unformed ones according to Ptolemy, but according to Bayer 32, and according to Kepler 36, of which those in the shoulder, of second magnitude,

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MATHEMATICVM. 159 natura Saturni, retinuit nomen Dubbe. Kircherus in Oedipo refert plaustrum hunc, seu Vrsam ab Arabibus Christianis vocari Naasch Laazar, hoc est feretrum Lazari, pio quidem affectu, quo abjectis poëtarum figmentis, non à fabulis, sed à sacrarum paginarum penu desumpta sideribus nomina indiderunt, quod postea audio fecisse de toto firmamento, eiusque imaginibus cælestibus nescio quem Iacobum schillerum appingendo singulis astris nomina sanctorum, & præsertim Zodiacum appellando ex nominibus duodecim Apostolorum: sed de hac re fusiùs in V. Imagines Ca'estes. Dvctio, idem est apud aliquos, ac Directio: significat < 69.> enim deductionem Promissorum ad loca Significatorum, atq[ue] artificiosam mensuram itineris, quod motu primi mobilis perficit Promissor, quousque ad locum Significatoris perueniat. Quod quomodo fiat, satisfictum est in V. Directio. Dvctoria, Arab. idem quod Græcè Doryphoria, de qua < 70.> non longè ante dictum. Sed enim eam aliter explicat Alchabitius. Est enim inquit Ductoria vt planeta sit in suo Hayχ, id est in parte sibi propria, & in aliquo angulorum ascendentis, & aliquod luminarium: similiter sit in loco sibi consimili in quadrante, videlicet in aliquo angulo, ita quod planeta in die sit Orientalis à Sole, in nocte Occidentalis à Luna. Hali verò super proposit. 16. Centiloquij dicit quod ad Ductoriam requiritur, vt superiores quidem sint Orientales à Sole, ac verò inferiores sint Occidentales: quoniam isti cùm Occidentales sunt, & illi cùm Orientales crescunt lumine, atq[ue] adeò fortiores, validioresque euadunt. Quid in hac re sit dicendum explicabimus in V. Satellitium. Dvodenaria planetarum, siue domorum, est vna ex superstitiosis, ac vanis Arabum considerationibus super duodecim Zodiaci signa, ac cælestes domos in situmundi; quemadmodum Nouenaria, Alfridaria &c. Itaque in quolibet signo vel domo inuenire satagunt dominum duodenariæ, atque ad id præstandum diuidunt vnumquodque signum in duodecim partes æquales; ita vt quælibet pars constet duobus gradibus &c dimidio: quo facto dicunt, quod dominus primæ duodenariæ est dominus illius signi; dominus secundæ duodenariæ est planeta succedens per ordinem descendendo, & sic de reliquis. Sic verbi gratia domiuius primæ duodenariæ Arietis est Mars: secundæ Sol: terriæ Venus: quartæ Mercurius: quintæ Luna: sextæ Saturnus: septimæ Iupiter: octaux iterùm Mars, & sic sequendo. Et hæc est explicatio duodenariæ quam tradit Ioannes de Saxonia in Alchabitium. Cum igitur, subdit, volueris scire duodenarias planetarum, vel domorum, vide quantum

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MATHEMATICVM. 159 nature of Saturn, retained the name Dubbe. Kircher, in Oedipus, relates that this wagon, or Bear, is called by the Christian Arabs Naasch Laazar, that is, the bier of Lazarus, with a pious feeling, by which, casting aside the fictions of the poets, they bestowed on the stars names taken not from fables but from the storehouse of the sacred pages; which I hear was later done for the whole firmament and its heavenly images by a certain Jacobus Schiller, by attaching to each star the names of saints, and especially calling the Zodiac by the names of the twelve Apostles: but on this matter more fully in V. Imagines Caelestes. Ductio, with some is the same as Directio: it signifies <69.> the deduction of the Promissors to the places of the Significators, and the artificial measure of the journey, which by the motion of the primum mobile the Promissor accomplishes, until it reaches the place of the Significator. How this is done is treated sufficiently in V. Directio. Ductor ia, Arab. the same as the Greek Doryphoria, of which <70.> was spoken not long before. But Alchabitius explains it otherwise. For it is, he says, Ductor ia, when a planet is in its own Hayχ, that is, in its proper place, and in one of the angles of the ascendant, and of some luminary; likewise it is in a place like itself in the quadrant, namely in one of the angles, so that the planet in the day is Oriental from the Sun, in the night Occidental from the Moon. Haly however, on proposition 16 of the Centiloquium, says that for Ductor ia it is required that the superior planets be Oriental from the Sun, and the inferior ones Occidental: because these, when they are Occidental, and those when they are Oriental, grow in light, and thus become stronger and more powerful. What should be said in this matter we shall explain in V. Satellitium. Duodenaria of the planets, or of the houses, is one of the superstitious and vain considerations of the Arabs regarding the twelve signs of the Zodiac and the celestial houses in the situation of the world; just as the Novenaria, Alfridaria, etc. Therefore in each sign or house they endeavor to find the lord of the duodenary, and in order to accomplish this they divide each sign into twelve equal parts; so that each part consists of two degrees and a half: which done, they say that the lord of the first duodenary is the lord of that sign; the lord of the second duodenary is the planet succeeding in descending order, and so of the rest. Thus, for example, the lord of the first duodenary of Aries is Mars: of the second the Sun: of the third Venus: of the fourth Mercury: of the fifth the Moon: of the sixth Saturn: of the seventh Jupiter: of the eighth again Mars, and so on in sequence. And this is the explanation of the duodenary as given by Johannes de Saxonia in Alchabitius. Therefore, he adds, when you wish to know the duodenaries of the planets or of the houses, see how much

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160 LEXICON transiuit planetæ de signo in quo est, aut de domo in qua est. E[rgò] numerum illorum graduum multiplica per duodecim, E[rgò] super numerum productum adde numerum graduum. quos multiplicasti: E[rgò] quod collectum fuerit proijce ab initio signi, in quo est planeta, dando vnsusque signo 30. gradus; E[rgò] vbi finitus fuerit numerus, ibieris duodenaris Ita ille. Inanis labor, atque eorum qui hæc commenti sunt centro dignus. 72. Dysis, Græcè d'eta est septima domus in cælesti Themate, & cardo Occidentis, oppositus directe angulo Orientali, ad quem perducti planetæ & sidera motu primi mob lis, in o[mn]e occultantur: ideoque & mortis significator asseritur. Vnde Gauricus cecinit. Septima quandoquid in domus est contraria prima: Prima domus vita; septima mortis erit. Ad hanc Ptolemæus dirigit vitæ moderatorem consistentem inter spatium à decima domo ad occasum, ad auspicandum vitæ spatium, motu conuerso directionem instituens. Quia inquit, dominum vita abs indis. Significat etiam septima conjugium, inimicos potentes &c ex membris humanis habet fæmora, lumbos, vmbilicum. Habet fortitudinis quatuor suffragia, & consignificatrix eius est Luna. E C ECCENTRICVS Orbis, ab Astronomis dicitur qui habet centrum diuersum à centro tellutis, quasi extra centrum. Sicut concentricus qui cum tellure, vel alio Orbis ad quem sit comparatio conuenit in vno centro. Sunt autem excogitati ab antiquis Astronomis huiusmodi orbes eccentrici, quemadmodum, & epicycli ad saluandas apparentias, irregularitates motuum, aliaque id genus, quæ ægrè intelligi possunt sine huiusmodi circulis. Est igitur Orbis eccentricus cuiuscum quo planetæ ille, cuius tam concauum, quàm conuexum deferentis habet centrum à centro vniue si diuersum: ita vt vni formis sit quoad crassitiem, instar cuiuslibet sphæræ cælestis, sicque immersus intra crassitiem cæli, ac terram ipsam ambiat Atque iste vocatur eccentricus simpliciter, quia est omni ex parte à centro. Vniuersi alienus, atque alium centrum habet. Quoniam autem isti Orbes eccentrici motu raptus circa tellurem mouentur; necesse est dari duos alios Orbes, qui Orbem eccentricum in medio concludant, & rapiant, qui tamen dicuntur eccentrici non simpliciter, sed secundum quid, hoc est ab vna tantùm parte, aut concaua, aut conuexa, atque ab altera parre concentrici; hoc est habentes idem centrum cum Vniuetso. Itaque in vnoquoque planeta tres Orbis concipiendi sunt, ex quibus medios, in cuius crassitie intium sit corpus planetæ, sit

Transcription: Translated (English)

160 LEXICON transits from the sign in which the planet is, or from the house in which it is. Therefore multiply the number of those degrees by twelve; therefore add the number of degrees which you multiplied to the resulting number; therefore cast away from the beginning of the sign in which the planet is, giving to each sign 30 degrees; therefore where the number shall have ended, there you will go by the twelvefold. So he. Useless labor, and worthy of the center of those who invented these things. 72. Dysis, in Greek d'eta, is the seventh house in the celestial theme, and the western angle, directly opposite the eastern angle, toward which the planets and stars led by the motion of the first moved are hidden in every way: and therefore it is asserted to be a significator of death. Whence Gauricus sang: The seventh, whenever it is in the house contrary to the first: The first house is life; the seventh will be death. To this Ptolemy directs the governor of life, standing between the space from the tenth house to the setting, for marking out the span of life, instituting direction by reverse motion. Because, he says, the lord of life is absent. It also signifies marriage, powerful enemies, etc.; among the members of the human body it has the thighs, loins, navel. It has four supports of strength, and its co-significator is the Moon. E C ECCENTRIC ORBIT, by astronomers is called that which has a center different from the center of the earth, as it were outside the center. As concentric is that which agrees with the earth, or with some other orbit to which comparison is made, in one center. Now such eccentric orbits were devised by the ancient astronomers, just as epicycles were, for saving appearances, irregularities of motions, and other things of that kind, which are scarcely understood without such circles. Therefore an eccentric orbit is that in which, for any planet whatsoever, both the concave and the convex of the deferent have a center different from the center of the universe: so that it is uniform in thickness, like any celestial sphere, and thus immersed within the thickness of the heavens, and encompasses the earth itself. And this is called eccentric simply, because it is in every respect alien from the center of the universe, and has another center. But since these eccentric orbits are moved around the earth by the motion of being carried along; it is necessary that there be given two other orbits, which enclose the eccentric orbit in the middle and carry it along, which however are called eccentric not simply, but in a qualified sense, that is, eccentric on one side only, either concave or convex, and concentric on the other side; that is, having the same center as the universe. Therefore in each planet three orbits must be conceived, among which the middle one, in whose thickness the body of the planet is first, is

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MATHEMATICVM. 161 sit simpliciter eccentricus tam secundum concauum, quàm secundum conuexum; alij duo sint ex vna parte concentricus, ex alia eccentricus, ex ea inquam, quæ simpliciter eccentrico sit contiguus. Sed de hac re melior notitia haberi poterit in Theoricis planetarum, vbi schemata horum orbium ad viuum delineata oculis exhibentur. Nobis sufficiat rem paucis verbis delibauisse. ECLIPSISS Græcè defectionem Latinè significat. Ab Astro- nomis pressiùs accipitur pro defectu luminarium, quando ex mutua coitione in orbita Solis, huius facies nobis ex interpositione corporis lunatis occultatur: aut ex eorumdem oppositione in eadem orbita Luna obscuratur, eò quia incidit in penumbram atmosphæræ, vel vt explicabant antiqui, in vmbram terræ. Et quia in Solis orbita id semper accidit, per quam si ferretur Luna continuè nulla vnquam prædita latitudine bis in mense videremus huiusmodi eclipses seu defectiones lucis modò in vno, modò in altera; ideo orbita Solis ipsa, quæ est veluti subjectum harum defectionum, Ecliptica dicta est. In pluribus autem differt eclipsis Solis ab eclipsi Lunæ. Primò quod in Lunari defectione eius facies verè obscuratur, & lumen deperdit ob telluris interpositionem, quæ obstat, ne à Sole illuminetur: In eclipsi verò Solis ipse defecit lumine, sed nos eius luce priuamur ob interpositionem disci Lunaris quæ impedit transmissionem radiorum Solarium ad superficiem terræ. Quod ideò dicenda ea potiùs essere eclipsis terræ, quàm Solis, cum ea omnia quæ in Lunæ eclipsi accidunt in eius directa oppositione cum Sole, accidant & in eius conjunctione, respectu terræ, cui, vt ita loquar, videtur vicem rependere priuationis lucis quam passa est in eius interpositione cum Sole, ijsdem affectibus eam afficiendo, in sua ipsius interpositione, qua vel ei lumen adimit sua vmbra, vel sanè impedit ne Solis radij ad eam illustrandam accedant. Qui sit vt si fortè quis in concauo Lunæ constitueretur (vbi sanè congruam hominibus habitationem esse non desunt, qui asserant) vtique ea omnia accidentia ac passiones telluris erga Solem, demirans conspicaretur; præcipuè verò hanc defectionem lucis, in luminarium coitione, quæ nos, vtpote obuia & continua videmus, sed non demiramur in Luna. Secundò differt eclipsis Lunæ ab eclipsi Solari, quia cùm illius obscuratio sit vera, & realis, est etiam vniuersalis, semper & vbique eadem, & semper eiusdem quantitatis apparet in omni superficie terræ, vnde visibilis est: At enim eclipsis Solis non est vniuersalis, sed pro diuersitate climatum variatur secundùm quod variatur respectus eius ad terram ob interpositionem disci Lunaris; ita vt L

Transcription: Translated (English)

MATHEMATICVM. 161 let it be simply eccentric, both according to the concave and according to the convex; let two others be concentric on one side, eccentric on the other, namely on that side which is contiguous to the simply eccentric one. But of this matter a better understanding may be obtained in the Theorics of the planets, where the figures of these spheres, drawn to life, are exhibited to the eye. Let it suffice for us to have touched on the matter in a few words. ECLIPSIS in Greek signifies a defect. Among astronomers it is more precisely taken for the loss of the luminaries, when, through their mutual conjunction in the orbit of the Sun, his face is hidden from us by the interposition of the moon’s body; or, through their opposition in the same orbit, the Moon is obscured, because it falls into the penumbra of the atmosphere, or, as the ancients explained it, into the shadow of the earth. And because this always happens in the orbit of the Sun, through which, if the Moon were carried continually without any latitude, we should twice a month see such eclipses or defects of light, now on one side, now on the other, therefore the orbit of the Sun itself, which is as it were the subject of these defects, has been called the Ecliptic. Yet in many respects the eclipse of the Sun differs from the eclipse of the Moon. First, because in a lunar eclipse its face is truly obscured, and loses its light by the interposition of the earth, which hinders it from being illuminated by the Sun. But in a solar eclipse the Sun itself loses light, while we are deprived of its light by the interposition of the lunar disk, which prevents the transmission of the solar rays to the surface of the earth. For this reason it ought rather to be called an eclipse of the earth than of the Sun, since all the things that happen in a lunar eclipse, in its direct opposition to the Sun, also happen in its conjunction with respect to the earth, which, so to speak, seems to repay the loss of light it suffered in its interposition with the Sun, afflicting it with the same effects in its own interposition, whereby either its shadow takes away its light, or certainly prevents the rays of the Sun from reaching it to illumine it. So that if by chance someone were placed in the hollow of the Moon (where indeed there are not wanting those who assert that there is a fitting habitation for men), he would surely behold in wonder all those events and affections of the earth toward the Sun; especially this defect of light in the conjunction of the luminaries, which we, as familiar and continual, see, but do not marvel at in the Moon. Secondly, a lunar eclipse differs from a solar eclipse, because whereas its obscuration is true and real, it is also universal, always and everywhere the same, and always appears of the same quantity on every surface of the earth from which it is visible. But a solar eclipse is not universal, but varies according to the diversity of climates, according as its relation to the earth is varied by the interposition of the lunar disk; so that L

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162 LEXICON alicubi fortassis videri posset totum Solare corpus eclipsatum, alibi pars, alibi nulla; eò quia, vt dixi, ibi totum corpus Lunare intercipitur, & directe, inter visum & corpus Solare, adeò vt nulla pars eius remaneat conspicua; hic autem ex parte tantum impediat, aut nullo modo. Tertiò differunt huiusmodi eclipses, quia Solaris incipit à parte Occidentali corporis eius, eò quia Luna, quæ ipsum suo corpore impedit, & obscurat, quia est motu leuior, & motu suo gradiens venit prior ad Solem, ab eoque ipsa recedit, consequenter ab Occidente venit ad conjunctionem, atque inde incipit obscuratio. In eclipsi verò Lunæ eius corpus incipit obscurari à parte Orientis, quia ipsa motu suo proptio procedens, vt dixi, ab Occidente in Orientem intrat in vmbram tertæ, quæ interponitur, quam primò incurrit per partem sui corporis Orientalem, licet vmbra, quæ ipsam aggreditur id primò faciat per sui partes Occidentaliores, ac deinde per reliquas. 1. INCIDENTIA scrupula in eclipsibus, quæ etiam dicuntur minuta Casus, sunt minutæ partium Zodiaci, quas Luna, superando motum Solis perambulat ab initio eclipsis ad medium, si non sit eclipsis totalis cum mora, vel ab initio eclipsis ad initium totalis obscurationis, si sit totalis cum mora. 4. REPLETIONIS scrupula, seu minuta emersionis, sunt minutæ partium Zodiaci, quas Luna superans motum Solis percurrit à medio eclipsis ad finem, si non sit eclipsis cum mora, atque totalis: vel ab initio apparitionis ex vmbra, si sit totalis, cum mora. 3. MORÆ dimidia scrupula sunt minutæ partium Zodiaci, quas Luna Solem in motu superans percurrit ab initio totalis obscurationis ad medium seu summum eclipsis, quibus equantur scrupula, quæ à medio ad initium nouæ apparitionis pertransit: tempus verò his respondens dicitur tempus incidentiæ repletionis, & moræ dimidix. Porrò quàm magna sint quæ portendunt eclipses, siue vnius, siue alterius luminaris, nemo est qui non videat; nosque malo nostro nuper experti sumus, ex duabus Solis, quarum altera celebrata fuit in Ariete anno 1652. altera in Leone anno 1654. Vtraque in signo igneo; quam postea sequuta est dita fames, ac pestis, celeberrimas, ac populatiores Italæ vrbæ Neapolim, & Genuam deuastans, Romamque ipsam aliaque Oppida non mediocriter lædens. Quo verò in genere ea mala futura sint, quæ minantur eclipses, & quam potissimum regionem afficiant, disertè tradit Ptolemæus lib. 2. Quadrip. cap. 7. ac nouissimè peculiari libro de Eclipsibus, & earum significatis in quacumque domo Ioannes Antonius Ciuffus Neapolitanus.

Transcription: Translated (English)

162 LEXICON in one place the whole solar body might seem eclipsed, in another part, in another none at all; because, as I said, there the whole lunar body is interposed, and directly between the sight and the solar body, so that no part of it remains visible; here, however, it hinders only in part, or not at all. Thirdly, eclipses of this kind differ because a solar eclipse begins from the western part of its body, because the Moon, which hinders and obscures it with its body, since it is lighter in motion, and advancing by its motion comes first to the Sun, and then withdraws from it, consequently comes from the west to conjunction, and from there the obscuration begins. But in a lunar eclipse its body begins to be obscured from the eastern part, because it, proceeding by its own motion, as I said, enters from west to east into the shadow of the earth, which is interposed, and first encounters it by the eastern part of its body, although the shadow which attacks it first does so by its more western parts, and then by the rest. 1. The scruples of incidence in eclipses, which are also called minuta cases, are the minutes of the parts of the Zodiac which the Moon, surpassing the motion of the Sun, traverses from the beginning of the eclipse to the middle, if it is not a total eclipse with a pause, or from the beginning of the eclipse to the beginning of total obscuration, if it is total with a pause. 4. The scruples of repletion, or minutes of emergence, are the minutes of the parts of the Zodiac which the Moon, surpassing the motion of the Sun, runs through from the middle of the eclipse to the end, if it is not with a pause and total; or from the beginning of appearance from the shadow, if it is total with a pause. 3. The half scruples of delay are the minutes of the parts of the Zodiac which the Moon, surpassing the Sun in motion, traverses from the beginning of total obscuration to the middle, or highest point, of the eclipse, and these are equal to the scruples which it passes from the middle to the beginning of new appearance; and the time corresponding to these is called the time of the scruples of incidence, repletion, and half delay. Moreover, how great are the things foretold by eclipses, whether of one luminary or the other, there is no one who does not see; and we ourselves have recently experienced this to our misfortune, from two solar eclipses, one of which took place in Aries in the year 1652, the other in Leo in the year 1654. Both in a fiery sign; after which followed that famous famine and pestilence, devastating the most celebrated and populous Italian cities, Naples and Genoa, and greatly damaging Rome itself and other towns. But what kind of evils those will be which eclipses threaten, and which region they especially affect, Ptolemy clearly teaches in Book 2 of the Quadripartitum, chapter 7, and most recently Johannes Antonius Ciuffus of Naples in a special book On Eclipses and their significations in any house.

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MATHEMATICVM: 163 < 6.> Opinatur autem Ricciolus in Almagesto, Eclipses non tam calamitates in mundum importare quàm bona, eaque maxima, licet nobis ignota, aut inconsiderata, qui eius conditionis su- mus, vt ad mala potius quæ in natuta sunt, oculos admoueamus, quàm ad plurima beneficia, quæ vel ex malis ipsis habemus. Neque enim, inquit, si aliquibus incommodæ sunt Eclipses, credendum est nulli omninò naturæ sublunarium prodesse: & sanè sicut noctis, & hyemis vicissitudines suas habens in natura oppor- tunitates; ita subtractio Lunaris luminis eo tempore, quo plenum alsoquin tetras illustraturum fuisset, & obstructio radsorum Solarium ad astemperandos, aut interrumpendos influxus persinere videtur. Hæc ille & sanè non sine maxima probabilitare. < 7.> Hic autem quoniam de luminarium defectionibus agitur, non erit ab te aliqua etiam de eclipsi, seu obscuratione aliorum exlestium corporum per interpositionem inferiorum, exponere. Equidem eo modo, quo Sol obscuratur, possunt & quinque erraticæ, possunt quinimò & fixæ, eandem defectionem pati, qua eorum lumen & influentiæ per inferiores intercipiantur. < 8.> Quod quando accidit præsertim in tribus superioribus, atque hæc luminis inhibitio sit ab ipsis luminaribus, qui cum corpore magni sint diu planetam superiorem tenent occultatum, eiusque radios, & influentias diu à nobis auertunt, tunc quidem grande aliquid; idque non ita obuium expectandum est. Talis fuit obscuratio, immò & occultatio Iouis per interpositionem corporis Lunaris ante annum 1648. de qua variè pronunciatum ab nostris Astronomis, & quia effectus isti incidebant in Poloniam, quæ suberat signo, in quo celebrata fuit: ideò nil mirum si ab eo tempore ea tam malè sit bellis vexata. < 9.> At enim eo modo quo obscuratur Luna per hoc quod incidat in vmbram terræ, aut alterius planetæ nullus eorum poterit obscurari. Patet, quia licet telluris vmbra pertingat ad orbem Veneris, ac proinde tangere possit, & Venerem, & Mercurium, sic etiam vmbra Mercurij ad orbem Veneris; nihilominus vmbra illa non rectè sursum porrigitur, nisi quando Luna, aut alius planeta est in oppositione Solis: At isti planetæ, Venus scilicet, & Mercurius nunquam elongantur à Sole plusquam vnum, aut duo signa, quî sit, vt neque in vmbram conicam terræ possint incidere, neque in Lunæ, neque in alterius alter, atque adeò nec etiam eclipsari. ECLIPTICA est linea in medio Zodiaci collocata, hinc inde sex gradus latitudinis relinquens, per quam Sol perpetuò incedit neque ad dextram, neque ad sinistram vnquam declinans, seu melius definiri potest ecliptica, quod sit Circulus magnus in calo aqualiter distans à polis Zodiaci, non secùs ac aquator à L ij

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MATHEMATICVM: 163 < 6.> Ricciolus, however, in the Almagest believes that eclipses bring into the world not so much calamities as good things, and those very great ones, though unknown to us or not considered by us, who are of such a condition that we turn our eyes rather to the evils that are in nature than to the many benefits which we derive even from the evils themselves. For, he says, if eclipses are troublesome to some, it must not be believed that they are of no use at all to sublunary nature; and indeed, just as night and winter have their own conveniences in nature by turns, so the subtraction of lunar light at the time when it would otherwise have fully illuminated the earth, and the obstruction of the solar rays, seems to serve for tempering or interrupting the influences. Thus he says, and indeed not without the greatest probability. < 7.> But since we are dealing with the darkenings of the luminaries, it will not be out of place for you to explain something also about the eclipse, or obscuration, of other celestial bodies through the interposition of lower ones. Indeed, in the same way as the Sun is darkened, the five wandering stars can also be darkened, and indeed even the fixed stars can suffer the same deprivation, by which their light and influences are intercepted by inferior bodies. < 8.> When this happens especially in the three superior planets, and this hindrance of light comes from the luminaries themselves, which with their large bodies keep a superior planet hidden for a long time and turn its rays and influences away from us for a long time, then indeed something great is to be expected; and not something so ordinary. Such was the obscuration, and even the concealment, of Jupiter through the interposition of the lunar body before the year 1648, about which our astronomers pronounced variously, and because these effects fell upon Poland, which was under the sign under which it was celebrated: therefore it is no wonder if from that time it has been so badly harassed by wars. < 9.> But in the same way that the Moon is darkened by falling into the shadow of the Earth, or of another planet, none of them can be darkened. It is clear, because although the Earth’s shadow reaches as far as the orbit of Venus, and therefore can touch both Venus and Mercury, and likewise the shadow of Mercury reaches the orbit of Venus, nevertheless that shadow does not extend rightly upward, except when the Moon or another planet is in opposition to the Sun. But these planets, Venus and Mercury, never move farther from the Sun than one or two signs; how then could it be that they should neither fall into the conical shadow of the Earth, nor into the Moon’s, nor into another’s, and therefore not even be eclipsed. ECLIPTICA is a line placed in the middle of the Zodiac, leaving six degrees of latitude on either side, through which the Sun perpetually proceeds, never inclining either to the right or to the left; or, more correctly, the ecliptic may be defined as a great circle in the heavens equally distant from the poles of the Zodiac, just as the equator is from the poles of the world. L ij

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164 LEXICON polis mundi, in eorum media distantia descriptus, per quem Sol perpetuò discurrit Hinc orbita Solis, via Solis, planum Solis, & alijs etiam nominibus est insignita. Potissimùm autem dicitur Ecliptica, eò quia in ea semper accidunt eclipses, ac luminarium defectiones: vt paulò antè tetigimus. Differt à Zodiaco tanquam pars à toto; quia hic appellat spatium latum, & amplum sex graduum hinc inde ab ecliptica, per quod vnsusquisque per suam orbitam incedendo discurre re intelligitur, vnde & ipsam eclipticam, & aliquid ampliùs comprehendit; Ecliptica verò est linea latitudinis expers in Zodiaci medio sita, per quam vnicus Sol perpetuò discurrit. Vbi aduertendum quod juxta Alphonsinorum sententiam tres imaginari debemus eclipticas. Vnam in primo mobili: alteram in nona sphæra; tertiam in octaua, seu firmamento. Harum dux propios habent polos, eosdemque fixos in eadem semper distantia à polis mundi: tertia verò, sub qua propriè mouetur Sol, habet polos semper mobiles, sicut in Theoricis planetarum demonstratur, qui nunc accedunt, nunc recedunt à dictis polis mundi, semper tamen manentes sub circulo transeunte per polos eclipticæ primi mobilis, & nonæ sphæræ, ac similiter per capita Arieris, & Libræ nonæ sphæræ, quem colurum æquinoctiorum vocamus; ac de ecliptica octauæ sphæræ, quæ hucusque diximus, verificantur. Alia huic spectantia vide in V. Zodiacus. 10. ECNEPHIAS, Græcè ad eam ventorum speciem referri potest, quam Philosophus fulminibus junxit, & sub vniuersali procellarum nomine appellauit, suntque Ecnephias, Turbo, & Præstera. Sic autem eius generatio ab eo perbellè traditur in lib. de Meteoris. Eleuatur, inquit, è terra humore imbibita permixtim halitus terrestris, & aequens, qui ad secundam aëris regionem perueniens cogitur in nubem: calentior autem exalatio se recolligit, & à vapore, & nube concluditur; & à circumsistentia contrarij validior reddita nubem scindit, & foras erumpit. Et si talis exhalatio sit subtilior, & à nube separetur non tota simul, sed interpolate per modicas partes, & ex diuersis ubium locis in tonitrua, & coruscationes conuertitur: sin autem spiritus intrà nubem coactus corpulentior, & crassior sit, & versus terram è nube prosiliat, non sparsim, sed confertim, ac totus simul sit Ecnephias: nimirum ob crassitiem non incenditur in coruscationem, non tonat, quia non agitatur, & reuoluitur intrà nubem, nec crassiora latera scindit, sed magna vi, tum ob celeritatem excretionis, tum ob partium multitudinem deorsum fertur, sicque procellosus Ecnephiæ ventus existit. Hæc Arist. ex quibus sic breuiter definiri potest Ecnephias. Est exhalatio copiosa & crassa, tota simul è nubi-

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164 LEXICON the pole of the world, described at equal distances from them, through which the Sun perpetually runs. Hence the Sun’s orbit, the Sun’s path, the plane of the Sun, and it is also distinguished by other names. But it is chiefly called the Ecliptic, because eclipses and defects of the luminaries always occur in it, as we noted a little before. It differs from the Zodiac as a part from the whole; because this word denotes the broad and wide space of six degrees on either side of the ecliptic, through which each one is understood to move and run in proceeding along its own orbit, whence it includes both the ecliptic itself and something more; but the Ecliptic is a line without latitude situated in the middle of the Zodiac, through which the single Sun perpetually runs. It must be noted that according to the opinion of the Alphonsines we must imagine three ecliptics. One in the first mobile; another in the ninth sphere; a third in the eighth, or firmament. Of these two have their own poles, and the same fixed in the same always distance from the poles of the world: the third, under which the Sun is properly moved, has poles always mobile, as is demonstrated in the Theories of the planets, which now approach, now recede from the said poles of the world, always nevertheless remaining under the circle passing through the poles of the ecliptic of the first mobile and of the ninth sphere, and likewise through the heads of Aries and Libra of the ninth sphere, which we call the equinoctial colure; and what has been said up to now is verified concerning the ecliptic of the eighth sphere. See also other things pertaining to this under V. Zodiacus. 10. ECNEPHIAS, in Greek, can be referred to that kind of wind which the Philosopher joined with thunderbolts, and named under the universal designation of storms; and they are Ecnephias, Turbo, and Præstera. Its generation is thus very elegantly described by him in book de Meteoris. “It is raised,” he says, “from earth soaked with moisture, together with mixed terrestrial and airy exhalation, which, reaching the second region of the air, is forced into a cloud: a warmer exhalation, however, gathers itself together, and is enclosed by vapor and cloud; and being made stronger by the resistance of what surrounds it, it rends the cloud and bursts forth. And if such an exhalation be subtler, and separated from the cloud not all at once, but intermittently in small portions, and from various places within it is turned into thunder and lightning flashes: but if the spirit, being forced within the cloud, be more corporeal and thicker, and rush from the cloud toward the earth, not scattered about but compact, and be all at once, then it is Ecnephias: namely, on account of its thickness it is not kindled into lightning, it does not thunder because it is not stirred up and whirled within the cloud, nor does it split the thicker sides, but with great force, both because of the speed of its discharge and because of the multitude of its parts, it is carried downward, and thus the stormy Ecnephian wind comes into existence.” This is Aristotle’s account, from which Ecnephias may briefly be defined thus. It is a copious and thick exhalation, all at once from a clo-

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MATHEMATICVM. 165 bus excussa, & magna vi deorsum impulsa absque gyro, & inflammatione. De eo multa habet Plinius lib. 2. cap. 48. & 49. Concluditur igitur Ecnephiam valdè à cæteris ventis natura, & conditione distare: illi enim omnes è terra prosiliunt, Ecnephias è nubibus est: illi non nisi aër commotus sunt, iste copiosa quædam, & crassa exhalatio tota simul è ruptis nubibus excussa, & magna vi deorsum impulsa, quæ quia nimium crassa est, ideò non coruscat. ECPHOSIS, Græcè idem sonat, ac Latinè delapsus; estque < 11> potissimè, vt testis est Valla, ab Astronomis vsurpatum ad explicandam profectionem annuam ascendentis in illud signum, in quo facta fuit præcedens luminarium conjunctio, aut oppositio in Genesi. ED EDELEV Arab. Latinè dicitur Aquarius vndecimum signum, < 12.> seu potius astrum in cælo constans stellis 42. de quo vide in V. Aquarius. EDVB, seu Dubbe dorsum Vrsæ maioris. Vide in V. Dubbe. < 13.> EF EFFLUXVS, idem significat ac defluxus: Cùm videlicet planeta discedit à conjunctione partili cum alio, & est adhuc in < 14.> platica, hoc est intrà quantitatem orbis lucis ipsius, quod in leuibus tantum ergà ponderosos verificari potest. Vide in V. Coitus. EL ELATHI, idem apud Arabes, ac Geniculator apud Latinos, < 15.> hoc est Hercules, Engonasis, sidus in cælo, de quo sæpè recurret sermo. ELDEGIAGICH Arab. & corrupto nomine Adigege dicitur < 16.> Gallina, Cygnus, sidus in cælo constans Ptolemæo stellis 17. & Kepler. 27. de quo satis dictum in V. Cygnus. ELECET, Arabicè dicitur Leo signum, & sidus in cælo, ad < 17.> borealem plagam constans stellis 27. (exceptis aliquibus sporadibus circa ipsum) promiscuæ naturæ, inter quas Calb Eleced cor Leonis: Deneb Eleced, cauda Leonis: Ras Eleced, caput Leonis insigniores, quarum naturam, & proprietates sub proprijs nominibus habes. ELECTIONES Astrologica sunt temporum opportunitates ad < 18.> aliquid aggrediendum assumptæ; cùm videlicet ex Astrologicis obseruationibus cantum est, quædam in certo siderum positu malè, quædam autem benè ac fausto omne auspicari Equidem vt ait Philosophus inferiora ista, tum in essendo, tum in operando à causis superioribus pendent, & eæ quidem naturaliter in suos effectus influunt, ac necessariò agunt: humana L iii

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MATHEMATICVM. 165 being blown up, and driven downward with great force without a whirl, and without inflammation. On this Pliny has much in lib. 2, cap. 48 and 49. It is therefore concluded that Ecnephias differs greatly from the other winds in nature and condition: for all the others spring forth from the earth, Ecnephias is from the clouds; all the others are nothing but agitated air, whereas this is some copious and thick exhalation, all at once driven out of broken clouds, and thrust downward with great force, which, because it is too thick, therefore does not flash. ECPHOSIS, in Greek sounds the same as in Latin delapsus; and it is especially, as Valla testifies, used by the astronomers to explain the annual advance of the ascendant into that sign in which the preceding conjunction or opposition of the luminaries in the nativity was made. ED EDELEV in Arabic is called Aquarius, the eleventh sign, or rather a starry figure in the sky consisting of 42 stars; see under Aquarius. EDVB, or Dubbe, the back of Ursa Major. See under Dubbe. EF EFFLUXVS means the same as defluxus: namely, when a planet departs from a partile conjunction with another, and is still in platica, that is, within the quantity of its own sphere of light, which can be verified only in the case of the bright planets with respect to the heavier ones. See under Coitus. EL ELATHI, among the Arabs the same as Geniculator among the Latins, that is, Hercules, Engonasis, a starry figure in the sky, of which there will often be mention. ELDEGIAGICH in Arabic, and by a corrupted name Adigege, is called Gallina, Cygnus, a starry figure in the sky consisting, according to Ptolemy, of 17 stars, and according to Kepler 27, about which enough has been said under Cygnus. ELECET, in Arabic is called the sign Leo, and the starry figure in the sky, toward the northern region, consisting of 27 stars (excepting certain scattered ones around it) of mixed nature, among which are Calb Eleced, the heart of Leo; Deneb Eleced, the tail of Leo; Ras Eleced, the more prominent head of Leo, whose nature and properties you have under their proper names. ELECTIONES in astrology are opportunities of time chosen for undertaking something; namely, when from astrological observations it is determined that some things are badly and others well and favorably to be begun in a certain position of the stars. Indeed, as the Philosopher says, these lower things, both in being and in operating, depend on superior causes, and these indeed naturally influence their effects and necessarily act: human L iii

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166 LEXICON aurem ratio ex prudenti præuisione potest eorum effectus multos præuertere, subtrahendo materiam, impedire, declinare, vel etiam cooperando adjuuare, disponere materiam, seseque bonis influxibus subjectum passibile exhibere. Sunt quippe ex- lorum influxus copiosus veluti imber, aut redundans aquis plurimis amnis, quas cum meo horto salutares intellexero, viam illis parare gestio, repagula tollo, in plantas omnes deriuo: at contra cum perniciosæ fuerint, viam claudo, extructo aggere occurro, & aliò earum imperum alluusionemque deflecto. Sic igitur electionis Astrologicæ est in rebus gerendis tempus opportunum assumere, quo astra inter se mutuò, & in situ mundi taliter disposita sunt, vt tum ratione, tum experientia irrefragabili id docente rei productioni, aut actioni instituendæ minimè officiant, sed, potiùs ad benè esse valdè conducant, & auspicatè se habeant: vnde Ouidius Temporibus medicina valet; data tempore prosunt, Et data non apto tempore vina nocent. Hinc si quis omnes siderum influentias, ac virtutes agnosceret, eorum cum sublunaribus hisce connexionem, ordinem, & sympathiam; vel etiam diffensum, discordiam, atque antipathiam calleret, proculdubiò is mira operari posset, seseque non sideribusmodò; sed ipsi naturæ imperitare posse præsumeret, auderetque suis contrà Deum donis pugnare. Ideò hæc ipsum latere jure voluit prouidentissimus rerum Opifex, atque vt inquit Plin. Omnia incerta ratione, & in natura majestate abdita: Sarque eius incolumitati vitæque rationi consumir, si quædam vniuersaliora, & grossiora quoad Medicinam, Agriculturam, & Navigatoriam artem permisit ei per experientiam comparare. <19.> Porrò hæc In duplici genere sunt: alia enim, quæ dicuntur Electiones vniuersales, quæ videlicet in omnibus locum habent, nec pendent à peculiari cuiusque nativitate, vel quia eius notitia haberi nequeat, vel sanè quia ad rei aggrediundæ rationem impertinens est quales sunt temporum mutationes, agricolationes, ædificia construenda, & similia: alia quæ à peculiari cuiusque genesi pendent, dicunturque ideo Electiones particulares, quæ aut necessariò aut congruentiùs ex eiusdem inspectione, & connexione quam habet ad præsens tempus sunt ineundæ: Huiusmodi sunt Medicinalibus vti, Navigationes, Itinera, opus aliquod maximè arduum aggredi, & similia. <10.> Quod ad Electiones vniuersales generaliter attinet, consideranda est primò negotij arripiendi qualiras, & conditio: tum corporum cælestium præcipuè verò Lunæ (quæ in sublu-

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166 LEXICON By reason and prudent foresight, one can anticipate many of their effects, by removing the matter, prevent, hinder, or even by cooperating, assist, arrange the matter, and exhibit oneself as a patient subject to good influences. For their abundant influences are as a rainstorm, or a river overflowing with many waters, which, when I have recognized them as salutary to my garden, I hasten to prepare a way for them, I remove the barriers, I direct them into all the plants: but on the contrary, when they are harmful, I close the way, I meet them with a raised embankment, and I deflect their flood and inundation elsewhere. Thus, then, the election of Astrology is, in the conduct of affairs, to take the opportune time, when the stars among themselves, and in the position of the world, are so disposed that then, both by reason and by unmistakable experience teaching it, they do not hinder the production of the thing, or the undertaking of the action, but rather greatly conduce to its well-being, and are auspiciously situated: whence Ovid Medicine is effective at the proper times; things given at the right time are beneficial, And wine given at an unsuitable time is harmful. Hence if anyone were to recognize all the influences and powers of the stars, their connection, order, and sympathy with these sublunar things; or even their opposition, discord, and antipathy, without doubt such a person could work wonders, and would presume that he could command not only the stars, but nature itself, and would dare to fight against God with his gifts. Therefore the most provident Maker of things rightly wished this to be hidden from him, and, as Pliny says, all things are uncertain in reason, and hidden in the majesty of nature: and his safety and the ordering of his life would be compromised if he were allowed to acquire by experience certain more universal and cruder things in Medicine, Agriculture, and the art of Navigation. <19.> Moreover, these are of a twofold kind: for some, which are called universal elections, are such as have place in all matters and do not depend on the particular nativity of each person, either because its knowledge cannot be had, or indeed because it is irrelevant to the manner of approaching the matter; such are the changes of times, cultivations, buildings to be constructed, and the like: others, which depend on the particular genesis of each person, are therefore called particular elections, which are to be undertaken either necessarily or more fittingly from consideration of that same genesis, and of the connection it has with the present time: of this sort are the use of medicines, voyages, journeys, the undertaking of some especially arduous work, and the like. <10.> As far as universal elections are concerned in general, one must first consider the nature and condition of the business to be undertaken: then the celestial bodies, and especially the Moon (which in sublu-

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MATHEMATICVM. 167 naria isthæc præ cæteris potissimam vim obtinet) in signis, ac domibus constitutio: vt si celeritate sit opus sint in mobilibus signis, si stabilitate, ac firmitate vt ædificationes, in fixis. Prætereà vt planeta rei aggrediundæ naturalis significator, li- ber sit à maleficis, atque in suis dignitatibus, honorumque aspectibus constitutus. Tandem, vt signum ascendens tempore operis incundi sit de natura propositæ rei, vt pro itineribus. signa mobilia, & pro navigationibus quidem aqvea, pro terre- stribus terrea, aut fixa: pro prælijs aut rixa feliciter ineunda in horoscopo sint signa aut sidera Martialia, vt Bellatrix, Palli- litium, Regulus, &c. Pro Navigationibus item inauspicati sunt congressus Lunæ cum Marte, aut sideribus prædictis de eiusdem natura, ortus, & occasus Arcturi, Orionis, Hædo- rum, Delphini, & Sirij: experientia enim nunquam fallens edocuit hæc tempestates inducere. Similiter quoad Potiones sumendas generaliter Ver est tempus maximè accommoda- tum: hyems & æstas, ac præcipuè dies caniculares in opportu- ni. In specie verò Luna quæ humoribus præsidet sit benè affe- cta, lumine minuta magis, quàm aucta, libera à maleficis, nec non à Sole, eorumque prauis aspectibus: ac sit in signo de na- tura humorum qui purgandi sunt vt si atrabilis euacuanda sit, Luna constituatur in signis terreis; si flaua in signis igneis; si phlegma in signis aqueis: Aries tamen, Gemini, Cancer, Leo, & signa ruminantia parum idonea sunt ad potiones sumendas, quia cum partibus superiotibus præsint: eas sursum euocant, & vomitum cient, vt experientia jugis testatur. Ni fortè Vo- mitoria præbeantur, in quo casu ea signa data opera sunt pe- tenda. Attendendus etiam est ipsius Lunæ cum planetis aspe- ctus, qui vt dixi maleficarum, quicumque tandem sint semper portionum effectus, impediunt. Sol è contrà, & Venus per be- nignos aspectus adjuuant: Iupiter non est adeò idoneus, quia naturam nimium roborat, qui sit, vt medicamentum in nutri- tionem potiùs abeat, quam in excretionem. Vniuersaliter au- <20.> tem planeta cui humor euacuandus subditur, non sit potens in angulo, aut suis dignitatibus necesse est, sed potiùs debilis, & sub terra, si enim fortis, & suprà terram humorem auget, sur- sum euocar, purgationique obsistit. Sic si phelgma purgare ve- lis, non sit fortis, eo tempore quo medicina sumitur Venus, sed Mars: si flauam bilem è contrà Mars debilis sit & sub ter- ra, Luna verò, aut Venus potentes, &c. Vbi aduertendum est aliam esse rationem signorum, aliam siderum. Nam in bile euacuanda, cauenda est quidem vt dixi fortitudo Martis illam augentis, ac roborantis, at eligendum est in horoscopo & in Luna signum igneum ob conformitatem naturæ, eò quia se L iiiij

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MATHEMATICVM. 167 of this kind, especially this numerical one, has the greatest force) in the configuration of signs and houses: so that if speed is required, let them be in movable signs; if stability and firmness, as in buildings, in fixed signs. Moreover, let the planet that is the natural significator of the matter to be undertaken be free from malefics and placed in its own dignities and in the aspects of benefics. Finally, let the ascending sign at the time of the work begun be of the nature of the proposed matter, as for journeys movable signs, and for voyages indeed watery signs; for land journeys, earthy or fixed ones; for battles or quarrels to be happily begun, let there be in the horoscope signs or stars Martial, such as Bellatrix, Pallitium, Regulus, &c. For voyages likewise, unlucky are the conjunctions of the Moon with Mars, or with the aforesaid stars of the same nature, and the rising and setting of Arcturus, Orion, the Goats, the Dolphin, and Sirius: for unerring experience has taught that these bring about storms. Likewise, with regard to potions to be taken, generally spring is the most suitable season; winter and summer, and especially the dog days, are unsuitable. More specifically, the Moon, which presides over humors, should be well affected, waning rather than waxing in light, free from malefics, and also from the Sun and their evil aspects; and it should be in a sign of the nature of the humors that are to be purged. Thus, if black bile is to be evacuated, let the Moon be placed in earthy signs; if yellow bile, in fiery signs; if phlegm, in watery signs. Aries, however, Gemini, Cancer, Leo, and the ruminating signs are rather unsuitable for taking potions, because as they preside over the upper parts, they draw them upward and provoke vomiting, as continual experience shows. Unless perhaps emetics are to be given, in which case those signs are to be deliberately sought. The aspects of the Moon itself with the planets must also be considered; these, as I said, whenever they are malefic, always hinder the effects of the purges. The Sun, on the other hand, and Venus assist by their benign aspects; Jupiter is not so suitable, because it too greatly strengthens nature, so that the medicine turns rather into nourishment than into evacuation. In general, however, the planet under whose rulership the humor to be evacuated is placed should not necessarily be powerful in an angle or in its own dignities, but rather weak and under the earth; for if it is strong and above the earth, it increases the humor, draws it upward, and resists purgation. Thus, if you wish to purge phlegm, Venus should not be strong at the time when the medicine is taken, but Mars; if yellow bile, on the contrary, Mars should be weak and under the earth, while the Moon or Venus are powerful, &c. Here it must be noted that the reasoning for signs is one thing, and for stars another. For in evacuating bile, one must indeed avoid, as I said, the strength of Mars, which increases and strengthens it; but in the horoscope and in the Moon an igneous sign should be chosen on account of the conformity of nature, because it se L iiiij

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168 LEXICON habet vt subjectum passibile, & in eo planeta pugnans cum humore purgando validiùs operatur. Excipe tamen semper Leonis signum nimis exæstuans, & quod nobilissimo membro præest, hoc est cordi totius vitæ operationumque vitalium fonti, atque origini. 21. Quoad Phlebotomiam pariter discurrendum, attendenda est enim cuiusque ætas, constitutio, & morbi qualitas. Nam pro juvenibus optimum est sanguinem mittere cum Luna ctescit lumine, pro senibus verò cùm deficit: si æger igneus sit, adustus, & in eo flauabilis redundet mittatur sanguis cum Luna est in signis aqueis Cancto, & Piscibus. Si phlegmaticus cum in Ariete, & agittario: si melancholicus cum Luna est in Aquario, & in ptima medietate Libræ. Cæterùm Geminorum signum cum Leone, & ptima medietate Scorpij, cum secunda Libræ, pro omnibus vniuersim inauspicata sunt, eò quia hæc via combusta est, in qua Luna multùm infortunatur. Leo cordi vt dictum est dominatur, vnde sanguis trahit originem: Gemini autem brachijs in quibus vt plurimùm scindirur vena. Atqui regula genetalis est membrum haud ferro tangendum eo tempore quo Luna signum illud petmeat, quod tali membro dominatur: cum enim eius sit humectare totum corpus, illud potissimùm membrum humoribus replere habet, quod signo illi subest, in quo ipsa moratur: ex quo sit vt vulnus difficulter consolidetur, & humotes alioqui commoti ferri contactu ardeant, & tabescant. Signa item tertia patum sunt mittendo sanguini idonea: Atque hæc de electionibus vniuersalibus dicta sint: Cætera quæ tum ad Agticolationem, tum ad Navigatoriam spectant videri possunt apud Austores Ephemeridum in Isagonicis, præcipuè vetò apud Argolum lib. 2. cap. 7. & seqq. Nobis enim in re præsertim obvia non licet esse nimium longis. 22. Quoad Electiones vetò particulares breuiter hæc regula seruanda est eas fore semper nato proficuas, & opportunas cum congruunt, & respondent radici natiuitatis: quæ verò absque vllo delectu sunt aut inutiles sunt, aut fortasse etiam perniciosæ. Vt exempli gratiâ si quis eligat sumere potionem tempore cæteroqui ex regulis supra tradiris opportuno; cum Luna vide- licet est in Cancro, aut in Piscibus; sed tamen in figura natiuiaris habeat signa hæc à maledicis infestata, tuuc quidem non modo non producit medicina, sed fortasse etiam nocebit, similiter non tam radix ipsa natiuitatis consideranda est, & cum electionis tempore conferenda, quam tempus per directiones signatum, & videndum si ad id tempus respondeat alioqui bona directio: Quoad negotia peragenda disquirendum, cui

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168 LEXICON has a susceptible subject, and in it the planet fighting with the humor to be purged works more strongly. Yet always except the sign of Leo, which is too fiery, and because it presides over the noblest member, that is, the heart, the source and origin of all life and vital operations. 21. As regards phlebotomy, the same must likewise be considered: for the age, constitution, and quality of the disease of each person must be attended to. For young people it is best to let blood when the Moon is waxing in light; for old people, when it is waning. If the patient is fiery, burnt, and has an excess of yellow bile, let blood be taken when the Moon is in the watery signs, Cancer and Pisces. If phlegmatic, when it is in Aries and Sagittarius; if melancholic, when the Moon is in Aquarius and in the first half of Libra. Moreover, the sign of Gemini with Leo, and the first half of Scorpio with the second half of Libra, are generally inauspicious for everyone, because this is a burnt path, in which the Moon is greatly afflicted. Leo rules the heart, as was said, whence blood draws its origin; Gemini, however, the arms, in which the vein is usually cut. But the general rule is that a limb must not be touched by the iron at the time when the Moon is passing through that sign which rules such a limb: for since it is its office to moisten the whole body, it must especially fill with humors that member which is subject to the sign in which it is dwelling; from which it follows that the wound is hard to heal, and the humors otherwise stirred by contact with the iron burn and waste away. Likewise the third signs are somewhat fit for letting blood. And these things may be said concerning universal elections: the rest, both what pertains to agriculture and to navigation, may be seen among the authors of almanacs in the Isagogics, especially in Argolus, book 2, chapter 7 and following. For in a matter especially common to us, we are not allowed to be too lengthy. 22. As regards particular elections, this brief rule must be observed: they will always be beneficial and opportune to the native when they agree and correspond to the radix of the nativity; but those which are without any selection are either useless, or perhaps even harmful. For example, if someone chooses to take medicine at a time otherwise opportune according to the rules given above, namely when the Moon is in Cancer or Pisces, but in the figure of the nativity these signs are afflicted by malefics, then the medicine not only does not benefit, but perhaps will even harm. Likewise, it is not so much the radix of the nativity itself that must be considered and compared with the time of the election, as the time marked by the directions; and it must be seen whether some otherwise good direction corresponds to that time. As regards affairs to be undertaken, it must be investigated to whom

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MATHEMATICVM. 169 rei quisque in radice natiuitatis ab siderum constitutione addi- ctus est, eique se dedat constituendum planetæ, vel signo illi quod talem significationem facit in ascendente. < 23.> Denique in quacumque Electione, ea semper ineatur cum Luna per ea signa mear, in quibus Iupiter, Venus, aut pars for- tunæ reperiebantur tempore natiuitatis, aut benigno radio res- piciatur à dictis planetis, sintque loca rerum significationi idoneæ: Experientia enim compertum est, quidquid boni & for- tunæ vnicuique obuenit, id potissimùm obuenire, eò quia Luna per loca beneficatum transit: sicut è contrà quidquid mali, ex ingressu eiusdem in loca in radice à maleficis infesta. < 24.> ELEMENTVM absolutè dicitur id, quod quauis in re prima radix est, & initium, ex quo alia componuntur. Vnde in vniuersi istius ambitu, quæ sunt prima rerum semina, ex quibus reliqua corpora coagmentantur, Elementa dicuntur; Ignis videlicet, Aër, Aqua, Terra, atque ex ijs elementatis regio quæ infrà cælum omnia elementa, & ex ijs mixta complecti- tur, dicta. Quare autem quatuor tantùm, & nec pluta, nec pauciora elementa rerum assignata sint, explicat Philosophus 2. de Generat & corrupt. cap. 4. Quia videlicet quatuor tan- tùm sunt primæ qualitates tangibilium, nempe caliditas, sic- citas, frigiditas, & humiditas, quæ adinuicem copulata, om- nem rerum tam simplicium, quàm mixtarum complexionem, ac temperiem comprehendunt. Quot enim sunt possibiles com- binationes harum primarum qualitatum in vno, eodemque subiecto, tot elementa assignantur: quippe oppositarum, vt caloris, & frigoris, humiditatis, & siccitatis impossibilis est combinatio. Tot igitur sunt Elementa. Quapropter & Ptole- mæus in prima parte Quadrip. omnes altorum influxus ad quatuor Elementorum qualitates reducit; quasi elementa ipsa ex cælorum, & siderum motibus suæ distinctionis originem trahant. Porrò, vt modò dixi, elementa inter se certo ordine constituta efficiunt regionem elementarem, proure ab Æthetea discernitur, quæ tamen vna cum ipsis hoc Vniuersum consti- tuunt. Et in Vniuersi quidem ipsius centro existit Terra omni- nò immobilis, & cæteris elementis grauior: inde Aqua: mox Aër: denique Ignis, qui immediatè subest concauo Lunæ An autem elementa (excepta Terra) moueantur circulanter ab Oriente in Occidentem motu vniuersitatis, & pumi mobilis: vnde Oceani motum non Lunæ, sed primi mobilis raptui tribuendum esse sunt qui affirmant apud Clauium in sphæram Io. de Sactobosco: & nos in loco diximus. Quod autem non exquisitè tapiantur, id prouenit ex eorum resistentia, & elon- gatione à primo mobili; quò enim grauiora sunt, ac situ remo-

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MATHEMATICVM. 169 everyone in the root of nativity is bound by the constitution of the stars, and let him commit himself to be governed by that planet, or by that sign which makes such a signification in the ascendant. <23.> Finally, in whatever Election, it should always be undertaken while the Moon moves through those signs in which Jupiter, Venus, or the Part of Fortune were found at the time of nativity, or is favorably aspected by the said planets, and let them be places suitable to the signification of the matter; for experience has made it clear that whatever good and fortune befall anyone, befall chiefly because the Moon passes through benefic places: just as, on the contrary, whatever evil occurs, arises from her entrance into places in the root that are afflicted by the malefics. <24.> An ELEMENT is absolutely said to be that which in any thing is the first root and beginning, from which other things are composed. Hence in the compass of this universe, those things which are the first seeds of things, from which the remaining bodies are joined together, are called Elements; namely Fire, Air, Water, Earth, and from these the elemental region is said to be that which beneath the heaven contains all elements and the mixtures made from them. But why only four, and neither more nor fewer, elements of things have been assigned is explained by the Philosopher in 2 De Generatione et Corruptione, cap. 4. Namely because there are only four primary qualities of tangible things, that is, heat, dryness, coldness, and moisture, which, joined together in pairs, comprehend every complexion and temper of things, both simple and mixed. For as many as are the possible combinations of these primary qualities in one and the same subject, so many elements are assigned; for of opposites, such as heat and cold, moisture and dryness, the combination is impossible. Therefore there are four Elements. Wherefore Ptolemy also, in the first part of the Quadripartitum, reduces all influences of the heavens to the four qualities of the Elements; as though the elements themselves derive the origin of their distinction from the motions of the heavens and the stars. Moreover, as I have just said, the elements, established among themselves in a fixed order, make up the elemental region, as it is distinguished from the ethereal region, which nevertheless together with them constitutes this Universe. And in the very center of the Universe there exists Earth, utterly immobile and heavier than the other elements; then Water; then Air; and finally Fire, which is immediately beneath the concavity of the Moon. But whether the elements (except Earth) are moved circularly from East to West by the motion of the universe and the mobile sphere: hence there are some who affirm that the motion of the ocean ought to be attributed, not to the Moon, but to the dragging of the first mobile, as in Clavius on the Sphere of Jo. de Sacrobosco: and we have spoken of it in the proper place. But that they are not exactly carried along arises from their resistance and their remoteness from the first mobile; for the heavier they are, and the farther removed in situation,

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170 LEXICON tiora, eò magis resistunt, ac morantur: vt patet in ipsis sphæris cælestibus. Vnde etiam intelligi potest, & has omnes flui- das esse, vt elementa sunt, & eò fluidiores, ac puriores, quo à centro magis elongantur. Et vnico tantùm motu cieri ab Oriente in Occidentem raptas à primo orbe; licet quæ ab eo sunt magis remotæ, magis impulsui dato sua ponderositate resistant, ac retrò in partibus Orientalioribus maneant, prout diximus in V. Calum. Cæterùm non negauerim multos ex recensioribus inter elementa Ignem minimè connumerare, quia & aliquos omnia elementa negare: inter quos est Aueria tom. 2. Philosoph. quast. 41. sect. 2. 25. ELEMENTA Geometrica, Antonomasticè audiunt Libri quindecim Geometricorum principiorum Euclidis Geometrarum Principis, & Magistri: eò quia sine ipsis nullum opus Mathematicum aggredi, nullum effatum percipi potest; sicut enim is qui legere vult (inquit Clauius in Prologom.) Elementa literarum discit prius, & illis assiduè repetitis vtitur in vocibus omnibus exprimendis, sic qui alias disciplinas Mathematicas desiderat sibi reddere familiares elementa hæc Geometrica plenè, ac perfectè calleat prius necesse est. Quandoquidem horum elementorum ope, omnis in cælo siderum ratio auspicatur, eorum motus, situs, distantia, altitudo, quantitas internoscitur. Ab ijs omnis in cælo, omnis in terra dimensio habetur: ac denique ingens hoc Dei, ac Naturæ opus, Vniuersi, inquam, istius machina non sine Geometricorum horum elementorum auxilio intelligi, & contemplari potest. Iure igitur hæc prima Geometriæ principia elementa Geometrica dicta sunt. 26. ELEVATIO apud Astronomos significat præcellentiam, ac prædominium vnius planetæ super alium, quando videlicet duo, vel plures concurrunt adinuicem, & conveniunt ad vnam, eandemque rem significandam: tunc qui alijs, viribus atque activitate prævaler, dicitur super illos eleuatus. Pontanus in 27. Commentar. super Centiloqu. hanc dicendi formam non probat, quia eleuare, inquit, apud Grammaticos indicat depressionem potiùs, quàm præeminentiam: Verùm nescio, an satis benè discurrat: cum Eleuo propriè significet sursum leuo, siue in altum tollo: quod idipsum prorsus est, quod explicare volumus in planetis se super alios eleuantibus, vt mox dice- mus. Quod autem quandoque per translationem accipiatur pro rei diminutione, quæ verbis fiat eam vituperando, id non officit propriæ notioni. Sed quidquid sit de modo loquendi, certum est in re, Eleuari apud Astronomos nil aliud significare quàm extollentiam vnius planetæ super alium: quod

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170 LEXICON the more they resist and impede, as is evident in the celestial spheres themselves. Hence it can also be understood that all these are fluid, as the elements are, and the more fluid and pure the farther they are removed from the center. And they are set in motion by a single movement, carried from East to West by the first orb; although those that are more remote from it resist the given impulse more by their heaviness, and remain behind in the more eastern parts, as we said in V. Caelum. However, I would not deny that many of the more recent writers do not count Fire among the elements at all, since some even deny all the elements: among whom is Aueria, tom. 2, Philosoph. quast. 41, sect. 2. 25. ELEMENTA Geometrica. By antonomasia, the fifteen books of the Geometric Principles of Euclid, Prince and Master of Geometers, are so called; because without them no mathematical work can be undertaken, no statement can be grasped; for just as one who wishes to read, as Clavius says in the Prologom., first learns the elements of letters, and by continually repeating them uses them in expressing all words, so he who desires to make the other mathematical disciplines familiar to himself must first thoroughly and perfectly master these geometrical elements. For by means of these elements, the whole astronomical account of the stars is begun: their motions, positions, distance, height, and magnitude are recognized. From them is obtained every measurement in heaven, every measurement on earth; and finally this great work of God and Nature, the fabric of the universe, I say, cannot be understood and contemplated without the help of these geometrical elements. Therefore these first principles of geometry were rightly called geometrical elements. 26. ELEVATIO among astronomers signifies the preeminence and predominance of one planet over another, when, namely, two or more come together and agree in indicating one and the same thing: then the one that prevails over the others in power and activity is said to be elevated above them. Pontanus, in his 27th Commentary on the Centiloquium, does not approve this way of speaking, because, he says, elevare among grammarians indicates rather a lowering than a preeminence: but I do not know whether he reasons quite well, since elevate properly signifies to lift upward, or to raise aloft: which is precisely what we wish to explain in planets elevating themselves over others, as we shall soon say. But that it is sometimes taken by translation to mean the diminishing of a thing, when it is done by words in blaming it, does not interfere with its proper meaning. But whatever may be said about the manner of speaking, it is certain in fact that to be elevated among astronomers signifies nothing other than the exaltation of one planet over another: which

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MATHEMATICVM. 171 quomodo fiat atque in quo consistat huiusmodi eleuatio, non æquè ab omnibus traditur. Aliqui enim volunt tunc planetam super alium eleuari, cum est in situ mundi eminentiore, vbi sit magis vicinus Vertici aut Meridiano: quod quidem nulli dubium est, cæteris paribus maximas vires sideribus addet[ur] quippequæ inde directiores radios ad mundum transmittunt. Verùm id non videtur tantam prærogatiuam planetis addere, vt exinde præcisè dici possint super alios extolli, maximè quando aliàs isti fortiores sunt, & prærogatiuam hanc situs alijs numeris superant, aut compensant. Alij dicunt illum vincere, & eleuari super alium, qui magis accedit ad Boream: sed hi etiam discrepant, nam aliqui intelligunt planetam habentem majorem latitudinem Borealem super alium eleuari, qui in majori, vel in australi, vel sanè in Ecliptica repetitur, & alij hoc intelligunt de declinatione, quod nempe maiorem habeat Borealem in regionibus borealibus, australem in australibus. Sunt qui volunt id attendendum esse respectu suorum Orbium; ita vt qui ascendunt magis, vel magis appropiant ad Apogæum sui siue Ecoentrici, siue Epicyeli sint super alios eleuati; qui descendunt ab Apogæo, vel ab eo magis distinerint. Cardanus est in sententia, vt ea sidera super alia eleuentur, quæ cùm sint tardioris motus, expectant ea quæ sunt velocioris vt ipsis jungantur. Argolus hos omnes modos admittit, docetque insuper faciendum esse scrutinium, & ille demum planeta dici debet super alium eleuatus, qui repertus fuerit maioribus numeris, ac potioribus calculis præditus. Verum, vt benè discurrit Titus in Cælesti Philosophia, lib. 2, 28: cap. 11. Hæc siderum super alia eleuatio, dicit concurrentiam duorum ad agendum, & quod in hoc concursu vincat illud, quod maiores vires habet, ac feratur super debilius, id est si diuersæ naturæ sint, alteret naturam illius ac multùm deprimat: hoc quippe intendit Ptolemæus pluribus in locis præsertim lib. 2. cap. 8. cum loquitur de prædominio stellarum super aliquem locum quoad effectus quos ergà illos producunt. Cum enim, inquit, sunt illa benefica, & conciliata locis obnoxijs, neque superantur ab alijs diversa secta muliò magis absolumt natura sua bonitatem, sicut & aliena, aut superata ab alijs minus prosunt. Quod si noxia hunc principatum caperint, conciliata cum obnoxijs locis, aut superata a stellis aduersaria secta minus nocens. Hæc Ptolemæus. Duo igitur requituntur ad eleuationem: & quod inter si- dera intercedat aliqua conuenientia, & familiaritas; & quod vnum sit præpotens, ac validius altero. Nam sidera nullam efficientiam habent ad inuicem, nisi aliquo modo configurem,

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MATHEMATICVM. 171 How this elevation is brought about, and wherein such elevation consists, is not explained equally by all. For some maintain that a planet is elevated above another when it is in a more eminent position in the world, that is, when it is nearer the Vertex or the Meridian; which indeed, all else being equal, undoubtedly adds the greatest force to the stars, since they then transmit their rays more directly to the world. But this does not seem to add such a prerogative to the planets that they can precisely be said thereby to be raised above others, especially when, in other respects, those are stronger and surpass or compensate for this advantage of position by other considerations. Others say that that one conquers and is elevated above another which approaches more toward the North: but even these differ, for some understand a planet having greater northern latitude to be elevated above another, who is in a greater latitude, or in the south, or even in the Ecliptic; and others understand this of declination, namely that it has a greater northern declination in northern regions, and a southern one in southern regions. There are those who wish this to be considered with respect to their own Orbits; so that those which ascend more, or approach more to the Apogee of their own eccentric or epicycle, are elevated above others; those which descend from the Apogee, or recede farther from it, are not. Cardanus is of the opinion that those stars are elevated above others which, being of slower motion, await those which are faster so that they may be joined to them. Argolus admits all these modes, and teaches moreover that an examination must be made; and that planet must finally be said to be elevated above another which is found to be furnished with greater numbers and more favorable calculations. But, as Titus argues well in the Celestial Philosophy, book 2, 28, chapter 11, this elevation of stars above others signifies the concurrence of two bodies in acting, and that in this encounter that one prevails which has greater force and is carried over the weaker; that is, if they are of different natures, it alters the nature of that other and greatly depresses it: for this is what Ptolemy intends in several places, especially book 2, chapter 8, when he speaks of the predominance of the stars over a certain place with respect to the effects which they produce toward it. For, he says, when they are beneficent and aligned with susceptible places, and are not overcome by others of a different sect, they much more fully bring about the goodness of their own nature, as also that of others; or, when overcome by others, they are less beneficial. But if harmful stars obtain this primacy, when aligned with susceptible places, or overcome by stars of an adverse sect, they are less harmful. Thus Ptolemy. Therefore two things are required for elevation: that there be some agreement and familiarity among the stars, and that one be more powerful and stronger than the other. For stars have no efficacy toward one another unless in some way they are configured,

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172 LEXICON tur, vt alibi obseruatum est. Neque in ista efficientia vnum aliud vincere potest, ac vires illius deprimere, nisi fuerit in se fortis, atque armis validioribus præmunitus. Quandoquidem quando sidera sunt inter se configurata agunt ad inuicem, ac repatiuntur: quod est validius, magis agir, & minus repatitur; quod est infirmius minus agir, & magis repatitur: Vnde est quod quæ sidera viribus præualent, dum alijs viribus imminutis aur corpore, aut radio copulantur, in illa agant, virtutem eorum altetenr, atque actiuitatem diminuanr. Quare, vt suprà habet Ptolemaeus, si benefici super malesicos eleuentur, bonum est; nam qualitates eorum maleficas deprimunt, & infringunt: si malefici super beneficos extollantur, noxium est: quippe corrumpunt eorum bonitatem, vt ipsa bonitas noxia fiar. 30. Hinc benè dixit Argolus faciendum esse scrutinium, & quod inuenietur vincere aliud in numero fortitudinum (cùm aliàs intercedat inter illa aliqua familiaritas, vt dictum est) illud dicetur super aliud eleuatum. Ordo autem, & præcellentia fortitudinum est primò situs in nobiliori cardine, & domo quoad mundum, siue maior propinquitas ad cardinem, ad quem feruntur; itaq[ue] vt hæc comparatio ad cardines præcæresis sit attendenda, cum sit omnibus prærogatiuis validior. Secundò Orientalitas à Sole, Occidentalitas à Luna. Tertiò quod sit in domo, altitudine, triplicitate, ac terminis suæ naturæ. Quartò maior ad polum arcticum propinquitas, si fuerint supra terram; ad antarcticum verò si fuerint sub terra. Quintò ascensio suprà terram, & descensio sub terra secundùm latitudinem, secundùm declinationem, & secundùm situm in mundo Sextò familiaritas siderum consimilis naturæ, & cum capite Draconis. Septimò cursus, velocitas. Octauò descensio ab Apogæo tam Eccentrici quàm Epicycli: & si qui sunt alij modi, quibus sidera augeant suas vires, omnes sunt artendendi; quia eleuatio, vt verbo concludam, aliud non requirit quàm familiaritatem, & maiorem virium instructionem. Hanc Arabes suo vocabulo Mamareh planetarum vocant: de qua plura habet Albumasar in fine sui introductorij. 31. ELHABOR Arab. Canis maior Sirius, vide Alhabor. 32. ELHAMMEL Arab. vt habet Kircherus in Oedipo, dicitur signum & constellatio Arietis: sicut etiam 33. ELHAVT item apud Arabes, vt testatur idem Kircherus significatur signum & constellatio Piscium. Quemadmodum 34. ELKAVS est signum & constellatio Sagittarij: necnon. 35. ELGEDI Signum & constellatio Capricorni. Vide sub propiocujusque nomine.

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172 LEXICON as has been observed elsewhere. Nor in that efficiency can one thing overcome another, and depress its forces, unless it be in itself strong, and fortified with more powerful weapons. Since when the stars are configured among themselves they act upon one another and react: that which is stronger acts more, and reacts less; that which is weaker acts less, and reacts more: whence it is that those stars which prevail in strength, when joined with weaker ones either by body or by ray, act upon them, restrain their power, and diminish their activity. Therefore, as Ptolemy has above, if benefics are raised above malefics, it is good; for they depress and break their evil qualities: if malefics are raised above benefics, it is harmful; for they corrupt their goodness, so that goodness itself becomes harmful. 30. Hence Argolus rightly said that scrutiny must be made, and that which is found to prevail over another in number of strengths (since there is otherwise some familiarity between them, as has been said) that one will be said to be elevated above the other. Now the order and preeminence of strengths is first in the nobler angle and house as regards the world, or greater nearness to the angle toward which they are moving; and therefore this comparison to the angles of precedence is to be observed, since it is stronger than all prerogatives. Secondly, orientality from the Sun, occidentality from the Moon. Thirdly, that it be in its own house, exaltation, triplicity, and terms of its nature. Fourthly, greater nearness to the Arctic pole, if they are above the earth; but to the Antarctic, if they are under the earth. Fifthly, ascent above the earth and descent under the earth according to latitude, according to declination, and according to position in the world. Sixthly, familiarity of stars of similar nature, and with the head of the Dragon. Seventhly, course, speed. Eighthly, descent from the Apogee, both of the Eccentric and of the Epicycle: and if there are any other ways by which stars increase their powers, all must be considered; because elevation, to conclude in a word, requires nothing else than familiarity and a greater endowment of strength. The Arabs in their own language call this Mamareh of the planets: concerning which Albumasar says more at the end of his Introduction. 31. ELHABOR, Arab. the Greater Dog, Sirius; see Alhabor. 32. ELHAMMEL, Arab., as Kircher says in the Oedipus, is the sign and constellation of Aries; as also 33. ELHAVT likewise among the Arabs, as the same Kircher testifies, signifies the sign and constellation of Pisces. Likewise 34. ELKAVS is the sign and constellation of Sagittarius; and also. 35. ELGEDI, the sign and constellation of Capricorn. See under the proper name of each.

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MATHEMATICVM. 173 ELKERD Bennenax, Arab. dicitur Stella fixa secundæ ma- < 36.> gnitudinis vltima in extremo laudæ Vrsæ majoris, de natura martis, dicta etiam Alalicch. id est nocturnum, eo quia semper visibilis sit de noctu, cum neque otia r ut, neque occidat in no- stro hæmisphærio, sed radat tantummodo horizontem. Vide fusius in verbo Vrse. ELKLEILSCHEMALI Arab. vocatur, vt testatur Kircherus in < 37.> Oedipo corona Gnossia, sidus in cælo ad Borealem plagam con- stans stellis 8, licet in Baieri Vranometria 20. omninò enume- rentur, quarum lucida & insignior appellatur proptio nomine Alpheta siue Alpheica, id est aperitio, & Mumir quasi pupilla, est enim per antonomasiam dicta cæli pupilla. Vide alibi vbi sæpiùs de ea mensionem secimus. ELLIPSIS dicitur figura Geometrica oculis vnica tantum < 38.> linea, quæ tamen circularis non sit, comprehensa, nec omnes partes æqualiter tendunt ad centrum. Vide Euclidem. ELTANIN Arab. Latinè Draco, sidus de quo paulò ante dictu. < 39.> ELVARAD Arab. vel etiam Elkir, & Pharmaz teste Kir- < 40.> chero, Latinè Crater sidus. Vide sub hoc vocabulo. ELZEGIALE siue Elatbi, hoc est Ingeniculator vocatur He- < 41.> rales Engonasis, sidus ad Borealem plagam propè Ophiacum, de quo plura suo loco. EM EMBOLISMVS Grecè propriè significat intercalationem il- < 42.> lam quæ antiquitùs fieri solebat, vt annorum ratio cum Solis cursu conueniret: Nunc autem magis strictè accipitur, vel pro ipso bissextili die qui singulis quadriennijs superadditur Februari- < 43.> io ad æquandam anni quantitatem motu Solis in Zodiaco, vel p[ro]to excessu anni solaris ad annum lunarem dierum vnde- cini sup[er]ta duodecim lunationes, itaut singulis annis Nouilunia contingant vndecim diebus prius, quam præcedenti anno, quæ præcessio cum ad numerum dierum triginta peruenerit: constituet nouam lunationem, quæ dicitur Embolismica su- < 44.> petaddenda, quousque annus communis lunaris exequet an- num solarem. Quare. EMBOLISMICA Lunatio est illa, quæ conflatur ex triginta < 45.> diebus superadditis modo explicato, & quæ constituit annum Embolismicum tredecim Lunationum, constantem diebus; < 384.> aut 383. Quippe Lunationes ijs mensibus tribuuntur, & ab ijs denominationem sumunt, in quibus siniuntur: itaut omnis Lunatio in Decembri incipiens, & in Ianuario finem habens, etiamsi prima die mensis, ab eo nihilominus denominanda sit, ac dicenda rotius anni pritna Lunatio. Hinc fieri potest, vt quibusdam annis post primam illam Lunationem supersunt

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MATHEMATICVM. 173 ELKERD Bennenax, in Arabic, is called a fixed star of the second, or last, magnitude at the end of the constellation of Ursa Major, of martial nature, also called Alalicch, that is, nocturnal, because it is always visible by night, since it neither sets nor disappears in our hemisphere, but only grazes the horizon. See more fully under the word Ursa. ELKLEILSCHEMALI, as Kircher testifies in his Oedipus coronae Gnossiae, is the star in the sky standing in the northern quarter with 8 stars, although in Bayer’s Uranometria 20 are altogether enumerated; the brightest and most notable is called by the proper name Alpheta or Alpheica, that is, opening, and Mumir, as it were the pupil, for by antonomasia it is called the pupil of the sky. See elsewhere, where we have often made mention of it. ELLIPSIS is called a geometric figure enclosed by the eye with only a single line, which however is not circular, nor do all its parts extend equally toward the center. See Euclid. ELTANIN, in Arabic, Latin Draco, a star of which it was said a little before. ELVARAD, in Arabic, or also Elkir and Pharmaz according to Kircher, in Latin Crater, a star. See under this entry. ELZEGIALE, or Elatbi, that is, Ingeniculator, is called Heracles Engonasis, a star in the northern quarter near Ophiuchus, of which more in its proper place. EM EMBOLISMUS in Greek properly signifies that intercalation which in antiquity used to be made so that the reckoning of the years might agree with the course of the Sun. But now it is taken more strictly, either for the intercalary leap day itself which is added every four years in February to equalize the length of the year by the motion of the Sun in the Zodiac, or for the excess of the solar year over the lunar year of eleven days beyond twelve lunations, so that each year the new moons occur eleven days earlier than in the preceding year; and when this advance has reached the number of thirty days, it constitutes a new lunation, which is called embolismic, to be added, until the common lunar year equals the solar year. Therefore. EMBOLISMICA Lunatio is that which is formed from the thirty days added in the manner explained, and which makes an Embolismic year of thirteen lunations, consisting of days; 384 or 383. For lunations are assigned to those months, and take their name from them, in which they end: so that every lunation beginning in December and ending in January, even if on the first day of the month, must nevertheless be named from that month, and be called the first lunation of the year. Hence it can happen that in some years after that first lunation there remain

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adhuc duodecim integræ lunationes, anequam ad primam lunationem alterius anni sequentis veniamus; si nimirum super sint post primam lunationem anni, dies 354. vel 353. quor satis sunt ad expleendum numerum duodecim lunationum. Sed de hac re consule librum nouæ rationis restituendi Calendarij Romani. EMPYREVM Cælum dicitur à Theologis, & Sanctis Patribus (nam Philosophi ejus notitiam non habuerunt) supremum illud, ac vastissimum cælum suprà omnes cælos firmatum, sedes Beatorum, & Thronus Dei, immobile & firmum, in quo omnes Angeli, & Sancti perennant. Eius qualitares describere coecutire est, quandoquidem, neque vllas stellas, haber vnde reddatur visibilis, nec vllum motum, vnde saltem argui possit ejus existentia, immensitas & pulchritudo. Vnde August. in lib. Soliloqu. ad Deum, cap. 31. Hoc est, inquit, Calum tuum Domine, calum calans superarcanum, superintelligibile, superrationale, & superessentiale lumen, de quo dicitur calum cali Domino. Calum cali cui terra est omne calum quia supermirabiliter exaltatum est super omne calum, ad quod etiam terra est ipsum calum Empyreum: hoc enim est cæum cali Domino, quia nullis motum nisi Domino. Credibile tamen est ipsum immensitate luce, materia cæteris omnibus antecellere: Vnde Empyreum dictum est non quasi ignitum sit, sed ob nimiam sui puritarem, ac lucem. Materiam crediderim esse ejusdem speciei cum cæteris, sed longe puriorem, ac defæcatiorem, situm, nulli dubium esse longe altissimum, quam concipi possit: si enim à superficie terræ vsque ad cælum stellarum computat Ptolomæus distantiam 65237500. milliariorum, quid credendum est de cælo Empyreo data proportione distanxiæ quæ est inter alios orbes ad inuicem, quæ semper in immensum excrescit: Hinc etiam colligi potest infinita propemodum amplitudo, quæ ab aliquibus tanta esse dicitur, vt si cuilibet Angelorum, ac Sanctorum suus locus, & certa portio deputaretur, plus illud spacium contineret, quam occupat vniuersa terra: & iure quidem eum secundu[m] omnes Astronomos minima stella quæ est in firmamentis nouies superet magnitudine terrestrem globum: quidni igitur firmamentum? quid cælum Empyreum quod ad minus centies firmamentum superat, sed & Franciscus Pauonius par. 2. introductionis in sacram doctrinam defini. 2507. affirmat diuinæ magnificentia congruum esse vt firmamentum ad concauam cæli Empyrei superficiem, seu ad conuexam primi mobilis comparatum se habeat, sicut punctum, quemadmodum se habet terra ad ipsum firmamentum comparata: Quanta portio erit ejusdem cæli crassities tanta profecto, quanta par est ad

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as yet twelve complete lunations, before we come to the first lunation of the following year; for if, after the first lunation of the year, there remain 354 or 353 days, these are enough to complete the number of twelve lunations. But on this matter consult the book on the new method of restoring the Roman Calendar. The EMPYREAN Heaven is called by Theologians and Holy Fathers (for the Philosophers had no knowledge of it) that highest and vastest heaven, fixed above all the heavens, the dwelling of the Blessed, and the Throne of God, immovable and firm, in which all the Angels and Saints abide forever. To describe its qualities is to grope in the dark, since it has no stars from which it may become visible, nor any motion from which its existence, immensity, and beauty may at least be inferred. Hence Augustine, in the book Soliloquies, ch. 31, says: This, O Lord, is Your heaven, the heaven of the supersecret, superintelligible, superrational, and superessential light, of which it is said, the heaven of heaven to the Lord. The heaven of heaven, to which the earth is as all heaven, because it has been exalted supermarvellously above every heaven; and to it also the earth itself is the Empyrean heaven: for this is the heaven of heaven to the Lord, because it is moved by none but the Lord. Yet it is believable that, by its immensity of light, it surpasses all the rest in matter. Hence it has been called Empyrean, not as though it were fiery, but on account of its excessive purity and light. I would believe its matter to be of the same species as the others, but far purer and more refined. Its position, beyond doubt, is far higher than can be conceived; for if Ptolemy reckons the distance from the surface of the earth to the heaven of the stars at 65,237,500 miles, what is to be believed of the Empyrean heaven, given the proportion of the distances that exist among the other spheres, which always increase into vastness? From this too one may gather the almost infinite expanse, which some say is so great that if a place and fixed portion were assigned to each of the Angels and Saints, that space would contain more than the whole earth occupies. And indeed, according to all astronomers, the smallest star in the firmament exceeds the terrestrial globe nine times in magnitude: why then not the firmament? Why not the Empyrean heaven, which is at least a hundred times greater than the firmament? But Francis Pauonius also, part 2 of the Introduction to Sacred Doctrine, definition 2507, affirms that it is fitting for divine magnificence that the firmament should bear relation to the concave surface of the Empyrean heaven, or to the convex surface of the first mover, as a point does, just as the earth bears relation to the firmament itself. What portion, then, will the thickness of that same heaven be? Assuredly as great as is fitting for

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MATHEMATICVM. 175 explicandum magnitudinem ejus, qui sibi talem domum extruxit, vnde Baruch. 3. dicitur: O Israel quam magna est domus Domini. & ingens locus possessionis ejus! magnus est, & non habet finem, excelsus, ac immensus. Vnde majorem ejus molem concipiendam esse subjungit idem auctor quam esser occupatura omnis Angelorum multirudo, si quilibet Angelus in sua se sphæra locaret extra cujusque Angeli spæram. Quare autem tam immensum creare placuerit omnipotenti Deo, tripli-cem causam adducit Guillelmus Parisiensis. Primò propter innitam sui potentiam ostendendam, quæ maximè in tam im-menso opere relucet. Secundò propter suam gloriam, & rega-lem magnificentiam comprobandam. Tertiò ad humani desi-derij vehementiam satiandam, quæ amplas possessiones lata-que terrarum dominia requirit: Ergò tantum præparauit quo inueniret supra quam cupere posset. Sed ad hac inardescit ani-mus, jamque illic cupit assistere, vbi se sperat sine fine gaudere, in-quit Gregorius Pont. bom. 37. in Euangelia. Faxit Deus, vt quò mens nostra sua desideria dirigit, eò etiam per bona opera tendens, perueniat. EN ENGONASIS Hercules, Ingeniculus, &c. sidus ad Borealem plagam propè serpentarium constans stellis 29. computata < 46.> etiam vna informi circa brachium dextrum: sed Baierus in sua Vranometria enumerat in hoc astro stellas omnino 48 omnes ferè de natura Martis ex quibus præcipua quæ in capite Ras Al-gesi apud Arabes tertiæ magnitudinis altera in manu sinistra, Arab. Marsic. Is in horoscopo, inquit Firmicus, facit callidum, mendacem varijs dolis instructum, quique homines varijs in-sidijs appetat, atque effrenara semper animositare grassetur. Cum testimonio aurem Lunæ facit agiles, funambulos, oriba-tas, & qui talia pertractent. In occasu verò repertum hoc sidus exponit aliorum insidijs, etsi cum malo radio Martis adducit periculum combustionis. ENIF Alpherat Arab. dicuntur scapulæ Equi, stellæ videli- < 47.> cer duæ fixæ secundæ magnitudinis de natura Martis, & Mercurij, existentes, altera quidem in gr. 19. Piscium, altera in 35. cum fere totidem latitudinis Borealis. Vide earum signi-ficata in V. Pegasus. ENIOCHVS Mulus Celsellatus, Auriga sidus in cælo. Vide < 48.> Auriga. ENNEAGONA Figura apud Geometras est figura nouem an-gulis constans: quemadmodum Pentagona, quæ quinque: Exagona, quæ sex, & sic de singulis de quarum ratione. Vide Clauium in Elementa Euclidis.

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explaining the greatness of Him who built for Himself such a house, whence Baruch 3 is said: “O Israel, how great is the house of the Lord, and the vast place of His possession! It is great and has no end, lofty and immeasurable.” Hence the same author adds that its greater bulk must be conceived as exceeding what the entire multitude of Angels would occupy, if each Angel were placed in his own sphere outside the sphere of every other Angel. Why, then, it pleased the omnipotent God to create something so immense, Guillelmus Parisiensis gives three reasons. First, to show His infinite power, which shines forth most especially in so immense a work. Second, to prove His glory and royal magnificence. Third, to satisfy the vehemence of human desire, which seeks broad possessions and wide dominions of land: therefore He prepared so much that it might be found beyond what one could desire. But the mind is inflamed by this, and already longs to be present there, where it hopes to rejoice without end, says Gregory the Pope, hom. 37 in the Gospels. May God grant that, to whichever goal our mind directs its desires, by pressing onward through good works it may also arrive there. EN ENGONASIS, Hercules, Ingeniculus, etc., a constellation near the northern pole, beside Serpentarius, consisting of 29 stars, counted with one dim star near the right arm also; but Bayer, in his Uranometria, enumerates in this constellation altogether 48 stars, almost all of the nature of Mars, of which the principal one is in the head, Ras Algesi among the Arabs, of third magnitude, another in the left hand, Arab. Marsic. In the horoscope, says Firmicus, it makes one crafty, deceitful, equipped with various tricks, one who attacks men with various snares, and always acts with unbridled boldness. With the testimony of the Moon it makes agile people, tightrope-walkers, rope-dancers, and those who practice such things. Found in the setting, this constellation exposes a person to the snares of others; yet with the evil ray of Mars it brings danger of combustion. ENIF Alpherat, Arab., are called the shoulders of the Horse, namely two fixed stars of the second magnitude, of the nature of Mars and Mercury, one of them being in 19 degrees of Pisces, the other in 35, with nearly the same latitude north. See their signification in V. Pegasus. ENIOCHVS, the harnessed mule, the constellation Auriga in the sky. See Auriga. ENNEAGONA is, among geometers, a figure consisting of nine angles: just as Pentagona, which has five; Exagona, which has six; and so on for each, concerning whose nature see Clavius in the Elements of Euclid.

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176 LEXICON 50. ENNEATICI Dies, vel Anni sunt Nouenarij quicque recurrentes dies, vel anni, à puncto Natiuitatis, vel initio morbi, in quibus profectò semper aliquam naturæ alterationem experimur, atque accessionem morbi, sicut & in septenarijs, ac manifestiùs quando ambo conveniunt, & septenarij, & nouenarij. Cuius rei, vti effectus patens est, & manifestus, ita & rario, & origo obscura nimis, & adhuc non benè nota. Qua de re fusè egimus in Verbo Critici dies. 51. Eosphorvs Grecè Latinè Luci er dicitur apud Astronomos Venus maturina, atque Orientalis à Sole, à Græco verbo, Eos, quod Orientalis sonat: sicut econtra Hesperus appellatur Vespertina, & quando est Occidentalis à Sole. E P 52. Epacta (quasi Epiaucta hoc est superexctescentia) nil aliud est, quam excessus anni communis solaris supra annum lunarem duodecim lunationum in diebus vndecim singulis annis: Cum enim annus communis solaris constet diebus 365. Lunaris verò diebus 354. consequenter lunaris terminatur, & antenettit solatem diebus vndecim, qui fit vt Nouilunia, tot etiam diebus præcedant finem anni solaris. Et quia id singulis quibusque annis accidit, inde etiam est, vt singulis decem, & nouem annis solaribus Luna compleat vicesies duodecim integras lunationes, seù superet vnum annum communem solarem, quo circuitu expleto conueniat cum Sole: atque ita semper procedendo in infinitum, singulis annis primis à dicta conuentione reperiatur Luna præcedere Solem diebus vndecim; secundo anno diebus 22. sicque Epacta istius anni sit 21. tertio anno præcedat diebus 31. sed cum diebus 30. fiat vna integra lunario, ideò ea prætermissa, immò potius admissa, atque in numerum integræ lunationis computata. Epacta, seu præcessio lunationum sit dictum 3. qui ad triginta supersunt: quarto verò anno sit dierum 14. & sic de singulis. Progrediuntur igitur Epactæ omnes per continuum augmentum dierum vndecim, abjectis tamen 30. semper cum abijci possunt. Numerumque istum vocamus Epactum, quia epactat Lunæ defectum, atque inseruit ad ejus æratem ad dies singulos dignoscendam. Quippe si addatur Epactæ currenti eo anno numerus dierum mensis, qui transierunt, nec non Calendarum quæ præcesserunt, incipiendo à mense Martio, vsque ad præsentem mensem in quo hæc scrutari volumus, inclusuè; statim elucent in producto numero dies ætatis Lunæ à præcedenti coitione cum Sole, demptis prius triginta, si fortè cum numerum excesserint, quia isti sufficiunt ad vnam integram lunationem constituendam. Procedit

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176 LEXICON 50. ENNEATICI. Days, or years, are the recurring ninth days, or years, from the point of birth, or from the beginning of illness, in which we indeed always experience some alteration of nature, and an increase of the disease, just as in the septenaries, and more manifestly when both coincide, both the septenaries and the ennearies. Of this matter, as the effect is evident and manifest, so also the cause and origin are exceedingly obscure, and as yet not well known. We have treated of this at length under the word Critical days. 51. Eosphorus in Greek, in Latin is called Lucifer by astronomers, the morning and eastern Venus, from the Greek word Eos, which signifies eastern; just as, conversely, Hesperus is called the evening star, and when it is western from the Sun. E P 52. Epacta (as if Epiaucta, that is, superaddition) is nothing other than the excess of the common solar year over the lunar year of twelve lunations, by eleven days each year. For since the common solar year consists of 365 days, while the lunar year consists of 354 days, consequently the lunar year ends earlier than the solar by eleven days, with the result that the new moons likewise precede the end of the solar year by as many days. And because this happens every year, it follows also that in every nineteen solar years the Moon completes twenty times twelve complete lunations, or surpasses one common solar year, after which circuit it agrees again with the Sun; and thus always proceeding infinitely, in the first year from the said conjunction the Moon is found to precede the Sun by eleven days; in the second year by 22 days, and so the Epact of that year is 21; in the third year it precedes by 31 days, but since 30 days make one complete lunation, that being omitted, or rather admitted and reckoned among the number of an entire lunation, the Epact, or preceding of the lunations, is said to be 3, because 30 remains over; in the fourth year it is 14 days, and so of each. Thus all Epacts advance by a continuous increase of eleven days, however 30 being always cast off whenever they can be cast off. And we call this number the Epact, because it epacts the Moon’s deficiency, and is inserted so that her age may be known day by day. For if to the current Epact there be added the number of the days of the month that have passed, as well as the Calends that have preceded, beginning from the month of March up to the present month in which we wish to make this inquiry, inclusive, there immediately appears in the resulting number the days of the Moon’s age from her preceding conjunction with the Sun, first subtracting thirty if perhaps they have exceeded that number, because these suffice to constitute one complete lunation. It proceeds

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MATHEMATICVM. 177 < 54.> Procedit igitur semper æquali modo ordo iste Epactorem per additionem vndecim dierum singulis annis, excepto tamen vltimo anno, in quo recurrit Epacta correspondens Auroc numero 19. quæ est dierum 29 quantum videlicet sufficit ad integram lunationem perficiendam: in quo casu non vndecim, sed duodecim dies imaginarie addendi sunt, vt abjectis 30. ex composito numero 41. habeatur rursus Epacta 11. prout erat in principio. Qua de re vide quæ optimè scripsit Clauius in Kalendario Gregeriano. EPHEMERIS Græcè proprie significat diarium, quod acta cujusque diei complectitur, ac interstincte exponit, sumpto vocabulo ex quodam animaleculo Ephemero dicto, de quo scribunt naturales, ipsum non nisi ad vnicam tantum diem vitam protrahere. Hinc apud Astronomos deriuvatum fuit, & antonomastice applicatum ad exprimendum motum diurnum omnium planetarum; quem in dies singulos perficiunt in Zodiaco, vnde libri, in quibus extant calculati hujusmodi motus planetarum, cum aspectibus, & alijs eorum passionibus ad dies singulos, Ephemerides appellantur. < 55.> EPICATAPHORA seù etiam Picasaphora Græcè dicitur octaua domus ab horoscopo succedens angulo Occidentis: Latinè sonat Portam supernam ad differentiam secundæ domus illi oppositæ, quæ quia succedit Horoscopo, ideo dicitur porta inferna. Est significatrix mortis, hæreditatum, quæ ex mortuis proueniunt, laboris, tristitiæ, & thesaurorum occultorum. Habet consignificatorem Saturnum. Ex membris humanis præest pudendis, & inducit stranguriam, calculum, hæmioroidas, & similis. Est locus infelix, eoquia nullam habet cum ascendente familiaritatem, & continujs vaporibus è terra profilientibus offenditur. Id circò vocatur à Firmico locus piger, & otiosus; ab alijs (quod idem sonat) Argos Tophes, &c. EPICYELVS est paruus Orbis, qui deferenti infixus motu illius circum agitur, & impactum sibi planetæ corpus peculiati suo motu circâ proptium centrum circumducit. Pro cujus rea intelligentia sciendum est, antiquos Astronomos, ad saduandos apparentias, ac diuersitates motuum, qui in singulis planetis peculiariter deprehenduntur, excogitasse varios circulos, Eccentricos, Concentricos, & Epicyclos: itaut, excepto Sole, singulis planetis tres circulos assignarint, quorum primus esset deferens, Eccentricus simpliciter (qualis autem is sit, suo loco explicuimus.) Secundus esset circulus, dictus æquans, quem ideò posuerunt, quia deferentes planetarum non mouentur æqualiter in eorum centris, sed valdè difformiter, & irregulariter, vt mox dicemus: Tertius orbis foret infixus in M

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MATHEMATICVM. 177 < 54.> Thus this order of Epacts always proceeds in the same way by the addition of eleven days each year, except however in the last year, in which the corresponding Epact recurs to the Auron number 19, which is 29 days, namely as much as suffices for the completion of a full lunation: in which case not eleven, but twelve imaginary days are to be added, so that, after removing 30 from the composed number 41, Epact 11 may again be obtained, as it was at the beginning. On this matter see what Clavius wrote very well in the Gregorian Calendar. EPHEMERIS in Greek properly signifies a daily record, which comprises the acts of each day and presents them separately, the word being taken from a certain little animal called ephemeron, concerning which natural philosophers write that it prolongs its life to only a single day. Hence, among astronomers, it was derived and by antonomasia applied to express the daily motion of all the planets, which they perform each day in the Zodiac; whence the books in which there are calculated motions of this kind of the planets, together with aspects and other conditions of them for each day, are called Ephemerides. < 55.> EPICATAPHORA, or also Picasaphora, is what the Greeks call the eighth house succeeding from the horoscope toward the western angle; in Latin it means the upper gate, as distinguished from the second house opposite it, which, because it succeeds the Horoscope, is therefore called the lower gate. It signifies death, inheritances that come from the dead, labor, sadness, and hidden treasures. Saturn is its co-significator. Among the members of the human body it governs the private parts, and brings on strangury, stone, hemorrhoids, and the like. It is an unfortunate place, because it has no familiarity with the ascendant and is disturbed by continuous vapors rising from the earth. For this reason Firmicus calls it a sluggish and idle place; by others (which means the same thing) Argos Tophes, etc. EPICYCLUS is a small orbit, fixed in the deferent, which is carried around by its motion, and by its own peculiar motion carries around the body of the planet fixed in it about its proper center. For a fuller understanding of this, it must be known that the ancient astronomers, in order to save the appearances and the diversities of motions that are found peculiarly in the individual planets, devised various circles, eccentrics, concentrics, and epicycles; so that, except for the Sun, they assigned three circles to each planet, of which the first would be the deferent, simply eccentric (what sort this is, we explained in its place). The second would be the circle called the equant, which they therefore posited because the deferents of the planets do not move equally in their centers, but very dissimilarly and irregularly, as we shall soon say. The third orbit would be fixed in the M

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168 LEXICON habet vt subjectum passibile, & in eo planeta pugnans cum humore purgando validiùs operatur. Excipe tamen semper Leonis signum nimis exæstuans, & quod nobilissimo membro præest, hoc est cordi totius vitæ operationumque vitalium fonti, atque origini. <21.> Quoad Phlebotomiam pariter discurrendum, attendenda est enim cuiusque xtas, constitutio, & morbi qualitas. Nam pro juvenibus optimum est sanguinem mitiere cum Luna crescit lumine, pro senibus verò cum deficit: si æger igneus sit, adustus, & in eo haud bilis redundet mittatur sanguis cum Luna est in signis aqueis Cancro, & Piscibus. Si phlegmaricus cum in Ariete, & agittario: si melancholicus cum Luna est in Aquatio, & in prima medietate Libræ. Cæterùm Geminorum signum cum Leone, & prima medietate Scorpij, cum secunda Libræ; pro omnibus vniuersim inauspicata sunt, eò quia hæc via combusta est, in qua Luna multùm infortunatur. Leo cordi vt dictum est dominatur, vnde sanguis trahit originem: Gemini autem brachijs in quibus vt plurimùm scinditur vena. Atqui regula generalis est membrum haud ferro tangendum eo tempore quo Luna signum illud permeat, quod tali membro dominatur: cum enim eius sit humectare totum corpus, illud potissimùm membrum humoribus replere habet, quod signo illi subest, in quo ipsa moratur: ex quo sit vt vulnus difficulter consolidetur, & humores alioqui commoti ferri contactu ardeant, & tabescant. Signa item terrea parum sunt mittendo sanguini idonea: Atque hæc de electionibus vniuersalibus dicta sint: Cætera quæ tum ad Agricolationem, tum ad Navigatoriam spectant videri possunt apud Auctores Ephemeridum in Isagonicis, præcipuè verò apud Argolum lib. 2. cap. 7. & seqq. Nobis enim in re præsertim obvia non licet esse nimium longis. <22.> Quoad Electiones verò particulares breuiter hæc regula seruanda est eas fore semper nato proficuas, & opportunas cum congruunt, & respondent radici natiuitatis: quæ verò absque vllo delectu sunt aut inutiles sunt, aut fortasse etiam perniciosæ. Vt exempli gratiâ si quis eligat sumere potionem tempore cæteroqui ex regulis supra traditis opportuno: cum Luna vide- licet est in Cancro, aut in Piscibus; sed tamen in figura natiuitatis habeat signa hæc à maleficiis infestata, tunc quidem non modo non producit medicina, sed fortasse etiam nocebit, similiter non tam radix ipsa natiuitatis consideranda est, & cum electionis tempore conferenda, quam tempus per directiones signatum, & videndum si ad id tempus respondeat alioqui bona directio: Quoad negotia peragenda disquirendum, cui

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168 LEXICON has a passible subject, and in it the planet contending with the humor to be purged works more strongly. But always except the sign of Leo, too much heated, and because it presides over the noblest member, that is, the heart, the source of the whole life and of vital operations. <21.> Concerning phlebotomy likewise, one must proceed by considerations, for the age of each person, his constitution, and the nature of the disease must be attended to. For young people it is best to let blood when the Moon is increasing in light; for old people, when it is decreasing. If the patient be fiery, burned, and in him bile does not abound, let blood be taken when the Moon is in watery signs, Cancer and Pisces. If phlegmatic, when it is in Aries and Sagittarius; if melancholic, when the Moon is in Aquarius and in the first half of Libra. Moreover, the sign of Gemini with Leo, and the first half of Scorpio, with the second half of Libra, are unfavorable for all in general, because this path is burnt, in which the Moon is greatly afflicted. Leo, as has been said, rules the heart, whence blood draws its origin; Gemini, however, the arms, in which the vein is most often cut. But the general rule is that a limb should not be touched with iron at that time when the Moon passes through that sign which governs that limb: for since it is her office to moisten the whole body, she must especially fill with humors that member which is subject to the sign in which she is abiding; from which it follows that a wound is healed with difficulty, and the humors, otherwise stirred by contact with iron, are inflamed and wasted away. Terrestrial signs are also little suited for letting blood. And let this be said concerning universal elections. The rest, both what pertains to agriculture and to navigation, may be seen in the authors of ephemerides in the Isagogenics, but especially in Argolus, book 2, chapter 7 and the following chapters. For we, especially in a matter so common, may not be too long. <22.> But concerning particular elections, briefly this rule is to be observed: they will always be beneficial and opportune for the native when they agree and correspond to the root of the nativity; but those which are without any discernment are either useless or perhaps even harmful. For example, if someone should choose to take medicine at a time otherwise opportune according to the rules set forth above, namely when the Moon is in Cancer or Pisces, but in the figure of nativity these signs are afflicted by malefics, then indeed the medicine not only does not help, but perhaps will also harm. Likewise, the root of the nativity itself must not so much be considered and compared with the time of election as the time marked out by the directions; and it must be seen whether some other good direction corresponds to that time. Concerning affairs to be carried out, one must inquire to whom

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MATHEMATICVM. 169 rei quisque in radice natuiitatis ab siderum constitutione addi- ctus est, eique se dedat constituendum planetæ, vel signo illi quod talem significationem facit in ascendente. < 23.> Denique in quacumque Electione, ea semper ineatur cum Luna per ea signa mear, in quibus Iupiter, Venus, aut pars for- tunæ reperiebantur tempore natuiitatis, aut benigno radio res- piciatur à dictis planetis, sintque loca rerum significationi idonea. Experientia enim compertum est, quidquid boni & for- tunæ vnicuique obuenit, id potissimùm obuenite, eò quia Luna per loca beneficarum transit: sicut è contrà quidquid mali, ex ingressu eiusdem in loca in radice à maleficis infesta. < 24.> ELEMENTVM absolutè dicitur id, quod quavis in re prima radix est, & iniium, ex quo alia componuntur. Vnde in vni- uersi istius ambitu, quæ sunt prima rerum semina, ex quibus reliqua corpora coagmentantur, Elementa dicuntur; Ignis videlicet, Aër, Aqua, Terra, atque ex ijs elementaris regio quæ infrà cælum omnia elementa, & ex ijs mixta complecti- tur, dicta. Quare autem quatuor tantùm, & nec plura, nec pauciora elementa rerum assignata sunt, explicat Philosophus 2. de Generas & corrup[ti]o. cap. 4. Quia videlicet quatuor tan- tùm sunt primæ qualitates tangibilium, nempe caliditas, sic- citas, frigiditas, & humiditas, quæ adinuicem copulata, om- nem rerum tam simplicium, quàm mixtarum complexionem, ac temperiem comprehendunt. Quot enim sunt possibiles com- binationes harum primarum qualitatum in vno, eodemque subiecto, tot elementa assignantur: quippe oppositarum, vt caloris, & frigoris, humiditatis, & siccitatis impossibilis est combinatio. Tot igitur sunt Elementa. Quapropter & Prole- mæus in prima parte Quadrip. omnes astrorum influxus ad quatuor Elementorum qualitates reducit; quasi elementa ipsa ex cælorum, & siderum moribus suæ distinctionis originem trahant. Porrò, vt modò dixi, elementa inter se certo ordine constituta efficiunt regionem elementarem, prout ab Ætherea discernitur, quæ tamen vna cum ipsis hoc Vniuersum consti- tuunt. Et in Vniuersi quidem ipsius centro existit Terra omni- nò immobilis, & cæteris elementis g[ene]ra[ti]or: inde Aqua: mox Aër: denique Ignis, qui immediatè subest concauo Lunæ An autem elementa (excepta Terra) moueantur circulanter ab Oriente in Occidentem moru vniuersitatis, & primi mobilis: vnde Oceani morum non Lunæ, sed primi mobilis raptui tribuendum esse sunt qui assimant apud Clauium in sphæram Io. de Sacrobosco: & nos in loco diximus. Quod autem non exquisitè rapiantur, id prouenit ex eorum resistentia, & elon- gatione à primo mobili; quò enim g[ene]ra[ti]ora sunt, ac siu remo-

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MATHEMATICVM. 169 Everyone, in the root of nativity, is bound by the constitution of the stars, and should therefore commit himself to the governing planet, or to that sign which gives such signification in the ascendant. < 23.> Finally, in any election, it should always be begun while the Moon passes through those signs in which Jupiter, Venus, or the Part of Fortune were found at the time of nativity, or while it is favorably aspected by the said planets, and the places should be suitable to the signification of the matter. For experience has clearly shown that whatever good and fortune befall anyone, they befall chiefly because the Moon passes through the places of the benefics; just as, on the contrary, whatever evil happens comes from its entering those places in the nativity that are afflicted by the malefics. < 24.> An element is said absolutely of that which in any thing is the first root and beginning, from which other things are composed. Hence, within the compass of this universe, those things which are the first seeds of things, from which the remaining bodies are joined together, are called elements: namely Fire, Air, Water, Earth, and from these the elemental region, which beneath the heavens comprises all elements and the mixed things formed from them, is so called. But why exactly four, and neither more nor fewer, elements have been assigned to things, the Philosopher explains in 2 de Generatione et corruptione , chap. 4. Namely, because there are only four primary qualities of tangible things, that is, heat, dryness, coldness, and moisture, which, combined with one another, comprehend every complexion and tempering of things, both simple and mixed. For as many possible combinations of these primary qualities as there are in one and the same subject, so many elements are assigned; for the combination of opposites, as of heat and cold, moisture and dryness, is impossible. Therefore there are four elements. Wherefore Ptolemy also, in the first part of the Quadripartitum , reduces all the influences of the stars to the qualities of the four elements, as if the elements themselves derive the origin of their distinction from the dispositions of the heavens and the stars. Moreover, as I have just said, the elements, established among themselves in a certain order, constitute the elemental region, as it is distinguished from the ethereal, which nevertheless together with them forms this Universe. And indeed at the center of the Universe itself there exists Earth, entirely immobile and generative of the other elements; next Water; then Air; and finally Fire, which lies immediately beneath the concavity of the Moon. But whether the elements (except Earth) are moved circularly from East to West by the motion of the universe and of the primum mobile: there are those who affirm that the motion of the ocean should be attributed not to the Moon, but to the dragging of the primum mobile, as Clavius says in the sphere of Jo. de Sacrobosco; and we said so in the proper place. But that they are not dragged exactly, this arises from their resistance and their distance from the primum mobile; for the more generative they are, the more...

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170 LEXICON tiora, eò magis resistunt, ac morantur: vt patet in ipsis sphæris cælestibus. Vnde etiam intelligi potest, & has omnes flui- das esse, vt elementa sunt, & eò fluidiores, ac puriores, quo à centro magis elongantur. Et vnico tantùm motu cieri ab Oriente in Occidentem raptas à primo orbe; licet quæ ab eo sunt magis remotæ, magis impulsui dato sua ponderositate resistant, ac retrò in partibus Orientalioribus maneant, prout diximus in V. Calum. Cæterùm non negauerim multos ex recensoribus inter elementa Ignem minimè connumerare, quia & aliquos omnia elementa negare: inter quos est Auersa som. 2 Philosoph. quast. 41. sect. 2. 25. ELEMENTA Geometrica, Antonomasticè audiunt Libri quindecim Geometricorum principiorum Euclidis Geometrarum Principis, & Magistri: eò quia sine ipsis nullum opus Mathematicum aggredi, nullum effatum percipi potest; sicut enim is qui legere vult (inquit Clauius in Prologom.) Elementa literarum discit prius, & illis affiduè repetitis vtilur in vocibus omnibus exprimendis, sic qui alias disciplinas Mathematicas desiderat sibi reddere familiares elementa hæc Geometrica plenè, ac perfectè calleat prius necesse est. Quandoquidem horum elementorum ope, omnis in cælo siderum ratio auspicatur, eorum motus, situs, distantia, altitudo, quantitas internoscitur. Ab ijs omnis in cælo, omnis in terra dimensio habetur: ac denique ingens hoc Dei, ac Naturæ opus, Vniuersi, inquam, istius machina non sine Geometricorum horum elementorum auxilio intelligi, & contemplari potest. Iure igitur hæc prima Geometriæ principia elementa Geometrica dicta sunt. 26. ELEVATIO apud Astronomos significat præcellentiam, ac prædominium vnius planetæ super alium, quando videlicet duo, vel plures concurrunt adinuicem, & conueniunt ad vnam, eandemque rem significandam 1 tunc qui alijs, viribus atque activitate præualet, dicitur super illos eleuatus. Pontanus in 27. Commentar. super Centiloqu. hanc dicendi formam non probat, quia eleuare, inquit, apud Grammaticos indicat depressionem potiùs, quàm præeminentiam: Verùm nescio, ausatis benè discurrat: cùm Eleuo propriè significet sursum leuo, siue in alium collo: quod idipsum prorsus est, quod explicare volumus in planetis se super alios eleuantibus, vt mox dice- mus. Quod autem quandoque per translationem accipiatur pro rei diminutione, quæ verbis fiat eam vituperando, id non officit propriæ notioni. Sed quidquid sit de modo loquendi, certum est in re, Eleuari apud Astronomos nil aliud significare quàm extollentiam vnius planetæ super alium: quod

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170 LEXICON the more they resist and delay: as is evident in the celestial spheres themselves. Whence it can also be understood that all these are fluid, as the elements are, and the more fluid and purer, the farther they are removed from the center. And that they are moved by a single motion, carried from East to West by the first orb; although those which are farther from it resist the given impulse more by their heaviness, and remain back in the more Eastern parts, as we said in V. Caelum. Moreover, I would not deny that many of the reviewers do not count Fire among the elements at all, because some even deny all the elements: among whom is Auersa som. 2 Philosoph. quast. 41. sect. 2. 25. GEOMETRICAL ELEMENTS are, by antonomasia, the fifteen books of the Elements of Geometry of Euclid, Prince and Master of Geometers; because without them no mathematical work can be undertaken, no statement perceived; for just as the one who wants to read (says Clavius in the Prologom.) first learns the elements of letters, and, by constantly repeating them, uses them in expressing all words, so he who desires to make other mathematical disciplines familiar to himself must first thoroughly and perfectly master these geometrical elements. Since by the aid of these elements the whole arrangement of the stars in the sky is begun, their motion, position, distance, height, and magnitude are distinguished. From them is obtained every measurement in heaven, every measurement on earth: and finally this immense work of God and Nature, the Universe, I say, this machine of ours, cannot be understood or contemplated without the aid of these geometrical elements. Therefore these first principles of geometry were rightly called geometrical elements. 26. ELEVATION among astronomers signifies the preeminence and dominion of one planet over another, when, namely, two or more come together with one another, and agree to signify one and the same thing; then the one that prevails over the others in power and activity is said to be elevated above them. Pontanus in 27. Commentar. super Centiloqu. does not approve this way of speaking, because to elevate, he says, among grammarians indicates rather a lowering than a preeminence: but I do not know whether he reasons well; since to elevate properly means to lift up, or to raise to another place: which is precisely what we wish to express in planets elevating themselves above others, as we shall soon say. But if at times it is taken by translation for a diminution of a thing, made by words in disparaging it, that does not interfere with the proper meaning. But whatever may be said about the manner of speaking, it is certain in fact that being elevated among astronomers signifies nothing other than the exaltation of one planet over another: which

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MATHEMATICVM. 171 quomodo fiat atque in quo consistat huiusmodi eleuatio, non æquè ab omnibus traditur. Aliqui enim volunt tunc planetam super alium eleuati, cum est in situ mundi eminentiore, vbi sit magis vicinus Vertici aut Meridiano: quod quidem nulli dubium est, cæteris paribus maximas vires sideribus addere; quippequæ inde directiores radios ad mundum transmitterunt. Verùm id non videtur tantam prærogatiuam planetis addere, vt exinde præcisè dici possint super alios extolli, maximè quando alias isti forriores sunt, & prærogatiuam hanc situs alijs numeris superant, aut compensant. Alij dicunt illum vincere, & eleuari super alium, qui magis accediv ad Boream: sed hi etiam discrepant, nam aliqui intelligunt planetam habentem majorem latitudinem Borealem super alium eleuari, qui in majori, vel in australi, vel sanè in Ecliptica reperitur, & alij hoc intelligunt de declinatione, quod nempe maiorem habeat Borealem in regionibus borealibus, australem in australibus. Sunt qui volunt id attendendum esse respectu suorum Orbium; ita vt qui ascendunt magis, vel magis appropiant ad Apogæum sui siue Ecoentrici, siue Epicycli sint super alios eleuari; qui descendunt ab Apogæo, vel ab eo magis distiterint. Cardanus est in sententia, vt ea sidera super alia eleuentur, quæ cùm sint tardioris motus, expectant ea quæ sunt velocioris vt ipsis jungantur. Argolus hos omnes modos admittit, docetque in super faciendum esse scrutinium, & ille demum planeta dici debet super alium eleuatus, qui repertus fuerit maioribus numeris, ac potioribus calculis præditus. Verum, vt benè discurrit Titus in Cælesti Philosophia, lib. 2, 28. cap. 11. Hæc siderum super alia eleuatio, dicit concurrentiam duorum ad agendum, & quod in hoc concursu vincat illud, quod maiores vires habet, ac feratur super debilius, id est si diuersæ naturæ sint, alteret naturam illius ac multùm deprimat: hoc quippe intendit Ptolemæus pluribus in locis præsertim lib. 2. cap. 8. cum loquitur de prædominio stellarum super aliquem locum quoad effectus quos ergà illos producunt. Cum enim, inquit, sunt illa benefica, & conciliata locis obnoxijs, neque superantur ab alijs diversa secta muliò magis absolunt natura sua bonitatem, sicut & aliena, aut superata ab alijs minus profunt. Quod si noxia hunc principatum caperint, conciliata cum obnoxijs locis, aut superata à stellis adversaria secta minus nocent. Hæc Ptolemæus. Duo igitur requiruntur ad eleuationem: & quod inter si- 29. dera intercedat aliqua conuenientia, & familiaritas; & quod vnum sit præpotens, ac validius altero. Nam sidera nullam efficientiam habent ad inuicem, nisi aliquo modo configuren-

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MATHEMATICUM. 171 how this elevation is made and in what it consists is not agreed upon by all alike. For some maintain that a planet is elevated above another when it is in a more eminent position in the world, where it is nearer the Zenith or the Meridian: and of this there is no doubt, ceteris paribus, that it adds the greatest strength to the stars; for from there they transmit more direct rays to the world. But this does not seem to add so great a prerogative to the planets, that they can precisely be said thereby to be raised above others, especially when, apart from that, these are stronger, and exceed or compensate for this prerogative of position by other numbers. Others say that that planet conquers, and is elevated above another, which approaches more toward the North: but these also differ, for some understand that a planet having greater northern latitude is elevated above another, which is found in a greater one, or in a southern one, or indeed on the Ecliptic, and others understand this of declination, namely that it should have a greater northern one in northern regions, a southern one in southern regions. There are those who wish that this be considered with respect to their orbs; so that those which ascend more, or approach more toward the Apogee of their own, whether of the eccentric or of the epicycle, are elevated above others; those which descend from the Apogee, or are farther removed from it. Cardanus is of the opinion that those stars are elevated above others which, since they are of slower motion, wait for those which are faster, in order to join with them. Argolus admits all these methods, and teaches that in addition scrutiny must be made, and that the planet must finally be said to be elevated above another which is found to be endowed with greater numbers and with more powerful calculations. But, as Titus reasons well in the Celestial Philosophy, book 2, ch. 11, sect. 28, this elevation of stars above others, he says, indicates the concurrence of two bodies in acting, and that in this concurrence that prevails which has the greater force and is borne above the weaker; that is, if they are of different natures, it alters the nature of the latter and greatly depresses it: for this is what Ptolemy intends in several places, especially book 2, ch. 8, when he speaks of the predominance of the stars over some place with regard to the effects which they produce toward it. For when, he says, those are beneficent, and in agreement with places subject to them, and are not overcome by others of a different sect, they much more fully realize their own nature of goodness, as also foreign ones, or those overcome by others, benefit less. But if harmful stars should obtain this principate, being in agreement with places subject to them, or overcome by stars of an adverse sect, they are less harmful. Thus Ptolemy. Therefore two things are required for elevation: namely that between the stars there should be some agreement and familiarity; and that one should be more powerful and stronger than the other. For stars have no efficacy toward one another unless in some way they are configured-

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172 LEXICON tur, vt alibi obseruatum est. Neque in ista efficientia vnum aliud vincere potest, ac vires illius deprimere, nisi fuerit in se fortis, atque armis validioribus præmunitus. Quandoquidem quando sidera sunt inter se configurata agunt ad inuicem, ac repatiuntur: quod est validius, magis agit, & minus repatitur; quod est infirmius minus agit, & magis repatitur: Vnde est quod quæ sidera viribus præualent, dum alijs viribus imminutis aut corpore, aut radio copulantur, in illa agant, virtutem eorum alterent, atque actiuitatem diminuant. Quare, vt suprà habet Ptolemaeus, si benefici super maleficos elucentur, bonum est; nam qualitates eorum maleficas deprimunt, & infringunt: si malefici super beneficos extollantur, noxium est: quippe corrumpunt eorum bonitatem, vt ipsa bonitas noxia fiat. 30. Hinc benè dixit Argolus faciendum esse scrutinium, & quod inuenietur vincere aliud in numero fortitudinum (cùm aliàs intercedat inter illa aliqua familiaritas, vt dictum est) illud dicetur super aliud eleuatum. Ordo autem, & præcellentia fortitudinum est primò situs in nobiliori cardine, & domo quoad mundum, siue maior propinquitas ad cardinem, ad quem feruntur; ita vt hæc comparatio ad cardines præcæresis sit ar tendenda, cum sit omnibus prærogatiuis validior. Secondò Orientalitas à Sole, Occidentalitas à Luna. Tertiò quod sit in domo, altitudine, triplicitate, ac terminis suæ naturæ. Quartò maior ad polum arcticum propinquitas, si fuerint supra terram; ad antarcticum verò si fuerint sub terra. Quintò ascensio supra terram, & descensio sub retra secundùm latitudinem, secundùm declinationem, & secundùm situm in mundo. Sextò familiaritas siderum consimilis naturæ, & cum capite Draconis. Septimò cursus, velocitas. Octauò descensio ab Apogæo tam Eccentrici quàm Epicycli: & si qui sunt alij modi, quibus sidera augeant suas vires, omnes sunt attendendi; quia eleuatio, vt verbo concludam, aliud non requirit quàm familiaritatem, & maiorem virium instructionem. Hanc Arabes suo vocabulo Mamareth planetarum vocant: de qua plura habet Albumasar in fine sui introductorij. 31. ELHABOR Arab. Canis maior Sirius, vide Alhabor. 32. ELHAMMEL Arab. vt habet Kircherus in Oedipo, dicitur signum & constellatio Arietis: sicut etiam 33. ELHAVT item apud Arabes, vt testatur idem Kircherus significatur signum & constellatio Piscium. Quemadmodum 34. ELKAYS est signum & constellatio Sagittarij: necnon. 35. ELGEDT Signum & constellatio Capricorni. Vide sub proptiocujusque nomine.

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172 LEXICON it is turned, as has been observed elsewhere. Nor can one thing overcome in that efficacy, and depress its force, unless it be strong in itself and fortified with stronger arms. For, when the stars are configured with one another, they act upon one another and react in return: that which is stronger acts more and reacts less; that which is weaker acts less and reacts more. Whence it follows that those stars which prevail in strength, when joined with others diminished in power, either by body or by ray, act upon them, alter their virtue, and diminish their activity. Therefore, as Ptolemy states above, if benefics are made to shine above malefics, it is good; for they depress and weaken their evil qualities: if malefics are exalted above benefics, it is harmful; for they corrupt their goodness, so that goodness itself becomes noxious. 30. Hence Argolus rightly said that an examination must be made, and that whatever is found to prevail over another in the number of strengths (since there may otherwise be some affinity between them, as has been said) will be said to be elevated above the other. The order and preeminence of strengths is, first, situation in the nobler angle and house with regard to the world, or greater nearness to the angle toward which they are carried; so that this comparison to the angles of precession is to be carefully observed, since it is stronger than all prerogatives. Second, Orientalality from the Sun, Occidentality from the Moon. Third, that it be in its own house, exaltation, triplicity, and terms of its nature. Fourth, greater nearness to the Arctic pole, if they be above the earth; but to the Antarctic if they be below the earth. Fifth, rising above the earth and setting below the earth according to latitude, according to declination, and according to position in the world. Sixth, the familiarity of stars of similar nature, and with the head of the Dragon. Seventh, motion, speed. Eighth, descent from the Apogee both of the eccentric and of the epicycle. And if there are any other ways by which stars increase their powers, all must be taken into account; because elevation, to conclude in a word, requires nothing else than familiarity and a greater ordering of powers. The Arabs, in their own term, call this Mamareth of the planets: concerning which Albumasar has more at the end of his Introduction. 31. ELHABOR, in Arabic, the Great Dog, Sirius; see Alhabor. 32. ELHAMMEL, as Kircher states in his Oedipus, is the name given to the sign and constellation of Aries; likewise 33. ELHAVT among the Arabs, as the same Kircher testifies, signifies the sign and constellation of Pisces. Likewise 34. ELKAYS is the sign and constellation of Sagittarius; and also. 35. ELGEDT, sign and constellation of Capricorn. See under the proper name of each.

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MATHEMATICVM. 173 ELKERD Bennenax, Arab. dicitur Stella fixa secundæ ma- < 36.> gnitudinis vltima in extremo caudæ Vrsæ majoris, de natura martis, dicta eriam Alalicsh. idest nocturnum, eo quia semper visibilis sit de noctu, cum neque oriatur, neque occidat in no- < 37.> stro hæmisphærio, sed radat tantummodo horizontem. Vide fusius in verbo Vrsæ. ELKLEILSCHEMALE Arab. vocatur, vt testatur Kircherus in < 38.> Oedipo corona Gnosia, sidus in cælo ad Borealem plagam con- < 39.> stans stellis 8, licet in Baieri Vranometria 20. omninò enume- < 40.> rentur, quarum lucida & insignior appellatur proprio nomine Alphetsal siue Alpheica, idest aperitio, & Mumir quasi pupilla, est enim per antonomasiam dicta cæli pupilla. Vide alibi vbi < 41.> sæpiùs de ea mensionem fecimus. ELLIPSI dicitur figura Geometrica o[mn]alis vnica tantum < 38.> linea, quæ tamen circulatis non sit, comprehensa, nec omnes partes æqualiter tendunt ad centrum. Vide Euclidem. ELTANIN Arab. Latinè Dtaco, sidus de quo paulò ante dictu[m]. < 39.> ELVARAD Arab. vel etiam Elkir, & Pharmaz teste Kir- < 40.> chero, Latinè Crater sidus. Vide sub hoc vocabulo. ELZEGIALE siue Elasbi, hoc est Ingeniculator vocatur He- < 41.> rales Engonasis, sidus ad Borealem plagam propè Ophiacum, de quo plura suo loco. EM EMBOLISMVS Grecè propriè significat intercalationem il- < 42.> lam quæ antiquitùs fieri solebæt, vt annorum ratio cum Solis cursu conueniret: Nunc autem magis strictè accipitur, vel pro- ipso bissextili die qui singulis quadriennijs superadditur Februari- < 43.> rio ad æquandam anni quantitatem morul Solis in Zodiaco, vel pro excessu anni solaris ad annum lunarem dierum vnde- < 44.> cim supra duodecim lunationes, itaut singulis annis Nouilunia contingant vndecim diebus prius, quam præcedenti anno, quæ præcessio cum ad numerum dierum triginta peruenerit: < 45.> constituet nouam lunationem, quæ dicitur Embolismica su- peraddenda, quousque annus communis lunaris exequet an- < 46.> num solarem. Quare. EMBOLISMICA Lunatio est illa, quæ conflatur ex triginta < 47.> diebus superadditis modo explicato, & quæ constituit annum Embolismicum tredecim Lunationum, constantem diebus 384. < 48.> aut 383. Quippe Lunationes ijs mensibus tribuuntur, & ab ijs denominationem sumunt, in quibus siniuntur: itaut omnis Lunatio in Decembri incipiens, & in Ianuario finem habens, < 49.> etiamsi prima die mensis, ab eo nihilominus denominanda sit, ac dicenda totius anni prima Lunatio. Hinc fieri potest, vt < 50.> quibusdam annis post primam illam Lunationem supersint

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MATHEMATICVM. 173 ELKERD Bennenax, in Arabic, is called a fixed star of the second magnitude, the last in the extremity of the tail of Ursa Major, of Martian nature, also called Alalicsh, that is, “nocturnal,” because it is always visible by night, since it neither rises nor sets in our hemisphere, but merely skims the horizon. See more fully under the word Ursa. ELKLEILSCHEMALE, as Kircher testifies in Oedipus coronae Gnosiae, is a star in the heavens fixed toward the northern region, consisting of 8 stars, although in Bayer’s Uranometria they are altogether enumerated as 20, of which the bright and more notable one is called by its proper name Alphetsal or Alpheica, that is, “opening,” and Mumir, as it were “pupil”; for by antonomasia it is called the pupil of the heavens. See elsewhere where we have more often made mention of it. ELLIPSE is called a geometric figure, an oval having only one line, which however is not enclosed by circular lines, nor do all its parts stretch equally toward the center. See Euclid. ELTANIN, in Arabic, in Latin Draco, a star of which mention was made a little before. ELVARAD, in Arabic, or also Elkir and Pharmaz, according to Kircher, in Latin Crater, a star. See under this word. ELZEGIALE, or Elasbi, that is, “the kneeler,” is called Heracles Engonasis, a star toward the northern region near Ophiacus, of which more in its proper place. EM EMBOLISM, in Greek, properly signifies that intercalation which in ancient times used to be made so that the reckoning of years might agree with the course of the Sun. Now, however, it is taken more strictly, either for the leap day itself which is added every four years in February to equalize the length of the year with the Sun’s motion in the zodiac, or for the excess of the solar year over the lunar year by eleven days beyond twelve lunations, so that each year the new moons occur eleven days earlier than in the preceding year; when this advance has reached thirty days, it forms a new lunation, which is called embolismic, to be added until the common lunar year matches the solar year. Therefore. An EMBOLISMIC Lunation is one which is made up of thirty days added in the manner explained, and which constitutes an embolismic year of thirteen lunations, consisting of 384 or 383 days. For the lunations are assigned to those months, and take their name from them, in which they end: so that any lunation beginning in December and ending in January, even if it begins on the first day of the month, must nevertheless be named from that month and called the first lunation of the whole year. Hence it may happen that in some years after that first lunation there remain

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174 LEXICON adhuc duodecim integræ lunationes, antequam ad primam lunationem alterius anni sequentis veniamus, si nimirum super sint post primam lunationem anni, dies 354. vel 353. quot satis sunt ad expendum numerum duodecim lunationum. Sed de hac re consule librum nouæ rationis restituendi Calendarij Romani. < 44.> EMPYREVM Cælum dicitur à Theologis, & Sanctis Patribus (nam Philosophi ejus notitiam non habuerunt) supremum illud, ac vastissimum cælum supra omnes cælos firmatum, sedes Beatorum, & Thronus Dei, immobile & firmum, in quo omnes Angeli, & Sancti perennant. Eius qualitates describere coecutire est, quandoquidem, neque vllas stellas, habet vnde reddatur visibilis, nec vllum motum, vnde saltem argui possit ejus existentia, immensitas & pulchritudo. Vnde August. in lib. Soliloqu. ad Deum, cap. 31. Hoc est, inquit, Calum tuum Domine, cælum calans superareanum, superintelligibile, superrationale, & superessentiale lumen, de quo dicitur calum cali Domino. Calum cali cui terra est omne calum quia supermirabiliter exaltatum est super omne cælum, ad quod etiam terra est ipsum calum Empyreum: hoc enim est cæum cali Domino, quia nullis notum nisi Domino. Credibile tamen est ipsum immensitate luce, materia cæteris omnibus antecellere: Vnde Empyreum dictum est non quasi ignitum sit, sed ob nimiam sui puritatem, ac lucem. Materiam crediderim esse ejusdem speciei cum cæteris, sed longe puriorem, ac defæcatiorem, situm, nulli dubium esse longe altissimum, quam concipi possit: si enim à superficie terræ vsque ad cælum stellarum computat Ptolomæus distantiam 65237500. milliariorum, quid credendum est de cælo Empyreo data proportione distantiæ quæ est inter alios orbes ad inuicem, quæ semper in immensum excrescit: Hinc etiam colligi potest infinita propemodum amplitudo, quæ ab aliquibus tanta esse dicitur, vt si cuilibet Angelorum, ac Sanctorum suus locus, & certa portio deputaretur, plusillud spacium contineret, quam occupat vniuersa terra: & iure quidem cum secundu[m] omnes Astronomos minima stella quæ est in firmamentobis nouies superer magnitudine terrestrem globum: quidni igitur firmamentum? quid cælum Empyreum quod ad minus centies firmamentum superar, sed & Franciscus Panonius par. 2. introductionis in sacram doctrinam defini. 2507. affirmat diuinæ magnificentia congruum esse vt firmamentum ad concauam cæli Empyrei superficiem, seu ad conuexam ptimi mobilis comparatum se habeat, sicut punctum, quemadmodum se habet terra ad ipsum firmamentum comparata: Quanta porrò erit ejusdem cæli crassities tanta profectò, quanta par est ad

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174 LEXICON there are still twelve complete lunations before we come to the first lunation of the following year, if indeed there remain after the first lunation of the year 354 or 353 days, which are enough to make up the number of twelve lunations. But on this matter consult the book on the new method of restoring the Roman Calendar. <44.> EMPYREAN Heaven is said by Theologians and Holy Fathers to be that supreme and most vast heaven, established above all the heavens, the abode of the Blessed and the Throne of God, immovable and firm, in which all the Angels and Saints abide forever. To describe its qualities is to grope in blindness, since it has neither any stars by which it may be made visible, nor any motion from which its existence, immensity, and beauty may even be inferred. Hence Augustine, in the book Soliloquies to God, chap. 31: This, he says, is your Heaven, O Lord, the supercelestial heaven, the superintelligible, super-rational, and super-essential light, of which it is said, the heaven of heavens to the Lord. The heaven of heavens, to which the earth is all heaven, because it is wonderfully exalted above every heaven, to which even the earth itself is the Empyrean Heaven: for this is the heaven of heavens to the Lord, because known to none except the Lord. Yet it is credible that in immensity of light it surpasses all the others in matter as well; hence it is called Empyrean, not as though it were fiery, but because of its excessive purity and light. I should think its matter is of the same species as the others, but far purer and more refined; its position is undoubtedly far higher than can be conceived. For if Ptolemy computes the distance from the surface of the earth to the heaven of the stars at 65,237,500 miles, what must be believed concerning the Empyrean heaven, given the proportion of the distances that are among the other spheres in relation to one another, which always increase to an immense degree? From this it can also be gathered that its amplitude is almost infinite, and some say it is so great that if a place and fixed portion were assigned to each of the Angels and Saints, that space would contain more than the whole earth occupies: and rightly so, since according to all astronomers the smallest star in the firmament exceeds the terrestrial globe nine times in magnitude; why then not the firmament? why not the Empyrean heaven, which exceeds the firmament by at least a hundredfold? And Francis Panonius, part 2 of the Introduction to Sacred Doctrine, definition 2507, also affirms that it is fitting to divine magnificence that the firmament should stand in relation to the concave surface of the Empyrean heaven, or to the convex surface of the first mobile, as a point, just as the earth stands in relation to the firmament itself. How great, then, will the thickness of that same heaven be? certainly as great as is fitting for

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MATHEMATICVM. 175 explicandum magnitudinem ejus, qui sibi talem domum extruxit, vnde Baruch. 3. dicitur: O Israël quam magna est domus Domini. Et ingens locus possessionis ejus! magnus est, Et non habet finem, excelsus, ac immensus. Vnde majorem ejus molem concipiendam esse subjungit idem author quam esset occupantia omnis Angelorum multitudo, si quilibet Angelus in sua se sphæra locaret extra cujusque Angeli speram. Quare autem tam immensum creare placuerit omnipotenti Deo, tripli-cem causam adducit Guillelmus Parisensis. Primò propter innitam sui potentiam ostendendam, quæ maximè in tam im-menso opere relucet. Secundò propter suam gloriam, & rega-lem magnificentiam comprobandam. Terriò ad humani desi-derij vehementiam satiandam, quæ amplas possessiones lata-que terrarum dominia requirit: Ergò tantum præparauit quo iuueniret supra quam cupere posset. Sed ad hac inardescit ani-mus, jamque illic cupit assistere, vbi se sperat sine fine gaudere, in-quit Gregorius Pont. hom. 37. in Euangelia. Faxit Deus, vt quò mens nostra sua desideria dirigit, eò etiam per bona opera tendens, perueniat. EN ENGONASIS Hercules, Ingeniculus, &c. sidus ad Borealem plagam propè serpentarium constans stellis 29. computata < 46.> etiam vna informi circa brachium dextrum: sed Baierus in sua Vranometria enumerat in hoc astro stellas omnino 48 omnes ferè de natura Martis ex quibus præcipua quæ in capite Ras Al-pets apud Arabes tertia magnitudinis altera in manu sinistra, Arab. Marsic. Is in horoscopo, inquit Firmicus, facit callidum, mendacem varijs dolis instructum, quique homines varijs in-sidijs appetat, atque effrenata semper animositate grassetur. Cum testimonio autem Lunæ facit agiles, funambulos, oriba-tas, & qui talia pertractent. In occasu verò repertum hoc sidus exponit aliorum insidijs, etsi cum malo radio Martis adducit periculum combustionis. ENIF Alpharatz Arab. dicuntur scapulæ Equi, stellæ videli- < 47.> cet duæ sixæ secundæ magnitudinis de natura Martis, & Mercurij, existentes, altera quidem in gr. 19. Piscium, altera in 25. cum fere totidem latitudinis Borealis. Vide earum signi-ficata in V. Pegasus. ENIOCHVS Mulus Cilsellatus, Auriga sidus in cælo. Vide < 48.> Auriga. ENNEAGONA Figura apud Geometras est figura nouem an-gulis constans: quemadmodum Pentagona, quæ quinque: Eragona, quæ sex, & sic de singulis de quarum ratione. Vide Clauium in Elementa Euclidis.

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MATHEMATICVM. 175 explaining the magnitude of Him who built for Himself such a house, whence Baruch 3 is said: O Israel, how great is the house of the Lord. And the vast place of His possession! great is it, and it has no end, lofty and immense. Hence the same author adds that its greater bulk must be conceived as greater than the space occupied by the whole multitude of Angels, if each Angel were placed in his own sphere, outside the sphere of every Angel. But why it may have pleased almighty God to create something so immense, Guillelmus Parisensis gives three reasons. First, for showing the power of His innate might, which shines forth most clearly in so immense a work. Secondly, for confirming His glory and royal magnificence. Thirdly, to satisfy the vehemence of human desire, which requires broad possessions and wide dominions of lands: therefore He has prepared so much that it should reach beyond what one could desire. But to this the mind grows inflamed, and already longs to be present there, where it hopes to rejoice without end, says Gregory the Pope, hom. 37 on the Gospels. May God grant that where our mind directs its desires, there also, striving through good works, it may arrive. EN ENGONASIS Hercules, Ingeniculus, etc., a constellation near the northern region by the Serpentarius, consisting of 29 stars, counted <46> and also one dim one near the right arm; but Bayer in his Uranometria counts in this constellation altogether 48 stars, almost all of the nature of Mars, among which the principal one in the head, Ras Al-pets among the Arabs, is of the third magnitude, another in the left hand, Arab. Marsic. This, in the horoscope, says Firmicus, makes one cunning, lying, furnished with various tricks, and one who attacks men with various ambushes, and always rages with unrestrained violence. With the testimony of the Moon it makes agile persons, tightrope-walkers, rope-dancers, and those who handle such things. Found in the setting, this star exposes one to the ambushes of others, though with an evil ray of Mars it brings danger of combustion. ENIF Alpharatz Arab. are called the shoulders of the Horse, namely the stars <47> two fixed stars of the second magnitude of the nature of Mars and Mercury, one being in 19 degrees of Pisces, the other in 25 degrees, with about the same amount of northern latitude. See their signification in V. Pegasus. ENIOCHVS, the bridled mule, the constellation of the Charioteer in the sky. See <48> Auriga. ENNEAGONA is, among geometers, a figure consisting of nine angles: just as Pentagona has five; Eragona, six, and so on for each of which see the account. See Clavius on the Elements of Euclid.

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176 LEXICON 50. ENNEATICI Dies, vel Annis sunt Nouenarij quique recurrentes dies, vel anni, à puncto Natiuitatis, vel initio morbi, in quibus profectò semper aliquam naturæ alterationem experimur, atque accessionem morbi, sicut & in septenarijs, ac manifestiùs quando ambo conveniunt, & septenarij, & nouenarij. Cuius iei, vti effectus patens est, & manifestus, ita & ratio, & origo obscura nimis, & adhuc non benè nota. Qua de re fusè egimus in Verbo Criticis dies. 51. Eosphorvs Grecè Latinè Luci er dicitur apud Astronomos Venus matutina, atque Orientalis à Sole, à Græco verbo Eos, quod Orientalis sonat: sicut econtra Hesperus appellatur Vespertina, & quando est Occidentalis à Sole. E P 52. Epacta (quasi Epiaucta hoc est superexcescentia) nil aliud est, quam excessus anni communis solaris supra annum lunarem duodecim lunationum in diebus vndecim singulis annis: Cum enim annus communis solaris constet diebus 365. Lunaris verò diebus 354. consequenter lunaris terminatur, & anteuertit solarem diebus vndecim, qui sit vt Noulunia, tot etiam diebus præcedant finem anni solaris. Et quia id singulis quibusque annis accidit, inde etiam est, vt singulis decem, & nouem annis solaribus Luna compleat vicesies duodecim integras lunationes, seù superet vnum annum communem solarem, quo circuitu expleto conueniat cum Sole: atque ita semper procedendo in infinitum, singulis annis primis à dicta conuentione reperiatur Luna præcedere Solem diebus vndecim; secundo anno diebus 22. sicque Epacta istius anni sit 22. tertio anno præcedat diebus 33. sed cum diebus 30. fiat vna integra lunario, ideò ea prætermissa, immò potius admissa, atque in numerum integræ lunationis computata. Epacta, seu præcessio lunationum sit dierum 3. qui ad triginta supersunt: quarto verò anno sit dierum 14. & sic de singulis. Progrediuntur igitur Epactæ omnes per continuum augmentum dierum vndecim, abjectis tamen 30. semper cum abijci possunt. Numerumque istum vocamus Epactum, quia epactat Lunæ defectum, atque inseruit ad ejus æratem ad dies singulos dignoscendam. Quippe si addatur Epactæ currenti eo anno numerus dierum mensis, qui transferunt, nec non Calendarum quæ præcesserunt, incipiendo à mense Martio, vsque ad præsentem mensem in quo hæc scrutari volumus, inclusiùè; statim elucent in producto numero dies ætatis Lunæ à præcedenti coitione cum Sole, demptis prius triginta, si fortè cum numerum excesserint, quia isti sufficiunt ad vnam integram lunationem constituendam. Procedit

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176 LEXICON 50. ENNEATICI. Days, or years, are the recurring ninth days, or years, from the point of birth, or from the beginning of the illness, in which we certainly always experience some alteration of nature, and an increase of the disease, just as in the septenaries, and more manifestly when both coincide, both the septenaries and the ennearies. Of these days, as the effect is evident and manifest, so also the reason and origin are exceedingly obscure, and as yet not well known. On this matter we spoke at length in the word Criticis dies . 51. Eosphoros, in Greek; in Latin Lucifer is called among astronomers the morning and eastern Venus from the Sun, from the Greek word Eos , which means eastern; just as conversely Hesperus is called the evening and, when it is western from the Sun. E P 52. Epacta (as it were Epiaucta , that is, superabounding) is nothing else than the excess of the common solar year over the lunar year of twelve lunations, by eleven days each year. For since the common solar year consists of 365 days, but the lunar year of 354 days, consequently the lunar year ends earlier than the solar year by eleven days, which, as the new moon, precede the end of the solar year by as many days. And because this happens every year, it follows also that in every ten and nine solar years the Moon completes twenty times twelve full lunations, or exceeds one common solar year, at the end of which circuit it coincides with the Sun; and thus always advancing in infinity, in the first year from the said conjunction the Moon is found to precede the Sun by eleven days; in the second year by 22 days, and so the epact of that year is 22. In the third year it precedes by 33 days; but since 30 days make one complete lunar month, therefore that being omitted, or rather admitted and counted as one complete lunation, the epact, or preceding of the lunations, is 3 days, which remain after thirty. In the fourth year, however, it is 14 days, and so of each year. Therefore all the epacts proceed by a continuous increase of eleven days, nevertheless always subtracting 30 whenever they can be subtracted. And we call that number the epact, because it epacts the defect of the Moon, and is inserted so that her age may be known day by day. Indeed, if to the current epact in that year there be added the number of days of the month that intervene, as well as the Kalends that have gone before, beginning from the month of March up to the present month in which we wish to investigate this, inclusively, immediately in the resulting number appear the days of the Moon’s age from the preceding conjunction with the Sun, after first subtracting thirty if perhaps they have exceeded the number, because these suffice to make up one full lunation. Procedit

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MATHEMATICVM. 177 Procedit igitur semper æquali modo ordo iste Epactarum per additionem vndecim dierum singulis annis, excepto tamen vltimo anno, in quo recurrit Epacta correspondens Aureo numero 19. quæ est dierum 29 quantum videlicet sufficit ad integram lunationem perficiendam: in quo casu non vndecim, sed duodecim dies imaginarie addendi sunt, vt abjectis 30. ex composito numero 41. habeatur rursus Epacta 11. prout erat in principio. Qua de re vide quæ optimè scripsit Clauius in Kalendario Gregoriano. EPHEMERIS Græcè proprie significat diarium, quod acta cujusque diei complectitur, ac interstincte exponit, sumpto vocabulo ex quodam animalculo Ephemero dicto, de quo scribunt natutales, ipsum non nisi ad vnicam tantum diem vitam protrahere. Hinc apud Astronomos deriatur fuit, & antonomastice applicatum ad exprimendum motum diurnum omnium planetarum; quem in dies singulos perficiunt in Zodiaco, vnde libri, in quibus extant calculati hujusmodi motus planetarum, cum aspectibus, & alijs eorum passionibus ad dies singulos, Ephemerides appellantur. EPICATAPHORA seù etiam Picataphora Græcè dicitur 55. octaua domus ab horoscopo succedens angulo Occidentis: Latinè sonat Portam supernam ad differentiam secundæ domus illi oppositæ, quæ quia succedit Horoscopo, ideo dicitur porta inferna. Est significatrix mortis, hæreditatum, quæ ex mortuis præveniunt, laboris, tistitiæ, & thesaurorum oceul- totum. Habet consignificatorem Saturnum. Ex membris hu- manis præest pudendis, & inducit strangutiam, calculum, hæmorroidas, & similia. Est locus infelix, eoquia nullam ha- bet cum ascendente familiaritatem, & continujs vaporibus è terra prosilientibus offenditur. Id circò vocatur à Firmico locus piger, & otiosus; ab alijs (quod idem sonat) Argus Tophet, &c. EPICYCLVS est paruus Orbis, qui defetenti infixus motu il- lius circum agitur, & impactum sibi planetæ corpus peculiari suo motu circâ proprium centrum circumducit. Pro cujus rei intelligentia sciendum est, antiquos Astronomos, ad saduandos apparentias, ac diuersitares motuum, qui in singulis planeris peculiariter deprehenduntur, excogitasse varios circulos, Eccentricos, Concentricos, & Epicyclos: itaut, excepto Sole, singulis planeris tres circulos assignarint, quorum primus esser deferens, Eccentricus simpliciter (qualis autem is sit, suo loco explicuimus.) Secundus esset circulus dictus æquans, quem ideò posuerunt, quia defetentes planerarum non mouentur æqualiter in eorum centris, sed valdè difformiter, & ir- regulariter, vt mox dicemus: Testius orbis foet infixus in M

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MATHEMATICVM. 177 Therefore this order of the Epacts proceeds always in the same way, by adding eleven days each year, except, however, in the last year, in which there recurs the Epact corresponding to the Golden Number 19, which is 29 days, as much, namely, as is sufficient for completing a full lunation: in which case not eleven, but twelve imaginary days are to be added, so that, after subtracting 30 from the composite number 41, the Epact 11 may again be obtained, as it was at the beginning. On this matter, see what Clavius wrote best in the Gregorian Calendar. EPHEMERIS in Greek properly signifies a diary, which contains the events of each day and sets them out in order, the word being taken from a certain little animal called Ephemerus, about which naturalists write that it prolongs its life for only a single day. Hence among astronomers it has been derived and applied by antonomasia to express the daily motion of all the planets, which they complete day by day in the Zodiac; whence books in which such calculated motions of the planets are found, together with their aspects and other conditions for each day, are called Ephemerides. EPICATAPHORA, or also Picataphora, is called in Greek 55 the eighth house succeeding the horoscope toward the angle of the West. In Latin it signifies the Upper Gate, by distinction from the second house opposite it, which, because it succeeds the Horoscope, is therefore called the Lower Gate. It signifies death, inheritances coming from the dead, labor, sadness, and hidden treasures. Saturn is its co-significator. Among the human members it governs the privy parts, and it causes strangury, stone, hemorrhoids, and the like. It is an unfortunate place, because it has no familiarity with the ascendant, and is offended by the continuous vapors rising from the earth. For this reason Firmicus calls it a sluggish and idle place; by others (which means the same thing) Argus Tophet, etc. EPICYCLVS is a small orbit, fixed to the deferent, and carried around by its motion, while by its own peculiar motion it carries around the body of the planet, which is placed upon it, around its own center. For an understanding of this matter, it must be known that the ancient astronomers, in order to satisfy the appearances and the diversities of motions which are specially observed in the individual planets, devised various circles, eccentrics, concentrics, and epicycles: so that, except for the Sun, they assigned three circles to each planet, of which the first would be the deferent, the eccentric simply (what sort that is, we have explained in its place). The second would be the circle called the equant, which they placed for this reason, that the deferents of the planets do not move equally in their centers, but very unevenly and irregularly, as we shall shortly say. The third orbit is fixed in M

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178 LEXICON ipso deferente, atque ejus centrum eccentricè circà tellurem moueretur vna cum ipso Orbe eccentrico, & adhuc corpus planetæ circà ipsum in ejus circumferentia moueretur, qui dictus est Epicyclus. Et hunc tertium omnibus planetis præterquam Soli attribuerunt: licet Ptolomæus in Almagesto demonstret, quod apparentiæ in Sole saluari possint ponendo in eo circulum eccentricum tantum, vel concentricum cum Epicyclo, tamen magis abbrobat eccentricum. Etenim planetæ modo apparent majores, modò minores; etiam in eadem altitudine supra horizontem: modo velocius mouentur, modò segniùs: modo videntur consistere, modò etiam retrocedere: quæ omnia talia sunt, quæ neque concipi possunt, neque explicari, nisi per orbes eccentricos, & Epiclycos. Et quoniam in Sole non videmus tantam motus diuersitatem, quanta est in reliquis planetis, qui omnes excepta Luna, modò videntur stare, modò celerius progredi, modò retrogredi in Zodiaco; ideò in ipso duos quidem priores circulos ponimus, Epicyclum, verò sine quo optime saluare eius apparentias possumus, remouemus. In Luna verò, etsi non tanta morus diuersitas dignoscatur quanta in reliquis quinque erraticis, neque etiam habeas retrocedere in Zodiaco; quia tamen in eodem loco eccentrici sui constituta, puta in Apogæo, vel Perigæo non semper habet eandem aspectus conformitatem; ideo necesse fuit, concipere, vt in eodem loco eccentrici sui sit nihilominùs modò terræ vicinior, modo ab ea remotior; quod vtique saluare minimè possumus, ni ponamus, & in ea vnum Epicyclum, in cujus Apogeo appareat minor, in Perigeo major, etiam cum alias est in Apogæo sui eccentrici. Sed de hac re vide quæ latiùs haber Clauius in Sharam Ioannis Sacro Bosco. 57. EPICVS ex Græco idem sonar, ac humi repens. Per translationem vsurparur ab Astronomis in Planeta, qui reperiatur in ima abside sui deferentis, vel Epicycli, in quo sit terræ proximior. 58. EPIMA in sphæra Barbarica dicitur secundus Decanus Capricorni manens sub dominatu Martis, præbens genium quærendi de rebus, quæ sciri non possunt, & sciscitandi de ijs, quæ ad finem perduci nequeunt. 59. EPITRION apud Ptolomæum lib. 1. cap. 11. vbi agit de aspectibus signorum, idem sonat ac sesquitertium. 60. EPOCHA Græcè, Latinè radix. Est initium certi cuiusdam temporis apud antiquos, vnde incipiebar motus aliquis, aut rei computus numeraræ, vt Olympiades apud Græcos, ac indictiones & lustra apud Romanos. Significat etiam, reste Rhodigino, ascensiones planetarum in Zodiaco, positusque stellarum adiquicem.

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if it were carried along by the deferent itself, and its center moved eccentrically around the earth together with the eccentric orbit itself, and moreover the body of the planet moved around it in its circumference, which was called the Epicycle. And this third circle they attributed to all the planets except the Sun; although Ptolemy in the Almagest shows that the appearances in the Sun can be preserved by placing in it only an eccentric circle, or else a concentric one with an epicycle, nevertheless he more strongly approves the eccentric. For the planets now appear larger, now smaller; even at the same altitude above the horizon: now they move more quickly, now more slowly: now they seem to stand still, now even to move backward: all of which are things that can neither be conceived nor explained except by eccentric orbits and epicycles. And since in the Sun we do not see such a diversity of motion as there is in the other planets, all of which except the Moon now seem to stand still, now to advance more quickly, now to retrograde in the Zodiac; therefore in it we indeed place the first two circles, but we remove the epicycle, without which we can best preserve its appearances. But in the Moon, although such a diversity of motion is not discerned as in the other five wandering stars, nor does it retrograde in the Zodiac; because yet, when placed in the same place of its eccentric, that is, in apogee or perigee, it does not always have the same conformity of aspect; therefore it was necessary to conceive that in the same place of its eccentric it is nevertheless now nearer the earth, now farther from it; which indeed we can by no means preserve unless we also posit in it one epicycle, in whose apogee it appears smaller, in perigee larger, even when otherwise it is in the apogee of its eccentric. But on this matter see what Clavius writes more fully in Sacrobosco’s Sphaera. 57. EPICVS in Greek means the same as creeping on the ground. By translation it is used by astronomers for a planet that is found in the lowest part of its deferent, or epicycle, in which it is closest to the earth. 58. EPIMA in the Barbarian sphere is called the second decan of Capricorn, remaining under the dominion of Mars, and giving a disposition for seeking after things that cannot be known, and for inquiring about things that cannot be brought to completion. 59. EPITRION, in Ptolemy book 1, chapter 11, where he treats of the aspects of the signs, means the same as sesquitertian. 60. EPOCHA, in Greek, Latin radix. It is the beginning of a certain time among the ancients, from which some motion or calculation of a counted thing was begun, as the Olympiads among the Greeks, and the indictions and lustrums among the Romans. It also signifies, according to Rhodiginus, the ascensions of the planets in the Zodiac, and the positions of the stars at the equinox.

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MATHEMATICVM. 179 EPTAGONVM est figura Geometrica septem æqualibus angulis constans. Vide Clauium in Euclidem. EQ EQVICVLVS, siue Equi sectio Hinniculus, &c. dicitur sidus mutilarum in cælo, repræsentans caput equi sectum: habet qua- <62.> tuor tantum stellas obscuras, quatum duæ priores sunt de natu- ra Martis, & Mercurij, reliquæ de natura Saturni. Consistit in longitudine in gr. 19. Aquarij, hinc inde ad æquatorem. Ara- bicè Alpheras Elmac. EQVVS alatus aliud sidus in cælo prope ipsum æquiculum, <63.> constans stellis viginti apud Ptolomæum, sed apud Keplerum, & Baierum 23. quarum insigniores sunt, quæ in ore dictamus cida equi, altera quæ in almo alæ Arabicè Marchab, id est, Currus, tertia quæ in extrema ala dicta sigenib. aliæ duæ in scapulis di- ctæ Ens. vltima tandem quæ in eductione cruris apud Arabes sebeat alpheræ: Is in alicujus horoscopo repertus, inquit Ponta- <64.> nus facit poetam, ingenio sublimem, miræ dexteriratis in nego- tijs petagendis, famæ, nominisque auram captarem, quem de- lectent arma currus & equos tractare. Dar etiam genium ad ex- quirendas herbarum virtutes, vt ijs medeatur hominibus ac brutis animantibus: Tandem de eo occidente concludit. Executis aut currus lacerrum, aut è calce cruentum, Aut de isto eiectum figias desurbat ad vudas. De eo aliter pronunciat Iulius Firmicus, vt videre est in V. Pegasus. ER EREGBVO, vocabulum Græco babarum in sphæra barbarica, <65.> quo significatur primus Decanus Sagitarij manens sub disposi- tione Mercurij, cujus proinde est significate audaciam, liber- tatem, militiam. ERICTHONIVS Agitaror, Auriga, Heniochus sidus in cælo <66.> ad Borealem plagam constans stellis 14. apud Ptolomæum, sed apud Baierum 37. de natura Martis, & Mercurij inter quas vna in ejus humero sinistro primæ magnitudinis, nomine Hercus seu Capella: duæ etiam minores in vola manus, dicti Hedi, tempestuosæ nimis, ac ventorum motrices eorum signi- <66.> ficata; quemadmodum & totius hujus sideris, vide suis locis & in V. Auriga ERIDANVS, seu Nilus sidus item in cælo ad australem plagam <66.> habens stellas trigenta tres omnes ferè de natura Saturni, præ- ter præcipuam in extremo fluminis sitam Arabice Acarnar seu <66.> Acarnaharim quæ Sola in siderè ominoso & malignantis natu- ræ omnem prauitatem compensat. Est enim stella fulgentissima de natura louis & Vaueris, primi honoris, quæ in horoscopo M ij

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MATHEMATICAL. 179 HEPTAGON is a geometrical figure consisting of seven equal angles. See Clavius on Euclid. EQ EQVICVLUS, or Horse-Headed Foal, etc., is called the constellation of the mutilated ones in the sky, representing a severed horse’s head: it has only qua- tuor four obscure stars, of which the first two are of the nature of Mars and Mercury, the rest of the nature of Saturn. It lies in longitude at 19 degrees of Aquarius, on either side of the equator. In Arabic, Alpheras Elmac. EQVVS alatus, another constellation in the sky near the same little horse, <63.> consisting of twenty stars according to Ptolemy, but according to Kepler and Bayer 23, of which the more notable are those in the mouth, which we call cida equi; another in the middle of the wing, Arabic Marchab, that is, the Chariot; the third in the outer wing, called sigenib; two others in the shoulders, called Ens; the last, finally, in the extension of the leg, among the Arabs sebeat alpheræ. If found in anyone’s horoscope, says Pontanus, it makes a poet, exalted in talent, of wonderful skill in conducting affairs, and one who catches the breeze of fame and reputation, one whom arms, chariots, and horses delight to handle. It also gives a genius for seeking out the virtues of herbs, so that by them he may heal both men and brute animals. Finally, concerning it when setting, he concludes: After the chariot is shattered, or bloodied at the heel, Or cast out from it, the fig-trees drive you from the woods. Julius Firmicus pronounces otherwise about it, as may be seen under V. Pegasus. ER EREGBVO, a word of the Greek barbarians in the barbaric sphere, <65.> by which is signified the first decan of Sagittarius, remaining under the disposition of Mercury, whose property therefore is to signify boldness, freedom, military life. ERICTHONIVS, the driver, Auriga, Heniochus, a constellation in the sky <66.> toward the northern region, consisting of 14 stars according to Ptolemy, but according to Bayer 37, of the nature of Mars and Mercury, among which one on his left shoulder is of first magnitude, by the name Hercus or Capella; two smaller ones also in the palm of the hand, called Hedi, too stormy and stirrers of winds, as signified by them; just as also by the whole of this constellation; see in its proper places and under V. Auriga ERIDANVS, or Nile, likewise a constellation in the sky toward the southern region <66.> having thirty-three stars, almost all of the nature of Saturn, except the chief one at the end of the river, situated, in Arabic, Acarnar or <66.> Acarnaharim, which, alone in this ominous constellation and of malignant nature, makes up for all its perversity. For it is a most brilliant star of the nature of Jupiter and Venus, of first honor, which in a horoscope M ij

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180 LEXICON dat venustatem, gratiam dicendi, leporem, fortunam in honoribus, ac diuirijs, eadem cum Sole occidens, aut cum Ioue exoriens facit serenum. Cæterum aliæ stellæ quæ sunt in studio, vt dixi non adeo faustæ sunt, quinimo rempestatas in mari vt plurimum excitant, & in alicujus horoscopo repertæ portendunt naufragium, & suffocationem in aquis, cum sint de natura Saturni, idque præsertim si is mali affulserit. De hoc sidere hæc habet Tullius, in Arasi Phænom. Namque etiam Eridanum cornes in parte locatum, Cali, funestum magnis cum viribus annem, Quem lachrimis mæsta Phaetontis sæpè sorores, Sparserunt latum mar. nti voce canentes. Oritur autem Romæ hoc sidus cum signo Aquatij, & occidit cum extremis partibus Piscium. 67. ERIGONE Manilio audit Virgo signum in cælo, sextum ab Ariete, de quo vide suo loco. 68. ERRATICÆ stellæ, seu Errones dicti sunt Planetæ presertim quinque Saturnus, Iupiter, Mars, Venus, & Mercurius; Luminaria enim nobiliore titulo gaudent. Dictæ inquam sunt errones, errantes, & erraticæ ad differentiam aliarum stellarum, quæ sunt in firmamento sub varijs imaginibus compræhensæ: Ista enim etsi motu primi mobilis ab Orienre in Occidentem circumagantur, atque eriam moru proprio ipsius firmamenti (lenro tamen, ac planè insenbili, ab occasu in orrum; nihilominus, quia non ipsæ vllo modo mouentur, semper eodem loco in firmamento consistunt, semper eandem distantiam ab inuicem seruant, atque à polis Zodiaci, ideo fixarum nomen soritæ sunt: quando planetæ econtra ob peculiarem cujusque motum, ob diuersas inter se habitudines, quas semper errando permutant, merito erraticæ stellæ sunt dictæ. 69. ETESIÆ apud Plinium, Strabonem, & alios dicti sunt venti quidam anniuersarij, staris temporibus recurrenres, qui eriam Prodromi vocitanur, ac pro locorum varierate, ab aliqua cæli plaga & certo tempore constanter exsufflant. Strabo eos nominat subsolanos. Vt plurimum autem spirant in æstate incipientes circa exortum Caniculæ manè post Solis orrum, & durant per quadraginta ferè dies summam semper aeris temperiem salubritaremque serenies. In Italia spirant à Seprentrione, in Hispania ab exortu æquinoctiali, in reliquis mundi partibus à meridie, & noctu semper silere consueuerunt. Sunt tamen in diuerso genere: quippe apud Occidentales solent esse ex Septentrionalibus, & mutari solent in Occidentales vsque ad Fauonium. Apud incolas vero Orientalium locorum spirant

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180 LEXICON that beauty, grace in speaking, charm, fortune in honors, and riches, the same, setting with the Sun or rising with Jupiter, makes fair weather. The other stars, which are, as I said, in the heart of a constellation, are not so fortunate; indeed they very often stir up storms at sea, and when found in someone’s horoscope they portend shipwreck and drowning in the waters, since they are of the nature of Saturn, and this especially if he has a malevolent aspect. Concerning this star Cicero has the following, in Aratus’ Phenomena. For there also, placed as companion in a part of the sky, A star fatal to the great river, Eridanus, which the sad sisters of Phaethon often, With tears, sprinkling the broad sea, sang with lamenting voice. This star rises at Rome with the sign of Aquarius, and sets with the extreme parts of Pisces. 67. ERIGONE, according to Manilius, is the sign Virgo in the sky, the sixth from Aries; see its place. 68. ERRATICÆ stars, or Errones, are called the planets, especially the five: Saturn, Jupiter, Mars, Venus, and Mercury; for the luminaries enjoy a nobler title. They are called, I say, errones, errantes, and erraticæ, in distinction from the other stars, which are enclosed in the firmament under various figures. For these, although by the motion of the primum mobile they are carried from East to West, and also by the proper motion of the firmament itself (though very slow, and quite imperceptible), from west to east; nevertheless, because they themselves are not moved in any way, they always remain in the same place in the firmament, always keep the same distance from one another and from the poles of the Zodiac; therefore they have received the name of fixed stars: whereas the planets, on the contrary, because of each one’s peculiar motion, and because of the different relations among themselves, which they always change by wandering, are rightly called erratic stars. 69. ETESIÆ, as in Pliny, Strabo, and others, are certain annual winds, recurring at fixed seasons, which are also called Prodromi, and, according to the diversity of places, blow steadily from some quarter of the sky and at a certain time. Strabo calls them subsolani. Usually, however, they blow in summer, beginning around the rising of the Dog Star, in the morning after sunrise, and they last for nearly forty days, always with the highest pleasantness and salubrity of the air and serenity. In Italy they blow from the north, in Spain from the equinoctial east, in the other parts of the world from the south, and at night they have always been accustomed to cease. Yet they are of a different kind: for among Western peoples they are usually from the north, and are accustomed to change into western winds as far as the Favonius. Among the inhabitants of eastern regions, however, they blow

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MATHEMATICVM. 181 item à Septentrione, & mutantur in Orientales vsque ad sub- solanum. Sunt & alij venti anniuersarij stantes hyberno tem- pore, hoc est post brumam diebus circiter 70. qui sunt æstiuis exiliores. Tandem sunt & alij, qui in Vere exsufflant circà velpertinum Arcturi exortum, omnium suauissimi, ac saluberrimi, qui posteà in Fauonium conuertuntur: & hi quidem ab aduentu hirundinum, aliarumque auicularum circà id tem- pus, quo ipsi spirare solent, Ornishias, & Chelidonius appel- lantur. De quibus vide Plin. lib. 37. cap. 5. & alibi sæpè. 70. ETEROSCII. Vide Heteroscij. 71. EVDÆMON Græcè idem sonat ac Latinè Bonus genius. Sic dicta est ab Astrologis vndecima domus ab Horoscopo succedens angulo Medij cæli ob felicitatem eius significatorum: significat enim amicos, accessiones gratiâ ipsorum, necessitudines cum Principibus viris, consequutionem rerum speratarum &c. Gaudet in ea Iupiter, & habet tria suffragia fortitudinis. Respicio de sexili ascendens: verùm in secunda eius 72. medietate, quæ accedit ad duodecimam ob semiquadratum ad dictum ascendens aduertit Titus, non esse idoneam ad prærogatiuam hilegialem luminari, siue alteri significatori in ea existenti communicandam: Ideoque in hoc munere est inferior nona, etsi alioqui hæc sit vna ex cadentibus. Nam ibi constitutus significator respicit de trino ascendens, qui est radius perfectæ familiaritatis. EVEHENS, seu Attollens dicitur apud Astronomos caput 73. Draconis, seu nodus Lunatis intersectionis orbitæ Lunæ cum Ecliptica, quam ad Septentrionem declinat, quia videlicet inde Luna incipit attolli, & eleuari à parte australi ad borealem. Vnde nodus ipse boreus non ab re dictus est attollens, & euehens: sicut è contrà nodus austrinus & cauda Draconis dicitur deprimens, & humilians, quia deprimere videtur Lunam ad partes australes. Bt hi quidem nodi, vt alibi oblectuatum est, nedum in Luna, sed & in reliquis planeris excepto Sole attenduntur: de quibus eadem ratio ac de Luna, cùm non incedant per Eclipticam, sed per propriam quisque orbitam, qua modò ad Boream, modò inclinant ad Austrum. EVGONIVS Græcè, Latinè rectangulus Figura quæcumque 74. apud Geometras rectis angulis constans. Sicut etiam EVGRAMMVS, & Euthigrammus dicitur figura Geometrica 75. rectis lineis constans: ab Eucho quod rectum, & Grammum quod apud Græcos lineam significat, deductum. EVRVS Græcè, Latinè Vol urus dicitur ventus adjacens sub- 77. solâno, & illi collateralis ad ortum brumalem: sic dictus à volando, quod altè spiret, & ferè vulturis volatum imitari M iij

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MATHEMATICUM. 181 likewise from the North, and they are changed into eastern winds as far as the south-east. There are also other annual winds, lasting in the winter season, that is, after the winter solstice for about 70 days, which are weaker than the summer winds. Finally, there are also others which blow in spring around the evening rising of Arcturus, the most gentle and healthful of all, which afterward turn into the Favonius: and these, indeed, from the arrival of swallows and other little birds at about the time when they are accustomed to blow, are called Ornithias and Chelidonius. For these see Plin. lib. 37. cap. 5. and elsewhere often. 70. HETEROSCII. See Heteroscij. 71. EUDÆMON in Greek means the same as in Latin Bonus genius. Thus the eleventh house succeeding the Horoscope, according to astrologers, is so called from the angle of the Midheaven because of the happiness of its significations: for it signifies friends, acquisitions through them, relations with princes and great men, the attainment of hoped-for things, etc. Jupiter rejoices in it, and has three testimonies of strength. It looks to the rising sextile: but in its second half, which approaches the twelfth because of the semiquadrate to the said ascendant, Titus notes that it is not suitable for the hilegial prerogative to be communicated to the luminary or to another significator present there. Therefore in this function the ninth is inferior, although otherwise this is one of the cadent houses. For the significator placed there looks by trine to the ascendant, which is the ray of perfect familiarity. EVEHENS, or Attollens, is called by astronomers the head of the Dragon, or the node of the lunar intersection of the Moon’s orbit with the Ecliptic, which inclines toward the North, because from there the Moon begins to be lifted up and raised from the southern part to the northern. Hence that node itself is not wrongly called the northern Attollens and Evehens; just as, on the contrary, the southern node and the Dragon’s tail is called Deprimens and Humilians, because it seems to depress the Moon toward the southern parts. And these nodes, as has elsewhere been noted, are considered not only in the Moon, but also in the other planets except the Sun; concerning which the same reasoning holds as for the Moon, since they do not move along the Ecliptic, but each along its own orbit, by which they incline now toward the North, now toward the South. EVGONIVS in Greek, in Latin Rectangular. Any figure among geometers consisting of right angles. Likewise EVGRAMMUS, and Euthigrammus, is called a geometrical figure consisting of straight lines, derived from Eucho, meaning straight, and Grammum, which among the Greeks signifies a line. EVRVS in Greek, in Latin Volurus, is called the wind adjacent to the south-east, and collateral to it toward the winter sunrise; so called from flying, because it blows high and is almost an imitation of a vulture’s flight. M iij

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182 LEXICON videatur. Est de natura sua calidus, & siccus: tamen ob de- flexionem ad austrum acquirit aliquid humiditatis. Imò, & quandoque in ipsius austri naturam convertitur. Idemque initio siccus, sub finem verò plerumque humidus, nubifer, perturbans aërem, gignensque repentinas mutationes, & tonitrua. Sed id in eo bonum, quod si à serena cæli parte flare incipiat, non multùm temporis durat. De hoc vento sic cautum reliquit Columella lib. 5 cap. 5. Cùm plerumque canicula tempore quædam partes esus regionis sic infestansur Euro, quem incola vuitur- num appellant, vt nisi teguminibus vistes opacentur veluti balitio flammeo fructus vrantur. Hinc Meseurus, Ipoeurus, venti minores illum circà stipantes, primus quidem inclinans ad austrum, secundus ad subsolanum: de quibus suo loco. Solet quandoque sumi pro ipso vento cardinali, cui adjacet. 77. EVRYTHMIA est modus qui attendiur in Architectura ex Geometriæ præceptis, facitque vt in partium composizione in ordine ad aliquod opus, aut ædificium, venustas quæ est in ipsis partibus seorsim seruetur; vt cùm membra operis conuenientia sunt altitudinis ad latitudinem, latitudinis ad longitudinem. Vide Vitruu. lib. 1. c. 2. & lib. 6. c. 2. 78. EXAGONVM, Græcè dicitur figura sex angulis constans Hinc ab Astronomis accipitur sæpè pro radio sextili, qui proijcitur à sexta parte circuli. 79. EXALTATIO apud Astronomos est quædam dignitas essentialis planetarum in Zodiaci partibus proximè accedens ad jus domicilij; in quibus planeta repertus perinde est ac si princeps foret in sua Regia: alio nomine dicitur Altitudo. Iulius Firmicus, & alij volunt, planetam maiorem dignitatem, & fortitudinem obtinere in Exaltatione, quàm in domicilio suo. Assimilatur enim, inquit, viro existenti in regno suo, & in gloria sua, cùm alioqui planeta existens in domo sua comparetur viro existenti in dominatione sua. Verum id, meo judicio, non benè deductum, quia cæteris paribus, semper plus juris haber vir in sua domo, quàm rex in suo regno, cùm id natura habeat, hoc autem ex populorum consensu: & alioqui vulgare est adagium, vnumquamque in domo sua regem esse. Cæterùm Ptolemæus, vt alibi obseruauimus, vult planetam exaltari in toto signo, Arabes verò in certa parte signi, Hermes in signi medieate; quod quidem ratione non vacat, nam in medio consistit maior fortitudo, & maior naturæ conformitas, quàm in principio, aut fine: vnde rationabile est, vt ibi planetæ magis, magisque exaltetur, ac validioribus viribus polleat. At enim rationes, quibus Arabes, præsertim Albuinatar tract. Sui Introductorij differ. 7. probare nituntur conue-

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182 LEXICON appears. It is by nature hot and dry; yet, by reason of its turning toward the south, it acquires some humidity. Indeed, at times it is even changed into the nature of the south wind itself. At the beginning it is dry, but toward the end it is usually humid, cloud-bearing, disturbing the air, and producing sudden changes and thunder. But this is good in it: if it begins to blow from the clear part of the sky, it does not last long. Concerning this wind Columella has left this caution, lib. 5 cap. 5: “When, in the dog days, certain parts of this region are infested by the Euro, which the inhabitants call the Vulturnus, unless the vines are shaded, the fruits are burned as if by a fiery blast.” Hence the Meseurus and Ipoeurus, lesser winds, accompany it on either side, the first inclining toward the south, the second toward the east-southeast: of these in their proper place. It is sometimes used for the very cardinal wind to which it is adjacent. 77. EVRYTHMIA is a mode observed in Architecture from the precepts of Geometry, and it makes it so that in the composition of parts with respect to some work or building, that beauty which is in the parts themselves separately may be preserved; as when the members of a work are proportionate in height to breadth, and breadth to length. See Vitruvius lib. 1 c. 2 and lib. 6 c. 2. 78. EXAGONVM, in Greek, is a figure consisting of six angles. Hence it is often taken by astronomers for the sextile ray, which is projected from the sixth part of the circle. 79. EXALTATIO among astronomers is a certain essential dignity of the planets in the parts of the Zodiac, approaching nearest to the right of domicile; in which a planet found there is as if it were a prince in his own royal palace: by another name it is called Altitude. Julius Firmicus and others hold that a planet obtains greater dignity and strength in Exaltation than in its domicile. For, he says, it is likened to a man existing in his own kingdom and in his own glory, whereas a planet existing in its own house is compared to a man existing in his own dominion. But this, in my judgment, is not well drawn, because all other things being equal, a man always has more right in his own house than a king in his own kingdom, since the former belongs to nature, the latter to the consent of peoples; and besides, there is the common saying that every man is king in his own house. Moreover, Ptolemy, as we have noted elsewhere, holds that a planet is exalted in the whole sign, whereas the Arabs in a certain part of the sign, Hermes in the middle of the sign; and this is not without reason, for greater strength and greater conformity with nature consist in the middle than in the beginning or end: whence it is reasonable that there the planet is more and more exalted, and possesses stronger powers. But the arguments by which the Arabs, especially Albuinatar in tract. Sui Introductorij differ. 7, endeavor to prove conve-

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MATHEMATICVM. 173 nientiam assignationis certorum exaltationis graduum, friuolæ admodum sunt, & non magni momenti. Ait enim Albumasar, ideò gradus 15. Cancri ponitur Exaltatio Iouis, quia hic gradus fuit ascendens in creatione mundi, & secundùm quod alij gradus exaltationum aspiciebant ascendens, ponit eos pro exaltatione aliorum planetarum, prout magis videbantur conuenire cum natura aspectus. Exempli gratiâ: Ex quo in prima mundi creatione fuit ascendens 15 gr. Cancri in medio cæli erant 19. Arieris: ideò conueniens erat, vt in 19. Arieris foret exaltatio Solis: & similiter discurrit de alijs planetis pro natura ipsorum, & positione signorum in apicibus domorum, quæ respiciebant aliquo radio ascendens, aut medium cæli. Vtcumque sit id forte obseruare superuacaneum non erit. Ideò hic non modò signa, sed & præcisas gradus signorum ponemus, in quibus volebant Arabes vnumquemque planetam potissimùm exaltari. Igitur exaltatio Solis est in Ariere, maximè verò in gr. 19. Lunæ in Tauro, potissimum in tertio gradu. Saturni in Libra, sed præsertim in gr. 21. Iouis in Cancro, sed vt dictum est in gr. 15. Martis in Capricorno, at specialiùs in gr. 27. Veneris in Piscibus, at ex Arabum placiris in gr. itidem 27. Tandem Mercurij exaltario est in Virgine, signatè verò in gr. 15. Rationem exaltationum affert Ptolemæus in cap. 17. lib. 1. Quadrup. quam nos supra in V. Altitudo tetigimus. Verum aliam pulchram, nec contemnendam profert Almansor antiquissimus astrologus in Aphorismis ad regem Saracenorum directis. Sic enim ait in verbo secundo. Cususquam planetarum septem exalatio in illo loco esse dicitur, in quo substantialiter putitur ab alio contrarium, velut Sol in Ariete, qui Saturni casus est. Sol enim habes claritatem, Saturnus tenebrositatem: Et vt Iupiter in Cancro, in quo Mars cadit, quorum alter cupit justitiam, alter vero injustitiam, Et sic Mercurius in Virgine, quis casus est Veneris: alter namque significat scientiam, Et philosophiam, altera verò causat alacritis, Et quidquid est saporiferum corpors. Hæc ille. EXASTERON, Antonomasticè dictum est apud Græcos sidus 81. in cælo valdè conspicuum, vulgo Pleiades, ac Vergilæ, quæ etsi reuera septeni sint, nihilominus ramen sex sunt conspicuæ, & inuicem appropinquare, vt noras etiam D. Thomas in cap. 38. Iobi. Quare aurem sepem dicantur, cùm ramen sex tantùm sint. Cicero in Arari Phænomenon ad vulgi imperitiam refert: sic enim canit. Paruas Vergilias tenui cum luce videbis; Ha septem vulgò perhibentur more vesusto Stella, cernuntur verò sex vndique parua M iiij

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The arguments for assigning certain exaltation degrees are very frivolous and of little importance. For Albumasar says that the 15th degree of Cancer is placed as the exaltation of Jupiter because this degree was rising at the creation of the world, and, according to the way the other degrees of the exaltations looked toward the ascendant, he assigned them as the exaltations of the other planets, as seemed more fitting to the nature of the aspects. For example: since at the first creation of the world the 15th degree of Cancer was rising, 19 degrees of Aries were in the midheaven; therefore it was fitting that the exaltation of the Sun should be in the 19th of Aries. And in the same way he proceeds concerning the other planets, according to their nature and the position of the signs at the cusps of the houses, which looked by some ray toward the ascendant or the midheaven. However that may be, it will perhaps not be superfluous to observe this. Therefore here we shall set down not only the signs, but also the precise degrees of the signs in which the Arabs wished each planet to be chiefly exalted. Thus the exaltation of the Sun is in Aries, but especially in the 19th degree; of the Moon in Taurus, chiefly in the 3rd degree; of Saturn in Libra, but especially in the 21st degree; of Jupiter in Cancer, but as has been said, in the 15th degree; of Mars in Capricorn, but more especially in the 27th degree; of Venus in Pisces, but according to the opinion of the Arabs likewise in the 27th degree. Finally, the exaltation of Mercury is in Virgo, and specifically in the 15th degree. Ptolemy gives the reason for the exaltations in chapter 17 of book 1 of the Quadrup., which we touched on above under V. Altitudo. But Almansor, the very ancient astrologer, presents another, beautiful, and not to be despised reason in the Aphorisms addressed to the king of the Saracens. For thus he says in the second saying: the exaltation of any of the seven planets is said to be in that place where, in substance, it is thought to be opposed by another, as the Sun in Aries, which is the place of Saturn’s fall. For the Sun has brightness, Saturn darkness. And Jupiter in Cancer, in which Mars falls, of which the one desires justice, the other injustice. And so Mercury in Virgo, which is the fall of Venus: for the one signifies knowledge and philosophy, the other, however, causes cheerfulness and whatever is savory to the body. Thus he. EXASTERON, spoken antonomastically among the Greeks, is a star very conspicuous in the sky, commonly called the Pleiades, and Vergiliae; although in truth they are seven, nevertheless only six are conspicuous and close together, as you may note also from St. Thomas in chapter 38 of Job. Hence the question why they are said to be seven when in truth only six are. Cicero in his Aratea attributes this to the ignorance of the common people; for thus he sings: You will see the little Vergiliae with faint light; they are commonly said, in the old custom, to be seven stars, but in fact six little ones are seen on every side. M iiij

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184 LEXICON At non interijsse putari convenit vnam: Sed frustra temero à vuiigi, rassone sine vlla Septem dicier, vt veteres statuere poëta Æterno, cunctus auo qui nomine dignant. Et Ouid. lib. 4. Facto. Pleiades incipiunt humeros reuocare paternos, Quæ septem dici, sex tamen esse solent. At non temerè id factum existimandum est, necèò tantum quia à Poëtarum fabulis mutuatæ sunt nomen, à Pleiadibus inquam septem sotoribus filiabus Atlantis, & Pleionis nymphæ: neque enim sapientissimis illis Astronomis alia nominadeesant, quibus, siue ex fabulis, siue aliunde, numero stellis correspondente illas indigitarent, sed verè dicendum est illas septem ominò esse imò & plures, vt modò ex Galilæi Nuncio sideteo apud omnes in confesso est. Sex tamen communiter numerantur, quia septima exilior est, & obscurior, atque adeo non omitum si negligatur: quamquam non desunt qui dicant illam renerà statis temporibus conspicuam fieri, ac postmodum occultari, vt videre est apud Ricciolum in suo Almagesto, necnon Petauium in Vranologio, & nos dicemus in V. Phanomenon. 82. EXCETRA, dicta est ab aliquibus Hydra, fidus in cælo ad Austrum declinans, sumpto nomine ab Hydra Lernea, cui cæso vno capite, tria iterùm maiori impetu excreseebant. Eius significata vide suo loco in V. Hydra. 83. EXERESTIMVS Cicetoni, alijtque audit dies ille eximendus à mense Lunari ad hoc, vt annus Solis cum Lunari congtuat, redeantque lunationes, vt erant priùs. Quandoquidem, cum singulis vndeuiginti annis solaribus reincidat annus lunaris cum solati: ita tamen vt Luna hora vna, & semisse præcedat; hinc sit, vt in annis 76. ipsa antieper per horas sex, & in annis 312. & sex mensibus antieper vnum integrum diem, vt dictum est in VV. Annus Metonicus, & Callippica Periodus. Hic ergo dies semper eum concurrit Epacta cum aureo numero 19. eximendus est à mense lunari 30. dierum, ad hoc vt probè correspondeat solari periodo, & ordo Epactarum, & aurei numeri recurrentium ad Lunæ ætatem indagandam minimè peruertatur. Et hic dies exeresimus dictus est. Quomodo autem compensari possit iste excessus; ita vt semper lunationes ad amussim respondeant cum recursu Solis: Vide apud Io. Lucidum Samotheum in Epitome Emendationis Calendarij prope finem. 84. EXHALATIO. Vide in V. Meteora. 85. EXHALMA Græcè, Latinè exultatio dici potest. Estque (vt testatur Valla) cum præcipui Modetatores, Sol videlicet, Lu-

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184 LEXICON It is agreed that one should think that one has not perished: But it is futile to say rashly, without any reason, that they are seven, as the ancient poets established, who by name are deemed everlasting, all of a single age. And Ovid, book 4. Facto. The Pleiades begin to draw back their paternal shoulders, which are said to be seven, yet are usually six. But it must not be thought that this was done without reason, nor merely because the name was borrowed from the fables of the poets, that is, from the Pleiades, the seven sisters, daughters of Atlas and the nymph Pleione: for those wisest Astronomers lacked no other names by which, whether from fables or from elsewhere, they might designate them according to the number of the stars corresponding to them; but truly it must be said that they are indeed seven in all, nay even more, as now from Galileo’s Messenger of the heavens it is agreed among all. Yet they are commonly counted as six, because the seventh is dimmer and more obscure, and therefore not to be included if it is neglected; although there are not wanting those who say that it indeed becomes visible at fixed times, and afterwards is hidden, as may be seen in Riccioli in his Almagest, as well as Petavius in Uranologia, and we shall speak of it in V. Phanomenon. 82. EXCETRA, was called by some Hydra, a constellation in the sky inclining toward the south, taking its name from the Lernaean Hydra, of which, when one head had been cut off, three more grew again with greater force. See its meaning in its proper place in V. Hydra. 83. EXERESTIMVS Ciceto, and by others that day which must be taken out of the lunar month for this purpose, namely, that the solar year may agree with the lunar, and the lunations return as they were before. Since, when every nineteenth solar year the lunar year falls back in step with the solar: yet so that the Moon goes ahead by one hour and a half; hence it comes about that in 76 years she is ahead by six hours, and in 312 years and six months ahead by one whole day, as was said in the entries Annus Metonicus and Callippica Periodus. This day therefore, since it always coincides, with Epact and with the golden number 19, must be taken out of the lunar month of 30 days, so that it may fit the solar period properly, and the order of the Epacts and of the golden numbers, which recur for investigating the age of the Moon, may not be at all disturbed. And this day is called exeresimus. But how this excess may be compensated, so that the lunations may always correspond exactly with the course of the Sun: see in Io. Lucidus Samotheus in the Epitome of the Reform of the Calendar near the end. 84. EXHALATIO. See in V. Meteora. 85. EXHALMA in Greek may be called exultatio in Latin. And it is (as Valla testifies) when the chief Rulers, that is, the Sun, Lu-

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MATHEMATICVM. 185 na, & pars fortunæ per suum naturalem incessum, è signo in quo etant in radice natuitatis, transeunt in aliud subsequens. FA 1. Facies, vt aliàs obsetuatum est, apud Astronomos bifariam vsurparur; & pro decanatu, hoc est terria quaque parte signorum, quarum dominium antiqui planetis per ordinem distribuebant (vnde & dicitur prima facies Arietis, secunda facies Tauri &c.) & etiam pro persona, seu habitudine planetarum ad luminaria, qualis est domorum ipsorum ad domos istorum: quæ communiter vocatur Almugæa: qua de re satis in loco dictum. 2. Falco dictum est ab aliquibus sidus in cælo, quod nos communiter Lyram, Vulturem Cadentem, Fidiculam nominamus. Vide paulo inferiùs. 3. FAMILIARITAS apud Astronomos est conuenientia & propotrio duorum siderum inter se, vnde contrahunt, quamdam nescio quam, tum erga se mutuo, tum potissimum erga subjectum in quod agunt præsertim inferiora isthæc alterandi potentiam per proportionalem luminum distantiam, ac lucis intentionem, quæ per accessum, aut recessum sidetum ad inuicem, vel etiam ad mundi catdines fiat. Porto, quoniam duplex morus, & duplex respectus siderum est, aliet in Zodiaco, quem proprio motu successum acquitunt, incedendo à præcedentibus ad consequentia signa; aliter circa mundum, quo motu raptus integro die rotantur ab Oriente in Occidentem per Medium, & Imum cæli, consequens est, vt duplex etiam genus familiaritarum concipiatur, quas sidera contrahunt per duplicem motum quem habent, & in Zodiaco, & in mundo. Quod sanè Prolemæus ipse non obscurè insinuavit. Primò in exordio sui Quadripartiti sic inquiens. Duo sunt Syre quibus peruenitur ad astrolgicas prædictions: Vnum quod primum, & loco est, & potestate, quo Solis, Lunæ, & stelarum motuum configurationes, tum erga se, tum terram deprehendimus: alterum & Ecce quomodo Ptolemæus duplex genus configurationum quas contrahere possunt planetæ, agnoscir, & inter se, hoc est in Zodiaco, & circa mundum: ut etiam clarius explicat in Almagesto lib. 8. cap. 4. in hæc verba. Relinquitur jam de aspectibus ipsarum (eraticarum scilicet) conscribere: horum exstur exceptis illis, qui inter se fiunt, atque stabiles habentur, sicut quando in recta linea, vel in aspectu triangularo, alijque huiusmodi quidam ad solos planetas, & Solem, & Lunam, aut Zodiaco partes conspicuntur, quidam ad terram tantummodo;

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na, and part of fortune by its natural course passes from the sign in which it stood in the root of nativity into another following one. FA 1. Face, as has been noted elsewhere, is used among the astronomers in two ways: both for a decan, that is, for the third part of the signs, whose rulership the ancients distributed among the planets in order (whence it is also called the first face of Aries, the second face of Taurus, etc.); and also for the relation, or habit, of the planets to the lights, such as that of their houses to the houses of those: this is commonly called almugäa; concerning which enough has been said in its place. 2. Falco has been called by some the star in the sky which we commonly call Lyra, Vulture Cadens, Fidicula. See a little further below. 3. FAMILIARITY among astronomers is the agreement and propriety of two stars with respect to one another, from which they acquire some—I know not what—quality, both toward each other and especially toward the subject on which they act, particularly those inferior ones, altering power by the proportional distance of the lights and the intensity of the light, which comes about through the approach or withdrawal of the stars toward one another, or even toward the quarters of the world. Moreover, since there is a double motion and a double respect of the stars, one in the Zodiac, which by their own motion they attain in succession, proceeding from the preceding signs to the following ones; another around the world, by which motion, carried along, they revolve in a complete day from East to West through the Midheaven and the Imum Coeli, it follows that a double kind of familiarities is also conceived, which the stars contract through the twofold motion they have, both in the Zodiac and in the world. This indeed Ptolemy himself indicated not obscurely. First, in the beginning of his Quadripartitum, saying thus: There are two things by which one arrives at astrological predictions: one, which is first and foremost, whereby we apprehend the configurations of the motions of the Sun, Moon, and stars, both among themselves and toward the earth; the other... And behold how Ptolemy acknowledges the double kind of configurations which the planets can contract, among themselves, that is, in the Zodiac, and around the world: as he explains even more clearly in the Almagest, book 8, chapter 4, in these words: It remains now to write about the aspects of the stars themselves (that is, the wandering ones): among these are excepted those which occur among themselves and are regarded as stable, as when they are in a straight line or in a triangular aspect, and other such things; some are observed only with respect to the planets and the Sun and Moon, or parts of the Zodiac; some with respect to the earth alone;

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186 LEXICON quidam ad terram simul, & ad erraticas stellas, & ad Solem Lunam vel partes Zodiaci. Datis igitur his duobus familiaritatum generibus, statim elucet, quibus modis configurari possint planetæ, quæue sint harum configurationum differentiæ, < 5.> quas ingeniosè hausit Keplerus ex harmonicis chordarum consonantijs, quæ cùm sint octo, vnìsona, tertia minor, tertia maior, quarta, quinta, sexta minor, sexta maior, & octaua (vt experiri est in chorda subtensa, quæ in dictis tantum distantijs consonantiam habet) consequenter, tor etiam sint, necesse est, familiaritatum differentiæ quas possunt contrahere ad inuicem sidera in certa, ac determinata distantia, nempe Conjunctio, Sextilis, Quintilis, Quadratus, Trinus, Sesquiquadratus, Biquintilis, & Oppositio. Et quoniam radij siderum quidam sunt à centro sideris producti vsque ad oppositionem, quæ est diametralis, profectò excepta conjunctione, & oppositione, omnes isti radij cùm hinc inde ad fidus proijciantur, & à dextris, & à sinistris, duplices sunt, ac proinde vnà cum illis duobus quatuordecim genera familiaritatum inuenientur: quibus si adjungatur etiam duplex semiquadratus alter à dextris, & alter à sinistris, qui cùm participet rationem quadrati, in morbis habet vim indicandi de futura crisi, vt ego sæpiùs obseruaui, & testatur etiam Argol. de diebus criticis; vtiqve sexdecim omninò erunt, & constituent figutam sexdecim laterum: de qua sermo est in Centiloquio propos. 60. 6. Præterea adsunt antiscia, seu vt alij vocant paralleli tam primarij, quàm secundarij, tam in Zodiaco, quàm in Mundo; quæ cùm sit species quædam familiaritatis resultans ex æquidistantia, ac proinde pati astrorum potentia, conuenienter reducuntur ad conjunctionem, si ea quidem sint eiusdem declinationis, aut hemisphærij, atque ad oppositionem si diuersæ. Sed de hac re vide Titum in Cælesti Philosophia lib 2. cap. 2. nosque fusiùs agemus in V. Parallelis. 7. Favonius, ventus vnus ex quatuor Cardinalibus spirans ab occasu æquinoctiali, directè oppositus subsolano, sic dictus à favendo, quod cunctis faueat, vel potiùs à fouendo, quod omnia foueat: quippe qui temperie quadam caloris, & humidi cedit cunctis animaribus opportunus, ac salutatis. Vnde & Plinius eum Genitalem mundi spiritum nominat, quo planca hyberno frigore adusta remiuscunt, animalia recreantur, & Venere m sobolis desiderio appertunt, & alibi, eo flante equas in Lusitania concipere testatur. Hinc jure à Græcis Zephyrus dicitur, hoc est vitam afferens. Spirar porissimùm in Italia æstatis tempore lenissimè post Meridiem, adducens serenitatem ma-

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186 LEXICON indeed to the earth itself, and to the wandering stars, and to the Sun, Moon, or parts of the Zodiac. These two kinds of familiarities being thus given, it immediately becomes clear by what modes the planets can be configured, and what the differences of these configurations are, <5.> which Kepler ingeniously drew from the harmonic consonances of strings, which, since there are eight of them—unison, minor third, major third, fourth, fifth, minor sixth, major sixth, and octave (as one may test in a stretched string, which has consonance only at the said distances)—it follows that there must also be the differences of familiarities which the stars can contract with one another at a certain and determinate distance, namely Conjunction, Sextile, Quintile, Square, Trine, Sesquiquadrate, Biquintile, and Opposition. And since some rays of the stars are projected from the center of the star up to the opposition, which is diametral, certainly, except for conjunction and opposition, all these rays, when projected on both sides toward the star, both to the right and to the left, are double; and therefore, together with those two, fourteen kinds of familiarities will be found: to which, if there is also added a double semi-square, one on the right and one on the left, which, since it participates in the nature of the square, in diseases has the power of indicating a future crisis, as I have often observed, and Argol also testifies in his book on critical days; there will in all be sixteen, and they will constitute a figure of sixteen sides: concerning which there is discussion in the Centiloquium, proposition 60. 6. Moreover, there are antiscia, or as others call them, parallels, both primary and secondary, both in the Zodiac and in the World; which, since they are a certain kind of familiarity resulting from equidistance, and therefore from the reciprocal action of the stars, are suitably reduced to conjunction if they are of the same declination or hemisphere, and to opposition if they are different. But on this matter see Titus in Celestial Philosophy, book 2, chapter 2; and we shall discuss it more fully in V. Parallels. 7. Favonius, one of the four cardinal winds, blowing from the west at the equinoctial setting, directly opposite to Subsolanus, so called from fovendo, because he favors all, or rather from fouendo, because he warms and cherishes all: for with a certain tempering of heat and moisture he is beneficial and salutary to all animals. Hence Pliny calls him the genial spirit of the world, by which plants scorched by winter cold revive, animals are refreshed, and with desire for offspring are stirred by Venus; and elsewhere he testifies that, with that wind blowing, mares in Lusitania conceive. Hence rightly among the Greeks he is called Zephyrus, that is, the bringer of life. He blows most pleasantly in Italy in the summer season, very gently after midday, bringing serenity to the sea-

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M A T H E M A T I C V M. 187 ximam, cum non minori corporum salubritate. Hyeme verò niues, & pluuias generat, & quandoque etiam repentinis flatibus matia concurit, corporibusque humorum ingerit commotionem. F E FERA Lupus, bestia Centauri &c. in Tabulis Persicis Bride-8. mif, sidus in cælo ad australem plagam sub Centauto, constans stellis seu 19. vt vult Ptolemæus, seu 20. vt obseruasse testatur Keplerus, & Baierus, omnibus ferè de natura Saturni, & parum Martis; quarum præcipuæ duæ in posteriori pedes, tertiæ magnitudinis. Ex in horoscopo semper infaustæ sunt, ac malorum nunciæ, licet in nostro hemisphærio non oriantur, nisi tantùm duæ posiræ in extremo pedis sinistri, idque fiat ad modicum tempus & parùm suprà horizontem attollanur. Oriuntur enim Romæ cum gr. 1. & 12. Sagittatij, occiduntque cum gr. 7. & 25. Virginis. FERALIA, signa sunt quæ ferinam speciem referunt, qualia 9. sunt Leo, & vltima pars Sagittarij, quibus annumerati possunt & sidera extrà Zodiacum, vt Lupus, Centaurus, &c. Quibus non ab re hoc nomen inditum, seu potiùs adjecta ferarum forma; quia videlicet nescio quid cum illis habent affine: bestiis illis præsunt, in hominum genituris aut feram edi, aut ferinam naturam ingerunt; præsertim si luminatia in ipsis reperiantur, & in cardinibus duo malesici, vt notat Ptolemæus lib. 3. cap. 8. FERALIS, apud Astronomos dicitur planeta, quando fuerit 10. in loco, vbi nullam cum reliquis familiaritatem habet: quod quidem maximum est detrimentum, & potissimè artenditur in Luna, quæ proinde in eo casu appellatur Agrestis, cursu vacua, &c. FERDARIÆ, Vide Fridaria. 11. F I FICARES, apud Babylonios nuncupatur Cepheus, constellatio 12. in firmamento prope Bootem, quod vocabulum apud nos idem sonat ac succensus. FIDICULA Lyra, Vultur cadens, &c. dicitur sidus in cælo 13. ad borealem plagam ferè verticalis Italiæ, constans apud Ptolemæum stellis tantummodò decem, quot videlicet chordæ sunt in Lyra, seu Spalterio decachordo. At verò Keplerus in eo considerat stellas 11. & Baietus adhuc 13 quæ omnes sunt de natura Veneris, & Mercurij. Inser has præcipua est quæ proprio nomine apud Arabes appellatur Vvega, Vagiah, & Brinek, seu Brinett, fixarum omnium (excepto Sitio) maxima, & fulgentissima, existens nunc in gr. 11. Capricorni cum declin-

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M A T H E M A T I C V M. 187 At its maximum, with no less benefit to bodies. In winter however it produces snow and rain, and sometimes even by sudden blasts it stirs up the sky, and brings a commotion to the humors of bodies. F E FERA, the Wolf, the Centaur beast, etc., in the Persian Tables Bride-8. mif, a star in the sky toward the southern part, under Centaurus, consisting of stars, either 19, as Ptolemy says, or 20, as Kepler and Bayer testify from observation, almost all of the nature of Saturn, and partly of Mars; among which the chief two are in the rear feet, the third magnitude. In a horoscope they are always unlucky, and heralds of evil, although in our hemisphere they do not rise except only the two placed at the end of the left foot, and that only for a short time and a little above the horizon. They rise at Rome with 1 and 12 degrees of Sagittarius, and set with 7 and 25 degrees of Virgo. FERALIA are signs which bear a wild appearance, such as the 9th are Leo and the last part of Sagittarius, to which may be added also the stars outside the Zodiac, such as Lupus, Centaurus, etc. It is not inappropriate that this name was given to them, or rather that the form of beasts was attached to them; because, namely, they have something akin to them: they preside over those beasts, and in men’s nativities either they produce a savage offspring, or impart a wild nature; especially if the luminaries are found in them, and two malefics in the angles, as Ptolemy notes lib. 3, cap. 8. FERALIS, among astronomers, a planet is said to be when it is in a place where it has no familiarity with the rest: which indeed is a great detriment, and is considered especially in the Moon, which therefore in that case is called Rustic, void of course, etc. FERDARIAE, see Fridaria. 11. F I FICARES, among the Babylonians is the name of Cepheus, a constellation in the firmament near Bootes, a word which among us means the same as kindled. FIDICULA, Lyra, the Falling Eagle, etc., is called a star in the sky toward the northern part, almost vertical to Italy, consisting according to Ptolemy of only ten stars, namely as many as there are strings in the Lyra, or ten-stringed psaltery. But Kepler considers in it 11 stars, and Bayer still 13, all of which are of the nature of Venus and Mercury. Among these the chief one is that which by its own name among the Arabs is called Vvega, Vagiah, and Brinek, or Brinett, the largest and brightest of all fixed stars (except Sirius), now being in 11 degrees of Capricorn with declin-

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188 LEXICON natione boreali, grad. 35. qui fir, vt jam modo sit verticalis Siciliæ, quod maximè aduerrendum. Ea partiliter in secunda domo, aut cum loue, Venere, & parte fortunæ reperta immensas diuitias pollicetur; sicut etiam in medio cæli magnam fortunam in honoribus, atque in opificio. Vide amplius eius decreta in horoscopo sub V. Lyra. 14. FIGVRA ex Euclide lib. 1. d. 14. definitur esse quantitas, quæ sub aliquo, vel aliquibus terminis clauditur. Quantitas enim secundum variam extemorum positionem, vatiam etiam dicitur figuram subire, etsi alioqui in seipsa inuariata remaneat: vnde intelligitur aduenire quantitati jam in suo genere constitutæ, quoniam illam modificat, facitque vt extensio parrium, quam alias ex se haber quantitas, seruet aliquem ordinem in partibus ritè dispositis, vnde se habet per modum qualitatis afficiens illas, ac superficiei terminum dicens. Hinc figura angularis, lateralis, rectilinea, curuilinea, triangularis, quadrangularis, solida, plana &c. de quibus suo loco. 15. FIGVRÆ Isoperimentra apud Geometras sunt duæ, vel plures figutæ, quæ ad inuicem comparatæ perimetros, id est circumferentias habent æquales. Deriatur enim hoc vocabulum à Græco isos quod est aquale; peri quod est circum & Metros quod est Mensura: quasi figutæ æqualium circumdantium mensuratum. Hinc figuræ omnes, quæ æquales ambitus continent Isoperimetra sunt. Vt quadratum sex pedes habens in ambitu, dicitur Isperimentum triangulo siue rectilineo, siue curuilineo, siue mixto, quod pariter sex pedes habeat in circuitu: ita ut quatuor lineæ quadrati ambitum constituentes, si in vnam, eandemque lineam aprentur, inueniantur æquales tribus rectis lineis trianguli, aut lateribus omnibus cuiuscunque figuræ in rectum quoque & continuum positis. Plura qui volet, consulat Clauium in Euclidem, qui easdem delineatas exhibet oculis conspiciendas. 16. FIGVRA sexdecim laterum, est complexus omnium aspectuum, seu radiorum, quos ab vno puncto in quo est significator in principi morus, acquirere potest, dum per suam realem viam incedit, quousque torum circulum compleat, atque ad eundem locum radicalem redeat, in quo erat ab initio motus. Eius potissimum menzionem facit Ptolemæus, siue quicumq[ue] alius sit auctor Centiloquij in Verbo. o. monens, in morbis dijudicandis considerandam esse Lunæ peragrationem in figura sexdecim laterum; & prout ea ibi benè vel malè fuerit affecta, præcipir, benè, vel malè de morbo pronuntiandum. Et sanè inde exorti critici dies, dectetorijque: sicut etiam indicatiui, quos sedulò obseruant ex Hippocratis

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188 LEXICON in northern latitude, 35 degrees, which should be, as it were, now vertical to Sicily, which is to be especially observed. Being partly in the second house, or with Jupiter, Venus, and part of Fortune, it promises immense riches; and likewise in the midheaven great fortune in honors and in workmanship. See more on its decrees in the horoscope under V. Lyra. 14. FIGURE, from Euclid, book 1, def. 14, is defined as a quantity enclosed under some one or several boundaries. For quantity, according to the varied position of its outer limits, is also said to undergo a varied figure, although otherwise it remains unchanged in itself: whence it is understood to belong to quantity already constituted in its own genus, since it modifies it and makes it so that the extension of the parts, which quantity otherwise has of itself, preserves some order in the parts rightly disposed, whence it stands in the manner of a quality affecting them, and is called the boundary of a surface. Hence angular, lateral, rectilinear, curvilinear, triangular, quadrangular, solid, plane, etc. figures, of which elsewhere. 15. ISOPERIMETRICAL FIGURES among geometers are two or more figures which, when compared with one another, have equal perimeters, that is, circumferences. For this word is derived from the Greek isos, which means equal; peri, which means around; and metros, which means measure: as though figures measured by equal surrounding. Hence all figures that contain equal boundaries are isoperimetrical. Thus a square having six feet in perimeter is called isoperimetrical to a triangle, whether rectilinear, curvilinear, or mixed, which likewise has six feet in circuit: so that the four lines constituting the perimeter of the square, if unfolded into one and the same line, are found equal to the three straight lines of the triangle, or to all the sides of any figure placed also in a straight and continuous line. Whoever wishes more, let him consult Clavius on Euclid, who presents the same drawn out for the eyes to behold. 16. A figure of sixteen sides is the aggregate of all the aspects, or rays, which the significator can acquire from one point in which it is in its principal motion, while it proceeds through its real path, until it completes the whole circle and returns to the same radical place in which it was at the beginning of the motion. Ptolemy makes mention of it especially, or whoever else may be the author of the Centiloquium in the word o., warning that in judging diseases, the Moon’s passage through the figure of sixteen sides must be considered; and according as it there has been affected well or badly, one must pronounce well or badly concerning the disease. And indeed hence arose the critical and decisive days; as also the indicative ones, which they diligently observe from Hippocrates

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præceptis Medici peritiores, ex Lunæ uidelicet peragratione ad loca quæ aliquam habeant configurationem cum loco radicali, in quo erat initio morbi. Igiturum sexdecim positus habere potest Luna ad locum suum radicalem, prout totidem sunt genera familiaritatum, quæ contrahere possunt ad inuicem sidera, & non ita pridem detexit Keplerus, atque ex modulis harmonicis confirmantur. Ea sunt sextilis per distantiam 60. graduum, seu sexiæ partis circuli. Simiquadratus per distantiam 45. graduum seù per octauam parrem circuli. Quintilis per quintam partem, & distantiam gr. 72. Quadratus per integrum quadrantem 90. graduum. Trinum per iertiam partem, & gr. 120. Sesquiquadratus per distantiam trium ex octo partibus, hoc est per gr. 135. Biquintilis, per distantiam duarum ex quinque partibus, hoc est per gr. 140. ac tandem oppositio, quæ est distantia semicirculi, & gr. 180. quæ vice versa iterum dextrorum numerata, & loco oppositionis, si addatur reditus Lunæ ad locum suum radicalem, profecto inuenientur omninò sexdecim, quæ constituunt figuram hanc sexdecim laterum, cuius peragationem obseruandam in Luna præcipit ceniloquij Auctor ad morborum judicium proferendum. Porrò ex his aspectibus, alij boni sunt, alij mali. Mali, semiquadrati, quadrati, sesquiquadrati, & oppositio sicut etiam reditus, seù conjunctio cum loco suo radicali. In bonis, ac benignis aspectibus morbi non accipiunt incrementum; immo potius natura vires ad illum pellandum: in malis è contrà morbus reuiuiscit, & aduersus naruram, ijsdem ferè armis, quibus prius eam oppugnauerar, viribus auctus insurgit. Inde conflictus, & pugno, vnde judicium pendet, atque sententia, quam Græci crisim appellant. Hinc dies critici, atque indicatiui omnes infausti, quibus Luna ad suos hostiles radios peruenit. Et si quidem natura ob præcedentes radios ad suum locum benignos inueniatur ità uiribus roborata, vt in die critico sustinere possit insultum; pugna, & crisis in bonum cedet; sin minus, præualebit morbis, ipsaque prosternetur. Quoniam autem semiquadrati, & sesquiquadrati imperfecti radij sunt, & perfectorum prodromi, (sunt enim quadrati, & oppositionis participatio,) ideò vera crisis accidir in quadratis, oppositione, & reditu Lunæ ad locum suum radicalem: diesque illi, in quibus accidit, dicuntur absolùre critici, & indicatiui; ij vetò in quibus Luna peruenit ad suos semiquadratos, & sesquiquadratos, dicuntur rantum indicatiui, eoquia sunt veluti indicium pugnæ critico die futuræ. Ideò rectè monet centiloquij auctor in morbiis, inspiciendos esse, nedum criticos dies, sed & reliquas Lunæ peragrationes in figura sexdecim laterum, quo-

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more skilled in the precepts of medicine, namely from the Moon’s passage to those places that have some configuration with the radical place, in which it was at the beginning of the illness. Therefore the Moon can have sixteen positions with respect to its radical place, just as there are sixteen kinds of familiarities which the stars can contract with one another, and which not long ago Kepler discovered, and they are confirmed by harmonic ratios. These are the sextile by a distance of 60 degrees, or the sixth part of the circle. The semiquadrate by a distance of 45 degrees, or by the eighth part of the circle. The quintile by the fifth part, and a distance of 72 degrees. The square by the full quadrant of 90 degrees. The trine by the third part, and 120 degrees. The sesquiquadrate by a distance of three out of eight parts, that is, 135 degrees. The biquintile, by a distance of two out of five parts, that is, 140 degrees; and finally opposition, which is the distance of a semicircle, and 180 degrees, which in turn again, counted from the right, and in the place of opposition, if the return of the Moon to its radical place be added, there will certainly be found in all sixteen, which constitute this figure of sixteen sides, whose passage the author of the Centiloquium bids be observed in the Moon for rendering judgment on diseases. Moreover, from these aspects, some are good, others bad. Bad are the semiquadrates, squares, sesquiquadrates, and opposition, as also the return, or conjunction with its radical place. In good and benign aspects, diseases do not receive increase; rather, nature gains strength to drive them away: in bad ones, on the contrary, the disease revives, and against nature, with almost the same weapons by which it had previously attacked her, it rises up strengthened. Hence conflict and battle, from which judgment depends, and the sentence which the Greeks call crisis. Hence critical and indicative days are all inauspicious, on which the Moon reaches its hostile rays. And if indeed nature, by reason of the preceding rays to its benign place, is found so strengthened in vigor that on the critical day it can withstand the assault, the battle and crisis will turn out for good; if not, the disease will prevail, and nature itself will be overthrown. But since the semiquadrates and sesquiquadrates are imperfect rays, and harbingers of the perfect ones, (for they are a participation in the squares and opposition,) therefore the true crisis occurs in the squares, opposition, and return of the Moon to its radical place; and the days on which it occurs are called absolutely critical and indicative; but those on which the Moon reaches its semiquadrates and sesquiquadrates are called only indicative, because they are as it were an indication of a battle to come on the critical day. Therefore the author of the Centiloquium rightly warns that in illnesses, not only the critical days should be examined, but also the remaining passages of the Moon in the figure of sixteen sides, wh-

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190 LEXICON niam ex aliorum aspectuum ratione collegi potest, quintæ sint naturæ vires, quantæ etiam morbi, vnde judicium proferri possit, quis tandem succumbere, quis præualere debeat: Ex quibus habes male pronunciasse Gallacium in theatro mundi & temporis, nec- non Henricum Alstedium in sua Enciclopedia, figuram hanc diuidendam esse in sexdecim latera æqualia: non enim in æqualibus spatijs, sed in configuratione consistit hæc vis, vt ipsimet notant. <17.> FINIS, seu, Termi apud Astronomos sunt certi quidam limites, & partes signorum Zodiaci, in quibus planetæ ratione habitudinis ad suas domos habent certam prærogatiuam, ac dignitatem, quæ vna est ex quinque essentialibus. Alij sunt apud Ægyptios, alij apud Ptolæmeum: sed magis probantur qui apud Ægyptios atque eorum distributionis convenientissimam rationem affert. Titus in cælesti Philosophia. Porrò tabulam terminorum, tam secundum Ægyptios, quam secundum Ptolomæum hic non exscribo, quoniam ea passim obuia est apud omnes scriptores. <18.> FINITOR apud Latinos audit quod Græci horizontem appellant: Circulum nempe maximum in sfera dirimentem superius hæmisphærium ab inferiore, inde dictum, quod visum finiat: Comprehendit enim quidquid supra terram visibile est; itaut quæ sidera ad finitorem Orientalem pertingunt, dicantur oriri, quæ verò Occidentalem tenent, occidere. Duplex est alter rationalis, seù naturalis, alter sensibilis: Primus diuidit sphæram seù totum cælum in duas partes æquales; vt proinde si concipiatur aliqua superficies eum terminans, ea transire debeat per centrum terræ: secundus est circulus conceptus ad terræ superficiem elevatus, itaur cum ea vnam planitiem efformare concipiatur; comprehendatque totum id, quod remotis omnibus impedimentis, oculorum acies circumducta conspicere potest. Sed de hac re vide Fusius in Verbo Horizon. Ab alijs dicitur etiam Finiens. <19.> FIRMAMENTVM dicitur communiter octauus otbis, & cælum stellarum, in quo stellæ omnes inerrantes fixæ sunt, atque in varios Asterismos tributæ. Nouem hausit ab eo, quod sit quasi firmamentum ac vallum, vel sanè quia in eo sidera firmiter semper adhærent, nec locum permutant in eo, sicut eandem ob causam ipsæ stellæ fixæ dicuntur, vt mox infid. Alij inter quos Blancanus, illud existimant dictum ab firmitate, seu soliditate qua præditum esse credunt: sic enim inquit Blancanus lib. 18. cap. 6. de mundi fabrica. Si qua pars cals duritie, ac firmitate prædita est, proculdubio erit firmamentum: Videmus enim stellas in eo affixas atque ad inuicem immotas, omnes

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190 LEXICON from the aspect of other things it can be gathered what nature the fifth powers are, and how great also are the diseases, from which judgment may be delivered as to which must finally yield, and which prevail: From which you may see that Gallacius, in the theater of the world and of time, as well as Henricus Alstedius in his Encyclopedia, has wrongly stated that this figure should be divided into sixteen equal sides: for this power consists not in equal spaces, but in configuration, as they themselves note. <17.> FINIS, or Termi, among astronomers are certain fixed boundaries and parts of the signs of the Zodiac, in which the planets, by reason of their relation to their houses, have a certain prerogative, and dignity, which is one of the five essentials. There are some among the Egyptians, others with Ptolemy: but those are more approved which are among the Egyptians, and Titus in his Celestial Philosophy gives the most suitable reason for their distribution. Moreover, I do not here copy the table of the terms, both according to the Egyptians and according to Ptolemy, since it is commonly found everywhere among all writers. <18.> FINITOR among the Latins is what the Greeks call the horizon: namely, the greatest circle in the sphere dividing the upper hemisphere from the lower, so called because it limits the sight: for it includes whatever is visible above the earth; so that those stars which reach the eastern horizon are said to rise, while those lying to the west are said to set. There is a twofold horizon, one rational, or natural, the other sensible: the first divides the sphere, or the whole heaven, into two equal parts; so that if some surface terminating it be conceived, it must pass through the center of the earth: the second is a circle conceived as elevated to the surface of the earth, so that it may be understood to form with it one plane; and it includes all that, with all obstacles removed, the range of the eyes can perceive when turned around. But on this matter see Fusius under the word Horizon. By others it is also called Finiens. <19.> FIRMAMENTVM is commonly called the eighth orb, and the heaven of the stars, in which all the fixed stars are set, and distributed among various asterisms. Nouem drew it from the fact that it is as it were a firmament and rampart, or certainly because in it the stars always cling firmly and do not change their place in it, just as for the same reason the fixed stars themselves are so called, as will be shown shortly. Others, among whom is Blancanus, think it is so called from the firmness, or solidity, with which it is believed to be endowed: thus Blancanus says, book 18, chapter 6, of the fabric of the world. If any part is endowed with cold hardness and firmness, without doubt it will be the firmament: for we see the stars fixed in it and unmoved with respect to one another, all

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MATHEMATICVM. 191 simul supra mundi polos ordnare ac spharicè moueri, id est perinde ac si corpori spharico affixarum cum eo revoluerentur quod euidens signum est firmitaris illius, & causâ simul cur vocatum sit firmamentum. Cæterum ea sufficiens ratio non est illud solidum astruendi, quandoquidem, vt cæli inferiores, vt aër ipse in omnium sensu fluidus ordinarè mouetur, rapiendo secum cometas in eo genitos asque eo quod in istis aliquem motum proprium deprehendamus, qui proinde fixi loco, vbi primùm apparent credendi sunt, non minus, quam stellæ in octauo orbe; ita & firmamentum tenuissimæ substantiæ, & summè fluidum concipere possumus, & ipsum ordinarè rotari, etiamsi stellæ in eo fixæ nullomodo loco dimoueantur. Neque huic rei Sacræ paginæ aduersantur cum præsertim Iob. 18. ex los solidissimos allerunt quasi ære fundatos. Nam (vt benè habet Pineda in cum locum) præterquam ibi sermo est de aeris regione, vt paret ex contextu literæ, ac alioqui cælorum nomine sæpè aera nuncupantur, non modo in sacris codicibus, sed etiam apud prophanos scripiores, quam quidem satis constat esse fluxum, & vagum; sed ideò solidissimus dictus est, quasi ære fundatus, vt commendetur Creatoris potentia atque sapientia, quod non minus constans, perpetuaque sit res fluxa, ac labilis, quam si solidissimo ex ære fusa esset, quare cum per extensionem soleant res nimium extenuari, & discumpi, tamen diuina potentia extenuando, & deducendo res potius confirmat & consolidat. Qui benè æri fusili comparatur: sicut enim æs fusile constantiam habet, & firmitatem; ita aer quamuis fluidus, & labilis, at constans & perpetuus est. Hæc ingeniosè Sinedæ. Quod item de firmamento vniuersaque cælorum substantia < 20.> dicendum est. Et sanè rationi optime congruit, vt quæ magis à terra distant tenuioris substantiæ sint, vt videmus in ipso aere qui semper purior, ac subtilior est in editioribus locis, & si cæreti cæli inferiores fluidi asserantur, nescio qui solum firmamentum solidum astrui possit, præsertim cum id repugnare videatur rationi motus illi ac cæteris cælis inferioribus imptessi à primo mobili, quo sit, vt qui propiores sunt, majori impetu rapiantur, qui remotiores, minori, atque aliquatenùs semper resistant, & conti à mirantur, regulari tamen atque ordinatissima irregularitate. Præterquam non desunt qui credant regionem omnem Archeream aliud plane non esse, quara tenuissimum aera eiusdem prorsus substantiæ, ac speciei, ac iste quem nos respiramus, licet longe defecatiorem ac puriorem; proindeque aereum nostrum cum illo vnum quid esse, quod nomine expansi venit, ac secunda die creatum sub nomine firmamenti. Et ita sentiunt Aretius in libris de Generatione, ac

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MATHEMATICVM. 191 simultaneously arranged above the poles of the world and moved in a spherical manner, that is, as if the fixed stars attached to a spherical body were revolving with it; this is a clear sign of its firmness, and also the reason why it was called the firmament. However, that is not a sufficient reason for asserting it to be solid, since, just as the lower heavens, just as air itself, fluid in everyone’s experience, is ordinarily moved, carrying along with it the comets generated in it, even though we do not detect in them any proper motion, and therefore they should be believed to be fixed in the place where they first appear, no less than the stars in the eighth orb; so too we can conceive the firmament as of the most subtle substance and supremely fluid, and still as ordinarily rotating, even though the stars fixed in it in no way move from their place. Nor do the Sacred Pages oppose this, especially since in Job 18 they describe the heavens as most solid, as if founded in bronze. For (as Pineda notes well on that passage) besides the fact that there the discourse is about the region of the air, as is evident from the context of the text, and otherwise the name of heavens is often given to the air, not only in the sacred books but also among profane writers, which indeed is plainly known to be fluid and unstable; but it is called most solid, as if founded in bronze, in order to commend the power and wisdom of the Creator, because a thing that is fluid and liable to fall is no less constant and perpetual than if it had been cast from the solidest bronze. Hence, although by extension things are usually made too thin and broken apart, divine power, by thinning and drawing them out, rather confirms and consolidates them. It is well compared to cast bronze: for just as cast bronze has constancy and firmness, so air, although fluid and unstable, is yet constant and perpetual. These are the ingenious observations of Sineda. The same must also be said about the firmament and the entire substance of the heavens <20.> And indeed it agrees best with reason that those things which are farther from the earth are of more subtle substance, as we see in air itself, which is always purer and more subtle in higher places; and if the lower heavens are said to be fluid, I do not know how only the firmament can be asserted to be solid, especially since this seems to conflict with the motion impressed on that and the other lower heavens by the first mover, whereby those that are nearer are carried along with greater force, those more distant with less, and, in a certain respect, always resist and are held back, yet in a regular and most orderly irregularity. Besides, there are not lacking those who believe the whole region of the ether to be nothing other than a very subtle air, of exactly the same substance and kind as that which we breathe, though far more refined and pure; and therefore our air and that are one thing, which comes under the name of the expanse, and was created on the second day under the name of the firmament. And so Aretius in the books On Generation, and

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102 LEXICON Franciscus Resta de Meteoris. Sed quidquid sit de hoc, nulli dubium, quin substantia istius orbis pretiosissima sit, infinitum propè spatium sua Crassitie continens ac mirabilis efficacix erga isthæc infetiora; cuius beneficio, & singulati virtute viuentibus omnibus vegetatiuam infundi potentiam antiqui Philosophi æstimarunt, vt testis est Argolus cap. 1. de diebus Criticis. Porrò quanta sit cæli istius Crassities, non adhuc omninò constat apud Astronomos: Communior tamen sententia sert apud Blancanum eius gyrum continere semidiametros tel- lutis 88000 hoc est milliaria 312412000 alij aliter opinantur. < 21.> Quoad eius motum is lentissimus est; imò veriùs rapidissimus, & ferè exæquat ipsum primum mobile ab Oriente in Occidentem tendens motu vniuersitatis raptus ab eodem primo mobili: adeò vt planè insensibilis sit ea contranitentia, seù quàm vulgò vocant motum proprium ab Occidente in Orientem, ac propteteà antiqui Astronomi illam discerne non valentes, idipsum primum mobile appellabant. Postea processu temporis obseruatum fuit ipsum singulis centenis annis elongari à partibus primi mobilis, sub quibus antea erat gradum vnum & 25. minuta: siue hæc elongario, vt modò innui procedat ex hoc, quod resistat aliquantulum motui primi mobilis siue quod habeat proprium motum ab Occidente in Orientem, super polos eclipticæ, quod ad rem de qua nunc agimus nihil refert. Certè huius diuersitatis primus obseruator fuit Hipparchus, quem postea sequuti sunt Ptolemæus, Albategnius, Alphonsus Hispaniæ rex, Copernicus, ac tandem Tycho Brahe huius deviationis diligentissimus inuestigator, qui proprereà reperitis calculis, atque obseruationibus compertum habuit octauam sphæram singulis annis recedere à primo mobili, seu ferri ab Occidente in Orientem secundùm successionem signorum 51, secundis minutis; ita vt spatium annorum 49000. requiratur, vt rotum Zodiacum perficiat, & redeat sub eodem puncto primi mobilis in quo erat cum primum Vniuersum hoc conditum fuit. Qua ratione, vt nos obseruauimus in V. Annus magnus, nonnulli opinantur. tantumdem temporis spatium. Summum Deum durationi sæculi huius constituisse, post quod immineat vltima dies & finis mundi. < 22.> Fixa Signs in Zodiaco sunt in vnoquoque quadrante constituente singula anni tempora, signa mediantia & veluti fixa, coquia in ijs potissimum relucet qualitas, & complexio illius temporis, cum alias siue in præcedentibus, siue in subsequentibus fluxerit, & in illis quidem incipiat, & augescat, in istis verò deficiat, & siat quodammodo sequenti communis. Idcirco hæc communia, illa mobilia, media vatò fixa dicun- tut.

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102 LEXICON Franciscus Resta de Meteoris. But whatever may be said about this, there is no doubt that the substance of that sphere is most precious, containing by its thickness an almost infinite space and possessing a marvelous efficacy toward these lower things; by whose benefit and singular virtue the ancient philosophers thought that the vegetative power was infused into all living things, as Argolus testifies, chap. 1, De Diebus Criticis. Moreover, how great the thickness of that heaven is has not yet been completely established among astronomers. The more common opinion, however, states, according to Blancanus, that its circuit contains 88,000 semidiameters of the earth, that is, 312,412,000 miles; others think otherwise. < 21.> As for its motion, it is very slow; or rather, more truly, extremely rapid, and almost equals the primum mobile itself, moving from East to West, carried along by the motion of the universe through the same first mobile. So much so that the counter-motion is plainly imperceptible, or what is commonly called the proper motion from West to East; and therefore the ancient astronomers, not being able to distinguish it, called it the primum mobile itself. Later, in the course of time, it was observed to be separated each hundred years from the parts of the first mobile beneath which it had formerly been by one degree and 25 minutes. Whether this separation, as I have now indicated, proceeds from this, that it somewhat resists the motion of the first mobile, or whether it has its own motion from West to East over the poles of the ecliptic, is of no relevance to the matter we are now discussing. Certainly the first observer of this difference was Hipparchus, whom later followed Ptolemy, Albategnius, King Alphonsus of Spain, Copernicus, and finally Tycho Brahe, the most diligent investigator of this deviation, who therefore, by calculations and observations made, found that the eighth sphere recedes each year from the first mobile, or is carried from West to East according to the succession of the signs, by 51 seconds; so that a period of 49,000 years is required for it to complete the whole Zodiac and return beneath the same point of the first mobile in which it was when this whole universe was first created. In this way, as we observed in V. Annus magnus, some think that so great a span of time was appointed by God for the duration of this age, after which the final day and the end of the world will be imminent. < 22.> The fixed signs in the Zodiac are placed in each quadrant, constituting the several seasons of the year; the middle signs, and, as it were, fixed, because in them chiefly shines the quality and temperament of that season, whereas in the others, whether preceding or following, it flows, and in those indeed it begins and increases, but in these it declines and becomes in a certain way common with the following. For this reason these are called common, those mobile, the middle, and by our custom fixed.

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MATHEMATICVM. 193 tur. Ea autem sunt Taurus, in quo dum sol reperitur, præ- ualet Ver: Leo in quo Æstas: Scorpio, in quo Autumnus: & Aquarius, in quo præualer Hyems, & frigus maximum. In Astrologicis plurimi sunt signa fixa in ædificijs, in ar- borum plantatione, atque in rerum stabilitate significanda. Qua de re vide quæ passim habent scriptores in Isagog. de præceptis seruandis in Agricultura, ædificatione, atque in Medicina. < 23.> Fixæ Stella dicuntur omnia cæli lumina, quæ in Æthere micare videmus præter planetas, idque ad differentiam eorumdem planetatum, qui cum semper hacillae discurrant, non eundem ordinem atque habitudinem ad inuicem ser- uant, errorum nomen sortiti sunt; illæ verò, quia non alium motum habent quam firmamenti, in quo situm nun- quam permutant, semper eundem ordinem seruant, eamdem distantiam, eamdem figuram (semper enim Pallilitium exempli gratia, ex diametro oppositum est cordi Scorpio- nis, Arcturus, Lucida lancis australis, & vltima in Cauda Vrlæ majoris semper in linea recta esse conspiciumtur; Item Arcturus, & duo carres; pes sinister Orionis, Cauda Leonis, & Canis Syrius in eadem linea recta: Spica Virginis, Arcturus, & Cauda Leonis in triangulo Isoceles, basi facta in Arcturo, & cauda, angulo verò in spica, &c.) ideo inquam omnes in vno cælo semper immobiliter consistentes, iure fixæ dictæ, æstimatæque sunt, mouerique tantum per accidens cum ipso cælo deferente. An autem ex digniores sint errantibus, ac vir- tute superiores, magna est inter Philosophos, Astronomos- que dissentio, vt præ cæteris aduersit Coelius Rhodiginus lib. 2. cap. 17 Certè obloci eminentiam, ob lucis intentionem, quippe seinsillant, quod planetæ non faciunt, vnde &c quandam insitam primigeniam lucem à Sole non mutuatam habere censendæ sunt, ob corporis magnitudinem, qua erra- ticas omnes excepto Sole longe exuperant, ob multitudinem, diversitatem, virtutis collectionem, aliasque circumstantias, magnam efficaciam in inferiora isthæc habere debent, præ- stantiorem vtique quam ipsi planetæ. Quod & Albumasar an- < 24.> tiquissimus testarum reliquit in suo introductorio in hæc ver- ba. Stella fixa dans doma grandia, & ex pauperato sublemans ad sublimitatem eam, quam non faciunt septem planata. Ne- que Prolocaeus ipse contradicit in suo centiloquio propos. 29. vbi, Stella fixa, sit irrationabiles asquo admirabiles felicissatos afferunt, quas tamen plerumque calamitatibus insigniunt, nisi & planeta ad felicitasem conveniunt. Cuius rei varias rationes N

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They are Taurus, in which, while the sun is found, Spring prevails; Leo, in which Summer; Scorpio, in which Autumn; and Aquarius, in which Winter and the greatest cold prevail. In astrology, the fixed signs are of greatest use in building, in the planting of trees, and in indicating stability in things. On this matter, see what writers everywhere have in their Isagoge concerning the precepts to be observed in agriculture, building, and medicine. < 23.> Fixed stars are called all the lights of the sky which we see shining in the ether, apart from the planets; and this in distinction from the planets themselves, which, since they always move hither and thither, do not preserve the same order and relation to one another, and have received the name of “wanderers.” But those, because they have no other motion than that of the firmament, in which they never change their position, always preserve the same order, the same distance, and the same figure (for, as an example, the Pleiades are always seen opposite the heart of Scorpio by diameter; Arcturus, the bright star of the southern scale, and the last in the tail of Ursa Major are always in a straight line. Likewise Arcturus and the two chariots; the left foot of Orion, the tail of Leo, and Sirius are on the same straight line; Spica of Virgo, Arcturus, and the tail of Leo are in an isosceles triangle, the base being made at Arcturus and the tail, but the angle at Spica, etc.). Therefore, since they always remain immovably in one heaven, they were rightly called and judged fixed, and are moved only by accident along with the heaven that carries them. Whether they are more worthy than the wandering stars, and superior in power, there is a great disagreement among philosophers and astronomers, as Coelius Rhodiginus especially states in book 2, chapter 17. Certainly, on account of their eminence, on account of the intensity of their light—for they sparkle, which the planets do not do—and therefore seem to have a certain innate, primitive light not borrowed from the Sun; on account of their size, by which they greatly surpass all the erratic stars except the Sun; on account of their multitude, diversity, collection of powers, and other circumstances, they must have great efficacy over these lower things, undoubtedly greater than the planets themselves. This is what Albumasar, the most ancient among them, left in his Introductory in these words: “Fixed stars give great homes, and raise the impoverished to sublimity, which the seven planets do not do.” Nor does Prolocaeus himself contradict this in his Centiloquium , proposition 29, where he says that fixed stars bring irrational but marvelous felicities, though they usually mark them with calamities, unless the planets also agree in felicity. Various reasons for this matter...

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194 LEXICON congerunt Auctores. Mihi ea magis arridet, quod cum sint longè à terra remotæ, semper pro regionum qualitate ab ijsdem horizontis partibus oriantur, & occidant; semper eundem arcum circà tellurem faciant, nec ferè diutiùs quam ipsæ partes primi mobilis supra terram morentur; idcircò earum influxus magni quidem sunt, sed extraordinarij, & repentini, proindeque egent planetarum fulcimento, quorum luce, quasi vehiculo, aut canali eorum lux ad nos deriuetur. Cæterum eas Astronomi antiquiores diuiserunt in plures classes cum ratione naturæ planetarum cum quibus participant, tum ratione apparentis magnitudinis earum diametri, quæ maior in vna, quam in alia semper conspicitur, existimantes omnes esse constitutas, & affixas in eadem superficie firmamenti, eademque à tellure distantia: quod tamen alij juniores non facilè admittunt, diuersis congruentijs moti, sed potius credunt non omnes in eadem cæli distantia firmatas esse, sed aliquas magis, aliquas minùs intra crassitiem vastissimi illius expansi, cæli inquam eas deferentis immersas Idque eò facilius assumunt, quod istud à Tychone, cæterisque qui post ipsum venerunt, altruirur fluidum. Indeque esse, cur aliæ alijs majores, minoresue apparent Quod & in ijs quæ in eodem ordine magnitudinis sunt (assignant quippe sex tandem magnitudinis ordines,) obseruare licebit. Canis enim sirius cæteris omnibus grandior apparet, mox Lucida Lytæ; inde Atcturus &c. istaut non omnes eiusdem prorsus diametri sint, apparentis, sed ideo aliqua grandior, quia propior, ideò exilior, quia remorior. Non negauerin tamen id non vni distantiæ tribuendum esse, sed adhuc & reali earum magnitudini, sicque alias esse reuerà alijs maiores, ac maiores: adeò vt non desint qui asserant canem maiorem, seù stellam in eius ore consistentem dictam Arabibus alhabor ipsum solem magnitudine superare; sed quia longè supra ipsum in infinita propè distantia constitutus sit, ideo nobis apparet corpore minor, & exilior. Quod perspicuum est in Marte, Ioue, Saturno, ad Venetem comparatis, imò in vno eodemque Marte constituto in Apogxo, aut in Perigeno. 25. Obseruauit antiquitas tantum 1022. stellas conspicuas in toto ambitu firmamenti, quas in 40. Asterismos, seu Imagines à natura earum, nomine & forma siue ex fabulis, siue ex historijs ijs indita, complicarunt. Veruntamen nostro æuo Telescopij ope plures aliæ propè infinitæ, quas priùs sine instrumentis noster oculus assequi minime poterat, detectæ sunt: præsertim in via lactea, quam nil aliud esse constat, quam conge-

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194 LEXICON concur. I prefer this opinion, because, since they are very far from the earth, they always rise and set from the same parts of the horizon according to the quality of the regions; they always make the same arc around the earth, and scarcely remain above the earth any longer than the parts of the first mover themselves; therefore their influence is indeed great, but extraordinary and sudden, and thus they need the support of the planets, whose light, as it were as a vehicle or channel, is conveyed to us. Furthermore, earlier astronomers divided them into several classes, both on account of the nature of the planets with which they participate, and on account of the apparent size of their diameter, which is always seen larger in one than in another, believing that all are placed and fixed in the same surface of the firmament, and at the same distance from the earth; but other later writers do not easily admit this, being moved by different considerations, but rather believe that not all are fixed at the same distance from the sky, but that some are immersed more, others less, within the thickness of that vast expanse, that is, of the sky which carries them. And they assume this all the more readily because it is, as it were, made fluid by Tycho and the others who came after him. And hence it is that some appear larger than others, smaller than others. This may also be observed in those that are of the same order of magnitude (for they assign six orders of magnitude in all): for Sirius appears larger than all the others, next Lucida Lyrae; then Arcturus, etc. Yet not all of these have exactly the same apparent diameter, but one appears larger because it is nearer, another smaller because it is farther away. I would not deny, however, that this should be attributed not only to distance, but also to their real magnitude, and thus that some are in fact larger than others, and larger by a great deal; so much so that there are those who assert that the greater Dog, or the star situated in its mouth called by the Arabs Alhabor, surpasses the sun itself in magnitude; but because it is placed far above it at an almost infinite distance, it therefore appears to us smaller in body and more slender. This is clear in Mars, Jupiter, and Saturn when compared with Venus, indeed even in the same Mars when placed in apogee or in perigee. 25. Antiquity observed only 1022 conspicuous stars in the whole sphere of the firmament, which it arranged into 40 asterisms, or images, named from the nature of the stars and given names and forms either from myths or from histories. But in our age, by means of the telescope, many others, almost infinite in number, which our eye could not previously reach without instruments, have been discovered: especially in the Milky Way, which is known to be nothing else than a conge-

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MATHEMATICVM. 195 rium minutarum stellarum. Et in Pleiadibus quidem vbi nos non nisi sex tantum stellas vix videmus. Galilæus in suo nuncio sidereo intrà spacium 85. minutorum quinquaginta plus stellas in vnum colligatas; se vidisse testatur. Omitto quæ de Orione dicit, de Vrsa, de serpentario, quæ plane videntur incredibilia, ni scriptura ipsa suo testimonio id firmaret, stellas omnes innumerabiles astruens, Gen. 26. Multiplicabo semen tuum sicut stellas cals, & sicut arenam maris, qua præ multitudine numerari non potest, & alibi, numera stellas, si potest. Qua de re vide ipsum Galilæum in citato nuncio Sidereo, Petauium, in suo Vranologio, & Baierum in Vranometria. Hac occasione non alienum ab instituto meo crediderim < 26.> esse, si & hic methodum tradam, quo pacto stellæ fixæ sereno cælo dignosci possint, & suis quæque nominibus designari, quia & id lectoribus non iniucundum erit, & inter ea quæ maximè Astronomum commendant, atque ipsum populo ineruditorum plausibilem faciunt, est stellas quascunque à quouis è populo indice designatas proprio cuique nomine compellare: quod per Globum Astronomicum facilè assequemur. Accipe igitur gradum Zodiaci, quem Sol perambulat eo tempore, quo stellas obseruare volueris, eumque vespere tantum infra horizontem deprime quantum sufficit ad stellas omnes probè conspiciendas citra omne impedimentum lucis crepusculinæ, quod est circa primam horam nectis. Deprime igitur cum eo gradu Solis ad Occidentem grad. 15. æquatoris, & habebis intentum: In hoc enim situ omnes stellæ superioris hemisphærij directè cadunt supra stellam in globo illi subjectam, & per lineam rectam tibi respondentem: nam proinde se habent partes superioris hemisphærij ad semiglobum, ad sphæræ cælestes ad superficiem terræ eo prorsus pacto, ac zonæ cælestes correspondent ad Zonas terrestres: vnde facilè poteris quascumque stellas dignoscere, & suis nominibus appellare. Sic, exempli gratia sit tibi nota aliqua stella, quam tu videas: accipe ejus altitudinem per quadrantem, deinde globum astronomicum motu diurno revolue, donec stella illa in globo depicta eandem altitudinem super horizontem materialem obtineat, quantam habet supra horizontem stella quam per quadrantem obseruasti. Sic igitur constituto globo in ea positione facile tibi erit, & reliquas stellas ex vicinitate aut distantia quam habent ad dictam fixam dignoscere, transferendo distantiam quæ est ad inuicem in globo ad distantiam quæ est inter illas in cælo. N ij

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…of the minute stars. And indeed in the Pleiades, where we scarcely see only six stars; Galileo, in his Sidereal Messenger, testifies that within the space of 85 minutes he saw more than fifty stars gathered into one cluster. I pass over what he says of Orion, of the Bear, and of Serpentarius, which seem altogether incredible, unless Holy Scripture itself, by its own testimony, confirmed it, declaring all the stars innumerable: Gen. 26, “I will multiply thy seed as the stars of heaven, and as the sand of the sea, which, by reason of its multitude, cannot be numbered”; and elsewhere, “Number the stars, if thou canst.” On this matter see Galileo himself in the cited Sidereal Messenger, Petavius in his Uranologium, and Bayer in his Uranometria. On this occasion I would not think it foreign to my purpose if here also I should set down the method by which the fixed stars may be distinguished in a clear sky and each designated by its own name, because this will not be unpleasant to readers, and among the things that most commend an astronomer, and make him acceptable even to the unlearned public, is the ability to call whatever stars are indicated by any common person by their proper names: this we shall easily accomplish by means of the Astronomical Globe. Take therefore the degree of the Zodiac through which the Sun passes at the time when you wish to observe the stars, and lower it in the evening only so far below the horizon as is sufficient for all the stars to be clearly seen, without any hindrance from twilight, which is about the first hour of the night. Lower therefore, with that degree of the Sun, 15 degrees of the equator toward the west, and you will have what you seek. For in this position all the stars of the upper hemisphere fall directly upon the star beneath them on the globe, and along the straight line corresponding to you; for in like manner do the parts of the upper hemisphere relate to the semiglobe, and the celestial spheres to the surface of the earth, as the celestial zones correspond to the terrestrial zones. Hence you will easily be able to identify any stars whatsoever and call them by their names. Thus, for example, let some star be known to you which you see: take its altitude with the quadrant, then turn the astronomical globe by the daily motion until that star depicted on the globe attains above the material horizon the same altitude as the star you observed with the quadrant has above the horizon. Thus, with the globe set in that position, it will be easy for you both to recognize the remaining stars from the nearness or distance they have to the said fixed star, transferring the distance that exists between them on the globe to the distance that exists between them in the sky. N ij

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196 LEXICON FL 27. FLAMMIGER ex natura fixarum, quæ in eo reperiuntur dictus est Cepheus, sidus in cælo ad Borealem plagam, de quo plura diximus suo loco. FO 28. FOCA ab aliquibus vocatur stella fixa in Dracone tertio magnitudinis de natura Veneris, & Mercurij Arabicè Al- felta. 29. FOEMININVM, aut Masculinum dicitur apud Astronomos si- gnum, planeta, aut aliud quid foemineis, aut masculis quali- tatibus pollens. Quandoquidem cum mascula vis sit actiua, foeminea verò passiua, atque è quatuor primis qualitatibus calor & frigus sint in genere actiui, humiditas verò & sic- citas sint in genere qualitatis passiux, vt docet Philosophus in lib. de Generat. & alibi sæpè; consequenter quæ signa, quive planetæ in his qualitatibus vincunt, masculina, vel foeminina pro ratione qualitatum prædominantium denominantur. Hinc quia Sol maximè calidus: Iupiter magis calidus, quam humidus: Saturnus, & Mercurius frigidi magis, quam sicci, ideò masculini dicuntur ac diurni: (eadem enim est ferè ra- tio diurni, & nocturni, ac masculini & foeminini.) Econtrà quia Venus humida magis, quam calida est; Luna humida magis, quam frigida, ideò foeminini planetæ sunr, & noctur- ni. Mars quia maximè calidus, ideò absolutè masculus; at quia vincit in eo calorem siccitas, ob id nocturnus astruirur, atque à Tito aliisque iure dicitur effæminatus. Porrò quæ de planetis diximus, locum habent, & in duodecim Zodiaci si- gnis: itaut quæ calore magis, ac frigore præqualent masculine sint; ea verò in quibus præponderar humiditas, vel siccitas, sint foeminina, sicque alternatim Aries masculinum signum est, & diurnum: Taurus foeminium, ac nocturnum: Gemini masculinum, & diurnum, Cancer foemininum, ac noctur- num: & sic de reliquis. 30. Præter autem integra signa, Arabes more suo (nescio su- perstiriose ne, an vero cum fundamento) obseruant in ipsis si- gnis cerros gradus, quos partim dicunt masculinos partim fo- mininos. Sic ab initio Arietis vsque ad octauum gradum inclu- sivè faciunt masculinos: nonum asserunt foemininum. Rur- sus sex sequentes masculinos; septem alios post, foemininos, ac tandem reliquos octo integros masculinos, & sic de reli- quis, prout ex subiecta tabella excipi potest, quam ex Alkabi- sis exscripsi: licet alij aliter eam exponant.

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196 LEXICON FL 27. FLAMMIGER, from the nature of the fixed stars found in it, Cepheus is so called, a star in the sky toward the northern region, of which we have spoken more fully in its proper place. FO 28. FOCA is the name used by some for a fixed star in Draco, of the third magnitude, of the nature of Venus and Mercury, in Arabic Al-felta. 29. FEMININE, or Masculine, is said by astronomers of a sign, planet, or anything else endowed with feminine or masculine qualities. For since masculine force is active, and feminine force passive, and since among the four primary qualities heat and cold are of the active kind, while humidity and dryness are of the passive kind, as the Philosopher teaches in the book On Generation and elsewhere often; consequently those signs or planets which prevail in these qualities are called masculine or feminine according to the predominance of the qualities. Hence, because the Sun is most hot; Jupiter more hot than humid; Saturn and Mercury more cold than dry, they are therefore called masculine and diurnal: (for the ratio of diurnal and nocturnal is almost the same as that of masculine and feminine.) On the other hand, because Venus is more humid than hot, and the Moon more humid than cold, they are therefore feminine planets and nocturnal. Mars, because he is most hot, is therefore absolutely masculine; but because in him dryness prevails over heat, for that reason he is assigned to the nocturnal class, and by Titus and others is rightly said to be effeminate. Moreover, what we have said of the planets also applies to the twelve signs of the Zodiac: thus those in which heat and cold prevail more are masculine; but those in which humidity or dryness predominate are feminine; and so, alternately, Aries is a masculine sign and diurnal; Taurus feminine and nocturnal; Gemini masculine and diurnal; Cancer feminine and nocturnal; and so on for the rest. 30. Besides the whole signs, however, the Arabs, in their customary way (I do not know whether superstitiously or rather with reason), observe in the signs certain degrees, which they call partly masculine and partly feminine. Thus from the beginning of Aries up to and including the eighth degree they make masculine; the ninth they declare feminine. Again, the next six masculine; the seven after that feminine; and finally the remaining eight entire degrees masculine, and so on for the rest, as may be gathered from the table below, which I have copied from Alkabisi: although others explain it differently.

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MATHEMATICVM. 197 Tabula Graduum Masc. & Fæmin. in quolibet signo. Aries. masc. 8. Taurus. masc. 5. Gemini. masc. 5. Cancer. masc. 2. Leo. masc. 3. Virgo. masc. 8. Libra. masc. 5. Scorpio. masc. 4. Sagittarius. masc. 2 Capricorn masc. 5. Aquarius. masc. 5. Pisces masc. 10. fæm. 1. fæm. 6. fæm. 6. fæm. 4. fæm. 4. fæm. 2. fæm. 8. fæm. 8. fæm. 10 fæm. 5. fæm. 7. fæm. 3. fæm. 4. fæm. 4. fæm. 11 fæm. 7 fæm. 10 fæm. 7. fæm. 3. fæm. 3. Arque hi sunt gradus Masculini, & Fæminini secundùm Arabes: ex quibus facto scrutinio, contendunt auspicari posse nùm partus futurus sit fæmininus, an masculinus. Nam si ascendens, inquiunt, & luminaria sint in pluribus partibus masculinis, quod nascetur, marem esse autumant, si in pluribus fæmininis, fæmellam. Quod equidem obseruare, non tam dignum eorum otio, qui hæc commenti sunt, judicamus, quàm indignum occupatione illorum, qui curis nobilioribus distantur. FOMAHAND Arab. corrupto vocabulo (cùm potiùs dici 32. debeat Phoemus, prout habet Kircherus in Oedipo) dicitur stella fixa primæ magnitudinis de natura Veneris & Mercurij posita in vltima effusione aquæ Aquarij, quæ Romæ vix horizontem radir. Ea hoc habere proprium fertur in Genethliacis, vt post mortem det nominis immortalitatem. FORTUNA dicitur apud Astronomos planera beneficus, qualitatibus suis naturam fouens, ac fortunam adducens: sicut è contrà Infortuna planeta maleficus, naturæ inimicus, & infortunam afferens. Dux sunt fortunæ, Iupiter, & Venus, quippe- N iij

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MATHEMATICUM. 197 Table of Male and Female Degrees in each sign. Aries. male 8. Taurus. male 5. Gemini. male 5. Cancer. male 2. Leo. male 3. Virgo. male 8. Libra. male 5. Scorpio. male 4. Sagittarius. male 2 Capricorn male 5. Aquarius. male 5. Pisces male 10. female 1. female 6. female 6. female 4. female 4. female 2. female 8. female 8. female 10 female 5. female 7. female 3. female 4. female 4. female 11 female 7 female 10 female 7. female 3. female 3. There are also male and female degrees according to the Arabs: from which, after making an inquiry, they claim it can be predicted whether the future birth will be female or male. For if the ascendant, they say, and the luminaries are in more masculine parts, that which will be born they judge to be male; if in more feminine parts, female. This observation, indeed, we judge not so much worthy of the leisure of those who devised these things, as unworthy of the occupation of those who are engaged in nobler concerns. FOMAHAND, an Arabic corrupted word (since it ought rather to be called Phoemus, as Kircher has it in the Oedipus), is said to be a fixed star of the first magnitude, of the nature of Venus and Mercury, placed in the last effusion of the water of Aquarius, which at Rome scarcely grazes the horizon. It is reported to have this special property in genethliacal matters, that after death it gives immortality to one’s name. FORTUNA is called among astronomers a benefic planet, fostering nature by its qualities and bringing good fortune; just as, on the contrary, Infortuna is a malefic planet, hostile to nature and bringing misfortune. The two fortunes are Jupiter and Venus, namely- N iii

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198 LEXICON qui temperatè calidi, & humidi, proindeque natium calorem, & humidum radicalem augentes, & conseruantes. Ille fortuna maior dictus, quia superior, masculus diurnus, calore magis abundans quàm humiditate; ista fortuna minor, quia inferior, corpore minor foeminea, nocturna, atque in qualitatibus passiuis abundans magis, quàm in actiuis. Similiter duæ infortunæ, Mars, & Saturnus: hic infortuna maior, qualitatis pollens calori atque humido naturali contrarijs, frigido nempe, & sicco: ille infortuna minor, quia nocturnus, quia calidus, sed enim intemperatè siccus, quo omnia sua vredine afficit, & absolver. Porrò alij planetæ mediocres sunt, & facile ex horum permixtione in fortunas, vel etiam in infortunas permutantur. Qua de re vide in proprijs locis. 34. Fortunæ pars dicitur horoscopus Lunaris, & locus in situ Mundi, vnde progredi incipit Luna, cùm Sol à linea Orientis emergit. Ita vt hæc eum ordinem habere debeat ad fortunæ partem, quam habet Sol ad Orientalem finitorem, prout docuit Ptolem. lib. 3. cap. 12. sortis seu fortunæ nomen ideò illi datum, quia in Genethliacis ex eo sumitur significatio de fortunis, ac diuitiarum sorte. Sed enim quisnam sit verus fortunæ locus, & quonam pacto ea extrahenda sit, id paulò fusiùs explicandum erit, quoniam Ptolemæi verba non satis perspicua sunt. Ergo Ptolemæus citato loco de fortunæ parte sermonem instituens, hæc habet: Fortuna quidem partem colligimus vbiq[ue] nocte non secus ac die ex numero partium interceptarum inter Solem, & Lunam, si totidem partes ab ascendente signo iuxta signorum consequutionem abijciamus: quò tunc sanè euaserit supputatio, eam signi partem, eumque locum dicimus fortunæ sortem continere; vt quam rastonem, siue configurationem habet Sol ad Orientalem finitoris partem, eam habet & Luna ad partem fortunæ, & sit veluti Lunaris quidem horoscopus. Hæc Ptolemæus. Hinc vulgus Astrologorum hanc supputandi methodum seruant in partibus Zodiaci, ita vt vbi desinat supputatio, ibi constituatur fortunæ pars, isque gradus Eclipticus dicatur Lunaris horoscopus, proindeque omni latitudine careat. At enim pro Solari horoscopo nos non accipimus gradum eclipticum, cum quo Sol mane oritur, & mukominùs is, qui quouis tempore in finitore Orientali reperiatur, cùm is materialiter se habeat ad horoscopum, aut diurnas configurationes cum Sole, sed præcisè lineam Orientalem, à qua Sol motu diurno discedit incedens per arcus sui paralleli, ita vt cùm fuerit in cuspide vndecimæ, siue perfecerit duas partes è tribus sui arcus semidiurni, tunc verè dicatur esse in sextili sui horoscopi; quando est in Meridiano, siue compleuerit totum arcum semidiurnum, sit in

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198 LEXICON which are temperately hot and moist, and therefore increase and preserve the heat of the nativity and the radical moisture. The former is called the greater fortune, because it is higher, masculine, diurnal, abounding more in heat than in moisture; the latter the lesser fortune, because it is lower, smaller in body, feminine, nocturnal, and abounding more in passive than in active qualities. Likewise the two infortunes, Mars and Saturn: this is the greater infortune, prevailing in a quality contrary to natural heat and moisture, namely cold and dry; that one the lesser infortune, because nocturnal, because hot, but nevertheless intemperately dry, whereby it affects and consumes all things with its dryness. Moreover, the other planets are of a middle nature, and are easily transformed into fortunes, or even into infortunes, by mixture with these. On this matter see in the proper places. 34. The part of Fortune is called the Lunar horoscope, and the place in the situation of the World from which the Moon begins to advance, when the Sun emerges from the line of the East. Thus it should have the same relation to the part of Fortune as the Sun has to the oriental boundary, as Ptolemy taught in book 3, chapter 12. The name of lot or fortune was given to it for this reason, because in genethlialogical matters the indication of fortunes and the lot of riches is taken from it. But what the true place of Fortune is, and in what way it should be extracted, this will have to be explained somewhat more fully, since Ptolemy’s words are not sufficiently clear. Therefore Ptolemy, in the cited place, when discussing the part of Fortune, has these words: We collect the part of Fortune everywhere, by night no less than by day, from the number of intercepted parts between the Sun and the Moon, if we subtract from the ascending sign the same number of parts in accordance with the succession of the signs; when then the calculation has clearly escaped, we call that part of the sign, and that place, to contain the lot of Fortune; as the ratio, or configuration, which the Sun has to the oriental part of the boundary, that the Moon also has to the part of Fortune, and it is as it were the Lunar horoscope. These are Ptolemy’s words. Hence the common run of astrologers preserve this method of calculation in the parts of the Zodiac, so that where the calculation ends, there the part of Fortune is established, and that degree of the ecliptic is called the Lunar horoscope, and therefore is without any latitude. But for the Solar horoscope we do not take the degree of the ecliptic with which the Sun rises in the morning, nor much less that which at any time may be found in the oriental boundary, since that is materially related to the horoscope, or to diurnal configurations with the Sun, but precisely the eastern line, from which the Sun departs by daily motion, proceeding through the arcs of its parallel, so that when it is in the cusp of the eleventh house, or has completed two parts out of three of its semi-diurnal arc, then it is truly said to be in the sextile of its horoscope; when it is in the Meridian, or has completed the whole semi-diurnal arc, it is in

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MATHEMATICVM. 199 quadrato; quando adhuc totum arcum semidium, & trien- tem sit in nona, & respiciat verè horoscopum suum de Trino: quando demum per totum arcum diurnum distiterit ab horos- copo, tunc sit verè illi oppositus, atque in cuspide Occidentis constitutus, & sic de reliquis domibus subterraneis; ita vt inte- gro die natutali Sol per suum parallelem incedens permutet successiuè omnes configurationes quas potest habere cum ho- roscopo: neque enim in Zodiaco computari possunt huiusmodi respectus, neque ad partes Zodiaci, cum in eo Sol moueatur inæqualiter, & admodum lentè ferè gradum vnum singulis diebus, ac præterea etiamsi fortè quandoque accidat, vt dum Sol in cæli culmine reperitur, reuet à tot gradus Zodiaci inter- cipiantur inter ipsum, & gradum Zodiaci horoscopantem, quot requiruntur ad aspectum quadratum, hoc est gr. 50. id tamen non semper accidit ob Zodiaci obliquitatem, & sæpè inter lineam Orientalem, & Meridianam modò duo in signis longarum ascensionum, modò quatuor in signis breuium as- censionum intercipiuntur signa, & aliàs materiali est ista ha- bitudo Solis ad gradum Zodiaci horoscopantem, cum horos- copus latitudinem habear, & eius locus successiuè varietur pro qualitate gradus ascendentis cum Sole prout maiorem, vel minotem habet declinationem: horoscopus enim Solaris pro- priè & rigorosè sumptus ad hunc diem non est nisi punctus, vnde emersit Sol è linea Orientali, in hac die, non ille in quo precisè reperitur alius gradus Eclipticæ, in quo Sol actu non reperitur: ergo impertinens est habitudo Solis ad hunc gradum horoscopantem, sed sanè eius configuratio quam successiuè acquirit attendi debet in partibus sui arcus diurni, seu paralle- li, quam integra die naturali describit circa tellurem, atque ad punctum, vnde emerserat mane, non ad alia, in quibus inci- dant singuli eclipticæ gradus successiuè motu primi mobilis emergentes, atque adeò hæc supputatio facienda est non in Zodiaco, sed in æquatore per ascensoria tempora, quandoqui- dem hæc sola seruant æqualitatem, & æqualem Solis incessio- nem denotare possunt, vnde appareat Solis distantia ab horos- copo, ac propterea eius ad illum configuratio. Nunc si hanc eandem habitudinem (prout præcipit Ptole- 35. mæus) attendere velimus in Luna erga suum horoscopum hic definiri debet in parallelo Lunæ, vt ingeniosissimè discurrit Adrianus Negusantius vir sanè eruditissimus amicus meus, & quem ob singularem humanitatem, eruditionem, atque huius aliorumque secretorum detectionem summopete veneror. Si- quidem, inquit ipse, cùm Sol ad Orientis peruenit Cardinem, tunc Lunam penes suum horizontem reperiri necesse est: mox aqua- N iiij

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MATHEMATICVM. 199 when it is still half an arc, and a third part in the ninth house, and it truly regards its own horoscopic point from the east; when at last it has departed through the whole diurnal arc from the horoscopic point, then it is truly opposite to it, and placed at the cusp of the West, and so likewise for the remaining subterranean houses; so that in the whole natural day the Sun, moving through its own parallel, successively changes all the configurations it can have with the horoscopic point. For such respects cannot be computed in the Zodiac, nor according to parts of the Zodiac, since in it the Sun moves unevenly, and very slowly, scarcely one degree each day; and besides, even if perhaps it should happen at any time that, while the Sun is found at the summit of the sky, so many degrees of the Zodiac are intercepted between it and the horoscopic degree of the Zodiac as are required for a square aspect, that is, 50 degrees, yet this does not always occur on account of the obliquity of the Zodiac; and often between the Eastern and the Meridian line, now two signs of long ascension, now four signs of short ascension, are intercepted, and otherwise the relation of the Sun to the horoscopic degree of the Zodiac is material, since the horoscopic point has latitude, and its place is successively varied according to the quality of the rising degree with the Sun, insofar as it has greater or lesser declination: for the solar horoscopic point, taken properly and rigorously for this day, is nothing other than the point from which the Sun emerged from the Eastern line on that day, not that in which precisely another degree of the Ecliptic is found, in which the Sun is not actually found. Therefore the relation of the Sun to this horoscopic degree is irrelevant; but indeed the configuration which it successively acquires must be considered in the parts of its diurnal arc, or parallel, which it describes in the whole natural day around the earth, and to the point from which it had emerged in the morning, not to others, in which the individual degrees of the ecliptic arise successively by the motion of the first mover; and therefore this computation must be made not in the Zodiac, but in the equator by ascensional times, since these alone preserve equality and can indicate the equal course of the Sun, whence the Sun’s distance from the horoscopic point may appear, and therefore its configuration with it. Now if we wish to observe this same relation, as Ptolemy prescribes, in the Moon with respect to its horoscopic point, here it must be defined in the Moon’s parallel, as the most ingenious Adrianus Negusantius discourses, a man most learned indeed, my friend, and one whom I venerate most highly on account of his singular kindness, learning, and the disclosure of these and other secrets. For, he says, when the Sun reaches the cardinal point of the East, then the Moon must necessarily be found near its horizon: soon after aqua- N iiij

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100 LEXICON is temporis spatio, Sole digresso, secundùm suas ascensiones ab ipsa remouers. Sicque dum Sol discedit ab ortu incedens per suum parallelum, & Luna discedit pari ratione à suo horoscopo per suum parallelum procedens, cùm Sol est in cuspide vndecimæ, Luna sit in sexili partis fortunæ: cum Sol in decima; Luna in quadrato, & sic de reliquis; adeout quot partibus de suo parallelo Sol fuerit à suo horoscopo elongatus, toridem, & Lunam contingat abesse à suo horoscopo, siue parte fortunæ. Vnde consequens erit, vt non semper verus locus partis fortunæ maneat in Zodiaco, sicur non semper cum gradibus Zodiaci convenit punctus horizontis, vnde emergit Sol; sed modò casu in eum incidat, modò ab eo elongatur, seu potius ab eo Zodiacus separetur; semper tamen maneat in parallelo Lunari, quemadmodum punctus ortus Solis in parallelo Solis, proindeque eamdem habeat cum Luna declinationem. 36. Hæc igitur est partis fortunæ Theotia, cui subscribit Pater de Titis magister meus, atque eiusdem Negusantij in primo mobili, in Ptolemæi Quadrip. quod nuper edidit Breuiarijs alijsque in locis, vltrò fallus, se diu circa fortuna partem laborasse, nihilque veri ad hac vsque tempora inuenisse: cum aliàs in Cælesti Philosophia lib. 3. cap. 5. docuisset, eam constituendam esse in orbita Lunæ. 37. Neque verò hæc noua doctrina est, quæ non ab antiquioribus etiam fuerit cognita. Consonat Ptolemæus in versione Arabica, quam protulit Hali Heben Rodoan primus eius Commentator. Consonat Georgius Valla celebtis author in commentar. ad Quadrip. Ptolemæi. Is enim de fortunæ parte differens hæc habet. Quod autem sors fortunæ horoscopus quidem sit nocturnus, & lunarii, manifestum est ex eis, qua ait Ptolemaus, eandem namque rationem partum habebis ad sortem fortunam Luna, eandemque figurationem, quam habes Sol ad horoscopum. Vt autem ostendat se hanc figurationem, & positum Lunæ ad suum horoscopum non intelligere in Zodiaco, sed in suis luminarium parallelis, mox subdit. Manifestum insuper magis erit, etiam ex his, si eadem disciplina temur per Canonem, qua etiam in horoscopo: inuensetur enim rursus vt horoscopus sors fortuna. Inducentes namque partem Luna in diurnis genesibus, in nocturnis autem per opposita capiendo Ascensoria Tempora, & Horas multiplicamus, & factum numerum componemus cum Ascensionibus quæremus in ipsorum climase, ubi cadat numerus, & ibiesse dicitum lunarem horoscopum. Portò Ascensiones, ascensoria tempora, & horæ appellant solum arcum diurnum, & nocturnum, qui fit in proprijs cuiusque parallelis, super quibus mouentur luminaria motu vniuersitatis, & efficiunt distantias à cardini-

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100 LEXICON in the space of time, when the Sun has departed, according to its ascensions, from it. And thus, while the Sun departs from the east, advancing through its own parallel, and the Moon likewise departs from its horoscope, proceeding through its own parallel, when the Sun is at the cusp of the eleventh house, the Moon will be in sextile to the part of fortune; when the Sun is in the tenth, the Moon in quadrature; and so of the rest; so that, by as many parts of its parallel as the Sun is removed from its horoscope, by so many likewise will the Moon happen to be absent from her horoscope, that is, from the part of fortune. Whence it will follow that the true place of the part of fortune does not always remain in the zodiac, just as the point of the horizon from which the Sun rises does not always correspond with the degrees of the zodiac; rather, sometimes it falls upon it, sometimes it is removed from it, or rather the zodiac is separated from it; yet it always remains in the lunar parallel, just as the point of the Sun’s rising is in the Sun’s parallel, and consequently has the same declination as the Moon. 36. This, then, is the theory of the part of fortune, to which Father de Titis, my teacher, subscribes, and also Negusantius, in the first mobile, in Ptolemy’s Quadripartitum, which he recently published in Breviaries and in other places, confessing freely that he had labored for a long time about the part of fortune and had found nothing true about it up to this time: although elsewhere, in Celestial Philosophy, book 3, chapter 5, he had taught that it must be established in the orbit of the Moon. 37. Nor is this in fact a new doctrine, for it was also known to the ancients. Ptolemy agrees, in the Arabic version, which Hali Heben Rodoan, his first commentator, produced. Georgius Valla, a celebrated author, also agrees in his commentary on Ptolemy’s Quadripartitum. For he says this concerning the part of fortune: “That the lot of fortune is indeed nocturnal and lunar is clear from what Ptolemy says; for you will have the same relation of the part of fortune to the Moon and the same configuration as you have of the Sun to the horoscope.” In order to show that he does not understand this configuration and the position of the Moon to its horoscope in the zodiac, but in the parallels of the luminaries, he adds immediately: “It will also be made clearer from these things, even if by the same discipline we are guided through the canon, as also in the horoscope: for it will again be found that the horoscope is the lot of fortune. For when we bring in the lunar part in day births, but in night births take by opposite means the ascensional times, and multiply the hours, and combine the resulting number with the ascensions, we shall seek in their climate where the number falls, and there it is said to be the lunar horoscope. Moreover, ascensions, ascensional times, and hours denote only the diurnal and nocturnal arc, which is made in the proper parallel of each, above which the luminaries move with the motion of the universe, and produce distances from the cardini-

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MATHEMATICVM. 201 bus mundi, vnde etiam fiunt configurationes ad horoscopum. Quare sicuti Sol non habet configurationes ad horoscopum nisi in mundo acceptos, ita & Luna non habet configurationes ad partem fortunæ, nisi tantùm in mundo. Ex his liquidò constat, quomodo supputanda sit pars fortunæ quod pluribus modis fieri potest: faciliùs tamen, & semper eodem modo, si sumatur vera distantia Solis ab horoscopo per ascensiones Climatis, auferendo semper ascensionem obliquam Solis sumptam in eleuatione horoscopi ab ascensione obliqua ipsius horoscopi, & quæ superest differentia addatur ascensioni rectæ Lunæ, nam vbi cadit numerus graduum productorum, in ascensionibus rectis, cum declinatione Lunæ, & numero, & regione eadem, ibi erit ascensio recta, & verus locus partis fortunæ, siue ea cadat in Zodiaco, siue extrà, quod parum refert, quandoquidem in hoc casu Zodiacus materialiter se habet, & perinde est, ac si non esset. Locetur autem in cælesti figura vbi cadit talis ascensio recta, cum tali declinatione. Quod si cui placeat, & locum illi in Zodiaco date, tam in 39: longum quàm in latum, id fiat per rabulas sinuum, quærendo quis gradus Zodiaci respondeat tam in longum, quàm in latum ad datam ascensionem rectam cum tali declinatione, eo prorsus modo, ac practicatur in stellis fixis. Similiter directiones partis fortunæ vtroque motu, & recto, < 40.> & conuerso fieri possunt ad familiaritates astrorum acceptas tantum in mundo: Recto quidem, si pars fortunæ consideretur immobilis in suo circulo horario, siue positionis expectans siderum corpora & aspectus, quæ ad ipsam motu vniuersitatis ferantur: Conuerso verò, si constituantur sidera, & aspectus occurrantes, immobiles, arque interim sors motu raptus ad eadem deuoluantur. Eius significata vide in V. horoscopus Lunaris. Pari ratione, & aliæ partes quinque extrahi possunt pro numero < 41.> reliquarum quinque erraticarum, quæ nihil aliud sunt quàm singulorum planetarum horizonta, & loca in situ mundi considerata, vnde emergunt planeræ, quando Sol emergit ab Oriente, ita vt eam semper habitudinem habeant isti planeræ ad suas partes, quam Sol ad suum horoscopum, acceptam in suis cuiusque parallelis eo prorsus pacto, ac dictum est de Luna, quæ proinde eandem habebunt declinationem, ac planetæ vnde extrahuntur. Hac sanè consideratione habita, non omninò inanies fortè reperienur partes ab Arabibus excogitatæ, & singulis rerum significarionibus attributæ; licet quæ passim circumferuntur, & inanes sint & fictitiæ, tum quia extrahuntur

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MATHEMATICVM. 201 of the world, whence also configurations to the horoscope are made. Therefore, just as the Sun does not have configurations to the horoscope except those received in the world, so also the Moon does not have configurations to the part of fortune except only in the world. From these things it is clearly established how the part of fortune is to be calculated, which can be done in many ways; more easily, however, and always in the same way, if one takes the true distance of the Sun from the horoscope by the ascensions of the climate, always subtracting the Sun’s oblique ascension, taken in the elevation of the horoscope, from the oblique ascension of the horoscope itself, and let the difference that remains be added to the Moon’s right ascension; for where the number of degrees produced falls, in the right ascensions, together with the Moon’s declination and the same number and region, there will be the right ascension and the true place of the part of fortune, whether it falls in the Zodiac or outside it, which matters little, since in this case the Zodiac is materially so considered, and it is the same as if it were not. But let it be placed in the celestial figure where such right ascension falls, with such declination. And if anyone prefers, and gives it a place in the Zodiac, both in 39: longitude and in latitude, let this be done by means of sine tables, seeking which degree of the Zodiac corresponds both in longitude and in latitude to the given right ascension with such declination, in precisely the same way as is practiced with fixed stars. Likewise, directions of the part of fortune in both motions, both direct and <40.> converse, can be made to the familiarities of the stars, received only in the world: by the direct motion, indeed, if the part of fortune is considered fixed in its hourly circle, or position, awaiting the bodies and aspects of the stars, which are carried to it by the motion of the universe: by the converse motion, however, if the stars and approaching aspects are set as fixed, and meanwhile the lot, carried by motion, is drawn down to them. See its significations in V. lunar horoscope. In like manner, the other five parts can also be drawn out for the number <41.> of the remaining five wandering stars, which are nothing other than the horizons of the individual planets, and the places considered in the position of the world, whence the planets emerge, when the Sun emerges from the East, so that these planets always have toward their parts the same relation as the Sun to its horoscope, taken in their respective parallels, in exactly the same way as was said of the Moon, which therefore will have the same declination as the planet from which they are drawn. With this consideration certainly in hand, the parts perhaps will not be found altogether empty, which were devised by the Arabs and attributed to each signification of things; although those that are everywhere circulated are empty and fictitious, both because they are drawn out

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LEXICON in partibus Zodiaci, qui hac in re locum non habet, tum etiam quia plures singuntur quam numerus planetarum postulet, atque accipiuntur à domibus ad planetas, & è contrà, vel etiam à planeta ad planetam, cùm reuerà tantum per habitudinem ad Solem accipiendæ sint, nec aliud esse possint, quàm ea habitudo planetæ ad locum vnde discesserat, Sole in Oriente constituto, quam habet Sol ad ipsum Orientem, vnde manè emerserat. Igitur ad calculandas istas partes accipiatur semper distantia Solis ab horoscopo, vt de fortunæ parte dictum est, eaque adijciatur ascensioni rectæ planetæ, cuius horoscopum quærimus, nam locus productus erit ascensio recta illius partis, & verus horoscopus planetæ quem quærimus, habens eandem declinationem planetę, cuius est pars, dirigendus eodem modo, ac diximus de parte fortunæ pro suis cuiusque significatis. FOVEA, Græcis Ipogon dicitur ab Astronomis quarta pars domus ab horoscopo & cardo Imi cæli ab inferiore situ, & loco; ac potissimè eò quod sit veluti fouea planetarum, vt proinde non ab re ab aliquibus constituatur inter præcipuos An[n]eretas, ad cuius lineam directus vitæ significator, seu ascendens, seu luminare in ascendente repertum, vltimam vitæ periodum faciat. Quod tamen ego ex Titi placitis haud probare possum, quippe erius consideratio sit tantùm in mundo, neque aut cardo Imi cæli, aut ascendens loco mouetur, vt alter in alterum impingat, neque moderatores planetæ motu suo reali, qui est idem ac primi mobilis ferri possunt ab Oriente ad Ium cæli, quin transeant prius per medium cæli & occasum: quem enim motum habent ad partes Orientaliores est cuique proprius in Zodiaco, cuius respectus materialiter tantùm habetur ad cardines mundi, ac perinde est, ac si non esset. Sed de hac re alibi satis. Cæterùm huius domus significata vide in V. Ium cæli. FRACTIONES dicuntur ab Arithmeticis, atque etiam ab <43.> Geometris partes minimę aliarum partium quantitatis, seu continuæ, seu discretæ. Vt sunt minuta in gradibus, secunda in minutis; terria in secundis &c. De modo eas inueniendi ex radice quadrata, lege lunctinium in Commentar. ad spæram Io. de Sacrobosco pag. mihi 360. FRIDARIE, seu Aifridarie apud Arabes est quædam temporaria potestas planetarum participantium cum domino decenniorum in gubernatione vitæ nati, ita vt si natiuitas sit diurna, primum decennium sibi vendicet Sol, cum participatione tamen aliorum planetarum per septimam partem, hac videlicet ratione vt Sol gubernet solus septimam partem decennij, quæ comprehendit vnum annum solarem, mens. 5. & dies circiter qua-

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LEXICON in partibus of the Zodiac, which in this matter has no place, and also because more parts are assigned than the number of the planets requires, and they are taken from houses to planets, and conversely, or even from planet to planet, whereas in truth they ought to be taken only in relation to the Sun, and can be nothing else than that relation of the planet to the place from which it departed, the Sun being placed in the East, which the Sun has to the very East from which it had risen in the morning. Therefore, in calculating these parts, let the distance of the Sun from the horoscope always be taken, as was said of the Part of Fortune, and let it be added to the right ascension of the planet whose horoscope we seek; for the resulting place will be the right ascension of that part, and the true horoscope of the planet we seek, having the same declination as the planet whose part it is, is to be directed in the same manner as we said of the Part of Fortune for each of its significations. FOVEA, called Ipogon by the Greeks, is by astronomers the fourth part of the house from the horoscope and the angle of the lower heaven, from the lower position and place; and especially because it is, as it were, a pit of the planets, so that therefore it is not without reason that by some it is placed among the chief Anaretae, toward whose line, if the significator of life, whether the ascendant, or the luminary found in the ascendant, be directed, it makes the final period of life. Yet this I cannot approve according to the doctrines of Titius, since its consideration is only in the world, and neither the angle of the lower heaven nor the ascendant is moved in place, so that one strikes into the other, nor can the ruling planets by their real motion, which is the same as that of the primum mobile, be carried from the East to the lower heaven without first passing through the midheaven and the west: for the motion they have toward the more eastern parts is proper to each one in the Zodiac, whose relation is regarded materially only with respect to the angles of the world, and so it is as if it were not. But enough of this matter elsewhere. Otherwise, see the significations of this house in the Midheaven. FRACTIONS are called by arithmeticians, and also by <43.> geometers, the smallest parts of other quantities, whether continuous or discrete. Such are minutes in degrees, seconds in minutes; thirds in seconds, etc. For the method of finding them from the square root, read Lunctinium in the Commentary on the Sphere of Johannes de Sacrobosco, page 360 in my copy. FRIDARIE, or Aifridarie among the Arabs, is a certain temporary power of the planets participating with the lord of the decennials in the governance of the native’s life, so that if the nativity is diurnal, the Sun claims the first decade for itself, with the participation, however, of the other planets by a seventh part, in this way, namely, that the Sun governs alone the seventh part of the decade, which comprises one solar year, 5 months, and about days...

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MATHEMATICVM. 203 tuor; post prosequatur ipsa dominium, sed cum participatiove Veneris itidem per septimam partem, quæ cum priori facit annos duos, menses decem, dies circiter 13. inde cum Mercurio vsque ad ann. quatuor mens. 3. dies 14. postea cum Luna, Saturno, Ioue, singulis per suas partes, ac tandem cum Marte compleat decennium, & suam fridariam potestatem. Post Solem sequitur Venus, ad quam spectat fridaria potestas per integros annos octo, ita vt facta diuisione in septem partes æquales, primam septimam gubernet ipsa sola, secundam cum participatione Mercurij, tertiam cum Luna, quartam cum Saturno, & sic de reliquis; ita vt cum Sole veniat ad complendos annos 18. Tertiò in dispositione fridariæ, sequirur Mercurius per annos tredecim, eodem modo prosequendo & solus, & cum participatione aliorum suam fridariam potestatem vsque dum eam compleat cum Varone ad annos 31. Quartò Luna, cuius anni fridariæ sunt nouem. Quintò Saturnus, qui haber fridariam potestatem per annos 11. Sextò Iupiter, qui gubernar annos 12. Septimò Mars, cuius anni fridariæ sunt septem. Post quem sequuntur caput, & cauda Draconis, illud per annos tres, hæc verò per annos duos; ita vt tota collectio annorum sit 75. Qua complera iterùm deuoluitur dispositio ad Solem eo modo quo superiùs explicatum. Et hic est ordo fridariæ potestatis planetarum per diem: Si verè nocturna fuerit natiuitas, incipit dispositio à Luna per suos annos, quos diximus esse nouem prosequendo suum dominium per primam septimam partem sola; per reliquas cum aliorum planetarum participatione; primò cum Saturno, deinde cum Ioue &c. Expletis nouem annis Lunæ, ingreditur Saturnus suam dispositionem eodem modo per suos annos vndecim: inde Iupiter, Mars, Sol, Venus, Mercurius, caput, & cauda per suos annos in septem partes tributos, ex quibus primam quisque sibi solus vendicat, postremam terminat cum participatione eius, qui ipsum præcesserat. Et hæc de fridarijs: quarum concinnam dispositionem pensiranti mihi in mentem venit lepidum illud Vulpeculæ apud Æsopum dictum, quæ inuentum in statuarij officina humanum caput ex lapide affabritè dedolatum demirans O quale, inquir, opus! sed cerebro cares. O pulchram, concinnamque dicam ego fridariæ planetarum distributionem! sed vanitate plenam Sanè eotum nescio quis de hac fridaria potestate sermonem faciens, in partibus, inquit, dictis fridaria nescio rationem; nisi quoniam sic experti sunt Persarum sapientes. Porrò earum considerationem consultiò hic attexere volui, tum ad operis complementum, tum maximè, ne curiosi magnum quid in eis concipientes suo

Transcription: Translated (English)

...together; after which the dominion itself proceeds, but with the participation of Venus likewise by the seventh part, which with the preceding makes two years, ten months, about 13 days; then with Mercury up to 4 years, 3 months, 14 days; afterward with the Moon, Saturn, Jupiter, each by their own portions, and finally with Mars it completes the decade and its fridarian power. After the Sun comes Venus, to whom belongs fridarian power for a full eight years, so that when divided into seven equal parts, the first seventh is governed by herself alone, the second with the participation of Mercury, the third with the Moon, the fourth with Saturn, and so on with the rest; thus with the Sun it comes to make up 18 years. Third in the arrangement of the fridaria, comes Mercury for thirteen years, proceeding in the same manner, both alone and with the participation of others, in his fridarian power until he completes it with Varona at 31 years. Fourth, the Moon, whose fridarian years are nine. Fifth, Saturn, who has fridarian power for 11 years. Sixth, Jupiter, who governs for 12 years. Seventh, Mars, whose fridarian years are seven. After whom follow the head and tail of the Dragon, the former for three years, the latter for two; so that the whole total of years is 75. When this is completed, the disposition again turns back to the Sun in the manner explained above. And this is the order of the fridarian power of the planets by day: If the birth were truly nocturnal, the arrangement begins from the Moon through her own years, which we said are nine, proceeding through her dominion for the first seventh part alone; through the remaining parts with the participation of the other planets; first with Saturn, then with Jupiter, and so on. When the nine years of the Moon are completed, Saturn enters his arrangement in the same way for his eleven years; then Jupiter, Mars, the Sun, Venus, Mercury, the head, and the tail, each through their own years divided into seven parts, of which the first each claims for itself alone, and the last it ends with the participation of the one who preceded it. And this concerning the fridaria: in contemplating their orderly arrangement, there came to my mind that witty saying of the Fox in Aesop, who, admiring a human head found in a sculptor’s workshop, finely carved from stone, said, “O what a work!” but you lack brains. O how beautiful, how orderly, would I say, is the distribution of the planets in the fridaria! but truly full of vanity. Long ago some unknown person, speaking of this fridarian power, said, in the parts, I know not the reason for the fridaria mentioned; except because the wise men of the Persians have experienced it thus. Moreover, I wished to append the consideration of these matters here more wisely, both to complete the work, and especially lest the curious, conceiving some great thing in them, should in their own...

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104 LEXICON desiderio frustrati incauti apud alios quærentes deciperentur, sed potiùs hic earum vanitatem edocti negligerent, arque ad meliora studia animum applicarent. Eaproper ab recensendis significatis abstinui. 45. FRUSTRATIO: vide in V. Alfazim. 46. FVLXIO, teste Valla, apud antiquos Astronomos vsurpabatur de ortu planetarum heliaco, quando videlicet existentes sub radijs Solis, arque adeò occultari posteà elongaris fulgere incipiebant, & se conspicuos reddere. Vide in V. Ormus heliacus. GA 1. GADIO, teste Kirchero, Chaldaicè dicitur signum, & constellatio Capricorni decimum ab Ariete: apud Hebræos autem Gedi. 2. GAIRALCOBOL, Arab. idem sonat, ac Latinè receptio. Estque cum planeta existens in suis dignitaribus, siue per aspectum, siue per conjunctionem alteri applicat, qui in eodem loco dignitatem aliquam obrineat: tunc enim inter se naturam communicant, ac mutuò se recipiunt. Fit etiam huiusmodi receptio, quando planeta superior est in dignitatibus inferioris, & inferior in dignitatibus superioris: quod quidem fortitudinem addit, & perinde est, ac si quisque in suis dignitatibus foret. 3. GALANCEN dicitur Arabicè planeta vacuus cursu; cùm videlicet ab alio separatur, nec proptereà alteri applicat siue aspectu, siue coniunctione: quod sanè maximum derrimentum est, præsertim in Luna: Quæ proinde apud Latinos denominatur feralis, agrestis &c. 4. GALAXIA est Circulus magnus, & latus instar fasciæ cuiusdam inæqualis in firmamento existens, & sua amplitudine circumplectens sidera Cassiopæ, Cygni, Aquilæ volantis, partem Sagittarij, caudam Scotpij, Centaurum, Argonauta, pedes Geminorum, & Perseum. Hic solus circulus est realis in cælo, quippe qui serena nocte semper conspicuus instar nubeculæ cuiusdam suboscuræ albedinem quandam præsefert, quæ quia lacti similis, Via lactea appellatur, atque à Poëris mirificè effertur: quos inter Ouidius lib. 1. Meramorphos. eam viam per quam ad superos, atque ad regna Tonantis itur, appellat. Sic inquiens: Est via sublimis Cælo manifesta sereno, (Lactea nomen habet) candore notabilis ipso: Hac iter est Superis ad magni regna Tonantis, Regalemque domum, &c.

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104 LEXICON desiring, frustrated and imprudent, lest in seeking them among others they should be deceived, but rather, having been taught here of their vanity, they should neglect them, and apply their minds to better studies. For this reason I have refrained from listing the meanings. 45. FRUSTRATIO: see in V. Alfazim. 46. FVLXIO, according to Valla, was used by the ancient Astronomers for the heliacal rising of the planets, when, namely, being under the rays of the Sun, and after having been hidden, when farther away they begin to shine and make themselves visible. See in V. Ormus heliacus. GA 1. GADIO, according to Kircher, in Chaldaic means the sign and constellation of Capricorn, the tenth from Aries; among the Hebrews, however, Gedi. 2. GAIRALCOBOL, in Arabic, means the same as Latin receptio. And it occurs when a planet existing in its dignities, whether by aspect or by conjunction, applies to another which has some dignity in the same place: then indeed they communicate nature with one another, and mutually receive one another. Such reception also occurs when the superior planet is in the dignities of the inferior, and the inferior in the dignities of the superior: which indeed adds strength, and is as though each were in its own dignities. 3. GALANCEN is said in Arabic of a planet void of course; namely when it separates from another, and therefore applies to no other, either by aspect or by conjunction: which is certainly a great detriment, especially in the Moon: which therefore among the Latins is called feralis, agrestis, etc. 4. GALAXIA is a great circle, broad like a certain uneven band, existing in the firmament, and with its width encompassing the stars of Cassiopeia, Cygnus, the Flying Eagle, part of Sagittarius, the tail of Scorpius, the Centaur, Argo, the feet of Gemini, and Perseus. This is the only circle that is real in the heavens, since on a clear night it is always visible like a certain slightly dark cloud, showing a kind of whiteness, which, because it is like milk, is called the Milky Way, and is wonderfully praised by the poets: among whom Ovid, in book 1 of the Metamorphoses, calls it the road by which one goes to the upper regions and to the realms of Tonans. Thus he says: There is a lofty road, clear in the serene sky, (It bears the name Milky) notable for its very whiteness: By this the way lies for the gods to the realms of mighty Tonans, and to the royal dwelling, etc.

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MATHEMATICVM. 205 Olim multa fuit de hoc Circulo disceptatio: Aristoteles 5. illum volebat in aëris regione consistere; sed id falsitatis euincitur; quippe hac ratione non semper cerneretur ex quacunque terræ plaga transire per easdem stellas firmamenti, vt patet de ignitis cometis, qui in aëre generantur. Alij opinati sunt esse partem firmamenti continuam, cæteris densiorem, ita ut Solis lumen accipere possit, non tamen ità densam, vt fixæ. Sed tamen nostro xuo ferè in compertissimo est, cum aliquid non esse, quam congeriem plurium stellularum inuicem collucentium, quæ ob multitudinem, vicinitatem, exilitatem, atque ob oculis nostris distantiam distinctè conspici nequeunt, sed apparent, vt confusa quædam nubes subalbicans, eo modo quo sunt duæ nubiculæ ad polum Antarticum, atque omnes stellæ, quas dicimus nebulosas, & nunc ope Telescopij, ac testimonio nuntij siderei scimus esse plures stellas in vnum colligatas. Roberatur id eò potissimum, quod noua Phænomena in cælo enata non nisi in Galaxia visa sunt; vt noua stella quæ in sede Cassiopæ anno 1572. apparuit, ac duos integros annos durauit; quæ item anno 1600. visa est in pectore Cygni, ac postea sensim euanuit, relicto in loco vbi erat quodam hiatu, qui etiam nùm visibilis est, ac taudem quæ anno 1604. in genu Serpentarij clarè enituit, & post annum discessit. Preterquam idipsum etiam credendum existimo de septima Pleiadum, quæ non nisi statis temporibus etiam lippis oculis se conspicabilem reddit, quæ cæteroqui ita latet, vt ab aliquibus cælo gratis affixa credatur. Quapropter haud imprababile est, eas aliud planè non extitille, quam plures stellulas loco dimotas, atque in vnum collectas ad certum tempus, ex quo vnum numero Astrum in tanta distantia peruisus illusionem æstimaretur: idque maximè locum habet si cælum ipsum cum Tychone ponamus fluidum, per cuius expansam facilè concipi possit vagus iste minutarum stellatum discursus. Porrò Galaxia varios & miros habet effectus, quorum plurimos refert Plinius lib. 18. cap. 29. GALGAL Hammaticalosb teste Kirchero in Oedipo Ægyptiaco < 6.> dicitur apud Hebreos Zodiacus, hoc est sphæra signorum: GALLINA, Olor, &c. fidus in cælo intrà Galaxiam constitutum. Vide in V. Cygnus. < 7.> GARBINVS vulgò Italorum dicitur ventus vnsus ex quatuor < 8.> intermedijs spirans ex xquo inter meridiem & occasum. Græcis Notolybicus, vide eius qualitates sub hoc Vocab. GAVDINM apud Astronomos est species quædam dignitatis, < 9.> & fortitudinis planetis accidens ab extrinsecio, cum profecto

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MATHEMATICVM. 205 There was once much dispute about this Circle: Aristotle wanted it to stand in the region of the air; but this is proved false, since on that basis it would not always be seen from any part of the earth to pass through the same stars of the firmament, as is evident from fiery comets, which are generated in the air. Others have thought it to be a continuous part of the firmament, denser than the rest, so that it can receive the light of the Sun, yet not so dense as the fixed stars. But in our own age it is almost certain that it is not one single thing, but a cluster of many little stars shining upon one another, which, because of their multitude, proximity, minuteness, and because of their distance from our eyes, cannot be distinctly seen, but appear as some confused whitish cloud, in the same way as the two little clouds near the Antarctic pole, and all those stars which we call nebulous; and now by means of the Telescope and the testimony of the sidereal messenger we know that they are several stars gathered into one. This is especially confirmed by the fact that new phenomena arisen in the heavens have been seen only in the Galaxy; such as the new star which appeared in the seat of Cassiopeia in the year 1572 and lasted two full years; and likewise that which was seen in the breast of Cygnus in the year 1600 and then slowly faded away, leaving in the place where it had been a certain gap, which is even now visible; and finally that which in the year 1604 shone clearly in the knee of the Serpent-bearer, and disappeared after a year. Beyond this, I think it should also be believed of the seventh of the Pleiades, which shows itself visible only at fixed times, even to weak eyes, and otherwise lies so hidden that by some it is thought to be fixed gratis in the sky. Wherefore it is not improbable that they had been nothing else than several little stars shifted from their place and gathered into one for a certain time, so that one star, when seen at such a great distance, would be judged an illusion of vision; and this especially holds if, with Tycho, we suppose the heaven itself to be fluid, through whose expanse that wandering course of minute stars can easily be conceived. Moreover, the Galaxy has various and wondrous effects, most of which Pliny recounts in book 18, chapter 29. GALGAL Hammaticalosb, as Kircher testifies in the Oedipus Aegyptiacus, is called among the Hebrews the Zodiac, that is, the sphere of the signs: GALLINA, Swan, &c., a star fixed in the heaven within the Galaxy. See under Cygnus. < 7.> GARBINVS is the name commonly given by the Italians to one of the four intermediate winds, blowing equally between south and west. Among the Greeks it is called Notolybicus; see its qualities under this word. GAVDINM among astronomers is a certain kind of dignity and strength accruing to the planets from outside, when indeed

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LEXICON 206 fuerint in locis sibi opportunis, in quibus eorum virtus augescit, & roboratur. Est in duplici differentia. Alterum in Zodiaco in loco planetæ eiusdem conditionis, & naturæ; vt Sol in domibus Iouis, Sarurnus in domibus Mercurij, Venus in domo Lunæ: Alterum in Mundo ratione situs, & domus exlestis sibi congruæ. Sic Saturnus gaudet in duodecima, eoquia, inquit Cardanus, ibi est suprà terram, & ab angulis procul, nec sublimis, nec in malesica domo, qualis est octaua, quæ est significarix mortis. Iupiter gaudet in vndecima, cum sit beneficus, & ille locus beneficus est, vnde & bonus gedius dictus, & ex eo habentur significara amicorum, & rerum consequendarum. Mars gaudet in sexta, quia planeta nocturnus, vnde & ei conuenit domus nocturna, non angulus, non succedens, sed cadens idque eò maximè quod Saturnus ei per naturam inimicus gauder in opposita: Sol gaudet in nono, eo quia Religionis; & itineris ea domus significatrix est. Venus in quinta, quæ est voluptatum domus, ac filiorum, quos ipsa largitur. Mercurius in prima, quæ in membris humanis caput habet; ipse autem præsidere habet cerebro, spiritibus, ingenio, memoriæ, linguæ. Tandem Luna gaudet in tertia, tum quia hæc est itinerum brevium significatrix quo modo, & ipsa Luna; tum maximè, quia alterum luminare, nempe Sol gauder in domo opposita. < xc.> Dicuntur etiam planetæ gaudere in signis, vbi plures obtinent dignitates essentiales, quod propria notione ab alijs dicitur Solium, seu Carpentum. Hac ratione Porphyrius dicit planetas habere quoddam peculiare in certis signis adeò vt, si minimum quid accedat, possit iure etiam dici esse in suo gaudio. Sic Sarurnus gaudere dicitur ex suis domibus maximè in Aquario, vbi habet ius domicilij, & Trianguli: Iupiter ob eandem rationem in Sagittario: Mars similiter in Scorpion: Sol in Leone: Venus in Tauro: Mercurius in Virgine: Luna denique in Cancro. GE < 21.> GEMINI Arab. Gienz hoc est Ladai luenes: vnum ex duodecim Zodiaci signis ad Boream vergens tertium ab Ariete, commune, aereum, humanum: sic dictum eoquia cum Sol ipsum intrat terræ sata germinant, ac radicibus complicantur. Est temperarum, mixrum, varium, ob idque domus Mercurij, licet ob tropici vicinitatem aliquantulum ad calorem, & siccitarem decliner. Fertur, eos qui sub hoc signo nascuntur euadere callidos, bifrontes, animo duplices, tenaces, rixosos, avaros. Geminorum fidus in octaua sphæra, quemadmodum reliqua iam recessit de loco suo, quem tenebat tempore Ptolemæi

Transcription: Translated (English)

LEXICON 206 are in places suited to them, in which their power increases and is strengthened. There is a twofold distinction. One is in the Zodiac, in the place of the planet of the same condition and nature; as the Sun in the houses of Jupiter, Saturn in the houses of Mercury, Venus in the house of the Moon. The other is in the World, by reason of situation, and of a celestial house suited to it. Thus Saturn rejoices in the twelfth, because, as Cardanus says, there he is above the earth, and far from the angles, neither lofty nor in an evil house, such as the eighth, which is the significator of death. Jupiter rejoices in the eleventh, since it is benefic, and that place is benefic; from it are obtained the significations of friends and of things to be accomplished. Mars rejoices in the sixth, because, being a nocturnal planet, a nocturnal house is fitting for him, not an angle, not a succedent, but a cadent one, and especially because Saturn, his enemy by nature, rejoices in the opposite. The Sun rejoices in the ninth, because that house is the significator of religion and of travel. Venus in the fifth, which is the house of pleasures and of children, which she herself bestows. Mercury in the first, which in the members of man has the head; he himself, however, has charge of the brain, spirits, intelligence, memory, and speech. Lastly, the Moon rejoices in the third, both because this is the significator of short journeys, just as the Moon herself is; and most of all because the other luminary, namely the Sun, rejoices in the opposite house. < xc.> The planets are also said to rejoice in signs in which they obtain several essential dignities, which by a proper term is called by others the Throne, or Carpentum. For this reason Porphyry says that the planets have something peculiar in certain signs, so that if the least thing be added, it may rightly also be said that they are in their joy. Thus Saturn is said to rejoice from among his own houses especially in Aquarius, where he has the right of domicile and of the Triangle: Jupiter for the same reason in Sagittarius: Mars similarly in Scorpio: the Sun in Leo: Venus in Taurus: Mercury in Virgo: the Moon finally in Cancer. GE < 21.> GEMINI. Arab. Gienz, that is, Ladai luenes: one of the twelve signs of the Zodiac, tending toward the north, the third from Aries, common, airy, human; so called because when the Sun enters it the crops of the earth sprout and are intertwined with roots. It is temperate, mixed, variable, and for that reason the house of Mercury, though because of its proximity to the tropic it inclines somewhat toward heat and dryness. It is said that those born under this sign turn out clever, two-faced, double-minded, tenacious, quarrelsome, and avaricious. The constellation of Gemini is in the eighth sphere, just as the rest has already receded from its place, which it held in the time of Ptolemy

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MATHEMATICVM. 107 atque incipit nunc à gradu 25. Geminorum primi mobilis, & protenditur vsque ad 24. Caneri. Primæ partes eius sunt humidæ, mediæ temperatæ, postremæ instabiles cum aliqua sicci- tate. Pars Borealis mouet ventos; australis facit maximam ariditatem. Compræhendit in totum stellas 25. comprehensis etiam septem alijs informibus circa ipsum, (licet Keplerus eas alterat esse 30. & Baierus adhuc 31..) quarum præcipuæ duæ in capitibus, vna Castoris dicti apud Arabes Elgiante secundæ magnitudinis de natura Martis, & Mercurij; altera Pollucis dicti Herculis Arabicè de natura solius Martis, item & tertia in pede sinistro eiusdem Pollucis dicta propus quartæ gnitudinis de natura veneris, & Mercurij. De quibus omnibus abundè diximus in suis locis. GENESIS, seu Genitura apud Astrologos dicitur natalitium < 12.> thema coelestis siderum positus arrificiosè erectum pro punctò temporis, quo quis in lucem editur, ad indagandas inde coelestes impressiones illi obuenientes, temperamentum corporis, propensiones animi, ingenij qualitatem, ac morbos, quibus obnoxius aliquando fururus sit. Quod quidem obseruare debita cum cautione, neque superstitiosum est, neque inutile, ac sanctorum Patrum, Theologorumque assertis, summorumque Pontificum sanctionibus minime contrarium. Quandoquidem sidera, præsertim Luminaria sunt viuentium omnium parentes; Sol quidem vitalis potentiæ fons, Luna humidi radicalis; vnde ex eorum dispositione optimè coniectari potest in genere valida, aut infirma corporis constitutio, temperamentum, affectiones animi, (non tamen per se, sed per accidens, quoniam istæ à phantasmatibus atque organis corporeis pendent) vt testarur D. Thomas in prima parte quast. 115. art 4. vbi dicit: Plerumque Astrologi verum discunt in iudicandis hominum moribus, paucienim sunt qui resistunt sensus. & 2. de Gener. < 13.> Cum planeta, inquit, in persodali circulo erunt forstiores plures dabunt annos, & cum debilosores; pauciores. Vnde si signorum, & stellarum in illis positarum virtutem aliquis posset scire, quanta esset cals influentia certè cognosceres, & de sota mascenss vita prognosticari posset, quamuis nulla illarum rerum necessitatem imponat. Benè autem Angelicus Doctor dicit: Si aliquis posset scire, quoniam hæc notitia difficilis admodum est; non modò quia cælorum motus rapidissimus est, & pro minima temporis variatione (quod facillimum est ob horologiorum, aliorumque instrumentorum inæqualitatem) variari potest non leuiter cælorum positus; sed potissimum, quia adhuc non bene inter Astrologos exploratum quodnam dicendum sit verum instans natiuitatis, quo quis vitali hac aura frui incipiat; quam Phi-

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MATHEMATICVM. 107 and it now begins from the 25th degree of Gemini, the first movable sign, and extends as far as the 24th of Cancer. Its first parts are humid, the middle temperate, the latter unstable with some dry- ness. The northern part stirs up winds; the southern causes the greatest aridity. It comprises in all 25 stars, including also seven other ill-formed ones around it, (though Kepler says there are 30 of them, and Bayer still 31), of which the principal are two in the heads, one of Castor, called by the Arabs Elgiante, of second magnitude, of the nature of Mars and Mercury; the other of Pollux, called Hercules in Arabic, of the nature of Mars alone; likewise the third in the left foot of the same Pollux, called propus, of fourth magnitude, of the nature of Venus and Mercury. We have spoken at length of all these in their proper places. GENESIS, or Genitura, is called by astrologers the natal theme, a celestial arrangement of the stars artfully erected for the point of time at which someone is brought forth into the light, in order to investigate from it the heavenly impressions affecting him, the temperament of the body, the propensities of the mind, the quality of the intellect, and the diseases to which he may at some time be subject. To observe this indeed with due caution is neither superstitious nor useless, and is by no means contrary to the statements of the holy Fathers, the Theologians, or the sanctions of the Supreme Pontiffs. For the stars, especially the Luminaries, are the parents of all living things; the Sun is indeed the source of vital power, the Moon of the radical moisture; whence from their disposition one can best infer in general a strong or weak bodily constitution, temperament, affections of the mind, (not however in themselves, but by accident, since these depend on phantasms and bodily organs) as St. Thomas testifies in the first part, question 115, art. 4, where he says: "For the most part astrologers learn the truth in judging human character, for few are those who resist the senses." And in 2 De Gener. When, he says, the planets are in the sidereal circle, the stronger ones will give more years, and when weaker ones; fewer. Hence, if someone could know the power of the signs and of the stars placed in them, how great would be the influence of the heavens, certainly you would know, and one could prognosticate about the whole course of a man’s life, although none of those things imposes necessity. But the Angelic Doctor says well: If someone could know, because this knowledge is extremely difficult; not only because the motion of the heavens is most rapid, and with a very small variation of time (which is very easy because of the inequality of clocks and other instruments) the positions of the heavens can be changed not a little; but especially because it has not yet been well determined among astrologers what should be considered the true instant of birth, when someone begins to enjoy this vital breath; which Phi-

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108 LEXICON < 14.> Losophi definiere Naturis caloris permanentiam vel sensitivis spiritus operationem. Ideò aliqui instans natuiitatis dixerunt punctum exitus nati ex vtero: Verum quia id successiuè fit, & per partes, ita vt quandoque integræ horæ labantur, sæ pè etiam integium diem fætus consistat per dimidium sui corporis intrà vterum Matris, per reliquam medietatem extrà, adhuc sub quæstione erit, quale dicendum sit verum natiuitatis momentum, ad quod cæleste thema erigi debeat. Titus in Cælesti Philosophia more suo erudissimi rem expendens, reiectis aliotum sententijs, ex intimis Philosophiæ principijs concludit id esse, cum fætus incipit fieri independens à sua causa proxima, proindeque destitui eius ministerio, & immediaro influxu. < 14.> Sed id etiam exploratum habere, perdifficile est. Perpensis igitur singulorum opinionibus, mihi maximè arridet opinio Cardani dicentis tunc puerum nasci dicendum, cum primum aerem per os respirare incipit extrà matris vterum. Quandoquidem cum vitæ principalis operatio sit halitus, vnde viuens sustentatur, & quo deperdito, vita finitur, id iure optimo dicendum erit vitæ principium, quo quis non genitricis ope, sed suo Marte incipit respirationis beneficio frui, atque aërem illum haurire, qui cum ob sui facilitatem, subtilitatem, & continui (nisi etiam materiei velimus dicere) vnitatem, præstò sit ad cælorum impressiones suscipiendas, iure spiritus Mundi, ac cælestium qualitatum vehiculum appellatur. Quaproptet etsi puer non adhuc ex vtero Matris emersus sit, modo caput extra illum habeat, & respirare incipiat, sat est, vt viuere dicatur, atque in lucem editus. Econttà, sit quamuis extrà vterum positus, lotus, pannis inuolutus &c. nunquam proprièviuere dici poterit, donec prima vitæ semina excipiat, adeoque cælorum influxus per aeris aspirationem non illi communicentur. Atque hæc de hoc argumento satis. Hinc. < 15.> GENETLIACVM dicitur quod ad Genesim spectat; quique ex natalitio themate de hominum vita fortunaque pronunciant, Genethliaci appellantur. < 16.> GENIGVLATOR, seù Ingeniculus dicitur Hercules Græco nomine Engonasis, fidus in cælo ad Borealem plagam, sic dictum, quod eius imago representet hominem in genua prouolutum, atque altero pede erecto Draconis caput gestientem opprimere. De eo vide iam dicta in V. Engonasis, ac dicenda in Hercule. < 17.> GENNA, teste Othone dicitur ab aliquibus Luna, cum post conjunctionem cum Sole recessit ab eo per grad. 15. vel sanè 17. quantum videlicet sufficit, vt è radijs ipsius emergat. Vide Vallam. GENZAHAR

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108 LEXICON < 14.> To define birth by the permanence of the heat of nature or by the operation of the sensitive spirit. Therefore some have said that the instant of birth is the point of exit of the child from the womb: but since this happens successively, and by parts, so that sometimes whole hours pass, and often even the whole day the fetus remains with half of its body within the mother’s womb and the remaining half outside, it will still remain under question what ought to be called the true moment of birth, to which the celestial theme should be cast. Titus, in his Celestial Philosophy, examining the matter in his usual learned manner, rejecting the opinions of others, concludes from the innermost principles of philosophy that it is when the fetus begins to become independent of its proximate cause, and thus is deprived of its ministry and immediate influx. < 14.> But even to have that established is very difficult. Therefore, after weighing each opinion, the opinion of Cardano especially pleases me, who says that a child should then be said to be born when it first begins to breathe air through the mouth outside the mother’s womb. For since the principal operation of life is breath, by which the living being is sustained, and when it is lost, life ends, with the best right that will be called the beginning of life by which one begins to enjoy the benefit of breathing not by the help of the mother, but by his own effort, and to draw in that air which, because of its ease, subtlety, and unity of continuity (unless we should also wish to call it matter), is present and ready to receive the impressions of the heavens; and for that reason it is rightly called the vehicle of the spirit of the world and of celestial qualities. Wherefore, although the child has not yet emerged from the mother’s womb, if only he have his head outside it and begin to breathe, that is enough for him to be said to live and to have been brought into the light. On the other hand, even if he be placed outside the womb, washed, wrapped in swaddling cloths, etc., he can never properly be said to live until he receives the first seeds of life, and thus the influxes of the heavens are communicated to him through the inhalation of air. And enough on this subject. Hence. < 15.> GENETLIACVM is said of what pertains to Genesis; and those who pronounce concerning the life and fortune of men from the natal theme are called Genethliacs. < 16.> GENIGVLATOR, or Ingeniculus, is the Greek-named Hercules, Engonasis, a fixed star in the sky toward the northern region, so called because its image represents a man prostrating himself upon his knees and, with the other foot raised, attempting to crush the head of the Dragon. See what has already been said under V. Engonasis, and what will be said under Hercules. < 17.> GENNA, according to Otho, is called by some the Moon, when after conjunction with the Sun it has moved away from him by 15 degrees, or indeed 17, as much as suffices, namely, for it to emerge from his rays. See Valla. GENZAHAR

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MATHematicVM. 209 GENZAHAR apud Alkabilium different. 3. num. 4. dieitur < 18.> intersectio orbitæ planetarum cum Ecliptica, qua parte ab australi plaga ab Borealem transeunt, & econtra. Ille igitur transitus Hebraicè, seu Chaldaicè appellatur Genzahar. < 19.> GEODÆSIA species est Geometriæ, vnaque ex Mathematicis disciplinis, quæ versatur in dimitiendis corporum ac particularium figurarum quantitatibus, vt materialium rerum aceruos per conos. & puteos, vt Cylindros, quod tamen non præstat per imaginarias lineas rectas, vt præcise facit Geometria, sed per res sensibiles, & visuales, vt puta per radios solares, vel per spartas, aut perpendiculum. Diuiditur, vt Geometria, in eam partem quæ planam superficiem, & in eam quæ corpora solidadimetitur. Quade re vide Clauium, Kircherum, & alios. < 20.> GEOGRAPHIA facultas est totius terrestris globi, seu terræ habitabilis descriptionem tradens, eius amplitudinem metiendo, distantias regionum & vrbium adjuicem, inquirendo locorum qualitates, alimata, aliaque artificiose per comparationem ad inuicem & cum coelestium corporum moribus inuestigando. Olim Geometria dicebatur quæ aliud Græcè non sonat, quam terræ mensurationem: verum postea hoc nomine in disciplinam longe nobiliorem amplioremque translato ipsa Geometriæ filia appellari contenta est, vltro gaudens suo antiquo nomine spoliari quo mater inuestiretur, ipsaque sub matris appellitreatione veniret, concurrerque. < 21.> GEOMETRIA nobilissima est inter omnes mathematicas disciplinas, à telluris quidem dimensione ex Græco nomen deriuans, sed longè nobiliori vocabulo digna: quippe quæ non terram modo, vnde primum originem traxit, sed & coelestia corpora speculatur, haberque pro obiecto Vniuersi istius molem, prout quanta est, & continua quam suis demonstrationibus nostris intellectibus ingerit mensurandam, eiusque partes vel remotissimas, vel immensas ad vnguem dimetitur, ac planè oculis subijcit. Vt proinde non minima laus Geometriæ sit, quod humanas mentes humi repentes ac terræ infixas in illam coelestem sedem innehat, & admirandam mundi huius constitutionem, rerum ordinem, corporum coelestium magnitudinem, distantiam, situm, regularem incessionem intellectui tostro exponat, ac manifestet; quando alias Philosophia, vel in minimis hærens, ne ipsius quidem continui compositionem, quod semper præ manibus haber, capere poest, & in suis speculationibus semper magis, magisque confunditur, & irretitur. Porrò Geometria diuiditur O

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MATHematicVM. 209 GENZAHAR apud Alkabilium different. 3. num. 4. is said to be <18.> the intersection of the orbit of the planets with the Ecliptic, at the point where they pass from the southern side to the northern, and vice versa. That passage is therefore called in Hebrew, or Chaldaic, Genzahar. <19.> GEODESY is a species of Geometry, and one of the mathematical disciplines, which is concerned with measuring the quantities of bodies and particular figures, as of material things by means of cones and wells, as Cylinders; yet this it does not perform by imaginary straight lines, as Geometry precisely does, but by sensible and visible things, such as by solar rays, or by cords, or a plumb line. It is divided, like Geometry, into that part which measures a plane surface, and that which measures solid bodies. On this matter see Clavius, Kircher, and others. <20.> GEOGRAPHY is the faculty that gives a description of the whole terrestrial globe, or of the habitable earth, by measuring its extent, by investigating the distances of regions and cities from one another, the qualities of places, climates, and other things, and by ingeniously comparing them with one another and with the motions of the heavenly bodies. Formerly Geometry was called thus, which in Greek means nothing other than the measurement of the earth: but later, when this name was transferred to a far nobler and broader discipline, it was content to be called the daughter of Geometry, gladly rejoicing to be stripped of its ancient name, so that its mother might be adorned with it, and it itself might come under the mother’s appellation, and concur. <21.> GEOMETRY is the noblest of all the mathematical disciplines, deriving its name indeed from the measuring of the earth from Greek, but worthy of a far nobler title: for it contemplates not only the earth, from which it first drew its origin, but also the heavenly bodies, and has as its object the mass of this Universe, insofar as it is measurable, and continuous, which it presents to our intellects through its demonstrations for us to measure, and it exactly measures its parts, whether most remote or immense, and plainly submits them to the eyes. Therefore it is no small praise of Geometry that it keeps human minds, creeping on the ground and fixed to the earth, in that heavenly seat, and sets forth to the intellect the admirable constitution of this world, the order of things, the greatness of the heavenly bodies, their distance, position, and regular motion; whereas otherwise Philosophy, even clinging to the smallest things, cannot grasp even the composition of continuity itself, which it always has ready at hand, and is always more and more confused and entangled in its speculations. Moreover Geometry is divided O

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LEXICON in eam partem, quæ in planorum consideratione versatur, & generali vocabulo retento Geometria strictiùs audit; & in eam qua corporum solidorum doctrina traditur, ac proprio, & peculiari nomine stereometria appellatur. Rursus quæ ex lestium corporum affectiones solummodò speculatur, astronomia dicitur, quæ in terræ descriptione versatur, Geographia. Itaque Geometria vniuersè hunc sibi scopum præsigit, vt plana, aut solida, vel constituat, vel constituta inter se comparet, aut diuidat, ac proinde corpora præcisè ac superficies speculatur. Eius laudes, arque vtilitates Claiius in Prologomenis ad Commentar. in Elementa Euclidis. GL 22. Globus Latinè idem, quod sphæra Græcè, definitur enim à Theodosio, quod sir Corpus solidum vnica superficie contentum in medio habens centrum à quo omnes linea ad superficiem ducta sint æquales. Differt à circulo quod iste sit figura plana vnicâ lineâ circunducta comprehensa; globus autem sit corpus sphæricum omnis dimensionis capax. Differt etiam ab Orbe propriè dicto, quod is vnicam tantum habet superficiem, exteriorem nempe, atque conuexam, qua clauditur, & finitur, cum aliàs concipiatur ex integro solidus vsque ad centrum; qualia dici possunt corpora planetarum, globus terrestris, &c. Orbis autem etsi alioqui solidus intelligatur, tamen eius solidiras, seù crassities compræhenditur duabus superficiebus, altera interiore concaua, altera exteriore conuexa, quales sunt omnes cæli, & deferentes corpora planetarum, aëris regio, &c. Id autem propriè, nam sæpè vocabula confunduntur. Quinimò nunc temporis vsus obtinuit, vt globi nomine pressiùs veniret vtraque mundi Mappam ex lestis, quam terrestris, in quarum vna descripta essent omnia fidera, ac cælestes imagines, circuli, sphæræ longitudines, latitudines, declinationes cuiuscumque partis cæli cum suo horizonte, ac Meridiano adaptandis ad quascumque poli eleuationes, cuius ope ortus, & occasus siderum, cæli mediatio, aliaque vnico intuitu haberentur: in altera descriptus esset totus terræ, marisque ambitus cum suis circulis parallelis, vnde locorum longitudines, latitudines, distantia inter se, proindeque vniuersa penè Geographia commodè addisci possit. GN 23. GNASCH Hebræo nomine dicitur Vrsa minor, fidus ad po-

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LEXICON In that part which concerns the consideration of plane figures, and retaining the general term, it is more strictly called Geometry; and in that which treats of the doctrine of solid bodies, it is called, by its proper and special name, stereometry. Again, that which considers only the affections of celestial bodies is called astronomy; that which is concerned with the description of the earth, Geography. Thus Geometry in general sets before itself this aim: to construct plane or solid figures, or, once constructed, to compare them with one another or divide them; and therefore it considers bodies precisely and surfaces. Its praises and uses are set forth by Clavius in the Prolegomena to the Commentary on Euclid's Elements. GL 22. Globus, in Latin the same as sphaira in Greek, is defined by Theodosius as a solid body enclosed by a single surface, having in the middle a center from which all lines drawn to the surface are equal. It differs from a circle in that the latter is a plane figure enclosed by one surrounding line; but a globe is a spherical body capable of every dimension. It also differs from an Orbis properly so called, because the latter has only one surface, namely the outer and convex one by which it is enclosed and bounded, although otherwise it is conceived as entirely solid all the way to the center; such are the bodies of the planets, the terrestrial globe, and so on. An Orbis, however, although otherwise understood as solid, has its solidity, or thickness, enclosed by two surfaces, one inner and concave, the other outer and convex, such as are all the heavens and the bodies they carry, the region of the air, and so on. This is the proper distinction, for the terms are often confused. Indeed, in modern usage it has become customary for the name globus to be used more strictly of either map of the world, celestial or terrestrial, in one of which would be represented all the stars and celestial figures, the circles, spheres, longitudes, latitudes, declinations of any part of the sky with its horizon and meridian adapted to whatever elevation of the pole may be desired, by means of which the risings and settings of the stars, the culmination of the sky, and other things would be had at a single glance; while in the other would be described the whole expanse of land and sea with its parallel circles, from which the longitudes, latitudes, distances of places from one another, and thus nearly all Geography, may conveniently be learned. GN 23. GNASCH, by a Hebrew name, is called Ursa Minor, a fixed star in the po-

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MATHEMATICVM. 211 lum Arcticum, quod teste Kirchero in Oedipo Ægypt. idem sonat, ac Gallinæcum filijs suis. GNOMON Græcè dicitur stylus ferreus in area horologij < 23.> sciotherici artificiosè locatus, qui vmbra sua horas indicat, atque æquinoctiorum & solstitiorum tempora manifestat: illum meritò Plinius lib. 2. cap 72. Solis vmbilicum vocat est enim mensura, & reguliteneris Solis, quo mediante, quota sit hora diei, & quantum Sol quoque die declinationis habeat, proindeque dierum longitudinem ac breuitarem facile internoscimus. Quoniam autem Gnomon est regula itineris Solis, iure. GNOMON Geometricus dictus est instrumentum ad regulæ < 24.> formam, quo medio venamur altitudinem, ac declinationem Solis, aliorumque siderum, nec non etiam locorum distantias, cuius vsum, atque vtilitates recenset Ignatius dantes, & Claius in Geometr. pract. hinc etiam. GNONOMICA dicta est ea Astronomiæ pars, quæ per vmbram < 25.> Solis & Lunæ artificiosè exceptam eorum cursus mensurat, adeoque temporis spatium, quod in hoc cursu labitur, oculisque spectandum in horologijs solaribus exhibet. De hac etiam integrum volumen scripsit idem Claius. GNOSSIA Corona: dicitur sidus in cælo ad Borealem plagam < 26.> propè Arcturum, Coronæ formam præseferens; habet enim per circuitum stellas octo tam benè dispositas, vt nullum planè sidus, tam apto suæ formæ nomine sit appellatum, quam istud. Sed de eo vide iam dicta in V. Corona Septentrionalis. GO GORGONIS Caput, seù, vt vulgò vocant, Caput Medusa < 27.> dicitur apud Astronomos stella fixa violentissima in constellatione Persei posita, secunda magnitudinis, de natura Saturni, & Iouis Arabice R[ecipe]s Al[ph]ol. De qua sic pronunciat Ptolemæus in Centiloquio propos. 73. Sol vbi repertus fuerit cum capite Gorgonis, si neque aspicitur à beneficia stella, neque benefica octavo loco præest; Dominisque conditionarij luminaris Marti opponetur, aut eum è quadrato percutit, nato caput truncabitur. Quod si luminare culminabit, corpus eius sauciabitur: Sin copulatio à Ceminis, aut Piscibus fuerit, manus, ac pedes eius amputabuntur. Idipsum ferè repetit in Quadrip. lib. 4. cap. 10. in hæc Verba. Insignis mutilis, aut quorum figura sunt imperfecta, aut circa caput Medusa, Mars significat, capite truncandos, aut membris mutilandos. Quæ omnia expendens D. Thomas in Opusc. 18. O ij

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MATHEMATICVM. 211 the Arctic Pole, which, according to Kircher in Oedipus Ægypt., sounds the same as Gallinæcum filijs suis . GNOMON, in Greek, is the iron style set artfully in the dial plate of a sundial <23.>, which by its shadow indicates the hours and reveals the times of the equinoxes and solstices. Pliny, lib. 2, cap. 72, rightly calls it the navel of the sun; for it is the measure and guiding rule of the sun, by means of which we know what hour of the day it is, and how much declination the sun has on each day, and thus we easily distinguish the length and shortness of the days. But since the gnomon is the rule of the sun’s course, it is rightly so called. GNOMON Geometricus is the name given to an instrument in the form of a ruler <24.>, by means of which we observe the altitude and declination of the sun and other stars, as well as the distances of places; Ignatius Dantes and Clavius in their practical geometry set forth its use and advantages. Hence also. GNONOMICA is that part of astronomy which measures, through the shadow of the sun and moon artfully received, their courses, and thus the span of time that passes in this course, presenting it to the eyes for observation in solar clocks. On this subject Clavius also wrote an entire volume. GNOSSIA Corona: a star is so called in the sky on the northern side <26.> near Arcturus, presenting the form of a crown; for it has eight stars around its circumference so well arranged that no other star has been called by a name so fitting its form as this one. But see what has already been said about it under V. Corona Septentrionalis. GO GORGONIS Caput, or, as it is commonly called, the Head of Medusa <27.>, is said by astronomers to be a fixed star of great violence, placed in the constellation of Perseus, of the second magnitude, of the nature of Saturn and Jupiter, in Arabic Regis Alghol . Ptolemy pronounces thus concerning it in the Centiloquium, proposition 73: “If the Sun be found with the Head of Gorgon, if it is not aspected by a benefic star, nor is a benefic in the eighth house; if the lord and the significator of the luminary oppose Mars, or he strikes it from a square, the native’s head shall be cut off. But if the luminary culminates, his body shall be wounded: if the conjunction is from Gemini or Pisces, his hands and feet shall be cut off.” He repeats nearly the same in the Quadripartitum, lib. 4, cap. 10, in these words: “The notable deformed, or those whose figure is imperfect, or those near the head of Medusa, Mars signifies to be beheaded or mutilated in their limbs.” D. Thomas, in Opusc. 18., considers all these things.

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LEXICON att. 4. dicit. Quod illa Stella funerea sunt, & monstruosam indivita terminationem: propter quod ipse Perseus caput auerso vulsio abscissum tenet: sed hoc sicut diximus non imponit rebus necessitatem, sed facilem, & mutabilem inclinationem habet. Hæc sanctus Doctor, cum priùs ex Ptolemæi authoritate dixisset, quod in his, & similibus rebus coniecturalibus, non nisi committeriudicare debemus, & potestates rerum consequentes, quas propriæ rerum causæ frequenter excludunt: Coniecturatio enim inquit, cum sit ex signis mobilibus, generas habitum minoris certitudinis, quam sit scientia, & opinio. Ex occasione autem huius violentæ stellæ, iuuar auertere hic communem illam, ac vulgurem obiectionem quæ contra Astrologos fieri soler. Quæ enim, inquiunt similitudo, quæ consensio inter Gorgonis caput è fabulis excerptum, & hanc stellam? inter canem sidereum, ac terrestrem: inter Scorpion sidus, & venenosum, qui reat in rerris? &c. Numquidne, quia antiquis fabulatoribus placuit nugas suas cælo inserere, ac vel ex formæ similitudine, vel alia de causa voluerunt cælestes imagines Leonis, Scorpij, Hydræ æquiuoco nomine indigitare, proptereà translata est in stellas eorum natura, vt qui sub his constellationibus oriuntur illorum qualitates induant, similem exitum sortiantur? Ergòne quia Gorgonis caput pethibetur à Perseo vuln auerso abscissum; quem posteà vna cum ipso capite fabulosa antiqui- quiras cælo inseruit, idcircò qui sub hoc sidere nascentur, capitis periclitabuntur? Quia pisces aquatici fæcundi sunt, proptereà qui sub Piscium cælestium Astro nascentur fæcundi erunt, & vice versa steriles qui sub Virgine, quia Virgo sterilis, & infæcunda? Ita plane: Neque enim frustra, aut sine consilio antiqui illi Astronomi stellarum naturam probè callentes, eas in tor diuersas formas ex fabulis plerumque desumptas coadunarunt, sed quia videbant eatum naturam, & qualitates terrenis his rebus persimiles, idcircò vt posteri eas dignoscerent ac penetrarent, à rerum similitudine, quarum imaginem præseferrent, vt ediscerent voluerunt. Sic quia Leo animal, dum Sol eiusdem nominis signum permear assidue Febre laborat, quia canes terrestres aguntur in tabiem caue sidereo exorienti cum Sole, Luna in Scorpione versante, Scorpiones in terris infensissimi sunt, Hydra stellis constat de natura Saturni, & Veneris, quæ humorum corruptrices sunt, ac venenose, nescio quem consensum, & sympathiam inter illa, quamuis natura dissita inercedere experti sunt; proinde ad hæc & similia nobis insinuanda, naturamque eorum aperiendam, sidera illa Leonis, Canis, Scorpij, Hydræ speciem nostris intellecti-

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LEXICON att. 4. He says that these are funereal stars, and an inanimate monstrous termination; for which reason Perseus himself holds the severed head turned backward by the wound. But this, as we have said, does not impose necessity on things, but has a gentle and changeable inclination. This is what the holy Doctor says, having first stated on the authority of Ptolemy that in these and similar conjectural matters we ought to make no judgment except by comparison, and by the powers consequent upon things, which the proper causes of things frequently exclude. For conjecture, he says, since it is from movable signs, produces a habit of lesser certainty than knowledge and opinion. On the occasion of this violent star, it is useful here to turn aside that common and vulgar objection which is usually made against astrologers. For, they ask, what likeness, what agreement is there between the head of Gorgon taken from fables and this star? between the starry dog and the earthly one? between the sign of the Scorpion and the poisonous creature which lives on earth? etc. Is it then because ancient fabulists chose to insert their trifles into the sky, and either from the likeness of shape or for some other reason wished to designate the celestial images by the ambiguous names of Lion, Scorpion, Hydra, that the nature of those things was transferred to the stars, so that those who are born under these constellations should take on their qualities and meet a similar end? Or is it because the head of Gorgon is said to have been severed by Perseus with a backward wound, and later, together with the head itself, legendary antiquity inserted into the sky, therefore those born under this star will be endangered in the head? Because aquatic fish are fertile, therefore those born under the celestial Astro of Pisces will be fertile, and conversely barren those under Virgo, because Virgo is barren and unfruitful? Indeed yes: for the ancient astronomers, who were thoroughly skilled in the nature of the stars, did not gather them into various forms taken mostly from fables without reason or plan, but because they saw that their nature and qualities were very similar to these earthly things, and therefore, so that later generations might recognize and penetrate them, they wished them to be learned from the likeness of the things whose images they displayed. Thus, because the animal Leo, while the Sun passes through the sign of the same name, is constantly afflicted with fever; because earthly dogs are wasting away as the starry Dog rises when the Sun is with the Moon in Scorpio; because Scorpions on earth are most hostile; because Hydra consists of stars of the nature of Saturn and Venus, which are corrupters and poisonous to the humors, I know not what agreement and sympathy have been experienced between them, though separated by nature. Therefore, for the purpose of indicating these and similar matters to us and of revealing their nature, those stars took on to our understanding the appearance of the Lion, the Dog, the Scorpion, the Hydra.

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MATHEMATICVM. 213 bus objecerunt, quod sanè proprium Ægyptiorum est sapientiam suam; non nisi per hieroglyphica explicate. Sic igitur in casu nostro ad explicandum monstrosum vitæ exitum, quem vt plurimum portendit cum luminaribus stella illa sua prauitate in signis, quæ sæpè, vt experimentis probatum est, obtrunca- tiones capitis intulit, assumpta Gorgonis fabula, caput eius cælo affixum est, atque ex eo sidus illud non incongruè deno- minarunt, vt eius natura, vel ex fabulis innotesceret. Propter- ca (inquit D. Th.) ipse Persens caput, aurose vuleu abscissum se- net, vt profectò, qui hæc viderit comprehendar stellas illas esse malignantis naturæ, & effectus eis similes importare, quos res à quibus illis nomen est inditum, gignere consueuerunt: sed longiùs quam par etat ex occasione capitis Gorgonis ab instituto digressi sumus. Redeamus ad nostra. GR 29. GRADVS apud Astronomos communitet significare solet tri- gesimam quamque partem cuiuscumque signi, seu potiùs to- tius circuli rescentesimam sexagesimam, quod præcipuè in Zodiaco & Æquatore sit, ad habendam signorum ascensionem, & quotæ cuiusque partis vnius circuli ad alterum correspon- dentiam Similiter gradus quisque diuisibilis est in 60. partes, quas, & minuta nominant, seu scrupula. Minutum in totidem fractiones, quas vocant secunda: secunda in totidem tertia: & sic deinceps vsque ad decem. Cuius aptissimæ distributionis rationem vide in Clauio in commentar. ad sphæram 10. de Sa- crobosco. Porrò distantia vnius gradus proportionalis in cælo, comprehendit in terris spatium stadiorum 500. hoc est millia- ria 62. cum dimidio, secundùm Prolemæi obseruationem: ita vt totus terræ ambitus sit milliatiorum 22500. Recensores verò, qui non semel Oceanum suis nauigijs trajecerunt, & to- tum Orbem circumegerunt, dicunt vnicuique gradui in mari per directum respondere milliaria 53. ita vt ambitus terræ per circuitum amplectatur milliaria 19080. Hinc etiam sumpta proportione venamur ambitum conuexi singulorum orbium cælestium, & quorumquisque itineris singulis horis conficiat, præcipuè firmamentum, quod antiquitas ipsum primum mo- bile esse existimauit. Cuius velocitas tanta est, vt mente con- cipi nequeat, ac spatio vnius horæ quælibet pars æquatoris, & stella in eo sita, qualis est prima, exempli gratia, in cingulo Orionis, tantum itineris conficiat, quantum vix posset quis sine vlla intermissiore currendo peragare in ann. 2904. etiam- O iij

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…they objected to them, which is indeed peculiar to the Egyptians, to explain their wisdom only by hieroglyphics. So then, in our case, in order to explain the monstrous end of life, which that star for the most part portends by its wickedness in the signs together with the luminaries, and which, as has often been proved by experience, has brought about decapitations, the fable of Gorgon was taken up; his head was fixed to the heavens, and from this they not inappropriately named that star, so that its nature might be made known, even from the myths. Therefore, says D. Th., Perseus himself is seen holding the head cut off with a golden hilt, so that surely whoever has seen these things will understand that those stars are of a malignant nature, and bring effects like those which the things from which they received their name were accustomed to produce. But we have digressed farther than was fitting from our subject on account of the head of Gorgon. Let us return to our matter. GR 29. GRADE among astronomers commonly signifies the thirtieth part of any sign whatsoever, or rather the three-hundred-and-sixtieth part of the whole circle, which is chiefly so in the Zodiac and Equator, for the computation of the rising of the signs, and for the correspondence of each part of one circle with another. Likewise each degree is divisible into 60 parts, which they call minutes, or scruples. A minute into as many fractions, which they call seconds; seconds into as many thirds; and so on, up to ten. See the most suitable reason for this distribution in Clavius, in his commentary on the Sphere of Sacrobosco, book 10. Moreover, the distance of one proportional degree in the heavens comprehends on earth a space of 500 stadia, that is, 62 and a half miles, according to Ptolemy’s observation; so that the whole circumference of the earth is 22,500 miles. But the revisers, who have more than once crossed the Ocean with their ships, and sailed around the whole world, say that in the sea each degree corresponds directly to 53 miles, so that the circumference of the earth amounts to 19,080 miles. Hence, taking proportion also from this, we investigate the circumference of the convexity of each of the celestial spheres, and how much each one completes in a single hour of travel, especially the firmament, which antiquity considered to be the first movable thing. Its speed is so great that it cannot be conceived by the mind; and in the space of one hour any part of the equator, and a star situated in it, such as, for example, the first in the belt of Orion, performs as much journey as a man could scarcely accomplish by running without any interruption in 2,904 years. Even- O iij

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LEXICON 214 si in dies singulos millaria 40. conficeret. Qui huius rei curiosus extuerit, videat Clauium loco citato, & Blancanum in 30. spharmusdi, lib. 4. cap. 5 Considerantur eriam ab Astronomis, præsertim antiquioribus, certi quidam gradus in signis, quos vocant vacuos, plenos, lucidos, tenebrosos, masculinos, fæmininos, pureales, fumosos, felices, infelices, augentes fortunam, vel minuentes, nescio prudenti ne ratione, an potius Arabum vanitate, ac figmento. Hos ego gradus, eorumque distributionem olim deridebam; vel eò maximè quod à recentioribus silentio obuoluuntur. Verum quia postmodum inueni Angelicum Doctorem D. Thomam eorum mentionem fecisse in opuscul. de Fato, nec proptereà improbasse (vt alias solet grauissimus vir in rebus superstitionem olentibus) placuit eos & hic inserere, neq[ue] approbando, neque improbando, sed solùm ad operis complementum, atque vt curiosorum desiderio satisfacerem. Eorum aliqua ratio elucer ex fixarum natura in illis incidentium, aur ex proportionalibus distantijs ad puncta cardinalia, vnde sidera influere incipiunt primas qualitates, quales sunt fines secundùm Ægyptios, vt nos dicemus in V. Termini. irem gradus fæminini, & masculini, &c. aliorum non item, cuiusmodi sunt gradus puteales, pleni, vacui, fumosi, lucidi, tenebrosi. Fortassis vocantur pleni, ac lucidi, in quibus stellæ fixæ corporaliter incidunt; sicut è contrà tenebrosi, & vacui qui nullis circà stellis præditi sunt. Licet & hoc quidem præsenti tempore obseruare superuacaneum foret ob Firmamenti peculiare motum, quo stellæ jam non in eadem longitudine sunt, proindeque in ijsdem Zodiaci gradibus, ac tempore Ptolemæi, sed longe antecessetunt ad grad. ferè 28. Quapropter & nouam graduum constitutionem construere oporter. Sed & eorum, qui felices, vel infelices vocantur non spernendam rationem affert Cardanus in Commentar. ad lib. 1. Quadrip. text. 61. Vbi enim, inquit, conveniunt fines vtriusque benefica, ij iure cateris feliciores censendi sunt, ob vtriusque mixtam naturam: contrà infelices habentur qui sunt contermini finibus maleficarum; quia ambæ concurrunt ad eos infortunandos. Sic septimus gradus Arietis, quia est finis terminorum Iouis, & initium Veneris, felix jure optimo nuncupatur. E contrà grad. 26. eiusdem Arietis infelix; quia ibi fines vtriusque maleficæ conjunguntur: sic discurrendum de reliquis, vt videre est in sequenti tabella.

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LEXICON 214 if he were to cover 40 miles each day. Whoever is curious about this matter should look at Clavius in the cited place, and Blancanus in 30. spharmusdi, lib. 4. cap. 5 Astronomers, especially the older ones, also consider certain degrees in the signs, which they call void, full, bright, dark, masculine, feminine, earthy, smoky, fortunate, unfortunate, increasing fortune, or diminishing it, I know not whether by a prudent reasoning, or rather by Arab vanity and fiction. I used formerly to laugh at these degrees and their distribution; especially because they are passed over in silence by more recent writers. But since afterward I found that the Angelic Doctor, St. Thomas, had mentioned them in the opusculum De Fato, and had not on that account disapproved them (as that most serious man usually does in matters smelling of superstition), it seemed good to insert them here as well, not approving them, nor disapproving them, but only for the completion of the work, and to satisfy the desire of the curious. Some reason for them may shine forth from the nature of the fixed stars falling upon them, or from the proportional distances to the cardinal points, from which the stars begin to exert influence through the primary qualities, such as the terms according to the Egyptians, as we shall say in V. Termini; likewise the feminine and masculine degrees, etc., but not the others, such as the earthy, full, void, smoky, bright, and dark degrees. Perhaps they are called full and bright in which the fixed stars bodily fall; just as, on the contrary, the dark and void are those that are provided with no stars around them. Although even this would be superfluous to observe at the present time, because of the peculiar motion of the Firmament, by which the stars are no longer at the same longitude, and therefore not in the same degrees of the Zodiac as in the time of Ptolemy, but have advanced far ahead, almost to the 28th degree. For this reason a new constitution of the degrees ought also to be constructed. But Cardanus also gives a not to be despised reason for those degrees called fortunate or unfortunate in the Commentary on lib. 1 of Quadrip., text. 61. For where, he says, the terms of both benefics meet, those by right ought to be judged more fortunate than the others, because of their mixed nature; on the contrary, those are considered unfortunate which are contiguous to the terms of the malefics; because both concur in making them unlucky. Thus the seventh degree of Aries, because it is the end of the terms of Jupiter and the beginning of Venus, is rightly called fortunate. Conversely, the 26th degree of the same Aries is unfortunate; because there the terms of both malefics are joined: so one must proceed with the rest, as can be seen in the following table.

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MATHEMATICVM. 235 Tabula Graduum Felicium, & Infelicium. 31. In Ariete. felix grad. 7. Infelix 26. In Tauro. felix nullus Infelix 26. In Geminis. felix 15. Infelix 25. In Cancro. nullus felix, neque infelix. In Leone. felix 20. Infelix nullus. In Virgine. felix 14. Infelix 24 & 30. In Libra. felix 12. Infelix nullus. In Scorpione. felix 15. Infelix nullus. In Sagittario. felix 9. Infelix 25. In Capricorno. nullus felix Infelix 25. In Aquario. felix 21. nullus infelix. In Piscibus. felix 9. Infelix 30. Eò quia, vt disci, contermini sunt finibus beneficarum, aut malesicarum. Hac etiam, vel sanè ex consimili ratione repertos crediderim gradus augentes fortunam: suntque gr. 19. Arietis: item gr. 3. 15. 27. Tauti: 11. Geminorum: 1. 2. 3 4. Cancri. 2. 5. 7. 19. Leonis. 3. 14. 20. Virginis. 3. 5. 21. Libræ. 7. 18. 20. Scorpij. 13. 20. Sagittarij. 12. 13 14. 20. Capricorni. 7. 16. 17. 20. Aquarij: tandem gr. 13. & 20. Piscium. Minuentes fortunam sunt ijsdem ac puteales. Sequuntur Gradus Lucidi, & Tenebrosi. In Ariete grad. lucid 27. tenebrosi 2. 6. 11. 33. In Tauro grad. lucidi. 6. 14. 25. tenebr. 2. & 29. 34. In Geminis grad. lucid 2. 10. 20. tenebr. 6. 29. In Cancro grad. lucid. 7. tenebr. 13. 19. 24. In Leone grad. lucid. null. tenebr. 6. 15. 28. In Virgine grad. lucid. 7 14. tenebr. 3. 20 29. In Libra gr. lucid. 3. 14. 24. tenebr. 3. & 20. In Scorpione gr. lucid. 6 & 17. tenebr: 2. 21 29. In Sagittario grad. lucid. & tenebr. nulli. In Capricorno gr. lucid. 9. & 17. tenebr. 4. 13. 21. 28. O 111

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MATHEMATICVM. 235 Table of Happy and Unhappy Degrees. 31. In Aries. happy degree 7. Unhappy 26. In Taurus. no happy degree Unhappy 26. In Gemini. happy 15. Unhappy 25. In Cancer. no happy one, nor unhappy. In Leo. happy 20. Unhappy none. In Virgo. happy 14. Unhappy 24 & 30. In Libra. happy 12. Unhappy none. In Scorpio. happy 15. Unhappy none. In Sagittarius. happy 9. Unhappy 25. In Capricorn. no happy one Unhappy 25. In Aquarius. happy 21. no unhappy one. In Pisces. happy 9. Unhappy 30. For the reason, as one may learn, they are adjoining the bounds of the benefic or malefic [signs]. By this also, or surely from a similar reason, I would believe were found the degrees increasing fortune: and they are degrees 19 of Aries; likewise degrees 3, 15, 27 of Taurus; 11 of Gemini; 1, 2, 3, 4 of Cancer. 2, 5, 7, 19 of Leo. 3, 14, 20 of Virgo. 3, 5, 21 of Libra. 7, 18, 20 of Scorpio. 13, 20 of Sagittarius. 12, 13, 14, 20 of Capricorn. 7, 16, 17, 20 of Aquarius: finally degrees 13 and 20 of Pisces. The degrees diminishing fortune are the same as the well-like ones. Follow the Bright and Dark Degrees. In Aries, bright degree 27; dark 2, 6, 11, 33. In Taurus, bright degrees 6, 14, 25; dark 2 & 29, 34. In Gemini, bright 2, 10, 20; dark 6, 29. In Cancer, bright 7; dark 13, 19, 24. In Leo, bright none; dark 6, 15, 28. In Virgo, bright 7, 14; dark 3, 20, 29. In Libra, bright degrees 3, 14, 24; dark 3 & 20. In Scorpio, bright 6 & 17; dark 2, 21, 29. In Sagittarius, bright and dark degrees none. In Capricorn, bright 9 & 17; dark 4, 13, 21, 28. O 111

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216 LEXICON In Aquario gr. lucid. 7. 17. 28. tenebr. 3. 12. In Piscibus gr. lucid. 10. 20. 27. tenebr. 3. 16. 30. Gradus Puteales. 35. In Ariete. 6. 11. 16. 23. 29. In Tauro. 5. 12. 24. 25. In Geminis. 2. 12. 17. 26. 30. In Cancio. 12. 17. 23. 26. 30. In Leone 6. 13. 15. 22. 23. 28. In Virgine. 8. 13. 16. 21. 25. In Libra. 2. 7. 10. 30. In Scorpione. 9. 10. 21. 23. 27. In Sagittario. 7. 12. 15. 24. 27. 30. In Capricorno. 2. 7. 17. 22. 24. 28. In Aquario. 1. 12. 17. 24. 29. In Piscibus. 4. 9. 24. 27. 28. Puteales dicuntur eò quia in ijs planeta existens videtur esse in puteo. Gradus Vacui & Pleni. 36. In Ariet. gr. vac. 3. plen. 8. vac. 17. plen. 20. vac. 26. plen. 30. In Taur. vac. 3. pl. 11. vac. 13. pl. 21. vac. 26. pl. 30. In Gem. vac. 0. pl. 7. vac. 9. pl. 14. vac. 17 pl. 23. vac. 30. In Caner. vac. 6. pl 12. vac. 11. pl. 18. vac. 20. pl. 29. vac. 30. In Leon. vac. 0. pl. 7. vac. 10 pl. 14. vac. 20. pl. 30. In Virgin. vac. 5. pl. 9. vac. 11. pl. 17. vac. 21. pl 27. vac. 30. In Libr. vac. 0. pl. 5. vac. 13. pl. 16 vac. 24 pl 27. vac 30. In Scorp. vac. 3. pl. 8. vac. 14 pl. 20. vac. 22. pl. 27. vac. 30. In Sagitt. vac. 0. pl. 8. vac. 11. pl. 19. vac. 21. pl. 30. In Capric. vac. 7 pl. 10. vac. 15. pl. 20. vac. 24. pl. 30. In Aquar. vac. 4. pl. 7. vac. 13. pl. 19. vac. 22. pl. 30. In Pisc. vac. 6. pl. 12. vac. 15. pl. 19. vac. 25. pl. 28. Atque hi sunt gradus quos minus inanitatis habere credendum est, quàm alij penè innumeri, quos Arabes confinxerunt, sunt etiam gradus Azemene, hoc est debilitatis corporis, quos in loco retulimus, necnon masculini, ac fæminini: de quibus sermo etiam fuit in V. Fæminimum. 37. Græcvs, apud nos vulgò dicitur ventus intermedius inter Septentrionem, & Subsolanum, eò quod per mediam Græciam transeat. Græcis Borrhapeliores, directè oppositus Garbino, seu Notolybico. Est natura sua frigidus, & succus ob vicinitatem Boreæ, adducens aliquando niues. 38. Grvs, sidus in cælo ad polum antarcticum à recensoribus de nouo cum alijs vndecim, detectum, & hoc nomine præsignatum. Continet intra se stellas tredecim, quarum præcipua est, quæ in oculo secundæ magnitundis; sed est eadem, quæ

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216 LEXICON In Aquarius, gray/cold? lucid. 7. 17. 28. dark. 3. 12. In Pisces, lucid. 10. 20. 27. dark. 3. 16. 30. Pit degrees. 35. In Aries. 6. 11. 16. 23. 29. In Taurus. 5. 12. 24. 25. In Gemini. 2. 12. 17. 26. 30. In Cancer. 12. 17. 23. 26. 30. In Leo 6. 13. 15. 22. 23. 28. In Virgo. 8. 13. 16. 21. 25. In Libra. 2. 7. 10. 30. In Scorpio. 9. 10. 21. 23. 27. In Sagittarius. 7. 12. 15. 24. 27. 30. In Capricorn. 2. 7. 17. 22. 24. 28. In Aquarius. 1. 12. 17. 24. 29. In Pisces. 4. 9. 24. 27. 28. They are called pit degrees because in them a planet existing is seen as if in a pit. Empty and Full Degrees. 36. In Aries, empty degree 3. full 8. empty 17. full 20. empty 26. full 30. In Taurus, empty 3. full 11. empty 13. full 21. empty 26. full 30. In Gemini, empty 0. full 7. empty 9. full 14. empty 17. full 23. empty 30. In Cancer, empty 6. full 12. empty 11. full 18. empty 20. full 29. empty 30. In Leo, empty 0. full 7. empty 10. full 14. empty 20. full 30. In Virgo, empty 5. full 9. empty 11. full 17. empty 21. full 27. empty 30. In Libra, empty 0. full 5. empty 13. full 16. empty 24. full 27. empty 30. In Scorpio, empty 3. full 8. empty 14. full 20. empty 22. full 27. empty 30. In Sagittarius, empty 0. full 8. empty 11. full 19. empty 21. full 30. In Capricorn, empty 7 full 10. empty 15. full 20. empty 24. full 30. In Aquarius, empty 4. full 7. empty 13. full 19. empty 22. full 30. In Pisces, empty 6. full 12. empty 15. full 19. empty 25. full 28. And these are the degrees which are to be believed to have less emptiness than the almost countless others which the Arabs have devised; there are also degrees of Azemene, that is, weakness of the body, which we have mentioned in the proper place, as well as masculine and feminine degrees, of which mention was also made under V. Feminine. 37. Graecus, among us commonly called the intermediate wind between Septentrion and Subsolanus, because it passes through the middle of Greece. Among the Greeks, Borrhapeliores, directly opposite Garbinus, or Notolybicus. By nature it is cold, and, because of its nearness to Boreas, brings snows at times. 38. Grus, a constellation in the sky near the south pole, newly discovered by the observers together with eleven others, and marked with this name. It contains within itself thirteen stars, of which the principal is the one in the eye of second magnitude; but it is the same as that which

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MATHEMATICVM. 217 in cauda piscis Rotij: In longitudine totum est sub signo Aquarij, nobis perpetuò inconspicuum. HA HADRONITHO Demalushe, Chaldaicè dicitur Zodiacus, 1. hoc est Orbis signorum, teste Kirchero in Oedipo Ægygiaco. HAIA, id est serpens dicitur apud Hebræos Hydra sidus, 2. teste Kyrchero, in Oedipo. liem Hackasa. HALON, seu Halones, Græcè dicuntur circuli illi, qui sæpè 3. numero apparere solent circà sidera fulgorem quemdam crassum præseferentes, ad instar radiorum, qui sanè aliud non sunt, quàm densati quidam vapores, & adhuc non resoluti, in eam aëris regionem conuenientes, quæ subest sideri quod circumire videntur, qui posteà ab eius radijs illustrantur nihilò seciùs ac circa horizontem Atmosfera à radijs Solis, vel jamjam emergentis, vel infrafinitorem depressi. Hos & areas vocavere Prisci, quia, inquit Seneca, rotunda sunt loca rerendis frugibus destinata, quibus isti valdè consimiles. Memo- rabilis Halonis suo tempore apparentis meminit Plinius, nec- 4. non & aliorum duorum Suetonius, atque Dio, ex quibus histo- riam accipiens Cornelius Gemma lib. 2. de diuinis Natura cha- racterism. cap. 8 hæc habet: Sub imperium augustis Casaris, vt author est Plinium, ingens circulus circa Solem seu radiantibus stel- lis insignis corona apparuit: desude & alij duo, vt ex Suetonio pa- tet, atque Dione; quorum alter Iridis elegantissima formam, al- ter ex spicis triticeis sertum præseferebat. His affinia sunt parælia, fouex, virgæ, & alia: de quibus suo loco. Vide etiam quæ di- ximus sub V. Circuli. HALYSIS non multum discrepat ab Halone: est enim teste 5. Apuleio lib. de mundo catena quædam ( illius verbis vtor) lu- minis clarioris per Solis ambitum in se reuertens: atque inter hanc & iridem illud interesse, quod Iris multicolor est, & semicirculo figurata procul à Sole, atque Luna; Catena cla- rior est, astrumque ambit orbe incolumi, corona non disco- lori. HAMMEL, seu El. Hammel, prout in loco adnotauimus, di- 6. citur apud Arabes signum, & constellatio Arietis, teste Kir- chero in suo Oedipo Ægyptiaco: sicut etiam HAMMOSCHLVSCH, hoc est tripartitus dicitur apud Hebræos 7. Triangulus: sidus de quo vide in V. Delteton. HAVT, & Ehaus signum, & constellatio Piscium. 8. HAPSI apud Astronomos dicuntur nubeculæ quædam, seu 9. maculæ pendulæ sub Luna in eius defectione nascentes, & sus- pensæ sub illa, de quibus testatur Vendelinus in præf. ad Eclips. p. 3. sæpè à se visas nubes qualdam pendulas sub Luna adhuc su

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MATHEMATICVM. 217 in the tail of the fish of Rotij: in length it is entirely under the sign of Aquarius, and for us perpetually invisible. HA HADRONITHO Demalushe, in Chaldean, means the Zodiac, 1. that is, the Circle of the Signs, as Kircher testifies in the Oedipus Aegyptiacus. HAIA, that is, a serpent, is called by the Hebrews the star Hydra, 2. as testifies Kircher, in the Oedipus. liem Hackasa. HALON, or Halones, in Greek are called those circles which often 3. appear around the stars, exhibiting a certain thick brightness, like rays; which truly are nothing else than certain condensed vapors, and not yet dissolved, gathering in that region of the air which lies beneath the star they seem to encircle, and which afterward are illuminated by its rays, no less than around the horizon the atmosphere is by the rays of the Sun, either just rising, or depressed below the horizon. The ancients also called these areas, because, says Seneca, they are round places destined for gathering grain, to which these are very similar. Pliny mentions a memorable halo appearing in his time, and 4. likewise Suetonius and Dio mention two others; from whom, taking the history, Cornelius Gemma, book 2, De divinis Naturae characterismis, chapter 8, has these words: Under the empire of Augustus Caesar, as Pliny is the authority, a huge circle around the Sun, or a radiant star distinguished by a bright crown, appeared: and then also two others, as Suetonius shows, and Dio; one of which bore the form of a most elegant rainbow, the other a garland resembling ears of wheat. Similar to these are parhelia, foveæ, virgæ, and others, of which elsewhere. See also what we said under V. Circuli. HALYSIS differs little from Halon: for it is, according to Apuleius, book De Mundo, a certain chain (I use his words) 5. of brighter light turning back upon itself through the orbit of the Sun: and the difference between this and the rainbow is, that the rainbow is multicolored, and formed in a semicircle far from the Sun and Moon; the chain is brighter, and surrounds the star in an unbroken circle, a crown not of varied colors. HAMMEL, or El. Hammel, as noted in the place, 6. is called among the Arabs the sign and constellation of Aries, as Kircher testifies in his Oedipus Aegyptiacus: as also HAMMOSCHLUSCH, that is, tripartite, is called among the Hebrews 7. a Triangle: the star of which see under V. Delteton. HAVT, and Ehaus, the sign and constellation of Pisces. 8. HAPSI, among astronomers, are certain little clouds, or 9. hanging spots, arising beneath the Moon in its eclipse, and suspended under it, of which Vendelinus testifies in the preface to the Eclipses, p. 3, that he often saw certain hanging clouds beneath the Moon still su

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LEXICON 218 tenebris constituta, quasi aqua multa grauidas, quæ aliquando, ob figuram, quam præseferunt vmbæ more arcuatam exquisitissimè imitantur initium, & finem Eclipsis à penumbræ terræ realiter factæ, qua in re ait, deceptosuisse Tychonem & alios sæpissimè in Eclipsium lunarium obseruatione. 10. HAYZ, siue, vt alij scribunt Alhaz, apud Arabes est qui-dam accessus fortitudinis, ac dignitatis factus planetæ, eò quod existat in signo sibi sexu conformi, atque in situ mundi in loco sibi conditionario, vt si masculinus, & diurnus de die reperiatur suprà terram, & in signo masculino; si nocturnus & masculinus de nocte reperiatur suprà terram, & in signo masculino. Similiter si planeta sit foeminæ conditionis, constituatur in signo foeminino, & suprà terram de nocte, sub tetram interdiù, & si diurnus suprà terram de die. Sic Saturnus, exempli gratiâ, existens in L[un]one in decima (Sole suprà terram existente) dicitur esse in suo Hayz; eò quia cùm sit masculus, & diurnus, reperitur in signo sibi in sexu conformi, scilicet masculino, & de die etiam suprà terram. Mars autem ad hoc vt ibidem dicatur in suo Hayz, debet habere Solem sub terra, cùm ipse sit planeta nocturnus. Si verò planeta seruet quidem conditionem temporis, at non actu reperiatur in loco sibi idoneo in situ mundi, vt esset si Saturnus de nocte reperitur sub terra, & in signo masculino, Luna de die sub terra, & in signo foeminino; tunc sanè dicetur esse in suo lumine, quia est in loco sibi proportionato, minimè verò in suo Hayz. 11. HADI duæ sunt stellæ perniciosæ, horridæque (quales appellat Plin. lib. 18 c. 36.) in sinistra manu Aurigæ consistentes de natura Martis, & Mercurij, quartæ magnitudinis, in longitudine nunc temporis in gr. 12. & 14. Geminorum. De ijs in Oriente repertis in alicuius natiuitate, sic petbellè cecinit Pontanus in Vransælib. 3. Promittunt igitur duros à fronte Catones Nascentes Hadi, turpi sed inertia mentem Occupat, & molles languent in pectore curæ. Triste supercilium, molls sed degener vmbra: Est animus luxu languens, & deside somno Frons fieta, obsceni mores, petulansque ibido. Armorum, & deses fuga, nobiliumque laborum. Hinc mortem sibi conciscunt, infamis vt vmbra Erret letheos non transmittenda per amnes. Quod aliter explicat Firmicus in hæc verba. Si Hædi, inquit, in alicuius natiuitate in horoscopo reperti fuerint; natus aliud ex fronte pollicetur, aliud latenter in moribus exlabit: Brit enim austera facie, prolixa barba, obstinata fronte; ita vt Ca-

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LEXICON 218 constituted in darkness, like waters swollen, which sometimes, because of the shape they present, most exquisitely imitate the arched form of shadows. The beginning and end of an eclipse are really produced by the Earth’s penumbra, in which matter Tycho and others, he says, were very often deceived in observing lunar eclipses. 10. HAYZ, or, as others write, Alhaz, among the Arabs is a certain accession of strength and dignity bestowed on a planet, because it is found in a sign conformable to its sex, and in the place of the world proper to its condition; as if a masculine and diurnal planet is found by day above the earth, and in a masculine sign; if nocturnal and masculine, by night above the earth, and in a masculine sign. Likewise, if a planet is of feminine condition, let it be placed in a feminine sign, and above the earth by night, below the earth by day; and if diurnal, above the earth by day. Thus Saturn, for example, being in Leo in the tenth house (the Sun being above the earth), is said to be in its Hayz; because, since it is masculine and diurnal, it is found in a sign conformable to it in sex, namely masculine, and by day also above the earth. Mars, however, in order to be said there to be in its Hayz, must have the Sun below the earth, since it is a nocturnal planet. But if a planet indeed preserves the condition of time, yet is not actually found in a suitable place in the situation of the world, as if Saturn by night is found below the earth and in a masculine sign, the Moon by day below the earth and in a feminine sign; then certainly it will be said to be in its light, because it is in a place proportioned to it, but by no means in its Hayz. 11. HADI are two pernicious and dreadful stars (such as Pliny calls them, book 18, ch. 36), standing in the left hand of Auriga, of the nature of Mars and Mercury, of the fourth magnitude, and in longitude at the present time 12° and 14° Gemini. Of these, when found in the East in someone’s nativity, Pontanus in Urania book 3 thus very neatly sang: They promise, then, stern Catos from the forehead, The Hadi at birth; but a base inertia occupies the mind, And soft cares languish in the breast. A sad brow, but a mean shadow: The spirit is languishing in luxury, and with idle sleep The brow is stained, shameless morals, and wanton shame. A dislike of arms, and slackness, and flight from noble labors. Hence they bring death upon themselves, so that an infamous shadow May wander, not to be carried across the Lethean rivers. Which Firmicus explains otherwise in these words: If the Hyae, he says, are found in the horoscope in anyone’s nativity, the native promises one thing from the forehead, another lies hidden in his character: for he is pale of face, with a long beard, a stubborn brow; so that Ca-

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MATHEMATICVM. 219 tonis prorsus institutum mitari videatur: sed rotum hoc fucato mentietur affectu. Quippe intrinsecus erit lascivus, & qui latenter amorum illecebris semper exæstuet, &c. Nascuntur etiam sub hoc sidere ouium pastores, quicque siluestri fistula modulaires, rustici catminis dulcissimos modulos edant. Si verò in occasu fuerint cum piauo aspectu Saturni; nati in ipso vitæ momento moriuntur, aut in ipso nascenti lumine constituti deficientibus Matris viribus strangulantur; aut tumescen- tibus faucibus acerbum illis mortis infertur exitium. Quod si Mars cum ipsis in occasu fuerit, omni beneuolarum testimoni destitutus, plecti factiet natos, aut religionis causa exuri. Hæc Firmicus, quæ tamen cautè intelligenda sunt. Sed quoad aëris mutationem Hædi exorientes ventos cire solent, pluuias violentas adducere, & tempestates in mari excitare. Vnde inimicum nauigantibus fidus canit Germanicus. HELIACVS ortus, & occasus, stellæ apud Astronomos signi- <12.> ficat eius emerstonem è radijs Solis, ita vt fiat conspicua, aut cum in illos immergitur, & ampliùs videri nequit, siue id fiat ob Solis approximationem, vel elongationem ab ea, siue ipsius stellæ ad Solem, quod locum habet tantummodo in planetis. Quod fit ad distantiam plus minus 17. graduum in Luna, in cæteris autem ferè vnius signi. Ortum heliacum Aquarij sic describit Ouidius lib. 2 Factorum dum cecinit: Iam leuis obliqua subsedit Aquarius vna: Proximus ad hæres excepe Piscis equos. Mense etenim Februario Sol existit in Aquario, eumque proptereà suo splendore occultat: verùm cùm sub finem Februarij Pisces ingreditur, incipit Aquarius paulatim è Solis radijs emergere, sicque mane ante Solis ortum fieri conspicuus. E contra occasum heliacum Canis intellexit Virgilius lib. 1. Georg. quando dixit: Candidus auratus aperit cum cornibus annum Taurus, & aduerso cedens Canis occidit astro. Quia cùm olim Canis maior existeret in Geminis, Sole sibi appropinquante in Tauro, occidebat heliacè; cùm priùs enim esset conspicuus, jam inde incipiebat occultari, atque in Solis radijs iminegi; ita vt ampliùs videri non posset. HELIAC Græco nomine, sicut etiam Callisto, & Megisto dici <13.> tur Vasa maior, fidus in cælo propè polum arcticum ex aduerso Cassiopææ, sic dictum à circumuolutione, quod diei, noctisque spatio breui circumlatione circa polum voluatur. Habet stellas apud Prolemæum omninò 35 hoc est 27. intra imaginem inclusas, octo autem extra vagantes, & informes, licet Baierus in eo numeret tautùm 32. Cùm Keplerus obseruasse se di-

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MATHEMATICVM. 219 it would seem to imitate the whole institution of the planets: but all this will lie with a painted affectation. For inwardly he will be wanton, and one who secretly ever boils with the allurements of love, etc. Under this constellation also are born shepherds of sheep, and whoever make sweet melodies with the rustic reed, giving out the sweetest strains of country song. But if they are at setting with the fair aspect of Saturn, those born die at the very moment of life, or, being set at the very light of birth, are strangled as the mother’s strength fails; or with the throat swelling, a bitter end of death is brought upon them. But if Mars is at setting with them, lacking every testimony of good will, it will cause the born to be punished, or burned for the sake of religion. These are Firmicus’s words, which nevertheless must be understood cautiously. But as regards changes of weather, the Hyades rising are wont to bring winds, violent rains, and to stir up storms at sea. Hence Germanicus sings that they are hostile to sailors. HELIACAL rising and setting of a star, among astronomers, signifies its emergence from the rays of the Sun, so that it becomes visible, or when it is immersed in them and can no longer be seen, whether this happens because of the Sun’s approach to it or its recession from it, or of the star itself toward the Sun, which occurs only in the planets. This happens at a distance of more or less 17 degrees in the Moon, but in the others at about one sign’s breadth. Ovid describes the heliacal rising of Aquarius in book 2 of the Fasti, when he sang: Now light Aquarius had sunk beneath the slanting wave; Near him the succeeding Fish received the horses. For in the month of February the Sun is in Aquarius, and therefore hides it with its brightness; but when toward the end of February it enters Pisces, Aquarius begins gradually to emerge from the Sun’s rays, and thus in the morning before sunrise it becomes visible. By contrast, Virgil in book 1 of the Georgics understood the heliacal setting of the Dog when he said: When the bright Taurus opens the year with gilded horns, and the Dog, yielding to the opposite star, sets. Because when once the Greater Dog was in Gemini, as the Sun approached it in Taurus, it set heliacally; for whereas before it was visible, then it began to be hidden and to be immersed in the Sun’s rays, so that it could no longer be seen. HELIACAL, by the Greek name, as it is also called Callisto and Megisto, is the Great Bear, a constellation in the sky near the Arctic Pole, opposite Cassiopeia, so called from its revolving, because by the span of day and night it is turned about by a short rotation around the pole. Ptolemy gives it altogether 35 stars, that is, 27 enclosed within the figure, and eight wandering outside and shapeless, although Bayer counts only 32 in it. When Kepler observed that he di-

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LEXICON cat 56. Inter has septem sunt præcipuæ, quæ constituunt plaustum omnibus notum, secundæ magnitudinis, omnes præter vnam de natura Martis. Hoc sidus Romæ semper conspicuum est; quippe nullæ eius stellæ occidunt, nisi paucæ quædam infimæ notæ in summis pedibus. Sua amplitudine complectitur tria signa Cancerum videlicet, Leonem, & Virginem. Plura vide in V. Plaustum, & Vrsa. 14. HELLESPONTIVS dictus est Cæias ventus: de quo suo loco dictum, eò quod per Hellespontum transeat. 15. HEMICYCLVS, Græcè idem sonat, ac Latinè semicirculus: potissimùm verò accipitur pro altera parte Epicycli planeta, in qua directi denominantur, aut retrogradi, Occidentales, vel Orientales. Hinc etiam 16. HEMISPHERIUM dicitur dimidia pars sphæræ, quæ ope alicius magni circuli in duas æquas partes tribuatur; absolutè verò & pressiùs accipitur pro ea diuisionis parte, quam præstat horizone dirimens cælum in duo segmenta, quorum alterum est semper nobis conspicuum, alterum verò, quod semper inferiùs latet: ita vt communiter dicatur & superius, & inferius hemisphærium; & has stellas in nostro hemisphærio, vel esse semper conspicuas, illas autem occidere scilicet subtus horizontem ad occasum deprimi, vel esse semper occultas. 17. HENIOCHVS. Vide Emiochus. 18. HEPTAGONVS Græcè, Latinè figura septem angulorum interprætari potest: ea vox passim ab Euclide, & ab alijs Geometris vsurpatur. 19. HERCIDES, Græcè dicitur manus alterius Geminorum, stella, inquam, fixa secondæ magnitudinis. de natura Martis, & Mercurij: veriùs tamen ipsum caput Pollucis, cùm in manu nulla sit stella talis magnitudinis, & naturæ. V. Pollux. 20. HERCVLES, apud Astronomos quandoque accipitur pro Engonasi, seu Ingeniculatore integro sidere constituto ex stellis 29. propè Ophincum; aliquando etiam pro altero Geminorum dicto Polluce; & signanter pro fixa Martia in eius capite fulgente, quæ inter regias, & violentas computatur. Sæpè enim apud scriptotes vna stella, quæ in capite Engonasis confunditur cum ea quæ in capite Pollucis est, ac promiscuè caput Herculis vocitatur. 21. HERMIPPVS à Plinio dicitur Delphinus (nescio qua ratione) quem etiam Cicero procellosum sidus appellat. De hoc satis dictum in V. Delphim. 22. HESPERVS dicta est Venus Occidentalis à Sole constituta in prima medietate sui Epicycli: sicut contrà Lucifer cum est Orientalis à Sole, & mane ante ipsum exoritur exultens in secunda

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LEXICON cat 56. Between the seven there are the chief ones, which constitute the wagon known to all, of the second magnitude, all except one by the nature of Mars. This star is always visible at Rome; for none of its stars sets, except a few very faint ones at the tips of the feet. By its size it includes three signs, namely Cancer, Leo, and Virgo. See more in V. Wagon, and Bear. 14. Hellespontius is the name given to the Cæian wind: of which it has been said in its proper place, because it passes through the Hellespont. 15. Hemicyclus, in Greek, means the same as semicircle in Latin: but it is especially taken for the other part of the epicycle of a planet, in which those are called direct, or retrograde, Western, or Eastern. Hence also 16. Hemispherium means the half of a sphere, which, by means of some great circle, is divided into two equal parts; but absolutely and more strictly it is taken for that part of the division which the horizon provides by separating the heavens into two segments, one of which is always visible to us, while the other always lies lower: thus it is commonly said that there is a superior and an inferior hemisphere; and of those stars in our hemisphere, some are always visible, while others set, that is, are depressed beneath the horizon toward the west, or are always hidden. 17. Heniocbus. See Emiochus. 18. Heptagonus, in Greek, can be interpreted in Latin as a figure of seven angles: this word is used everywhere by Euclid and by other geometers. 19. HERCIDES, in Greek, is said of the hand of one of the Twins, that is, a fixed star of the second magnitude, of the nature of Mars and Mercury: more truly, however, it is the very head of Pollux, since there is in the hand no star of such size and nature. See Pollux. 20. Hercules, among astronomers, is sometimes taken for Engonasi, or the whole Kneeler, a constellation made up of 29 stars, near Ophiuchus; sometimes also for the other of the Twins, called Pollux; and especially for the fixed Martial star shining in his head, which is counted among the royal and violent stars. For often in writers one star, which is confused with that in the head of Engonasis, is the same as that which is in the head of Pollux, and is commonly called the head of Hercules. 21. Hermippus is called by Pliny the Dolphin (I know not for what reason), whom Cicero also calls a stormy star. Enough has been said about this in V. Dolphin. 22. Hesperus is the Western Venus, placed by the Sun in the first half of its epicycle: just as, on the contrary, Lucifer, when he is Eastern from the Sun, rises before it in the morning exulting in the second

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MATHEMATICVM. 221 medietate Epicycli. Vide Cicero de natura Deorum lib. 2. de ea loquens infima est, inquit, quinque errantium, terraque proximæ stella Veneris, qua Latinè Lucifer dicitur cum antegradetur Solem; cum subsequitur autem, Hesperus. Porrò Venus Occidentalis à Sole fortior est quam Orientalis, sicut & Mercurius, & Luna, quia aucti lumine, ad differentiam superiorum, qui augentur lumine, cum sunt Orientales, minuuntur, cum fiunt Occidentales. HETEROSC. 1 apud Astronomos scriptores passim atque < 22.> Cosmographos appellantur populi habitantes in Regionibus, seu Zonis temperatis ab Tropicis ad Circulos Arcticum & Antarcticum; quo nomine & nos venimus, eoquia experi- mur vmbram vnam tantum ad Septentrionem vergentem, vel econtrà qui vltrà Tropicum Capricorni degunt, ad Au- strum, licet retineant semper Orientalem, atque Occidenta- lem: & qui immediatè sub Tropicis habitant, vel propè ipsos semel in anno nullam habeant in metidie, cum Sol illis fiat ver- ticalis. HEXAGONVM. Vide Exagonum. H 1 HINNICVLVS, Equi sectio, Rostrum Equi, &c. dicitur si- < 23.> dus in cælo repræsentans caput equi mutilatum, quod habet stellas quatuor obscuras de natura Saturni, Martis, & Mercurij. Vide in V. Equiculus. HIBRESIM Arab. dicitur constellatio Cygni, quasi rosa, vel < 24.> lilium redolens. Habet stellas 17. cum duabus informibus, de qua in V. Cygnus. HIREVS, Capella Arab. Alaios fidus, seu potius vnica stella < 25.> ptimæ magnitudinis, de natura Martis, & Mercurij existens in sinistro humero Aurigæ, ac repræsentans Capellam lactantem duos hædos in eiusdem manu sinistra hærentes. Est fidus tem- pestuosum procellosum, & Nautis inimicum, vt vocat Ger- manicus, ventos impetuosos producens, & Mare concutiens. De eo horoscopante in alicuius natuitate, hæc habet Firmi- cus. Nati erunt nimia mentis trepidatione solliciti, & quo- rum corpus assiduus tremor semper impugnet. Hi leuibus com- motionibus optimentur, & leuibus etiam nuncijs graui timo- ris incursione quassabuntur. Erunt tamem omnium rerum cu- riosi, & qui quodcumque nouum dictum fuerit, id impatien- ti cupiditate desiderent; vt semper noua quæque curiosa desi- derij cupiditate sectentur, eaque intelligere studeant. Si verò in occasu fverit, ex pradijs habebunt substantiæ facultatem: sed si propter læsas religiones graui pulsabuntur inuidia. Ha- bebunt etiam substantiam, aut ex naufragijs collectam, aut ex

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MATHEMATICVM. 221 by the half of the epicycle. See Cicero, On the Nature of the Gods , book 2. Speaking of it, he says it is the lowest of the five wandering stars, and the star nearest the earth is Venus, which in Latin is called Lucifer when it precedes the Sun; but when it follows after, Hesperus. Moreover, the western Venus is stronger than the eastern, as also are Mercury and the Moon, because, having increased in light, unlike the superior planets, which are increased in light when they are eastern, they are diminished when they become western. HETEROSC. 1 Among astronomical writers and everywhere among <22.> cosmographers, the peoples living in the regions, or temperate zones, from the Tropics to the Arctic and Antarctic Circles, are called by this name; to this class we also belong, because we experience only one shadow leaning toward the north, or, on the contrary, those who dwell beyond the Tropic of Capricorn, toward the south, although they always retain an eastern and a western shadow; and those who live immediately under the Tropics, or near them, once a year have none at midday, when the Sun becomes vertical to them. HEXAGONVM. See Exagonum. H 1 HINNICVLVS, a section of the Horse, Horse's Snout, etc., is the constellation representing the mutilated head of a horse, which has four dim stars of the nature of Saturn, Mars, and Mercury. See under V. Equiculus. HIBRESIM, in Arabic, is said of the constellation of the Swan, as though fragrant like a rose or lily. It has 17 stars with two unformed ones; see under V. Cygnus. HIREVS, Capella in Arabic, Alaios fidus, or rather a single star of the first magnitude, of the nature of Mars and Mercury, situated in the left shoulder of Auriga, and representing a she-goat nursing two kids clinging to her left hand. It is a stormy and tempestuous star, hostile to sailors, as Germanicus calls it, producing violent winds and shaking the sea. Concerning it when it is placed on the horoscope of someone’s nativity, Firmicus says the following: they will be born excessively anxious, with trembling of mind, and their body will always be troubled by constant shaking. They will be moved by slight disturbances, and even by slight reports they will be shaken by an attack of heavy fear. Yet they will be curious about all things, and whatever new thing is said they will desire with impatient eagerness; so they will always pursue every novelty with eager curiosity and strive to understand it. But if it is in the setting, they will have means from booty: but if, because of violated religions, they are struck by heavy envy. They will also have property, either gathered from shipwrecks, or from

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212 LEXICON aluminumibus comparatam. Hucusque Firmicus in hac re minimè audiendus. Oritur Romæ Hircus cum gr. 12. Arietis, occidet cum ferè 27, Cancri, sed tamen notandum, quod habet maximam latitudinem, seù declinationem Borealem grad. nempe 46. adeoque sit Verticalis Andegauo, Oeniponto, Ber- næ, alijque sinitimus cuitatibus. 28. HIREVS etiam dicitur species quædam Cometæ tenuissimis radiorum sibris, tanquam villis quibusdam stipari admodum hitei hispidi, & villosi, de quo Plin. lib. 2. cap. 25. Græcè di- citur Tragoides. 29. HIREVS æquoris aliquibus dictus est Capricornus, deci- mum ab Ariere signum, eoquod eius imago monstrum mari- num referat, & in finem abeat in piscem. Vel forte sic dicitur ab effectu; est enim sidus æquori ominosum, vnde & Pelagi procella, & imbriser appellatur, Arabice Elgedi, vel Alchan- tarus. HO 30. HOLOMETRVM est instrumentum Mathematicum, quo fa- cillime, omnia quæ oculis subijciuntur mensurari possunt. Eius fabricam, & vsum docet Abel Tullo eius inuentor peculiari libello hac de re edito Venetijs anno 1564. 31. HOMOCENTRICVM Græcolat. idem sonat ac Concentricum, de quo quo sese egimus suo loco. 32. HOMOTH ex Græco Barbar. dicitur in sphæra Barbarica tertius Decanus Capricorni competens Soli, significans cupi- ditatem gubernandi familiam, suspiciones, insufficientiam, &c. 33. HOMOZONA vocantur signa se inuicem intuentia paris virtutis, parisque declinationis, quæ nos Antiscia, seu pe- rallelos declinationis diceremus. Eius vocabuli vsus fræquens est in scaligero in Commentar. ad Manilium. 34. HORA est æquale temporis spatium in quod dies diuiditur. Eius etymon alij hauriunt à Sole horarum distributoris, quem Ægyptrij Horum vocabant: Alij à Græco vocabulo Horizim, quod terminare significat, distingvere, ac diuidere: Alij ab vrina, quam Græci tò v po dicunt. Ferunt enim Hermerem Trismegistum horarum distributionem primum fecisse, at- que obseruasse ab vrina sacri cuiusdam Animalis Cynocephali nomine, quod serapidi erat dicatum, nam cum obseruasset ani- mal illud spatio vnius diei artificialis duodecies vrinam mit- tere æqualibus semper spatijs intèjectis, totum tempus diei respondens pariterque nocti, in 24. æqualia spatia dispescuit, eò maxime quod hæc distributio optime responderet integræ circulationi primi mobilis ascendentibus singulis spatijs tem- poris quidemis semper gradibus æquatoris; ideò inquam ab

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212 LEXICON compared with aluminum. Up to this point Firmicus is by no means to be listened to in this matter. Hircus rises at Rome with 12° Gemini, and sets with almost 27° Cancer; but it is nevertheless to be noted that it has the greatest latitude, or northern declination, namely 46°, and thus is vertical at Angers, Innsbruck, Bern, and other similar cities. 28. HIREVS is also said of a certain kind of Comet, with very thin filaments of rays, as it were bristling with certain hairs, shaggy and hairy, concerning which Pliny, lib. 2, cap. 25. In Greek it is called Tragoides. 29. HIREVS, by some, is the Capricorn, the tenth sign from Aries, because its image resembles a marine monster and ends in a fish. Or perhaps it is so called from its effect; for it is a star ominous for the sea, and hence it is called the storm of sailors and the bringer of rain; in Arabic, Elgedi, or Alchantarus. HO 30. HOLOMETRVM is a mathematical instrument by which, most easily, all things that are presented to the eyes can be measured. Its construction and use are taught by Abel Tullo, its inventor, in a special booklet published on this subject in Venice in the year 1564. 31. HOMOCENTRICVM, in Greek and Latin usage, has the same meaning as Concentricum, which we have already discussed in its proper place. 32. HOMOTH, from barbarous Greek, is said in the barbaric sphere to be the third decan of Capricorn, belonging to the Sun, signifying a desire to govern the household, suspicions, insufficiency, etc. 33. HOMOZONA are called signs looking at one another with equal virtue and equal declination, which we would call antiscia, or parallels of declination. The use of this word is frequent in Scaliger in his Commentary on Manilius. 34. HORA is an equal span of time into which the day is divided. Some derive its etymology from the Sun, distributor of the hours, whom the Egyptians called Horus; others from the Greek word Horizim, which means to terminate, distinguish, and divide; others from urine, which the Greeks call tò v po . For they say that Hermes Trismegistus first made and observed the division of the hours from the urine of a certain sacred animal called the cynocephalus, which was dedicated to Serapis; for when he had observed that that animal, over the span of one artificial day, discharged urine twelve times at always equal intervals, he divided the whole time of the day, corresponding likewise to the night, into 24 equal parts, especially because this distribution best corresponded to the complete circulation of the primum mobile, the ascending degrees of time in each equal interval, indeed always of the equator; therefore, I say, from

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MATHematicVM. 223 vrina Cynocephali horas æqualia isthæc spacia nominauit. Vtrumque sit, certum est horas 24. vt modò innui, esse mensuram temporis, quo Sol integro die naturali cum sum suum absoluit circà tellurem motu non suo sed primi mobilis ab Oriente in Occidentem. Sunt autem duo horarum genera: aliæ quæ dicuntur æquales, seu æquinoctiales, & est tempus respondens ascensioni singulorum quindecim graduum æquatoris; (reiecto paruo illo temporis interuallo, ferè insensibili, quod singulis addi deberet propter motum proprium Solis in Zodiaco, qui sit vt integra revolutio primi mobilis perficiatur in horia 23. & min. 56. Solis autem in 24. quatuor minutis plus.) Aliæ dictæ inæquales, temporariæ, naturales ac Planetariæ, & est duodecima quæque pars diei vel noctis artificialis; cuius spatio exoritur medietas cuiuslibet signi; quæ tempore æquinoctij tantum cum æqualibus conueniunt; cæterum alijs temporibus vel augescunt, vel minuuntur, prout augentur, vel decrescunt dies aut noctes. Dicuntur etiam planetariæ, quoniam singulis horis inæqualibus singulos planetas dominari contendant Astrologi, facto initio à planet diem denominante, qui præest primæ horæ ab exortu Solis, ac successiuè dominium prosequentibus, reliquis planetis per ordinem dispositis in hebdomada, ( cuius dispositionis ratio hinc ortum habuit) vt, pro exemplo, primæ horæ sabbati Saturno dicati dominetur Saturnus; secundæ Iupiter; tertiæ Mars, & sic de singulis. Similiter primæ horæ noctis dominabitur Mercurius, qui proximè succedit Veneri, quæ dominatum obtinuit vltimæ, & duodecimæ horæ diei artificialis; vltimæ verò horæ noctis proximè ante Solis exortum die sequenti, Mars: itaut die dominico Soli attributo succedat ipse Sol in dominium primæ horæ diei, quæ, vt dixi ab eiusdem Solis exortu computanda erit. Porrò istarum horarum beneficio cognoscitur arcus diurnus, & nocturnus cuiuscumque partis Zodiaci, sicque etiam singulorum planetarum, inibi existentium: quot enim gradus æquatoris cum ipsa Zodiaci parte supra terram consistente ascendunt, erit arcus diurnus; quot ab occasu descendunt ipsa in inferiori hemisphærio commorante, conficiunt arcum nocturnum: itaut facile sit obseruare, quota ea sir, quorue partibus excedat; aut excedatur ab hora æquali correspondente singulis quindecim gradibus æquatoris. Sic proposita maxima die artificiali 15. horarum; hora inæqualis diurna erit hor. 1. min. 15. Nocturna verò constabit 45. minutis. Hinc. HORARIA tempora dicta sunt sexta quæque pars arcus semidiurni, vel seminocturni cuiusque partis Zodiaci, seù etiam arcus æquatoris correspondens singulis horis inæqualibus, 35.

Transcription: Translated (English)

MATHematicVM. 223 Frina Cynocephali called these spaces equal hours. Whichever it may be, it is certain that 24 hours, as I have just indicated, is the measure of time in which the Sun completes its whole natural day, with its course around the earth, not by its own motion but by that of the first mobile, from East to West. But there are two kinds of hours: some are called equal, or equinoctial, and are the time corresponding to the rising of each fifteen degrees of the equator, (setting aside that small interval of time, scarcely perceptible, which should be added to each because of the Sun’s proper motion in the Zodiac, so that the full revolution of the first mobile is completed in 23 h. 56 min., and the Sun’s in 24 h. by four minutes more.) Others are called unequal, temporal, natural, and planetary, and each is the twelfth part of the artificial day or night; in which space half of any sign rises; and at the time of the equinox they agree only with the equal hours; at other times they either increase or decrease, according as days or nights increase or decrease. They are also called planetary, since astrologers contend that in each unequal hour a different planet rules, beginning from the planet giving name to the day, which presides over the first hour from sunrise, and successively carries on the dominion, the remaining planets being arranged in order through the week, (the reason for which arrangement originated here,) so that, for example, Saturn rules the first hour of Saturday, dedicated to Saturn; Jupiter the second; Mars the third, and so on with each. Likewise Mercury will rule the first hour of the night, next after Venus, which obtained dominion over the last, and twelfth, hour of the artificial day; but Mars will rule the last hour of the night, immediately before the sunrise of the following day; so that on Sunday, attributed to the Sun, the Sun itself succeeds to the rule of the first hour of the day, which, as I said, is to be reckoned from that Sun’s rising. Moreover, by means of these hours the diurnal and nocturnal arc of any part of the Zodiac is known, and thus also of each of the planets therein present: for however many degrees of the equator, together with the part of the Zodiac itself standing above the earth, ascend, there will be the diurnal arc; however many descend after sunset, while it remains in the lower hemisphere, they make the nocturnal arc; so that it is easy to observe what it is equal to, or by what parts it exceeds; or is exceeded by, the equal hour corresponding to each fifteen degrees of the equator. Thus, if the maximum artificial day is taken as 15 hours, the unequal diurnal hour will be 1 h. 15 min.; the nocturnal, however, will consist of 45 minutes. Hence. HOURLY times are called the sixth part of the semidiurnal or seminocturnal arc of any part of the Zodiac, or also the arc of the equator corresponding to each unequal hour, 35.

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124 LEXICON quas complectitur quota pars Zodiaci coascendens aut condescendens: quorum ope perficiuntur directiones ad mentem Ptolomæi, ac singularum domorum cælestium, tam supra quam infrà terram existentium sit distributio. Nam bina horaria tempora diurna, seù tertia pars arcus semidiurni constituit spatium singularum domorum suprà terram existentium: geminata item horaria tempora nocturna, seù tertia pars arcus seminocturni constituit quantitatem singularum domorum infrà terram existentium. Tabulam horariorum temporum ad singulas Eclipticæ partes habent ferè omnes scriptores in introductorijs ad Ephemeridas. Si planeta habeat latitudinem, & vera eius horaria tempora venari volueris, < 14.> acceptam eius declinationem ad rationem latitudinis quam habet reuoca ad eclipticam, ac postea cum gradu illo eclipticæ accipe horaria tempora, quæ illi respondent in tabula, & fies voti compos. Quod si tanta sit declinatio planetæ, vt excedat illam eclipticæ, vel fixarum maximam latitudinem habentium horaria tempora velis extrahere, diuide eius arcum semidiurnum, vel seminocturnum acceptum in gradibus & minutis, in sex partes, & singulæ erunt horaria tempora diurna, vel nocturna Arcus autem semidiurnus, vel seminocturnus cujuscumque sideris quacunque latitudine præditi, habetur per additionem differentiæ ascensionalis competentis declinationi sideris ad gr. 90. si quidem declinatio fuerit Borealis, vel per diminutionem ab gr. 90, si declinatio fuerit australis: & econtra arcus seminocturnus habetur per additionem differentiæ ascensionalis ad gr. 90. si declinatio stellæ fuerit australis, per subtractionem, si fuerit Borealis, & residuum, vel summa erit arcus semidiurnus, vel seminocturnus diuidendus, vt dixi in sex partes æquales, ad hoc vt habeantur horaria tempora diurna, vel nocturna; nec non horæ inæquales, seu planetariæ, < 15.> si gradus & minuta æquatoris conuertantur in horas, & minuta temporis, tribuendo, vt supra, quindecim gradus singulis horis æquinoctialibus, & singulis minutis æquatoris singula minuta temporis. HORINÆVM vocat Ptolemæus lib. 3 cop. 14. Quadrip. motum directionis conuersum, quo significator motu primi mobile raptus fertur in locum promissoris à consequentibus ad præcedentia signa: docetque motu dirigendum esse vitæ moderatorem existentem in quarta Occidentali supraterranea, à < 17.> medio videlicet cæli ad occasum, ad ipsum occiduum finitorem, quem solum in eo casu agnoscit habere vim Anæreticam, eo quia inquit Dominum visa abscondit Hoc motu dirigi possunt omnes moderatores qui mouentur in Zodiaco, & rapiuntur.

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124 LEXICON which comprises the portion of the Zodiac ascending or descending: by means of these are accomplished directions according to the method of Ptolemy, and the distribution of the celestial houses, both above and below the earth, is determined. For two diurnal hourly times, or the third part of the semi-diurnal arc, constitute the span of the several houses existing above the earth: likewise, twofold nocturnal hourly times, or the third part of the semi-nocturnal arc, constitute the quantity of the several houses existing below the earth. Almost all writers on introductory works to Ephemerides have a table of hourly times for the individual parts of the Ecliptic. If a planet has latitude, and you wish to find its true hourly times, <14.> reduce its declination, taken with regard to the latitude it has, to the ecliptic, and then, with that degree of the ecliptic, take the hourly times that correspond to it in the table, and you will achieve your aim. But if the declination of the planet is so great that it exceeds the maximum latitude of the ecliptic, or of the fixed stars whose hourly times you wish to extract, divide its semi-diurnal or semi-nocturnal arc, taken in degrees and minutes, into six parts, and each will be a diurnal or nocturnal hourly time. The semi-diurnal or semi-nocturnal arc of any star, whatever latitude it possesses, is obtained by adding the ascensional difference appropriate to the star’s declination to 90 degrees if the declination is northern, or by subtracting it from 90 degrees if the declination is southern; and conversely, the semi-nocturnal arc is obtained by adding the ascensional difference to 90 degrees if the star’s declination is southern, and by subtraction if it is northern, and the remainder, or the sum, will be the semi-diurnal or semi-nocturnal arc to be divided, as I said, into six equal parts, in order that diurnal or nocturnal hourly times may be obtained; and also unequal hours, or planetary hours, if the degrees and minutes of the equator are converted into hours and minutes of time, assigning, as above, fifteen degrees to each equinoctial hour, and to each minute of the equator a minute of time. HORINÆVM Ptolemy calls, in Book 3, chapter 14 of the Quadripartite, the reversed motion of direction, by which the significator, carried along by the motion of the first mobile, is brought into the place of the promissor from the following to the preceding signs: and he teaches that the mover of life, existing in the western quadrant above the earth, that is, from the midheaven to the setting, right up to the very setting boundary, is to be directed by this motion, which alone in that case he recognizes as having Anaretic power, because, he says, it hides the Lord from sight. By this motion can be directed all movers that move in the Zodiac and are carried along.

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MATHEMATICVM. 225 tur motu primi mobilis circà tellurem; quales sunt Sol, Luna, Fortunæ pars, & omnes planetæ, si eos dirigere placeat. Cardines verò cum semper considerentur immobiles nullo pacto dirigi possunt motu conuerso, sed tantum recto, quatenus Promissores motu primi mobilis rapti ferantur ad ipsos, vt optimè probar Titus in Cælesti Philosophia. HORIZON Græcè, Latinè Finitor dicitur Circulus magnus 38. in sphæra diuidens superiùs hemisphærium conspicuum ab inferiori inconspicuo; qui pro qualitate eleuationis Poli variatur; ita vt infinita propemodum concipi possint horizonta, sicut & infiniti meridiani pro maiori, vel minori eleuatione Poli. Et si quidem neuter polorum altero magis attollatur, sed ambo incidant in horizontalem lineam, dicitur horizon rectus, eò quia æquator rectè ascendit, & culminat. Si verò alter polorum eleuetur, alter deprimatur, dicitur horizon obliquus, quia obliquè ascendit æquator: & quò maior erit eleuatio Poli, eò maior erit horizontis obliquitas, & diuersitas ascensionum, ita vt in maiori Poli altitudine, quæ excedere nequit gt. 90. cum ipse Polus incidat in verticem, atque æquator sit obliquissimus & in ipsum recidat horizontem, inde est vt sit & parallelus, ac proinde ipse horizon parallelus dicatur. Porrò horizon in cælesti themate duos angulos constituit, Orientalem, vnde emergunt sidera, & fiunt nobis conspicua (qui vocatur Cardo Orientalis, Ascendens & Prima domus) & Occidentalem vbi sidera deprimuntur ad inferius hemisphærium, qui dicitur Cardo Occidentalis, & Septima domus. Plura sunt horizontis officia quæ omnia diligenter enumerat Clauius in spharam lo. de Sacrobosco: potissimum autem est determinare diem, ac noctem artificialem, atque ostendere puncta ortus, & occasus siderum, nec non gradum eclipticæ cum quo quælibet stella oriatur, & occidat: sicur etiam quæ stellæ sint perpetuæ apparitionis, quæue continuæ occultationis. Vide etiam quæ diximus in V. Finitor. Horoscopvs Græcè dicitur Cardo Orientalis, & ea pars 39. exli quæ qualibet hora ascendit ab inferiori hemisphærio in Orientali finitore: vnde ab Astronomis communiter Ascendens appellatur. Differt ab horizonte, quod hic totum circulum finitorem dicat, & vtrumque cardinem comprehendat, vt modò dictum est, Orientalem, atque Occidentalem: horoscopus verò non modò denotat solum cardinem Orientalem, & primam domum, sed potissimum sumitur pro gradu eclipticæ in eam lineam incidente. Ea propter significat rerum initia, vitæ & corporis affectiones, temperamentum, &c. Cuius rei 40. rationem ingeniosissimam affert Titus in Cælesti Philosophia, P

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MATHEMATICVM. 225 through the motion of the first mover around the earth; such are the Sun, Moon, the part of Fortune, and all the planets, if it please us to direct them. But the angles, since they are always considered immobile, can in no way be directed by a reverse motion, but only by a straight one, insofar as the Promissors, carried by the motion of the first mover, may be borne to them, as Titus proves very well in Celestial Philosophy. HORIZON is called in Greek, in Latin Finitor, the great circle 38. in the sphere dividing the upper visible hemisphere from the lower invisible one; this varies according to the elevation of the Pole, so that almost infinite horizons may be conceived, just as there are infinite meridians for a greater or lesser elevation of the Pole. And if neither of the poles is raised more than the other, but both fall on the horizontal line, it is called a right horizon, because the equator rises and culminates directly. But if one of the poles is elevated and the other depressed, it is called an oblique horizon, because the equator rises obliquely; and the greater the elevation of the Pole, the greater will be the obliquity of the horizon and the difference of ascensions, so that at the greatest altitude of the Pole, which cannot exceed 90°, when the Pole itself falls at the zenith, and the equator is most oblique and falls upon the horizon itself, from this it is that it is also parallel, and therefore that the horizon itself is called parallel. Moreover, in the celestial figure the horizon constitutes two angles, the Eastern, from which the stars emerge and become visible to us (which is called the Eastern Angle, Ascendant, and First House) and the Western, where the stars are depressed into the lower hemisphere, which is called the Western Angle, and the Seventh House. There are many functions of the horizon, all of which Clavius carefully enumerates in sphaeram lo. de Sacrobosco: its principal one, however, is to determine the artificial day and night, and to show the points of rising and setting of the stars, as well as the degree of the ecliptic with which every star rises and sets: likewise which stars are of perpetual appearance and which of continual occultation. See also what we said in V. Finitor. Horoscopus is called in Greek the Eastern Angle, and that part 39. of the sky which at any hour ascends from the lower hemisphere in the Eastern finitor; hence it is commonly called by astronomers the Ascendant. It differs from the horizon, in that the latter denotes the whole circle of the finitor and includes both angles, as was just said, the Eastern and the Western; but horoscopus not only denotes the Eastern angle and the first house, but is chiefly taken for the degree of the ecliptic falling on that line. For that reason it signifies the beginnings of things, the affections of life and body, temperament, etc. For this matter 40. Titus gives a most ingenious explanation in Celestial Philosophy, P

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226 LEXICON lib. 1. cap. 17. conclus. 7. Quia videlicet Sol vitalis caloris largitor, & Luna humidi radicalis incipiunt influere has qualitates in ipso horoscopo, & licet ibi actu semper non sint, nihilominus semper habent realem relationem ad hunc locum incautionis; immò ad omnia puncta mobilia, sicut est præcæteris etiam culmen: & per hanc relationem efficiunt correspondentem intensionem caloris, & humiditatis: vnde sequitur, vt semper horoscopus sit initium productionis harum qualitatum, & sit semper alius terminus correlatiuus distantiæ luminarium à principio productionis suarum qualitatum. Proptereà non ab re æstimatur ab aliquibus nobilior cæli pats, & omnium angulorum potissimus, licet Prolemæus ei culmen præficiat. Gaudet in horoscopo Mercurius: Consignificator est Saturnus, & ex membris humanis habet caput. Plura vide in V. Ascendens. 41. HOROSCOPVS Lunaris dicitur locus ille in situ mundi acceptus, vnde emergit Luna, quo tempore Sol reperitur in apice Orientis; qui etiam à vulgo Astrologorum pars Fortunæ nuncupatur, eò quia est fortunarum significator: & sicut Oriens disponit vitam, quia ab eo incipit Sol influere calorem vitalem de die, vt modò explicatum est; ita etiam horoscopus Lunaris de noctè habet disponere humidum radicale, quia inde incipit Luna qualitates naturales influere secundùm habitudinem, quam habet ad Solem. Quam rationem acutissimè etiam < *> affert Titus vbi supra lib. 1. cap. 7. sic inquiens. Quoniam verò de nocte præualer humiditas, hinc est, quod de nocte hæc pats < 42.> Lunaris possit esse etiam vitæ prorogatrix: semper autem moderatur facultates, quia alimoniæ subministrat materiam & humiditatem ad alendum calorem vitalem. Et paulò inferiùs subdit. Hinc verò patet, quàm grauiter ertent, & decipiantur, qui absque discrimine facultates à luminaribus, dignitates à parte Fortunæ, filios à Luna, atque alios effectus præter naturam à dissimilibus causis inquirunt. Et hæc quidem de significatis. Cæterum de vero huius Lunaris horoscopi loco nouam doctrinam Philosophiæ, & experientiæ consonam, eius dirigendi rationem, quomodo in mundo tantum constituendus, & quàm deformiter errent qui eum in Zodiaco collocant, luculenter tradidimus in V. Fortuna pars. 43. HOROSCOPVM dicitur instrumentum planum, & rotundum, duas habens facies, quarum anterior ostendit quantitatem diei, ac noctis, vbique locorum, & quouis anni tempore: posterior verò habet descriptos circulos omnes qui sunt in Iphæra armillari, nec-non & altos intersecantes singulas partes Zodiaci, casque in horarum circumferentias includentes. Qua

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226 LEXICON lib. 1. cap. 17. conclus. 7. For the Sun, namely, as bestower of vital heat, and the Moon, as bestower of radical moisture, begin to influence these qualities in the very horoscope; and although they are not always actually there, nevertheless they always have a real relation to this place of incaution; indeed, to all the movable points, as also, before the rest, the Midheaven: and through this relation they produce a corresponding intensity of heat and moisture. Whence it follows that the horoscope is always the beginning of the production of these qualities, and is always the other correlating term of the distance of the luminaries from the beginning of the production of their qualities. Therefore it is not without reason considered by some to be the nobler part of the sky, and the chief of all the angles, although Ptolemy assigns the Midheaven to it. Mercury rejoices in the horoscope: Saturn is its co-significator, and among the human members it has the head. See more in V. Ascendens. 41. The Lunar HOROSCOPE is called that place, taken in the position of the world, from which the Moon rises, at the time when the Sun is found in the apex of the East; which is also commonly called by Astrologers the Part of Fortune, because it is a significator of fortunes: and just as the East disposes of life, because from it the Sun begins to influence vital heat by day, as has just been explained; so also the Lunar horoscope at night has to dispose of radical moisture, because from there the Moon begins to influence natural qualities according to the relationship it has to the Sun. This reason is also most keenly given by Titus above, lib. 1, cap. 7, speaking thus. Since, however, by night moisture prevails, hence it is that by night this part <42.> of the Moon may also be the prolonger of life: yet it always moderates the faculties, because it supplies nourishment and moisture as material for feeding vital heat. And a little below he adds: Hence it is clear how gravely they err and are deceived who, without distinction, seek faculties from the luminaries, dignities from the Part of Fortune, children from the Moon, and other effects contrary to nature from dissimilar causes. And these things indeed concern the significations. As for the true place of this Lunar horoscope, we have clearly set forth a new doctrine consonant with philosophy and experience, its rule for directing, how it is to be constituted only in the world, and how disgracefully those err who place it in the Zodiac, in V. Fortuna pars. 43. HOROSCOPE is called a flat and round instrument, having two faces, of which the front one shows the quantity of day and night everywhere and at any season of the year; the back, however, has described on it all the circles that are in the armillary sphere, as well as the great circles intersecting each part of the Zodiac and enclosing them in the circumferences of the hours. Which

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MATHEMATICVM. 227 de re, quemadmodum, & de eius vsu, arque vtilitate. Vide Io. Paduanium in peculiari libello de Horoscopio. < 44.> Hvmana signa vocantur apud Astronomos, non modo ea signa Zodiaci, quæ habent speciem quasi hominis, qualia sunt Gemini, Virgo, Aquarius, & prima medietas Sagittarij; verum etiam sidera, & Asterismi extrà Zodiacum, qui in humana figura oculis exhibentur; vt Perseus, Andromeda, Cassiopea, Cepheus, Orion &c. Experientia enim compertum est eas stellas, quæ in figuram humanam conglomeraræ sunt à sapientissimis illis venerandæ autiquitatis Astronomis, nescio quam cum hominibus affinitatem sympathiam, & connexionem habere, quemadmodum ferina signa cum feris, quadru. pedia cum quadrupedibus, venenata cum venenatis &c. vt nos etiam alibi obseruauimus. Hinc vulgatum illud Axioma, Congressum infortunarum in signo humano præsertim in octaua domp, mortalitatem, & pestilentiam inducere in hominibus. Quod vti- nam proximis hisce temporibus nostro malo expetti non fuissemus, pestilentia vniversam penè Italiam depopulanre; præcipuè verò amplissimas vibes, Romam, Neapolim, Genuam: quam proximè præcessit, ac præsignavit conuinctio Saturni, & Martis in signo Virginis, complera die 13. Septembris anni 1654. post horrendam Solis eclipsim celebatam in Leone precedenti mense Augusto, & replicata etiam die 4. Octobris 1656. per retrogradationem Saturni in dicto signo: quod certè magnum quid portendebat. Sic mundi revolutiones, directiones, transirus, & alia quæ accidunt in signis humanæ figuræ semper aliquid obnunciant in hominibus, aut ab hominibus eventurum, bonum, aut malum pro qualitare revolurionum, aut directionum. Concludo igitur cum iis quæ habet Prolemaeus in centil. propos. 41. Quisquis genitura sua dominatores, aut ascendens in signis humanis non habet ab humanitate alienus etiam sibi ipsi erit. < 45.> Hvzimethon Schicchardo dicitur coma Berenices, quasi spicarum manipulus, seu fascis. < 46.> Hyades Græcè, Latinè Succulæ stellæ fixæ septem in capite Tauri existentes, quarum præcipua est Pallilisium, seu oculus Australis eiusdem Tauri, Arabicè Aldebaran. Stellæ sunt famosæ nimis & memorabiles à pluuijs, quas quoties oriuntur, & occidunt, vsque ad fastidium procreant. Vnde Quid. 6. Pastor. canit: Postera lux Hyadas taurina cornua frontis Euocat, & multà terra madescos aquæ. Incipiunt autem oriri Romæ circà festum sancti Eleutherij Papæ, die 26. Maij cum grad. 6. Geminorum. De ijs in horoscopij

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MATHEMATICVM. 227 on the matter, namely, concerning its use and utility. See Io. Paduanius in a special little book on the Horoscopium. <44.> Human signs are called among astronomers not only those signs of the Zodiac which have the appearance of a human being, such as Gemini, Virgo, Aquarius, and the first half of Sagittarius; but also the stars and asterisms outside the Zodiac which are shown to the eye in human form; as Perseus, Andromeda, Cassiopeia, Cepheus, Orion, etc. For by experience it has been found that those stars which have been grouped into a human figure by those most wise astronomers of venerable antiquity have, I know not what, a kinship, sympathy, and connection with human beings, just as beastly signs with beasts, quadrupedal signs with quadrupeds, poisonous signs with the poisonous, etc., as we have also observed elsewhere. Hence that common axiom: the conjunction of malefics in a human sign, especially in the eighth house, brings mortality and pestilence among human beings. Would that in these recent times we had not had to experience this to our harm, when pestilence devastated nearly all Italy; especially the very great cities, Rome, Naples, Genoa: which was most nearly preceded and foreshadowed by the conjunction of Saturn and Mars in the sign of Virgo, completed on the 13th day of September of the year 1654, after the terrible eclipse of the Sun celebrated in Leo the preceding month of August, and repeated also on the 4th day of October 1656, by the retrogradation of Saturn in the said sign: which certainly portended something great. Thus the revolutions of the world, directions, transits, and other things that happen in the signs of the human figure always foretell something among human beings, or something to come from human beings, whether good or bad according to the quality of the revolutions, or directions. I therefore conclude with what Ptolemy has in the Centil. proposition 41: Whoever in his nativity does not have the rulers, or the ascendant, in human signs will also be alien to humanity in himself. <45.> Hvzimethon, according to Schicchardus, is the Coma Berenices, as it were a sheaf of ears, or a bundle. <46.> Hyades, in Greek; in Latin Succulæ; seven fixed stars in the head of Taurus, the principal of which is Pallilisium, or the southern eye of the same Taurus, in Arabic Aldebaran. They are stars too famous and memorable for their rains, which whenever they rise and set, produce them to the point of weariness. Hence Ovid, in book 6 of the Pastorals, sings: The next light summons the Hyades, the horns of the bull’s brow, and the earth is made wet with much water. They begin to rise at Rome around the feast of Saint Eleutherius the Pope, on the 26th day of May, at 6 degrees of Gemini. Concerning them in the horoscopi

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128 LEXICON copo repertis sic cecinit Pontanus in Vrania. Mox Hyadum chorus, eois emergit ab vndis, Fratris Hyæ quas perpetuus dolor indidit Astris, Non animi faciles somnos, non membra soporem Abcipiunt; & cura nouo parat vsque labores. Quis chorus hic ipso nascentibus astitis orit: Hos tumidos populi fauor, & plaudentia nostra; Sollicitant ferere arma inter plebemque patresque, Est amor: & positos rursum instaurare tumultus, Civilesque manus armare, & stringere ferrum: Tantum seditio placet, atque hac pascit amentes. In occasu verò ait quod portendant exitum violentum, menbrorum auulsionem, & his similia, maximè si maleuolæ astipulauerint. Earundem significara quoad aeris mutationes apud omnes habes, sed præcipue apud Plinium. 47. HYDRA sidus in cælo ad australem Plagam constans stellis 25. Ptolemæo, at Baiero 29. computatis etiam septem circà, sporadibus. Quæ omnes ferè sunt de natura Veneris, & Saturni, proptereà venenosæ, humorum corruptrices, pessimæ: vnde si cum Anæreta fuerint (maximè quæ primæ magnitudinis est Tychoni, Ptolemæo verò secundæ, dicta cor Hydræ, Arab. Alpharad) veneni potionem portendunt. Amplectitur totum sidus in longitudine bonam partem Leonis, Virginis, & Libræ. Vocatur etiam ab aliquibus Excetra ab Hydra lernæa, quod exsecto illi vno capite, tria de nouo exsurgerent. Item &c Hydrus &c, reuera tamen. 48. HYDRVS est nouum Astrum in cælo detectum in Plaga australi propè polum antarcticum, nobis inuisum, atque à recensioribus astronomis inter 12. imagines, quas alijs prioribus à Ptolemæo admissis adiecerunt, connumeratum. Habet stellas omninò 15. apud Baierum, & in Keplero enumerantur 20. præter nubeculam illi vicinam, quarum præcipua est, quæ in oculo propè extremam fluuij, tertiæ magnitudinis, quæ est vicinior omnibus, polò mundi, & nunc temporis non distat nisi duobus ferè gradibus. In longitudine amplectitur tria signa Capricor. Aquar. & Pisc. 49. HYDROGRAPHIA est facultas quæ in aquarum marisque descriptione ac dimensioneversatur, tradens quonam pacto remeari possit, sinuum naturam, quibusnam ventis pecularia loca subiaceant, quantum per rectam lineam vns distet ab alio &c. Quæ omnia fusè explicat Iansonius in ea Atlantis parte quam orbem maritimum inscripsit. 50. HYEMS dicebatur olim ea anni medietas in qua Sol in Zodiaco discursens reperitur in signis meridionalibus, incipiendo ab

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128 LEXICON copo repertis, so Pontanus sang in Vrania. Soon the chorus of the Hyads rises from the eastern waves, the Hyades, for whom the perpetual grief of their brother has been set among the stars; they do not receive easy sleep of the mind, nor does slumber take their limbs, and care continually prepares new labors. What chorus is this that arises at their birth under the very stars: these are the swelling favors of the people, and our applause; they stir up bearing arms among the common people and the fathers, there is affection: and to renew the settled tumults again, and to arm civil hands, and draw the sword: so much does sedition please, and with this it feeds the mad. In setting, however, it says that it portends a violent end, the severing of limbs, and things like these, especially if evil ones have assented. You have the meanings of the same, as far as changes in the air, among all writers, but especially in Pliny. 47. HYDRA is a constellation in the sky, extending toward the southern quarter, with 25 stars according to Ptolemy, but 29 according to Bayer, even counting seven scattered stars around it. Almost all of these are of the nature of Venus and Saturn, therefore poisonous, corruptive of humors, and very bad: hence if they should be with the Anareta (especially the one of first magnitude according to Tycho, but of second according to Ptolemy, called the heart of Hydra, Arab. Alpharad) they portend the drinking of poison. It occupies in length a good part of Leo, Virgo, and Libra. It is also called by some Excetra, from the Lernaean Hydra, because if one head were cut off, three would spring up anew. Also Hydrus, and so on; yet in truth... 48. HYDRUS is a new star discovered in the southern part of the sky near the Antarctic pole, invisible to us, and counted by more recent astronomers among the 12 figures which they added to the earlier ones admitted by Ptolemy. It has 15 stars altogether according to Bayer, and in Kepler 20 are listed, besides the little cloud near it, of which the principal is the one in the eye, near the end of the river, of third magnitude, which is closer than all the others to the pole of the world, and at present is not distant by more than about two degrees. In longitude it extends over three signs, Capricorn, Aquarius, and Pisces. 49. HYDROGRAPHIA is the skill concerned with the description and measurement of waters and seas, teaching in what way one may sail back, the nature of the bays, to what winds particular places are subject, how much one place is distant from another in a straight line, etc. All these matters Ianssonius explains at length in that part of the Atlantis which he entitled the Maritime World. 50. HYEMS used formerly to be called that half of the year in which the Sun, traveling through the Zodiac, is found in the southern signs, beginning from

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MATHEMATICVM. 229 Æquinoctio autumnali vsque ad Venum, & contactum Solis ad primum punctum Arietis. Nunc verò facta anni diuisione in quatore tempora, dicitur ea pars, quæ mediat inter Autum- num, & Ver, omnium frigidissima; atque amplectitur tempus quo Sol tria signa perlustrat Capricornum, Aquarium, & Pis- ces. Accipitur etiam hyems pro maxima elongatione Solis à vertice, vnde dicitur sub polis perpetuò hyemare: & sub æqua- tore duas esse hyemes, coquia bis Sol elongatur à vertice in sua maxima declinatione, quando reperitur in Tropicis. Hoc tempore notat Plinius lib. 2. cap. 50. rara esse fulmina, nisi in vrbe, & in toto tractu campaniæ; atque scithiam aliasque fi- nitimas regiones ob summum frigus immunem esse à fulmine: Quoniam, inquit, hyeme densatus aer nubium crassiore corso spis- fatur: omnisque exhalatio rigens, ac gelida quisquid accipit ignei vaporis extinguis. Hæc Plinius explicans subinde cæteras hyemis qualitates, à quibus nos recensendis breuitatis studio absti- nemus. HYLEG, seù Hylech Arab. Latinè dimissor: estque apud Astro- < 51.> logos Planeta, vel locus in cælo, qui in hominum natiuitate vitæ moderationem sortitur. Græcis apheta dicitur: Apud nos communiter Vitæ dator. Vide ibi. Hinc HYLEGIALIA loca dicuntur ea, in quibus repertus Planeta, < 52.> vel pars fortunæ sortiri potest vitæ moderationem; suntque horoscopus à quinque gradibus suprà cuspidem vsque ad 25. infrà: (licet in spatio crepusculorum in quibus nouissimè docet Titus dirigendum esse Solem cum sit vitæ moderator, possit etiam vltra 25. gradus protendi, vt nos docuimus in V. Cre- pusculum.) Medium cæli quod de quadrato respicit horosco- pum; Cardo Occidentis, qui de opposito: nona, quæ de tri- no: & vndecim, quæ de sextili. Solum tamen aduertit Titus in primo mobili canone 29. in vndecima non euadere prorogato- < 53.> rem planetam in omni ejus spatio consistentem, sed tantum in prima medietate (secundam ipse vocat procedendo ordine anuerso ad rationem motus primi mobibilis) coquia citra illam medietatem versus duodecimam incurrit in semiquadraum ad horoscopum; vnde ratione istius radij imperfecti & contra- < 54.> rij ad rationem sextilis non potest sortiri vitæ prorogatiouem. HYPAVGVS, teste Valla dicitur Planera compræhensus sub < 55.> Solis radijs hinc inde ad distantiam graduum 17. quæ quidem est maxima planetæ debilitas: nam omnis eius virtus à poten- tia Solis absorbetur; & quò maior fuerit cum Sole vicinitas, eò maior erit debilitas, & eneruatio. Vide quæ diximus in V. Combustus, & in V. CaZimi. HYPOGÆVM Græcè propriè dicitur aliquid subterraneum: < 54i> P 11j

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MATHEMATICVM. 229 From the autumnal equinox to the spring, and the contact of the Sun with the first point of Aries. Now, however, the year being divided into four seasons, that part which lies between Autumn and Spring is said to be the coldest of all; and it embraces the time during which the Sun traverses the three signs Capricorn, Aquarius, and Pisces. Winter is also taken for the greatest distance of the Sun from the zenith, whence it is said that beneath the poles there is perpetual winter: and that beneath the equator there are two winters, because twice the Sun is distant from the zenith in its greatest declination, when it is found in the Tropics. At this time Pliny notes, in book 2, chapter 50, that lightning is rare, except in the city, and in the whole region of Campania; and that Scythia and other neighboring regions, because of the extreme cold, are free from lightning: For, he says, in winter the thickened air is made denser by the thicker course of the clouds: and every exhalation, being stiff and frozen, extinguishes whatever fiery vapor it receives. Pliny, explaining these and the other qualities of winter in turn, we refrain from listing, for the sake of brevity. HYLEG, or Hylech, Arab.; in Latin dimissor: and among astrologers it is the planet, or the place in the sky, which in the nativity of men receives the governance of life. Among the Greeks it is called apheta: among us commonly the giver of life. See there. Hence HYLEGIAL places are called those in which the planet found there, < 52.> or the part of fortune, may receive the governance of life; and they are the horoscope from five degrees above the cusp down to 25 degrees below; (although in the space of the crepuscules, in which Titus most recently teaches that the Sun must be directed, since it is the governor of life, it may also be extended beyond 25 degrees, as we have taught in V. Crepusculum.) The midheaven, which from a square aspect looks toward the horoscope; the western angle, which is in opposition; the ninth, which is by trine; and the eleventh, which is by sextile. However, Titus notes only in the first mobile canon, 29, that in the eleventh the prorogator planet does not escape < 53.> throughout its whole extent, but only in the first half (the second he himself calls, proceeding in reverse order according to the motion of the first mobile), because before that half toward the twelfth it falls into a semisquare with the horoscope; whence, by reason of this imperfect and < 54.> opposite ray in relation to the sextile, it cannot receive the prolongation of life. HYPAVGVS, according to Valla, is said of a planet encompassed under the rays of the Sun on either side at a distance of 17 degrees, which indeed is the greatest weakness of a planet: for all its power is absorbed by the power of the Sun; and the greater its nearness to the Sun is, the greater will be its weakness and enervation. See what we said in V. Combustus, and in V. CaZimi. HYPOGÆVM is properly said in Greek of something subterranean: P 11j

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130 LEXICON Hinc apud Astronomos vsurpatur ad significandas domos cæli subterraneas, ac præcipuè lnum Cali. 35. HYPOTHENUSA apud Geometras dicitur linea recta subtensa duabus lineis pariter rectis angulum rectum efformantibus, quarum tamen vna sit maior altera: tunc quidem hypothenusa & hanc & illam in longitudine excedat necesse est. Vide Clauium in Euclidem, vbi etiam oculis exhibet ipsam figuram inspiciendam. 36. HYPPEVS apud Plin. lib. 2. cap 25. dicitur Cometæ species, qui radios hinc inde equinas iubas referentes, atque in orbem fese rotantes motu celerrimo, vnde & ab illis nomen sortitus est: Hyppon quippè Græcè Latinè equus interpretatur. 1 A 1. IACHA Arab. dicitur stella fixa nebulosa informis circæ Scorpionem sequens aculeum, de narura Martis, & Lunæ consistens in longitudine in gr. 23. Sagittarij, cum latitudine australi serè gr. 13. Ea in horoscopo, aut cum luminari præsertim conditionario reperta portendit affectiones oculorum, & si luminare ipsum sit Luna id longè pejus; quandoquidem ibi & circà est via combusta de qua supra diximus, vbi Luna maximè inforiunatur. 2. IACVLVM, Sagirta, telum, demon Meridianus, &c. dicitur sidus in Aquila ex transuerso existens, de quo alibi dictum. 3. IACVLVM etiam dicitur stella fixa in apice sagittæ sagittarij existens, de natura Martis & Lunæ, itidem oculis infensa, de qua alibi. 4. IACVLVM item dicitur genus quoddam crinitarum qui, & Acontia vibrantur enim, inquit Plin. longa radiorum serie instar iaculi. 5. IANCOS Græcè apud Ptolem. in vettione Arab. lib. 3. cap. 7. vbi agit de Gemellis significat genituram trium foeminarum, in quam conveniant Venus, Mercurius, & Luna. Arabice albaris. 6. IAPIX ventus provincialis Calabriæ, de quo Seneca in quæst. nautral. lib. 5. cap. 7. Gellius hunc Caurum esse existimat. 7. ICNOGRAPAIÆ apud Geometras est descriptio areæ alicuius corporis, aut ædificij ex Geometricis præceptis facta, ad cuius normam postea Architectura suam molitionem aggreditur. Hanc nos vulgò planam domus vocamus. Vide Vitruu. lib. 1. cap. 2. 8. ICOSAEDRVM ex Euclide lib. 11. est figura solida sub viginti triangulis æqualibus, & æquilateris comprehensa. Quæ quidem est vnum ex quinque generibus corporum regularium, quæ sic dicuntur, eoquod omnia plana quibus continentur æqualia sunt,

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130 LEXICON Hence among astronomers it is used to signify the subterranean houses of the sky, and especially the lower heaven. 35. HYPOTHENUSA among geometers is called the straight line stretched beneath two straight lines forming a right angle, of which, however, one is greater than the other: then indeed the hypothenuse must exceed both this and that in length. See Clavius on Euclid, where he also displays the figure itself for inspection with the eyes. 36. HYPPEVS, in Pliny, book 2, ch. 25, is said to be a species of comet, which, with rays on this side and that resembling horses’ manes, and revolving in a circle with very swift motion, from which also it has derived its name: for Hyppon in Greek is interpreted in Latin as horse. 1 A 1. IACHA, Arab., is said to be a fixed nebulous star, shapeless, near the Scorpion, following the sting, of the nature of Mars and the Moon, situated at longitude 23° Sagittarius, with southern latitude of nearly 13°. Found in the horoscope, or especially when it is with a luminary as significator, it portends afflictions of the eyes, and if the luminary itself is the Moon it is much worse; since there and around it is the burned path, of which we spoke above, where the Moon is most afflicted. 2. IACVLVM, dart, weapon, southern demon, etc., is said to be a star existing crosswise in Aquila, of which mention has been made elsewhere. 3. IACVLVM is also said of a fixed star existing in the tip of the Archer’s arrow, of the nature of Mars and the Moon, likewise hostile to the eyes, about which elsewhere. 4. IACVLVM likewise is said to be a certain kind of comet, which, being streaked, is indeed set in motion, as Pliny says, with a long series of rays like a javelin. 5. IANCOS, in Greek according to Ptolemy in the Arabic version, book 3, ch. 7, where he treats of Gemini, signifies the nativity of three females, in which Venus, Mercury, and the Moon concur. In Arabic, albaris. 6. IAPIX, a provincial wind of Calabria, of which Seneca in Quaest. Natural. book 5, ch. 7. Gellius thinks this is the Caurus. 7. ICNOGRAPAIÆ among geometers is the description of the ground plan of some body or building made according to geometrical precepts, by whose standard architecture later undertakes its construction. We commonly call this the ground plan of a house. See Vitruvius, book 1, ch. 2. 8. ICOSAEDRVM, from Euclid book 11, is a solid figure enclosed by twenty equal, equilateral triangles. This is one of the five kinds of regular bodies, so called because all the planes by which they are bounded are equal,

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MATHEMATICVM. 231 æquilatera, & æquiangula. Dicuntur etiam ab aliquibus corpora Platonica, quia Plato in Tymæo quinque mundi corpora, quæ simplicia à Philosophis nuncupantur, nempe Ætherem; & quatuor elementa Ignem, Aërem, Aquam, ac Terram his quinque corporibus assimilat. Sunt autem Cubus, Tetraedrum, Octaedrum, Dodecaedrum, & Icosaedrum. Quorum omnium explanationem, atque figuras, vide apud Clauium in Commentar. ab lib, 13. Elem. Euclidis. Necnon apud Alstedium figuras perbellè delineatas in sua Geometria. < 9.> ICTISAL, seu Alstedfal Arab idem sonat ac Latinè applicatio ad coniunctionem, estque cum planeta leuior existens intrà orbem sphæræ lucis alterius ponderosi vadit ad eum, donec iungatur illi corpore, & in puncto, frequens eius vsus est in centissoquio. I G < 10.> IGNIS vnum ex quatuor elementis omnium pulcherrimum ac leuissimum, castitatis, & puritatis apud antiquos symbolum à non gignendo dictus, quippe qui omnia sibi obuiantia sua vredine, atque actiuitate absumit, nec quiequam ex eo gignitur. Quamuis id Plinius non ità facilè affirmaret, qui lib. 3. cap. 107. inter omnia elementa vnius ignis foecundam astruit rationem. Cum se ipse pariat, inquit, & minimis crescat scintillis: & aliàs vitam ipse foueat in animantibus; vnde cum Elementum vita nominat Lactantius Firmianus. Et sanè si eius qualitates attendamus, ipsum maximè actiuum asserere; proindeque cæteris omnibus anteire in vittute foecunda necesse erit. Quandoquidem qualitates actiux, vt ait Philosophus sunt calor & frigiditas, sicut passiux sunt siccitas, & humiditas; magis autem actiuius est calor: Ignis autem abundat caliditate, & siccitate, sed vincit in eo caliditas; sicque conuenienter astruitut omnibus elementis actiuior, & foecundior. Hinc Albetrus magnus, Ignis, inquit, est magis forma, quam casera elementa. Eius locum supra actem infra Lunæ orbem constituere antiqui Philosophi: At verò recensiores ignis sphæram < 11.> de medio tollunt vel eò maximè quod totum orbem debuisset incendere. Sed enim leue, ac puerile est argumentum, quippe vt ait Arist. lib. 3. de Cale, & Mundo. Vredo non ei per essentiam inest, sed secundum accidens, eoquia extrà suam sphæram contrarijs oppugnatur: vnde indiget pabulo quo sustentetur; contrarium enim, (vt habet idem Philosophus, 2. de Anima textu 43.) contrario alitur. Atqui ignis in sua sphæra contrarium vllum non habet, à quo oppugnetur, sed est omninò quietus tanquam rex in suo regno, adeo vt ne stupam quidem si illi approximaretur ibi consummeret. Aliam ratio- P iii

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MATHEMATICVM. 231 equilateral and equiangular. They are also called by some the Platonic bodies, because Plato in the Timaeus, the five bodies of the world, which are called simple by the philosophers, namely Ether; and the four elements, Fire, Air, Water, and Earth, he compares to these five bodies. These are Cube, Tetrahedron, Octahedron, Dodecahedron, and Icosahedron. For the explanation of all these, and their figures, see Clavius in the Commentary on book 13. of Euclid's Elements. Also in Alsted's Geometry, where the figures are very beautifully drawn. < 9.> ICTISAL, or Alstedfal in Arabic, signifies the same as in Latin application to junction, and it is when a lighter planet, existing within the orb of the sphere of another, more weighty light, goes toward it until it is joined to it in body, and in point; its use is frequent in centissoquium. I G < 10.> FIRE, one of the four elements, the fairest and lightest of all, a symbol among the ancients of chastity and purity, said from “not generating,” since it consumes with its burning and activity everything that meets it, and nothing is generated from it. Although Pliny did not affirm this so easily, who in book 3, chapter 107, among all the elements establishes of fire alone a fruitful nature. “For it begets itself,” he says, “and grows by the smallest sparks; and elsewhere it itself fosters life in living creatures”; whence Lactantius Firmianus calls it the element of life. And truly, if we attend to its qualities, we shall most especially assert it to be active; and therefore it will necessarily surpass all the others in fruitful power. For, as the Philosopher says, the active qualities are heat and coldness, just as the passive are dryness and humidity; but heat is the more active. Fire, however, abounds in heat and dryness, but heat prevails in it; and thus it is fittingly established as more active and more fruitful than all the elements. Hence Albertus Magnus says, “Fire is more form than the other elements.” The ancient philosophers placed its location above the ether, below the sphere of the Moon; but the more recent remove the sphere of fire < 11.> from the middle, especially because it ought to have set the whole world on fire. But indeed this is a weak and childish argument, since, as Aristotle says in book 3 of On Heaven and the World, the burning is not inherent in it by essence, but by accident, because outside its sphere it is attacked by contraries; hence it needs fuel by which it may be sustained, for contraries, as the same Philosopher says in De Anima, text 43, are nourished by contraries. But fire in its sphere has no contrary at all, by which it may be attacked, but is altogether quiet, like a king in his own kingdom, so much so that even tow, if brought near it there, it would consume. Another ratio- P iii

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LEXICON nem sphæræ ignis cuertendæ affett Argolus in Pandos: sphæricæ cap. 18. ex refractionum doctrina. Quia, inquit, si per tria diaphana radij stellarum ad nos peruenirent, maior redderetur refractio; sicque loca stellarum non apparerent vbi realiter sunt. Sed & hæc friuola ratio est; immò potiùs inde ego magis concluderem sphæram ignis. Quandoquidem refractio non accidit, nisi vbi duo diaphana densa in vnum coeunt, per quæ transeunt obiecti visibilis species, vnde in regione ætherea, sine cælorum substantia non accidere refractiones dice[mus]; cum de ijs sermo recurret; eoqui substantia illa est tenuissima, & subtilissima. Dum igitur refractiones accidunt, signum est conuenire aerem simul, & ignem ad eas faciendas. Quod autein non tantæ accidant, quantas quisque crederet, id euenit quia sphæra ignis longe est aere purior, ac defoecator (non enim concipienda est flammea, aut densior, vt est noster ignis alteri materiæ applicitus, sed longè tenuissima) habens substantiam omninò diaphanam vnde est quod neque lucem is habeat, neque cælestia lumina occultare possit, quin probe à nobis conspiciantur: quapropter ex tantum refractiones accidunt, quas interiecti halitus, vna cum aere constituunt, & ideò omninò dicendum est, verè extare locum ignis sub concauo Lunæ, longè autem nostro defoecatoris, & purioris, cuius figura circularis est, vt est ratio omnium sphærarum, præsertim Lunæ, & aeris illi conterminarum: aliàs intet ipsum, & aerem daretur vacuum. Zabarella autem, Scaliger, & multi alij Peripathetici tenent eius figuram non esse sphæricam sed oualem, eoquia sub polis, vbi rardior est motus non potest ita facile materia rarefieti, atque adeò ignis generari: ideoque & ibi ignem non dari asseuerant. Quæ tamen nec quicquam solidi euincunt, cum ibi materia ignis concipienda sit nostræ prorsus absimilis, & eiusdem conditionis ac totum cæli, seu potius Ætheris expansum, quod amplectitur omnem ætheream, atque aëream regionem: quapropter quæ de ipsis dicuntur, debent & de ignis sphæra concludi: sicque & ipsum motu vniuersitatis cieri ab Oriente in Occidentem raptum à primo mobili, quemadmodum, & Aer, & Aqua, vt suo loco diximus eaudem motum sequuntur. 13. Sed & non desunt qui sphæram ignis in inferno, hoc est in mundi meditullio collocant; eoquia in homine, inquiunt, qui ad Macrocosmi typum formatus est in corde, hoc est in Microcosmi centro calor naturalis residet igni respondens. Sed de hac re fusiùs in V. Infernus. 14. Igni aliqualem vitam tribuit Franciscus Resta de Meteoris, lib.1. tr.5. seù quasdam vitæ operationes infrà plantas eoquod

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LEXICON On the sphere of fire, against Argolus in Pandos: spherical chapter 18. from the doctrine of refractions. Because, he says, if through three transparent bodies the rays of the stars came to us, the refraction would be greater; and thus the places of the stars would not appear where they actually are. But this too is a frivolous argument; rather, I would more readily conclude the existence of a sphere of fire. For refraction does not occur except where two dense transparent bodies come together into one, through which the visible species of objects pass; whence in the ethereal region, without the substance of the heavens, refractions do not occur, as we shall say when the discussion returns to these matters; for that substance is most subtle and most fine. Therefore, while refractions occur, it is a sign that air and fire are present together to produce them. That they do not occur as often as one might believe, this happens because the sphere of fire is far purer than air, and more refined (for it must not be conceived as fiery, or denser, as is our fire applied to another matter, but as very tenuous), having a substance altogether transparent; whence it is that it has neither light itself, nor can it hide the heavenly lights, but they can be plainly seen by us: wherefore refractions occur only to the extent that the intervening vapors, together with the air, make them up; and therefore it must be said that the place of fire truly exists beneath the concave of the Moon, and is far more refined and pure than our own, whose figure is circular, as is the nature of all spheres, especially of the Moon and of the air adjoining it: otherwise, between it and the air, a vacuum would be given. But Zabarella, Scaliger, and many other Peripatetics hold that its figure is not spherical but oval, because under the poles, where motion is more sluggish, matter cannot so easily be rarefied, and thus fire generated: and therefore they assert that fire is not found there either. These arguments, however, prove nothing solid, since there the matter of fire must be conceived as wholly unlike ours, and of the same condition as the whole expanse of the heavens, or rather of the Ether, which embraces every ethereal and aerial region: wherefore what is said concerning these things, must also be concluded of the sphere of fire: and thus it too is stirred by the motion of the universe, carried from East to West by the first mobile, just as air and water, as we said in their place, follow the same motion. 13. But there are also those who place the sphere of fire in hell, that is, in the very center of the world; because, they say, in man, who was formed as the type of the Macrocosm, natural heat dwells in the heart, that is, in the center of the Microcosm, corresponding to fire. But on this matter more fully in V. Infernus. 14. Francis Resta, in De Meteoris, book 1, tract 5, attributes a kind of life to fire, or certain operations of life beneath plants, because

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MATHEMATICVM: 233 ratio vitæ ex motu dignoscitur. Sed de hac re etiam agemus cum de Vita Mundi. < 35.> IGNIS fatuus dicitur species quædam accensionum, atque ostentorum, quæ generantur in insima aëris regione ex materia pingui, ac viscosa accensa, vel per antiperistasim frigoris nocturni ambientis, vel per agitationem aëris attenuantis materiam ipsam, quæ ad motum aëris inflammatur. Et quia saltus quosdam irregulates edit ad instar hominis satui, idcircò ignis fatuus dictus est. Apparet frequenter in cæmeterijs, in patibulis, & locis huiusmodi, vbi mortuorum corpora congesta sunt, aut tumulantur. Formatur enim ex copia halituum ex ipsis mortuorum corporibus erumpentium, & hac illac irregulariter discurrit, sed plerumque cum apparet, solet insequi fugientes, & aufugere à sequenribus non sine terrore, & consternatione animi eorum, qui illius naturam probè non callent. A liquibus orta suspicio, quod mortuorum animæ sint, aut dæmones ea loca custodientes. Verum id naturaliter accidere compertum est: dum enim fugimus aër post tergum nostrum, ad repleendum vacuum sequitur, secum ducens suspensam flammam: at verò dum fugientem insequimur fugit, quia fluctuatio aëris, quam motu violento facimus aërem ipsum qui est aute nos propellit, atque adeò flammam ibi consistentem. < 16.> IGNIS lambens, est flammula ex crinibus animalium exiliens, aut hominum capitibus adhærens, producta ex tenui exhalatione, quæ transpirat ex eorum corporibus ex affricatione, aut ex motu violento accensa, & lambens non itadicam corpora, & membra vnde exurgit, & mox euanescit. Is frequens est in felibus, & similibus animantibus: si enim noctu, atque in tenebris crebriùs confricetur eorum dorsum, confestim exsurgit hæc flammula, vt mihi sæpissimè consigit. Scripsit de hac re Petrus de Castro mihi cum primis familiaritate coniunctus in libro quem indigitauit Ignis lambens ex occasione cuiusdam Matronæ Veronensis, cui familiaris erat hæc flammula. Ad hæc reduci possunt quæ ab Ethnicis & Helene, & Castor & Pollux dictæ fuere: crassæ videlicet exhalationes, quæ ingruentis in mari tempestatis tempore in aëre accenduntur, & nauigamnibus apparere soleut, & si ea quidem vna sit, & hac illac discuriat ominosa est, & tempestatem indicat: si verò duplex & nauium malis insidet, salutaris ac serenitatis index, vt habet Plin. lib. 2. cap. 37. Gemina, inquit, saluares ac prosperè cursus pranuncia, quarum aduensu fugare doram illam, ac minacem appellatamque Helenam ferunt. Sed & contra hanc sordidum, nescio an ridiculum magis remedium affert Solinus in suo Polyhistore, hoc est sanguinem meustum: ait enim de eo. Habet

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MATHEMATICVM: 233 the ratio of life is discerned from motion. But on this matter we shall also speak when we come to the Life of the World. < 35.> WILL-o’-the-wisp is the name given to a certain kind of ignitions and appearances, which are generated in the lowest region of the air from a fatty and viscous substance set alight, either by the antiperistasis of the surrounding night cold, or by the agitation of the air, which thins the substance itself, and which is inflamed by the motion of the air. And because it makes certain irregular leaps like a satiated man, it was therefore called will-o’-the-wisp. It appears frequently in cemeteries, on gallows, and in places of this kind, where the bodies of the dead have been gathered together or buried. For it is formed from an abundance of vapors issuing from the very bodies of the dead, and it runs irregularly this way and that, but for the most part, when it appears, it is accustomed to follow those who flee, and to flee from those who pursue it, not without terror and disturbance of mind in those who do not know its nature well. From this arose among some the suspicion that they are the souls of the dead, or demons guarding those places. But it has been found that this happens naturally: for when we flee, the air behind us, to fill the vacuum, follows, drawing along with itself the suspended flame; but when we pursue the fleeing one, it flees, because the disturbance of the air, which we produce by violent motion, pushes forward the air itself that is before us, and thus the flame standing there. < 16.> LAMBENT FIRE is a little flame leaping from the hairs of animals, or adhering to the heads of men, produced from a subtle exhalation that transpires from their bodies through friction, or kindled by violent motion, and not licking so much the bodies and limbs from which it arises, and soon disappearing. It is common in cats and similar animals: for if at night, and in darkness, their backs are rubbed more often, this little flame immediately rises, as very often happens to me. Peter de Castro, closely connected with me in particular familiarity, wrote on this matter in a book which he entitled Ignis lambens on the occasion of a certain lady of Verona, to whom this flame was familiar. To these may be referred what by the pagans were called Helen, and Castor and Pollux: namely, thick exhalations which, at the time of a storm arising at sea, are kindled in the air, and are accustomed to appear to sailors; and if there be only one, and it runs this way and that, it is an evil omen and indicates a storm; but if there be two, and they settle upon the ships’ masts, it is a sign of safety and fair weather, as Pliny has in book 2, chapter 37. “Twin ones,” he says, “safe and prosperous harbingers of a voyage, at whose coming they say that that dark and threatening one named Helen is put to flight.” But against this sordid, I know not whether rather ridiculous, remedy Solinus in his Polyhistor offers the following, that is, stag’s blood: for he says of it. It has

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234 LEXICON planè id solum salusare quod auertis fidus Helena perniciosissimum navigantibus. De ijs multa habent idem Plin. loco cit. Plurarchus de placitis Philosophorum cap. 17. Cardanus de subtilit. & alij passim. Quas quidem Cardanus existimat esse vapores anchoris insidentes, & alij superstitiosa multa connectunt. Reueta tamen naturales sunt ignes & naturaliter serenitatem, aut tempestatem denunciant, nam cum aëra discurrunt ventorum impetus inuicem pugnantium denotant, vnde tempestas otitur, cum quiescunt & malis, aut antennis adhætent signum est quod cessarunt venti, & iam resolui accensæ illæ exhalationes petant. Vide qui habet Resta de Meteoris lib.... 18. IGNEA signa appellantur signa illa Zodiaci, quæ vincunt reliqua in qualitatibus igneis, nempe calore, & siccitate; eaque sunt Leo, Aries, & Sagittarius: tria videlicet signa masculina, quæ sunt domicilia Solis, Martis, & Iouis, & constituunt triplicitatem igneam, cuius dominatores sunt Sol, & Iupiter: & Sol quidem de die Iupiter vetò de nocte. Mars autem ideo ab eius dominio exclusus est, quia, vtinquit Ptolemæus lib.1. cap. 16. Solis conditioni aduersatur. Sed ego id dixerim, & quia planeta noctutnus, & quia quamuis alioqui masculus interdum etiam feminescit; præpollet enim in eo magis siccitas quam caliditas, vt præ cæteris aduertit erudissimus Titus in sua coelesti Philosophia hic triangulus, (inquit Ptolemæus) potissimum septentrionalis est, quia Iupiter ibi partem dominij tenet, quo fæcundus est, & flatuosus conveniens ventis qui censur in septentrione. Quæ autem regiones subsint huic triangulo vide in eodem Ptolem. lib. a. cap. 2. IM 19. IMAGINES cælestes dicuntur singulæ constellationes, & Asterismi in octaua sphæra plures stellas fixas intrà se in vnum colligaras continentes. Cum enim vetustissimi illi retum cælestium obseruatores tot stellarum multitudinem, varietatem, diuersitatem viderent in firmamento consistere, sine ordine, sine connexion, sine aliqua vnitate; ne euiusquam consideratio aliquem præteriret, atque vt certo ordine, & numero designari possent, prudentissimè statuerunt eas in certas quasdam imagines complicare, quæ singularum naturam exptimerent, ac determinatum numerum præseferrent. Hanc enim extitisse causam imagines istas in cœlestibus appingendi, testatur Theon in expositione ad Arati Phænomenon. Quod quidem multis sæculis ante Christum factum fuisse constat ex libro lobi, in quo & Arcturus & Oriona, & Pleiades, & Hyades memotantur. Porro etsi ex fabulis potissimum excerptæ sint imagines, quas cælo affixerunt Astronomi, non tamen fabulosa est, & inanis affi-

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234 LEXICON plainly that alone is salutary which the faithful Helen turns away, most pernicious to sailors. Of these things the same Pliny has much in the place cited; Plutarch, De placitis Philosophorum , chapter 17; Cardanus, De subtilitate , and others everywhere. Cardanus indeed thinks that these are vapors adhering to anchors, and others connect many superstitious notions with them. Yet they are natural fires and naturally announce fair weather or storm; for when they dart through the air they indicate the clash of opposing winds, whence the storm arises. When they cease and adhere to the masts or yardarms, it is a sign that the winds have stopped and that those kindled exhalations are now beginning to disperse. See whoever has Resta, De Meteoris , book ... 18. FIERY signs are called those signs of the Zodiac that surpass the rest in fiery qualities, namely heat and dryness; and these are Leo, Aries, and Sagittarius: that is, the three masculine signs, which are the domiciles of the Sun, Mars, and Jupiter, and constitute the fiery triplicity, whose rulers are the Sun and Jupiter: the Sun by day, Jupiter by night. Mars, however, was excluded from this dominion because, as Ptolemy says, book 1, chapter 16, he is contrary to the Sun’s condition. But I would also say this, because he is a nocturnal planet, and because, although otherwise masculine, he sometimes even becomes feminine; for in him dryness prevails more than heat, as the learned Titus especially notes in his Celestial Philosophy . This triangle, says Ptolemy, is especially northern, because Jupiter holds part of the dominion there, whereby it is fertile and full of airs, fitting the winds that are reckoned in the north. What regions are subject to this triangle, see in the same Ptolemy, book 4, chapter 2. IM 19. CELESTIAL images are called the individual constellations, and the asterisms in the eighth sphere, containing within themselves many fixed stars gathered into one. For when those most ancient observers of heavenly things saw so great a multitude, variety, and diversity of stars standing in the firmament, without order, without connection, without any unity, they most prudently decided, so that no one’s observation might pass over any of them, and so that they might be designated in a definite order and number, to arrange them into certain images which would express the nature of each and present a determinate number. That this was indeed the cause of attaching these images to the heavens is attested by Theon in his exposition of Aratus’ Phaenomena . And it is certain from the book of Job that this was done many centuries before Christ, in which Arcturus, Orion, the Pleiades, and the Hyades are mentioned. Moreover, although the images which the astronomers affixed to the sky were taken chiefly from fables, yet the matter is not fabulous, nor empty in itself.

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MATHEMATICVM. 235 xio, aut istarum potiùs, quam aliarum rerum electio: sed id magno consilio factum est; perpensis benè eorum qualitatibus, natura, influeniijs faustis, & infaustis combinationibus cum erraticis arque effectibus inde manantibus, quæ omnia longo vsu, longo tempore, longa experientiâ obseruantes eorum noticiam perfectissimè compararunt: quam & in posteros re- rum cælestium amatores, per certas imagines, & hieroglyphica (.vt antiquus Ægyptiorum mosest) deriuare, quibus sa- pientibus aperta foret, insipientibus tecta constituerunt. Ideò tanta siderum diuersitas; ideò tot disparatæ, & nullam conne- zionem ad inuicem habentes guræ: ideò sæpè in vna, eadem- que imagine, & aliæ plures omninò discrepantes affixæ, vt in Avriga, Hædi & Capra; & hæc quidem in humero, illi autem in vola manus: in Vultute cadente Lyra, in Aquila sagitta: in Tauro suculæ, & Vegiliæ, in Cancto Præsepe, & Aselli: in Virgine spica: in Visa Plaustrum, & equi, &c. quia videlicet vna figura non sat erat ad explicandam completè imaginis illius cælestis naturam, ac proprietates, quas omnes ex natura rerum quas imagines ipsæ referrent perspectas esse volue- runt sapientissimi illi Astrophi. Hinc facta distributio om- nium siderum in 48. imagines, duodecim in Zodiaco per quem planetæ seruntur, reliquarum extrà Zodiacum in reli- quo ambitu firmamenti, cuius distributionis primus author extitisse Anaximander milesius fertur Olympiade 58. postmo- dum signis nomina affixisse Cleostratum testatur Plin. lib. 3. cap. 8. inde alijs alios nomina indidisse. Quibus recensiores duodecim alias adiunxerunt circà Polum Antarcticum ab His- panis naucleris, (qui ad Occidentales indos soluerunt, proin- de omnes australes oras lustrarunt,) nouissimè obseruatas, quas & nos suo loco censebimus. Itaut iam nunc omnes imagines cælestes sint numero 60. omisis, vt Ptolemæo placuit Equi- culo, quem rejcit in Pegasus; antinoum quem ponit inter in- formes Aquilæ & Coma berenicis quam considerat sub nomine Triches inter informes circ acaudam Leonis, & hunc nume- rum admiserunt Keplerus Bulliardus, & alij ac sequunt sunt cælestium Globorum structores Hondius, Ianssonius, & Bleau. Sed redeamus ad stellarum per imagines ratam, prudentem- 22. que distributionem. Aietis species (vt à capite exordiar) iure affixa est primo signo, quia hoc cum Ariete nescio quam habet affinitatem. Eclipses namque Luminarium in Ariete contin- gentes manifestum effectum in arietibus, alijsque pecudibus ostendunt. Aries totum robur habet in capite: & hoc signum capiti præest. Tandem qui sub eo nascuntur corporis figura, ar- que animi affectionibus Arieti assimilantur. Sequitur Tauri

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MATHEMATICVM. 235 the choice of these, rather than of other things: but this was done with great design; after well weighing their qualities, nature, favorable and unfavorable influences, and their combinations with the wandering stars and the effects flowing from them, all of which they observed by long use, long time, and long experience, and thus acquired a perfect knowledge of them: which knowledge they also wished to hand down to later lovers of celestial matters by means of certain images and hieroglyphics (as was the ancient custom of the Egyptians), by which they established that it should be open to the wise and hidden from the unwise. Hence the great diversity of the stars; hence so many different figures, having no connection with one another; hence often in one and the same image several quite dissimilar things are affixed, as in Auriga, the Kids and the Goat; and one on the shoulder, the other in the palm of the hand: in the Falling Charioteer, the Lyre; in Aquila, the arrow: in Taurus, the little carts and the Pleiades; in Cancer, the Manger and the Asses; in Virgo, the spike; in the Ship, the Wain and the horses, etc. because, namely, one figure was not enough to explain fully the nature and properties of that celestial image, which all those most wise astronomers wished to be seen from the nature of the things which the images themselves represented. Hence the division of all the stars into 48 images, twelve in the Zodiac through which the planets are carried, the rest outside the Zodiac in the remaining expanse of the firmament, of which division Anaximander of Miletus is said to have been the first author in the 58th Olympiad; afterward Pliny, book 3, chapter 8, attests that Cleostratus affixed names to the signs; and thereafter others assigned other names. To these later writers added twelve others around the Antarctic Pole, first observed by Spanish sailors, who sailed to the West Indies and therefore explored all the southern coasts, and we too shall set them down in their proper place. Thus now all the celestial images are 60 in number, omitting, as Ptolemy wished, Equiculus, which he rejects into Pegasus; Antinous, which he places among the unformed stars of Aquila; and Coma Berenices, which he considers under the name Triches among the unformed stars near the tail of Leo; and this number was accepted by Kepler, Bulliard, and others, and followed by the makers of celestial globes, Hondius, Janssonius, and Bleau. But let us return to the prudent distribution of the stars through the images. The figure of Aries is rightly assigned to the first sign (to begin with the head), because this has some affinity, I know not what, with the ram. For eclipses of the luminaries occurring in Aries show a manifest effect in rams and other cattle. Aries has all its strength in the head; and this sign presides over the head. Finally, those born under it resemble the ram in bodily shape and in the affections of the mind. There follows Taurus

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LEXICON 236 signum quod ideò tali figura expressum est, quia Tauri robur in collo: & collo etiam hoc signum dominatur. Tum demum homines sub illo nati Tauri physiognomiam præseferunt: sunt etenim magnis oculis, rorunda facie, grosso collo, sed breui, mente stolidi &c. sicque de singulis discurrendum. Quapropter benè dixit Ticho, 10 2. Progymnasm. pag 778. Coelestes imagines occultam quandam philosophiam continere, & longè anre ipsum Ptolemæus, seù quicumque tandem sit Centiloquij author propos. 9. vultus terrestres subiectos esse vulribus coelestibus. Sic terrestres canes coelestibus adeò subiecti sunt, vt illis cum Sole exorientibus, isti agantur in rabiem. Sole Leonis signum petmeante Leones ardenti febre laborant. Scorpij sudus habet quandam naturam veneficam præcipue cor & aculeus, similem Scorpioni terrestri; & quod mirum est, Luna signum illud tenente, iste infensissimus est, & mortiferus. Hinc tanta signorum distinctio in humana, quæ cum hominibus affinitatem habent, qualia sunt Gemini, Virgo, Aquarius, & prima medietas Sagittarij. Ferina, vt Leo, & vltima pars eiusdem Sagittarij. Mutilata, vt Taurus, Caput Medusæ, equi sectio. Vineta, vt Cepheus, & Andromeda. Venenosa, vt Scorpio, Hydra, Serpens. Aquatica, vt Pisces Delphinus, Eridanus, Regalia, vt Corona tam Borealis, quam Australis. Prolifica, vt Cancer, Capricornus, & Pisces. Sterilia, vt Gemini, Leo, & Virgo. Ruminantia, vt Aries, Taurus, Capricornus, &c. Quæ omnia, vt dixi longo vsu, & experientia comparata sunt, & magna consilio excogitata, vt vel ex fabulis, vel ex affixarum rerum qualitate stellarum omnium nobis natura innotesceret, atque ab expansarum cælo imaginum vultibus, velut mutis characterismis naturam siderum edoce- remur. 21. Quapropter pietatem magis, quam sapientiam, aut consilium laudare debemus Iulij cuiusdam Schilleri Augustani qui antiquas, atque ex fabulis depromptas imagines auersatus, cælum christianum fecit, ac sidera ex Apostolorum, aliorumque Sanctorum nominibus, aut Martyriorum instrumentis compellauit, prout videre est in Encyclopedia Io: Henrici Alstedij, atque in Almagesto Riccioli ad calcem secundi tomi, proindeque ab ijs hic recensendis abstineo. 22. Prætereà sunt, qui in ipsa nona sphæra, seù in primo mobile imagines appingant; quinimò & singulis signorum gradibus quædam, vt ita dicam, hieroglyphica cum suis significatis respondentibus tribuunt: quæ omnia videre est in sphæra Barbarica, quæ est ad calcem commentariotum IosephiS caligeri ad Manilium. Certè Petrus Aponensis, qui & conciliator dictus

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LEXICON 236 sign, which was therefore expressed in such a figure because the strength of Taurus is in the neck; and this sign also rules the neck. Then, finally, those men born under it show the physiognomy of Taurus: for they have large eyes, a round face, a thick neck, but a short one, a dull mind, etc.; and so one must proceed through the rest individually. For which reason Tycho spoke well, 10 2. Progymnasm. p. 778, when he said that celestial images contain a certain hidden philosophy; and long before him Ptolemy, or whoever else may be the author of the Centiloquium, proposition 9, held that earthly faces are subject to heavenly faces. Thus earthly dogs are so subject to heavenly ones that, when these rise with the Sun, the former are driven into a frenzy. When the Sun passes through the sign of Leo, lions suffer from a burning fever. Scorpio has a certain poisonous nature, especially in the heart and the sting, similar to the earthly scorpion; and what is remarkable, when the Moon occupies that sign, it is most hostile and deadly. Hence there is such a distinction of the signs in relation to human beings, which have an affinity with men, such as Gemini, Virgo, Aquarius, and the first half of Sagittarius. Animal, as Leo, and the last part of the same Sagittarius. Mutilated, as Taurus, the Head of Medusa, the part of the horse. Winged, as Cepheus and Andromeda. Poisonous, as Scorpio, Hydra, Serpent. Aquatic, as Pisces, Delphinus, Eridanus. Royal, as Corona, both Boreal and Australis. Prolific, as Cancer, Capricorn, and Pisces. Sterile, as Gemini, Leo, and Virgo. Ruminant, as Aries, Taurus, Capricorn, etc. All these things, as I said, have been learned by long use and experience, and devised with great consideration, so that, whether from fables or from the properties of the things attached to them, the nature of all the stars might become known to us, and that from the faces of the images spread across the sky we might, as though by mute characters, be instructed in the nature of the stars. 21. Therefore we ought to praise piety rather than wisdom or prudence in a certain Julius Schiller of Augsburg, who, rejecting the ancient images taken from fables, made a Christian heaven and called the stars by the names of the Apostles and other Saints, or by the instruments of their martyrdom, as may be seen in the Encyclopedia of Io. Henricus Alstedius and in Riccioli’s Almagest at the end of the second volume; and therefore I refrain from listing them here. 22. Moreover, there are some who depict images in the ninth sphere itself, or in the primum mobile; indeed, they assign to each degree of the signs certain, so to speak, hieroglyphics with their corresponding meanings: all of which may be seen in the Barbaric sphere, which is at the end of Joseph Scaliger’s commentaries on Manilius. Certainly Peter of Abano, who was also called the Conciliator

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MATHEMATICVM. 237 est, signorum, nec non singulorum graduum in quas illa di- stribuuntur proprietates in 260. imagines conclusit, quas in magna, ac celebri Aulæ patauinæ fornice depingi curauit, vbi etiam cum exrant, & ego hisce oculis vidi: & forsan eadem sunt, quæ in sphæra Baibarica, licet ob temporis iniuriam, probè discerni non possit. Lucius Bellancius eas memorat quast. 5. art. 5. ac probat his verbis. Sunt igitur in nona sphæra primò imagines totius signi, deinde facierum, postea graduum, quas scimus: alias quoque reperiri ex natura partium cali non est negandum, sed iam dictum est nullam completam scientiam ab hominibus haberi. Et hæc de imaginibus cælestibus. De quibus iterum redibit sermo cum de primo mobili, vbi examinabimus, an verè in eo imagines vllæ sint, aut concipi debeant. IMAGINES Astronomicæ communiter appellantur figuræ < 23.> quædam & sigilli in certa materia puta auro, argento, cupro, aut in lapide pretioso exsculptę & fabricatæ sub certo siderum positu, vnde posteà ob impressam à cælis virturem retineant aut retinere credantur occultam quandam, & insitam qualitatem ad memoriam roborandam, ingenium exacuendam, sanitatem custodiendam, morbumque aliquem pellendum; qualis est imago Leonis in auro impressa, vel sculpta, de qua testatur Marcilius Ficinus lib. 3. de vita Calitùs comparanda, quod sir aptissima ad morbos cardiacos nec non ad dolores renum sedandos, quod etiam refert Stoephlerus in Proclum. Dicuntur autem Astronomicæ, quia per Astronomiæ præcepta fabricantur, atque habent formam signi cælestis, vt Leonis, Scorpij, Arietis, &c. quorum naturam ac virtutes induisse creduntur cum primum fabricatæ sunt. Ptolemæus earum meminit in centiloquio, dicens sapientes solitos fuisse certas tunc, imagines fabricare, quando planeræ, similes in cælo facies, quasi inferiorum exemplaria ingrediebantur. Quod etiam comprobat Hali Rodoan, in commentarijs dicens, vtilem serpentis imaginem confici posse, quado Luna cælestem serpentem subit, aur feliciter aspicit Similiter Scorpionis effigiem efficacem esse, quando Scorpij signum Luna, ingreditur, ac signum hoc tenet vnum ex quatuor angulis. Quod in Ægypto suis temporibus factum testatur, seque intertuisse, vbi ex sigillo Scorpionis in lapide Bezaar ita facto, imprimebatur figura in thure, quod posteà dabatur in posum ei quem Scopus pupugerar, & subito curabatur. Plura de hac re habet Ficinus supra citatus à cap. 12. vsque ad 20. inclusiùè. Theologi omnes communiter eas improbant, vti superstitiosas, exceptro vno Caicetano, qui tum in Commentar. ad secundam secundæ D. Thomæ quæst. 96. art. 2. tum in Summa mordicùs eas defendit, aut licitas & natura-

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MATHEMATICVM. 237 has, of the signs, and likewise of the individual degrees into which they are distributed, he enclosed in 260 images, which he had painted in the great and famous arch of the Paduan palace, where they were still also present, and I myself saw them with these eyes: and perhaps they are the same as those in the Baibarian sphere, though because of the damage of time they can no longer be properly distinguished. Lucius Bellancius mentions them in q. 5, art. 5, and proves them with these words. Therefore in the ninth sphere, first are the images of the whole sign, then of the faces, afterwards of the degrees, as we know; that others also may be found from the nature of the parts of the heavens is not to be denied, but it has already been said that no complete science is possessed by men. And this is enough about celestial images. Of these there will again be discussion when we come to the primum mobile, where we shall examine whether there are truly any images in it, or whether any ought to be conceived. Astronomical images are commonly called certain figures and seals, carved and fashioned in a certain material, such as gold, silver, copper, or precious stone, under a certain position of the stars, from which thereafter, because of a virtue impressed from the heavens, they retain or are believed to retain some hidden and innate quality for strengthening memory, sharpening the intellect, preserving health, and driving away some disease; such is the image of a Lion impressed or engraved in gold, concerning which Marsilius Ficinus testifies in book 3, De vita coelitus comparanda, that it is most suitable for calming cardiac ailments as well as pains of the kidneys, which Stoephler likewise reports in Proclus. They are called astronomical, however, because they are made by the precepts of astronomy, and they bear the form of a heavenly sign, such as Leo, Scorpio, Aries, etc., whose nature and powers they are believed to have taken on when they were first fashioned. Ptolemy mentions them in the Centiloquium, saying that the wise were accustomed to fashion certain images then, when planets, with similar faces in the sky, were entering, as it were, as exemplars of the lower things. This also is confirmed by Hali Rodoan in his commentaries, saying that a useful image of a serpent can be made when the Moon enters the heavenly serpent, or happily looks upon it. Similarly, the figure of Scorpio is effective when the Moon enters the sign of Scorpio and this sign occupies one of the four angles. He testifies that this was done in Egypt in his time, and that he was present, where from a seal of Scorpio in a Bezoar stone thus made, the figure was impressed into incense, which was afterwards given to drink to the man whom the scorpion had stung, and he was suddenly healed. Ficinus, cited above, has more on this matter from chapter 12 up to 20 inclusive. All the theologians commonly disapprove of them as superstitious, except for one Cajetan, who both in the Commentary on the Second of the Second of St. Thomas, question 96, article 2, and in the Summa vehemently defends them, as lawful and natura-

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LEXICON 238 les asserit quandocumque non admittat certas literas, chara- cteres, numeros, aut puncta, quæ planè signa sunt ad tacitam & implicitam dæmonis invocationem, vt bene habet D. Thomas. Cæterum imagines purè artificiales, quæ conformentur cum cælestibus signis, vt Leonis, Virginis, &c. & fabricatas in certa constellatione, immunes facit ab omni prorsùs superstitione. Atque in confirmationem sui dicti affert ipsum Angelicum Doctorum 3. contra Gentes cap. 105. vbi videtur abbrobare huiusmodi imagines, quando sine characteribus, & notis incognitis fiant. Quod putat Caietanus sanctum Doctorum non retractasse in dicto articulo secundo, sermonem de dictis imaginibus inducendo, quas dicit continere pactum tacitum cum dæmone, eoquia necesse est, ait, eis inscribi quosdam characteres, qui naturaliter ad nil operantur. Ergò, infert Caietanus, quæ hos characteres non habent, sed puras imaginos cælestes præseferunt, eas non excludit Angelicus Doctor, aliàs debuisset aliam rationem adducere, & alterius loci vbi de ijs sermonem habuit meminisse, & retractasse. Sed & Bustamantius apud Vecchium in obseruationibus medicis in Sacram scripturam obseruat. 140. existimat, serpentem illum æneum à Moise fabricatum in deserto, naturali vi potuisse hominibus ab ignitis serpenribus ictis hac ratione opitulari. Poruit enim, inquit, tali cæli climate, & configuratione constitui, vt non secus ac nonnullæ aliæ figuræ ad aliorum animalium morsum, leonum, tigridum, &c. sic ad morsum serpentum, serpens ille æneus remedio fuerit, Deo eius fabricandi rationem Moistreuelante. Hæc ille. Ego verò in hoc negotio quod ad serpentem æneum attinet, Bustamantio assentiri nullatenùs possum; quandoquidem serpens ille miraculosus omninò extitit, & quemadmodum miraculosi fuerunt serpentes immissi, sic & opis, cælitus datæ; quæ non in analogia serpentis ænei ad Cælestem, sed in mystica significatione Christi Redemptoris in Cruce exaltati, qui antiqui serpentis fraudibus mederetur, sita erat, sicut ipsemet dixerat in Euangelio, & ego si exaltatus fuero à terra omnia trahamad me ipsum. Quare merito Bustamantij opinatio ab omnibus reijcitur, & improbatur. Cæterum non negauerim, & id naturaliter fieri potuisse, Deo sic disponente fieri; sed rem ipse altiùs ordinabat: & sicut serpenti illi æneo naturalis vis in serpentes à cælestibus poterat indidi, sic & eadem ratione potuisse fabricandarum istarum imaginum rationem in certo siderum positu, aut ex reuelatione, aut longo vsu hominibus innouisse, vt naturalis omninò sit, quamuis occulta mira earum virtus, atque efficientia: Neque enim tam subitò damnanda sunt, tanquam

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LEXICON 238 argues whenever it does not admit certain letters, characters, numbers, or dots, which are plainly signs of a tacit and implicit invocation of the demon, as D. Thomas well explains. However, purely artificial images, which are conformed to the celestial signs, such as Leo, Virgo, etc., and are made under a certain constellation, are made immune from all superstition whatsoever. And in confirmation of his statement he cites the Angelic Doctor himself, in 3 contra Gentes , chapter 105, where he seems to approve such images, when they are made without characters and unknown marks. Caietan thinks that the holy Doctor did not retract this in the said second article, introducing a discussion of those images, which he says contain a tacit pact with the demon, because it is necessary, he says, that certain characters be inscribed on them, which by their nature do nothing. Therefore, Caietan infers, those which do not have these characters, but only bear celestial images, are not excluded by the Angelic Doctor; otherwise he ought to have brought forward another reason, and have mentioned and retracted the other passage where he spoke of them. And Bustamantius too, as Vecchius observes in the medical observations on Sacred Scripture, observation 140, thinks that that bronze serpent fashioned by Moses in the desert could by natural power help men bitten by fiery serpents in this manner. For it could, he says, have been placed under such a climate and configuration of heaven that, no differently from certain other figures against the bite of other animals, lions, tigers, etc., so against the bite of serpents that bronze serpent was a remedy, God revealing to Moses the manner of making it. Thus he. But as for me, in this matter concerning the bronze serpent, I can in no way agree with Bustamantius; for that serpent was altogether miraculous, and just as the serpents sent upon them were miraculous, so also was the help given from heaven. This was not founded on any analogy of the bronze serpent to the celestial order, but on the mystical signification of Christ the Redeemer, exalted on the Cross, who would heal the deceits of the ancient serpent, as he himself said in the Gospel: “And I, if I be lifted up from the earth, will draw all things to myself.” Therefore Bustamantius’s opinion is rightly rejected and disapproved by all. Nevertheless, I would not deny that this could also have happened naturally, if God so disposed it; but he himself ordered the matter more deeply: and just as in that bronze serpent a natural force against serpents could have been imparted by the heavenly bodies, so too, by the same reasoning, the manner of making those images could have been made known to men under a certain position of the stars, either by revelation or by long use, so that their virtue and efficacy are altogether natural, although hidden and marvelous. Nor indeed should they be condemned so abruptly, as if

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MATHEMATICVM. 239 superstitiosa, quorum naturalem operandi methodum non agnoscimus, quia hoc & naturæ iniuriosum est, quæ multa bona nobis ex abdito dare voluit, & nobis ipsis inuidiosum, qui vana formidiue quæ obscura sunt, quæ dubia, tanquam superstitionem olentia auersamur: quasi modò diabolus non magis inuidus sit nostri boni, & naturæ dona potiùs occultare, infirmare, suis tricis replere studeat, vt vel corrumpat, vel nobis suspecta reddat; quam vltrò exhibitat, aut sua beneficia in vniuersum sub specie quod è natura prodeant, ignorantibus, proindeque infontibus præstet. Semper ergò cum dubium est de aliquo affectu, cuius causam ignoramus, num naturalis sit, an verò superstitiosus, censendus est naturalis, vt concinunt omnes Theologi. Sæuè olim ego huiusmodi imagines deridebam non modo vti superstitiosas, sed etiam vt euanidas, & inutiles, putabam enim, nullam imprimi posse virtutem rebus artificialibus à cælorum influxibus, sed tantum rebus viuenti- bus, & naturalibus. At enim experientia duce edoctus sum etiam rebus artificialibus imprimi occultam quandam virtutem à corporibus cælestibus, quam quandiu durant, retineant. Legeram in Centiloquio Verbo 22. Vestes nec incidendas, nec < 25.> primò induendas, vbi Luna fuerit in Leone collocata. Rationem mecum ipse quærens non inueni, sed nec apud scriptores, aut alios viros doctos, quos consului, quæ mentem firmarent: Volut periculum facere. Excluso prius omni dæmonis adminiculo, si forte sese ingereret, vestem dedita opera incidendam dedit, Luna in Leone existente, eodemque tempore indui: Mirum! non eâ duos integros menses vsus sum, cum penè rota discissa, atque combusta, perinde ac si in cibano extitisset. Cuius rei aliam causam tunc excogitare non potui, nisi cælestem constitutionem, & miram signi Leonis vredinem, quæ eriam in artificialia turæ temporis facta protenditur. Quapropter optimè dixit D. Thomas opusc. 28. art. 4. anceps adhuc de naturali istarum imaginum virtute deque efficientia cælestium corporum in isthæc artificiata quod sicut radiatio periodi dispositionem ordinis, & durationis imprimis rebus naturalibus; ita etiam imprimis artificiatis: propter quod figura imaginum magicarum ad aspectum stellarum imprimuntur, & fieri permis- suntur. Tandem concludam cum ij quæ habet idem Caietanus in < 26.> summa. Imaginibus, inquit, purè Astronomicis vti ad effectus subiectos calestibus corporibus nullum peccatum esse videtur, quia, vt res purè naturales habemur, nec debemus secreta natura, præsertim calestes influxus nostri ingenij viribus metiri; vt priscis astronomos

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MATHEMATICVM. 239 superstitious things, whose natural method of operation we do not recognize, because this is injurious to nature, which wished to give us many good things from hidden sources, and also envious to ourselves, who turn away in vain fear from things that are obscure, from things that are doubtful, as though smelling of superstition: as if the devil were not much more envious of our good, and did not rather strive to conceal nature’s gifts, to weaken them, and to fill them with his tricks, so that he may either corrupt them or make them suspect to us; rather than willingly display them, or make his benefits available in general, under the appearance that they proceed from nature, to the ignorant, and therefore to the innocent. Therefore, whenever there is doubt about some affection, whose cause we do not know, whether it is natural or indeed superstitious, it must be judged natural, as all the theologians agree. Long ago I myself mocked images of this kind, not only as superstitious, but also as vanishing and useless; for I thought that no virtue from the influences of the heavens could be impressed upon artificial things, but only upon living and natural things. But in truth, taught by experience as my guide, I learned that even artificial things are impressed with a certain hidden power from heavenly bodies, which, as long as they last, they retain. I had read in the Centiloquium, Word 22: “Garments are neither to be cut nor first put on when the Moon is placed in Leo.” Seeking the reason myself I found none, nor did I find among writers or other learned men, whom I consulted, anything to confirm my mind: I wished to make the experiment. First excluding all aid of the devil, in case he should perhaps intrude himself, I purposely had a garment cut while the Moon was in Leo, and at the same time put it on: Wonderful! I used it for two full months, although it was almost split apart and burned through, as though it had been in a furnace. At that time I could think of no other cause for this thing than the celestial configuration, and the remarkable violence of the sign of Leo, which extends even to artificial things made at that time. Wherefore Master Thomas said excellently, opusc. 28, art. 4, that he was still uncertain about the natural virtue of such images and about the efficiency of heavenly bodies in these artifices, since just as the radiation of a period impresses the arrangement of order and duration above all on natural things; so also above all on artificial things: for which reason the figure of magical images is impressed by the aspect of the stars, and is allowed to come to be. Finally, I will conclude with what the same Cajetan has in the Summa: “To use images,” he says, “that are purely astronomical for effects subject to celestial bodies seems to be no sin, because, as we are considered purely natural things, we ought not measure the secrets of nature, especially celestial influences, by the powers of our own intellect; as the ancient astronomers

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LEXICON 240 non deferamus. Dixi autem, purè Astronomicas, vt nulla superstitiosa observatio sit adsuncta, aut suffumigationum, aut characte- rum; quoniam hac constat non pertinere ad cælestes influxus, sed ad secretos intellectus, quorum societas nobis est interdicta. Hucus- que Caietanus. Fateor tamen, vt supra innui, etiam in ipsis imaginibus purè astronomicis posito, quod naturaliter agant, & occulta vi à cælestibus mutuata, posse (vt credibile est) dæmonem ex inuidia se vltro sæpiùs immiscere, vel eò potissimum, quod occultæ sunt efficientiæ; adeoque ipsum inuidiæ æstro percitum, gestire occulta naturæ beneficia, aut religioso timore nobis suspecta rectere, vt ab illis abstineamus, aut sanè sua assistentia, & superstitiosis vanitatibus inuoluta liberiùs exhibere. Eapropter in ijs fabricandis, aut exercendis consulerem, magna cum cautela, & prudentia procedendum, & non nisi prius exclusa, omni quacumque dæmonis ope, aut pacto, vt puris n[ost]ruræ donis vti, nobis liberum sit, nec vlla formidine ab illis remoueamur. 27. IMVM Cali à loci situ dicitur quarta domus ab Horoscopo, & Meridianus subterraneus, qui & Fouea Planetarum, & Angulus terræ dicitur. Ab eo sumuntur significata de parentibus, eorumque statu, de bonis immobilibus, ædificijs, fundis, aquis, fodinis metallicis, thesauris absconditis, & similibus. Vide quæ diximus in V. Ipogon. & in V. Fouea. 28. IMPERANTIA signa appellantur ab Astronomis quæ, cum habeant parem cum alijs declinationem ab æquatore, sed diuersæ denominationis, ipsa tamen declinant ad Boream, alijs sibi ex aduerso respondentibus ad austrum, quæ propterea obedientia nuncupantur, quia quæ ad austrum deflectunt, videntur quodammodo cedere, & obedire ijs quæ ad boream, sicut nox diei cedit, atque substernitur. Quandoquidem ambo eosdem describunt parallelos, sed in signis borealibus arcus diurnus est maior nocturno, & in australibus nocturnus est maior diurno: veruntamen quantus est arcus diurnus ignorum borealium, tantus est nocturnus australium, & econtrà. Et ideò illa dicuntur imperantia ista, verò obedientia. Sic Aries imperat Piscibus, quia æqualiter ab æquatore distant, eosdemque describunt parallelos hincinde; ita ut, primus gradus Arietis correspondeat vltimo gradui Piscium, secundus 29. &c. Taurus eadem ratione imperat 13. Aquario: Gemini Capricorno: Cancer Sagittario: Leo Scorpioni: Virgo Libræ. Econtra INVENTIA

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LEXICON 240 we must not defer. But I said, purely astronomical, so that no superstitious observation is joined to it, whether of fumigations or of charac- ters; since it is clear that this does not pertain to celestial influences, but to secret intelligences, whose society is forbidden to us. Thus far Cajetan. Yet I confess, as I hinted above, that even in the case of purely astronomical images, granted that they act naturally and by a hidden power borrowed from the heavens, the demon can, as is credible, through envy more often of his own accord interpose himself, either chiefly because the operations are hidden; and thus, stirred by the frenzy of envy, he may delight in concealing nature’s benefits, or, out of religious fear suspect to us, to divert them, so that we abstain from them, or indeed, with his assistance, and wrapped in superstitious vanities, to display them more freely. For this reason, in making or using these things, I would advise that one proceed with great caution and prudence, and not unless every assistance or pact of the demon has first been excluded, so that it may be free for us to use the pure gifts of nature, and no fear may drive us away from them. 27. IMUM Caeli is so called from the position of the place, the fourth house from the Horoscope, and the subterranean Meridian, which is also called the Pit of the Planets, and the Angle of the Earth. From it are taken significations about parents, their condition, immovable goods, buildings, estates, waters, metallic mines, hidden treasures, and the like. See what we said in V. Ipogon. and in V. Fouea. 28. IMPERANTIA are called by astronomers those signs which, though they have the same declination from the equator as others, but of a different denomination, nevertheless declinate toward the North, while the others answer to them on the opposite side toward the south, which are therefore called obedient, because those that bend toward the south seem in a way to yield and obey those toward the north, just as night yields to, and lies beneath, day. For since both describe the same parallels, yet in northern signs the diurnal arc is greater than the nocturnal, and in southern signs the nocturnal is greater than the diurnal; nevertheless as great as is the diurnal arc of the northern signs, so great is the nocturnal of the southern, and vice versa. And therefore those are called imperant, these obedient. Thus Aries rules Pisces, because they are equally distant from the equator and describe the same parallels on both sides; so that the first degree of Aries corresponds to the last degree of Pisces, the second to the 29th, and so on. Taurus in the same way rules Aquarius by 13 degrees: Gemini Capricorn: Cancer Sagittarius: Leo Scorpio: Virgo Libra. On the contrary INVENTIA

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MATHEMATICVM. IN INVENTIA signa dicuntur quæ ex pari distantia hinc in- <29> de à tropicis se mutuò intuentur, proindeque eandem habent declinationem non modò numero, sed etiam nomine: vt sunt vltimæ partes Geminorum cum prioribus Cancri, Tauri cum Leone: Arietis cum Virgine: Sagittarij cum Capricorno: Scorpij cum Aquario: Libræ cum Piscibus. Si enim ad inuicem conferantur, inuenientur omnes eosdem describere parallelos; fitem ( vt Ptolemæi verbis vtar) per illas partes Sole meante, vt sparsia dierum, ac noctium, itemque horarum sibi respondeant. Hæc Antiscia primaria vocari solent, quemadmodum, quæ immediate ante hæc exposuimus, secundaria. Titus vero expressiore vocabulo, parallelos declinationis appellat. Vide quæ diximus in V. Antiscia, & quæ dicentur in V. Parallels. INACHIDES Cyllenius. Vide Perseus. INCONIVNCTA signa dicuntur quæ nulla familiaritate ad <30> inuicem copulantur: hoc est, neque se intuentur modo paulò ante dicto, neque alterum alteri obedit, aut imperat, neque se aliquo aspectu respiciunt, vt opposito, quadrato, trino, aut sextili. Talia sunt omnia signa contigua, quæ non sunt antiscia, seù eosdem describentes parallelos, & consequenter signa oppositasibi contiguis. Rationem reddit Ptolemæus, quia, inquit, quæ secunda sunt auersa sunt à sese, & duo signa continua coniuncta vnum efficiunt angulum, illa vero, quæ sextanumerantur totum orbem in partes inæquales secans, cum alia figura eum in partes æquales diuidant. Ex quibus liquet, eos, qui aspectum semisextilem admittunt ad distantiam 30. graduum omninò decipi, cum Ptolemæus hic talem distantiam nullius efficientiæ censeat; proindeque duo signa sibi solum contigua vocat inconiuncta. Igitur signa fixa hac ratione habent inconiuncta duo signa hinc, & inde, præcedentia, & subsequentia, atque illorum opposita: Mobilia habent inconiuncta signa succedentia, & illorum opposita, cum ad præcedentia habeant familiaritatem Antisciorum. Communia tandem habent inconiuncta solum antecedentia, & eorum opposita, cum ad subsequentia proijciant similiter antiscium, vel primarium, vel secundarium. Sed totum hoc per sequentem tabellam plapum fiet. Q

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MATHEMATICVM. IN IN INVERTIA, signs are called those which, at an equal distance on this side and <29> on that side from the tropics, look toward one another, and therefore have the same declination, not only in number, but also in name: such are the last parts of Gemini with the first of Cancer, Taurus with Leo, Aries with Virgo, Sagittarius with Capricorn, Scorpio with Aquarius, Libra with Pisces. For if they be compared with one another, they will be found to describe all the same parallels; so that, as I may use Ptolemy’s words, through those parts as the Sun passes, the days and nights, and likewise the hours, correspond to one another. These are usually called primary antiscia, just as those we have immediately explained above are called secondary. Titus, however, uses a more expressive term, calling them parallels of declination. See what we said under V. Antiscia, and what will be said under V. Parallels. INACHIDES, Cyllenius. See Perseus. INCONIUNCTA signs are called those which are joined to one another by no familiarity: that is, they neither look toward one another in the way just mentioned, nor does one obey or command the other, nor do they regard one another by any aspect, such as opposition, square, trine, or sextile. Such are all contiguous signs which are not antiscia, or which describe the same parallels, and consequently signs opposite to their contiguous ones. Ptolemy gives the reason, because, he says, the second are turned away from one another, and two continuous signs joined together make one angle, whereas those which are reckoned as sixths divide the whole circle, cutting it into unequal parts, while with another figure they divide it into equal parts. From this it is clear that those who admit the semisextile aspect at a distance of 30 degrees are altogether deceived, since Ptolemy here judges such a distance to have no efficacy; and therefore he calls only two signs merely contiguous to one another inconiuncta. Thus fixed signs, in this way, have as inconiuncta the two signs on this side and on that side, the preceding and the following, and their opposites. Mutable signs have as inconiuncta the following signs, and their opposites, since toward the preceding they have the familiarity of antiscia. Common signs finally have as inconiuncta only the antecedent signs, and their opposites, since toward the subsequent they likewise throw the antiscium, either primary or secondary. But the whole of this will be made plain by the following small table. Q

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14x LEXICON Tabula Signorum inconiunctorum. Aries habet inconiunctum Taurum, & Scorpium. Taurus Arietem, Geminos, Libram, & Sagittarium. Gemini Taurum, & Scorpium. Cancer Leonem, & Aquarium. Leo Cancrum, Virginem, Capricornum, & Pisces. Virgo Leonem, & Aquarium. Libra Scorpium, & Taurum. Scorpio Sagittarium, Libram, Arietem, & Geminos. Sagittarius Scorpium, & Taurum. Capricornus Leonem, & Aquarium. Aquarius Capricornum Pisces, Cancrum, & Virginem. Pisces tandem, Leonem, & Aquarium. 22. Porrò horum signorum, quæ, vt modo diximus, ideò coniuncta vocantur, quia nullo inter se ordine, ac familiaritate sunt nexa, nemo ferè est, qui rationem habeat, atque obseruet quænam in inferioribus hisce, seù bona, seù mala importent: cum tamen, meo iudicio, ea maximè seruari debeant; atque vt bonus ordo rerum ex ordine, colligatione, & consonantia cælestium corporum, quibuscum aliquam essendi habent necessitudinem, pendet, ita & perturbatio, discordia, & discrasia ab eorundem affectionibus, mutuo dissidio, ac disiunctione, seù disparitate naturæ, trahit originem. Etenim partium nexus, & amor, vt volebat Plato mundi anima est: hunc ordinem, hanc harmoniam si minimum turbes, & ipsum orbem turbari, confundi, infirmarique videbis, perinde ac in humano corpore ex humorum bono ordine perturbato, partiumque diuisione, dolores, moibos, vitæ discrimina prodire passim videmus. Igitur, vt in loco fusè dicemus, omnis in inferioribus hisce discordiæ, auersionis, atque antipathiæ ratio, huic vni signorum nulli colligantiæ & ordini accepta ferenda est: vti econtrà omnis ratio sympathiæ, amoris, concordiæ, animi propensionis, ad signorum, siderumque familiaritates, quibuscum ordinem causalitariis habent (vt haber etiam Ptolemæus in Quadrip. lib. 4. cap. 7) reducenda. 33. Hac etiam ratione, ni fallor, anni climacterici, seu schalares, in quibus semper aliqua corporum nostrorum discreta expectanda est, prodeunt, & inconiuncta hac inconiunctorum signorum serie ordinantur. Siquidem singulis septenarijs, ac nouenarijs recurrentibus, quoniam omnis bona siderum ad radicem Natalis configuratio expleta est, & non sequi-

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14x LEXICON Table of Inconjunct Signs. Aries has Taurus and Scorpio as inconjunct. Taurus has Aries, Gemini, Libra, and Sagittarius. Gemini has Taurus and Scorpio. Cancer has Leo and Aquarius. Leo has Cancer, Virgo, Capricorn, and Pisces. Virgo has Leo and Aquarius. Libra has Scorpio and Taurus. Scorpio has Sagittarius, Libra, Aries, and Gemini. Sagittarius has Scorpio and Taurus. Capricorn has Leo and Aquarius. Aquarius has Capricorn, Pisces, Cancer, and Virgo. Pisces, finally, has Leo and Aquarius. 22. Moreover, as for these signs which, as we have just said, are called conjunct for this reason, because they are linked among themselves by no order or familiarity, there is hardly anyone who takes care to observe what they bring in these lower things, whether good or bad; yet in my judgment they ought especially to be regarded. And just as the good order of things depends on the order, combination, and harmony of the celestial bodies, with which they have some connection of being, so disturbance, discord, and disarray take their origin from their affections, mutual conflict, and disjunction, or difference in nature. For the bond and love of parts, as Plato wished, is the soul of the world: if you disturb this order, this harmony even in the slightest degree, you will see the world itself disturbed, confused, and weakened, just as in the human body we constantly see pains, diseases, and dangers to life arise from the disturbance of the proper order of the humors and the division of the parts. Therefore, as we shall explain at length in the proper place, all the cause of discord, aversion, and antipathy in these lower regions is to be attributed to this one lack of conjunction and order among the signs; while on the contrary, all the cause of sympathy, love, concord, and inclination of mind must be referred to the familiarities of the signs and stars, with which they have causal relations of order (as Ptolemy also has in Quadrip. book 4, chap. 7). 33. For this reason also, if I am not mistaken, the climacteric years, or staircase years, in which some change of our bodies must always be expected, arise and are arranged by this series of inconjunct signs. Indeed, with the recurrence of each seven-year and nine-year period, since every good configuration of the stars to the root of the Nativity has been completed, and not to follow-

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MATHEMATICVM. 34. quitur accessus ad inconiuncta signa, quæ nullam cum radice natiuitatis familiaritatem habent, ideo sequitur etiam corporis discretia, præcipuè verò in annis 21. 42. 49. 56. 63. in quibus vt plurimum nulla intercedere potest familiaritas, ac necessitudo Luminarium ad horoscopum, vnde necesse est etiam vitam, deficienie rectore, abscindi, aut plurimum quati. Quod etsi alij, (& quidem communiter) dominatui recurrenti Saturni naturæ inimico tribuant; probabilius tamen est id ortum habere à signis recurrentibus, ad horoscopum, atque ad præcipua genitutæ loca, præsertim Luminaria, inconiunctis. Hinc etiam expiscari liceat congruentiam abditissimi illius < 34.> arcani; Cur, inquam, octimestris partus non superuiuat? de qua re tantopere exquisierunt sapientissimi Philosophorum, atque Astrologorum, ac integro insignique volumine scripsit eruditissime Federicus Bonauentura. Equidem nugæ sunt quæ habent Astrologi apud Schonerum lib. 1. de Iudicijs, ac latè prosequitur Natalis Comes in Mytholog. lib. 4. quia, inquiunt, in primo mense dominatur Saturnus Embrioni, in secundo Iupiter, in tertio Mars, in quarto Sol; & tunc est animal rationale; postea Venus, inde Mercurius, in septimo tandem mense Luna; & tunc si nascatur viuit, & completus est cursus: si transit, & venit ad octauum, regnat Saturnus, qui sua frigiditate, & siccitate interficit foetum; sed in nono regnat Jupiter, qui naturæ fotor est, atque adeò maturat, & fæliciter educit foetum, &c. Nugæ, inquam, hæc sunt; Nam peto, cur quarto, & (quod maximè notandum est) sexto mense in quo sanè matutior est quam in quinto foetus editus non superuiuit, cum tamen superuiuat in quinto? An quia quarto mensi Sol præest? At si vllus est, qui vitam sustentare valeat, Sol est, qui vitalis potentiæ fons est, & origo: vt proinde sicut ipsi inquiunt, vel inde foetus animal rationale esse incipit ac viralis: Deinde cur sexto mense editus non superuiuit? An quia illi præest Mercurius? at is neque naturæ inimicus est, nec si foret, vitam foetui posset adimere, cum sit minimæ actiuitatis, atque adeo vtalibi adnotauimus, vel ob id in regendæ vitæ munus in locis aphæticis constitutus subintrare non valet. Cur decimo mense, & vndecimo editus viuit (nam & multæ mulieres decem, vndecim, & eo ampliùs mensibus vtero gerentes visæ sunt) cum tamen ex eorum doctrina Mars naturæ infensissimus in regimen deberet venire? Mitto alias validissimas rationesquas abunde congerit Gotifridus in l. Insectac, &c. atque idem Bonau. lib. 7. cap. 14. Sed & Franciscus Valesius in Controvers. M. d. lib. 2. cap. 10. < 35.> Qij

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MATHEMATICVM. 34. there follows the approach of inconjunct signs, which have no familiarity with the native root, therefore there follows also a separation of the body, especially indeed in the years 21, 42, 49, 56, 63, in which for the most part there can be no familiarity intervening, nor connection of the Luminaries with the horoscope, whence it is necessary also that life, the ruler failing, be cut off, or greatly shaken. Although others, (and indeed commonly) ascribe this to the recurrent dominion of Saturn, hostile to nature; yet it is more probable that this has its origin from recurrent signs, inconjunct to the horoscope, and to the principal places of the nativity, especially the Luminaries. Hence also it may be permitted to investigate the agreement of that most hidden secret: why, I say, does an eight-month child not survive? concerning which matter the wisest of Philosophers and Astrologers have made such great inquiry, and Federico Bonaventura, most learnedly, wrote an entire and notable volume. Truly, those are trifles which the Astrologers have in Schoner, lib. 1. de Iudicijs, and Natalis Comes treats them at length in Mytholog. lib. 4, because, they say, in the first month Saturn rules the embryo, in the second Jupiter, in the third Mars, in the fourth the Sun; and then it is an animal rationale; afterward Venus, then Mercury, and in the seventh at last month the Moon; and then if it is born it lives, and the course is completed: if it passes on, and comes to the eighth, Saturn reigns, who by his own coldness and dryness kills the fetus; but in the ninth Jupiter reigns, who is the nourisher of nature, and thus matures and happily brings the fetus forth, etc. These are trifles, I say; for I ask, why in the fourth, and (which is especially to be noted) in the sixth month, in which surely the fetus born is earlier than in the fifth does not survive, when nevertheless it does survive in the fifth? Is it because in the fourth month the Sun presides? But if there is any one who can sustain life, it is the Sun, who is the fountain and origin of vital power: so that, as they themselves say, from that point the fetus begins to be a rational animal and virile. Then why does one born in the sixth month not survive? Is it because Mercury presides over it? But he is neither hostile to nature, nor, if he were, could he take life away from the fetus, since he is of the least activity, and thus as elsewhere we have noted, even for that reason, being placed in the office of governing life in aphäetic places, he cannot enter in. Why does one born in the tenth and eleventh month live (for many women have also been seen carrying in the womb for ten, eleven, and even more months) when nevertheless, according to their doctrine, Mars, most hostile to nature, ought to come into the governance? I pass over other very strong reasons, which Gottifridus abundantly gathers in l. Insectac, etc., and likewise Bonav. lib. 7. cap. 14. But also Franciscus Valesius in Controvers. M. d. lib. 2. cap. 10. Qij

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LEXICON 246 rum est Lustrum, quia eo tempore venientes nuncij prouinciarum ad ferendum tributum cum magna pompa, & comitatu vrbem lustrabant. Olim hic cyclus annorum numerari iucipiebat à die 24. Septembris. Nunc autem post correctionem Gregorianam incipit à Ianuario. Quod si quis quolibet anno currente indictionem venari voluerit, sic facili sive præstabit. Anuis à Natiuitate Domini excursis adjiciat tres: deinde productum diuidat per quinque, & quod residuum fuerit ex quotiente erit indictio illius anni. Quod si nihil supersit, signum erit, quod eo anno indictio est 15. & complementum cycli. Sic exempli gratia: Anno currenti 1660. addo 3. & fient 1663. summam diuido per 15 & prouenient in quotiente 108. & adhuc residuum erit 13 hæc igitur erit indictio præsentis anni. Quod memoriæ ergo non nemo his versibus expressit. Si tribus adsuntiss Domini diuiseris annos, Per ter quinque datur indictio certificata. Et hæc quidem de indictione, eiusque instituendæ ratione. INDVS sidus in Cælo ad polum Antarcticum, nobis inconspicuum à recensionibus vnà cum alijs vndecim detectum non ita pridem, atque in hominis indi formam, manu tenentis jaculum, figuratum: stellas habet 13. quintæ & sextæ magnitudinis sub signo Capricorni. 39. INFERNVS: & hic nostræ molitionis subiectum. Est enim Vniuersi istius centrum, (unde Isydoro dictus tanquam intus furnus, id est niger.) Locus omnium infimus, obscurus, & abjectissimus, in quem perinde atque in humano corpore visceræ, & vmbilicus, omnes mundi sordes, & retrimenta, tanquam in propriam sedem abijcienda sunt peracto finali iudicio, vt ex Basilio aduertit D. Thomas in 4. Sentent. distinct. 47. qu. 2. art. 5. Ea propter condignus dæmonum, & damnatorum carcer vbi perpetuô morabuntur æternis ignibus addicti. Ex eo verus locus siderum procul quacumque parallaxis deuiatione, obseruari exquisitissimè posset, ni telluris densitas, obuiret. Lessius existimar eius diametrum non excedere vnius milliarij belgici mensuram: quippe, air circumferentia eius rantæ amplitudinis erit, vt opimè capax esse possit rot millium corporum, quor planè vero similiter coniectari possumus, futuros esse damnaros. Purat enim eos ibi locandos post acceptam Iudicis sententiam illam . maledicti in ignem æternum, tanquam mutiaticos pisces in dolio, ita vt alter alterum premat, nec vllum aliud spatium sit, quod non corporibus repleatur. Franciscus Ribera in Apocalyps. cap. 14 probabiliter coniectat infernæ diametrum esse longam ducentis italicis milliarijs

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LEXICON 246 The Roman cycle of years is called the Lustrum, because at that time the messengers of the provinces, coming to bring tribute, used to go round the city with great pomp and retinue. Formerly this cycle of years began to be counted from the 24th of September. But now, after the Gregorian correction, it begins in January. If anyone wishes, in any current year, to determine the indiction, he may do so very easily. To the years elapsed since the Nativity of the Lord, add three; then divide the product by five, and whatever remains from the quotient will be the indiction of that year. If nothing remains, it will be a sign that in that year the indiction is 15, and the completion of the cycle. For example: in the current year 1660, I add 3, and 1663 results. I divide the sum by 15, and the quotient comes to 108, and there still remains 13; this therefore will be the indiction of the present year. For the sake of memory, someone has expressed this in the following verses: If you divide the years of the Lord by three and thus take them, By three times five the established indiction is given. And this indeed is enough about the indiction, and the method of establishing it. INDUS, a constellation in the sky near the Antarctic pole, unseen by us, discovered not long ago together with eleven others in the recent survey, and figured in the form of a man of India holding a spear in his hand; it has 13 stars of the fifth and sixth magnitude, beneath the sign of Capricorn. 39. INFERNUS: and here is the subject of our undertaking. For it is the center of this whole universe, (whence, according to Isidore, it is called as though “inside the furnace,” that is, black.) The lowest, darkest, and most abject place of all, into which, just as in the human body the viscera and navel, all the filth and refuse of the world are to be cast as into their proper seat after the final judgment, as St. Thomas notes from Basil in the 4th Sentences, distinction 47, question 2, article 5. For that reason it is the fitting prison of demons and the damned, where they will abide forever, consigned to eternal fires. From it the true position of the stars could be observed most exactly, at whatever deviation of parallax, were it not that the density of the earth hinders. Lessius thinks its diameter does not exceed the measure of one Belgian mile; indeed, the circumference of it will be of such vastness that it can abundantly contain so many thousands of bodies, from which we may quite reasonably infer that the damned will be there. For he supposes that they are to be placed there after receiving the Judge’s sentence: “Depart, accursed, into eternal fire,” like fish packed in a barrel, so that one presses upon another, and there is no other space that is not filled with bodies. Francisco Ribera, in Apocalypse chapter 14, conjectures that the diameter of hell is two hundred Italian miles long.

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MATHEMATICVM. 347 atque ex eo deducit, quod ibi effusus dicitur sanguis laci iræ Dei ad stadia 1600. alij aliter opinantur: quæ res sanè difficilis est definiri; cum id neque ex scripturis, neque ex Mathematicis obseruationibus colligi possit, sed pendeat ex mero conditoris beneplacito. Cæterum ibi tria sunt receptacula, vt communis SS. Patrum, & Ecclesiæ traditio est: quorum inferius, quod Mundi meditullium includit, damnatorum supplicio est destinatum; aliud, quod istud immediatè ambit, expiandis animabus ad Coelestem gloriam tandem migraturis addictum est: Tertium amplius, & spatiosius, qui Limbus SS. Patrum, & puerorum cum originali macula decedentium dictus est, vbi neque ignis, & fortassis neque tenebræ sunt, sed locus est valdè amoenus, aliquali luce ex terræ hiatibus transpirante perfusus, distatque à superficie terræ iuxta Bonardi observationes milliaris 37. 48. cum quadrante. Porrò Inferni, & Purgatorij loca vero, atque elementari < 40.> igne esse repleta, testantur sæpissimè sacræ paginæ, & communis omnium Catholicorum sensus. Vt videre est apud Bellarmin. 10m. 1. de Purg. lib. 2. cap. 11. & licet Damas. de fide Ortod. lib. 4. cap. 28. asserat Æternum ignem cum materia instar huiusce nostri constare: & D. Greg. Papa lib. 15. Moral. cap. 17. eum vocat incorporeum; tamen intelligendi sunt non quod eiusdem substantiæ, ac naturæ non sit: proindeque verè immaterialis, & incorporeus sit, sed quod corporeo pabulo non egeat vt conseruetur, neque materia, vt accendatur: cum alioqui idem Greg. lib. 4 Dialogorum cap. 29. percontanti Petro num ignis gehennæ sit corporeus an incorporeus, respondet Ignem gehennæ corporeum esse non ambigo, in quo certum est corpora cruciari. Vnde oportet amanuensium, vel librariorum fuisse errorem quod in moralibus habetur, incorporeus, & verius scribi debuisse corporeum, vt habet idem Bellarm. ac D. Thomas, qui in 4. sentent. dist. 44. qu. 3. hunc locum citans ponit, corporeus: & latè explicat dictum Greg. & excusat Damascenum, inquens eum non negasse ignem inferni materialem esse quoad substantiam, sed quoad punitionis effectum, punit enim corpora spirituali quadam actione, cum ea nec dissoluat nec consummat, sed incorruptibiliter cruciet, & ipsas animas spirituales modo quodam ineffabili, & imperceptibili. Quod quomodo fiat varie, & late explicant Theologi, ad quos cum res nostra non intersit lectorem remitto. Est igitur absque dubio ignis gehennæ eiusdem rationis cum nostro, licet longè horribilior, ac potentior. Quinimò non defuere Philosophi, qui dicetent ignis sphæram, & locum illi connaturalem esse in Mundi centro, hoc est in Inferno; vel ex eo probantes, Q 111j

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and from this he infers that there, as it is said, the blood of the lake of the wrath of God was poured out, to the extent of 1600 stadia. Others think otherwise: which matter is indeed difficult to determine, since it can be gathered neither from the scriptures nor from mathematical observations, but depends on the mere good pleasure of the Creator. Moreover, there are three receptacles there, as the common tradition of the most holy Fathers and of the Church holds: of which the lower one, which contains the center of the World, is destined for the punishment of the damned; another, which immediately surrounds that one, is assigned to souls to be purified and at last to pass to heavenly glory; the third, broader and more spacious, which is called the Limbo of the holy Fathers and of children dying with original stain, where there is neither fire, and perhaps neither darkness, but a very pleasant place, infused with some light transpiring through the openings of the earth, and it is distant from the surface of the earth, according to Bonard's observations, 37 miles, 48 quarters. Furthermore, the sacred pages very often testify, and the common sense of all Catholics, that the places of Hell and Purgatory are truly filled with elemental fire. As may be seen in Bellarmine, 10m. 1. de Purg. lib. 2. cap. 11. And although Damas. de fide Ortod. lib. 4. cap. 28. states that the Eternal fire consists of matter like this our own: and St. Gregory the Pope, lib. 15. Moral. cap. 17, calls it incorporeal; nevertheless, these must be understood not as if it were not of the same substance and nature: and therefore truly immaterial and incorporeal, but because it does not need bodily fuel in order to be preserved, nor matter in order to be kindled: since otherwise the same Gregory, lib. 4 Dialogorum cap. 29, when Peter asks whether the fire of Gehenna is corporeal or incorporeal, replies: “I do not doubt that the fire of Gehenna is corporeal, in which it is certain that bodies are tormented.” Hence it must have been an error of the copyists or scribes that in the Moralities it is found incorporeus, and it should more correctly have been written corporeus, as the same Bellarmine has it, and St. Thomas, who in the 4th Sentences, dist. 44, qu. 3, citing this passage, sets down corporeus; and explains Gregory at length, and excuses Damascene, saying that he did not deny the fire of hell to be material as to its substance, but as to the effect of punishment, for it punishes bodies by a certain spiritual action, since it neither dissolves nor consumes them, but torments them incorruptibly, and the souls themselves spiritually in a certain ineffable and imperceptible manner. In what way this happens the theologians explain variously and at length, to whom, since the matter does not concern us, I refer the reader. Therefore the fire of Gehenna is without doubt of the same kind as our own, though far more horrible and more powerful. Indeed, there have not been lacking philosophers who said that the sphere of fire and its connatural place is in the center of the World, that is, in Hell; proving it either from this, Q 111j

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148 LEXICON quod in Mactocosmo, eum locum occupare debet, quem in Microcosmo vitalis calor, cui est iu corde, hoc est in hominis meditullio sedes. Tum quia ignis natura, inquiunt, est summè mobilis, & vndequaque diffugiens: debuit ergò habere locum in medio vniuersorum, vnde probè calorem suum vndequaque transfunderet, atque in arcta, vt ita dicam, custodia ita deveneretur, vt non facilè dissipari posset. Ita discurrebant Pythagorici, quibus modò nonnulli recensionibus addicti sunt. <41.> Sed enim siue ignis Inferni ibi sit tanquam in propria, ac naturali sede, siue ex conditoris arbitrio (neque enim quod ab initio ab ipso naturæ authore constitutum fuit, ab ipso naturæ ordine alienum esse censendum est.) An autem adhuc lumine præditus sit magna est inter Theologos ac SS. Patres controuersia. Negat Ch[rist]l[es]sosthomus, Ambros. Theodoretus, Athanas. Cyrillus, Prospet Aquitanus, Basilius, Innocentius, & alij communiter. Affirmat autem Gregot. lib. 9 Moral. cap. 39. dicens illum non ad consolationem, sed ad maiorem terrorem lucere, luce tamen suboscura & nigricante, quale est lumen tædorum quod potius terrorem incutit quam delectat: subscribit Isidorus lib. 4. de summo bono, cap. 31. inquiens Ignem gehenna ad aliquid lumen habere, & ad aliquid non habere, hoc est habere lumen ad damnationem, vt videant impij vnde doleant & non habere ad consolationem, ne videant, vnde gaudeant. Neque in hoc sunt contrarij Ambros. & Innocentius vbi supra, quorum posterior dicit inter alios damnatorum cruciatos vnam esse visionem dæmonum, qui videbuntur in excussione scintillarum de igne ascendentium. Et sanè si ignis ille naturalis, & corporeus est, illum ijsdem prorsus qualitatibus præditum, quibus noster iste visualis ignis est affitmare oporret; nisi quod ibi maior actiuitas, maior vrendi vis, quam in hac telluris superficie, vbi aëris ambientis facilitate, ac stigore plurimum debilitatur. atque obtunditur (quod vide re est in clibano, alijsque vndique constipatis ignibus, qui potentiùs agunt quam reliqui.) Ob id, nil mirum, si subterranei ignes, & qui passim è moutibus eructant, tam violenti sint, vt penè diuersæ ab nostro, speciei esse videantur, ob idque à nonnullis eiusdem rationis, atque infernalis esse credantur. Quod ego non derrectauerim; immò certo certius habeo, hos terræ hiatus, vnde passim videmus ignes erumpere aliud non esse quani Inferni spiracula, vnde ignis ille evaporat, & quandoque accensus eructat, & vicinas regiones deuastat. Tales sunt Sulphureæ Puteolorum venæ ignem, & sumum perpetuò eructantes: Vesuuius mors prope Neapolium: Æthna in Sicilia:

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148 LEXICON which in the Mactocosm ought to occupy the place that vital heat occupies in the Microcosm, whose seat is in the heart, that is, in the center of man. Then, because, they say, fire by nature is most mobile and diffusing itself in every direction, it ought therefore to have its place in the middle of the universe, from which it might well spread its heat everywhere, and be reduced, so to speak, to a close custody, so that it could not easily be dissipated. Thus the Pythagoreans discoursed, to whom some are now devoted in their revisions. <41.> But whether the fire of Hell is there as in its proper and natural seat, or by the will of the Creator (for what was established from the beginning by the author of nature himself is not to be judged alien to the order of nature). And whether it is still endowed with light is a great controversy among the Theologians and the holy Fathers. Chrysostom denies it, Ambrose, Theodoret, Athanasius, Cyril, Prosper of Aquitaine, Basil, Innocent, and others in common. But Gregory affirms it in book 9 of the Moralia, chapter 39, saying that it shines not for consolation but for greater terror, yet with a dim and blackish light, such as the light of torches, which rather strikes fear than delights: Isidore subscribes to this, book 4, On the Supreme Good, chapter 31, saying that the fire of Gehenna has light in one respect and not in another; that is, it has light for damnation, so that the wicked may see from what they suffer, and not for consolation, lest they see from what they might rejoice. Nor are Ambrose and Innocent above contrary in this, for the latter says, among the other torments of the damned, one is the sight of demons, who will be seen in the shaking of sparks rising from the fire. And indeed, if that fire is natural and corporeal, it ought to be endowed with precisely the same qualities as this visible fire of ours; except that there is greater activity there, and greater power of burning, than on this surface of the earth, where the ease and coldness of the surrounding air greatly weaken and blunt it (as can be seen in a kiln and other fires packed in on every side, which act more powerfully than the rest). For that reason, it is no wonder if subterranean fires, and those that burst forth from mountains in many places, are so violent that they seem almost to be of a different kind from ours, and for that reason are believed by some to be of the same nature as the infernal fire. I would not deny this; indeed, I hold it for certain that those openings in the earth from which we see fires erupt in many places are nothing other than the vents of Hell, from which that fire evaporates and sometimes, when kindled, bursts forth and devastates neighboring regions. Such are the sulfurous veins of Puteoli, perpetually belching fire and smoke; Vesuvius, death near Naples; Etna in Sicily:

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MATHEMATICVM. 249 Arequipa in Peruano regno: Hecla mons in Islandia: Pittacia in Petside: alijque quos referunt Plinius, Maiolus & alij. Quod tum ratio naturalis suader, tum frequentissimæ historiæ; ac plurium Philosophorum auctoritas. Ratio, inquam, quia ignis quicumque naturaliter euaporare petit, & quoddam spiraculum, vnde exhalare queat, & sumum traijcete, ergò id etiam infernali competet, qui sanè per huiusmodi terræ hiatus exhalat. Accedunt historiæ. Refert enim Henricus Kermanus in lib. de miræ. mortuor in Tutingia apud montem Ferrariam extare quandam voraginem, seu terræ hiatus, qui horrisonus est, & communiter reputatur esse ostium quoddam Inferni; eoquod sæpissimè ex eo audiuntur clamotes, & vlutatus animarum, & circa ipsum ignes quosdam apparere. Simile quid refert, Sutius de Hecla Islandiæ monte, Pompilius Azzelus de rebus natural. lib. 5. cap. 16. Olaus magnus Saxo Grammaticus. Brocardus, & alij multi. Claudianus etiam Poëta in Rufin. lib. 10. meminit cuiusdam loci in Hybernia, qui nunc creditur esse Vorago illa, quam idcircò vulgo appellant Pu- seum S. Patricij, vnde auditur frequens luctus, & eiulatus ani- marum. Sic enim ait. Est locus extremum, qua pandit Gallialittus, Oceani prætextus æquus, quo fertur Vlÿsses, Sanguine libato populum monuisse silentum. Illic vmbrarum tenui stridore voluntum, Fiebilis auditur quassus simulachra coloni, Pallida, defunctasque vident migrare figuras. Huius rei ampliorem historiam, & quomodo precibus S. Patricij Hybernorum Apostoli ad aliquam infernalium tormentorum cognitionem populis ingerendam, vt à malis pattandis auocarentur, fuetit ei à Christo Domino sibi visibili- ter apparente monstrata quædam spelunca rotunda, & obscura, quam qui ingrederentur referrent, ibi se immania tormenta perpessos, & vidisse foucas quasdam, & ostia inferni, per quæ damnati proijciebantur: qui, inquam, huius rei vberiorem notitiam volet pluraque testimonia, videat Franciscum Restam de Meteoris lib. 1. Tract. 4. cap. 4. Denique in hanc sententiam inclinant, vel certè apertè ve- niunt multi ex SS. Patribus, Augustinus, Gregorius, Bernar- dus, Isidorus, Tertullianus, Bonauentura, Petrus Damianus, Bernardinus Senensis, & alij. Vt iam modò noanihil temeri- tatis habeat affitmare huiusmodi igniuomos montes, & antra non esse Inferni ostia, & ignis ibi existentis euaporamenta si non ad aliud, certè ad hoc vnum ab Authore Naturæ in varijs terreni orbis locis aperta, vt homines inde ediscerent, leo est-

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MATHEMATICVM. 249 Arequipa in the kingdom of Peru; Mount Hecla in Iceland; Pittacia in Petside; and others whom Pliny, Maiolus, and others mention. This is supported both by natural reason and by the very frequent histories; and by the authority of many philosophers. The reason, I say, is that whatever fire naturally seeks to vaporize, and needs some opening through which it may exhale and pass out its smoke, therefore this also will belong to infernal fire, which indeed exhales through such breaks in the earth. Histories are added as well. For Henricus Kermanus relates in the book de miræ. mortuor in Tutingia, near Mount Ferraria, there is a certain pit, or break in the earth, which is frightfully loud, and commonly regarded as a kind of gate of Hell; because very often from it are heard cries and howlings of souls, and around it certain fires appear. A similar thing is related by Sutius about Mount Hecla in Iceland, Pompilius Azzelus in de rebus natural. lib. 5. cap. 16, Olaus Magnus, Saxo Grammaticus, Brocardus, and many others. The poet Claudian also in Rufin. lib. 10. mentions a certain place in Ireland, which is now believed to be that pit which for that reason the common people call Pu- seum S. Patricij, from which a frequent lament and wailing of souls is heard. For thus he says: Est locus extremum, qua pandit Gallialittus, Oceani prætextus æquus, quo fertur Vlÿsses, Sanguine libato populum monuisse silentum. Illic vmbrarum tenui stridore voluntum, Fiebilis auditur quassus simulachra coloni, Pallida, defunctasque vident migrare figuras. The fuller history of this matter, and how, through the prayers of St. Patrick, Apostle of the Irish, for some knowledge of infernal torments to be impressed upon the people, so that they might be turned away from the suffering of evils, it was shown to him by Christ the Lord, appearing visibly to him, that a certain round and dark cave had been shown, which those who entered it reported, saying that there they had endured monstrous torments, and had seen certain pits and gates of hell, through which the damned were cast out: whoever, I say, wishes a fuller knowledge of this matter and more testimonies, let him see Franciscus Resta, de Meteoris lib. 1. Tract. 4. cap. 4. Finally, many of the Holy Fathers incline to this opinion, or certainly openly come to it: Augustine, Gregory, Bernar- dus, Isidorus, Tertullian, Bonaventura, Petrus Damianus, Bernardinus Senensis, and others. So that there is now no little te- merity in asserting that such fire-breathing mountains and caves are not the gates of Hell, and the exhalations of the fire existing there, if for no other purpose, certainly for this one, opened by the Author of Nature in various places of the earthly globe, so that men might learn from them, leo est-

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LEXICON 250 cum vbi impiorum animæ post mortem puniuntur, sicque . pattrandis criminibus arceantur, quod & Pythagoras, quamuis Ethnicus intellexit inquiens ignes hos subterraneos cruciare animas improborum. 42. INFORTUNA dicitur Planera maleficus Saturnus, qui nuncupatur infortuna maior, & Mars infortuna minor; eo quod loca in quibus reperiuntur, infortunent. Similiter infortuna dicitur quicumque alius planeta qui ab istis infortunetur. Vide in V. Fortuna. 43. INGENICVLVS, Hercules, Engonasis: sidus in Cælo ad Borealem plagam, hominem repræsentans, qui dextro genuixus, sinistro pede draconis Caput opprimere videtur. Continet stellas 29 de quibus diximus sub V. Engonasis. 44. INGRESSVS apud Astronomos, præsertim Ptolem. cap. vls. Quadripartem, significat familiaritatem quandam, quam sidera quotidianis lationibus, præsertim in annua revolutione acquirant, cum locis directionis, seu radicalibus tum sui, tum aliorum Prorogatorum Quandoquidam ingressus beneficarum semper prosunt vt benè aduertit Titus in cælesti Philosophia lib 3. cap. 11. maximè in conuenienri familiaritate maleficarum semper obsunt. Præcipuè verò ingressus valent ad eliciendos ad actum effectus illos, qui sunt in potentia proxima ptæordinari per motum directionis, si modo effectus sint naturæ suæ conformes: sin minus illos retardant, aut diminuunt. Sunt autem ingressus in duplici differentia, vt idem 45. Tirus obseruat: alij actiui qui fiunt à stellis actiuam virtutem habentibus, quando ingrediuntur aut corpore, aut radio loca directionum, & progressuum moderatorum; nam tunc agit in ipsos moderatores: alij passiui, qui fiunt ab ipsis moderatoribus, Sole videlicet, Luna, ascendente, medio cæli, ac fortunæ parte, quando ingrediuntur ad familiaritates locorum directionis, & progressuum Astrorum omnium quæ virtutem actiuam habeant: tunc enim ipsi Prorogatores patiuntur vt ita dicam ab Astris, & recipiunt effectus illorum. Porrò quos effectus habeant in hisce inferioribus ingressus tam actiui, quam passiui, ingeniosissimè explicat Tirus lococirato. 46. INTERLVNIVM dicitur tempus illud, quo Luna silet: hoc est sub radijs Solis existens à nulla nobis parte conspicua sit, sed supernè tantummodo in parte Soli obusta illustratur: quod quidem tempus complectitur aliquid Lunæ veteris, & aliquid nouæ, cum vetus, antequam Soli jungatur corpore, ad ipsum accedens non amplius apparet; & noua ab ipso recedens non adhuc conspicua est. Interlunij tempore si sata serantur ea non esse vermiculis obnoxia testatur Plin. lib. 18. cap. 17.

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as when the souls of the wicked are punished after death, and so are kept from committing crimes; which even Pythagoras, though a heathen, understood when he said that these subterranean fires torment the souls of the evil. 42. INFORTUNA is the planet Saturn, the evil-doing one, called the greater infortune, and Mars the lesser infortune; because the places in which they are found bring ill fortune. Likewise, any other planet is called an infortune if it is afflicted by these. See Fortuna under F. 43. INGENICVLVS, Hercules, Engonasis: a constellation in the sky toward the northern part, representing a man who, kneeling on the right knee, seems to crush the Dragon's head with his left foot. It contains 29 stars, of which we have spoken under Engonasis. 44. INGRESSVS, among astronomers, especially Ptolemy, chap. vls. Quadripartem, signifies a certain familiarity that the stars acquire by their daily motions, especially in the annual revolution, with the places of direction, or radical places, both of their own and of other Prorogators. For in some cases the ingresses of benefic planets always help, as Titus rightly notes in Celestial Philosophy, book 3, chap. 11; they always hinder, especially in suitable familiarity, the malefic ones. Ingresses are especially useful for drawing into act those effects which are in proximate potency to be preordained by the motion of direction, if only the effects are in conformity with their nature; if not, they delay or diminish them. There are ingresses of two kinds, as the same 45. Titus observes: some active, which occur when stars possessing active virtue enter, either by body or by ray, the places of directions and regulated progressions; for then they act upon those regulators; others passive, which occur from the regulators themselves, namely the Sun, Moon, Ascendant, Midheaven, and Part of Fortune, when they enter into the familiarities of the places of direction and progression of all the stars that have active power; for then the Prorogators, so to speak, suffer from the stars and receive their effects. Moreover, what effects active and passive ingresses have in these lower regions is most ingeniously explained by Titus in the place cited. 46. INTERLVNIVM is called that time when the Moon is silent: that is, when being under the Sun's rays she is visible to us in no part, but above only in the part scorched by the Sun she is illuminated; and this time includes something of the old Moon and something of the new, since the old, before it joins the Sun bodily, no longer appears as it approaches him; and the new, as it moves away from him, is not yet visible. Pliny, book 18, chap. 17, states that seeds sown during the interlunar period are not liable to worms.

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MATHEMATICVM. 251 <47.> INTERROGATIONES, seù Quæstiones Astrologicæ dicuntur quæ ex naturali, vt aiunt impulsu de te aliqua, fiunt Astrologo coniectori, vt inde is ex figura cæli ad momentum quæstionis erecta prædicat, quid de tali te futurum sit. De ijs multa vanè scripserunt Atabes, & Iudæi, quos inter ex professo Hali Aben-Ragel, & Guido Bonatus. Non nulla etiam verba ad hanc rem habet Centiloquij Author, vt vel inde euidenter appareat, non esse id Ptolemæi opus, qui in nullo suorum operum eas vnam admisit, aut admisisse videretur. Et quidem si si qua est in rebus Astrologicis vanitas, & dementia, hæc summum apicem tenet. Neque enim naturalis ratio elucet, quomodo cum fortuito interrogantis occursu connexionem ullam habeat cæli positus; quomodo hic & rem futuram indicet, & interrogantem ad sciscitandum impellat; vt benè discurrit Titus in cælesti Philosophia lib. 1. cap. 6. Namque, ait ipse, res futuræ habent naturales suas causas dependentes à radice Natalis, vel à diutnis lationibus, quæ non cohærent cum præsenti siderum habitudine, quæ mouet nolsta phantasmatæ opus est enim, vt inter signa, & res significatas sit aliqua connexio. Denique explicati non potest quomodo ex eadem cæli figura ad momentum factæ interrogationis erecta prædici vni ex præliantibus, aut dimicantibus mors, alteri victoria; si profectò eodem tempore, & in ijsdem circumstantijs ab ambobus fiat interrogatio. Sed hanc vanitatem fusè imbrobar Cardanus non vno in loco suorum operum. Maius sanè fundamentum habent Electiones s tum in certo siderum positu factæ, quippe quæ nec ratione, neque experimentis carent. Sed & hæ quoque cum radice natiuitatis conferendæ sunt, & inde, vt feliciter exeant aggrediendæ. <48.> INVERSARIF apud Arabes est oppositum Mutatil, cum videlicet Planera existens in corde alterius, & agglutinatus ei vsque ad minutum separatur ab eo vel ad gradum vnum. Ptolemæus in versione Arabica Hali Rodoan. IR <49.> IRIS Græcè denotat arcum illum cælestem, qui aduerso sole formatur in nube roscida, vel in minutissimis aquæ cadentis guttulis, in quibus tanquam in speculo excipianius solares radij, in orbem diffusi, ac miram illam repræsentent colorum varietatem sua specie mentes hominum præstringentem, atque in Dei laudem trahentem. Vnde Eccl. 4t. dicitur Vide arcum & benedic Deum qui fecit illum: valde spectosus est in splendore suo. Hinc etiam antiquis Thaumantias, hoc est admi-

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MATHEMATICVM. 251 <47.> INTERROGATIONES, or Questions, are called Astrological questions, which, as they say, arise from some natural impulse in you to the astrologer diviner, so that from the figure of the heavens erected for the moment of the question he may predict what will happen to you concerning such a matter. The Arabs and Jews have written many foolish things about these, among whom especially Hali Aben-Ragel and Guido Bonatus. The author of the Centiloquium also has some words pertaining to this matter, so that it may even from this clearly appear that it is not the work of Ptolemy, who in none of his works admitted these, or seemed to have admitted them. And indeed if if there is any vanity and madness in astrological matters, this holds the highest peak. For no natural reason is evident how the position of the heavens should have any connection with the chance encounter of the questioner; how it should both indicate the future matter and impel the questioner to inquire; as Titus argues well in Celestial Philosophy, book 1, chapter 6. For, he says, future things have their natural causes depending on the root of nativity, or on long continuations, which do not cohere with the present condition of the stars, which moves the work of our phantasms; for it is necessary that between the signs and the things signified there be some connection. Finally, it cannot be explained how from the same figure of the heavens erected for the moment when the question is made, death may be predicted to one of two fighters or combatants, victory to the other; if indeed at the same time, and under the same circumstances, the question is asked by both. But this vanity Cardanus has abundantly refuted in more than one place in his works. Electiones indeed have a greater foundation, those made at a certain position of the stars, since they lack neither reason nor experience. But these too must be compared with the root of nativity, and from that, if they are to turn out well, they must be undertaken. <48.> INVERSARIF among the Arabs is the opposite of Mutatil, when, namely, a planet existing in the heart of another and attached to it even to the minute is separated from it, or by one degree. Ptolemy in the Arabic version of Hali Rodoan. IR <49.> IRIS in Greek denotes that heavenly bow, which is formed opposite the sun in a dewy cloud, or in the tiniest drops of falling water, in which, as in a mirror, the solar rays are received, spread in a circle, and represent that marvelous variety of colors, striking the minds of men by its appearance and drawing them to the praise of God. Hence in Ecclesiasticus 4: it is said: Look upon the bow and bless God who made it: very beautiful it is in its splendor. From this also among the ancients, Thaumantias, that is, admi-

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252 LEXICON rationis Filia dicta est, ac Deorum nuncia credita. Formatur autem duo tempore siue à Sole, siue à Luna (licet hæc rarò admodum iridem faciat, eamque vnius coloris, & semper albicantem) per refractionem solarium radiorum in dicta nube caua, & ex parte diaphana, ex parte autem opaca, vnde pro diuersitate incidentiæ radiorum causetur diuersitas illa apparentiæ, & colorum. Vt plurimum autem in solari Iride tres colotes apparere solent. Puniceus, viridis & purpureus: & quidem ex parte arcus exteriori, puniceus, ex parte interiori purpureus, mediùs autem viridis; quia cum in parte extima sit minor opacitas, sit color flauus, seu puniceus: econtrà quia in parte interiori est maxima opacitas sit color purpureus: in medio verò, quia est moderata opacitas, ideò radij solates coeunt in colotem viridem. Et quoniam solates radij in orbem diffunduntur, ideò orbicularis est colorum apparentia: semper autem in Solis opposito; itavt centrum arcus sit ex diametro oppositus centro Solis. Et idcircò numquam apparet nisi semicitculus; & quò sol depressior est, & horizonti proximior, eò maiorem arcum efformat, & contrà quò elatior eò minorem. Hinc fètè semper cum se præbet Iris inspiciendam, id sit matutino, vel vespertino tempore. In meridie verò ferè numquam, nisi fortè in hyeme, quo tempore sol humilis valdè est, & magis horizonti, quam vertici nostro proximus, vnde & visibilem arcum efformare potest. Immò & quandoque accidit, vt Sole in linea meridiana existente duæ, & quandoque plutes Irides hinc inde Orientem versus, & Occidentem formentur, licet ex valdè debiles, ac depressæ, si videlicet duæ nubes hinc inde eauæ, & vdae solaribus radijs illustrentur Eius præsagia apud rusticos refert Cælius Rhodiginus in hæc verba. Si enim, inquit, fueros color rubens in albense, fersolissatem præsigna: quia salis color sit ex materia raritate; rara autem materia à Sole facilè resoluer, & ideò non sequuntur copiosæ pluuæ quibus agrorum fera: itas nimirum impediatur. Quando color viridis maior est reliquis significat olei, & oliuorum rubertasem. Denique cum color puniceus vicerit, frumenti copiam; cum purpureus, reliquorum fructuum, pollis etur. Hucusque Cælius. Mizaldus arcanorum lib. 2. ex Plin. & Ruell. refert arbores fieri odoratiores si in eas apparens Iris incubuerit Cæterum generaliter Iris est serenitatis index, vel etiam pluuiæ mox futuræ pro temporum diuersitate. Nam si matutino tempore appareat, & non præmissa pluua, significat solem incipere iam resolutionem nubium, quam necessariò pluuia comitatur: econta si vespertino tempore, & post pluuiam indicat solem nubium resolutionem perficere, & complere, quam mox serenum tempus con-

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252 LEXICON is called the daughter of Reason, and believed to be the messenger of the gods. It is formed at the same time either by the Sun or by the Moon (although the latter very rarely produces a rainbow, and then one of a single color, always whitish) by the refraction of the solar rays in the said hollow cloud, partly diaphanous and partly opaque, whence, according to the difference of incidence of the rays, that diversity of appearance and colors is caused. Usually, however, three colors are seen in the solar rainbow: red, green, and purple; and indeed, on the outer part of the arc, red; on the inner part, purple; and in the middle, green; because, since there is less opacity in the outer part, the color is yellowish or red; on the other hand, because there is the greatest opacity in the inner part, the color is purple; but in the middle, because the opacity is moderate, therefore the solar rays combine into the color green. And since the solar rays are spread out in a circle, the appearance of the colors is likewise circular; but it is always opposite the Sun, so that the center of the arc is diametrically opposite the center of the Sun. And for that reason it never appears except as a semicircle; and the lower the Sun is, and the nearer to the horizon, the larger an arc it forms, and conversely, the higher it is, the smaller. Hence it almost always happens that the Rainbow offers itself to be seen in the morning or evening. At midday, however, almost never, unless perhaps in winter, when the Sun is very low, and closer to the horizon than to our zenith, whence it can also form a visible arc. Indeed, it sometimes happens that when the Sun is in the meridian line, two, and sometimes more, Rainbows are formed on this side and that toward the East and West, although very weak and low, namely if two hollow and wet clouds on either side are illuminated by the solar rays. Cælius Rhodiginus reports its omens among rustics in these words: for if, he says, the color is reddish rather than whitish, it foretells sunshine; because the color of the rainbow is from the rarity of the matter; but rare matter is easily dissolved by the Sun, and therefore abundant rains do not follow, by which the fertility of the fields is, as it were, hindered. When the green color is greater than the others, it signifies the ripening of oil and olives. Finally, when the red color prevails, abundance of grain is indicated; when the purple, the abundance of the remaining fruits. So far Cælius. Mizaldus, in book 2 of the Secrets, citing Pliny and Ruellius, reports that trees become more fragrant if a Rainbow has rested upon them. Generally, however, the Rainbow is an index of fair weather, or also of rain soon to come, according to the difference of the seasons. For if it appears in the morning, and no rain has preceded, it signifies that the Sun is beginning now the dissolution of the clouds, which rain necessarily accompanies; but if in the evening, and after rain, it indicates that the Sun is completing and finishing the dissolution of the clouds, which soon the clear weather con-

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MATHEMATICVM. 253 sequitur. Vnde ab ipsomer Conditore Deo post diluui[m] po- sita est in signum serenitatis, & foederis, inter ipsum & homines, ne deinceps aquis diluuij perderet omnem carnem. Quod quidem mysticè explicat de Christi humanitate Iacobus Episcopus Christopolitanus in expositione Cantici Habacuc in illa verba suscitan suscitabis arcum suum, iuramenta tribubus, quæ loquutus es. < 52.> Dices, qualiter Deus Pater sit instar Solis fontis, & principij omnis lucis diuinitatis, qui debebat imprimere imaginem suam in nube humanitatis, id est mittere filium suum, qui est imago Patris in carnem; qui debebat latere in nube humanitatis: in qua persona sunt tres substantia, scilicet Verbum, anima, & Caro, ex quibus constituitur vnica persona sub vnico esse personali, & diuino. Qui quidem arcus diuinus debebat fugare omnem tempestatem, & totum diluuium peccatorum, & sedare omnes tenbras veteris pacti, & inducere lucem, & serenitatem gratiæ. Ad quem arcum sapiens pater non amplius debebat recordari veteris pacti: immò Deus respiciens illum arcum qui est filius incarnatus, illicò recordatur foederis promissi inter ipsum, & genus humanum. Et sic Pater respiciens illum arcum in cruce recordatus foederis promissi remisit pactum toti generi humano. Hucusque Episcopus Christopolitanus piè quidem, & eruditè nimis. Sed longè à nostro instituto abetrauimus. Hæc sufficiant. IRINA Virgarum species apud Arist. ab Inde dicta pluuix < 53.> certum præsagium: de qua vide in V. Virga. I S ISARITHMI Græcè significant prima numerorum elementa < 54.> quæ in decem figuris continentur, quas nos in V. Abaculi explicauimus ab isag, quod initium, & ryshmos qui numerum denotat, deriuarum. Porro Isoryshma numero paria significat, ab Iso, quod est æquale. Hinc Isomaros dicitur quod æquales continer partes. Sic ISAGONIVS est figura Geometrica æqualibus angulis constans. < 55.> ISOPERIMETRÆ figuræ, quæ æqualem habent circumferentiam, & his similia pari ratione. < 56.> ISOMARINOS sæpissimè apud scriptores Græcanicos dicitur Æquator, & Circulus æquinoctialis, eoquod æquet diebus < 57.> noctes, & æquales diuidatur in partes. Istis etiam Græcè præcipuè apud Hermetem dicitur stella < 58.> fixa in Canisaure sinistra. At Auteno audir Virginis fidus. ISOSCELES est figura Geometrica triangularis, quæ duo tan- < 59.> tum latera habeat æqualia, tertium verò neutro æquale, sed aut

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MATHEMATICVM. 253 follows. Hence after the flood it was placed by God, the Creator Himself, as a sign of serenity and of the covenant between Him and men, lest thereafter He should destroy all flesh by the waters of the flood. This, indeed, James, Bishop of Christopolis, explains mystically of Christ’s humanity in his exposition of the Song of Habakkuk in those words: “Thou shalt raise, thou shalt raise thy bow, the oaths to the tribes which thou hast spoken.” <52.> You will say, how God the Father is like the sun, the source and beginning of all divine light, who was to imprint His image in the cloud of humanity, that is, send His Son, who is the image of the Father, into flesh; who was to dwell hidden in the cloud of humanity, in which person there are three substances, namely Word, soul, and flesh, from which one person is constituted under one personal and divine being. This divine bow was indeed to drive away every storm, and the whole flood of sins, and to appease all the darkness of the old covenant, and to bring in the light and serenity of grace. At this bow the wise father was no longer to remember the old covenant; rather, God, looking upon that bow which is the incarnate Son, at once remembers the covenant promised between Himself and the human race. And thus the Father, looking upon that bow on the cross, remembered the promised covenant and remitted the pact to the whole human race. So far the Bishop of Christopolis, piously indeed, and learnedly enough. But we have wandered far from our purpose. Enough of this. IRINA. A kind of rod among Aristotle’s terms, so called from rain <53.>: see under V. Virga. ISARITHMI in Greek signify the first elements of numbers <54.>, which are contained in the ten figures, which we have explained in V. Abaculi, derived from isag, meaning beginning, and ryshmos, which denotes number. Moreover, Isoryshma signifies equal numbers, from iso, which means equal. Hence Isomaros is said of that which contains equal parts. Thus ISAGONIVS is a geometric figure consisting of equal angles. <55.> ISOPERIMETRÆ are figures which have an equal circumference, and the like by a similar rule. <56.> ISOMARINOS is very often called among Greek writers the Equator, and the equinoctial circle, because it makes the days equal to the nights, and is divided into equal parts. <57.> Among the Greeks, and especially with Hermes, the fixed star in Canis Major on the left is also called this. But Auteno heard the faithful of Virgo. ISOSCELES is a triangular geometric figure, which has only two equal sides, but the third equal to neither, but either

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142 LEXICON Tabula Signorum inconiunctorum. Aries habet inconiunctum Taurum, & Scorpium. Taurus Arietem, Geminos, Libram, & Sagittarium. Gemini Taurum, & Scorpium. Cancer Leonem, & Aquarium. Leo Cancrum, Virginem, Capricornum, & Pisces. Virgo Leonem, & Aquarium. Libra Scorpium, & Taurum. Scorpio Sagittarium, Libram, Arietem, & Geminos. Sagittarius Scorpium, & Taurum. Capricornus Leonem, & Aquarium. Aquarius Capricornum Pisces, Cancrum, & Virginem. Pisces tandem, Leonem, & Aquarium. 12. Portò horum signorum, quæ, vt modo diximus, ideò coniuncta vocantur, quia nullo inter se ordine, ac familiaritate sunt nexa, nemo ferè est, qui rationem habeat, atque obseruet quænam in inferioribus hisce, seù bona, seù mala importent: cum tamen, meo iudicio, ea maximè seruari debeant; atque vt bonus ordo rerum ex ordine, colligatione, & consonantia ex lestium corporum, quibuscum aliquam essendi habent necessitudinem, pendet, ita & perturbatio, discordia, & discrasia ab eorundem affectionibus, mutuo dissidio, ac disiunctione, seù disparitate naturæ, trahit originem. Etenim partium nexus, & amor, vt volebat Plato mundi anima est: hunc ordinem, hanc harmoniam si minimum turbes, & ipsum orbem turbari, consuudi, infirmarique videbis, petinde ac in humano corpore ex humorum bono ordine perturbato, partiumque diuisione, dolores, moibos, vitæ discrimina prodire passim videmus. Igitur, vt in loco susè dicemus, omnis in inferioribus hisce discordiæ, auersionis, atque antipathiæ ratio, huic vni signorum nulli colligantiæ & ordini accepta ferenda est: vti econtrà omnis ratio sympathiæ, amoris, concordiæ, animi propensionis, ad signorum, siderumque familiaritates, quibuscum ordinem causalitatis habent (vt habet etiam Ptolemæus in Quadrop. lib. 4. cap. 7) reducenda. 13. Haceriam ratione, ni fallor, anni climacterici, seu schalares, in quibus semper aliqua corporum nostrorum discrata expectanda est, prodeunt, & inconiuncta hac inconiunctorum signorum serie ordinantur. Siquidem singulis septenarijs, ac nouenarijs recurrentibus, quoniam omnis bona sidesum ad radicem Natalis configuratio expleta est, & non sequi-

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142 LEXICON Table of in-conjoined signs. Aries has as in-conjoined Taurus and Scorpio. Taurus, Aries, Gemini, Libra, and Sagittarius. Gemini, Taurus, and Scorpio. Cancer, Leo, and Aquarius. Leo, Cancer, Virgo, Capricorn, and Pisces. Virgo, Leo, and Aquarius. Libra, Scorpio, and Taurus. Scorpio, Sagittarius, Libra, Aries, and Gemini. Sagittarius, Scorpio, and Taurus. Capricorn, Leo, and Aquarius. Aquarius, Capricorn, Pisces, Cancer, and Virgo. Pisces, lastly, Leo, and Aquarius. 12. Therefore, few there are who, regarding these signs which, as we have just said, are called conjoined, because they are linked among themselves by no order or familiarity, take account of and observe what they bring about in these lower things, whether good or evil; although, in my judgment, they ought especially to be considered. And just as the good order of things depends on order, connection, and harmony from the heavenly bodies, with which they have some relation of existence, so also disorder, discord, and unsoundness take their origin from their affections, mutual disagreement, and disjunction, or dissimilarity of nature. For the union and love of the parts, as Plato wished, is the soul of the world: if you disturb this order, this harmony even in the least, you will see the globe itself disturbed, confused, and weakened, just as in the human body, when the good order of the humors is disturbed and the parts are divided, pains, diseases, and dangers to life are seen everywhere to arise. Therefore, as we shall say in the place cited, the whole reason for discord, aversion, and antipathy in these lower things must be attributed to this one lack of conjunction and order among the signs; while, on the contrary, every reason for sympathy, love, concord, and inclination of mind must be referred to the familiarities of the signs and stars, with which they have a order of causality, as Ptolemy also has in the Quadrop., book 4, chapter 7. 13. In this way, if I am not mistaken, the climacteric, or scalar, years arise, in which some disarray of our bodies is always to be expected, and are arranged by this series of in-conjoined signs. Indeed, with each recurrence of the sevens and nines, since every good configuration of the stars to the root of the Nativity has been completed, and not follow-

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MATHEMATICVM. 141 quitur accessus ad inconiuncta signa, quæ nullam cum radice natiuitatis familiaritatem habent, ideo sequitur eriam corporis discretia, p[er]tæcipuè verò in annis 21. 42. 49. 56. 63. in quibus vt plurimum nulla intercedere potest familiaritas, ac necessitudo Luminatium ad horoscopum, vnde necesse est etiam vitam, deficiente rectore, abscindi, aut plurimum quæti. Quod etsi alij, (& quidem communiter) dominatui recurrenti Satutni naturæ inimico tribuant; probabilius tamen est id ortum habere à signis recurrentibus, ad horoscopum, atque ad præcipua genituræ loca, præsertim Luminaria, inconiunctis. Hinc etiam expiscari liceat congruentiam abditissimi illius < 34.> arcani; Cur, inquam, octimestris partus non superuiuat? de qua re tantopere exquisierunt sapientissimi Philosophorum, atque Astrologorum, ac integro insignique volumine scripsit eruditissime Federicus Bonauentuta. Equidem nugæ sunt quæ habent Astrologi apud Schonetum lib. 1. de Iudicijs, ac latè prosequitur Natalis Comes in Mytholog. lib. 4. quia, inquiunt, in primo mense dominatur Saturnus Embrioni, in secundo Iupiter, in tertio Mars, in quarto Sol; & tunc est animal rationale; postea Venus, inde Mercurius, in septimo tandem mense Luna; & tunc si nascatur viuit, & completus est cursus: si transir, & venit ad octauum, regnat Saturnus, qui sua frigiditate, & siccitate interficit foetum; sed in nono regnat Jupiter, qui naturæ fotor est, atque adeò matutat, & fæliciter educit foetum, &c. Nugæ, inquam, hæc sunt; Nam peto, cur quarto, & (quod maximè notandum est) sexto mense in quo sanè matutior est quam in quinto foetus editus non superuiuius, cum tamen superuiuar in quinto? An quia quarto mensi Sol præest? At si vllus est, qui vitam sustentare valeat, Sol est, qui vitalis potentiæ fons est, & otigo: vt proinde sicut ipsi inquiunt, vel inde foetus animal rationale esse incipit ac vitalis: Deinde cur sexto mense editus non superuiuius? An quia illi præest Mercurius? at is neque naturæ inimicus est, nec si fotet, vitam foetui posser adimere, cum sit minimæ actiuitatis, atque adeo vtalibi adnorauimus, vel ob id in regendæ vitæ munus in locis aphæticis constitutus subintrare non valet. Cut decimo mense, & vndecimo editus viuit (nam & multæ mulieres decem, vndecim, & eo ampliùs mensibus vtero petentes visæ sunt) cum tamen ex eorum doctrina Mars naturæ infensissimus in regimen deberet venite? Mitto alias validissimas rationesquas abunde congerit Gotifridus in l. incestas, &c. atque idem Bonau. lib. 7. cap. 14. Sed & Franciscus Valestus in Controuers. M. d. lib. 2. cap. 10. < 35.> Qij

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MATHEMATICVM. 141 follows the approach of inauspicious signs, which have no familiarity with the root of the nativity; therefore the body’s separation also follows, especially indeed in the years 21, 42, 49, 56, 63, in which by far no familiarity and connection of the Lights to the horoscope can intervene; whence it is also necessary that life, the ruler being lacking, be cut off, or at least greatly weakened. Although some others (and indeed commonly) attribute this to the recurring dominion of Saturn, hostile to nature, it is nevertheless more probable that it has its origin from recurring signs, inconjunct to the horoscope and to the principal places of the nativity, especially the Luminaries. From this also one may investigate the congruence of that most hidden secret: why, I say, does an eight-month child not survive? Concerning this matter the wisest of philosophers and astrologers have inquired at great length, and most learnedly Federico Bonaventuta wrote an entire and notable volume. Indeed, those things which the astrologers have with Schonetus, book 1, De Iudicijs, are nonsense, and Natalis Comes follows it broadly in Mytholog., book 4, because, they say, in the first month Saturn rules the embryo, in the second Jupiter, in the third Mars, in the fourth the Sun; and then it is a rational animal; afterward Venus, then Mercury, and finally in the seventh month the Moon; and then, if it is born, it lives, and the course is completed: if it passes on, and comes to the eighth, Saturn reigns, who with his coldness and dryness kills the fetus; but in the ninth Jupiter reigns, who is the nurturer of nature, and therefore matures it and brings the fetus forth happily, etc. These, I say, are nonsense; for I ask, why in the fourth, and (what is most to be noted) sixth month, in which the fetus is certainly born earlier than in the fifth, does it not survive, when nevertheless it survives in the fifth? Is it because in the fourth month the Sun presides? But if there is any planet able to sustain life, it is the Sun, which is the source and origin of vital power; so that, as they themselves say, from that point the fetus begins to be a rational and living animal. Then why does a fetus born in the sixth month not survive? Is it because Mercury presides over it? But he is neither hostile to nature, nor, if he were nurturing it, could he take life away from the fetus, since he has very little activity, and therefore, as we have observed elsewhere, or for that reason as well, being placed in the office of governing life in the aphætic places, he is not able to intervene. Why does one born in the tenth and eleventh month live? For many women too have been seen carrying in the womb for ten, eleven, and even more months; whereas according to their doctrine Mars, most hostile to nature, ought to have come into the governance? I pass over other very strong arguments, which Gotifridus heaps up abundantly in l. incestas, etc., and likewise Bonau. book 7, cap. 14. But also Franciscus Valestus in Controuers. M. d., book 2, cap. 10. 35. Qij

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LEXICON ex Hyppoer rte, alijsque Medicis aliam ingeniosissimam ra- tionem affert, cur Octimestris partus non superuiuat, ex ra- tione videlicet conceptionis, & conformationis. Nam mutationes, inquit, præcipua, qua contingunt fætibus, certis quibusdam temporibus, dum in vtero [con]runtur, sunt figuratio, & motus, & partus: horum temporum ad se inuicem est proportio: hoc tempus motus duplum est tempori figurationis; & tempus partus est triplum tempori motus. Igitur pendet tempus partus à tempore figurationis, cuius non est simplex terminus, sed varius: atque proinde tam muti sunt termini partus humani, vt & septimo, & nono, & undecimo fieri, & duodecimo contingat; quia & quod mulio magis mirandum quartodecimo etiam vt inquit auncenna 3. lib. Fen. 21. nisi fortè detrahenda fides et est, quia ex relatu oquebasur: ita enim inquit Et iam dixit mihi fideiis quidem, quandam muiserem peperisse quartodecimo mense; & benè dixit. Termini figurationis, vt apud Hippocratem videre est lib. de alimento, sunt nunc 30. nunc 35. nunc 40. nunc 50. dies: quo loco, eam quam diximus proportionem obseruat Hippocrasen. meos qui 35 figurantur, 70 moueri, & 210. edi tradidit Ex his itaque terminis licet coligere partus naturalis terminum esse septimum mensem, qu. constat 210. diebus, & nonum, qui completur 270. die us: qui terminus sit ex 45. bis sumptis, atque constituent bus 30. ad motum, atque ex illis rursum ter sumptis ad exitum. Vos est verò etiam in principio septimi mense edi, quando scilicet solis 30 diebus figuratur fætus: mouetur enim 60. diebus, & editur 180. quod est anni dimidium & principium septimi: atque etiam in undecimo editur qui configuratur 50 mouetur siquidem 100. & editur 300 atque ita, aut citiùs, aut tardiùs, prout citio, aut tardè figu atur Tamen nullus octauo mense editur; nam qui 40. figuratur (figurantur autem paucissimi) hæc bis centum, & 40. ediis qui quatuor tam dies ex nono mense d sumpsit. Constant enim singus menses ex 20. diebus eum dimidio. Hæc Valesius, ex Barbarorum Medicorum placitis. Verum, vt benè ipsemet obseruat, hæc ratio, etsi alioqui ingeniosissima plurimum claudicat. Nam quod foetus formari possint quadragesimo die docuit Hippocrates locois Nunc si qui formantur quadraginta diebus, opus est, vt in octo mensibus maturescat atque in lucem edantur. Quod si temen aliquam partem ex nono mense velis desumere, iam inuenies, eos, qui spatio 35. dierum figurantur, octauo ad amussim mense edi. < 36.> Quod ideò concludendum est, nullam esse, quæ mentem magis affirmet, atque ad verum collincet, rationem, quam quæ desumitur ex ordine, & connexione signorum ad id quod conceptus tempore horoscopum, seù alium quemuis locum,

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LEXICON from Hyppoer rte and other physicians offers another most ingenious reason why an eight-month birth does not survive, namely from the reason of conception and formation. For the principal changes, he says, which happen to fetuses at certain times while they are being formed in the womb, are formation, movement, and birth: between these times there is a proportion to one another; this time of movement is double the time of formation; and the time of birth is triple the time of movement. Therefore the time of birth depends on the time of formation, whose limit is not simple, but various; and accordingly the limits of human birth are so varied that it happens both in the seventh, and ninth, and eleventh, and even twelfth month; and, what is much more surprising, even in the fourteenth, as Avicenna says, book 3, Fen. 21, unless perhaps the faith is to be diminished, and it is from report that he spoke; for thus he says: “And now a trustworthy man told me that a certain woman gave birth in the fourteenth month”; and he spoke well. The limits of formation, as may be seen in Hippocrates, book On Nourishment, are now 30, now 35, now 40, now 50 days: in this place Hippocrates observes the proportion we mentioned. Those formed in 35 days, he says, are moved in 70, and delivered in 210. From these limits, then, it may be gathered that the natural term of birth is the seventh month, which consists of 210 days, and the ninth, which is completed in 270 days; which term is made up of 45 taken twice, and constituting 30 for movement, and from those again taken three times for the issue. It is also possible to be born at the beginning of the seventh month, when the fetus is formed in only 30 days; for it is moved in 60 days, and born in 180, which is half a year and the beginning of the seventh month; and likewise in the eleventh month one is born who is formed in 50, moved in 100, and born in 300; and thus, sooner or later, according as it is formed sooner or later. Yet no one is born in the eighth month; for whoever is formed in 40 days (and very few are formed so) is born in 240 days, which is four days short of the ninth month. For each month consists of 20 days and a half. This is Valesius, from the opinions of the barbarian physicians. But, as he himself rightly observes, this reasoning, although otherwise most ingenious, is greatly defective. For Hippocrates taught in the cited place that fetuses can be formed in forty days: “Now if some are formed in forty days, it is necessary that they mature in eight months and be brought forth into the light.” But if you wish to take some part from the ninth month, you will now find that those who are formed in a span of 35 days are brought forth exactly in the eighth month. < 36.> Therefore it must be concluded that there is no reason which more strongly confirms the view and comes closer to the truth than that which is drawn from the order and connection of the signs with respect to that which, at the time of conception, the horoscope, or some other place,

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MATHEMATICVM. 245 qui vitam regendam, substentandamque suscepit, occupabat. Siquidem, quia quarto, sexto, octavo mense succedit in re- gimen signum, quod nulla familiaritate signo horoscopo conceptionis præsidenti conuinctum est, ideò nulla vitæ pro- rogatio expectanda, bene verò cum signa contingunt, quæ cui radicali aliquo ordine, ac familiaritate nectuntur, qualia sunt, quæ quinto, septimo, nono, & reliquis mensibus, ex necessitate subintrant. Denique hæc eadem ratio arrisisse vi- detur Plutarcho lib. 5. de placitis Philosophorum cap. 18. vbi hæc habet. Mathematici, inquit, otto menses ad quemuis partum in- sociabiles aiunt, septem sociabiles, quæ incidunt in stellas demibus cælestibus dominantes, & sub se natis vitam infælicem, ac non longauam portendunt. Sunt autem in sociabilis, quorum vnum cum altero octauum numeratur, vt Aries ad Scorpium, Taurus ad Sagittarium, &c. Hinc fieri, vt septimo, vel decimo mense in lu- cem edita vitalia sint; octavo nati, ob dissidium mundi pereant. Hæc Plutarchus, cui astipulari videtur etiam Fracastorius de Sympathia cap. 1. asserens omnem huius rei rationem refun- dendam esse in sympathiam mensium, adeoque signorum, at- que antipathiam. INDICTIO est certus quidam annorum numerus & compu- <37.> tus describi solitus in Principum Diplomatibus, & scripturis publicis addignoscenda recurrentia tempora, sicut Olympia- des, Lustra, & similia: amplectitur enim revolutionem quin- decim annorum, qua explera, iterum reditur ad vnitatem. Ortum habuit, & nomen sortita est ab indictione Vestigalium, ac tributorum, quam Romani Principes olim vniuerso o[mn]ibi imperitantes populis publicè faciebant. Cum enim comperis- sent, difficile admodum esse ab remotissimis mundi plagis ve- nire singulis annis Romam subiectarum prouinciatum legatos ad soluenda tributa, statuerunt, vt singulis quinquennijs sin- gula soluerentur, & in quindecim totis annis, compleretur tota indicti vestigalis solutio: itaut in primo quinquennio apporta- rent pro tributo ferrum, pro fabricandis a[m]mis: in secundo ar- gentum pro stipendijs militaribus copijs erogandis: in tertio aurum pro Deorum simulachris fabricandis: & sic semper post aurum, quod in quintodecimo quoque anno ferebatur, inci- piebat quinquennium deputatum ad apportandum ferrum; sicque noua indictio, quasi nouus quidam temporis circuitus incipiebat, vnde nomen huic spatio datum est, quod in publi- cis annalibus describebatur, ac successiuè postea in scripturis pu- blicis registrari semper consueuit, & etiam num eius vsus ei- ger, licet alioqui eius ratio cum Romani Imperij sceptro iam exciderit. Prædictum autem spatium quinque annorum voca- (11)

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MATHEMATICVM. 245 who occupied himself with governing and sustaining life. For since, in the fourth, sixth, and eighth month there succeeds in the rule a sign which is bound by no familiarity to the sign presiding at conception in the horoscope, therefore no prolongation of life is to be expected; but rather, when those signs occur which are joined to the radical sign by some order and familiarity, such as those which necessarily intervene in the fifth, seventh, ninth, and remaining months. Finally, this same reasoning seems to have pleased Plutarch, book 5 of the Placetia Philosophorum , chapter 18, where he writes thus: “Mathematicians,” he says, “say that eight months are inharmonious to any birth, seven harmonious, which fall under the stars ruling the heavenly decans, and portend an unhappy and not long life to those born under them. Inharmonious are those of which one is reckoned eighth to another, as Aries to Scorpio, Taurus to Sagittarius, and so on. Hence it comes about that those born in the seventh or tenth month are vital; those born in the eighth perish on account of the discord of the world.” This is Plutarch, to whom Fracastorius also seems to assent in De Sympathia , chapter 1, asserting that the whole reason for this matter must be referred to the sympathy of the months, and thus of the signs, and to antipathy. INDICTION is a certain number and reckoning of years, customarily set down in the diplomas of princes and in public writings for identifying recurring times, like Olympiads, lustrums, and the like; for it embraces a revolution of fifteen years, which once completed, returns again to unity. It had its origin and received its name from the indiction of dues and taxes, which the Roman emperors, formerly ruling publicly over all peoples, used to impose. For since they had discovered that it was extremely difficult for the envoys of the subjugated provinces to come every year to Rome from the remotest parts of the world to pay the taxes, they decreed that every five years each contribution should be paid, and that in the whole fifteen years the entire payment of the indicted tax should be completed; so that in the first five-year period they would bring iron as tribute, for making weapons: in the second, silver, to be distributed for military stipends to the troops: in the third, gold, for making images of the gods: and thus always after the gold, which was also carried in the fifteenth year, there began the five-year period assigned for bringing iron; and so a new indiction, as it were a new circuit of time, began, whence this span received its name, which was entered in public annals, and afterward it was always accustomed to be recorded successively in public writings; and even now its use remains, although otherwise its basis has already fallen away together with the scepter of the Roman Empire. But the aforesaid span of five years is called (11)

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LEXICON 246 rum est Lustrum, quia eo tempore venientes nuncij prouinciarum ad ferendum triburum cum magna pompa, & comitatu vrbem lustrabant. Olim hic cyclus annorum numerari iucipiebat à die 24. Septembris. Nunc autem post correctionem Gregorianam incipit à Ianuario. Quod si quis quolibet anno currente indictionem venari voluerit, sic facili iure præstabit. Annis à Nariuitate Domini excursis adjiciat tres: deinde productum diuidat per quinque, & quod residuum fuerit ex quoriente erit indictio illius anni. Quod si nihil super sit, signum erit, quod eo anno indictio est 15. & complementum cycli. Sic exempli gratia: Anno currenti 1660. addo 3. & fiens 1663. summam diuido per 15 & provenient in quoriente 108. & adhuc residuum erit 13. hæc igitur erit indictio præsentis anni. Quod memoriæ ergo non nemo his versibus expressit. Si tribus adsuntis Domini diuiseris annos, Per ter quinque datur indicto certificata. Et hæc quidem de indictione, eiusque instituendæ ratione. INDVS sidus in Cælo ad polum Antarcticum, nobis inconspicuum à recensoribus vnà cum alijs vndecim detectum non ita pridem, atque in hominis indi formam, manu tenentis jaculum, figurarum: stellas habet 13. quintæ & sextæ magnitudinis sub signo Capricorni. 39. INFERNVS: & hic nostræ molitionis subiectum. Est enim Vniuersi istius centrum, (unde Isydoro dictus tanquam insus furnus, id est niger.) Locus omnium infimus, obscurus, & abiectissimus, in quem perinde arque in humano corpore visceræ, & vmbilicus, omnes mundi sordes, & retrimenta, tanquam in propriam sedem abijcienda sunt peracto finali iudicio, vt ex Basilio aduertit D. Thomas in 4. Sentent. distinct. 47. qu. 2. art. 5. Ea propter condignus dæmonum, & damnarorum carcer vbi perperuô morabuntur æternis ignibus addicti. Ex eo verus locus siderum procul quacumque parallaxis deuiatione, obseruari exquisitissimè posset, ni telluris densiras, obuiret. Lessius existimar eius diametrum non excedere vnius milliarj belgici mensuram: quippe, ait circumferentia eius tantæ amplitudinis erit, vt optimè capax esse possit rot millium corporum, quor planè vero similiter coniectari possumus, futuros esse damnatos. Putat enim eos ibi locandos post acceptam Iudicis senteniam illam Ite maledicti in ignem acernum, tanquam muriaricos pisces in dolio, ita vt aliter alterum premat, nec vllum aliud spatium sit, quod non corporibus repleatur. Franciscus Ribeta in Apocalyps. cap. 14 probabiliter coniectæ infernæ diametrum esse longam ducentis italicis milliaris,

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LEXICON 246 is Lustrum, because at that time the messengers coming from the provinces, to bring the tribute with great pomp and retinue, used to purify the city. In olden times this cycle of years began to be counted from the 24th day of September. Now, however, after the Gregorian correction, it begins from January. If anyone wishes, in whatever year it may be, to find the Indiction, he will easily do so in this way. To the years elapsed since the Nativity of the Lord, let him add three; then let him divide the product by five, and whatever remains from the quotient will be the indiction of that year. But if nothing remains, it will be a sign that in that year the indiction is 15 and the completion of the cycle. Thus, for example: in the current year 1660, I add 3, and becoming 1663, I divide the sum by 15, and there will result in the quotient 108, and still there will remain 13; this therefore will be the indiction of the present year. For the sake of memory, someone has expressed this in these verses: If you divide the years of the Lord that are added in threes, By three times five the indiction is given, duly certified. And this indeed concerns the indiction, and the way it is established. INDUS, a constellation in the sky near the Antarctic pole, invisible to us, discovered not long ago by observers together with eleven others, and figured in the form of a man holding a spear; it has 13 stars of the fifth and sixth magnitude under the sign of Capricorn. 39. INFERNUS: and here the subject of our work. For it is the center of this Universe, (whence, according to Isidore, it is so called as in furnus, that is, black.) The lowest, darkest, and most abject place of all, into which, just as in the human body the entrails and the navel, all the filth and refuse of the world must be cast after the final judgment has been carried out, as St. Thomas notes from Basil in 4 Sentences, dist. 47, q. 2, art. 5. For that reason it is the fitting prison of demons and the damned, where they will dwell forever, consigned to eternal fires. From it, the true place of the stars could most exactly be observed, free from any deviation of parallax, were it not for the density of the earth standing in the way. Lessius judged its diameter not to exceed the measure of one Belgian mile: for, he says, its circumference will be of such vast extent that it can very well be capable of holding so many thousands of bodies, as we can quite similarly conjecture the damned will be. For he thinks they are to be placed there after receiving the Judge’s sentence, “Go, accursed ones, into eternal fire,” like salted fish in a barrel, so that one presses upon another, and there is no other space left that is not filled with bodies. Franciscus Ribera, in his commentary on Apocalypse chapter 14, conjectures, probably, that the diameter of hell is two hundred Italian miles long,

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MATHEMATICVM: 347 atque ex eo deducit, quod ibi effusus dicitur sanguis laci iræ Dei ad stadia 1600. alij aliter opinantur: quæ res sanè difficilis est desiniri; cum id neque ex scripturis, neque ex Mathematicis obseruationibus colligi possit, sed pendeat ex meo conditoris beneplacito. Cæterum ibi tria sunt receptacula, vt communis SS. Patrum, & Ecclesiæ traditio est: quorum inferius, quod Mundi meditullium includit, damnatorum supplicio est destinatum; aliud, quod istud immediatè ambit, expiandis animabus ad Coelestem gloriam tandem migraturis addictum est: Tertium amplius, & spatiosius, qui Limbus SS. Patrum, & puerorum cum originali macula decedentium dictus est, vbi neque ignis, & fortassis neque tenebræ sunt, sed locus est valdè amoenus, aliquali luce ex terræ hiatibus transpirante perfusus, distarque à superficie terræ iuxta Bonardi obseruationes millarijs 37. 48. cum quadrante. < 40.> Porrò Inferni, & Purgatorij loca vero, atque elementari igne esse repleta, testantur sæpissimè sacræ paginæ, & communis omnium Catholicorum sensus. Vt videre est apud Bellarmin. 10m. 1. de Purg. lib. 2. cap. 11. & licet Damas. de fide Ortod. lib. 4. cap. 28. asserat Æternum ignem cum materia instar huiusce nostri constare: & D. Greg. Papa lib. 15. Moral. cap. 17. eum vocat incorporeum; tamen intelligendi sunt non quod eiusdem substantiæ, ac naturæ non sit: proindeque verè immaterialis, & incorporeus sit, sed quod corporeo pabulo non egeat vt conseruetur, neque materia, vt accendatur: cum alioqui idem Greg. lib. 4 Dialogorum cap. 29. percontanti Petro num ignis gehennæ sit corporeus an incorporeus, respondet Ignem gehenna corporeum esse non ambigo, in quo certum est corpora crucari. Vnde oporter amanuensium, vel librarium fuisse errorem quod in moralibus habetur, incorporeus, & verius scribi debuisse corporeum, vt habet idem Bellarm. ac D. Thomas, qui in 4. sentent. dist. 44. qu. 3. hunc locum citans ponit, corporeus: & latè explicat dictum Greg. & excusat Damascenum, inquens eum non negasse ignem inferni materialem esse quoad substantiam, sed quoad punitionis effectum, punit enim corpora spirituali quadam actione, cum ea nec dissoluat nec consummat, sed incorruptibiliter cruciet, & ipsas animas spirituales modo quodam ineffabili, & imperceptibili. Quod quomodo fiat varie, & late explicant Theologi, ad quos cum res nostra non intersit lectorem remitto. Est igitur absque dubio ignis gehennæ eiusdem rationis cum nostro, licet longè horribilior, ac potentior. Quinimò non defuere Philosophi, qui dicerent ignis sphæram, & locum illi connaturalem esse in Mundi centro, hoc est in Inferno; vel ex eo probantes, Q 111j

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MATHEMATICVM: 347 and from this he infers that there the blood of God’s wrath is said to have been poured out, for a distance of 1600 stadia. Others think differently: a matter which is truly difficult to determine, since it can be gathered neither from the Scriptures nor from mathematical observations, but depends on the good pleasure of my Creator. Moreover, there are there three receptacles, as is the common tradition of the holy Fathers and of the Church: the lowest of these, which encloses the middle of the world, is destined for the punishment of the damned; another, which immediately surrounds it, is assigned to souls to be purified and at last to migrate to heavenly glory; the third, larger and more spacious, is called the Limbo of the holy Fathers and of infants dying with original stain, where there is neither fire, and perhaps neither darkness, but a very pleasant place, bathed in some light transpiring through chasms of the earth, and distant from the surface of the earth, according to Bonardi’s observations, by 37 48/100 miles and a quarter. < 40.> Furthermore, the sacred pages very often testify, and the common sense of all Catholics holds, that the places of Hell and Purgatory are truly filled with elemental fire. As may be seen in Bellarmine, vol. 10, book 1, On Purgatory, chap. 11. And although Damasus, On the Orthodox Faith, book 4, chap. 28, asserts that the eternal fire is made up of matter like this our own, and St. Gregory the Pope, book 15 of the Morals, chap. 17, calls it incorporeal, nevertheless they must be understood not as if it were not of the same substance and nature, and therefore truly immaterial and incorporeal, but because it does not need bodily fuel in order to be preserved, nor matter in order to be ignited; since otherwise the same Gregory, book 4 of the Dialogues, chap. 29, when Peter asks whether the fire of Gehenna is corporeal or incorporeal, answers: “I do not doubt that the fire of Gehenna is corporeal, in which it is certain that bodies are tormented.” Hence it must have been a mistake of the copyists or scribes that in the Morals it is found as incorporeal, and it should more correctly have been written corporeal, as the same Bellarmine and St. Thomas have it, who, citing this passage in the 4th Sentences, dist. 44, q. 3, gives corporeal, and explains Gregory’s statement at length and excuses Damascene, saying that he did not deny that the fire of Hell is material as to substance, but as to the effect of punishment; for it punishes bodies by a certain spiritual action, since it neither dissolves nor consumes them, but torments them incorruptibly, and the spiritual souls themselves in some ineffable and imperceptible manner. How this takes place is explained by theologians in various ways and at length, and since the matter is not relevant to us, I refer the reader to them. Therefore the fire of Gehenna is undoubtedly of the same kind as ours, though far more dreadful and more powerful. Indeed, there have not been lacking philosophers who said that the sphere of fire, and the place naturally belonging to it, is in the center of the world, that is, in Hell; proving it either from this, Q 111j

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148 LEXICON quod in Macrocosmo, eum locum occupare debet, quem in Microcosmo vitalis calor, cui est iu corde, hoc est in hominis meditullio sedes. Tum quia ignis natura, inquiunt, est summè mobilis, & vndequaque diffugiens: debuit ergò habere locum in medio vniuersorum, vnde probè calorem suum vndequaque transfunderet, atque in arcta, vt ita dicam, custodia ita detineterur, vt non facilè dissipari posset. Ita discurrebant Pythagorici, quibus modò nonnulli recensionibus addicti sunt. <41.> Sed enim siue ignis Inferni ibi sit tanquam in propria, ac naturali sede, siue ex conditoris arbitrio (neque enim quod ab initio ab ipso naturæ authore constitutum fuit, ab ipso naturæ ordine alienum esse censendum est.) An autem adhuc lumine præditus sit magna est inter Theologos ac SS. Patres controversia. Negar Chrlsosthomus, Ambros. Theodoretus, Athanas. Cyrillus, Prosper Aquitanus, Basilius, Innocentius, & alij communiter. Affirmat autem Gregor. lib. 9 Moral. cap. 39. dicens illum non ad consolationem, sed ad maiorem terrorem lucere, luce tamen suboscura & nigricanre, quale est lumen tædarum quod potius terrorem incurit quam delectar: subscribit Isidorus lib. 4. de summo bono, cap. 31. inquiens Ignem gehenna ad aliquid lumen habere, & ad aliquid non habere, hoc est habere lumen ad damnationem, vt videant impij vnde doleant & non habere ad consolationem, ne videant, vnde gaudeant. Neque in hoc sunt contrarij Ambros. & Innocentius vbi supra, quorum posterior dicit inter alios damnatorum cruciatos vnam esse visionem dæmonum, qui videbuntur in excussione scintillarum de igne ascendentium. Et sanè si ignis ille naturalis, & corporeus est, illum ijsdem prorsus qualitatibus præditum, quibus noster iste visualis ignis est affirmare oporrer; nisi quod ibi maior actiuitas, maior vrendi vis, quam in hac relluris superficie, vbi aëris ambientis facilitate, ac frigore plurimum debilitatur. atque obtunditur (quod vide re est in elibano, alijsque vndique constipatis ignibus, qui potentiùs agunt quam reliqui.) Ob id, nil mirum, si subterranei ignes, & qui passim è montibus eructant, tam violenti sint, vt penè diuersæ ab nostro, speciei esse videantur, ob idque à nonnullis eiusdem rationis, atque infernalis esse credantur. Quod ego non detrectauerim; immò certo certius habeo, hos terræ hiatus, vnde passim videmus ignes erumpere aliud non esse quam Inferni spiracula, vnde ignis ille euaporat, & quandoque accensus eructat, & vicinas regiones deuastat. Tales sunt Sulphureæ Puteolorum venæ ignem, & sumum perpetuò erucentes: Vesuuius mons prope Neapolim: Æthna in Sicilia:

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148 LEXICON which, in the Macrocosm, ought to occupy the place that vital heat occupies in the Microcosm, which is in the heart, that is, in the center of man’s body. Then, because fire by nature, they say, is most mobile and everywhere diffusing itself, it ought therefore to have its place in the middle of all things, from which it might duly spread its heat everywhere, and be held, so to speak, in strict custody, so that it could not easily be dissipated. Thus the Pythagoreans reasoned, to whom now some are attached by revisions. <41.> But whether the fire of Hell is there as in its proper and natural seat, or by the will of the Creator (for what was established from the beginning by the author of nature himself is not to be judged alien to the order of nature), whether it is still endowed with light is a great controversy among theologians and the holy Fathers. Chrysostom, Ambrose, Theodoret, Athanasius, Cyril, Prosper of Aquitaine, Basil, Innocent, and others commonly deny it. But Gregory affirms it in book 9 of the Morals, ch. 39, saying that it shines not for comfort but for greater terror, yet with a somewhat dim and blackish light, such as the light of torches, which brings fear rather than delight; Isidore subscribes to this in book 4, On the Supreme Good, ch. 31, saying that the fire of Gehenna has light in one respect and not in another, that is, it has light for damnation, so that the wicked may see from what they grieve, and does not have it for consolation, lest they see from what they rejoice. Nor are Ambrose and Innocent contrary to this, as above, whose latter says that among the torments of the damned one is the sight of the demons, who will be seen in the scattering of sparks rising from the fire. And indeed, if that fire is natural and corporeal, it ought to be regarded as endowed with the very same qualities with which this visual fire of ours is endowed; except that there, greater activity and greater power of burning exist than on this surface of the earth, where it is greatly weakened and blunted by the ease and coldness of the surrounding air (as may be seen in the elibanon and other fires pressed in on all sides, which act more powerfully than the rest). For that reason, it is no wonder if subterranean fires, and those which everywhere burst forth from mountains, are so violent that they seem almost to be of a species different from ours, and for that reason are believed by some to be of the same kind as the infernal fire. I would not deny this; indeed I hold for certain that these openings in the earth, from which we see fires bursting out everywhere, are nothing other than the vents of Hell, from which that fire exhales, and sometimes, when kindled, erupts and devastates the neighboring regions. Such are the sulfurous veins of Pozzuoli, perpetually breathing forth fire and smoke: Mount Vesuvius near Naples: Etna in Sicily:

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MATHEMATICVM. 249 Arequipa in Peruano regno: Hecla mons in Islandia: Pittacia in Perside: alijque quos referunt Plinius, Maiolus & alij. Quod tum ratio naturalis suader, tum frequentissimæ historiæ; ac plurium Philosophorum auctoritas. Ratio, inquam, quia ignis quicumque naturaliter euaporare perit, & quoddam spi- raculum, vnde exhalare queat, & fumum traijcere, ergò id etiam infernali comperet, qui sanè per huiusmodi terræ hiatus exhalat. Accedunt historiæ. Refert enim Hentricus Kerman- nus in lib. de miræ. mortuor in Turingia apud montem Ferrariam exiare quandam voraginem, seu terræ hiatus, qui hor- risonus est, & communiter reputatur esse ostium quoddam In- ferni; eoquod sæpissimè ex eo audiuntur clamores, & vlula- tus animarum, & circa ipsum ignes quosdam apparere. Simi- le quid refer, Surius de Hecla Islandiæ monte, Pompilius Azzelus de rebus natural. lib. 5. cap. 16. Olaus magnus Saxo Gram- maticus. Brocardus, & alij multi. Claudianus etiam Poëta in Rufin. lib. 10. meminit cuiusdam loci in Hybernia, qui nunc creditur esse Vorago illa, quam idcircò vulgo appellant Pu- reum S. Patricij, vnde audiatur frequens luctus, & ciulatus ani- marum. Sic enim ait. Est locus extremum, qua pandit Gallialittus, Oceani prætextus æquis, quo fertur Vlysses, Sanguine libato populum meuisse silentum. Illæ vmbrarum tenui stridore volantium, Fiebilis auditur quasius simulachra coloni, Pallida, defunctasque vident migrare figuras. Huius rei ampliorem historiam, & quomodo precibus S. Patricij Hybernorum Apostoli ad aliquam infernalium tor- mentorum cognitionem populis ingerendam, vt à malis pa- trandis auocarentur, fuerit ei à Christo Domino sibi visibili- ter apparenre monstrata quædam spelunca rounda, & obscu- ra, quam qui ingrederentur referrent, ibi se immania tor- menta perpessos, & vidisse foucas quasdam, & ostia inferni, per quæ damnati proijciebantur: qui, inquam, huius rei vbe- riorem notitiam volet pluraque testimonia, videat Franciscum Restam de Meteoris lib. 1. Tract. 4. cap. 4. Denique in hanc sententiam inclinant, vel certè apertè ve- niunt mulii ex SS. Patribus, Augustinus, Gregorius, Bernar- dus, Isidorus, Tertullianus, Bonaueniura, Perrus Damianus, Bernardinus Senensis, & alij. Vt iam modò nonnihil temeri- tatis habeat affirmare huiusmodi igniuomos montes, & antra non esse Inferni ostia, & ignis ibi existentiis euaporamenta si non ad aliud, certè ad hoc vnum ab Aushore Naturæ in varijs terreni orbis locis aperta, vt homines inde ediscerent, leo est-

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MATHEMATICVM. 249 Arequipa in the kingdom of Peru; Mount Hecla in Iceland; Pittacia in Persia; and others mentioned by Pliny, Maiolus, and others. This is supported both by natural reason and by the very frequent histories, as well as by the authority of many philosophers. Reason, I say, because any fire that naturally tends to evaporate, and that has some vent through which it may exhale and send forth smoke, therefore also, it seems, has such a vent in the infernal regions; and indeed it exhales through openings of the earth of this kind. Histories are added to this. For Henricus Kermannus relates in his book De miris mortuorum that in Thuringia, near Mount Ferrariam, there is a certain abyss, or opening in the earth, which is dreadful, and is commonly thought to be a certain gate of Hell, because from it are very often heard cries and howlings of souls, and around it certain fires appear. A similar account is given by Surius of Mount Hecla in Iceland, Pompilius Azzelius in De rebus naturalibus, book 5, chapter 16, Olaus Magnus, Saxo Grammaticus, Brocardus, and many others. The poet Claudian also, in Rufinus book 10, mentions a certain place in Ireland, which is now believed to be that abyss which the common people therefore call the Well of Saint Patrick, from which is heard the frequent lamenting and wailing of souls. For thus he says: There is a place, where the farthest world opens, where Gallia lies, Over the waters of the Ocean, where Ulysses is said to have gone, After blood was offered, and the silent people moved. The shadows of those flying with a faint rustling, The image of the mournful peasant is heard, Pale, and the dead forms are seen to depart. For a fuller history of this matter, and how, through the prayers of Saint Patrick, Apostle of the Irish, for the purpose of imparting to the people some knowledge of the torments of hell, so that they might be turned away from evil deeds, there was shown to him by Christ the Lord, visibly appearing, a certain round and dark cave, which those who entered reported to have suffered there immense torments, and to have seen certain pits and gates of hell through which the damned were cast in: whoever wishes for fuller knowledge and more testimonies on this matter should consult Franciscus Resta, De Meteoris, book 1, tract 4, chapter 4. Finally, many of the Holy Fathers incline to this opinion, or certainly openly come to it: Augustine, Gregory, Bernard, Isidore, Tertullian, Bonaventure, Peter Damian, Bernardino of Siena, and others. So that now it has somewhat of rashness to affirm that such fire-breathing mountains and caves are not the gates of Hell, and that the exhalations of the fire there existing were opened by the Author of Nature in various places of the earth, if not for any other purpose, certainly for this one: that men might learn from them, ...

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LEXICON 250 cum vbi impiorum animæ post mortem puniuntur, sicque 2 pattandis cui minibus arceantur, quod & Pythagoras, quamuis Ethnicus intellexit inquiens ignes hos subterraneos cruciare animas improborum. 42. INFORTUNA dicitur Planeta maleficus Saturnus, qui nuncupatur infortuna maior, & Mars infortuna minor; eo quod loca in quibus reperiuntur, infortunent. Similiter infortuna dicitur quicumque alius planeta qui ab istis infortunetur. Vide in V. Fortuna. 43. INGENICVLVS, Hercules, Engonasis: sidus in Cælo ad Borealem plagam, hominem repræsentans, qui dextro genu nixus, sinistrò pede draconis Caput opprimere videtur. Continet stellas 19 de quibus diximus sub V. Engonasis. 44. INGRESSVS apud Astronomos, præsertim Ptolem. cap. vls. Quadrupartem, significar familiaritatem quandam, quam sidera quotidianis lationibus, præsertim in annua revolutione acquirant, cum locis directionis, seù radicalibus tum sui, tum aliorum Prorogatorum Quandoquidam ingressus beneficarum semper præsunt vt benè aduertit Titus in cælesti Philosophia lib 3. cap. 11. maximè in conuenienri familiaritare maleficarum semper obsunt. Præcipuè verò ingressus valent ad eliciendos ad actum effectus illos, qui sunt in potentia proxima præordinati per motum directionis, si modo effectus sint naturæ suæ conformes: sin minus illos retatdant, aut diminuunt. Sunt aurem ingressus in duplici differentia, vt idem Titus obseruat: alij actiui qui fiunt à stellis actiuam virtutem habentibus, quando ingrediuntur aut corpore, aut radio loca directionum, & progressuum moderatorum; nam tunc agit in ipsos moderatores: alij passiui, qui fiunt ab ipsis moderatoribus, Sole videlicet, Luna, ascendente, medio cæli, ac fortunæ parte, quando ingrediuntur ad familiaritates locorum directionis, & progressuum Astrorum omnium quæ virtutem actiuam habeant: tunc enim ipsi Prorogatores patiuntur vt ita dicam ab Astris, & recipiunt effectus illorum. Porrò quos effectus habeant in hisce inferioribus ingressus tam actiui, quam passiui, ingeniosissimè explicat Titus loco cirato. 46. INTERLVNIUM dicitur tempus illud, quo Luna siler: hoc est sub radijs Solis existens à nulla nobis parte conspicua sit, sed supernè tantummodo in parre Soli oburia illustratur: quod quidem tempus complectitur aliquid Lunæ veteris, & aliquid nouæ; cum vetus, anequam Soli iungatur corpore, ad ipsum accedens non amplius apparet; & noua ab ipso recedens non adhuc conspicua est. Interlunij tempore si sata serantur ea non esse vermiculis obnoxia testatur Plin. lib. 18. cap. 17.

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LEXICON 250 when the souls of the impious are punished after death, and so they are kept away from the said losses; which also Pythagoras, though a pagan, understood, saying that these subterranean fires torment the souls of the wicked. 42. INFORTUNA is the name given to the malefic planet Saturn, which is called the greater infortune, and Mars the lesser infortune; because the places in which they are found bring misfortune. Likewise, any other planet is called an infortune when it is made unfortunate by these. See under V. Fortuna. 43. INGENICVLVS, Hercules, Engonasis: a constellation in the sky toward the northern region, representing a man who, supported on his right knee, seems to be pressing down the Dragon’s Head with his left foot. It contains 19 stars, of which we spoke under V. Engonasis. 44. INGRESSVS, among astronomers, especially Ptolemy, cap. vls. Quadrupartem, signifies a certain familiarity which the stars acquire through their daily motions, especially in the annual revolution, with the places of direction, or radical places, both of themselves and of other prorogators. For some in- gressions of the benefic planets always preside, as Titus rightly notes in Celestial Philosophy, book 3, chap. 11, while those of the malefic planets are always harmful in an especially unsuitable familiarity. But ingressions are chiefly effective in drawing into act those effects which are in proximate potentiality, previously ordained by the motion of direction, provided that the effects are in accordance with their own nature; if not, they delay or diminish them. There are, however, ingressions of two kinds, as the same Titus observes: some active, which occur from stars having active virtue, when they enter, either by body or by ray, the places of directions and regulated progressions; for then they act upon those regulators themselves: others passive, which occur from the regulators themselves, namely the Sun, Moon, Ascendant, Midheaven, and Part of Fortune, when they enter into the familiarities of the places of direction and of the progressions of all stars that have active virtue; for then the prorogators themselves, so to speak, suffer from the stars and receive their effects. Moreover, what effects these active and passive ingressions have in these lower things, Titus explains most ingeniously in the cited passage. 46. INTERLVNIUM is the term for that time when the Moon is silent; that is, when, being under the rays of the Sun, it is visible to us from no side, but is illuminated only from above on the part facing the Sun: and this period includes something of the old Moon and something of the new; for the old Moon, before it joins the Sun bodily, as it approaches him, no longer appears, and the new Moon, receding from him, is not yet visible. Pliny, book 18, chap. 17, testifies that seeds sown during the time of the interlunar period are not subject to worms.

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MATHEMATICVM. 251 < 47.> INTERROGATIONES, seù Quæstiones Astrologicæ dicuntur quæ ex naturali, vt aiunt impulsu de re aliqua, fiunt Astrologo coniectori, vt inde is ex figura cæli ad momentum quæstionis erecta prædicat, quid de tali re futurum sit. De ijs multa vanè scripserunt Arabes, & Iudæi, quos inter ex professo Hali Aben-Ragel, & Guido Bonatus. Non nulla etiam verba ad hanc rem habet Ceniloquij Author, vt vel inde euidenter appareat, non esse id Ptolemæi opus, qui in nullo suorum operum eas vnam admisit, aut admisisse videtur. Et quidem si si qua est in rebus Astrologicis vaniras, & dementia, hæc summum apicem tenet. Neque enim naturalis ratio elucer, quomodo cum fortuiro interroganris occursu connexionem vllam habeat cæli positus; quomodo hic & rem futuram indicet, & interrogantem ad sciscitandum impellat; vt benè discutrit Titus in cælesti Philosophia lib. 1. cap. 6. Namque, sit ipse, res sururæ habent naturales suas causas dependentes à radice Natalis, vel à diurnisationibus, quæ non cohærent cum præsenti siderum habitudine, quæ mouet nolsta phantasmatæ opus est enim, vt inter signa, & res significatas sit aliqua connexio. Denique explicari non potest quomodo ex eadem cæli figura ad momentum factæ interrogationis erecta prædici vni ex præliantibus, aut dimicantibus mors, alteri victoria; si profectò eodem tempore, & in ijsdem circumstantijs ab ambobus fiat interrogatio. Sed hanc vanitatem fusè imbrobat Cardanus non vno in loco suorum operum. Maius sanè fundamentum habent Electiones in certo siderum positu factæ, quippe quæ nec ratione, neque experimentis carent. Sed & hæ quoque cum radice natuitatis conferendæ sunt, & inde, vt feliciter exeant aggrediendæ. < 48.> INVERSARIF apud Arabes est oppositum Mutatil, cum videlicet Planera existens in corde alterius, & agglutinatus ei vsque ad minutum sepatatur ab eo vel ad gradum vnum. Ptolemæus in versione Arabica Hali Rodoan. IR < 49.> IRIS Græcè denotat arcum illum cælestem, qui aduerso Sole formatur in nube roscida, vel in minutissimis aquæ cadentis guttulis, in quibus tanquam in speculo excipiantur solares radij, in orbem diffusi, ac miram illam repræsentent colorum varietatem sua specie mentes hominum præstringentem, atque in Dei laudem trahentem. Vnde Eccl. 41. dicitur Vide arcum & benedice Deum qui fecit illum: valde spectosus est in splendore suo. Hinc etiam antiquis Thaumantias, hoc est admi-

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MATHEMATICVM. 251 < 47.> INTERROGATIONS, or what are called Astrological Questions, are those which, from a natural impulse, as they say, about some matter, are made to the astrologer-judge, so that from the figure of the heavens erected for the moment of the question he may predict what will happen concerning such a matter. The Arabs and Jews wrote many foolish things about these, among whom especially Hali Aben-Ragel and Guido Bonatus. The author of the Ceniloquium also has certain words on this matter, so that it may be clearly apparent from that alone that this is not the work of Ptolemy, who in none of his works admitted such things, nor does he seem to have admitted them. And indeed, if there is any vanity and madness in astrological matters, this holds the highest place. For no natural reason appears by which the position of the heavens should have any connection with the chance occurrence of the questioner; how it should indicate both this and a future event, and impel the inquirer to ask; as Titus discusses well in Celestial Philosophy, book 1, chapter 6. For, if it be so, future things have their natural causes depending on the root of the nativity, or on daily variations, which do not agree with the present condition of the stars, which moves our imagination; for it is necessary that there be some connection between the signs and the things signified. Finally, it cannot be explained how, from the same figure of the heavens erected for the moment when a question is asked, it can be predicted to one of two combatants or fighters death, to the other victory, if indeed the question is asked by both at the same time and in the same circumstances. But Cardan refutes this vanity at length in more than one place in his works. Electiones made in a fixed position of the stars certainly have a better foundation, since they lack neither reason nor experience. But these too must be compared with the root of nativity, and from there, if they are to succeed, they must be undertaken. < 48.> INVERSARIF among the Arabs is the opposite of Mutatil, namely when a planet, existing in the heart of another, and glued to it up to a minute, is separated from it by one degree or more. Ptolemy in the Arabic version of Hali Rodoan. IR < 49.> IRIS in Greek denotes that heavenly bow which is formed opposite the Sun in a dewy cloud, or in the tiniest drops of falling water, in which, as in a mirror, the sun's rays are received, spread in a circle, and represent that wonderful variety of colors, striking the minds of men by their appearance and drawing them to the praise of God. Hence in Ecclesiasticus 41 it is said: Look upon the rainbow and bless God who made it: it is very beautiful in its splendor. Whence also among the ancients it was called Thaumantias, that is, admi-

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252 LEXICON rationis Filia dicta est, ac Deorum nuncia credita. Formatur autem duo tempore siue à Sole, siue à Luna (licet hæc rarò admodum iridem faciat, eamque vnius coloris, & semper albicantem) per refractionem solarium radiorum in dicta nube caua, & ex parte diaphana, ex parte autem opaca, vnde pro diuersitate incidentiæ radiorum causetur diuersitas illa apparentiæ, & colorum. Vt plurimum autem in solari Iride tres colores apparere solent. Puniceus, viridis & purpureus: & quidem ex parte arcus exteriori, puniceus, ex parte interiori purpureus, mediùs autem viridis; quia cum in parte extima sit minor opacitas, sit color flauus, seu puniceus: econtrà quia in parte interiori est maxima opacitas sit color purpureus: in medio verò, quia est moderata opacitas, ideò radij solares coeunt in colorem viridem. Et quoniam solares radij in orbem diffunduntur, ideò orbicularis est colorum apparentia: semper autem in Solis opposito; itavt centrum arcus sit ex diametro oppositus centro Solis. Et idcircò numquam apparer nisi semicirculus; & quò sol depressior est, & horizonti proximior, eò maiorem arcum efformat, & contrà quò elatior eò minorem. Hinc ferè semper cum se præbet Iris inspiciendam, id sit matutino, vel vespettino tempore. In meridie verò ferè numquam, nisi fortè in hyeme, quo tempore sol humilis valdè est, & magis horizonti, quam vertici nostro proximus, vnde & visibilem arcum efformare potest. Immò & quandoque accidit, vt Sole in linea meridiana existente dux, & quandoque plures Irides hinc inde Orientem versus, & Occidentem formentur, licet ex valdè debiles, ac depressæ, si videlicet dux nubes hinc inde eauæ, & vdae solatibus radijs illustrentur Eius præsagia apud rusticos refert Cælius Rhodiginus in hæc verba. Si enim, inquit, fuere color rubeus in albente, fertilitatem præsignat, quia salis color sit ex materia raritate; rara autem materia a Sole facilè resoluitur, & ideò non sequuntur copiosa pluuæ quibus agrorum ferætas nimium impeditur. Quando color viridis maior est reliquis significat oleo, & oliuorum ubertatem. Denique cum color puniceus vicerit, frumenti copiam; cum purpureus, reliquorum fructuum, polli etur. Hucusque Cælius. Mizaldus arcanorum lib. 2. ex Plin. & Ruell. refert arbores fieri odoratiores si in eas apparens Iris incubuerit Cæterum generaliter Iris est serenitatis index, vel etiam pluuæ mox futuræ pro temporum diuersitate. Nam si matutino tempore appareat, & non præmissa pluuia, significat solem incipere iam resolutionem nubium, quam necessariò pluuia comitatur: econtra si vespertino tempore, & post pluuiam indicat solem nubium resolutionem perficere, & complere, quam mox serenum tempus con-

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252 LEXICON called the daughter of Reason, and believed to be the messenger of the gods. It is formed, at both times, either by the Sun or by the Moon (though the latter very rarely produces a rainbow, and then one of a single color, always whitish), through the refraction of the sun’s rays in the said cloud, hollow and partly transparent, partly opaque; whence, according to the diversity of the rays’ incidence, that diversity of appearance and colors arises. Usually, however, three colors are seen in the solar rainbow: crimson, green, and purple. And indeed, on the outer part of the arch, crimson; on the inner part, purple; and in the middle, green. For since the opacity is less in the outer part, the color is yellowish or crimson; on the contrary, because the opacity is greatest in the inner part, the color is purple; but in the middle, because the opacity is moderate, the sun’s rays combine into a green color. And because the sun’s rays are spread in a circle, therefore the appearance of the colors is circular; and it is always opposite the Sun, so that the center of the arch is diametrically opposite the center of the Sun. And therefore it never appears except as a semicircle; and the lower the sun is, and the nearer it is to the horizon, the greater an arc it forms, and conversely the higher it is, the smaller. Hence it is almost always when the Rainbow presents itself to be seen, that is, in the morning or in the evening. At midday, however, almost never, unless perhaps in winter, when the sun is very low and closer to the horizon than to our zenith, whence it can also form a visible arc. Indeed, it sometimes happens that when the Sun is in the meridian line, two, and sometimes more, rainbows are formed here and there toward the East and the West, though very weak and low, namely when two hollow and wet clouds here and there are illuminated by the sun’s rays. Its omens among rustics are related by Caelius Rhodiginus in these words: “If,” he says, “a red color appears in a whitish one, it presages fertility, because a salty color is from rarity of matter; but rare matter is easily dissolved by the Sun, and therefore no heavy rains follow, by which the fruitfulness of the fields is greatly hindered. When the green color is greater than the others, it signifies abundance of oil and olives. Finally, when the crimson color prevails, abundance of grain; when the purple, of the remaining fruits.” So far Caelius. Mizaldus, in book 2 of the Arcana, citing Pliny and Ruellius, reports that trees become more fragrant if a rainbow appears to rest upon them. Moreover, generally, the rainbow is an indicator of fair weather, or also of rain soon to come, according to the variation of the seasons. For if it appears in the morning and no rain has preceded it, it signifies that the sun is beginning the dissipation of the clouds, which necessarily is accompanied by rain; on the other hand, if it appears in the evening and after rain, it indicates that the sun is completing and finishing the dissipation of the clouds, after which fair weather will soon con-

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MATHEMATICVM. 253 Tequitur. Vnde ab ipsomet Conditore Deo post diluuum po- sita est in signum serenitatis, & foederis, inter ipsum & homi- nes, ne deinceps aquis diluuij peiderer omnem carnem. Quod quidem mysticè explicat de Christi humanitate Iacobus Episcopus Christopolitanus in expositione Cantici Habacuc in illa verba suscitans suscitabis arcum suum, iuramenta tribubus, quæ loquutus es. < 52.> Dices, qualiter Deus Pater sit instar Solis fontis, & principij omnis lucis diuinitatis, qui debebat imprimere imaginem suam in nube humanitatis, id est mittere filium suum, qui est imago Patris in carnem; qui debebat lasere in nube humanitatis: in qua persona sunt tres substantia, scilices Verbum, Anima, & Caro, ex quibus constituitur vnica persona sub vnico esse perso- nali, & diuino. Qui quidem arcus diuinus debebat fugare omnem tempestatem, & totum diluuium peccatorum, & sedare omnes te- nebras veteris pactis, & inducere lucem, & serenitatem grata. Ad quem arcum sapiens pater non amplius debebat recordari ve- teris pacti: immò Deus respiciens illum arcum qui est filius incarnatus, illiscò recordatur foederis promissi inter ipsum, & genus humanum. Et sic Pater respiciens illum arcum in cruce recordatus foederis promissi remisit pactum toti generi humano. Hucusque Episcopus Christopolitanus piè quidem, & eruditè nimis. Sed longè à nostro instituto aberrauimus. Hæc sufficiant. IRINA Virgarum speciés apud Arist. ab Inde dicta pluuix certum præsagium: de qua vide in V. Virga. < 53.> I S ISARITHMI Græcè significant prima numerorum elementa quæ in decem figuris continentur, quas nos in V. Abaculi ex- < 54.> plicauimus ab isæq, quod initium, & rythmos qui numerum denotat, deriuatum. Porro Isorythma numero paria significat, ab Iso, quod est æquale. Hiuc Isomaros dicitur quod æquales continet partes. Sic ISAGONIVS est figura Geometrica æqualibus angulis con- < 55.> stans. ISOPERIMETRÆ figuræ, quæ æqualem habent circumfe- < 56.> rentiam, & his similia pari ratione. ISOMÆRINOS sæpissimè apud scriptores Græcanicos dici- < 57.> tur Æquator, & Circulus æquinoctialis, eoquod æquet diebus noctes, & æquales diuidatur in partes. Iis etiam Græcè præcipuè apud Hermetem dicitur stella < 58.> fixa in Canis aure sinistra. At Auieno audit Virginis sidus. ISOSCELES est figura Geometrica triangularis, quæ duo tan- < 59.> tum latera habeat æqualia, tertium vetò neutro æquale, sed aut

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MATHEMATICVM. 253 follows. Hence, by God himself the Creator after the flood it was placed as a sign of serenity and of the covenant between himself and men, so that thereafter all flesh should not perish by the waters of the flood. This is mystically explained concerning Christ’s humanity by James, Bishop of Christopolis, in the exposition of the Song of Habakkuk, in those words, “raising thou shalt raise his bow, the oaths to the tribes which thou hast spoken.” <52.> You will say, how God the Father is like the Sun, the source and beginning of all light of divinity, who ought to impress his image in the cloud of humanity, that is, to send his Son, who is the image of the Father, into flesh; who ought to shine in the cloud of humanity: in which person there are three substances, namely Word, Soul, and Flesh, from which one person is constituted under one personal and divine being. This divine bow was to drive away every storm, and the whole flood of sins, and to quiet all the darkness of the old covenant, and to bring in light and pleasing serenity. Concerning this bow the wise father was no longer to remember the old covenant; rather God, looking upon that bow, which is the incarnate Son, immediately remembers the promised covenant between himself and the human race. And thus the Father, looking upon that bow on the cross, remembered the promised covenant and remitted the compact to the whole human race. Thus far the Bishop of Christopolis, piously indeed, and too learnedly. But we have wandered far from our subject. Let these things suffice. IRINA, a species of rods, so called by Aristotle from rain, a certain presage; see under V. Virga. <53.> I S ISARITHMI in Greek signify the first elements of numbers, which are contained in the ten figures, which we explained in V. Abaculi <54.> deriving from isæq, meaning beginning, and rythmos, which denotes number. Moreover, isorythma signifies numbers equal, from iso, which means equal. Hence isomaros is said, because it contains equal parts. Thus ISAGONIVS is a geometrical figure consisting of equal angles. <55.> ISOPERIMETRÆ are figures which have an equal circumference, and things similar to these in the same way. <56.> ISOMÆRINOS is very often called by Greek writers the Equator, and the equinoctial circle, because it makes the days equal to the nights, and is divided into equal parts. <57.> Also among the Greeks, especially in Hermes, it is called the fixed star in the left ear of the Dog. But in Avienus it is called the Virgin’s star. <58.> ISOSCELES is a triangular geometrical figure, which has only two sides equal, but the third equal to neither, but either

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254 LEXICON maius, aut minus: Angulos autem duos æquales omninò ha- bere debet, reliquum, aut obtusum, aut certè alijs duobus ma- gis acutum. Vnde est, quod duæ species Trianguli Iosceles dari possint, alterum, cuius tertium latus sit reliquis duobus maius, sicque reliqua duo, cum se tangunt efforment angulum obtusum: alterum, cuius latus tertium sit minus vtrouis æqua- lium, sicque ista desinant in augulum magis acutum. Vide de- monstrationes apud Euclidem. IV 60. IVGVLÆ sidus in Cælo, quod notiore vocabulo dicitur Orion stellas habens 38. de quo suo loco. Dictum à Lugulo, quod præ- seferre videntur tres stellæ constitutæ in medio, & supra duas alias satis claras, quas Orionis humeros nuncuparunt. Hinc Plaut. in Amph. Orionem intelligens, Neque Lugula, inquit, neque Vesperugo, neque Vergilæ occidunt. Propriè verò, & magis strictæ Lugularum nomine veniunt tres stellæ in cingulo Orio- nis consistentes in linea recta ad æquatorem, secundæ magni- tudinis, quatum quæ ad Austrum declinat, habet naturam Sa- turni, & Veneris; reliquæ dux sint de natura eiusdem Satur- ni, & Iouis. Sunt stellæ tempestuosæ quæ ventos mouent ful- gura, & tonitrua. De ijs exouentibus in alicuius Natiuitate Pontanus in Vrania dicit, quod faciunt Venatorem, Militem strenuum, maximè si Mars aspexerit, & Iupiter benigno radio affulserit. Fæmina etiam sub Iugulis nata erit ferox, intrepi- da, venationi, & armis addicta. Tantum adeò Lugularum ortus per tela, cruoremque In siluis, in speluncis, & in æquore saure. Si Saturnus malè aspexerit, portendit naufragium, & diram mortem in somnis. Occidentes verò cum Marte posito propè Asellos maiota portendunt mala, & funestissimum exitum. Ac si Mercurius, & Luna hæc loca insederint, morietur placida morte in somnis. 61. IVGVLÆ etiam apud Manilium dicuntur duo Aselli in pecto- re Cancri consistentes, de quibus suo loco dictum. 62. IVGVM Ptolemæo & Cicerone dicitur Libræ sidus; nesci- mus qua ratione. 63. IVPITER olim Iouis à iuuando dictus quasi Iuuans Pater. Planeta masculinus, ac diurnus vnsus ex septem eraticis stellis proximè suprà Martem sub Saturno collocatus: à nobis enim cum longius absit, atque inter duo extrema & frigoris & ca- liditatis constiturus, neque exsiccatè, neque excalefacere ni- mium potest, quinimò eorum excessiua qualitates obtundit, ipseque interim caliditatem, humiditatemque moderatam fa- cit, quæ ad vitæ munia obeunda apprimè idonea sunt. Patitur

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254 LEXICON greater or less: it must have exactly two equal angles; the remaining one must be either obtuse, or certainly sharper than the other two. Hence it follows that two kinds of isosceles triangle may be given: one, whose third side is greater than the other two, so that those two, when they meet, form an obtuse angle; another, whose third side is less than either of the equal sides, so that these end in a sharper angle. See the demonstrations in Euclid. IV 60. IUGULAE is a star in the sky, which by a more familiar name is called Orion, having 38 stars; of which in its proper place. It is so called from Lugula, because three stars placed in the middle, and above two other rather bright ones, which they have named the shoulders of Orion, seem to carry it. Hence Plautus, in Amphitruo, speaking of Orion, says: “Neither Lugula, nor Vesperugo, nor the Vergiliae set.” But properly, and more strictly, under the name of the Lugulae are included the three stars standing in the girdle of Orion in a straight line toward the equator, of the second magnitude; insofar as that which declines toward the South has the nature of Saturn and Venus; the remaining two are of the nature of Saturn and Jupiter. They are tempestuous stars, which stir up winds, lightning, and thunder. Concerning those rising in someone’s nativity, Pontanus in Urania says that they make a hunter, a valiant soldier, especially if Mars looks upon them, and Jupiter shines with a favorable ray. A woman also born under the Iugulae will be fierce, fearless, devoted to hunting and arms. So greatly indeed do the rising of the Iugulae, through weapons and bloodshed, In forests, in caves, and on the sea. If Saturn has looked upon them unfavorably, it portends shipwreck and a dreadful death in sleep. Their setting, however, with Mars placed near the Asses, portends greater evils and a most disastrous end. And if Mercury and the Moon have occupied these places, one will die a peaceful death in sleep. 61. IUGULAE are also said by Manilius to be the two Asses situated in the breast of Cancer, of which mention has been made in its proper place. 62. IUGUM is called by Ptolemy and Cicero the star of Libra; we do not know for what reason. 63. JUPITER was once called Jovis from iuvando, as though “helping Father.” The masculine and diurnal planet, one of the seven wandering stars, placed nearest above Mars and below Saturn: for as it is farther from us, and situated between the two extremes both of coldness and of heat, it is able neither to dry out nor to heat excessively; rather, it moderates their excessive qualities, and in the meantime itself produces a moderate warmth and moisture, which are especially suited to carrying out the tasks of life. It suffers

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MATHEMATICVM. 155 Eclipsim à Sole, à Luna, & à Marte: à reliquis minimè occultatur. Complet-circuitum suum in annis 12. & diebus ferè 312. habens pro Centro solem, vt Tycho diligentissimus Astronomus obseruauit. Obseruatæ sunt non ità pridem à Galilæo primùm, mox ab alijs ope Telescopij aliæ quatuor stellulæ circa Iouem illum comitantes, atque assidua vertigine constipantes; quippe aliquando ab eo remouentur, aliquando magis approximantur, aliquando etiam modò omnes, modo aliquæ sub eius corpore occultantur, quod indicio est, ipsas moueri in Epicyclo circa ipsum: nec quidem æqualiter; nam primam, & viciniorem obseruatum est complere circuitum circa Iouem die vno, & hor. circitet 18. secundam diebus tribus cum horis ferè 13. tertiam diebus 7. & hor. 4. quartam tandem diebus sexdecim, cum horis 18. quæ & ipsæ illuminantur à Sole non secus ac corpus Iouis, atque eclipsantur ab ipso Ioue, quando interponitur inter ipsas, & Solem, qui proptereà ad ipsas nequit lucem suam transmittere. Eclipsantur etiam quoad nos, quando videlicet Iupiter se interponit inter ipsas, & nostrum obtutum; sicut etiam quando ipsæ immediate sub Ioue constituuntur videri nequeunt ob nimiam Iouis claritatem. Has stellas Iouis comites Galilæus primus detector Mediceis Etruriæ Principibus dedicauit, atque ab ijs mutuato nomine. Mediceas appellauit. At enim verò ipsum Iouis corpus obseruatum est, non esse vndequaque clarum, sed habere duas maculas instar Zonarum, quibus circumuoluatur, quæ quoniam modò rectæ, modò transuersæ apparent, argumento sunt, ipsum Iouis corpus in gyrum rotari, quemadmodum de Sole, in Rosa Vrsina, aliisque planetis alibi dicitur. Cæterum quoad significata, Iupiter denotat prudentiam, temperantiam, liberalitatem, magnanimitatem, modestiam, mansuetudinem, &c. Præest viris Ecclesiasticis, Prælatis, Episcopis, Aduocatis, Religiosis, Nobilibus, Præfectis Prouinciarum, &c. Ex membris humanis dominatur Iecori, sanguini, pulmoni, tactui, carni, iccorisque humoribus. Morbos inducit, qui ex flatibus fætore, ante sanguinis putrefactione oriuntur: vt pleuram, Cardiacam, Anginam, Apoplexiam, spasmum, siue conuulsionem, & stuporem, inflammationes hæpatis, dolorem capitis, & similia. IX IXIONIS ROTA dicitur ab aliquibus Corona Australis, fidus ad australem plagam tredecim stellas habens conspicuas in longitudine sub signo Libræ, de qua satis abundè discimus suo loco.

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MATHEMATICAL. 155 An eclipse by the Sun, by the Moon, and by Mars; by the rest it is scarcely occulted. It completes its circuit in 12 years and about 312 days, having the Sun for its center, as Tycho, the most diligent astronomer, observed. Recently there have been observed by Galileo first, and soon after by others with the aid of the telescope, four other little stars accompanying that Jupiter and clustering about it in constant rotation; for sometimes they are removed from it, sometimes brought nearer, sometimes indeed all, sometimes some of them, are hidden under its body, which is an indication that they move in an epicycle around itself; nor indeed equally, for the first and nearest has been observed to complete its circuit around Jupiter in one day and about 18 hours. The second in three days with about 13 hours. The third in 7 days and 4 hours. The fourth at last in sixteen days, with 18 hours. These too are illuminated by the Sun no differently than the body of Jupiter, and are eclipsed by Jupiter himself, when he is interposed between them and the Sun, who therefore cannot transmit his light to them. They are also eclipsed in relation to us, when namely Jupiter is interposed between them and our sight; just as also when they are placed immediately beneath Jupiter they cannot be seen because of the excessive brightness of Jupiter. Galileo, the first discoverer of these stars, the companions of Jupiter, dedicated them to the Medici, Princes of Etruria, and named them Medicean after the name borrowed from them. But indeed the body of Jupiter itself has been observed not to be uniformly bright, but to have two spots like zones, with which it is encircled, and since these now appear straight, now transverse, it is a sign that the body of Jupiter itself rotates in a circle, just as is said elsewhere of the Sun, in the Rosa Ursina, and of other planets. As for significations, Jupiter denotes prudence, temperance, liberality, magnanimity, modesty, gentleness, etc. He rules over ecclesiastical men, prelates, bishops, advocates, religious, nobles, provincial governors, etc. From the human members he rules the liver, blood, lungs, touch, flesh, and the humors of the liver. He brings on diseases which arise from vapors with stench, before putrefaction of the blood: such as pleurisy, cardiac disease, angina, apoplexy, spasm, or convulsion, and stupor, inflammations of the liver, headache, and the like. IX The WHEEL OF IXION is called by some the Southern Crown, a fixed star having thirteen conspicuous stars toward the southern region in longitude under the sign of Libra, of which we learn enough in its proper place.

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LEXICON K. 1. KABAR, seu Elkabar Elscheer Chaldaice Latinè Canis maior sidus, ita Kircherus in Oedipo. 2. KACHITICHI Græcè Latinè interpretatur Mala fortuna. Apud Astronomos hac notione signarut sexra domus ab Horoscopo cadens ab angulo Imi Cæli, locus infælix, & omnium iocorum cæli abiectissimus: quippequi, & cadens, & suberraneus, & nulla familiaritate cum horoscopo copularur. Ideò ex ea sumuntur significaciones de nari valetudine, infirmitate, sururis morbis, ac vitijs corporis, alijsque malis bonam corporis constitutionem, ac temperiem infestantibus. Significar eriam seruos, ancillas, animalia minora, & commoda, vel incommoda, quæ inde perceprurus sit natus. Habet debilitatis quatuor parres: colorem sibi vendicat nigrum, & gaudet in ea Mars. KALB. Arabicè idem sonat, ac meditullium, penetralia, 3. Cor. Vnde Kalb Alarrab idem valet, ac Cor scorpij. Kalb Alpharad, ac Latinè cor hydræ. Kalb Eleced, Cor Leonis, & sic discurre. Quorum omnium naturam & qualitates siquæris vide sub propijs nominibus. 4. KAYTOS vel cum articulo Elkaytos Arab. idem sonat ac Latinè Cerus, balena, &c. sidus in australi plaga continens apud Ptolemæum stellas 22 apud Keplerum 21. & apud Bayerum 27. in eo præcipuà Natis, quæ etiam Mandibula dicitur, Arab. Menchar: Tum Lucidior, & australior in cauda dicta Deneb Kaytos: tandem media in Venre, Baten siue Bara-Kaytos omnes de natura Saturni. 5. KALVROPS, seu Alkaluops. Arab. dicitur hastile Bootis stella fixa de qua in V. Ceginus. 6. KENEN SATVRNI dicitur in sphæra barbarica, tertius Decanus Sagittarij manens sub dominatu Saturni, habensque significare obstinacionem in proposito contradicendi, dexteritatem in malis rixis, & factis abominabilibus. 7. KERTHO Chaldaicè dicitur signum, & constellatio Sagittarij apud Hebræos aurem Kescheth. Testis est Kircherus in Oedipo Ægyptriaco. 8. KESIL seu Kesil Hebraicè dicitur sidus Orionis, de quo vide in V. Lugula. Item 9. KETPHOLT SVMMAN corrupto nomine Garaclos Chaldaicè dicitur Hercules sen fixa secundæ magnitudinis in capite alterius Geminorum existens: dicitur etiam Abrachalens de qua vide ibi. KIMACH

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LEXICON K. 1. KABAR, or Elkabar, Chaldaice, in Latin, the Great Dog star, as Kircher says in the Oedipus. 2. KACHITICHI, in Greek, is interpreted in Latin as ill fortune. Among astronomers this term denotes the sixth house, falling from the horoscope, from the angle of the Imum Cæli, an unlucky place and the lowest of all places in the heavens: for it is both falling and subterranean, and has no intimacy with the horoscope. Hence are taken significations concerning health, weakness, illnesses of women, and bodily defects, and other evils that attack a good bodily constitution and temperament. It also signifies servants, handmaids, lesser animals, and the advantages or inconveniences that the native shall receive from it. It has four parts of debility: it claims black as its color, and Mars rejoices in it. KALB. In Arabic it signifies the same as center, innermost parts, 3. Heart. Whence Kalb Alarrab means the Heart of the Scorpion. Kalb Alpharad, the Heart of Hydra in Latin. Kalb Eleced, the Heart of Leo, and so on. If you seek the nature and qualities of all these, see under their proper names. 4. KAYTOS, or with the article Elkaytos, in Arabic, signifies the same as the Latin Cetus, the whale, and so on: a constellation in the southern region containing, according to Ptolemy, 22 stars, according to Kepler 21, and according to Bayer 27. In it, especially, the Natis, which is also called the Jaw, Arab. Menchar; then the brighter and more southern one in the tail, called Deneb Kaytos; finally the middle one in the belly, Baten or Bara-Kaytos, all of them of the nature of Saturn. 5. KALVROPS, or Alkaluops. In Arabic, the shaft of the fixed star of Bootes is so called, of which see in V. Ceginus. 6. KENEN SATURNI is called in the barbaric sphere the third decan of Sagittarius, remaining under the dominion of Saturn, and signifying obstinacy in one’s purpose of contradicting, skill in evil quarrels, and abominable deeds. 7. KERTHO in Chaldaic is the sign and constellation of Sagittarius, called by the Hebrews the ear of Kescheth. Kircher is witness in the Oedipus Aegyptiacus. 8. KESIL, or Kesil in Hebrew, is called the star of Orion, of which see under V. Lugula. Likewise 9. KETPHOLT SVMMAN, by a corrupted name Garaclos, in Chaldaic is called Hercules, or a fixed star of second magnitude situated in the head of one of the Twins: it is also called Abrachalens, of which see there. KIMACH

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MATHEMATICVM. 157 KIMACH Hebraicè teste Kirchero audiunt Hyades stellæ in capite Tauri. 10. KOCLASMENON Chaldaice hoc est discus paruus teste eodem Kirchero dicitur Corona borea, sidus de quo alibi dictum. 11. Kvs apud Hebræos idem sonat ac Poculum; vnde ab scriptoribus rerum cælestium accipirut pro Cratere sidere posito supra dorsum Hydræ, de quo alibi dictum. 12. Reliqua quære sub litera C. LA LABANAH apud Hæbreos scriptores dicitur Luna lumina- re minus ab albedine V in V. Luna. 1. LACTEA VIA, Circulus lacteus Galaxia, &c. dicitur in cælo callis subalbicans & subobcutus, candori lactis persimilis existens, vt creditur, in Firmamento, & totum illud complectens ad modum circuli, vt præsertim serena nocte videre est, transiens per signa Geminorum, & Sagittarij; item per Cassiopeam, Cygnum, Aquilam, Aurigam, & Perseum, de eo satis fuse diximus in V. Galaxia. 2. LÆLAPS apud Apuleium, & Arist lib. de Mundo cap. 3. dicitur Ventus de genere procellarum, qui infernè spirans sursum versus repentè conuoluitur. Huic affinis est strobilus & Anaphysema qui dicitur ventus sublimè sese rapiens cum è specu depresso status emicuerit, aut è terra in hyarum descendente: Vide in V. Typhon. Lælaps item apud Ricciol. dicitur aliquibus canis maior sirius, de quo alibi dictum. 3. LAMPAS, & Facula vulgo ab Astronomis appellatur Pallilitium, seu Aldebaran stella fixa primæ magnitudinis de natuta Martis in oculo australi Tauri consistens, eoquod magnitudine sua, atque fulgore igneo velut lanipas resplendeat. 4. LAMPADIS etiam apud Plin. lib. 2, cap. 25: [etc] 26. dicuntur species quædam Cometarum, seu ignitarum accensionum, quæ fulgore suo faces ardentes imitantur. Has ipse restatur non nisi cum decidunt, visas, qualis quæ, Germanico Cæsare gladiatorum spectaculum edente, præter ora populi in meridie transcurrit. Has in duplici ait esse differentia, alias, quas simpliciter faces appellet, quæ vestigia longa faciunt, priore ardente parte: alias Bolides dictas, perpetuò ardentes, ac longiorem trahentes limitem, qualis fuit quæ Mutinensibus malis visa est. Hæc Plinius. Vide in V. Comeses. 5. LANCEA Vide iaculum, ignitæ impressionis species. 6. LAR, Tharibulum, Ara dictum est sidus in cælo ad australem R

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MATHEMATICVM. 157 KIMACH, in Hebrew, according to Kircher, the Hyades, stars in the head of Taurus, are called. 10. KOCLASMENON, in Chaldean, that is, a small disk, according to the same Kircher, is said to be Corona Borea, the star of which mention is made elsewhere. 11. Kvs among the Hebrews has the same meaning as a cup; hence by writers on celestial matters it is taken for the Crater, the star placed above the back of Hydra, of which mention has been made elsewhere. 12. The rest, look under the letter C. LA LABANAH, among Hebrew writers, is the Moon, the lesser luminary, from whiteness. 1. LACTEA VIA, the Milky Circle, Galaxia, etc., is called in the sky a whitish and somewhat obscured path, resembling the whiteness of milk, as is believed, in the Firmament, and embracing the whole of it in the manner of a circle, as may especially be seen on a clear night, passing through the signs of Gemini and Sagittarius; likewise through Cassiopeia, Cygnus, Aquila, Auriga, and Perseus; we have spoken at sufficient length of it under V. Galaxia. 2. LÆLAPS, in Apuleius and Aristotle, book De Mundo, chap. 3, is said to be a wind of the class of storms, which, blowing from below, suddenly whirls upward. Related to this are strobilus and Anaphysema, which is called a wind violently snatching itself aloft when it has flashed out from a depressed cavernous place, or descending from the earth into a hollow: see under V. Typhon. Lælaps is also, according to Ricciolus, called by some the greater dog, Sirius, of which mention has been made elsewhere. 3. LAMPAS, and Facula, is commonly called by astronomers Pallilitium, or Aldebaran, a fixed star of the first magnitude, of the nature of Mars, situated in the southern eye of Taurus, because by its size and fiery brightness it shines like a lamp. 4. LAMPADIS also, in Pliny, book 2, chap. 25, [etc.] 26, are called certain kinds of comets, or fiery exhalations, which by their brightness imitate burning torches. He states that these are seen only when they fall, such as the one which, when the gladiatorial show was being given by Caesar Germanicus, ran past the faces of the people at midday. He says that these are of two kinds: some, which he simply calls torches, making long trails with the front part burning; others, called bolides, burning continuously and drawing a longer track, such as the one that was seen by the people of Modena in their misfortunes. Thus Pliny. See under V. Comeses. 5. LANCEA, see iaculum, a species of fiery impression. 6. LAR, Tharibulum, Ara, is said to be a star in the sky toward the south

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258 LEXICON plagam sub signo libræ septem stellis formatum, quæ sunt de natura Veneris, & parum Mercurij. De eo scribit Pontanus in Vrania, quod si in alicuius natiuitate reperiatur ascendens, facit sacris addictum, sacerdotalibus infulis præfulgentem, præsertim si Louis fidus benignè affulgeat. In Occidente vetò cum prauo Martis, aut Saturni aspectu facit sacrilegos, & prophanos debito igne mulctati. Quodsi Iupiter adstet, hæc omnia prohibet: quinimò facit religiosum claustralem, votis obligatum numini, & sacris ritibus incombentem. 8. LARGITIO, teste Abraham Auenare est quædam erectio, & vitium stabilimentum planetæ existentis in puteo, aut in depressione, & ei alius iungatur, qui sit amicus, vel dispositos loci, in quo ille reperiatur: tunc enim dicitur largiri illi suum iuuamen, & eripere illum à puteo, vel sua eiectione. 9. LATERCVLVS, Græco nomine Dosis apud Geometras dicitur id quod latitudine, & crassitudine caret; est tamen præditum longitudine. Vide Vallam. 10. LATERONES dicuntur planetæ constipantes Luminaria; qui prosectò sint illis ad latus, ac suo munimine fulciant: alio nomine stipatores, & satellites. Et hæc planetarum ad luminaria constitutio dicitur Ductoria, Doryphoria, nostro vocabulo, satellitium, quæ quonam pacto fiat vide in eodem verbo. Prætereà Latrones dicuntur aliæ stellæ nuper à Galilæo ope Telescopij detectæ in Saturno duæ, quæ ipsum quandoque oualem figuram habere demonstrant; nec non in lue quatuor satis conspicuæ, quæ circa ipsum setuntur, ab eo mediceas nuncupatas. Sed de hac re satis dictum suo loco. 11. LATIO apud Astronomos idem valet, ac motus: Vnde lationes sunt non modò vniuersales siderum circuirtiones, quas in dies singulos perficiunt ab Oriente in Occidentem per motum vniuetsalem primi mobilis, sed etiam eo nomine veniunt omnes motus siderum quotidiani, quibus influunt hanc materiam sublunatem. Qua de re vide quæ habet Titus in cælesti Philosophia lib. 3. cap. 10. 12. LATITVDO apud Astronomos appellatur deuiatio Planetæ, siue alterius altri ab Ecliptica, & orbita Solis versus alterutrum polorum Zodiaci; itaut quo maior sit deuiatio, eò maior sit latitudo: quæ etiam à plaga ad quam deflectit denominationem sumit; sieque australis dicitur quæ ad polum australem flectit, borealis, quæ ad Borealem: eo prorsus pacto ac diximus de declinatione; nisi quod hæc sit deuiatio ab æquatore versus alterutrum polorum Mundi, latitudo vero vt dixi, deuiatio ab Ecliptica versus alterutrum polorum ipsius Eclipticæ. Porrò sol nullam habet latitudinem, cum perpetuo incedat

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258 LEXICON plagam under the sign of Libra, formed with seven stars, which are of the nature of Venus, and a little of Mercury. Pontanus writes of it in Urania, that if in anyone’s nativity the ascendant be found there, it makes him devoted to sacred things, shining with priestly fillets, especially if faithful Venus should look on benignly. In the West, however, with a bad aspect of Mars or Saturn, it makes men sacrilegious and profane, punished with the fire they deserve. But if Jupiter stands by, he prevents all these things; nay rather he makes one a religious cloistered man, bound by vows to the deity, and intent on sacred rites. 8. LARGITIO, according to Abraham Auenare, is a certain exaltation, and a correction of the stable condition of a planet existing in a pit, or in depression, when another is joined to it, one that is friendly, or disposed to the place in which it is found: then it is said to grant it its aid, and to rescue it from the pit, or from its fall. 9. LATERCVLUS, in Greek the term Dosis is used by the geometers to mean that which lacks breadth and thickness; yet it is endowed with length. See Valla. 10. LATERONES are called the planets that cluster around the Luminaries; those that indeed are beside them, and support them with their protection: by another name, attendants and satellites. And this arrangement of the planets toward the luminaries is called Ductoria, Doryphoria, in our vocabulary satellitium, by what means this happens, see under the same word. Moreover, Latrones are also called certain other stars recently detected by Galileo with the aid of the Telescope in Saturn, two of which show that it sometimes has an oval shape; and also four quite conspicuous ones in the region, which circle around it, called by him the Medicean stars. But enough has been said of this matter in its proper place. 11. LATIO among astronomers has the same meaning as motion: hence lationes are not only the universal revolutions of the stars, which they complete each day from East to West by the universal motion of the first mover, but by this name are also understood all the daily motions of the stars, by which they influence this sublunary matter. On this matter see what Titus in cælesti Philosophy, book 3, chapter 10, has. 12. LATITVDO among astronomers is called the deviation of a planet, or of another body, from the Ecliptic and the orbit of the Sun toward either pole of the Zodiac; so that the greater the deviation, the greater the latitude: it also takes its name from the region toward which it inclines, and thus that which bends toward the southern pole is called southern, that which bends toward the northern, northern: precisely in the same way as we have said of declination; except that this is deviation from the equator toward either pole of the World, whereas latitude, as I said, is deviation from the Ecliptic toward either pole of the Ecliptic itself. Furthermore, the sun has no latitude, since it continually proceeds

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MATHEMATICVM. 159 in Ecliptica: in reliquis planetis ea maior, quam nouem gra- duum hinc inde esse non potest. Hinc Zodiacus larus hinc inde toridem gradibus ab notus Astronomis astruitur, cum tamen antiqui, qui Marris, & Veneris peragationem non benè noue- runt, sex tantum graduum latitudinem illi hinc inde consti- tuerint. At verò in fixis ea maior, ac maior esse potest, quò magis se ab Ecliptica elongauerint, atque ad eiusdem polos accesserint: Maior tamen 90. gradibus esse non potest; cum non plus distent ab Ecliptica ipsi eiusdem poli. Maxima latitu- do. planetarum tam borealis, quam australis ex Tychonicis obseruationibus ea est, vt Saturnus ad boream non magis acce- dat, quam gr. 2. min. 48. ad austrum gr. 2. min. 49. Iupiter ad polum arcticum gr. 1. min. 38. ad antarcticum gr. 1. min. 40. Mars ad boream gr. 4. min. 34. ad Austrum gr. 6. min. 47. Venus hinc inde ab Ecliptica deflectat gr. 9. min. 2. Mer- curius similiter hinc inde gr. 3 min. 33. Luna tamen in quadra- turis cum Sole gr. 5. min. 17. in oppositione verò & coniun- ctione gr. 4. m 18. Vbi sunt in maxima latitudine dicuntur esse in ventre sui Draconis; vbi nullam habent, sed incidunt in Eclipticam sunt in suis nodis, qui dicuntur communiter caput & cauda Draconis, prout in loco obseruatum est. LATITUDO apud Geographos, est distantia æquatoris à 13. vertice alicuius regionis, aut ciuitatis: ita vt tanta dicatur esse latitudo loci illius, quanta est inter eius verticem, & æquato- rem; numerisque graduum interceptus sit latitudinis mensu- ra. Porrò latitudo regionum convenit cum elevatione poli su- prà horizontem; & elevatio æquatoris suprà horizontem conuenit cum distantia poli à vertice; cum enim polus distet ab æquatore gr. 90. totidem intercipiantur inter verticem, & horizontem; hinc est vt residuum ad gr. 90. quos sibi vendi- cat elevatio poli, sit distantia eiusdem poli à vertice, & econ- tià residuum ad maiorem altitudinem æquatoris suprà horizon- tem sit eius distantia à vertice, tanta certe, quanta est eleua- tio poli: propterea sæpè à scriptoribus eleuatio poli cum lati- tudine regionis confunditur. LATITUDO ortiua, vel occidua stellæ, aut cuiusuis partis 14. Eclipticæ apud Astronomos est eiusdem deuiatio à punctis æquinoctialibus, seu ab ijs horizontis punctis, vnde puncta æquinoctialia oriuntur, & occidunt: itaut arcus horizontis interceptus inter puncta ortus, & occasus æquatoris, & puncta ortus, & occasus alicuius sideris dicatur eius latitudo, siue etiam amplitudo ortiua, vel occidua quæ quidem æquales sunt inter se; & ex ijs venamur quantitatem arcus diurni siderum, itaut quò maior sit amplitudo ortiua, vel occidua, eò maior R ij

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MATHEMATICVM. 159 in the ecliptic; in the other planets it is greater, and cannot be more than nine degrees on either side. Hence the Zodiac is understood by astronomers to extend fifteen degrees on either side; yet the ancients, who did not well know the courses of Mars and Venus, assigned to it only six degrees of breadth on either side. But in the fixed stars it can be greater and greater, the more they depart from the ecliptic and approach its poles: nevertheless it cannot be greater than 90 degrees, since the poles themselves are not farther from the ecliptic than that. The maximum latitude of the planets, both northern and southern, from Tycho’s observations is such that Saturn moves no farther north than 2° 48′, and south 2° 49′; Jupiter toward the arctic pole 1° 38′, toward the antarctic 1° 40′; Mars north 4° 34′, south 6° 47′; Venus deflects from the ecliptic on either side 9° 2′; Mercury likewise on either side 3° 33′; the Moon, however, in quadratures with the Sun 5° 17′, but in opposition and conjunction 4° 18′. Where they are at maximum latitude they are said to be in the belly of their Dragon; where they have none, but fall upon the ecliptic, they are in their nodes, which are commonly called the head and tail of the Dragon, as has been observed in the place. LATITUDE among geographers is the distance of the equator from the zenith of some region or city: so that the latitude of that place is said to be as great as the distance between its zenith and the equator; and the number of degrees intercepted is the measure of latitude. Moreover, the latitude of regions agrees with the elevation of the pole above the horizon; and the elevation of the equator above the horizon agrees with the distance of the pole from the zenith; for since the pole is distant from the equator by 90 degrees, so many degrees are intercepted between the zenith and the horizon; hence it is that the remainder to 90 degrees, which the elevation of the pole claims for itself, is the distance of the same pole from the zenith, and conversely the remainder to the greater altitude of the equator above the horizon is its distance from the zenith, certainly as great as the elevation of the pole: for this reason, in writers, the elevation of the pole is often confused with the latitude of a region. LATITUDE of rising, or setting, of a star or of any part of the ecliptic, among astronomers is its deviation from the equinoctial points, or from those points of the horizon from which the equinoctial points rise and set; so that the arc of the horizon intercepted between the rising and setting points of the equator and the rising and setting points of any star is called its latitude, or also its rising or setting amplitude, which are equal to each other; and from these we seek the quantity of the diurnal arc of the stars, so that the greater the rising or setting amplitude, the greater the R ij

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260 LEXICON sit differentia arcus diurni à nocturno: & si quidem ea sit versus austrum, arguat maiorem arcum nocturnum, quam diurnum; si verò versus Septentrionem, maior sit arcus diurnus quam nocturnus. In ipsis autem punctis ortus, & occasus æquatoris nulla est latitudo, atque adeò arcus nocturni, ac diurni siderum sunt omninò æquales. LE 15. LELAPS apud Ricciol. dicitur ab aliquibus canis maior sidus, de quo alibi dictum, Arab Schear Elsemeni. 16. LEO vnum ex duodecim Zodiaci signis quintum ab Ariete (Atab. Eleced, seu Essed) Domicilium Solis, vbi hic maximum æstum facit, sic dictum à similitudine quam habet cum Leone animali in natura, & effectibus, & quia Sole in hoc signo existenre, leones maximè afficiantur, & continuis febribus caleant. Est signum fixum, calidum, & siccum tripliciraris igneæ, ferale, sterile, &c. Dominarur cordi, stomacho, dorso, lateribus, ac diaphragmari: proindeque noxium est potiones sumere Sole, vel Luna in eò existentibus, item & languinem mittere: sicut eriam Luna ibidem commorante nouas vestes induere, vt Ptolemæus habet in centiloquio, probatque D. Thomas in opus. 28. cap. 4. & nos alibi obseruauimus. 17. Potro Leonis sidus in octaua sphæra recessit à loco suo sub primo mobili ad 13. ferè gradus, estque nunc magis temperatum quam tempore Ptolemæi. Habet stelles omninò 17. Ptolemæo vltrà informes 8. at Keplero 40, & adhuc Baiero 43. inter quas Regulum secundæ quidem magnitudinis, sed ob tui præstantiam inter primas computatum ferè in Ecliptica: item & caudam primæ magnitudinis, & aliam in capite secundæ, de quibus omnibus peculiaris redibit sermo. 18. LEPVS sidus in octaua sphæra ad australem plagam sub genibus orionis habens stellas duodecim de natura Saturni, & Mercurij omnes in longitudine sub Geminorum signo. Is in horoscopo, inquit Pontanus facit hominem miræ celeritatis, qui que in cursu brauium sit obrenturus: erit quippe toto corpore flexilis, & agilis, idque eò maximè si affulserit Mars. Quod si Mercurius astipulauerit, erit adhuc gesticulator, egregius lusor, & luctator eximius, si Venus, erit minus, salctor, ac musicus. Si Luna cum bono aspectu Saturni, erit nouarum artium inuentor. Ar si malo radio iste solus aspexerit, edicit derelictionem patrij soli & nullam curam suorum. Si verò in occasu repertus fuerit, & si benè irradiatus, nihilomini-

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the difference of the diurnal arc from the nocturnal: and if indeed it lies toward the south, it shows the greater nocturnal arc than the diurnal; but if toward the north, the diurnal arc is greater than the nocturnal. But in the very points of rising and setting of the equator there is no latitude, and therefore the nocturnal and diurnal arcs of the stars are altogether equal. LE 15. LELAPS, according to Ricciolus, is said by some to be the greater dog-star, of which mention has been made elsewhere, Arab. Schear Elsemeni. 16. LEO, one of the twelve signs of the Zodiac, the fifth from Aries (Atab. Eleced, or Essed), the domicile of the Sun, where it produces the greatest heat, so named from the similarity it has to the animal lion in nature and effects, and because when the Sun is in this sign the lions are most affected and burn with continual fevers. It is a fixed sign, hot and dry, of the fiery triplicity, feral, sterile, etc. It rules the heart, stomach, back, sides, and diaphragm; and therefore it is harmful to take potions when the Sun or Moon are in it, and likewise to let blood; just as also, when the Moon is staying there, to put on new clothes, as Ptolemy says in the Centiloquium, and St. Thomas proves in Opus 28, ch. 4, and we have noted elsewhere. 17. But the lion's constellation has receded in the eighth sphere from its place under the first mover to about 13 degrees, and is now more temperate than in the time of Ptolemy. It has 17 stars in all; to Ptolemy besides the 8 unformed stars, but to Kepler 40, and to Bayer 43 as well, among which is Regulus, of the second magnitude, but because of its excellence counted among the first, almost in the Ecliptic; likewise the tail of first magnitude, and another in the head of second, of all of which a special discussion will follow. 18. LEPUS, a constellation in the eighth sphere on the southern side under the knees of Orion, having twelve stars, of the nature of Saturn and Mercury, all in longitude under the sign of Gemini. In a horoscope, says Pontanus, it makes a man of marvelous speed, who will be destined to win prizes in running; for he will be flexible and agile in the whole body, and this especially if Mars shines upon him. But if Mercury assists, he will still be a gesticulator, an excellent player, and an outstanding wrestler; if Venus, he will be less so, a dancer and musician. If the Moon, with a good aspect of Saturn, he will be an inventor of new arts. But if this one alone looks upon him with a bad ray, it indicates abandonment of the native soil and no concern for his own people. But if he is found in the west, and if well irradiated, neverthe-

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MATHEMATICVM. 261 nus non sine labore alimenta sibi comparabit: si adhuc maleuolæ hostili radio consenserint exponent periculo, quod à feris, & canibus sit discerpendus. Concludit tandem Pontanus. Hæc leporem nam fata manent: hinc nomen & Astro. LESATHI Arab. vel potiùs Lessaa, teste Kirchero in Oedi- 19. po, dicitur stella fixa antecedens aculeum Scorpij, quasi mor- sus Scorpij. LEVCONOTI dicuntur venti austrini de genere ethesiarum, sic 20. dicti, vt author est Theophrastus, ab affectu, quippe præter austri naturam, quam referunt, reddunt cælum album & sere- num: licet strabo aduertat ipsos non esse omninò serenitatis la- tores, sed aliquando nubes etiam quamuis paruas adducere. LEVIS dicitur planeta alteri comparatus, qui cursu ipso sit 21. tardior, vt Luna respectu omnium planetarum, Sol respectu trium superiorum &c. Absolutè verò tres inferiores Venus, Mercurius, & Luna dicuntur leues; superiores viceuersa pon- derosi, quia vt plurimum motus diurnus istorum non adæquat cursum reliquorum, licet, quandoque Venus & Mercurius, cum fiunt retrogradi, vel sunt stationarij ab illis in motu vin- cantur. LI LIBANOTVS. Vide Lybanotus. LIBERALITAS apud Astronomos vsurpatur pro significan- 22. da mutua duorum planetarum beneficentia, & fulcimento; 23. quando videlicet alter eorum fuerit in domo, aut exaltatione alterius, etiam si radius non intercedat: sit tamen inter ipsos commutatio dignitatum, & receptio mutua; vt esset si Venus in Scorpione, Mars in libra reperirentur. LIBRA vnum ex duodecim Zodiaci signis Arieti ex diamet- 24. tro oppositum, sic dictum, eoquod Sole in æquinoctio au- tumnali in ipso existente dies noctibvs æquales sint, quasi in statera librati. Est signum aereum calidum, & humidum, mo- bile, pulchrum, domicilium Veneris, & exaltatio Saturni; propter quod inter violenta computatur: præest lumbis; reni- bus, & inferioribus ventris. Libræ sidus in octaua sphæra inci- pit nunc temporis à gr. 6. Scorpij & protenditur. vsque ad gr. 27. formatur ex stellis octo secundum Ptolemævm, exceptis 9. quas linquit informes, Keplerus autem in eo enumerat om- ninò 18. omnes ferè de natura Saturni, & Martis, quarum præcipua est quæ in lance australi secundæ magnitudinis inter regias computata. Priores eius partes siccæ admodum sunt; medix temperatæ, posteriores humidæ, & aquosæ. Quæ in R ii)

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MATHEMATICVM. 261 will not without labor procure food for himself: if still the hostile rays of the malevolent have assented, he will expose himself to danger, because he is to be torn by wild beasts and dogs. Pontanus finally concludes: These fates await the hare: hence the name and Astro. LESATHI, Arabic, or more properly Lessaa, according to Kircher in Oedipo 19, is said to be the fixed star preceding the sting of Scorpio, as it were the bite of Scorpio. LEVCONOTI are called the southern winds of the class of etesian winds, so 20 named, as Theophrastus authoritatively states, from their effect, for contrary to the nature of the south wind which they represent, they make the sky white and clear; although Strabo notes that they are not altogether bringers of clear weather, but sometimes even bring clouds, though small ones. LEVIS is a planet compared with another that is slower in its actual course, as the Moon in relation to all the planets, the Sun in relation to the three superior ones, etc. Absolutely speaking, however, the three inferior planets, Venus, Mercury, and the Moon, are called light; the superior planets, on the other hand, weighty, because for the most part their daily motion does not equal the course of the others, although sometimes Venus and Mercury, when they become retrograde or are stationary, are surpassed by them in motion. LI LIBANOTVS. See Lybanotus. LIBERALITAS is used by astronomers to signify the mutual beneficence and support of two planets; that is, when one of them is in the house or exaltation of the other, even if no ray intervenes: provided, however, there is an exchange of dignities and mutual reception between them; as would be the case if Venus were found in Scorpio and Mars in Libra. LIBRA, one of the twelve signs of the Zodiac, opposite Aries diametrically, is so called because, when the Sun is in it at the autumnal equinox, the days are equal to the nights, as if balanced on a scale. It is an airy sign, hot and humid, movable, beautiful, the domicile of Venus and the exaltation of Saturn; for which reason it is counted among the violent signs: it governs the loins, kidneys, and lower abdomen. The constellation of Libra now begins in the eighth sphere at 6 degrees of Scorpio and extends to 27 degrees. It is formed of eight stars according to Ptolemy, except for the 9 that he leaves unformed, whereas Kepler lists 18 in all. Almost all are of the nature of Saturn and Mars; the principal one is that in the southern scale, counted among the royal stars of the second magnitude. Its earlier parts are very dry; the middle parts temperate; the later parts humid and watery. The ones in

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162 LEXICON Boream flectunt, ventosæ, quæ ad austrum mortiferæ, & pestilentes. Hoc sub sidere nati, siue mares sint, siue foeminæ pulchra sacie sunt, planis capillis, moribus placidis, sed vt plurimum mortis suæ causa erunt, ut habet Ptolemæus in Censo loquso V. 37. 35. LIMBVs apud Astronomos dicitur extremum labium astrolabij, siue alterius consimilis instrumenti Geometrici, in cuius plano descriptæ sunt horæ post meridiem, gradus æquatoris in 360. partes dissecti, ac singulis horarum diuisionibus respon- dentes, Ventorum nomina, & alia huiusmodi, cuius beneficio tam istorum flatus dignoscimus, tum etiam Astrotum altitu- dinem dimetimur, sicut etiam 36. LIMBVs SS. Patrum. Vide Infernus, sinus Abrahæ. 37. LINDA seu linea fiducia dicitur regula lineam designans per medium Astrolabij transeuntem, atque ad extremum limbum porrectam ad altitudines siderum dimetiendas, quam alio no- mine Dioptram, Alhidadam, Mediclinium appellamus. 38. LINEA ab Geometricis; definitur, quod sit Longitudo omnis latitudinis expers, quam, vt imaginemur, proponunt nobis, vt punctum concipiamus omnis dimensionis incapax è loco in locum moueri. Vnde est, quod alij dixerint lineam aliud planè non esse, quam puncti fluxum. Hinc lineæ termini sunt duo puncta, quibus concluditur, & terminatur: non quod ne- cessariò omnis linea terminos habeat, cum nec circularis vl- lum admittat, nec infinitè protensa, si cadati posset, sed quia quælibet linea habens extremâ, in suis terminis puncta ad- mittat, & in quacumque lineæ parte concepta duo puncta sic in illa hinc inde velut terminos designant. Liueatum aliæ rectæ sunt, aliæ curvæ: item aliæ parallelæ aliæ in angulum desinen- tes: Parallelæ sunt quæ etiamsi in infinitum protendantur, nunquam tamen ad sui contactum peruenient, atque angulum efficient: non sic quousi modo declives Hinc denominantur anguli rectilinei, curuilinei, &c. quorum naturam alibi expli- cui mus. 39. LINEA incidentia est radius à luminoso corpore exiliens atque ad alicuius superficiei punctum terminatus, & pun- ctum illud dicimus etiam punctum incidentiæ. Eius cognitio præcipuè necessaria est ad Eclipsis magnitudinem, ac durationem venandam. 40. LINEA medi[us] motus est linea recta terminans medium mo- tum, aut locum sideris: quæ in Epicyclo concipitur ducta ab centro mundi ad eiusdem sideris centrum; in eccentrico autem à centro ecceutrici per centrum stellæ, transiens vsque in Eclipticam.

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162 LEXICON They bend toward the north, the winds that toward the south are deadly and pestilential. Those born under this constellation, whether male or female, are fair of face, with straight hair, and mild in character, but for the most part will be the cause of their own death, as Ptolemy has in the Tetrabiblos V. 37. 35. LIMBUS among astronomers is called the outer edge of the astrolabe, or of another similar geometric instrument, on whose plane are drawn the hours after noon, the degrees of the equator divided into 360 parts, and the names of the winds, and other such things, by whose aid we both recognize the direction of those winds, and also measure the altitude of the stars, as also 36. LIMBUS SS. Patrum. See Hell, Abraham's bosom. 37. LINDA, or line of confidence, is called the rule marking the line passing through the middle of the astrolabe, and extended to the outer limb for measuring the altitudes of the stars, which by another name we call the dioptra, alidade, mediclinium. 38. LINE from the geometers is defined as that which is length without any breadth, which, in order that we may imagine it, is proposed to us, so that we may conceive a point incapable of all dimension, moving from place to place. Hence it is that others have said that a line is nothing else than the flux of a point. Thus the termini of a line are two points, by which it is enclosed and terminated: not that necessarily every line has termini, since neither does a circular line admit any, nor one extended to infinity, if one could fall into it, but because whatever line has ends admits points at its extremities, and in whatever part of a line two points conceived in it mark out such termini on this side and on that. Lines are some straight, others curved; likewise some parallel, others ending in an angle: parallel are those which, even if extended to infinity, nevertheless never come to touch one another, and will not form an angle: not so those that are sloping. Hence rectilinear, curvilinear, etc. angles are named, whose nature we have explained elsewhere. 39. An incident line is a ray darting from a luminous body and ending at a point of some surface, and we also call that point the point of incidence. Its knowledge is especially necessary for hunting down the magnitude and duration of an eclipse. 40. The line of mean motion is a straight line determining the mean mo- tion, or place of a star: which is conceived in the epicycle as drawn from the center of the world to the center of the same star; but in the eccentric, from the center of the eccentric through the center of the star, passing as far as the ecliptic.

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MATHEMATICVM. 263 LINEA autem veri motus, vel apparentis est linea recta ducta à centro terræ per centrum sideris vsque ad Eclipticam, vel sane à superficie terræ. Qua de re vide Ricciol. in Almagesto lib. 10. sect. 6. cap. 2. LO LOGARYTHMICA est pars Arithmeticæ, quæ per loga- rythmos hoc est per numeros absolutos tradit facilem metho- dum soluendi triangula præsertim sphærica, & ex solutione docet condere tabulas astronomicas: siquidem ope illius regu- la illa celebris aurea dicta per quam facile absoluitur sola ad- ditione facta numerorum artificialium, & muliò citiùs res ex- peditur, quam per tabulas sinuum tangentium & secantium. De qua re vide etiam ipsum Ricciol. to. 2. Almagesti lib. 1. trigonometrico. Hinc LOGARITHMI sunt numeri artificiales ab Arithmeticis eo studio excogitati, vt substituti loco numerorum naturalium, apti sint in ijs manifestare quancumque differentiam progres- suum. Seruant enim easdem differentias numerales, seù mauis dicam, seruant in seipsis semper, & constantissimè eandem pro- gressionem arithmaticam, quandù illi, quorum loco sunt con- stituti seruât progressionem geometricam. Hinc est, vt quando 4 numeri habent proportionem ad inuicem, summa logarithmorum primi, & vltimi numeri sit æqualis summæ mediorum. vt si v. g. statuantur duo numeri 4. & 8. quorum alter est altero duplo maior, inde sit, vt eadem proportio sit inter om- nes numeros duplo maiores ad inuicem: sicque inter 5. & 10. inter 12. & 14. inter 24. & 48 inter 50. & 100. & sic deinceps eadem proportio semper seruetur: Quapropter logarithmi num. 4. & 10. 4. & 14. 4. & 48. 4. & 100. &c. simul iuncti æquales inueniuntur aggregato logarithmorum 8 & 5. 8. & 12. 8. & 24. 8. & 50. &c. coquia, vt dictum est, eadem proportio arithmatica seruatur in logarithmire, quæ geometricè inueni- tur in numeris naturalibus, quorum loco illi substituuntur. Ex quo sit, vt magna vtilitas eorum ope arithmeticis cedat, ma- gnumque temporis lucrum: Quod enim per regulam auream fastidioso calculo, ac longo nimis circuitu per multiplicationem, ac diuisionem sit, vt tandem inueniatur quartus nume- rus ignorus ex tribus notis; id per logarithmos vna & simplici operatione perficitur. Nam si duo numeri multiplicandi sint, acceptis eorum logarithmis, habetur intentum sola additione. Si alter il alterum diuidendus; id per logarithmos sit sola sub- tractione. Quinimò si adhibetur residuum logarithmi, quod complementum arithmaticum vocant, exhibebunt nuluplica- R iii)

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MATHEMATICVM. 263 The line of true motion, or apparent motion, is a straight line drawn from the center of the earth through the center of the star to the Ecliptic, or indeed from the surface of the earth. On this matter see Ricciol. in Almagest lib. 10. sect. 6. cap. 2. LO LOGARYTHMICA is a part of Arithmetic, which by logarithms, that is by absolute numbers, teaches a facile meth- od of solving triangles, especially spherical, and from the solution teaches how to construct astronomical tables: since by its aid that cele- brated rule called the golden rule is easily completed, by which, with the simple addition of artificial numbers, the work is dispatch- ed much more quickly than by the tables of sines, tangents, and secants. On this matter see also Ricciol. himself, vol. 2, Almagest, lib. 1, trigonometrico. Hence LOGARITHMS are artificial numbers devised by mathematicians with this intent, that, being substituted in place of natural numbers, they may be fit to make manifest in them whatever difference of pro- gressions there may be. For they preserve the same numerical differences, or rather, if I may say so, they always preserve in themselves, and most steadfastly, the same arithmetic pro- gression, while those in whose place they are set preserve the geometric progression. Hence it is that when four numbers have a proportion among themselves, the sum of the logarithms of the first and last number is equal to the sum of the middle terms. For example, if two numbers are set, 4 and 8, of which one is double the other, it follows that the same proportion exists among all numbers double one another: thus between 5 and 10, between 12 and 14, between 24 and 48, between 50 and 100, and so on, the same proportion is always preserved: wherefore the logarithms of 4 and 10, 4 and 14, 4 and 48, 4 and 100, etc., taken together are found equal to the sum of the logarithms of 8 and 5, 8 and 12, 8 and 24, 8 and 50, etc., because, as has been said, the same arithmetic proportion is preserved in logarithms, which is found geometrically in the natural numbers in whose place they are substituted. From this it follows that by their aid a great usefulness accrues to arithmetic, and a great saving of time: for what by the golden rule would be done with tedious calculation, and with a circuit much too long through multiplication and division, so that at last there may be found the fourth unknown number from three known ones; this is accomplished by logarithms in one and simple operation. For if two numbers are to be multiplied, taking their logarithms, the intended result is obtained by simple addition. If one is to be divided by the other, this is done by logarithms by simple subtraction. Indeed, if the remainder of the logarithm be used, which they call the arithmetic complement, they will show muliplica- R iii)

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164 LEXICON tionem, ac diuisionem iam factam sola expunctione primæ si- guræ: quod sanè ingens operæ compendium est, magnum la- boris leuamen, dignumque magnæ illius autæ regulæ operam frustrare laudem assequi, palmam pioripere. Ideoircò ad maiorem commoditatem, quò numerorum natu- ralium fractiones penè insensibiles fiant, logarithmus nume- ri 1. ab inuentoribus artis statutus est 0. logarithmus 10. 10000000. logarithm. 100. 20000000 logarithm. 1000. 30000000. & sic de reliquis progrediendo in infinitum, ob- seruando semper quod prima figura logarithmi, quæ ideò ap- pellatur Characteristica, sit in numero vno minor figuris, qui- bus numerus naturalis consistit, vt si numerus propositus sit sex figurarum, prima figura logarithmi sit 7. si constet ille decem figuris prima logarithmi sit 9. &c. eoquia numerum eius implei numerus figurarum logarithmi sic constitui. Porrò logarithmi alij constituti sunt pro numeris naturali- bus absoluè sumpiis, alij pro numeris arcuum circuli, seu angulorum, quos arcus ipsi metuntur, vicemque gerunt ac sibi officium feliciùs assumunt, quod est proprium tabulæ si- num, tangentium, & secantium. Quandoquidem accipiuntur logarithmi duorum mediorum sinuum, seu tangentium, aut secantium, quibus simul iustis, si ex summa subtrahatur lo- garithmus primi numeri, reliquum erit logarithmus quarti quem querimus, è regione cuius in tabulis sinuum, tangen- tium, & secantium habetur numerus quartus quæsitus. Extant tabulæ absolutissimæ logarithmorum iam numerorum natura- lium ab vaitare ad 10000. quam sinuum, & tangentium è re- gione ipsarum tabularum, magno cum laboris foenore editæ nuper ab Adriano Vlacq. Hagæ comitum anno 1661. vbi vni- co ictu oculi habentur, & gradus, & minuta arcuum; & sinus, tangentes atque secantes, & regione ipsarum eorum logarith- mi, vt iam nil desu studioso Trignomerriæ, quin omnem triangulorum resolutionem facili iure assequi possit, nec fasti- dioso labore teneri. Qui plura hac de re volei adeat Arithme- ticam logarithmicam Henrici Briggij, vbi tota natura, fun- damentum, & excellentissimus vsus logarithmorum in omni- bus quæstionibus Arithmeticis, & Geometricis luculentissimè demonstratur. <34.> LOGRSTICA item pars est Arithmeticæ, quæ regulas suppu- tandi, multiplicandi, & parviendi applicar gradibus signorum, circulorum, & angulorum: nec non & diebus horisque atque ipsorum graduum, horarumque munitis, seu sexagenis, & se- xagenarum sexagenis vsque ad decima. <35.> LONGITUDO apud Astronomos atteuditur in Zodiaco à pri-

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164 LEXICON tion and division already made by the mere striking out of the first figure: which surely is a great saving of labor, a great relief of toil, and worthy of obtaining the praise of frustrating the work of that great old rule, and carrying off the palm. Therefore, for greater convenience, so that the fractions of natural numbers may become almost imperceptible, the logarithm of the number 1 was established by the inventors of the art as 0; the logarithm of 10 as 10000000; the logarithm of 100 as 20000000; the logarithm of 1000 as 30000000; and so on with the rest, proceeding to infinity, always observing that the first figure of the logarithm, which is therefore called the Characteristic, is one less than the figures by which the natural number is made up. Thus, if the proposed number has six figures, the first figure of the logarithm is 7; if it consists of ten figures, the first figure of the logarithm is 9; and so on, because the number of figures of its logarithm is thus determined to fill out that number. Moreover, some logarithms are established for natural numbers taken absolutely, others for numbers of arcs of the circle, or of the angles which those arcs measure, and which they represent and more happily assume the office that properly belongs to the table of sines, tangents, and secants. For the logarithms of two mean sines, or tangents, or secants, are taken together; and if the logarithm of the first number be subtracted from the sum, the remainder will be the logarithm of the fourth number which we seek, opposite which in the tables of sines, tangents, and secants is found the fourth number sought. There are now most complete tables of logarithms of natural numbers from one to 10000, as well as of sines and tangents opposite the tables themselves, published with great saving of labor recently by Adrian Vlacq at The Hague in the year 1661, where at a single glance are seen both degrees and minutes of arcs, and sines, tangents, and secants, and opposite them their logarithms, so that nothing now remains lacking to the student of Trigonometry, except that he may easily attain every solution of triangles and not be held back by laborious toil. Whoever wishes to know more on this subject should consult Henry Briggs’s Arithmetica Logarithmica, where the whole nature, foundation, and most excellent use of logarithms in all Arithmetic and Geometric questions are most clearly demonstrated. <34.> LOGRSTICA is also a part of Arithmetic, which teaches the rules of computing, multiplying, and dividing according to the degrees of signs, circles, and angles; and also of days and hours, and of the minutes of those degrees and hours, or sexagesimals, and of sexagesimal parts of sexagesimals, even to decimals. <35.> LONGITUDE among astronomers is considered in the Zodiac from the firs

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MATHEMATICVM. 165 mo gradu Arietis ad extremum Piscium; idque per circulos transeuntes per polos Zodiaci, & singulos eius gradus ad loca opposita: itaut arcus Eclipticæ interceptus inter primum gra- dum Arieris, & circulum illum, qui transit per centrum stellæ sit quantitas longitudinis ipsius stellæ, & quæ magis à dicto puncto distiterit, maiori dicenda sit prædita longi- tudine. LONGITUDO apud Geographos est arcus æquatoris inter- < 36.> ceptus inter Meridianum alicuius loci, aut ciuitatis, & primum constitutum in Occidente non procul ab insulis fortunatis. Vnde maior, vel minor distantia vnius loci à dictis insulis siue alterius ab altero, auspicatur à numero graduum inter- ceptorum: singuli autem gradus æquatoris inferunt distan- tiam milliatiorum 13. licet in locis, quæ ab æquatore deflectunt singulis gradibus, (quoniam semper magis, ac magis restringuntur, quò maior sit ad polos approximario) minor etiam respondeat distantia. Ex differentia etiam longitudinis apparet, an locus sit altero Orientalior! vel Occidentalior: quò enim maior longitudo erit vnius loci, eo is erit Orienta- lior, ac p[er]tine in eo Sol citiùs otietur in horizonte, citiùs ad meridiem vadit citiùs etiam ad occasum deprimiur. Por- rò vnde verius computanda sit longitudo, vide in V. Azorum insulæ. LV LVCTIFER dicitur Venus Orientalis à Sole, & matutina, < 37.> quasi lucem ferens: idque non modo, quia cum marutina est sua luce noctis renebras fugat, sed potissimum, quia Solis pro- droma existens, lucis fontem iamiam aduentantem præsignat. sicut econtrà Hespetus appellatur quando vespertina est, & Occidentalis à Sole. LVMEN, suo vocabulo satis notum, est præcipua dos cor- < 38.> porum cælestium, atque vnicum, & singulate instrumentum, quo agunt in hæc inferiora. Neque enim admittenda est vlla quæcumque tandem ea sit occulta cælotum influentia, quando hoc vnum, seculo, sufficiens est ad producendas omnes pri- mas qualitates, quibus vniuersum genus naturalium effectuum attinguntur, prout egregiè demonstrat Titus in coelesti Phi- losophia; docueruntque ante ipsum Auerroës, Georgius Agricola, & Franciscus Piccolomineus. Porrò luminis omnis fons, & origo Sol, qui illud posteà cæteris sideribus fænerat. Hæc dein lumen ipsum suis qualitatibus alterantia varietatem istam effectuum pariunt, quos videmus, cuius dissimilitudi- nis causa partim est lucis ipsius intensio, & extensio, quæ sunt

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MATHEMATICVM. 165 from the first degree of Aries to the extreme of Pisces; and that through circles passing through the poles of the Zodiac, and through each of its degrees to opposite places: so that the arc of the Ecliptic intercepted between the first degree of Aries and that circle which passes through the center of the star may be the quantity of the star’s longitude, and that which is farther from the said point ought to be said to have the greater longitude. LONGITUDE among geographers is the arc of the equator intercepted between the meridian of some place or city and the first established point in the West not far from the Fortunate Isles. Hence the greater or lesser distance of one place from the said isles or of one from another is reckoned from the number of degrees intercepted: but each degree of the equator carries a distance of 13 miles, although in places that deviate from the equator, for each degree, (since they are always more and more narrowed the closer they approach the poles) a smaller distance also corresponds. From the difference of longitude it also appears whether a place is more Oriental or more Occidental than another; for the greater the longitude of one place, the more Oriental it will be, and in it the Sun rises sooner on the horizon, sooner goes to midday, and sooner also is brought down to setting. Moreover, from what source longitude should more truly be computed, see in V. the island of Azores. LV LUCIFER is said of Venus when Oriental to the Sun and morning star, as if bearing light: and this not only because, when she is morning star, she drives away the darkness of night with her light, but chiefly because, existing as the Sun’s forerunner, she announces the source of light now already approaching. Conversely she is called Hesperus when she is evening star and Occidental to the Sun. LUMEN, sufficiently known by its own name, is the chief endowment of heavenly bodies, and the unique and singular instrument by which they act upon these lower things. For no so-called occult influence of the heavens is to be admitted, when this one, in itself, is sufficient for producing all the primary qualities by which the whole genus of natural effects is reached, as Titus excellently demonstrates in Celestial Philosophy; and before him Averroes, Georgius Agricola, and Franciscus Piccolomineus taught the same. Moreover, the source and origin of all light is the Sun, which afterward loans it to the other stars. These then, altering the light itself by their qualities, produce that variety of effects which we see, the cause of whose dissimilarity is partly the intensity and extension of the light itself, which are

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LEXICON primæ, & præcipuæ luminis proprietates, partim colores, quos in Astris videmus, & quibus reuerà pollent, vt probat idem Titus. Vnde & Saturnus coloris plumbei est; Iupiter cærulei; Mars candentis; Sol aurei; Venus crocei; Mercurius cæsi, & mixti, Luna tandem albicantis, & argentei, vt vel ipsis <39.> lippis oculis constat. Ex hac ergò colorum diuersitate diuersitas, & præpollentia singularum qualitatum, diuersitas etiam, & varietas ista effectuum, quam videbus dimanat. An autem lumen astrorum agat in hæc sublunaria secundum suam intensiorem, & extensionem veram, an potiùs apparentem, dubium est maximum inter Philosophos. At enim si non ratione, saltem expetientia, & ex effectibus ipsis concludere debemus, sidera operari in hæc sublunaria secundum illum gradum intensione, & quantitatem extensionis lucis, non quibus ipsa reuerà pollent, sed quibus arringunt corpora passibilia; quæ quò magis à sideribus remouentur, quo minùs eorum lucem participant, eò minùs in se recipiunt siderum impressiones. Videmus id clarissimè in Luna quæ silens, siue Soli coniuncta, nulli dubium, quin in se maius, atque intensius lumen participet, quam cum illi opposim; & nihilominus maioribus viribus pollet in isthæc inferiora cum à Sole discedit, proindeque lumine semper crescens nobis apparet à coniunctione ad oppositionem, quam cùm ad ipsum accedens, quoad ad nos sensim lumen deperdit. Videmus in Eclipsibus, quæ non afficiunt ea loca, in quibus nullatenus conspiciuntur: Videmus tandem in nouis Phænomenis, quæ non agunt nisi in eas prouincias, in quibus apparent. Cæterum lucis intensio, & extenso quoad nos causæ sunt omnium primarum qualitatum in inferioribus hisce: & ab intensione quidem procedunt qualitates actiæ, & ab extensione passiæ; itaut ex accessu, & propinquitate siderum sequatur augmentatio luminis secundum extensionem, & ex augmentatione secundum extensum sequatur etiam maior intensio luminis secundum gradus, saltem in effectibus. Ex augmentatione luminis præcisè in intensione, sequitur augmentum caloris, sicut econtrà ex diminutione intensione lucis frigiditas: & ex maiore exensione lucis sequitur augmentum humiditatis; sicut ex minore extensione <40.> siccitas. Hinc quatuor illæ coniugationes & modi influendi siderum in augmento luminis, & prope esse, in decremento, & propè esse, in augmento, & longe esse, in decremento, & longè esse; quibus constituuntur quatuor anni tempora, quatuor primarum qualitatum coniugationes, quibus elementa constant, quibus vniuersum mixtorum genus coagmentatur. Hinc Philosophus 2, de Generas. textu. 56. hunc vni cælestium

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LEXICON the primary and principal properties of light are partly the colors which we see in the stars, and by which they truly abound, as the same Titus proves. Hence Saturn is of leaden color; Jupiter of blue; Mars of shining white; the Sun of gold; Venus of saffron; Mercury of gray, and mixed; the Moon at last of a whitish and silvery hue, as even <39.> with our very bleary eyes it is evident. From this diversity therefore of colors, the diversity and preeminence of the individual qualities, and also this diversity and variety of effects, as you will see, flows. But whether the light of the stars acts upon these sublunary things according to its more intense and extended true state, or rather according to the apparent one, is a very great question among the philosophers. Yet if not by reason, at least by experience and from the effects themselves, we must conclude that the stars operate upon these sublunary things according to that degree of intensity and quantity of extension of light, not by which they really abound, but by which they strike passible bodies; the more they are removed from the stars, the less they participate in their light, and the less they receive in themselves the impressions of the stars. We see this most clearly in the Moon, which, when silent, or joined with the Sun, there is no doubt that it participates in itself in a greater and more intense light than when opposed to it; and yet it has greater power over these lower things when it moves away from the Sun, and therefore it appears to us always increasing in light from conjunction to opposition, than when, approaching it, it gradually loses light as regards us. We see it in eclipses, which do not affect those places in which they are in no way seen: we see finally in new phenomena, which act only on those provinces in which they appear. Moreover, the intensity and extension of light, as far as we are concerned, are the causes of all the primary qualities in these lower things; and indeed from intensity proceed the active qualities, and from extension the passive ones; so that from the approach and proximity of the stars there follows an increase of light according to extension, and from the increase according to extension there follows also a greater intensity of light according to degrees, at least in effects. From the increase of light precisely in intensity there follows an increase of heat, just as conversely from the diminution in intensity of light, cold; and from a greater extension of light there follows an increase of moisture, just as from a lesser extension <40.> comes dryness. Hence those four conjunctions and modes of the influence of the stars: in the increase of light, and nearness; in decrease, and nearness; in increase, and distance; and in decrease, and distance; by which are constituted the four seasons of the year, the four conjunctions of the primary qualities, by which the elements subsist, and by which the whole genus of mixed things is bound together. Hence the Philosopher, bk. 2, On Generation, text 56, this one of celestial things

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MATHEMATICVM. 267 luminum perpetuæ vicissitudini causam ortus & interitus rerum. Sed de hac re vide quæ fusius & eruditè nimis habet Titus in Cæleste Philosophia intero libro primo. LVMINARIA non modò Apud Astronomos, sed & apud omnes ferè scriptores vocantur anthonomasticè præcipua cæli lumina, Sol videlicet, & Luna bina ista diuinitatis simulaehra, Mundi faces, orbis ornamenta, ac rerum omnium vita vel ipsis brutis animanibus nota. Ea sic dicta sunt ob luminis redundantiam: qua ratione Genesis 1. dicitur fecisse Deum ab initio duo luminaria magna, Solem, vt præesset diei, & Lunam vt præesser nocti. Non quod ea in comparatione cæterorum astrorum admodum grandia sint, (quandoquidem certum est Lunam ipso terrestri globo minorem esse, proiudeque omnibus astris tam fixis, quam erraticis excepto Mercurio, vt mox dicemus, & Sole maiorem faciant aliqui canem sirium) sed quod lumine stellas omnes ante-eant, Sol quidem lucis intensione, vnde in ipso præualent qualitates actiuvæ, Luna verò eiusdem lucis extensione & qualitatibus passiuis. Hinc benè dixit Centiloquij author verbo &c Solem esse jontem vitalis potentia, Lunam naturalis, quia perfectò Sol in viuentibus est caloris innati author, Luna humidi radicalis; vnde & administrant materiam, & formam materialem in cunctis rebus, & disponunt qualitates cælestes in mixtis, reducentes eas ad actum, & coadiuuantes causas immediatas ad productionem suorum effectuum, quos omnes virtute continent, & potentia: Itaque omnis animantium vita à luminaribus pendet tanquam à causis vniuersalibus, & æquiuocis subordinaris tamen causæ primæ, & vniuersalissimæ, quæ concurru generali ad omnes effectus naturales concurrit, datque ipsis causis secundis posse, & operari. Verum tamen inter causas secundas luminaria quandam sibi vniuersalem agendi vendicant principatum: & sic quidem cum beneficis copulentur producunt animalia, & mixta de eorum natura, scilicet temperata, in commodum, atque vtilitatem humani generis, si verò cum malescis conq[ui]rediantur, concurrunt ad productionem animalium perniciosorum mixtis quibusque bonis hostilium, & infensorum, ad aëris corruptelam, fructuum perniciem, terræ sterilitatem, &c. vnde pestilentiæ, fames, morbi & alia huiusmodi mala deriunt: & hinc etiam pater, quomodo ex luminarium defectibus potissimum hæc mala oriautur, quia, ( vt bene aduerrit Titus lib. 1. cap. 14. atque ex auctoritate lactæ Congregationis explicat & confirma doctissimus Pater Auerta in notis, & declarationibus præfixis ad eiusdem Titi opera) Luminaria inter ausas secundas sunt vniuersales moderatores,

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MATHEMATICS. 267 the cause of the perpetual alternation of light, the birth and death of things. But on this matter see what Titus has more fully and learnedly in the Celestial Philosophy, book one in its entirety. LUMINARIES are called, not only among astronomers, but also among almost all writers, by antonomasia, the chief lights of heaven: the Sun, namely, and the Moon, those two likenesses of divinity, the torches of the world, the adornments of the orb, and the life of all things, known even to brute animals. They are so called because of the abundance of light: for which reason Genesis 1 says that God made from the beginning two great luminaries, the Sun, to preside over the day, and the Moon, to preside over the night. Not because they are very large in comparison with the other stars, (for indeed it is certain that the Moon is smaller than the terrestrial globe itself, and therefore smaller than all the stars, both fixed and wandering, except Mercury, as we shall soon say, and some make the Sun greater than Sirius) but because they surpass all the stars in light, the Sun indeed by the intensity of light, in which active qualities prevail in it, the Moon by the extension of the same light and by passive qualities. Hence well did the author of the Centiloquium say, in brief, that the Sun is the source of vital power, the Moon of natural power, because in living beings the Sun is truly the author of innate heat, the Moon of radical moisture; whence also they administer matter and material form in all things, and dispose celestial qualities in mixed things, reducing them to act, and aiding immediate causes toward the production of their own effects, all of which they contain in virtue and power. Therefore the whole life of living beings depends on the luminaries as on universal causes, and as equivocal causes subordinate nevertheless to the first and most universal cause, which in a general concurrence with all natural effects concurs, and gives even to the secondary causes the ability and power to act. Yet among secondary causes the luminaries claim for themselves a certain universal primacy in action: and so when joined with benefic causes they produce animals and mixed things of a temperate nature, for the benefit and usefulness of the human race; but if they should be joined with malefic causes, they contribute to the production of harmful animals, hostile to any good mixtures, and destructive of them, to the corruption of the air, the ruin of fruits, the sterility of the earth, etc. whence pestilences, famines, diseases, and other such evils arise: and from this too it is apparent how these evils arise chiefly from the defects of the luminaries, because, (as Titus rightly noted, book 1, chap. 14, and explains and confirms on the authority of the Holy Congregation, the most learned Father Auerta in the notes and declarations prefixed to the works of the same Titus) the luminaries among secondary causes are universal regulators,

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268 LEXICON significatores ac largitores omnium bonorum vnde nil mirum, si impedita in deliquijs eorum luce, impediatur etiam aliquatenus actio, & influxus, ex quo demum eueniant morbi aëris corruptela, sterilitas terræ, caloris innati defectus, humidi radicalis extinctio, & alia id genus, quæ deficientibus causis primarijs arguunt etiam effectuum consequentiam. Quapropter iure, & consequenter arguens magnus ille Areopagita in magno illo, ac præternaturali Luminarium defectu in passione Domini exclamasse fertur: Aut Deus natura patitur, aut mundi machina dissoluetur , quia videlicet fine peculiari Dei assistentia, & miraculo mundi machina diù consistere non potuisset, quandiu à luminaribus, ac Sole præsertim tanto tempore obscurato, lucem adeoque vitam, haurire non ei foret permissum Sed de hac re satis: Plura cum de ipsis luminaribus singillatim redibit sermo. <43.> In suo lumine dici solet esse Planeta cum sit in loco suæ naturæ conformi, hoc est, vt diurnus sit de die suprà terram, & de nocte sub terra: sicut econtrà nocturnus de nocte sit supra terram, & de die sub terra: & insuper sit in loco apto ad rem quæ per ipsum naturaliter significetur. <44.> LVNA luminare minus sic dicta quasi contracti à lueuna eo quod cum Sole aliquando luceat, vel vt placet Isidoro à Lucina, abiecta media sillaba, vna ex septem erraticis proximior terræ, planeta foemininus, ac nocturnus, quippequi (vt paulò ante dictum est) cum habeat lumen à Sole mutuatum, & extensum magis, quam intensum vincit in qualitatibus passiuis, atque in humiditate: & ideò, vt Sol præest cordi, spiritibus, sanguini, &c. ita & Luna præest cerebro, visceribus, pituitæ, & quemadmodum Sol potentiæ vitalis scaturigo est, ita Luna potentiæ naturalis. Quantam verò in terris actiuiratem habeat Luna, nemo est, qui non videat: vnde meritò à D. Ambrosio in Hexamer. Maseroris, decor noctis, ministræ humoris, maris dominatrix, mensura temporis, motrix aëris Solis, denique æmula appellatur. Idque oritur tum ex eius propinquitate ad terram, tum etiam ex maiori consistentia: plus enim quam reliqui planetæ suprà terram consistit, motu suo resistens motui primi mobilis, atque vna ferè integra hora plus alijs nostrum hemisphærium perlustrans. Perficit enim cursum suum in Zodiaco spatio dierum 27. hor. 7. min. 41. cum alias quousque ad Solem iterum feratur, requirantur dies 29. hor. 12. min. 44. Hinc triplex mensis, & Lunarium vicissitudinum momenta tria à scriptoribus communiter assignantur. Periodicus, scù peragrationis, in quo Luna complet integram revolutionem in Zodiaco, & reuertitur ad idem

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268 LEXICON signifiers and bestowers of all good things, whence it is no wonder if, when their light is hindered by the faults committed in them, their action and influence are also hindered to some extent, from which there eventually arise diseases, corruption of the air, sterility of the earth, failure of innate heat, extinction of radical moisture, and other things of that kind, which, the primary causes failing, also argue the consequence of the effects. Wherefore the great Areopagite, arguing rightly and consequently, is reported to have cried out on that great and supernatural defect of the luminaries in the Passion of the Lord: Either God suffers by nature, or the machine of the world will be dissolved , because, namely, without God’s special assistance and a miracle, the machine of the world could not long have stood, since, with the luminaries, and especially the Sun, so long obscured, it was not permitted to it to draw light and thus life. But enough on this matter: more will be said about the luminaries themselves in due course. <43.> A planet is said to be in its own light when it is in a place conformable to its nature, that is, when a diurnal planet is above the earth by day and beneath the earth by night; conversely, when a nocturnal planet is above the earth by night and beneath the earth by day; and moreover when it is in a place fit for the thing naturally signified by it. <44.> The MOON, the lesser luminary, is so called, as if contracted from lueuna, because it sometimes shines with the Sun, or, as Isidore prefers, from Lucina, with the middle syllable omitted. It is one of the seven wandering stars, nearest to the earth, a feminine and nocturnal planet, since (as was said a little before) although it has light borrowed from the Sun, and is more extended than intense, it prevails in passive qualities and in humidity; and therefore, just as the Sun presides over the heart, spirits, blood, etc., so the Moon presides over the brain, the viscera, phlegm; and just as the Sun is the source of vital power, so the Moon is of natural power. How much activity the Moon has on earth, there is no one who does not see: whence it is rightly called by St. Ambrose in the Hexameron, the adornment of the night, the servant of moisture, mistress of the sea, measure of time, mover of the air, and finally the rival of the Sun. And this arises both from its nearness to the earth and also from its greater consistency: for it remains above the earth more than the other planets, resisting by its motion the motion of the primum mobile, and traversing our hemisphere by almost a full hour more than the others. For it completes its course in the zodiac in the space of 27 days, 7 hours, 41 minutes; whereas, before it is again brought to the Sun, 29 days, 12 hours, 44 minutes are required. Hence three kinds of month, and three moments of lunar vicissitudes, are commonly assigned by writers. Periodic, that is, of revolution, in which the Moon completes a full revolution in the zodiac and returns to the same

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MATHEMATICVM. 169 punctum, vnde discesserat; synodicus, seu coniunctionalis, & est quem modò explicaui, in quo à Sole discedens, iterum ad ipsum reueritur, vt ei corpore iungatur; ac terrius, quem dicunt apparitionis, seu illuminationis in quo Luna viubilis est, & lumen suum exerit, quod sit spatio dierum 26. hor. 12. reliquis tribus diebus silens quæ causa omnis motionis in hisce inferioribus, vt præ cæteris obseruat Plinius lib. 2. cap. 45. 99. Cæterum Lunare corpus sphæricum est, densum, opacumque, nulla præditum luce, sed tota quam habet à Sole mutuata: Hinc pro diverso, ac multiplici ad Solem positu, aspectus, ac figuræ diuersitas, quas Phases dixere. Nam quamuis perpetuò eius medietas illustretur à Sole, & eò magis quò Sol vicinior; (vt enim habetur ex opticis, sphæra maior luminosa intensiùs, & ampliùs lumen suum commuicat sphæræ minori è proximo illi obiectæ, quam è longinquo,) nihilominus non eodem modo semper à nobis conspicitur, sed pro diuersa ad terram habitudine, modò tota obscura (quod in Solari defectione, maximè obseruari potest, vbi conspicitur quidem Lunare corpus Soli aduersum, sed prorsus obscurum, cum ea medietas nobis obuersa à solaribus radijs minimè attingatur, sed ea tantum, quæ nobis inconspicua est,) modò corniculata, modò dichotoma, modò demum in Solis oppositione, plena, & eâ parie tota, quæ nobis offerrur, tota etiam illuminata conspicitur. Quod autem etiam in plenilunio aliquæ maculæ, seù eius particulæ minùs illustratæ videantur, existimauit Plinius lib. 2. cap. 9. eas aliud non esse, quam terra raptas cum humore sordes. Arcesila verò partes adustas, & nigras. Tales econìra partes humidiores, quibus igneus orbis attemperatur; sicut inquit etiam Diodorus in Cælena: Luna semperat ignis astum, ne orbem consummas, & perdas: Philolaus, eas monies, ac sylvas autumar: alij demum puerari id oriri ex telluris effigie imbutæ aliqua luce à Sole illi communicata (quod ego sanè non item inficias) quam postea Luna tanquam speculum in se recipêret, ac referret. Verum ex hoc necessariò sequeretur, in varijs horizontis paribus, & pro diuersa telluris ad Lunam habitudine variandas fore huiusmodi maculas; quod tamen experientia falsitatis euincit; cum semper, & vbique locorum ipsa eandem formam retineat. Quare concludendum est, eas nil aliud esse, quam partes densiores, pressiores, & rudiores ipsius corporis Lunaris, quæ Solis lumen excipere æquè non possunt, ac quæ magis planæ ac lauigatæ: Quod etiam in tellure à Solis radijs illustrata fieri credendum est. Hinc diuersitas illa aspectuum; maria, montes, valles, fluiuos, campos

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point, from which it had departed; synodic, or conjunctive, and this is the one I have just explained, in which, departing from the Sun, it returns again to it, so as to be joined to it in body; and the third, which they call apparition, or illumination, in which the Moon is visible and exerts its light, which lasts for 26 days and 12 hours, the remaining three days being silent, the cause of all motion in these lower things, as Pliny observes above all others, book 2, chapter 45. 99. Moreover, the lunar body is spherical, dense, and opaque, endowed with no light of its own, but with all that it has borrowed from the Sun. Hence, according to its different and multiple position relative to the Sun, there is a diversity of appearance and figure, which they called phases. For although its half is perpetually illuminated by the Sun, and the more so the nearer the Sun is; (for, as is stated in optics, a larger luminous sphere communicates its light more intensely and more abundantly to a smaller sphere placed near it than to one farther away,) nevertheless it is not always seen by us in the same way, but according to its different relation to the earth, sometimes wholly dark (which can be especially observed in a solar eclipse, where the lunar body is indeed seen opposed to the Sun, but is completely dark, since that half turned toward us is scarcely reached by the solar rays, but only that part which is invisible to us), sometimes crescent-shaped, sometimes dichotomous, and finally, in opposition to the Sun, full, and then wholly illuminated in that part which is presented to us. But that even in full moon some spots, or parts of it less illuminated, are seen, Pliny, book 2, chapter 9, thought these to be nothing other than dirt torn up from the earth together with moisture. Arcesilaus, however, thought they were burned and black parts. Others, on the contrary, thought they were moister parts, by which the fiery orb is tempered; as Diodorus also says in Celena: the Moon always sustains the heat of fire, lest it consume and destroy the orb. Philolaus imagines them to be mountains and forests. Others at last suppose that this arises from the shape of the earth, imbued with some light communicated to it by the Sun, which, I certainly do not deny, and which the Moon then received into itself and reflected back as a mirror. But from this it would necessarily follow that in various equal horizons, and according to the different relation of the earth to the Moon, such spots would have to vary; yet experience proves this falsehood, since it always and everywhere retains the same form. Therefore it must be concluded that they are nothing other than denser, more compact, and rougher parts of the lunar body itself, which cannot receive the Sun’s light as well as those that are more flat and smooth: which must also be believed to occur in the earth illuminated by the Sun’s rays. Hence that diversity of appearances; seas, mountains, valleys, rivers, fields

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170 LEXICON <46.> aliaque id genus referentium. Nam qui dicunt Lunam esse corpus terreum ibique habitatores degere, atque animantia. quæ hac illac discursiant, (vri protrita fronte vidisse se iactat Daud Fabritius apud argolum) planè delirant. Non defuere tamen non ex antiquis modò, vt refert Cicero Quæst. Academ. lib. 4. sed ex recentioris multi, qui opinati sunt Lunam esse habitationi hominum valdè idoneam; quod ego non omninò improbarem; maximè quod respirationi, (quæ totum negotium facessit) saris esse potest leuissimum illud expansum, quod eiusdem rationis, ac noster iste aër, supra diximus esse: licet longè puriùs ac subtiliùs. At enim de facto ibi homines viuere, ac pecudes, proindeque habitatores illos Antichibones, hoc est, in altera opposita terra habitantes, vt volebat Macrobius in somnium seipionis cap. 11. error intolerabilis est in fide catholica, vel ad minùs temeritas magna, vt aduerrit Tannerus in dissertat. de Calo quæst. 4. sequeretur enim homines esse non ex Adamo progenitos, proindeque nec à Christo redemptos. Quod si quis eatenus id affirmaret, quatenus vellet, Paradisum illam voluptatis, hortum deliciarum Dei manu consitum, & plantatum, in quo positus fuit primus homo ab initio suæ conditionis, & à quo tandem eiectus est post peccatum in hanc terram ærumnis, & miserijs plenam: hanc inquam paradisum in Lunæ globo concipere, vbi nunc sanctissimi illi viri Henoch, & Elias miraculosè translati, loco depositi degant, iucundissimamque vitam ducant, quoadusque Mundi finis, & prædicationis tempus adueniat; id etsi nouum, non ideò tamen intolerabile dicerem, nec sacra scripturæ, aut Fidei dogmatibus vllo modo repugnans, prout fusè examinabimus suo loco, in verbo Paradisus terrestris, quantum rei dignitas exigit. <47.> Cæterum Luna ambitu suo comprehendit milliar. 21600. cum semidiameter eius sit milliar. 3440. Eius Cælum, seu regio expansi quod occupat, & per quam diuagatur, est lata milliar. 27520. Quod vel ex eo liquet, quia videmus ipsam in perigro constitutam distare à centro telluris semidiametr. terra 52. in apogro verò semidiametr. 60. inde est quod tota regio eius expansi est semidiametr. 8. quæ in millaria conuersæ faciunt summam milliar. 27520 Denique Luna in Genethliacis significat itinera, genus fæmininum, plebem, animi qualitates, humidi radicalis abundantiam, & his similia de quibus alibi videbir sermo. LVNÆ mansiones, seu stationes sunt partes quædam Zodiaci quas Luna cursu suo peragrans ob congressum cum stellis fixis inibi consistentibus imbuitur earumdem bonis, vel malis quæ-

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170 LEXICON <46.> and others of that kind who report such things. For those who say that the Moon is a terrestrial body and that inhabitants dwell there, and animals that run about here and there, (as David Fabritius boasts to have seen with his brow worn by use, apud Argolum) are plainly raving. Nevertheless, there have not been wanting, not only from among the ancients, as Cicero reports, Quæst. Academ. lib. 4, but also many more recent writers, who have thought that the Moon is very suitable for human habitation; which I would not altogether disapprove; especially because for respiration, (which makes up the whole business) that very light expanse may suffice, which we said above is of the same nature as this air of ours, though far purer and subtler. But as for the fact that men and cattle live there, and therefore those inhabitants called Antichthones, that is, those dwelling in the other, opposite earth, as Macrobius wanted in his Commentary on the Dream of Scipio, cap. 11, this is an intolerable error in the Catholic faith, or at least great rashness, as Tanner observes in his dissertation De Cælo, question 4; for it would follow that men were not descended from Adam, and therefore were not redeemed by Christ. But if someone were to affirm this only in so far as he wished to conceive the Paradise of pleasure, the garden of delights planted and set by the hand of God, in which the first man was placed from the beginning of his condition, and from which he was finally cast out after sin into this earth full of hardships and miseries: this Paradise, I say, in the globe of the Moon, where now those most holy men Enoch and Elias, miraculously translated, dwell in a place set apart, and lead a most pleasant life until the end of the world and the time of preaching shall come; though this is new, I would nevertheless not call it intolerable, nor in any way contrary to Holy Scripture or the dogmas of the Faith, as we shall examine at length in its proper place, under the word Terrestrial Paradise, as far as the dignity of the matter requires. <47.> Moreover, the Moon, in its orbit, comprises 21,600 miles, since its semidiameter is 3,440 miles. Its heaven, or region of the expanse which it occupies and through which it moves, is 27,520 miles broad. This is clear even from the fact that we see it, when in perigee, distant from the center of the earth by a semidiameter of 52; but in apogee by a semidiameter of 60. Hence the whole region of its expanse is a semidiameter of 8, which, when converted into miles, makes a total of 27,520 miles. Finally, in genethliacs the Moon signifies journeys, the feminine sex, the common people, qualities of the mind, abundance of radical moisture, and similar things, of which there will be mention elsewhere. The Moon’s mansions, or stations, are certain parts of the Zodiac which, as the Moon passes through them in its course and comes into conjunction with the fixed stars standing there, are imbued with their good or evil qualities, which-

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MATHEMATICVM: 271 litatibus, quibus proinde affectam, obseruauit antiquitas, varios diuersosque influendi modos induere in isthæc inferio- ra. Earum origo vti ab initio bona, innocens, naturalis, ta- tioni atque experientiæ conformis fuit; sic post modum Ægyptiorum vanitatibus deprauata, nullum est in rota Astro- logia commentum, cui in vanitate cedat. Copi eas suo gentili vocabulo quasi Lunæ diuersoria, seu habitacula nominant, alij Deorum stationes, rectius cum Kirchero dixeris, Dæ- moniorum stabula, cum tot tantisque superstitionibus sint referta. Et quoniam Luna cursum suum perficit diebus ferè 28. ideò singulis diebus singulas mansiones constituerunt, singulis proprias notiones, ac certa rerum significata attribuentes, & quod magis miteris, singulis suos genios, seu dæmones ad- ministros præficientes. Placet hic ad lectorum curiosirem leuandam ex Kircheri Oedipo, prout in eorum monumentis iacent, transcribere: inde eas nitori suo redditas, atque ab Argolo ad isthuc tempus diligenrissimè supputatas ex ponere, quoniam, vt dixi, omni superstitione abiecta ad solum natu- raliter consideratæ ex diuerso Lunæ cum stellis fixis congressu, experientia duce plurimum valent in rerum electionibus. Ergò Prima Lunæ mansio, quam Ægyptij stationem piscis dixerunt à ventre Ceti stella videlicet fixa dè natura Saturni, quæ incidebat in eam, proindeque infestationis inimicorum appellabant, cuique genium præficiebant nemine Kiacel, com- butabatur olim ab initio Arietis vsque ad 12. gradum eiusdem. Hanc modò Argolus temperatam vocat, ac figit in gr. 22. Arietis, dicitque esse idoneam ad medicinam laxatiuam su- mendam, atque iter quodcumque arripiendum. < II.> Statio, quam antiqui reconciliationis Principum appellabant, dantes ei pro genio Hiael computabatur à 12. gradu Arietis, vsque ad 25. ob fixam in capite eiusdem Arietis. Moderni autem eam constituunt in gr. 4. Tauri, quam dicunt aptam ad ferendum plantandum, atque iter faciendum per aquam, verum purgationibus inopportunam. < III.> Statio, quam Ægyptij vocabant prosperitatis, & bona fortu- na præfecto ei genio Ginchiael, erat olim à gr. 25. Arietis, vbi incidebat triangulum propè ventrem Ceti. Nunc autem est in gr. 17. Tauri, & eam vice versa vocat Argolus humidam, afferentem mala in itineribus. < IV.> Statio est in Pleiadibus, estque apud Arabes statio inimici- tiæ, & vindictæ dicta suo gentili vocabulo Altarich, cuius genius dicebatur Delhaicel. Hanc recensiores vocant tempe- ratè humidam, proindeque bonam ad ferendum, plantandum, iterque faciendu per aquas, & eam constituunt, in gr. 30. Tauri.

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MATHEMATICVM: 271 The ancients observed that these things, being affected by such qualities, thus to induce various and diverse modes of influence into these lower regions. Their origin, as at the beginning it was good, innocent, natural, and conformable to reason and experience, so later, corrupted by Egyptian vanities, there is no invention in the whole of astrology to which it yields in vanity. The Copi, in their native term, call them, as it were, the diversories or habitations of the Moon; others call them the stations of the gods; more correctly, with Kircher, you would call them the stables of demons, since they are filled with so many and such great superstitions. And since the Moon completes her course in about 28 days, they therefore established as many mansions as there are days, assigning to each its own meanings and fixed significations of things, and, what is more astonishing, appointing over each its own genii, or ministering demons. It seems good here, for the relief of the reader’s curiosity, to transcribe from Kircher’s Oedipus, as they lie in their monuments, and then to set them forth, restored to their proper form and as most diligently computed by Argolus up to this time; because, as I said, with all superstition cast aside, they are considered only as naturally regarded from the varying conjunction of the Moon with the fixed stars, and under the guidance of experience are of much value in the choice of things. Therefore the First mansion of the Moon, which the Egyptians called the station of the fish, from the belly of the Whale, namely the fixed star of the nature of Saturn, which fell within it, and therefore they called it the infestation of enemies, and assigned to it the genius Kiacel, was anciently computed from the beginning of Aries up to the 12th degree of the same. Argolus now calls this tempered, and places it at the 22nd degree of Aries, and says that it is suitable for taking a laxative medicine and for undertaking any journey. < II.> The station which the ancients called that of the reconciliation of princes, assigning to it for genius Hiael, was computed from the 12th degree of Aries up to the 25th, because of the fixed star in the head of Aries. The moderns, however, place it in the 4th degree of Taurus, which they say is fit for transplanting plants and for traveling by water, though unsuitable for purgations. < III.> The station which the Egyptians called that of prosperity and good fortune, with the genius Ginchiael presiding over it, was formerly from the 25th degree of Aries, where the triangle near the belly of the Whale fell. But now it is in the 17th degree of Taurus, and Argolus, conversely, calls it moist, bringing evils in journeys. < IV.> There is a station in the Pleiades, and among the Arabs it is called the station of enmity and vengeance, by its native name Altarich, whose genius was said to be Delhaicel. More recent writers call it moderately moist, and therefore good for transplanting, planting, and traveling by waters, and they place it in the 30th degree of Taurus.

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272 LEXICON. V. Statio posita est in Aldebaram, seu oculo australi Tauti, quam vocabant Hori maiorem, fauoris magnatum cui dabant pro genio Huaiel. Apud Argolum dicitur sicca, congruens itineribus, medicinisque sumendis. Computatur nunc in gr. 13. Geminorum. VI. Statio antiquis dicebarur claustrum formabaturque à duabus stellis Geminorum, quarum altera vocatur propus altera Ras Algiense (de quibus suo loco dictum) proindeque statio bene- lentiæ, & amoris nuncupata, cui genium præficiebant nomine Phigiacel. Nunc autem est in gr. 26. Geminorum, atque apud Argolum dicitur temperata, sed ad nihil idonea ob stellas maleficas in ea sitas. VII. Dicitur statio acquisitionis bonorum, quam Abenragel scapulas Geminorum vocat ab stellis in ea contentis, eamque computat à gr. 18. vsque ad 30. Geminorum, dando ei pro genio Zisael. Argolus verò nunc eam figit in gr. 9. Cancri, dicitque humidam, atque adeo bonam ad serendum, arandum, sed infensam itineri nisi aggrediantur per aquas. VIII. Ægyptijs dicta Cubitus Hilis, alijs Cubirus Leonis, incipiebat ab initio Cancri, & protendebarur vsque ad gr. 13. eiusdem signi. Genius eius'erat Hathael, dicebaturque victoriæ in bello. Ea nunc est in 22. Cancri, quam dicir Argolus nubilosam, remperatam, aptam ad medicinam sumendam, iterque arripiendum. IX. Dicta Alnuthreh Statio infirmitatum, constituirur ab Antiquis in Asellis à gr. 13. vsque ad 26. Cancri, cuius Genius dicebatur Tiaiel. Argolus eam figit in gr. 8. Leonis ac dicit siccam, ad omnia in opportunam. X. Arab. dicta Eltarph, felicitatis partus, computabatur olim à gr. 26. Cancri vsque ad gr. 9. Leonis: cui genius præficiebatur Biacel. Nunc autem figitur in gr. 17. Leonis, diciturque humida, proindeque ad plantandum apra, sed itineri non idonea. XI. Arabibus dicebatur Elgielbe; Latine frons computata à gr. 9. Leonis vsque ad 21. Genius eius dictus est Kekaiel. Argolus eam constituit in gr. 30. Leonis, dicitque remperare frigidam, bonam ad iter, plantandum, serendum, sed sumendis medicinis incongruam. XII. Apud Ægyptios dicta Alcharkah, alijs Alzabre statio separationis amicitiæ, numerata à gr. 21. Leonis vsque ad gr. 4. Virginis, præfixo ei Genio Laael. Nunc verò eadem figitur in gr. 13. Virginis, eamque vocat Argolus humidam, bonam ad ædificandum, plantandum, sed ad cætera inopportunam. XIII. Antiquis

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272 LEXICON. V. A station is placed in Aldebaram, or the southern eye of Tautus, which they called the greater Hori, the favor of the great ones, to whose genius they gave the name Huaiel. Among Argol it is said to be dry, suitable for journeys, and for taking medicines. It is now computed at 13° of Gemini. VI. In ancient times the station was called a cloister, and was formed by two stars of Gemini, one of which is called Propus, the other Ras Algiense (of which mention has been made in its place), and therefore the station was named of benevolence and love, to which they assigned a genius by the name of Phigiacel. But now it is at 26° of Gemini, and among Argol it is said to be temperate, but suitable for nothing because of the evil stars situated there. VII. It is called the station of the acquisition of goods, which Abenragel calls the shoulders of Gemini from the stars contained in it, and he computes it from 18° to 30° of Gemini, giving it as genius Zisael. Argol, however, now fixes it at 9° of Cancer, and says it is moist, and therefore good for sowing, ploughing, but hostile to travel unless they go by water. VIII. Called by the Egyptians Cubitus Hilis, by others Cubirus Leonis, it began from the beginning of Cancer, and extended as far as 13° of the same sign. Its genius was Hathael, and it was said to be for victory in war. It is now at 22° of Cancer, which Argol says is cloudy, temperate, suitable for taking medicine, and for setting out on a journey. IX. Called Alnuthreh, the station of infirmities, it was established by the Ancients in the Aselli from 13° to 26° of Cancer, whose genius was said to be Tiaiel. Argol fixes it at 8° of Leo and says it is dry, suitable for everything. X. In Arabic called Eltarph, the felicity of childbirth, it was formerly computed from 26° of Cancer to 9° of Leo: over it the genius Biacel was appointed. Now however it is fixed at 17° of Leo, and is said to be moist, and therefore fit for planting, but not suitable for travel. XI. Among the Arabs it was called Elgielbe; in Latin, the front computed from 9° of Leo to 21°. Its genius was called Kekaiel. Argol places it at 30° of Leo, and says it is moderately cold, good for travel, planting, sowing, but unsuitable for taking medicines. XII. Among the Egyptians called Alcharkah, by others Alzabre, the station of separation of friendship, numbered from 21° of Leo to 4° of Virgo, with the Genius Laael assigned to it. Now, however, the same is fixed at 13° of Virgo, and Argol calls it moist, good for building, planting, but unsuitable for other things. XIII. The ancients

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MATHEMATICVM. 273 Antiquis dicta statio amoris Arab. Alszarphet à gr. 4. Vir- <XIII.> ginis vsque ad 18. genius eius dicitur..... Argolus hanc con- stituit in gr. 26. Virginis aitque esse temperatam, bonam ad serendum, arandum, iter arripiendum. Dicta statio larrantis. ( forsan à Cane) Arab. Algaua à gr. <XIV.> 18. vsque ad finem Virginis, cuius Genius dictus est Kakuaiel. Stario diuortij, ab Argolo dicitur temperata, bona ad semi- nandum, planrandum, medicinam sumendam: sed ad iter pessimæ constituitur ab eo in gr. 9. Libræ. Ratio altitudinis nuncupata, acquisitionis amicorum Arab. <XV.> Alsamak, cui genius assignabatur Kekaiel computata ab initio Libræ vsque ad gr. 13. Nunc autem est in 21. Libræ, estque humida; in qua bonum fodere puteos, at non iter attripere. Dicta Stario propitiationis lucri, & mercimoniæ Arab. <XVI.> Algaphra computata à gr. 13. vsque ad 26. Libræ, Genicum habebat nomine Aklaiel. Argolus eam figit in gr. 4. Scorp. eandemque vocat frigidam, & humidam, malamque mansio- nem in omnibus. Dicta Statio Latrociniotum Arab. Alzananach, olim om- <XVII.> putabatur à gr. 16. Libræ ad 9. Scorpij, sub genio Papaiel. Nunc autem est in gr. 17. Scorpij, vocaturque humida, bona ad emendas bestias, sed non ad iter. Dicta Corona Arab. Eclil. à 9. Scorpij ad 21. Statio infirmi- <XVIII.> tatum cui genius erat nomine Misraiel. Ab Argolo dicitur sicca, bona ad ædificandum, serendum, planrandum, atque ad nauigandum, computatur modo in gr. 30. Scorpij. Antiquis dicebatur cor, quia erat prope cor Scorpij, Statio <XIX.> recuperationis sanitaris sub genio Kephaiel à gr. 21. Scorp. vsque ad 4. Sagittarij. Nunc verò est in gr. 13 eiusdem signi, humida, bona ad serendum, plantandum, iter aggrediendum. Dicta sancta Arab. Alschaulet, Statio Venationis quæ ge- <XX.> nium sorriebatur nomine Rezaiel, à gr. 4. vsque ad 17. Sagit- tarij. Argolus eam figit in gr. 28. Sagittar. vocatque humi- dam, ad bestias, siue pretio siue venatione comparandas ap- primè idoneam. Arab. dicta Elnaim, hoc est Statio gratiæ, & iucundiratis, <XXI.> seu quod laram produceret segetem, habebar genium dictum Setatiel à gr. 17. vsque ad finem Sagittat. Nunc aurem est in gr. 8. Capricorni, diciturque ab Argolo temperata, bona ad ædificandum, serendum, fundos, & terras emendum. Olim computabarur ab initio Copricorni vsque ad 13. dicta <XXII.> Statio sugæ & exilij, Arab. Elbldch, sub genio Tetaiel. Ar- golus eam dicir humidam, apram ad nauigandum, atque ad medicinas sumendas, constituitur autem nunc in gr. 22. Capric. S

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MATHEMATICVM. 273 The ancients called this the station of love, Arab. Alszarphet, from 4° of Vir- <XIII.> go to 18°; its genius is said to be..... Argolus places it at 26° of Virgo and says that it is temperate, good for sowing, ploughing, and undertaking a journey. The station called of wandering, perhaps from the Dog, Arab. Algaua, from 18° <XIV.> to the end of Virgo, whose Genius was called Kakuaiel. The station of divorce, by Argolus is said to be temperate, good for sowing, planting, taking medicine; but for travel it is assigned in the worst way by him at 9° of Libra. The height called Ratio, of acquiring friends, Arab. <XV.> Alsamak, to which the genius Kekaiel was assigned, calculated from the beginning of Libra to 13°. It is now in 21° of Libra, and is humid; in which it is good to dig wells, but not to set out on a journey. The station called of propitiation, gain, and trade, Arab. <XVI.> Algaphra, calculated from 13° to 26° of Libra, had the angelic being named Aklaiel. Argolus fixes it at 4° of Scorpio, and calls it cold and humid, and a bad mansion in all respects. The station called of robberies, Arab. Alzananach, formerly <XVII.> was reckoned from 16° of Libra to 9° of Scorpio, under the genius Papaiel. Now it is at 17° of Scorpio, and is called humid, good for buying beasts, but not for travel. Called Corona, Arab. Eclil, from 9° of Scorpio to 21°; the station of infirmities, whose genius was named Misraiel. Argolus calls it dry, good for building, sowing, planting, and also for sailing; it is now reckoned at 30° of Scorpio. To the ancients it was called the heart, because it was near the heart of Scorpio, the station <XIX.> of recovery of health under the genius Kephaiel, from 21° of Scorpio to 4° of Sagittarius. But now it is at 13° of the same sign, humid, good for sowing, planting, and setting out on a journey. Called holy, Arab. Alschaulet, the station of hunting, which had the genius named Rezaiel, from 4° to 17° of Sagit- <XX.> tarius. Argolus fixes it at 28° of Sagittarius, and calls it humid, very suitable for procuring beasts, whether by purchase or by hunting. Arab. called Elnaim, that is, the station of grace and pleasantness, <XXI.> or because it produced a rich crop, it had the genius called Setatiel from 17° to the end of Sagittarius. Now it is in 8° of Capricorn, and is said by Argolus to be temperate, good for building, sowing, buying estates and lands. Formerly it was reckoned from the beginning of Capricorn to 13°; called <XXII.> the station of flight and exile, Arab. Elbldch, under the genius Tetaiel. Argolus says it is humid, fitting for sailing and for taking medicines, but it is now set at 22° of Capric. S

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274 LEXICON XXIII. Dicta Brachium sacrificij, Arab. Saadeldabakh Statio de- structionis, & expilationis computata à gr. 13. ad 26. Capric. sub genio Tetzaiel. Nunc autem est in gr. 4. Aquarij, tem- perata apta ad medicinas, nec non ad iter. XXIV. Statio foecunditatis gregum beatitudo seu brachium absor- tumnuncupata, Arab. Saadbelaa sub genio Kachael à gr. 29. Capric. vsque ad 9. Aquarij sita in ipsa fixa caudæ Capricorni, nunc autem est in gr. 17. Aquarij temperata, medicinis su- mendis optima. XXV. Statio affluentiæ bonorum terræ dicta beatitudo beatitudi- num, seu brachium brachiorum Arab. Saad Elsaand, alijs Phem Elhaut, hoc est os piscis, computabatur à gr. 9. vsque ad 21. Aquarij: Geniuseius erat Dedaliel. Argolus verò eam si- git in gr. 26. Aquarij, ac dicit siccam, bonam ad iter, atque ad fundandum, XXVI. Dicta, brachium abscenditum, Arab. Saad Elachbich Statio voluptatum sub genionomine Szaszaiel computata ad gr. 21. Aqvar. ad 4. Piscium. Nunc autem est in gr. 13. Piscium dici- turque ab Argolo sicca, medicinis vtilis, ad alia verò infausta. XXVII. Statio siccitatis dicta prioris germinationis Arab. Alphara Elmakodden, à gr. 4: vsque ad 17. Piscium, cui genius affi- gebatur dictus Tassael, à recensoribus constituitur in gr. 26. Piscium, appellaturque humida, bona ad medicinas su- mendas. XXVII. Tandem Statio ab antiquis dicta posterioris germinationis Arab Alphara Elinuchar computata à gr. 17. vsque ad finem Piscium sub regimine genij Haichaziel; dicta etiam statio inundationum. Hæc modo est in gr. 8. Arietis, diciturque ab Argolo temperata, bona ad serendum, atque ad medicandum. Atque hæ sunt mansiones Lunæ astu dæmonis, Ægyptiorum nugamentis, & mille superstitionibus deprauatæ, quò ars Alioqui bona experimentis, viribusque naturalibus siderum nixa deturparetur, & vel religionis ergò homines ab eius vsu absterrerentur, vel eam vltrò capesserent cum pietatis discrimine. Hoc, inquam, est bonum semen semitatum in agro, cui inimicus homo liuore percitus, superseminauit zizania: sed non ideò eradicanda, ne simul cum eis eradicemus, & tri- ticum, adeoque bona naturæ à nobis remoueamus, studio superstitionis vitandæ: quin potius sinamus vtraque cresceretum segregatis, resecatisque omnibus vanitatibus, quæ purè naturalia sunt colligamus, atque ijs in bonum nostrum vta- mur. 49. Lyrus, Fera, Bestia Centauri, Arab. Esseda, in tabulis persicis pridemus, Hæbeis autem Nemer, id est Pardus, Sidus in

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274 LEXICON XXIII. Called the arm of sacrifice, Arab. Saadeldabakh, the station of destruction and plundering, reckoned from 13° to 26° of Capricorn, under the genius Tetzaiel. But now it is at 4° of Aquarius, temperate, suitable for medicines, and also for travel. XXIV. The station of the fertility of flocks, called beatitude, or the abandoned arm, Arab. Saadbelaa, under the genius Kachael, from 29° Capricorn to 9° Aquarius, situated in the very fixed tail of Capricorn; but now it is at 17° Aquarius, temperate, and best for taking medicines. XXV. The station of the abundance of the goods of the earth, called the beatitude of beatitudes, or the arm of arms, Arab. Saad Elsaand, in others Phem Elhaut, that is, the mouth of the fish, was reckoned from 9° to 21° Aquarius; its genius was Dedaliel. Argolus, however, places it at 26° Aquarius, and says it is dry, good for travel, and for founding. XXVI. Called the ascending arm, Arab. Saad Elachbich, the station of pleasures under the name of the genius Szaszaiel was reckoned from 21° Aquarius to 4° Pisces. But now it is at 13° Pisces, and according to Argolus it is dry, useful for medicines, but otherwise inauspicious. XXVII. The station of dryness, called the first germination, Arab. Alphara Elmakodden, from 4° to 17° Pisces, to which a genius called Tassael was assigned, is placed by the revisers at 26° Pisces, and is called moist, good for taking medicines. XXVII. Finally, the station called by the ancients the second germination, Arab. Alphara Elinuchar, reckoned from 17° to the end of Pisces under the rule of the genius Haichaziel; this station is also called the station of inundations. It now is at 8° Aries, and is said by Argolus to be temperate, good for sowing and for healing. And these are the mansions of the Moon, distorted by the trick of the demon and by the follies of the Egyptians, and by a thousand superstitions, so that an art which otherwise is good, founded on experience and on the natural powers of the stars, should be disfigured, and either men, for religion’s sake, should be deterred from using it, or else should embrace it of their own accord at the risk of piety. This, I say, is the good seed sown in the field, which an enemy, a man moved by envy, has oversown with tares; but they are not therefore to be uprooted, lest together with them we uproot the wheat also, and thus remove from ourselves the goods of nature, out of a desire to avoid superstition. Rather let us allow both to grow together, and, with all vanities set aside and cut away, let us gather what is purely natural and use it for our good. 49. Lyrus, Fera, Beast of the Centaur, Arab. Esseda, in the Persian tables of old, but among the Hebrews Nemer, that is, the Leopard, a star in

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MATHEMATICVM. 275 vox ad australem plagam sub signo Libræ constans stellis 29. de natura Malesicarum. Vide fusius in verbo Bestia Cantauri. Lx est qualitas quædam corporis lucidi ei propria ab 50. eoque intrinsecè emanans: vnde differt à lumine, quod est quid posterius ab ipsa luce productum per effluxum radiorum ab ipsa luce ad alia corpora luminis receptiua quale est quod in aëre, seù alio quouis diaphano producitur per reflexionem ra- diorum ab ipsa luce emanantium, vel quod etiam videmus in corporibus opacis, sed leuigatis, in quibus recipitur lumen à luce primigenia derivatum, ac præcipuè in sideribus lumen suum à Sole mutuantibus. Quare lux propriè dicitur Soli com- petere omnis luminis fonti, lumen verò sideribus. Radius verò est instrumentum proximum, quo ipsa lux se communi- cat, & lumen gignit, licet sæpissimè etiam lux cum lumine conuertatur. De qua re vide quæ erudite habet Kircherus in libro Artis magnæ lucis, & vmbræ. Lux etiam quandoque accipitur pro ipsis stellis: sic Cicero in Arati Phænom. Illæ, qua fulgent luces ex hore corusco, Sunt inter partes gelidas Aquilone locatas, Acque inter spatium, & lati vestigia Solis. LY LYBICVS ventus, idem, qui Africus, vnsus ex ventis Occi- <51.> dentalibus, lateralis Fauonio, oppositus directè Cæciæ, spirans ab occasu bruniali, sic dictus, à Lybia per quam spirando transit. Est de natura sua frigidus, & humidus, pluuiosus, ac tempestatis indez, de eo scribit Plinius, vt alibi obseruatum est, quod flatu suo facit pecudes foemineam prolem concipere. Vide in V. Africus. LYBANOTVS ventus item Lateralis, sed adiacens Austro <52.> dictas etiam Austro-Africus, directè oppositus Aquiloni. Est de natura sua calidus, sed magis humidus, pluuiosus; noxius, & morbificus, habet sibi collaterales V polybanorum adiacentem Notolibico ad occasum, Mesolybanorum verò ad Austrum ipsi vento Cardinali immediatum. LYRA Vultur cadens, Fidicula Græcis Chelys Arab. verò <53.> Vvega, &c. sidus in octaua sphæra ad borealem plagam, ha- bens stellas decem de natura Veneris, & Mercurij, quarum potissima est, quæ Arabicè dicitur Brinek primæ magnitudi- nis, existens nunc in gr. 11. Capricorni cum latitudine bor. ferè gr. 62 Hæc oritur Romæ circà Kalendas Nouembris cum gr. 10. Scorpij. occidit verò cum vltimo gradu Aquarij; S ij

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MATHEMATICVM. 275 a voice, constant with 29 stars, in the southern region under the sign of Libra. on the nature of Malesicae. See more fully under the word Bestia Cantauri. Lux is a certain quality of a luminous body proper to it from itself and intrinsically emanating from it; whence it differs from lumen, which is something later, produced by light itself through the efflux of rays from the light itself to other receptive bodies of light, such as is produced in air, or any other diaphanous body, by the reflection of rays emanating from the light itself, or that which we also see in opaque but polished bodies, in which lumen derived from primordial light is received, and especially in the stars, which borrow their light from the Sun. Therefore lux is properly said to belong to the Sun, the source of all light, and lumen to the stars. Radius, however, is the nearest instrument by which light itself communicates itself and generates lumen, although very often light and lumen are also interchanged. On this matter see what Kircher has learnedly written in the book Artis magnae lucis, & umbrae. Lux is also sometimes taken to mean the stars themselves: thus Cicero in Aratus' Phænomena: Those, shining brightly with a glittering gleam, Are among the cold regions placed by the North Wind, And between the space and the wide traces of the Sun. LY LYBICUS wind, the same as Africus, one of the western winds, lateral to Favonius, directly opposite Caecias, blowing from the western quarter, so called from Libya through which it passes while blowing. By its nature it is cold and moist, rainy, and a sign of storm. Pliny writes of it, as has elsewhere been observed, that by its blast it causes livestock to conceive female offspring. See under Africus. LYBANOTVS wind likewise lateral, but adjacent to the South, also called Austro-Africus, directly opposite Aquilo. By its nature it is warm, but more moist, rainy, harmful, and disease-producing; it has as its side winds V polybanorum adjacent to Notolibicus on the west, and Mesolybanorum to the south, immediately next to the cardinal wind itself. LYRA, Vultur cadens, Fidicula of the Greeks, Chelys of the Arabs, Vega, etc., a constellation in the eighth sphere in the northern region, having ten stars of the nature of Venus and Mercury, the chief of which is that called in Arabic Brinek of first magnitude, now being in 11° Capricorn with northern latitude of about 62°. It rises at Rome around the Kalends of November with 10° Scorpio; and it sets with the last degree of Aquarius; S ij

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LEXICON quo tempore pluuias, & humiditates affert; sicut etiam cum Satutno aera nubilosum, & aquosum: Cum Mercurio verò subitam mutationem in humiditate, ac ventorum status. De ea in alicuius Natiuitate horoscopante sic loquitur Firmicus lib. 8. cap. 6. Nati erunt æqui, recti, cupidi, & ad omne æquitatis officium apti, scelerumque vindices, & quibus publica judicia, quæstionesque credantur. Si verò hunc locum Saturnus quacumque irradiatione respezerit, tortores erunt, carnifices, & qui malos homines prono studio prosequantur. At si in Occidente reperiatur, nati publicis tormentis lacerati, aut ignibus exusti seu tortione legitima peribunt. Præsertim si hunc locum Mars, Saturnus ve respezerint. Hæc Firmicus. Pæterèà Fidicula cum luminaribus, Ioue, aut parte fortunæ in idoneis figuræ locis, aut in secunda domo reperta magnas felicitates affert, magnasque diuitias. Vide adhuc quæ diximus in V. Fidicula. Explicit L. MA 1. MAGIA olim scientia siderum dicebatur per se alioqui bona innocens, & naturalis, qua ex cognitione, & mutua applicatione naturalium virium, atque influxuum, quibus sidera pollent, tradebatur ratio mirabilia operandi, quæ naturæ miracula appellantur. De hac Philo in lib. de specialibus legibus sic loquitur. Veram Magiam hoc est perspectiuam scientiam, per quam natura opera cernuntur clarius vt honestam, expetendamque non plebeij solum sectantur, sed etiam Reges Regum maximi, præsertim Persici tam curiosi harum artium, vt regnare non liceat, nisi cum magis versato familiariter. Vnde & Magi dicti sunt tres Reges Orientales, qui ex siderum contemplatione in Saluatoris ortu nouum Regem natum intelligentes, in Bethleem ad ipsum adorandum venerunt. Verùm posteà ipsa siderali scientia ab Arabibus deprauata, ac superstitionibus multis referta, Magiæ nomen iamiam malè audire coepit, ac tandem dicta est ars omnium scelestissima, quæ relictis veræ Philosophiæ præceptis solo demonum commercio gaudet, eiusque adminiculo mira quidem sed infauda, seù verè, seù illusoriè operatur. Huius auctorem facit Plinius Zoroastrem, quem refert vicies centum millia versuum de hac pernitiosissima arte scripsisse. Cæterum magiam legitimam, & naturalem dicit idem Plinius confari ex Medicina, ex Astrologia, atque ex Religione. Plura qui volet consulat Oedipum Ægyptiacum Kircheri tom. 2. 2. MAGISTRALIS VENTVS vulgò Nautarum dictus est Borro-

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LEXICON at which time it brings rains and humidity; as also when with Saturn it makes the air cloudy and watery; but with Mercury, a sudden change in humidity and in the state of the winds. Concerning this Firmicus speaks thus in the horoscope of someone’s Nativity, book 8, chap. 6: “They will be equitable, upright, desirous, and suited to every duty of justice, and avengers of crimes, and to them public judgments and examinations will be entrusted. But if Saturn should regard this place with any irradiation, they will be torturers, executioners, and people who pursue evil men with eager zeal. But if it be found in the West, the children will perish mangled by public torments, or consumed by fire, or by lawful torture, especially if Mars or Saturn should have regarded this place.” Thus Firmicus. Moreover, Fidicula, when found with the luminaries, Jupiter, or the part of fortune in favorable places of the figure, or in the second house, brings great happiness and great riches. See further what we said under V. Fidicula. End of L. MA 1. MAGIC was formerly called the science of the stars, in itself otherwise good, innocent, and natural, by which, from knowledge and mutual application of the natural forces and influences by which the stars are endowed, there was handed down the method of performing wonders, which are called miracles of nature. Concerning this, Philo in the book On Special Laws speaks thus: “True Magic, that is, a science of foresight, through which the works of nature are perceived more clearly, is pursued not only by honorable common people, but also by the greatest Kings of Kings, especially the Persian kings, so curious about these arts that they are not allowed to reign unless they are familiar with magi. Hence the three Eastern Kings were also called Magi, who, from contemplation of the stars, understanding at the birth of the Savior that a new King had been born, came to Bethlehem to worship him. But afterwards that very stellar science, corrupted by the Arabs and filled with many superstitions, began to bring the name of Magic into bad repute, and at last it was called the most wicked of all arts, which, abandoning the precepts of true Philosophy, rejoices only in commerce with demons, and by their aid works wonders indeed, but ominous ones, whether truly or deceptively. Pliny makes Zoroaster its author, and relates that he wrote two hundred thousand verses on this most pernicious art. However, the same Pliny says that legitimate and natural magic consists of Medicine, Astrology, and Religion. Whoever wishes more should consult Kircher’s Oedipus Aegyptiacus, vol. 2. 2. MAGISTRALIS WIND is commonly called by sailors Borro-

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MATHEMATICVM. 277 lybicus v[er]nus ex quatuor intermedijs, inter Septentionem, & Fauonium, eoquod sit veluti navigatoriæ artis magister: ab eo enim primum velificatio instituta fuit in mari Mediterraneo vt author est Plinius. Naturam eius abunde tradidimus in V. Borrolybicus. MALEVENTVM dictus est etiam Circius ob sui malignitatem: 3. vnde etiam Oppido illi maxime obnoxio idem nomen cessit olim, licet postea verso in bonum omne Beneuentum fuerit appellatum. MALEFICÆ antonomastice dictæ sunt duæ erraticæ mali- gnantiis naturæ, atque humano generi, quin & viuentibus om- 4. nibus inimicæ, Mars videlicet & Saturnus, sicut viceuersa beneficæ lupier, & Venus ob bona, quæ secum afferunt. MALEFICARE Chaldaicè dicitur Corona Gnoftia, fidus in 5. cælo propè Bootem, de quo vide suo loco. MAMARETH apud Arabes idem valet ac apud nos eleuatio, 6. siue supereminentia siderum super sidera, quando existentibus in aliqua familiaritate coniunctis, aliterum eorum vincit, & maioribus fortitudinum calculis pollet, tunc illud dicitur esse in Mamareth super aliud, frequens huius vocabuli v[er]sus in Albumasar, nec non in alijs scriptoribus Arabibus. Porrò in quo verè consistat huiusmodi siderum prærogatiua ex diuerso- rum placitis abundè diximus in V. Eleuatio. MANDIBULA Casi, vide Memchar. 7. MANIPVEVS spicarum, scu etiam fascis dicta est Arabibus teste schicchardo, Coma Beneniees, suo gentili vocabulo Huzimehom, de qua vide quæ diximus in V. Coma. MANNA, quod & Ros Syriacus, & mel acreum dici solet 8. liquor est dulcissimus virtute siderum ex vapore tenui & mixta quadam exhalatione concretus. De quo plura dicemus in V. Ros, quoniam eiusdem rationis est, & à calote insito dulcedinem illam, & spissitudinem contrahit. Vide ibi. MANVCODIATA Indorum vocabulo dicitur Auis Para- 9. disiaca, fidus nouum ad australem plagam nobis inuisum, di- ctum etiam Apus, constans stellis II. insimæ notæ. MAPPÆ apud tam Geographos, quam Astronomos vo- 10. cantur duo globi materiales, ac solidi, in quorum altero descriptæ sint omnes imagines octauæ sphæræ cum suis stellis exquisitissimè calculatis, referentes eum positum sub pri- mo mobili, (cujus circuli poli, diuisiones Zodiaci, & alia eiusmodi ibi etiam sint delineata,) eundem situm, eandem distantiam ad inuicem: quam nunc temporis in cælo sidera habent: in altero verò delineatus sit vniuersus orbis terrarum cum suis prouincijs, maribus, insulis promontorijs amni- S iij

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MATHEMATICVM. 277 A Lybian or western wind, one of the four intermediate winds, between the North and the West, because it is as it were the master of the navigator’s art: for by it, as Pliny says, sailing was first introduced in the Mediterranean Sea. We have sufficiently set forth its nature in V. Borrolybicus. MALEVENTVM was also called Circius on account of its malignity: 3. whence also the name once passed to that town especially exposed to it, although later, with the meaning changed to something good in every respect, it came to be called Beneventum. MALEFICÆ, by antonomasia, are the two wandering stars so called because of their malign influences upon nature and upon the human race, indeed hostile to all living things: namely Mars and Saturn; just as, conversely, the benefic ones are Jupiter and Venus, because of the good things they bring with them. MALEFICARE in Chaldaic is called Corona Gnoftia, a star in the sky near Boötes, of which see in its proper place. MAMARETH among the Arabs means the same as, among us, elevation or supereminence of the stars over the stars, when, among those existing joined in some familiarity, one overcomes the other and is possessed of greater strength in influence; then it is said to be in Mamareth over the other. This term is frequent in Albumasar, as well as in other Arabic writers. Moreover, what this prerogative of the stars truly consists in, according to the opinions of various authors, we have sufficiently discussed in V. Eleuatio. MANDIBULA Casi, see Memchar. 7. MANIPVEVS of spikes, or also of a sheaf, was called by the Arabs, according to Schickard, Coma Beneniees, by its own native name Huzimehom, concerning which see what we said in V. Coma. MANNA, which is also commonly called Ros Syriacus and bitter honey, is a most sweet liquid, concreted by the power of the stars from a thin vapor and a certain mixed exhalation. We shall say more about it in V. Ros, since it is of the same kind, and it derives that sweetness and thickness from innate heat. See there. MANVCODIATA in the Indian tongue is the name given to the Bird of Paradise, a new star invisible to us toward the southern region, also called Apus, consisting of II stars of the lowest magnitude. MAPPÆ are called by both geographers and astronomers two material and solid globes, in one of which are described all the figures of the eighth sphere with their stars most exactly calculated, representing it as placed beneath the primum mobile, with the poles of its circles, the divisions of the Zodiac, and other such things also delineated there, in the same position and at the same mutual distance as the stars now have in the sky; but in the other is delineated the whole orb of the earth with its provinces, seas, islands, promontories, rivers S iij

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LEXICON 278 bur vnaquæque pars sub proprijs parallelis, ac Zonis; vt facilè cuique sit vnico intuitu obseruare in vno, quam longitudinem, latitudinem, poli eleuationem quisque locus, aur ciuitas habeat, quam longè dister ab altera, quæ loca sint sibi opposita, quæ Antiscia, quæ Periscia, &c. in altero, stellas omnes in cælo dignoscere, suis nominibus compellare, earum situm habere, distrantiam quam ad invicem habeant metiri, quæ stella singulis locis sit verricalis, quæ singulis momentis oriatur, cælum culminer, &c in occasum uergat, cum quo gradu Zodiaci singulæ ad quamcumque poli eleuationem ascendant, cum quoue occidant; quæ semper lateant, quæ sint perpetuæ apparitionis, &c. quæ omnia, nisi mapparum ope, longo studio, atque indefessis laboribus vix comparari possent. Inter has præstant quas Hondius, Iansonius, & Bleu nuper diligentissimè fabricarunt adiectis etiam nouis Astris cælo affixis, nec non prouincijs in australi plaga vsque adhuc non detectis. 12. MARAT Musalselest hoc est mulier cathanata Arabicè dicitur Andromedæ, sidus ad Borealem plagam constans stellis 27. secundum nouas Baieri obseruationes, de natura Veneris, & Mercurij, de quo suo loco dictum, sed enim hic non prætereundum quod de hoc sidere horoscopante in alicuius ortu venustè habet Manilius in Astronom. lib. 3. sic enim canit. Quisquis in Andromedæ surgentis tempore ponto, Nascitur, immits veniet, pænæque minister: Carceris, & duricullos, quo stante superbo Prostrata iaceant miserorum in l'mine matres; Per noctesque patres cupiant extrema suorum Oscula, & in proprias animam transferre medullas, Carnificisque venit mortem ducenis imago, Accensisque regis, & stricta sapè securi, Supplicium vectigalerit, qui denique possit, pendensem è scopulis ipsam spectare puellam. Nec mirum (etsi aliàs Manilius more poëtico diffundatur) quandoquidem hoc est sidus infaustum destinans ad carceres, calamitates, supplicia, vnde eam ob rem sidus vinculum dicitur, & mulieris ad supplicium destinatæ imaginem præ se ferre voluerunt, qui eius naturam ab initio rimati sunt. 13. MARGHAB hoc est currus Arab. dicitur stella fixa secundæ magnitudinis de natura Martis, & Louis existens in prima ala, seù potiùs in Scapulis Pegasi in longitudine gr. 18.

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LEXICON 278 for each part under its own parallels and zones, so that it may be easy for anyone at a single glance to observe in one what longitude, latitude, and elevation of the pole each place or city has, how far it is distant from another, what places are opposite to it, which are Antiscia, which Periscia, etc.; in the other, to recognize all the stars in the heavens, to call them by their names, to know their position, to measure the distance they have from one another, which star is vertical to each place, which rises at each moment, culminates in the heavens, etc., and turns to setting; with what degree of the Zodiac each one, for whatever elevation of the pole, ascends, and with what it sets; which always remain hidden, which are of perpetual appearance, etc. All these things, unless by means of maps, could scarcely be acquired through long study and unwearied labor. Among these, the ones made especially excellent by Hondius, Janssonius, and Bleu, recently most diligently produced, with new stars also added, fixed in the heavens, and also provinces in the southern region hitherto not yet discovered. 12. MARAT Musalselest, that is, the chained woman, is called in Arabic Andromeda, a constellation in the northern region consisting of 27 stars according to the new observations of Bayer, of the nature of Venus and Mercury, of which something has been said in its proper place; but here it should not be passed over what Manilius has charmingly said about this constellation when it is horoscopic in someone's birth, in Astronom. book 3. For thus he sings: Whoever is born at the time of rising Andromeda on the sea, will come cruel, and a minister of punishment: of prison and hardships, while proud authority stands above, the mothers of the wretched lying prostrate on the threshold; and through the nights fathers longing for the last kisses of their own, and to transfer their soul into their own marrow, and the image of a hangman comes to die, and with the king kindled, and often with the drawn axe, a punishment exacted, who finally may be able, to gaze upon the girl herself hanging from the rocks. Nor is it surprising (though elsewhere Manilius may flow on in poetic manner), since this is an unlucky constellation, denoting prisons, misfortunes, punishments; for this reason it is called the chain-constellation, and those who first investigated its nature wished it to bear before itself the image of a woman destined for punishment. 13. MARGHAB, that is, a chariot in Arabic, is called a fixed star of the second magnitude, of the nature of Mars and Saturn, existing in the first wing, or rather in the Shoulders of Pegasus, in longitude 18 degrees.

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MATHEMATICVM. 279 Piscium cum latitudine Boreali gr. 19. quam magni faciunt Astronomi tum in mutationibus aeris obseruandis, tum in directionibus. MARCHEB. Item alia stella fixa quartæ quidam magni- < 14.> tudinis, sed valdè præsignis in medio scuri Argonauis fulgens de natura Louis, & Saturni, existens nunc in gt. 29. Cancri cum latitudine meridiana grad. ferè 47. Ea in horoscopo, vel horoscopus ad eam directus affert cordis hilaritatem, pru- < 15.> dentiam, grauitatem, itinera honorata, iniuriarum patien- < 16.> tiam atque amicitiam cum Iouialibus, & Satutninis non sine accessione honoris, & opum. Oritur Romæ cum gt. 26. Leonis, occidit cum 7. Geminorum. MARE. Vide Aqua. MARFIC Arab. hoc est reclinatotium, vel Marsikon id est < 17.> Axilla, teste teste Schikhardo in sua Vranomettia, dicitur stella fixa tertiæ magnitudinis, quæ est media in manu He- < 18.> niochi de natura Martis, & Mercurij, de qua vide in V. Auriga. MARS Planeta masculinus & nocturnus, vt pote calidus, < 19.> & siccus, sed vincens in siccitate (ideò vt notat Titus effæ- minatus) proximè sub Ioue supra Solem consistens, cursum suum absoluit spatio duorum ferè annorum solarium: Habet pto centroSolem, vt reliqui planetæ, excepta Luna, semper cir- < 18.> ca illum sese ipsum rotando; ideoque ita est cum eiusdem Solis circulo deferente dispositus, vt cum fuerit illi achronycè oppositus, videatur infra ipsum terræ vicinior, corpore prægrandis, itaut ipsam Veneremlferè exæquet, ac maiorem habet parallaxim quam ipse Sol, minutorum videlicet qua- < 18.> tuor, vt ego semel & iterum obseruaui. Hinc per descensum eius in imam absidem suis orbis magna illi sit caloris intensio in æstate, ac remissio frigoris in hyeme: terræ enim approxi- < 18.> matus vires suas valdè exerit, & inteadit: sicut econtia oppo- < 19.> situm experimur quando reperiur in Apogæo valdè à terra remotus; est enim differentia in diametris 1 68. quæ in mil- < 19.> liaria italica conuersæ faciunt summam 169020. Vt proinde nil mirum sit, si tanta diuersitas insit. Affirmat Kepletus in < 19.> Epistom. lib. 6. Martem aliquando videri dichotomum in qua- < 19.> draturis ad Solem, quod & in Ioue, atque in Saturno eue- < 19.> nire putat, eo maximè quod certum est reliquis planetis in- < 19.> ferioribus id competere. Fontana in eius medio maculam ni- < 19.> gram obseruasse se refert, cuius schema exhibet in suis ob- < 19.> seruationibus rr. 6. cap. 1. vnde & probabile est, hanc esse stellulam eius comitem, & quemadmodum duo superiores S iiiij

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MATHEMATICVM. 279 Piscium with northern latitude 19 degrees, which Astronomers greatly value, both in observing changes of the air and in directions. MARCHEB. Likewise another fixed star of the fourth, somewhat large magnitude, but very bright in the middle of the shield of Argo, of the nature of Jupiter and Saturn, now in 29 degrees of Cancer with southern latitude of nearly 47 degrees. In a horoscope, or when the horoscope is directed to it, it brings cheerfulness of heart, prudence, seriousness, honorable journeys, patience of injuries, and friendship with Jovial and Saturnine people, not without an increase of honor and wealth. It rises at Rome with 26 degrees of Leo, and sets with 7 degrees of Gemini. MARE. See Aqua. MARFIC Arab. that is, a reclining place, or Marsikon, that is, axilla, as Schickard testifies in his Vranometria, is called a fixed star of the third magnitude, which is the middle one in the hand of the Charioteer, of the nature of Mars and Mercury; see in V. Auriga. MARS. A masculine and nocturnal planet, as being hot and dry, but prevailing in dryness, therefore, as Titus notes, effeminate, next below Jupiter and above the Sun; it completes its course in about two solar years. It has the Sun at its center, as do the other planets, except the Moon, always revolving around it; and therefore it is so arranged with the deferent circle of the same Sun that, when it is achronically opposite to it, it seems below it, nearer to the earth, very large in body, so that it almost equals Venus herself, and it has a greater parallax than the Sun itself, namely four minutes, as I have observed once and again. Hence, by its descent into the lowest apsis of its orbit, there is great intensity of heat in summer, and relief of cold in winter: for when it is brought near the earth it greatly exerts and strengthens its powers; just as, on the contrary, we experience the opposite when it is found in apogee, very remote from the earth; for the difference in diameters is 168, which converted into Italian miles makes a total of 169020. Therefore it is no wonder if so great a diversity is found in it. Kepler states in Epistom. lib. 6 that Mars is sometimes seen dichotomous in quadratures to the Sun, which he thinks also occurs in Jupiter and Saturn, especially since it is certain that this is true of the inferior planets. Fontana reports that he observed a black spot in its middle, the sketch of which he shows in his observations, rr. 6, cap. 1; whence it is also probable that this is its little companion star, and just as the two superior S iiiij

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180 LEXICON Lupiter & Saturnus suos stipatores habent, ac minores planetulas, qui ipsos circumdent, sic & in Marte idipsum credendum est: Qua de re extat testimonium, licet non adeò firmum Antonij Mariæ Rietæ lib. 4. radij sideromyst. vbi hæc habet. Murem fortè vti sæpè obseruauiimus, suis comitibus certo tempore furtiue stipatum. & cap. 4. de hac re valdè dubitat, anceps meo iudicio, an quæ viderit circà ipsum stellæ fixæ fuerint, an vero proprij Mattis satellites. Cæterum Mars <10.> dicitur infortuna minor naturæ humanæ ac viventibus omnibus inimicus, vt pote, qui sua vredine & siccitate humorem natiuum absumit, & tollit: quod etiam indicat color eius rufus, suboscurus & igneus. In genethliacis facit hominem ad iracundiam pronum, rubris, & candentibus oculis, capillitio flauum, incessu violentum, cui pontica, & amara placeant. Dominatur auditui sinistro, renibus, bili, felli, intestinis, & sedi. Causat morbos, qui ex bile, & torrefacto sanguine ortum trahunt; vt febres ardentes, acutas, hæmorragiam, phrænesim, maniam pthisim, ictericiam flauam, disenterias, erisipilas, exanthemata, & similia. Habet sub se milites, Duces, Capitaneos, Chirurgos, Medicos, tonsores, venatores, pyratas, carnifices, fabros, qui ferrum, & ignita opera tractent. In morbis maximè noxia est Lunæ cum Marte coniunctio, minus verò quadratus, vel oppositio, sicut etiam plus nocet Mars Orientalis, quam Occidentalis. <11.> MASACHE Chaldaice dicitur signum Libræ seprimum ab Ariete illique directè oppositum, vt testatur Kirchetus in Oedipo, Hebraicè autem Mÿnaim hoc est bilanx. <12.> MASCVLA CONDITIO, sicut & Fæminina verè, & realiter est in corporibus, ac signis coelestibus, vt eruditissimè probat Titus in Cælesti Philosophia lib. 1. cap. 11. non quidem quoad realem sexus distinctionem, sed quoad qualitatum cùm actiuarum, tum passiarum diuersitatem. Etenim cum mascula vis in eo consistat, vt actiuis qualitatibus polleat subiectum quod masculinum dicimus, passiuis quod foemininum; hinc est, vt quæ signa, quæue sidera in qualitatibus actiuis (sunt ea, vt alibi ex Philosopho obseruauiimus Calor, & Frigiditas) vincunt, sumpta ad sexum analogia dicantur iure mascula uirtute prædita, quæ verò vincunt in humiditate aut siccitate, appellentur foeminea. <13.> Porrò in Planetis hæc sexus distinctio, & præpollenæia qualitatum ex colore, adeoque ex intensiæ

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180 LEXICON Jupiter and Saturn have their attendants too, and smaller little planets that surround them; the same must be believed also of Mars. On this matter there exists testimony, though not a very firm one, in Antonio Maria Rieta, lib. 4, Radij sideromyst., where he says this: “We have often observed, perhaps like a mouse furtively attended by its companions at a certain time.” And in chapter 4 he greatly doubts about this matter, and, in my judgment, uncertain whether those things he saw around it were fixed stars, or rather the satellites of Mars itself. Moreover, Mars <10.> is said to be a lesser misfortune, an enemy of human nature and of all living things, since by its heat and dryness it consumes and removes native moisture; this is also indicated by its color, which is reddish, darkish, and fiery. In genethliacs it makes a man prone to anger, with red and gleaming eyes, blond hair, a violent gait, one who likes bitter and Pontic things. It rules the left ear, the kidneys, bile, gall, the intestines, and the seat. It causes diseases which arise from bile and scorched blood, such as burning fevers, acute fevers, hemorrhage, phrenzy, mania, phthisis, yellow jaundice, dysenteries, erysipelas, exanthems, and the like. Under it belong soldiers, commanders, captains, surgeons, physicians, barbers, hunters, pirates, executioners, smiths, and others who handle iron and fiery works. In illnesses, the conjunction of the Moon with Mars is especially harmful; less so the square or opposition, just as Mars in the East is more harmful than in the West. <11.> MASACHE in Chaldean is called the sign of Libra, the seventh from Aries and directly opposite to it, as Kircher testifies in Oedipus; in Hebrew, however, Mÿnaim, that is, a balance. <12.> MASCULINE CONDITION, just as feminine too, truly and really exists in bodies and heavenly signs, as Titus proves most learnedly in Celestial Philosophy, lib. 1, cap. 11, not indeed with regard to the real distinction of sex, but with regard to the diversity of qualities, both active and passive. For since masculine force consists in a subject, which we call masculine, prevailing in active qualities, and feminine in passive ones, hence it is that those signs or stars which prevail in active qualities (these are, as elsewhere I observed from the Philosopher, heat and coldness), when taken by analogy with sex, are rightly called endowed with masculine virtue; those that prevail in moisture or dryness are called feminine. <13.> Moreover, in the planets this distinction of sex, and predominance of qualities, from color, and therefore from intensi-

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MATHEMATICVM. 281 ne, & extensione lucis dignoscitur; in signis verò à punctis cardinalibus, arque ab distantia proportionali re- liquorum signorum ab illis, vnde sic initium productionis huiusmodi qualitatum tam actiuarum, quam passiuarum. Ex Luminaribus constat Solem habere virtutem actiuan ratione caloris, & intentionis maximæ suæ lucis; Lunam econtrà abundare in humiditate ac passiuam virtutem habere ratione extensionis suæ lucis, (licet enim in ambo- bus videre sic intentionem, & extensionem lucis, tamen nulli dubium est, in Sole prævalere intentionem, in Luna extensionem cum intensio lucis in hac sic valde exilis) id- circò hæc foeminca est, ille masculus, Iupiter, & Venus temperatam naturam habent ex calido, & humido, quod indicant colores quibus præditi sunt, croceus, & cæruleus: sed in cæruleo præponderat calor humiditati, ideo Iupiter cæruleus apparens masculus est, Venus croceum colorem habet, in quo humiditas calorem vincit, ideò foeminina, Saturnus, & Mars inremperatam naturam habent, ille quidem ex frigore, & siccitare constatam, hic ex calore, & siccitare, (quod arguit ipsorum calor plumbeus, & igneus) ideò masculini ambo, sed quia in Marte vincit quandoque siccitas, quæ qualitas passiua est, ideò, vt alibi obseruauimus, nocturnus, arque effæminatus. Mercurius ancipitis est naturæ pro qualitate eorum, cum quibus congreditur: quia tamen se solo est frigidus, & siccus, sed magis frigidus, ideò masculam conditionem sortitur. Pari etiam ratione in signis Zodiaci discurrendum; Quan- 24. quidem ea mascula virtute potiri debent, à quibus est initium productionis qualitatum actiuarum; ea foeminca dici debent, vnde originem trahunt qualitates passiuæ: Atqui à punctis cardinalibus videmus sidera incipere influentiam primarum quatuor qualitatum: Ab Tropicis humiditatem & siccitatem; ab æquinoctialibus punctis calorem, & frigiditatem. Igitur quia Aries, & Libra initia sunt productionis qualitatum actiuarum; actiua sunt, & masculina: Cancer, & Capricornus, quia inium faciunt productioni qualitatum passiuarum, passiua signa sunt, & foeminina. In reliquis signis uniformiter discurrendum per habitudinem, & proportionalem distantiam à dictis cardinibus vnde sic initium productionis primarum quatuor qualitatum. Gemini, Leo, Sagittarius, & Aquarius habent aspectus, & proportionales distantias ad Arietem, & Libram: Ergò

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MATHEMATICUM. 281 it is recognized by the extension of the light; but in the signs, from the cardinal points, and from the proportional distance of the remaining signs from them, whence also the beginning of the production of such qualities, both active and passive. From the luminaries it is clear that the Sun has an active power by reason of heat, and the greatest intensity of its light; the Moon, on the contrary, abounds in humidity and has a passive power by reason of the extension of its light. For although in both there is seen both intensity and extension of light, nevertheless there is no doubt that in the Sun intensity prevails, in the Moon extension, since the intensity of the light in the latter is very slight. Therefore this is feminine, that masculine. Jupiter and Venus have a temperate nature from hot and moist, as is indicated by the colors with which they are endowed, saffron and blue: but in blue heat predominates over humidity; therefore Jupiter, appearing blue, is masculine. Venus has a saffron color, in which humidity overcomes heat; therefore feminine. Saturn and Mars have an intemperate nature, the former indeed constituted from cold and dryness, the latter from heat and dryness, as is shown by their leaden and fiery heat; therefore both are masculine, but because in Mars dryness sometimes prevails, which is a passive quality, therefore, as we have observed elsewhere, nocturnal and effeminate. Mercury has a mixed nature according to the quality of those with whom it comes into conjunction: nevertheless, since by itself it is cold and dry, but more cold, therefore it obtains a masculine condition. By the same reasoning one must proceed also in the signs of the Zodiac; for those ought to have masculine virtue from which the beginning of the production of active qualities arises; those ought to be called feminine from which passive qualities derive their origin. But from the cardinal points we see the stars begin the influence of the first four qualities: from the Tropics, humidity and dryness; from the equinoctial points, heat and cold. Therefore, because Aries and Libra are the beginnings of the production of active qualities, they are active and masculine; Cancer and Capricorn, because they make the beginning of the production of passive qualities, are passive signs and feminine. In the remaining signs one must proceed uniformly by relation and proportional distance from the said cardines, whence the beginning of the production of the first four qualities. Gemini, Leo, Sagittarius, and Aquarius have aspects and proportional distances to Aries and Libra: therefore

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282 LEXICON vincunt in qualitatibus actiuis, ac proinde masculina signa dicenda sunt, Taurus, Virgo, Scorpio, & Pisces habent habitudinem, & familiaritatem cum Cancto, & Capricorno: igitur vincunt in qualitatibus passiuis, atque adeò foeminina sunt. Vide quæ fusiùs haber Titus loco citato. 25. MASVROTH Chaldaicè dicitur Zodiacus apud Cerdam, apud Kircherum vetò in Oedipo Ægyptiaco Aedronitho demalische hoc est otbis signorum. Vide in V. Zodiacus. 26. MATER dicitur à Latinis facies interior Astrolabij seù caua pats, quæ limbo exttinscus definita, intrinsecus amplituditut timpana, seù tabulas, & voluellum respondens ad singulas partes in planitie limbi descriptas: dicta est quasi mater quæ tabulas intrà se perinde ac foetus in vtero gerat. MATHEMATICA, seù Mathesis scientiarum omnium nobilissima, & quæ iute optimo mater omnium dici potest, quippe quæ in summo certitudinis apice sita vniuersa, quæ quanta sunt amplitudine sua complectitur, & scrutatur à Græco verbo uadvis quod disciplinam sonat, originem duxit. solæ enim mathematicæ facultates ad inserendam animo disciplinam idoneæ sunt, solæ scientiæ nomen merentur: quia solæ procedunt per demonstrationes, ac principia nota solæ ex principijs per se notis procedunt ad cognitionem eorum quæ miius nota sunt, vt & ipsa fiant nota, & manifesta, eaque cognitione parta procedunt vlterius ad inuestionem aliorum quæ adhuc minus nota etant, vt ea quoque manifesta reddantur, donec tandem admirabilem, ac certam rerum intelligentiam consequamur: quod profectò aliæ facultates non præstant, vt Philosophia, Logica, Metaphysica, &c. quæ non per principia nota, sed per argumentationes & syllogismos procedunt, suaque obiecta probant, non supponunt probata. Eius obiectum, circa quod versatur est quantum sub ratione extensi, & vt aptum est mensurare alia quanta, & ipsum vicissim per alia mensuretur per proportionalem comparationem ad inuicem. Et quoniam quantum considerati potest præcisè prout habet rationem mensutæ proportionisque vt sic sine vllo respectu ad materiam quantam, & vt tale est obiectum Geometriæ, quæ præscindit à ratione quantorum, & solum considerat illa quatenus extensa sunt, vel considerari potest cum respectu ad materiam quantam, & sic vel sistit incontemplatione, & mensuratione partium orbis terrarum, & vocatur Geographia vel mensurat & maria dicitur Hydrographia, vel materialium rerum aceruos vt fru-

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282 LEXICON prevail in active qualities, and therefore masculine signs ought to be called, Taurus, Virgo, Scorpio, & Pisces have a relation, and familiarity with Cancer, & Capricorn: therefore they prevail in passive qualities, and are therefore feminine. See more fully in Titus, in the place cited. 25. MASVROTH is called the Zodiac in Chaldaic by Cerda, but by Kircher in the Egyptian Oedipus, Aedronitho demalische, that is, the circle of the signs. See under V. Zodiacus. 26. MATER is called by the Latins the inner face of the Astrolabe or hollow part, which, defined externally by the limb, internally contains the tympana, or plates, and the volvelle corresponding to the several parts described on the plane of the limb: it is called as it were the mother, because it carries the plates within itself, just as a fetus in the womb. MATHEMATICA, or Mathesis, the noblest of all the sciences, and which in the truest sense may be called the mother of all, since it is placed at the highest peak of certainty, and embraces and investigates everything, however great in extent, derives its origin from the Greek word mathesis, which means discipline. For the mathematical faculties alone are fit to implant discipline in the mind, they alone deserve the name of sciences: because they alone proceed by demonstrations, and from known principles; they alone proceed from principles known in themselves to the knowledge of those things which are less known, so that they themselves may become known and manifest, and, that knowledge having been acquired, they proceed further to the investigation of other things which are still less known, so that these too may be made manifest, until at last we attain an admirable and certain understanding of things: which certainly the other faculties do not provide, such as Philosophy, Logic, Metaphysics, etc., which do not proceed by known principles, but by arguments and syllogisms, and prove their objects; they do not assume them as proved. Its object, about which it deals, is quantity under the aspect of extension, and as it is suitable for measuring other quantities, and itself in turn is measured by others through proportional comparison with one another. And since quantity considered can be taken precisely as it has the nature of measure and proportion, and thus without any regard to material quantity, and as such is the object of Geometry, which cuts away from the notion of quantities, and considers only those things insofar as they are extended, or it can be considered with regard to material quantity, and thus either it remains in the contemplation and measurement of the parts of the terrestrial globe, and is called Geography, or it measures the seas and is called Hydrography, or the heaps of material things, as fru-

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MATHEMATICVM. 18. mentum, & liquida vt oleum, & pondera, & alia huiusmodi, & hæc est Geodæsia, vel contemplatur quantum per figuras colores, & radios visuales medio lumine, & appellatur per- spectiua: vel denique se extollit ad quantitatem cæli, eiusque vallitatem, motus siderumque affectiones simatur, & ex hac investigatione constituitur Astronomia. Rursus omnis quan- titas considerari potest, vel vt est continua, vel discreta: vt continua est obiectum, vt dixi, Geometriæ: vt discreta fun- dat Arithmeticam, quæ in numerorum contemplatione ver- sarur, totam supputandi, multiplicandi, & diuidendi rationem diligentissimè tradens. Et hæc etiam si non iam in nume- ris per se sistit, sed vltetius progreditur ad comparationem eorum ad inuicem dispertiendo tempus per certum numero- rum tythnum, & consonantiam iam fundat Musicam, quæ tempus per quasdam notas, & sonorum interpolationes ita patitur, vt ad idem temporis spatium diuersæ respondeant mo- dulationes, & vocum concentus & harmonia. 28. Igiur Mathe- maticæ disciplinæ in quatuor præcipua membra diuidi possunt, Geometriam, Arithmeticam, Astronomiam, & Musicam. Si enim absolutè considerant quantum continuum, prout præ- scindit à materia quanta, vel eius mobilitate, aut immobili- tate retinet nomen vniuersale Geometriæ: Si numerum dis- cretum considerat, dicitur Arithmetica: si fertur in quantita- tem continuam nobilissimam, quæque adhuc regulari or- dine per temporis sparia volutatur, atque harmoniam quan- dam seruat, quales sunt coelestes orbes, & Astra; vocatur Astronomia: si adhuc quantitas discreta cum hac proportione ad tempus consideratur, per certos modulorum sonos effor- mando dulcissimam harmoniam, hoc est officium proptium Musices. Alias divisiones Mathesis ex Proclo, alijsque insi- gnibus Mathematicis affert Clanius in Ptologomenis ad Com- mentatia super Elementa Euclidis, quas nos huc asportiare superuacaneum duximus, maximè quia suis in locis, vbi sermo inciderit, eas hic (quod nostrum institutum est) sum- mo ore libamus. 29. MATVINT apud Astronomos appellantur sex etrones Pla- neræ Orientales à Sole, cum matutino tempore, Sole cardi- nem Orientalem tenente, ipsi suprà terram conspiciuntur. Sicut econtrà Vespertini, cum sunt Occidentales à Sole, & Vespere, Sole ad occasum vergente, ipsi nihilominus supra Solem sunt, & nostrum adhuc hemisphærium lustrant. Porro tres superiores dicuntur fortiores à Ptolemeo cum sunt Orien- tales, & matutini, sicut etiam reliqui tres infetiores cum sunt Occidentales, & vespertini. Rationem per pulchram

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MATHEMATICVM. 18. measurement, and liquids like oil, and weights, and other such things; and this is Geodesy; or it contemplates how much, through figures, colors, and visual rays by means of light, and is called perspective; or finally it rises to the quantity of the heavens, and its expanse, and the motions and influences of the stars are observed, and from this investigation Astronomy is constituted. Again, every quantity can be considered either as continuous or discrete: as continuous it is the object, as I said, of Geometry; as discrete it forms Arithmetic, which is occupied with the contemplation of numbers, most diligently handing down the whole method of counting, multiplying, and dividing. And this, although it no longer rests in numbers as such, but proceeds further to their comparison with one another, dividing time by a certain order of numbers, and already establishing consonance, founds Music, which so treats time through certain notes and interpositions of sounds that different modulations, and the harmony and concord of voices, correspond to the same span of time. 28. Therefore the mathematical disciplines can be divided into four principal parts: Geometry, Arithmetic, Astronomy, and Music. For if it considers absolutely continuous quantity, insofar as it abstracts from matter as quantity, or from its mobility or immobility, it retains the universal name of Geometry. If it considers discrete number, it is called Arithmetic. If it is directed to the noblest continuous quantity, which still moves in regular order through spans of time and preserves a certain harmony, such as the celestial spheres and the stars, it is called Astronomy. If discrete quantity is further considered with this proportion in relation to time, producing sweetest harmony through certain sounds of measures, that is the proper office of Music. Other divisions of Mathesis are given by Clanius from Proclus and other distinguished mathematicians in the Prolegomena to the Commentary on Euclid's Elements, which we have judged it superfluous to bring here, especially because in their proper places, where the discussion may occur, we touch upon them here only in passing, as is our purpose. 29. MATVINT among astronomers are called the six planets eastern from the Sun, when in the morning time, the Sun holding the eastern quarter, they are seen above the earth. Conversely, they are called vespertine when they are western from the Sun, and in the evening, the Sun inclining toward the setting, they nevertheless are above the Sun and still illuminate our hemisphere. Moreover, the three superior planets are called stronger by Ptolemy when they are eastern and morning stars, just as the remaining three inferior ones when they are western and evening stars. The reason is beautifully

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284 LEXICON huius diuersitatis affert Titus in Cælesti Philosophia lib. x: cap. 14. Quia, inquit, superiores matutini, & inferiores vespertini in his staribus descendunt ab Apogæo sui Epicycli: quare augentur lumine, atque ad nos approximantur, vespertini verò superiores, & matutini inferiores ascendunt à Perigæo ad Apagæum sui Epicicli; quare minuntur lumine, & longè à nobis fiunt: idcircò iure superiores Orientales & matutini, nec non inferiores Occidentales, & vespertini fortiores sunt, quoniam ambo, licet per diversam habitudinem ad Solem, ijsdem qualitatibus pollent, maioresque vires assumunt. ME 30. MEDIATIO, teste Abraham Auenarre, est quædam passio adueniens planetæ cum separatur ab infortuna, & iungitur alteri infortunæ, aut corpore, aut aspectu. Idque siue fortuna sit, vel malesica in signo præcedente, siue malefica in signo sibi posteriore. Verum tamen est, quod si Sol aspiciat planetam inter duas maleficas medium consistentem, multum illi de tali infortunio temouebit. 31. MEDICÆ STELLÆ sunt quatuor erroris Iouis comites nuper à Galilæo insigni mathematico detectæ, atque ab Mediceis Principibus, quibus eas dicatas voluit, honoris titulo appellatæ. Visuntur clarè nostro æuo ope Telescopij, modo Ioui propinquiores, modò remotiores, modo duo, modo tres, modò omnes quatuor, modò etiam nullæ: quod argumento est, ipsos in suis paruis orbibns moueri circà ipsum Iouem, quem pro centro retinent, ac proinde occultari, quando incidunt in eius vmbram, vel sup[er]ta ipsum constituuntur: qui sit, vt ob Iouis corpus sese inter ipsos, & nostrum visum interponentis videri non possint, de eorum motu multa diximus in Ioue: plura qui volet videat ipsum Galilæum in nuncio sidereo. 32. MEDICLINIVM ab aliquibus appellatur quæ apud Gtæco[n] Dioptra, linea videlicet siduciæ, & index in medio Astrolabij, quasi in medio clinij collocatum. Vocatur etiam radius, quia est veluti radius rectà ad patres circunferentiæ terminans. siue quia per eum stellarum radius transiens, earum situm, & altitudinem à terra demonstat. 33. MEDIVM CALI dicitur ab Astronomis culmem, & metidianum supraterraneum, quod etiam dicitur Cor cæli, Domus regia, decima ab Horoscopo, vbi planetæ, & sidera sunt in maiori altitudine quam obtinere possunt, proindeque direcctiores emitunt radios, validioresque exserunt vires. Vnde

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284 LEXICON Titus gives the cause of this diversity in the Celestial Philosophy, book x: chapter 14. Because, he says, the superior morning stars and the inferior evening stars descend from the apogee of their epicycle; wherefore they are increased in light and approach us. But the superior evening stars and the inferior morning stars ascend from the perigee to the apogee of their epicycle; wherefore they are diminished in light and become far from us. Therefore the superior Oriental and morning stars, as well as the inferior Occidental and evening stars, are rightly stronger, since both, although in a different relation to the Sun, possess the same qualities and take on greater powers. ME 30. MEDIATIO, according to Abraham Avenar, is a certain affection coming upon a planet when it is separated from one unfortunate planet and united to another unfortunate one, either by body or by aspect. And this whether a fortune or malefic be in the preceding sign, or a malefic in the sign following it. Yet it is true that if the Sun should regard a planet standing in the middle between two malefics, it will greatly remove from it such misfortune. 31. MEDICÆ STELLÆ are the four companions of Jupiter, recently discovered by the famous mathematician Galileo, and, at the desire of the Medici Princes to whom he wished them dedicated, named with a title of honor. They are clearly seen in our age by means of the Telescope, now nearer to Jupiter, now farther away, now two, now three, now all four, now even none: which is proof that they move in their small orbits around Jupiter himself, whom they keep as their center, and are therefore hidden when they fall into his shadow, or are placed above him: so that, because Jupiter’s body is interposed between them and our sight, they cannot be seen. We have said much about their motion in Jupiter; let whoever wishes see Galileo himself in the Sidereal Messenger. 32. MEDICLINIVM is called by some what among the Greeks is the Dioptra, namely the line of sight, and the index in the middle of the Astrolabe, as if placed in the middle of the clinium. It is also called the radius, because it is like a radius ending straight at the limits of the circumference, or because, as the stellar ray passes through it, it indicates their position and height from the earth. 33. MEDIVM CÆLI is called by astronomers the culmination and the supraterrene meridian, which is also called the Heart of Heaven, the Royal House, the tenth from the Horoscope, where planets and stars are at a greater altitude than they can attain, and therefore emit more direct rays and exert stronger powers. Hence

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MATHEMATICVM. 285 meritò à Ptolema[xi]o præficitur ipsi horoscopo. Significat dignitates Impetia, Magistratus, Officia publica, opificium, nec non & matrem; qua ratione dictum est in V. Culmem. Gaudet in ea Sol, qui ibi constitutus sicut & Iupiter, plurimum fortunatur: econtrà infortunæ ibi perniciosæ euadunt, & nimis infensæ. MEELF Arab. idem valet ac præsepè, significar enim < 34.> nebulosam in pectore cancri consistentem de qua suo loco. MEDVSÆ CAPVT. Vide in V. Algol, & Gorgonis caput. < 35.> MEL liquor suauissimus satis notus, cæli sudor, siderumque < 36.> saliua, vt vocant, est tenuis vapor aliqua leui exhalatione iminixtum atque à si sideribus in vnum coagulatus, de eo fuse egimus in V. Ros. MEMESCIATH Arab. hoc est mulus Clitellatus, dicitur < 37.> Auriga sidus in cælo ad Borealem plagam, de quo sæpius di- ctum est. MENCHAR, item Arab. dicitur Natis, seu Mandibula Ceti < 38.> stella fixa secundæ magnitudinis de natura Saturni existens nunc temporis in gr. 10. Tauri cum latitudine meridiana gr. ferè 13. Oritur Romæ cum ptimo gradu Geminorum, & oc- cidit cum 4. Tauri. Vide amplius in V. Getus. MENOIDES Græcè dicitur Luna corniculata, cum primum < 39.> è radijs solis emergit, ac se visibilem præbet secundo ferè die potest Nouilunium. MERCURYS. stella est erratica omnium minima, sed pel- < 40.> lucida & corusca nimis, quæ circà Solem tamquam eius stipa- tor vna cum Venete perpetuò voluitur, & circumfertur, ne- que ab ipso vnquam elongatur plusquam grad. 28. Elus orbis constituitur supra Lunam, licet recensiores in ipso Solis de- ferente ipsum collocent, neque ei proprium orbem attribuant, sed solum Epicyclum, qui sit vt quandoque feriam supra ipsum Solem constituatur, vbi inuisibilis redditur. Natura illius va- riabilis est pro planetarum quibus cum miscetur, varietate: ex se tamen siccus est ob Solis vicinitatem, & frequentem combustionem. Est motor ventorum; atque in Genethliacis < 41.> benè collocatus præsertim in Virgine domicilio, & exalta- tione sua, aut in domibus Saturni facit ingenio promptissi- mos & excellentes, vt notat Ptolema[xi]us in centiloquio, & probat Angelicus Doctor, licet natura instabiles, callidos, altutos, non adeò sincerè actiones suas tractantes: forma autem, ac temperatura corporis gracili, colore pallido tendente ad digredinem; pulchris oculis, sed mobilibus, supercilijs iun- ctis, facie angusta, longis digitis, passibus breuibus, & celeriter incedentes, corpore denique pusillos, vt ipse, qui terra vnde

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MATHEMATICVM. 285 is deservedly placed by Ptolemy before the horoscope itself. It signifies dignities, command, public offices, handicraft, and also the mother; for which reason it was said in V. Culmen. The Sun rejoices in it, and when placed there, as also Jupiter, is greatly favored; on the contrary, the infortunes there turn out harmful and too hostile. MEELF, Arab. means the same as a manger, for it signifies < 34.> the nebula standing in the breast of Cancer, of which in its own place. MEDUSAE CAPUT. See in V. Algol, and the head of Gorgon. < 35.> MEL, a very sweet liquor well known, the sweat of heaven, and the saliva of the stars < 36.> as they call it, is a thin vapor mingled with some slight exhalation and coagulated from the stars into one body; we have treated of it at length in V. Ros. MEMESCIATH, Arab., that is, a pack-saddle mule, is called < 37.> the constellation Auriga in the northern part of the sky, of which much has already been said. MENCHAR, likewise so called in Arabic, is called Natis, or the Jaw of the Whale < 38.> a fixed star of second magnitude, of the nature of Saturn, now at 10 degrees of Taurus with a southern latitude of nearly 13 degrees. It rises at Rome with the first degree of Gemini, and sets with 4 degrees of Taurus. See more in V. Getus. MENOIDES is the Greek term for the crescent moon, when it first < 39.> emerges from the rays of the sun and shows itself visible on about the second day; it may be called the new moon. MERCURY is the smallest wandering star of all, but < 40.> very bright and exceedingly sparkling, which around the Sun, like his attendant, perpetually revolves together with Venus and is carried about, nor is it ever separated from him by more than 28 degrees. Its orbit is placed above the Moon, though more recent writers place it on the Sun’s deferent itself and do not assign it a proper orbit, but only an epicycle, so that at times it is placed above the Sun itself, where it becomes invisible. Its nature is variable according to the variety of the planets with which it is mingled; yet in itself it is dry because of its nearness to the Sun and frequent burning. It is the mover of the winds; and in genethliacs, if < 41.> well placed, especially in Virgo, its domicile, and in its exaltation, or in the houses of Saturn, it makes men very quick-witted and excellent, as Ptolemy notes in the Centiloquy and the Angelic Doctor proves, though by nature unstable, crafty, deceitful, and not handling their actions with complete sincerity. As for the form and temperament of the body, they are slender, with a pale color tending toward a swarthy hue; with beautiful eyes, but restless, joined eyebrows, a narrow face, long fingers, short steps, and walking quickly; and lastly they are small in body, like the one who from the earth

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LEXICON 186 vicesies minor est. Dominatur linguæ, sermoni, phantasi, neruis, spiritibus, menti, ac rationi. Habet sub se mercatores, Nuncios, Cancellarios, Scriptores, Mathematicos, Arithmeticos, & id genus homines. Quoad morbos, malè positus causat cerebri affectus, maniam, delirium, epilepsiam, impedimentum sensus communis, linguæ defectus, iussim, & his similia. 41. Cæterum quæ de Mercurio ab Astronomis præsertim antiquioribus traduntur minus certa sunt, ac quæ de reliquis planetis; cum enim à Sole parum digrediatur, & sit quantitare omnium minimus, rarò admodum obseruari potest, ob Solis vicinitatem & vapores qui horiyontem ambiunt; quandoquidem non nisi propè horizontem mane, & vespere eum videre licet; idque ratissimè cum eum à Sole ad 20. ferè gradus elongati contingit. 42. MERIDIANVS est Circulus magnus conceptus in Cælo, qui transeat per polos mundi, & verticem capitis nostri, qui que in sphæra materiali cæretis circulis supereminet, sustinerque axem mundi, circa quem reliqui voluntur. Inde dicitur, quod Sol motu primi mobilis ad eum delatus vbique locotum, & quocumque anni tempore meridiem efficit. Proindeque eius ope dignoscitur quantitas dici ac noctis, artificialis, punctum meridiei, & mediæ noctis, arcus semidiurnus, & seminocturnus cuiuscumque sideris, maior altitudo, quam quous tempore habete possit supra retram, & alia, quæ enumerat Claiuius in sphæram Io: de sacro bosco Astronomi omnes, quemadmodum Hispani, Galli, & multæ nationes Septentrionales incipiunt computare diem à meridiano, seù ab eo temporis puncto, quo Sol meridianum tenet, non ab occasu, vt nos Itali facimus, neque ab ortu Solis vt Ægyptij, & Mahumeranis vbi pro diuersitate horizontum magis, ac magis obliquorum diuersa est etiam magisque obliquior ratio ascensionum. At verò in Meridiano omnes partes eclipsæ, æquè ascendunt, ac cælum mediant, atque adeo in eo vbique locorum eadem est ascensio cuiuscumque gradus Zodiaci. Porrò sicut horizonta diuersa sunt, & pro locorum diuersitate infinita prope modum concipi possunt; ita & Meridiaui: nihilominus Cosmographi centum tantum, & octaginta meridianos circa tellurem describunt, quos & Azimutha, seù circulos verticales Arabes vocant, quorum singuli transeunt per polos mundi, & binos gradus æquatoris sibi ad inuicem oppositos: quinimò in Mappis mundi duodecim tantum describi solent, qui totum terræ tractum in 24. partes æquales dispecunt, adeo vt inter duos proximos, quindecim gradus æquatoris intercipiantur, quantum videlicet requiritur ad vnam horam constituendam: vnde

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LEXICON 186 vicesies minor est. It dominates language, speech, fancy, nerves, spirits, mind, and reason. Under it are merchants, envoys, chancellors, writers, mathematicians, arithmeticians, and men of that kind. As for diseases, when badly placed it causes affections of the brain, mania, delirium, epilepsy, impairment of common sense, defect of speech, hiccough, and the like. 41. Moreover, what astronomers, especially the older ones, relate about Mercury is less certain than what is said of the other planets; for since it departs only a little from the Sun, and is the smallest of all in size, it can very rarely be observed, because of its proximity to the Sun and the vapors that surround the horizon; since it can be seen only near the horizon in the morning and in the evening, and that most rarely when it is about 20 degrees away from the Sun. 42. The MERIDIAN is a great circle conceived in the heavens, which passes through the poles of the world and the zenith of our head, and which in the material sphere surpasses the other circles, sustaining the axis of the world, around which the rest turn. It is so called because the Sun, carried to it by the motion of the first mobile, everywhere and at any season of the year makes midday. By its help are recognized the length of day and night, artificial, the point of midday and of midnight, the semi-diurnal and semi-nocturnal arc of any star, the greatest altitude, which for the same time it may have above the Earth, and other things which Clavius enumerates in his sphere; Johannes de Sacro Bosco [and] all astronomers likewise; just as the Spaniards, French, and many northern nations begin to count the day from midday, or from that point of time when the Sun holds the meridian, not from sunset, as we Italians do, nor from sunrise, as the Egyptians and Mahometans [do], since, according to the diversity of horizons, more and more oblique, the ratio of ascensions is also different and more oblique. But in the Meridian all parts of the eclipse rise equally and culminate in the sky, and therefore in it, everywhere, the ascent of any degree of the Zodiac is the same. Moreover, just as horizons are different, and according to the diversity of places can be conceived almost infinitely; so too are meridians: nevertheless cosmographers describe only one hundred and eighty meridians around the globe, which they also call Azimuths, or vertical circles of the Arabs, each of which passes through the poles of the world and two degrees of the equator opposite each other; indeed, on world maps only twelve are usually drawn, which divide the whole tract of the earth into 24 equal parts, so that between two neighboring ones fifteen degrees of the equator are intercepted, as much as is required, namely, to constitute one hour: whence

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MATHEMATICVM. 187 cognoscitur diuersitas locorum, & quot horis citiùs in vna ciuitate meridies efficiatur quam in alia. Nam si vna ciuitas ab alreta remoucatur versus ortum tribus ex his duodecim me- ridianis, signum est quod tribus horis priùs ibi Sol oriatur, me- ridiesque har & nox quam in altera, & sic de singulis. Hæc ve- rò distantia, & differentia Meridianorum dicitur Longitudo, < 44.> quæ computari solet ab Insulis fortunatis sitis in Occidente, versus Orientem; itaut quò maior fuerit longitudo, & arcus æquatoris interceptus inter vtrumque meridianu[m], eius inquam loci, de quo quærimus, & dictarum insularum, eò ipse locus sit Orientalior, priusque dies accidat, ac meridies. Verùm recen- tiores Astronomi, qui transacto sæculo nauigijs suis inrimas Occidentis oras penetrarunt, experientia didicerunt, verum Occidens computandum esse ab insulis Azorum non longè ab Hieron Promentorio: ac proinde ibi constituendum esse pri- mum Meridianum, qua de re vide qua diximus in V. Azorum insula. MEROPS Græcè dicitur Aquila sidus in cælo ad borealem < 45.> plagam intrà Galaxiam propè Delphinum, & Cygnum. Ba cum Sole, vel Matte exoriens producit nives cum inrentissimo fri- gore, cum Mercurio ventos commouet: Occidens verò ma- turino tempore procreat Austrum, & calorem magnum. Vide quæ diximus in V. Aquila. MESANGVO Chaldaicè idem valet ac decachordum: vnde < 46.> apud Chaldæos Astronomos eo nomine appellatur Lyra situs quod Ptolemæo decem stellis constat, quod prorsus chordæ constituunt Psalterium decachordum. Alio nomine dicitur Asanges. Reliqua vide in V. Lyra. MESCIMACH ALAAZEL Hebraicè, seu potius Chaldaicè dici- < 47.> tur spica Virginis, vt author est Abraham Iudæus in suo intro- ductorio stella inquam fixa primæ magnitudinis, benignissima, de natura Veneris, & Mercurij Arabicè Azimech. Hæc cu[m] Mer- curio congrediens ventos mouet, & facit subitam mutationem in aëre: sicut etiam cum Saturno impetuosos imbres generat, & ionitrua, Vide alia eius significata sub alijs nominibus. MESEN Græcè dicitur Ventus intermedius inter Septentrionem < 48.> & subsolanum, alio nomine Borrapeliotes, nostris verò, quia per Græciam transit, Græcus. Eius naturam, & conditiones, vide in Borrapeliote. MESAQVILO, Mesocorus, Mesocircius, Meseurus, &c. dicun- < 49.> tur quartæ ventorum, seù venti minores collaterales ad læuam Aquiloni, Coro, Circio, Euro, &c. sicut econtra Y paquilo Y po- corus, Y pocicius, Y poeurus, &c. qui ventis hisce lateralibus adstant ad dexteram. De quibus omnibus cum de Ventis in

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MATHEMATICVM. 187 the diversity of places is known, and how many hours earlier midday is made in one city than in another. For if one city is removed from the equator toward the east by three of these twelve meridians, it is a sign that there the Sun rises three hours earlier, and midday and night occur sooner than in the other; and so with each one. But this distance and difference of meridians is called longitude, < 44.> which is usually reckoned from the Fortunate Isles, situated in the West, toward the East; so that the greater the longitude shall be, and the arc of the equator intercepted between the two meridians, that is, between the place in question and the said islands, the more eastern the place itself is, and the day and midday occur earlier. But more recent astronomers, who in the past century penetrated with their ships into the farthest parts of the West, have learned from experience that the true West must be reckoned from the Azores, not far from the promontory of Hieron: and therefore the first meridian ought to be established there; concerning which matter see what we have said in V. Azorum insula. MEROPS in Greek is the name given to the star Aquila in the sky toward the northern < 45.> region within the Galaxy, near Delphinus and Cygnum. Rising with the Sun, or with Matte, it produces snow with very intense cold; with Mercury it stirs up winds. Setting, however, in the morning, it begets the south wind and great heat. See what we have said in V. Aquila. MESANGVO in Chaldaic means the same as decachordum: hence < 46.> among the Chaldean astronomers by that name is called the Lyra, because for Ptolemy it consists of ten stars, which altogether form the strings of a decachordal psaltery. By another name it is called Asanges. See the rest in V. Lyra. MESCIMACH ALAAZEL in Hebrew, or rather in Chaldaic, is < 47.> called the ear of Virgo, as Abraham the Jew states in his introductory work, that is, a fixed star of the first magnitude, very benign, of the nature of Venus and Mercury, in Arabic Azimech. When this comes into conjunction with Mercury it stirs up winds and causes a sudden change in the air; as also when with Saturn it generates violent rains and thunder. See other meanings of it under other names. MESEN in Greek is called a wind intermediate between the North and < 48.> the Subsolanus, by another name Borrapeliotes, but by us, because it passes through Greece, Greek. See its nature and conditions in Borrapeliote. MESAQVILO, Mesocorus, Mesocircius, Meseurus, etc. are called the fourth winds, or the lesser collateral winds on the left side of Aquilo, Corus, Circius, Eurus, etc., just as conversely Y paquilo Y pocorus, Y pocicius, Y poeurus, etc. stand on the right side of these lateral winds. Concerning all of these, when speaking of Winds in

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188 LEXICON generali, sermonem instituemus. < 50.> METEORA, quæ fructus siderum nominat Paracelsus sunt mixta imperfecta, eiusdem quidem substantiæ, ac ipsa elementa prima videlicet rerum semina; verum vi siderum in sublime elata accidentaliter immutantur, vel adinuicem transformantur, ita ut iam non elementarem formam retinere videantur; sed aliâ longe diuersam, & sublimior[um] ipsis etiam perfectis mixtis; quales sunt Cometæ, Virgæ, Trabes & his similia, vel si frigida, grando, nix glacies, pruina, &c. qua postquam aliquandiu duraerut in pristinam elementorum suorum formam reuertuntur. Appellantur etia Aëræ impressiones, quia incerta aëris regione ex primarum qualitatum coitione, & pugna, instar ceræ facilè imprimuntur, facileque etiam cuanescunt. Eorum causa materialis Paracelso est sulphur, sal & Mercurius (& ipsa quidem < 51.> imperfecta mixta) reliquis verò Philosophis Vapor, & Exhalatio: Et hæc quidem vtpote calida, & sicca, atque igneæ naturæ, eleuatur in supremam aëris regionem; ibique si multa sit, crassa, & viscosa condensatur in sidus, quod vulgò Cometam vocamus, tandiù durans, quousque ab concepro igne absumatur: si exilis, & gracilis est, transmutatur in faculas, si nimium tenuis in stellas, quas cadentes appellitamus; si saltus edat dum ignem concipit, caprarum exilientium formam sumit: si extendatur in longum, & aliqua ex parte crassescat, trabs, columua, ciaculum, prout ijs magis assimilatur, dicitur: si volarum edat, & speciem quandam Draconis assumat, Draco volans nominatur: si cadaueribus, ac detruucatis hominum capitibus assideat, ignis farui nomen habet: si ex attritis animalium pilis, & crinibus assurgat, ignis lambentis nomine exprimitur: si demum malo, & antennis nauium adhæreat, Castor, & Pollux antiquis, nobis verò sancti Elmi fausta lumina appellantur. Hæc, inquam, omnia ab exhalatione procedunt, quæ aliud planè non est, quam terrex partes, sed leuiores, sed rariores, quæ sursum elatæ facilè alterantur, ac ignem concipiunt, & ardent, quoadusque resoluta eorum materia in pristinam formam reuertantur, vel in aliud, elementum, puta aërem vel ignem transmutentur. < 52.> Vapor autem partes aqueæ sunt item subtiliores, ac rariores, quæ in mediam aëris regionem elatæ modo condensantur inuubes modò aliquantur in imbres, modò tenuantur in nebulas, modo rigescunt in grandines, modo spissantur in niues: ac pro diuerso siderum positu diuersas formas accidentales induentes miram hanc Meteororum diuersitatem faciunt, atque Vniuersum nouo isto productionum genere exornant. Quod si tandem, iuncto fædere, vapor, & exhalatio in vnum coeant resultant

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188 LEXICON In general, we shall discuss speech. < 50.> METEORS, which Paracelsus calls the fruits of the stars, are imperfect mixtures, of the same substance indeed as the primary elements themselves, namely the seeds of things; but, raised on high by the power of the stars, they are accidentally changed, or transformed into one another, so that they now seem no longer to retain an elemental form; but one altogether different, and more sublime than even perfect mixtures themselves; such are comets, beams, columns, and the like, or if cold, hail, snow, ice, frost, etc., after they have remained hard for some time they return to the original form of their elements. They are also called aerial impressions, because in the uncertain region of the air, from the union and struggle of the primary qualities, they are easily impressed like wax, and easily also vanish. Their material cause, according to Paracelsus, is sulphur, salt, and mercury (& indeed these are themselves < 51.> imperfect mixtures), but according to the other philosophers, vapor and exhalation: and these, being hot and dry and of fiery nature, are lifted into the highest region of the air; and there, if they are abundant, thick, and viscous, they are condensed into a star, which we commonly call a comet, lasting so long until it is consumed by the fire conceived in it; if it is thin and slender, it is transformed into torches; if too subtle, into stars, which we call shooting stars; if it makes leaps while it conceives fire, it takes the form of leaping goats; if it is extended in length and in some part becomes thickened, it is called a beam, a column, a javelin, according as it more closely resembles these; if it gives forth flames and assumes a certain form of dragon, it is called a flying dragon; if it settles upon corpses and severed human heads, it takes the name of fire of the dead; if it rises from the rubbed fur and hair of animals, it is expressed by the name of licking fire; if finally it adheres to the mast and antennas of ships, it is called, by the ancients, Castor and Pollux, but by us the propitious lights of St. Elmo. All these things, I say, proceed from exhalation, which is nothing else than earthy parts, but lighter, but rarer, which, lifted upward, are easily altered, and take fire, and burn, until the matter resolved from them returns to its original form, or is transformed into another element, namely air or fire. < 52.> Vapor, however, consists of watery parts, likewise more subtle and rarer, which, being lifted into the middle region of the air, are now condensed into clouds, now at times into rains, now made thin into mists, now freeze into hail, now thicken into snow: and according to the diverse position of the stars, assuming diverse accidental forms, they produce this marvelous diversity of meteors, and adorn the universe with this new kind of productions. But if at last, with a joined bond, vapor and exhalation come together into one, they result

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MATHEMATHICVM. 189 Resultant inde Mineralia, & fossilia, vt Autum, Argen- tum, lapides pretiosi, &c. humanæ cupiditatis, atque auaritiæ subiectum, reuerà tamen longè viliora, quam cætera mixta perfecta, plantæ, animalia, homo. Ex his liquet in quo differant vapor, & exhalatio: Ambo < 53.> enim vi siderum, præcipuè verò solis è terra prosiliunt, at- que in sublime trahuntur; sed enim hæc, vt pote calida & lieca sursum euehirur, atque in ignem vt plurimum trans- mutatur, vel in aëtem, vnde venti exsurgunt: ille verò ha- bet calorem mixtum humiditati, quæ tamen paulatim ca- lorem debilitat, itavit vapor ille nequeat sursum in supre- mam aëris regionem ascendere, sed in media tantum con- sistat, ibique tandem calore exincto, vel sanè extenuato conuertatur in imbes, niues, nebulas, aliaque superius enumerata. Hæc omnia ex Arist. I. Meteor. cap 4. Metonicus Annuus. Vide Annus. Micromèga est instrumentum geometricum representans < 54.> sextam partem quadrantis hoc est gr. 15. descriptos in lim- bo, cuius ope rerum stantiæ, & altitudines metiuntur. Eius vsum abunde tracta peculiari libro Lucius Scaranus in- uentor. Micros Contaratos. teste Kirchero, dicitur spica Vir- < 55.> ginis ad differentiam Arcturi, qui dicitur Magnus Conta- ratus. Miles apud Astronomos, seu potiùs Meteorologicos est < 56.> species quædam Cometæ criniti, & caudati de natura Ve- neris, magnitudine sua, aeducis fulgore ferè Lunam exæ- quans, qui quando apparet diu conspicuus est, & solet quan- doque peragrare totum Zodiacum. Habet significare se- ctas, contentiones, fæminum sexum, & adolescentes. Item magnas ariditates, aëris corruptelam, humorum tur- bationem, & quæ inde proueniunt mala: Idque maximè portendit in locis, ad qua terenderit eius cauda. Talem ap- paruisse ferunt, cum Xerces Persarum Rex in Græciam traiecit. MINVM, ET SCRIPVLVM apud Astronomos dicitur mi- < 57.> nima, & sexagesima quæque pars fractionis inregri gradus, aut horæ: itavit quælibet hora, vel gradus æquatoris, aut Zodiaci diuidatur in sexaginta minuta: quodlibet minutum in sexaginta secunda, vt vocant: Secunda adhuuc in toti- dem Tertia: & sic deinceps vsque ad Decima, & si quis volet vsque in infinitum. Vide quæ diximus in V. Græ- dus. MIRACHARAB. dicitur Cingulus, seu Vmbilicus Andro- < 58.>

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From these arise minerals and fossils, such as gold, silver, precious stones, and the like, subject to human desire and avarice, though in truth far more base than the other perfect mixed things, plants, animals, man. From this it is clear how vapor and exhalation differ: both, indeed, by the power of the stars, especially of the sun, spring forth from the earth and are drawn upward; but the latter, as being warm and dry, is carried upward and for the most part is changed into fire, or into air, from which winds arise: the former, however, has heat mixed with moisture, which nevertheless gradually weakens the heat, so that that vapor cannot ascend to the highest region of the air, but remains only in the middle, and there at last, with the heat extinguished, or indeed greatly diminished, is turned into rain, snow, mists, and the other things listed above. All this from Aristotle, Meteorology I, chapter 4. Metonic year. See Year. Micromega is a geometric instrument representing the sixth part of a quadrant, that is, 15 degrees marked on the limb, by whose aid the positions and heights of objects are measured. Lucius Scaranus, the inventor, has fully discussed its use in a special book. Micros Contaratos, according to Kircher, is the name given to the spike of Virgo, in distinction from Arcturus, which is called Magnus Contaratus. a certain kind of comet, hairy and tailed, of the nature of Venus, in size and in the brilliance of its rays almost equaling the Moon; when it appears, it is long visible, and it is sometimes accustomed to traverse the whole Zodiac. It is said to signify factions, disputes, the female sex, and young men. It also portends great dryness, corruption of the air, disturbance of the humors, and the evils arising therefrom; and this especially in the places toward which its tail points. They say that such a one appeared when Xerxes, king of the Persians, crossed into Greece. Minum and scripulum, among astronomers, are said to be the smallest, and every sixtieth part, of a fraction of a whole degree or hour; thus each hour, or degree of the equator or Zodiac, is divided into sixty minutes; each minute into sixty seconds, as they are called: the seconds again into as many thirds; and so on up to the tenth, and, if one wishes, even to infinity. See what we said under V. Degree. Miracharab is called the girdle, or umbilicus, of Andro- <58.

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LEXICON 290 madæ, Stella fixa secundæ magnitudinis de natura Veneris; nô abs re tali nomine insignita, quippe quæ si in alicutus horoscopo reperta fuerit, facit eum ad luxus, ac libidines propensum, atque ob id adducit infamiam, & pericula. Cum sole exoriens affert tempus tutbidum; & aquosum: Cum Saturno frigus magnum, nebulas, pluuias, & pro temporum conditione nives. 59. MIRACH etiam per analogiam dictus est Cingulus Cæli hoc est Zodiacus: idque præsertim in Planisphærio, vbi descriptus cingulum planè refert. 60. MIXTA apud Philosophos dicuntur corpore non simplicia qualia sunt elementa, sed quæ ex ipsis coagmentantur. Siquidem Mixtio (vt inquit Arist. ptimo de Gener. text. 90.) est miscibilium alteratorum vnio. Per quod intelligit quatuor elementa ad inuicem pugnantia contrariis qualitatibus, quibus pollent, itavt ex pugna mixta omnia prodeant. Qui sit, vt quodlibet mixtum resultans omnes quatuor qualitates in se contineat, cum alias pura elementa duplici tantum sibique propriis potiantur. Quod docet idem Arist. z. lib. textu 48. dicens ex qualitatibus elementorum inuicem pugnantibus corrumpi excellentias qualitatum, & resultare mixtum. Et hinc est, vt id obiter dicam, viuentium alimentum mixtum aliqvod debere esse, non pura elementa, quemadmodum docuit Arist. de sensu cap. 4 quoniam qualitates elementorum cum potentiores sint, non possunt à viuentium qualitatibus quæ debiliores sunt alterari, atque adeo in suam substantiam transmutari, benè verò mixtorum præsertim perfectorum, quorum qualitates facile vinci possint, sicque in viuentium alimentum transire. 61. Verum Tirus in Cælesti Philosophia lib. 2. cap. 8 & alibi sæpè eruditissimè ostendit mixtorum virutes, & admirabiles qualitates non esse elementares, neque ab elementis emanare; sed omninò cælestes esse, atque à cælesti lumine ortum ducere: præcipuè verò calorem innatum, & humidum radicale in viuendibus deriuare à lumine solis, & Lunæ, concurrentibus etiam aliis aëris, à quibus sit distinctio, diuersitas, conuenientia & disconuenientia in naturis animalium, exterorumque mixtorum. Vnde Luminaria, inquit, cum inforunis habent producere animalia, mixtaque perniciosa, & è contraria mixtis optimis, ac perfectis: cum fortunis verò producunt mixta temperatæ naturæ, humano generi conducentia, salutifera, atque viuentium conservationi apprimè idonea. Hinc magna illa cælestium corporum cum terrestribus harmonia, quam Mundi spiritum Pla-

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LEXICON 290 madæ, a fixed star of the second magnitude, of the nature of Venus; not without reason marked with such a name, since if it is found in anyone’s horoscope, it makes him inclined to luxuries and lusts, and for that reason brings infamy and dangers. Rising with the Sun, it brings cloudy and rainy weather; with Saturn, great cold, fogs, rains, and, according to the condition of the seasons, snow. 59. MIRACH is also said by analogy to be the Belt of Heaven, that is, the Zodiac: and especially so on the Planisphere, where, as drawn, it clearly resembles a belt. 60. MIXED things are called by philosophers bodies that are not simple, such as the elements, but those which are formed from them. For Mixtion (as Aristotle says in the first book De Generatione, text 90) is the union of alterable things that are capable of being mixed. By this he understands the four elements fighting one another with the contrary qualities they possess, so that from their struggle all mixed things arise. Whence it comes about that every mixed thing resulting contains in itself all four qualities, whereas the pure elements possess only two, and those proper to themselves. The same Aristotle teaches in book 7, text 48, saying that from the opposing qualities of the elements the excellences of qualities are destroyed, and the mixed thing results. And from this it is, as I may note in passing, that the nourishment of living beings ought to be something mixed, not pure elements, as Aristotle taught in De Sensu, chapter 4, since the qualities of the elements, being stronger, cannot be altered by the qualities of living beings, which are weaker, and thus be changed into their substance; but they can well be altered by mixed things, especially perfect ones, whose qualities can easily be overcome, and thus pass into the nourishment of living beings. 61. Yet Tirus, in Celestial Philosophy, book 2, chapter 8, and elsewhere often, most learnedly shows that the powers and admirable qualities of mixed things are not elemental, nor do they emanate from the elements; but are altogether celestial, and derive their origin from celestial light: especially, indeed, he derives innate heat and radical moisture in living things from the light of the Sun and Moon, with the concurrence also of other properties of the air, from which there is distinction, diversity, agreement, and disagreement in the natures of animals and other mixed things. Hence the Luminaries, he says, when in unfavorable positions, produce animals and harmful mixtures, and, by contrast, excellent and perfect mixtures; whereas in fortunate positions they produce mixtures of a temperate nature, useful to the human race, health-giving, and most fit for the preservation of living things. Hence that great harmony of the heavenly bodies with terrestrial things, which the spirit of the world Pla-

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MATHEMATICVM. 195 co, Nosque vulgò sympathiam, Antipathiamque voca- mus, de qua eruditissimos Dialogos vndecim scripsit Anto- dius Mizaldus medicus Moluciensis, introducens belle Æsculapium, & Vraniam colloquentes. Etenim quam- quam si de primis qualitatibus, quæ temperamentum con- sequuntur loquamur, nulli dubium, quin ex elementares sint, atque ex mixtione elementorum resultent, vt modò dicebamus; nihilominus quoad occultas quasdam virtutes, quibus altiùs potiuntur, tum etiam quoad ipsorum miscibi- lium admirabilem vnionem, nescio quid cælitus in se ipsa mixta contineant. Quandoquidem videmus in eis miram quamdam varietatem, admirandosque effectus, qui non ab elementorum commixtione, quorum naturam longè exu- perant, sed à superiori quadam virtute prodeant, necesse est. Vnde enimuerò effectus illi mirabiles, quos eædem qualitates in elementis, aliisque mixtis, ne digito quidem atenus, possunt attingere? Vnde similitudo illa tempera- menti, quæ proinde si ab elementis exhauriretur, eandem conuenientiam qualitatum, eandem graduum intentionem mixta deberent oppidò participare? Et tamen reipsa non modò non eandem, uel similem, sed natura, actiuitate, virtute longè diuersam videmus. < 61.> Quæ quidem omnia clarè innuunt, non ex sola elemen- torum permixtione resultare mixta; (si enim ea sola inui- cem copules, iam non mixtum per se resultat, sed compo- situm per accidens, & confusio) sed ex cælesti quadam in- sita qualitate, elementaribus quidem per simili, sed enim longe sublimiori, & altioris ordinis, quæ miros hos faciat prodire effectus, quos qualitates purè elementares, quam- tumuis intensiores assequi omninò non possunt. Sic Mine- ralia cuncta, (quæ tamen à vulgo Philosophorum inter mixta perfecta minimè annumerantur) sic vegetabilia, sic Venena plurima mirabilia operantur, quæ non alia mixta, quæ non ipsa elementa, quamtumuis maiori qualitatum intensione præstantia. Cicuta sua frigiditate perimit, ac na- tiuum calorem extinguir; at non glacies, licet in summo frigida, vt ipsa docet experientia, notauitque Philosophus 2. de generat. text. 21. Ei sua caliditate vinum occurrit, vt author est Plinius lib. 14. cap. 5. sed non cætera mixta quamtumuis longè calidiora. Hidtagyrus deleterium est ob excessum frigidi, & sicci; quem tamen excessum longè ma- iorem videre est in aliis mixtis, quin & in ipso elemento terræ; & nihilominus hæc naturæ inimica non sunt, imò potius fouent, conseruant, & tellus plantis alimenta sufficit. T. ij

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co, what we commonly call Sympathy and Antipathy, concerning which Antodius Mizaldus, a physician of Moluces, wrote eleven most learned Dialogues, elegantly introducing Aesculapius and Urania conversing. For although, if we speak of the primary qualities that follow temperament, there is no doubt that they are elementary, and result from the mixture of the elements, as we were just saying; nevertheless, as regards certain hidden powers by which they are possessed more deeply, and also with regard to the admirable union of their constituents, they seem to contain in themselves, as it were, something heavenly. Since we see in them a certain marvellous variety and astonishing effects, which must proceed not from the commingling of the elements, whose nature they far surpass, but from some higher power. For whence indeed come those wondrous effects which the same qualities in the elements and in other mixtures cannot even touch with a finger? Whence that likeness of temperament, which, if it were drawn from the elements, mixtures ought likewise to partake of the same agreement of qualities, the same intensity of degrees? And yet in fact we see not only that they are not the same or similar, but that they are far different in nature, activity, and power. < 61.> All these things clearly indicate that mixtures do not arise from the mere commingling of the elements; for if you only join these together with one another, what results is no mixture in itself, but an accidental compound and confusion; rather they arise from a certain heavenly quality inherent in them, indeed similar to the elementary qualities, but nevertheless far more sublime and of a higher order, which causes these marvellous effects to emerge, effects which purely elementary qualities, however greatly intensified, can by no means attain. Thus all minerals, which nevertheless are by the common opinion of philosophers not counted among perfect mixtures; thus plants; thus very many poisons work marvels, which no other mixtures, and not even the elements themselves, however much they may excel in greater intensity of qualities, can do. Hemlock kills by its coldness and extinguishes native heat; but not ice, although it is very cold, as experience itself teaches and the Philosopher noted in De generatione, text 21. Wine confronts it with its heat, as Pliny says in book 14, chapter 5, but not other mixtures, however much warmer they may be. Hidtagyrus is deleterious because of an excess of cold and dryness; yet that excess is seen far greater in other mixtures, and even in the element of earth itself; and nevertheless these are not inimical to nature, but rather support and preserve it, and the earth provides nourishment for plants. T. ij

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LEXICON 63. Aconitum venenorum omnium violenissimum esse constat, & naturæ cuiuis exitiale; ea tamen est veneni huius conditio, vt deleteriis omnibus tam frigida quam calida qualitate pollentibus sit aduerium, atque (vt Plinij verbis vtar lib. 27. cap. 1.) hominem occidat, nisi inuenerit, quod in homine perimat: cum eo solo colludatur, velut pari intus inuento: sola hæc pugna est, cui venenum in viscerebus reperit; mi- rumque exstulsa per se ambo cùm sint, duo venena in homine commoriuntur, vt homo supersit. Quod & in cornu Vnicornis, in Lapide Bezaar, atque, vt simplicia corpora præteream in Theriaca, & Mitridatico passim videmus, quæ contra omnia nobis venena opitulanitur. 64. Constat igitur miram hanc mixtorum virtutem non ab elementaribus qualitatibus ortum ducere, sed ab cælorum impressa virtute, corporibusque cælestibus quibuscum af- finirarem contrahunt deriuate. Sic Sapphyrus, Prassius, Mentha, Artemisia, Mandragora, Iouiam, arque Saturniam naturam referunt, atque assimilantur Hircostellæ si- xæ posuæ in Auriga. Sic Smaragdi virtutes à Spica Virginis asserunt deriutas: sic Beryllus, & Achates virtutes suas tra- hunt acceptas ab vtroque Cane sidero; propter quod gra- tiam gerentibus præstare feruntur: Sic Iaspis Arcturo subest: &c. quorum longam seriem, virtures, & cum Astris vnde illas hauriunt admirabilem connexionem congerit Marsilius Hicinus etuditus æque ac pius author in libro de Vita cælestis comparanda cap. 8. & alibi passim. Nobis hæc attigisse tan- tum supersit 65. MOBI IASIGNA apud Astronomos eadem sunt quæ Car- dinalia, à quibus videlicet sunt temporum mutationes in Ve- re, Æstate, Autumno, & Hyeme, eò dicta, quod motio- nis temporum argumenta, sunt & transitus vnius in aliam è quatuor primis qualitatibus prædominatem: Ea sunt Aries, Cancer, Libra, & Capricornus, quorum singula singulos anni quadrantes ab alio dirimunt, & dispescunt; & Aries quidem ac Libra inducunt Ver & Autumno; Cancer, verò & Capriconus Æstatem, & Hyemem, singulis suis propriis qualitatibus præpollentibus. Porrò hæc signa sicut in cæ e- stibus sunt iniria mutationum, ita & in inferroribus hisce mutabilitatem pariunt, ac murationum indicia sunt, sicut econtra fixa, stabilitaris. 66. MODERATORES appellantur apud Astronomos præcipui rerum significatores, planctæ, vel alia loca in cælo, quæ ex certa constitutione ac positu aliquid specialiùs regere ha- bent, & moderari: proindeque se habent tanquam subie-

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LEXICON 63. It is agreed that aconitum is the most violent of all poisons, and deadly to every kind of nature; yet such is the condition of this poison, that it is opposed to all deleterious things that possess either a cold or a hot quality, and that, to use Pliny’s words, book 27, chapter 1, it kills a man unless it finds something in man that it may destroy: it contends only with that, as though it had found an equal within; this is the only struggle, in which poison finds in the entrails; and wonderfully, when both are taken away of themselves, the two poisons perish together in the man, so that the man may survive. This is also seen in the horn of the Unicorn, in the Bezaar Stone, and, to pass over simple bodies, in Theriaca and Mithridate, which everywhere are found to assist us against all poisons. 64. It is therefore agreed that this wondrous power of mixed things does not derive its origin from elementary qualities, but from the virtue impressed by the heavens, and is derived from the celestial bodies with which they contract a kinship. Thus Sapphire, Prassius, Mint, Artemisia, Mandrake, refer to a Jovian and Saturnian nature, and are assimilated to Hircostella, placed in Auriga. Thus the virtues of emeralds are said to be derived from the Spike of Virgo; thus Beryl and Agate draw their powers from the two Dog-stars; for which reason they are said to confer favor upon those who are grateful. Thus Jasper is subject to Arcturus: and so on; a long series of these, their virtues, and the admirable connection with the stars from which they draw them, is gathered by Marsilius Ficinus, a learned and equally pious author, in the book On the Comparison of Heavenly Life, chapter 8, and elsewhere often. For us, let it suffice only to have touched on these things. 65. MOBI IASIGNA among astronomers are the same as the Cardines, by which, namely, the changes of the seasons occur in Spring, Summer, Autumn, and Winter; they are so called because the signs of the seasons are motions, and the passage of one into another from the four primary qualities predominates. These are Aries, Cancer, Libra, and Capricorn, each of which separates and divides the four quadrants of the year from the others; and Aries and Libra indeed bring in Spring and Autumn; Cancer, however, and Capricorn, Summer and Winter, with their own proper qualities prevailing in each. Moreover, these signs, just as in the celestial realm they are the beginnings of changes, so also in these lower things they bring about mutability, and are signs of changes, just as, on the other hand, the fixed are signs of stability. 66. MODERATORS are called among astronomers the principal indicators of things, the planets, or other places in the heavens, which, from a certain constitution and position, have to govern something more specially, and to regulate it: and therefore they are as subordinates...

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MATHEMATICVM. 193 etum passibile respectu actiuitatis aliorum siderum: ita vt eorum intersti moderari, & significare res in suo genere, & irà quidem, vt vnusquisque rem sibi commissam, vt ita dicam, regat, nec v[er]lo pacto sese immisceat in iis quæ ad alium spectant; siderum verò oecursantium, quæ etiam Promissores dicuntur) sit specifieare rem per moderatorem significatam, & eo a[n]tare ad certam speciem, de tui natura, siue beneficam, siue maledicam, bonam, aut malam, sic, exempli gratia, Horoscopus est vniuersalis Moderator vitæ, affectionum corporis, valutudinis, insirmitatum, &c. proindeque in omni oecursu astrorum reipit aliquam alterationem in ordine ad ista significata, de natura tamen, & qualitate Astri oecursantis, ita vt si fuerit oecursans maledica, mala in eo genere, si benetiea bona significet in iis quæ nuper enumerauimus. Sie Saturnus, eiutve aspectus hostili ad horoscopum addueit mala in vita, & valetudine de natura & qualitate ipsius, vt arræ bilis commotiones, febres chronicas, frigidas, lentas, pericula saturnina, &c. sic Mars febres acutas, ardentes, flauæ bilis excessum, pericula ignis ignitorum, &c. Sic Iupiter eontrà benè affectus, & ex benigno radio affert alacritatem, firmam corporis valetudinem, accessiones ex Iovialibus, &c. male affectus & hostili radio oecursans causæ pleurisides, Anginam spasmum, Cardiacam, Apoplexiam, dolorem capitis & similia. <67.> Porrò quinque tantum rerum moderatores statuit Prolemeus, vtrumque Luminare, Horoscopum, Cæli Culmen, & Partem fortunæ, quoniam existimat omnia accidenia in vita humanâ tam intrinsecùs in valetudine, corporisque & animi affectionibus, quam in bonis, malisque extrinsecùs aduentantibus, ab iis quinque æquè bene demonstrari posse, regi, & complecti. Sol etenim caloris innati naturalis significator est, & origo: Luna humidi radicalis; Horoscopus corporis, & animi affectionum, Medium Cæli gloriæ, dignitatum, honorum, opificij, Pars fortunæ diuitiarum, aliarumque accessionum, vt alias demonstratum est: Vnde nil planè restare videtur. quod non ab horum aliquo naturaliter, & iure suo significari possit. <68.> Verum Argolus, & plerique recentiores contendunt tum reliquos cardines, imò, & omnes cælestes domos, tum etiam omnes erraticas posse munus moderarionis obire in rebus, quæ sunt de eorum naturâ, & quorum sunt significatores: possunt enim, inquiunt recipere impressiones aliorum siderum oecursantium; atque adeò plurima accidentia tam prospera, quam aduersa per suas directiones inducere, T ijj

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MATHEMATICVM. 193 so that it is passive with respect to the activity of the other stars: thus, it may moderate their intervals and signify things in its own kind, and indeed in such a way that each one governs, so to speak, the matter entrusted to it, and in no way interferes in those things that pertain to another; but the meeting stars, which are also called Promissores, have the role of specifying the matter signified by the moderator, and thus determining it to a certain species, according to their nature, whether benefic or malefic, good or bad. Thus, for example, the Horoscopus is the universal Moderator of life, bodily affections, health, illnesses, etc.; and therefore in every encounter of the stars it receives some alteration in relation to those things signified, however according to the nature and quality of the encountering star, so that if the encounter is malefic, it signifies evil in that kind; if benefic, good in those things we have just enumerated. Thus Saturn, or its hostile aspect to the horoscope, brings evil in life and health according to its own nature and quality, such as attacks of bilious humors, chronic fevers, cold and lingering illnesses, Saturnine dangers, etc.; thus Mars brings acute fevers, burning fevers, excess of yellow bile, dangers from fire, fiery things, etc. So Jupiter, when well affected and by a benign ray, brings cheerfulness, firm bodily health, and jovial affections, etc.; when ill affected and encountering by a hostile ray, it causes pleurisy, angina, spasm, cardiac disease, apoplexy, headache, and the like. <67.> Moreover, Ptolemy establishes only five moderators of things: both Luminaries, the Horoscope, the Midheaven, and the Part of Fortune, because he judges that all accidents in human life, both inwardly in health and in bodily and mental affections, and outwardly in goods and evils that befall us, can be equally well demonstrated, governed, and comprehended by those five. For the Sun is the significator and source of innate natural heat; the Moon of radical moisture; the Horoscope of bodily and mental affections; the Midheaven of glory, dignities, honors, and craftsmanship; the Part of Fortune of riches and other acquisitions, as has been shown elsewhere. Whence nothing at all seems to remain that cannot naturally and by its own right be signified by one of these. <68.> But Argolus, and most recent writers, maintain that not only the remaining angles, nay even all the celestial houses, but also all the wandering stars can perform the function of moderation in matters that are of their nature and of which they are significators; for they say they can receive impressions from other encountering stars, and thus bring about many accidents, both favorable and adverse, through their own directions, T ijj

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194 LEXICON quorum ne vmbratilis quidem notitia à dictis quinque primis rerum moderatoribus auspicatur. Nec illis deficit, aut experientia: Cum enim in Metheorologicis alij quinque Planetæ possint esse rerum significatores, non elucet cur eadem prærogatiua non gaudeant & in omnibus. Sanè Problemæus ipse cum de electione Aphetæ seu Vitæ Moderatoris verba facit, docet vt quando Sol, & Luna non teperiuntur in locis idoneis, Apheticis, eligi debeat in Vitæ prorogatorem planetæ ille qui in cælesti figura plures dignitates habuerit in locis Luminarium, Ascendentis, Partis Fortunæ, & præcedentis proximè ante Natiuitatem coniunctionis aut oppositionis Luminarium. Si igitur in hoc casu vitæ moderandæ raionem suscipere potest planeta talibus prærogatiuis prædirus. & in aliorum defectu, cur non & in iis quæ naturaliter significare habet dirigi poterit? si is, cur non & alij? Argolus testatur se summa felicitate eorum directiones in geneihiacis perfecisse, sicut etiam secundæ domus pro diuitiis, & subdit, quod si Professores aliarum Domorum cuspides dirigerent, non omninò spernenda compere- rent. Liberum sit cuique rei periculum facere; & quantum huiusmodi directiones aliorum planetarum valeat perscrutaris. Sufficiat nobis insinuasse. 9. MONOMENÆ ÆGYPTIORVM dicuntur symbola, & Figuræ ab Ægyptiis in Nona sphæra confictæ, applicitæque ad singulos signorum decanos, nec non & gradus eorum naturam referentes, & explicantes. Pro qua re sciendum est, ex Kirchero in Oedipo Ægyptiaco part. 2. tom. 2 class. 7 in Digressione Nùm calum liber sit, &c. Multorum Arabum, & Hebræorum sententiam, seu amentiam esse calum omne non modo sideribus in inferiora isthæc influentibus esse conspersum, sed & diuersis symbolis characteribus, & imaginibus esse delineatum, in quibus tanquam in libro descriptæ sint omnes actiones humanæ, & quæ futura sint & quæ facta: in cuius rei probationem mirum est quam enormiter torqueant plurima loca sacræ scripturæ vt illud Isa. 34. vbi dicitur, complicabuntur cali sicut liber. Psalm. 18. Calienarrant gloriam Dei. Item Gen. 1. vbi dicitur: In principio creauit Deus calum, & terram. legunt ex Heræo literam cali, & literam terra seu scripturam cali Authores præcipui huius deliramenti ex Hebræis sunt Akibam, author nescio cuius libri Iessiræ, Rambam Abenezra, & alij: suffragantur ex Latinis Cornelius Agrippæ de occulta Philosophia, Paracelsus, Robertus de ductibus, Postellus, & Ciccus; nescio quis, Calaber Astrologus, cognomento

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194 LEXICON the slightest shadowy notice does not begin from the sayings of the first five rulers of things. Nor do they lack experience: for since in the Meteorologica the other five planets can be significators of things, it does not appear why they should not enjoy the same prerogative in all matters as well. Indeed, Ptolemaeus himself, when he speaks of the choice of the Apheta, or Ruler of Life, teaches that when the Sun and Moon are not found in suitable places, in the Aphetic places, that planet should be chosen as prolonger of life which in the celestial figure has the greater number of dignities in the places of the Luminaries, of the Ascendant, of the Part of Fortune, and of the conjunction or opposition of the Luminaries immediately preceding the Nativity. If therefore in this case a planet adorned with such prerogatives can take upon itself the office of governing life, and in the absence of the others, why can it not also be directed in those things which it is naturally supposed to signify? If it can, why not the others as well? Argolus testifies that he completed their directions in genethliacs with the utmost success, as also those of the second house for wealth, and adds that if the cusps of the other Houses were directed, they would not be found altogether to be despised. Let it be free for anyone to make trial of the matter; and to investigate how much value the directions of other planets have. It is enough for us to have indicated this. 9. The Egyptian Monomene are said to be symbols and figures fashioned by the Egyptians in the Ninth sphere, and applied to each of the decans of the signs, as well as to their degrees, representing and explaining their nature. For this matter it should be known, from Kircher in the Oedipus Aegyptiacus, part 2, vol. 2, class. 7, in the Digression “Num caelum liber sit,” etc., that the opinion, or folly, of many Arabs and Hebrews is that the whole heaven is not only sprinkled with stars influencing things below, but is also outlined with various symbols, characters, and images, in which, as in a book, are described all human actions, both what shall be and what has been done: in proof of which it is astonishing how violently they twist many passages of sacred Scripture, such as that of Isa. 34, where it is said, “The heavens shall be rolled together as a book.” Psalm 18: “The heavens declare the glory of God.” Likewise Gen. 1, where it is said: “In the beginning God created the heaven and the earth.” From Heræus they read the letter of heaven, and the letter of earth, or the writing of heaven. The chief authors of this delirium among the Hebrews are Akibam, author of some book called Iessira, Rambam, Abenezra, and others; among the Latins Cornelius Agrippa, of Occult Philosophy, Paracelsus, Robertus de ductibus, Postellus, and Ciecus; I know not who else, the Calabrian astrologer, surnamed

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MATHEMATICVM. 195 Esculanus, qui in Commentaris super Centiloq. Ptolomæi de huiusmodi Cæli characterismis sermonem ingerens, hæc habet. Sententia communis sapientum astrologorum est, quod non solum octaua sphara, sed & nona, & decima sint tanquam tabula variis configurationibus imaginibus, & notis dep[er]tta: nam in signo Arietis est imago iuuenis formosi, & in signo Virginis imago Virginis gestantis puerum, & in cæteris signis, & partibus cæli sunt diuersa effigies, & characteres, & iure demonstrantes nobis causas horum inferiorum; de quibus intelligenda est illa sententia Patriarcha Iacob. Legi in tabulis cæli quæcumque contingent vobis Ha autem figura non sentoriosa, sed influunt diuersos effectus in hunc mundum. Et idcircò dicit Ptolomaus in hæc parte Centiloquij VVLTVS huius seculi subectis sunt vultibus corporum superiorum, idest figurationibus & aspectibus imaginum; qua insunt corporibus cælestibus. Sed & hic planè delirat: sequitur. Et quamquam ista figura non possint ab omnibus indifferenter videri, tamen ab his, qui acutissimum visum, & purgatissimum animum habent, certis temporibus, & in clarissima noctis ferentate conspici possunt. Vnde ex horum observatione collecta fuit à sapientibus ars illa, qua Notoria appellatur, cuius virtute iidem sapientes multa miranda experimenta fecerunt ad hominum vtilitatem: sculpebant enim, vel in metallis, vel in lapidibus electis, vel in gummi, vel in cera, vel argilla imprimebant notas figurarum cælestium, quas in tæcæli viderant, & nomina angelorum addebant, quos Deo reuelante cognouerant, præesse figuris illis, & sic ex horum sculptura & impressione mutos admirabiles effectus ad laudem Dei, & beneficium hominum operabantur Sed postea quidem corruptores huius artis adiecerunt ei quasdam figuras, & notas infernales, qua in regione damnatorum inueniri dicebant, & nomina Damonum, ex quibus Diabolo suadente firmabant imagines ad inducendum libidinem, discordias, homicidia, furta, agitudines, fascinationes veneficia, malesficia, &c. & ideò propter hanc corruptionem accidit adem, vt ars per se bona propter superadditam malitiam fuerit damnata, & prohibita. Hucusque Ciccus apud Sixtum senentem in Bibliotheca sancta com. 1. lib. 2 vbi incidit sermo de libro quodam Apocrypho intuulato Harvatio Ioseph, quem citat, & magnifacit Origenes pluribus in locis, sed præsertim in explanationibus Genesis, vbi sic ait: Vniuersum cælum est quasi liber quidam apertus omnia futura in se conscripta continens; idcirco in oratione Ioseph sic in- T iii}

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MATHEMATICVM. 195 Esculanus, who in his Commentaries on Ptolemy’s Centiloquium, introducing a discussion on these sorts of celestial characters, says the following. The common opinion of wise astrologers is that not only the eighth sphere, but also the ninth and tenth, are as if tablets inscribed with various configurations, images, and signs; for in the sign of Aries there is the image of a handsome youth, and in the sign of Virgo the image of a Virgin bearing a child, and in the other signs and parts of the heavens there are various figures and characters, rightly showing us the causes of these lower things; of which that saying of the patriarch Jacob is to be understood: “I have read in the tablets of heaven whatever shall befall you.” But these figures are not sent by sound, but they influence various effects in this world. And therefore Ptolemy says in this part of the Centiloquium: “THE FACE of this age is subject to the faces of the superior bodies,” that is, to the configurations and aspects of the images that are in the celestial bodies. But here too he plainly raves; he continues. And although these figures cannot be seen by everyone indiscriminately, nevertheless by those who have the sharpest sight and the purest mind they can be perceived at certain times, and in the brightest clarity of the night. Hence from the observation of these things that art was collected by the wise, which is called Notoria; by its power the same wise men performed many marvelous experiments for the benefit of men: for they engraved, either in metals, or in chosen stones, or in gum, or in wax, or in clay, the marks of the celestial figures which they had seen in that heaven, and they added the names of the angels, whom they had learned, God revealing it, to preside over those figures; and thus by the engraving and imprinting of these they performed mute but admirable effects to the praise of God and the benefit of men. But later corruptors of this art added to it certain infernal figures and signs, which they said were to be found in the region of the damned, and the names of demons; and by these, at the devil’s prompting, they maintained images for the purpose of inducing lust, discord, murders, thefts, illnesses, fascination, poisonings, evils, and so forth. And therefore, because of this corruption, it came about that an art good in itself was condemned and prohibited on account of the malice superadded to it. Thus far Ciccus, cited by Sixtus Senensis in the Bibliotheca Sancta, vol. 1, book 2, where there is a discussion of a certain apocryphal book entitled Harvatio Joseph, which Origen cites and greatly values in many places, but especially in his explanations of Genesis, where he says thus: The whole heaven is like a certain open book containing within itself all future things written down; therefore in the prayer of Joseph thus— T iii}

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LEXICON < 70.> telligi potest, quod à Iacob ad filios ad citur legi in tabulis cæli quacumque contingens vobis, & filius vestris Sed aliud est cælum esse, veluti librum, in quo ex vario siderum positu configuratione, & habiundine, astrologica coniectura prænosci possint quæ futura sint, præsertim secundum naturalem ordinem causarum secundarum: aliud in eo veris novis, & quibu'dam characterismis aliquid esse impressum, quod à sapientibus legi possit. A iud est quod Ptolemæus vult de subiectione, & respondentia vultuum horum inferiorum vultibus corporum cælestium, hoc est imaginibus octauæ sphæræ, ob sympathiam, & connexionem sublunarium cum stellis fisis, vt nos supra tetigimus; aliud has imagines verè cælo inferere, protrinaque fronte asseuerare, eas vissibiles esse. Sanè Postellus in commentarium ad supracitatum libru[m] Iesiræ nescio nùm stolidè magis quam impiè hæc effurierit. Si dixero in Calome vidisse in ipsis sacra lingua character bus ab Esdræ primum pulchre expositis ea omnia, quæ sunt in naturarum constituta, vt vidi non explicitè, sed implicitè vix vllus mihi crediderit: testis tamen mihi est Deus & Christus eius, quod non mentier. Sed & Kircherus refert, & exponit oculis contemplandum pulchrum quidem, & curiosum ipsius Cæli schematismum dictis characteribus delineatum à nescio quo Gaffarello relatum in libro cui multis gallicè les curiosit: 7 inoÿes, hoc est, curiositates in audiræ quem Alphabetum benè vanitatis auguit idem Kircherus ibi cap. 7. pag. 222. Nobis eadem nugamenta retulisse, perinde ac refellisse sit: Quandoquidem nemo sanæ mentis erit, qui hæc audiens illicò non contemnat. At enim hic me temperare non possum quin grauiter indigner Calabro illi superiùs relato, qui rem alioqui grauem & summis philosophis dignam suis philaieriis mititur eleuare, & paucis multa concludens, aut hominibus illudere vuli, aut errores multos artificioso astu studet obtrudere. Imprimis artem illam Notoriam pessimam damnatam, nunquam non perfidam superstitione ac Dæmone plenam, tanquam cælitus missam ab initio innocentem, & licitam astruit. Mor imagines astronomicas artificiosas cum cælestibus confundit, easque vel eò suspectas facit, quod superstitionibus refert, ac suspectis rebus annectit. Denum transit ab imaginibus octauæ sphæræ de quibus loquitur Ptolemeus in Centiloquio, ad imagines phantasticas, & suo cerebro dignas, quæ nullam realem efficientiam habere possunt, quia neque lumine præditæ partes Zodiaci sunt, neque vlla actiuitate, vt alibi monstrarum est. Atque

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LEXICON < 70.> it can be understood, that from Jacob to the children it is added to be read in the tablets of heaven whatever may happen to you, and to your children But it is one thing for heaven to be, as it were, a book, in which from the varied position, configuration, and disposition of the stars, astrological conjecture may foresee what things are to come, especially according to the natural order of secondary causes: another thing is for in it, by truly new and certain characters, something to be impressed, which may be read by the wise. Another thing is what Ptolemy means by the subjection and correspondence of the faces of these lower things with the faces of the celestial bodies, that is, the images of the eighth sphere, by sympathy and connection of sublunary things with the fixed stars, as we mentioned above; another thing is to bring these images truly down to heaven, and on a brazen forehead to assert that they are visible. Certainly Postellus, in the commentary on the above-cited book of Iesira, I know not whether more foolishly than impiously, has babbled these things. If I should say that in Calom I saw in the very sacred language characters first beautifully set forth by Ezra all those things which are established in nature, as I saw not explicitly but implicitly, scarcely anyone would believe me: yet God and his Christ are witness to me that I shall not lie. But Kircher also relates, and lays open for the eyes to contemplate, the truly beautiful and curious schematism of heaven itself, drawn with said characters, reported by some Gaffarell in a book which in French he calls les curiosit: 7 inoÿes, that is, unheard-of curiosities, which same Kircher in his Alphabet of vanity praises there, chap. 7, p. 222. For us to have reported the same follies is as much as to refute them. Since there will be no man of sound mind who, hearing these things, does not straightway despise them. But indeed I cannot restrain myself here from gravely being indignant at that Calabrian mentioned above, who seeks to make light of a matter otherwise serious and worthy of the greatest philosophers with his trifles, and, summing up much in few words, either wishes to mock men, or by cunning art strives to thrust upon them many errors. First of all, he condemns that most wicked art of Notory, never not perfidious, full of superstition and the Devil, yet as though sent from heaven from the beginning he maintains to be innocent and lawful. Then he confounds astronomical artificial images with celestial ones, and makes them suspicious even by the fact that he refers them to superstitions and attaches them to suspect things. Finally he passes from the images of the eighth sphere, of which Ptolemy speaks in the Centiloquium, to phantastic images, and worthy of his own brain, which can have no real efficacy, because the parts of the Zodiac are endowed with neither light nor any activity, as is shown elsewhere. And thus

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MATHEMATICVM. 297 impudentissime imponit cum ait eas certis temporibus, ac determinatis hominibus fieri manifestas. Quare cachinnis excipiendus est impudentissimus circulator, ac dignis increpationibus coercendus. MO CHLEK Arab. dicitur stella fixa in cauda scorpionis, quæ < 71.> proximè antecedit aculeum, quam tamen Kircherus in Oedipo affirmat melius vocari Lessaa Elaakrab. MOTVS est passio, & proprietas cælestium corporum, < 72.> quem qui negaret, sensu & ratione carere censendus esset. Per eum enim orbis vniuersus consistit, & si minimum quid cælorum motus sisteret, & cessaret, cessaret etiam rerum ordo, quilibet alius motus, adeoque generatio, & corruptio rerum necesse esset, vt author est Abulensis, ac D. Thomas in 1. dist. 1. quæst. 1. ar. 3. & alij, communiter tam ex Patribus, quam ex Theologis, & Philosophis. Nùm verò cælorum motus sit causa productionis rerum, an dicenda tantum condicio, controuersia magna est inter Philosophos. Capreolus in 2. distinct. 14. quæst. 1 & in 4. distinct. 44. quæst. 4. Bannes aliique, multi existimant motum cæli non tantum esse conditionem, sed & rationem agendi siderum, quo veluti instrumenta'i causa inferiora isthæc exagirent: Verum Durandus, ac nouissimè Titus in cælesti Philosophia, longè veriùs sustinent, motum esse solum conditionem applicantem cæli virtutem, quæ demum solo lumine communicatur; arque ex longè & propè fieri siderum, fiat maior, vel minor intensio, & extensio Lucis; ad cuius rationem postea effectus resultat. Id quod & ratio suader, & experientia euincit (quandoquidem motus localis nil addit reale rebus motis) & denique Aristoteles ipse sua authoritate confirmat, 2. de Generat. text. 55. sic dicens. Motum eatenus esse causam generationis, & corruptionis, quatenus est causa accessus, & recessus solis. Quod autem motus in hac regione elementari sit causa < 73.> caloris, id non arguit, etiam cælorum motum eundem effectu producere: tum quia calor expisticatione corporum prosilit, quorum alterum saltem sit solidum, secus autem ex mou corporum pure auxilium, (vt paret in ventis, qui aliud non sunt, quam aeris morio maximè violenta, & tamen natura sua frigidi sunt, vt in loco dicemus: cælorum autem substantia longè fluxilior est quam aer) tum etiam quia cælorum motus semper æqualis est, & æqualiter concitatus: vnde semper æqualem calorem deberet producere tam ratione locorum, quam temporum, quod ta-

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MATHEMATICVM. 297 most shamelessly imposes on people when he says that these things become manifest at certain times and to certain men determined. Therefore the most impudent charlatan must be received with laughter and restrained with due rebukes. MO CHLEK, in Arabic, is said to be the fixed star in the tail of the scorpion, which is nearest before the sting; yet Kircher in the Oedipus affirms that it is better called Lessaa Elaakrab. MOTUS is the passion and property of the heavenly bodies, and anyone who would deny this would be judged to lack both sense and reason. For by it the whole universe subsists, and if the slightest movement of the heavens should cease and stop, the order of things would also cease, and every other motion, and thus generation and corruption of things would necessarily cease, as Abulensis says, and St. Thomas in 1. dist. 1. quaest. 1. art. 3, and others commonly, both from the Fathers and from theologians and philosophers. But whether the motion of the heavens is the cause of the production of things, or should be said only to be a condition, is a great controversy among philosophers. Capreolus in 2. dist. 14. quaest. 1 and in 4. dist. 44. quaest. 4. Bannes and many others think that the motion of the heaven is not only a condition, but also the reason of the action of the stars, by which, as if they were instrumental causes, these lower things are brought about. But Durandus, and most recently Titus in Celestial Philosophy, maintain much more truly that motion is only the condition applying the power of heaven, which is then communicated by light alone; and from the near and distant position of the stars there is a greater or lesser intensification and extension of light; according to which the effect afterward results. This is supported both by reason and confirmed by experience (since local motion adds nothing real to things moved), and finally Aristotle himself confirms it by his authority, 2. de Generat. text. 55, saying thus: Motion is the cause of generation and corruption only insofar as it is the cause of the sun's approach and recession. Now, although motion in this elemental region is the cause of heat, this does not prove that the motion of the heavens also produces the same effect: first, because heat springs forth from the rubbing of bodies, one of which is at least solid, whereas from the motion of bodies in pure air only assistance arises, as is clear in winds, which are nothing other than a very violent motion of air, and yet by their nature they are cold, as we shall say in the proper place; and the substance of the heavens is much more fluid than air. Then also because the motion of the heavens is always equal and equally accelerated; hence it ought always to produce equal heat, both in respect of places and of times, which wou-

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LEXICON men falsum esse videmus. Demum quia regiones aëris superiores frigidiores sunt, quam insima, & terræ vicinior, cum tamen si verum esset, quod cælorum motus calorem in sublunaribus hisce produceret, maiorem vtique atque intentiorem ibi quam isthic deberet efficere: quò enim passum proximius est agenti, eò validius patitur; ac virtus illius intenditur. Quod cum reipsa minimè experiamur, concludendum est, cælorum motus nil aliud efficere in hæc sublunaria, quam applicare, ac diffundere lumen siderum, pro cuius diuersa applicatione diuersi etiam producuntur effectus. Itaque motus est præcipuum instrumentum luminis astrorum, quo mediante lumen ipsum diffunditur, cuaditque aptum ad tot genera effectuum producenda. Porrò duplicem motum cælestium corporum communiter <74.> asserunt omnes tam Philosophi, quam Astronomi, alterum raptus, & vniuersalem, quo simul omnia rapiuntur à Nònà, siue quæcumque tandem ea sit, postrema omnium infrà Empyreum, sphæra, concitatissimo motu ab Oriente in Occidentem, spatio ferè 24. horarum: alterum proprium cuiusque orbis, qui sit modò explicato contrarius, & eò ferantur in partes orientaliores, quo quisque orbis, aut planeta statuto tempore periodum suam perficit in Zodiaco. Hinc duo mobilium geneta: Alterum quod autonomasticè dicitur. <75.> Primum Mobile, quod est supradicta nona sphæra, vel decima, aut etiam vndecima, quæ in quam reliquas omnes complectitur, & simul trahit ab ortu ad occasum super polos mundi revolutionem suam perficiens spatio integræ diei naturalis, & hoc cælum solo motu dignoscitur, quippe nullæ in eo stellæ, nullæ imagines, nullæ lineationes aut characteres (vt aliqui sóniantes volebant, quos non ita pridé cum de Monomeriis egimus deridentes reiecimus) sed signa, & circuli, quos in eo imaginamur, fictiùj sunt, & vel ab Firmamento, & octaua sphæra, quam olim ob motus carditatem cum nona sphæra confundebant, vel ab effectibus illi tributi. Cæterum insensibile est, vnde & ignoratur, quanta sit eius crassities, & conuexi amplitudo. Aliqui verò Astronomi, inter quos viderur esse Tycho, vt apparet ex eiusdem Epistolis existimant, nullum esse cælum Anastron, atque ad solum motum quempiam efficiendum addictum. Quapropter probabiliter putant, diurnam mundi conuersionem à nullo primo mobili provt ab aliis distincto sieri sed à tota cælesti regione, hoc est totum ætherem simul

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LEXICON we see it to be false. Finally, because the upper regions of the air are colder than the lower, and nearer the earth, when nevertheless, if it were true that the motion of the heavens produced heat in these sublunary things, it ought indeed to produce it there greater and more intense than here; for the closer a patient is to an agent, the more strongly it suffers, and the power of the latter is intensified. Since in fact we experience no such thing, it must be concluded that the motion of the heavens effects nothing else in these sublunary things than to apply and diffuse the light of the stars, according to whose different application different effects are also produced. Therefore motion is the chief instrument of the light of the stars, through which the light itself is diffused, and becomes suitable for producing so many kinds of effects. Moreover, all philosophers as well as astronomers commonly assert a double motion of celestial bodies, the one of rapture and universal motion, by which all things are carried together from the ninth sphere, or whatever it may be, the last of all beneath the Empyrean, by a very swift motion from East to West, in about the space of 24 hours; the other the proper motion of each orb, which is contrary to the one just explained, and by which they are carried toward the eastern parts, as each orb, or planet, completes its period in the Zodiac at the appointed time. Hence two kinds of movable things: the one which is called by its proper name the Primum Mobile , which is the aforesaid ninth sphere, or tenth, or even eleventh, which includes all the rest, and at the same time draws them from east to west over the poles of the world, completing its revolution in the space of a whole natural day; and this heaven is recognized by motion alone, since there are no stars in it, no images, no lines or characters (as certain dreamers wished, whom we recently rejected with ridicule when we were discussing the Monomeries); but the signs and circles which we imagine in it are fictitious, and attributed either to the Firmament and the eighth sphere, which formerly they confused with the ninth sphere on account of the slowness of its motion, or to the effects assigned to it. Moreover, it is imperceptible, and therefore it is unknown how great its thickness and the amplitude of its curvature are. Yet some astronomers, among whom Tycho seems to be, as appears from his letters, think that there is no starless heaven, and that it is devoted solely to producing some motion. Wherefore they probably think that the daily revolution of the world is effected by no first mobile distinct from the rest, but by the whole celestial region, that is, by the whole ether together

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MATHEMATICVM. 299 moueri in polis mundi propria virute ab Oriente in Occidentem: in quo interim sidera omnia, & Planetæ pro- priis motibus ab occasu in or:um super polos Zodiaci ferantur, quasi contrà primum mobile, vel sanè, vt ego aliàs explicaui, lentius ob sui resistentiam ab ipso primo mobilj rapiantur qui ideirco. < 76.> Secundi Mobiles, appellantur ad differentiam primi mo- tus, suntque siue orbis singulorum planetarum, necnon octaua sphæra fixarum, siue ipsa siderum corpora, quæ nitantur contrà motum primi mobilis in consequentia si- gna ab Occidente in Orientem super polos Zodiaci statis temporibus singulis integrum Zodiacum permeantibus. Et Firmamentum quidem id præstat in annis 36000. seu, vt volunt recensiores spatio annorum 49000. singulis 70. an- nis vnum tantum gradum assequendo: Saturnus totam suam circulationem complet in annis triginta: Iupiter in duodecim: Mars in duobus: Sol, Venus, Mercurius ferè in vno: Luna tandem spatio dierum 27. hor. 7. min. 47. sunt tamen qui asserunt cælum ipsum non moueri, sed Astra in ipso, tanquam aues in aëre; quippe vnum tan- tum cælum admittunt, illudque fluidum, & vagum instar aëris habens magnam crassitiem, in cuius determinatis spa- tiis sidera constituantur: quæ postea per eius ambitum mo- ueantur, causentque hanc apparentiarum varietatem: in qua opinione est Aretius de Generat. disp. 2. quæst. 27. Sett. 7. aitque in ea etiam fuisse antiquos Patres Chrysostomum, Origenem, Eusebium, Emisenum, Diodorum Tarsensem, & alios. Verum ego esti certo certius haheam cælum esse fluidum idque omninò vnum; non tamen in hoc conuenire possum; vt illud absoluè immobile astruant, sed ex- stimo ipsum, seu potius omne æthereæ regionis expan- sum, quod complectitur totum id, quod inter nos, & cæ- lum Empyreum intercipitur. vnico motu ab Oriente in Oc- cidentem moueri, secumque trahere sidera in eius crassi- tie in determinatis quæq[ue] spatiis constituta, quo pacto mo- uetur etiam aër, & noua Phenomena, seu Cometæ in eo geniti; ita tamen, vt hæc ex se minimè moueantur, sed partes cæli, & aëris in quibus reperiuntur, quæ secum postea sidera inibi constituta sua violentia rapiant, & circumducunt. Et partes quidem superiores velocius, in- feriores verò lentius, & lentius in infinitum quò magis ad terram approximantur, ac longè fiunt à primo motore semper magis, ac magis huius impulsi resistentes. Neque enim aliter saluati possunt & fixarum motus semper æqua-

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MATHEMATICVM. 299 to be moved in the poles of the world by its own force from East to West: in which meanwhile all the stars and planets, by their proper motions from west to east, are carried over the poles of the Zodiac, as if contrary to the first mobile, or indeed, as I have elsewhere explained, more slowly, by reason of their resistance, they are drawn by the first mobile itself, which therefore. < 76.> Secondary Mobiles are called, in distinction from the first motion; and they are either the spheres of the individual planets, or else the eighth sphere of the fixed stars, or the very bodies of the stars, which, striving against the motion of the first mobile in the succession of signs, pass through the whole Zodiac at fixed times, each one over the poles of the Zodiac from West to East. And the Firmament indeed accomplishes this in 36,000 years, or, as more recent writers hold, in a span of 49,000 years, gaining only one degree in every 70 years: Saturn completes his whole circuit in thirty years; Jupiter in twelve; Mars in two; the Sun, Venus, Mercury, almost in one; the Moon finally in the space of 27 days, 7 hours, 47 minutes. There are, however, some who assert that the heaven itself does not move, but the stars in it, like birds in the air; for they admit only one heaven, and that fluid and wandering like air, having great thickness, in whose determinate spaces the stars are set, and afterwards move through its expanse, causing this variety of appearances. Of this opinion is Aretius in De Generatione, disp. 2, question 27, sect. 7; and he says that among the ancients were also Chrysostom, Origen, Eusebius, Emisenus, Diodorus of Tarsus, and others. But although I hold it most certainly that the heaven is fluid, and altogether one, I cannot agree to this, namely, that they maintain it to be absolutely immobile; rather I think that it, or rather the whole expanse of the ethereal region, which embraces all that is intercepted between us and the Empyrean heaven, is moved by a single motion from East to West, and with it draws the stars, established in its thickness in determinate spaces, in which manner the air also is moved, and the new phenomena, or comets, generated in it; yet so that these are by no means moved of themselves, but are parts of the heaven and air in which they are found, which afterwards by their violence bear along and carry around the stars established there. And the upper parts indeed more swiftly, the lower more slowly, and more slowly still without limit the more they approach the earth, and become ever more distant from the first mover, always more and more resisting this impulse. For otherwise neither can the motions of the fixed stars be preserved always equal.

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LEXICON 300 lis, & æqualis semper inter ipsas distantia, & motus omnium cælestium corporum ab Oriente in Occidentem, & insuper inferiorum quomagis à primo mobili remouentur co maior contranitentia, nisi dicamus: sup[er]a ipsas fixas verè esse aliquam partem cæli quæ moueatur [con]cissimè, & circulationem suam complet spatio 24. horarum, redeundo ad idem punctum, vnde discesserat, pars vbi fixæ consistunt, quia inferior aliquanto seriùs moueatur, ita tamen, vt fixas omnes imaginemur in eadem à terra distantia, & successiuè planetæ in partibus ulterioribus collocentur, ac simul cum illis moueantur, siuè serius, siuè citius pro ut magis vel minus à primo motore elongantur. Quod autem sidera videamus moueri non super polos mundi, vt mouentur ipsæ partes cæli, in quibus tamquam in continente moueri dicimus, sed super polos Zodiaci, quod solum probate potest peculiarem singulis motum (& magni facit Clauius) id non officit, sed dico id prouenire ex dispositione suarum orbitarum, & respectu quem habent ad diuersos polos, vt aliqualiter concipere est in rotis alicuius currus, quæ etsi omnes vno motu raptus ferentur, omnes ab vno temone reganrur, diuersas ramen orbitas imprimunt, ad diuersasque metas contendunt, quod multo magis concepi potest in ipsis sideribus, quæ licet rapta, non sunt tamen ita alligata cælo, vt rotæ currus. 77. Cæteru[m] hæc sententia de vnico motu sideru[m] non est adeò nova, vt in eam etiam non conuenerint multi ex antiquioribus in primisq; Auetroës & Alpetrasius: sequuti sunt postea Alexander Achillinus, lib. 1. de Orbibus, Franciscus Patri- tius, Io: Antonius Delphinus, ac novissime Paulus Are- lius, lib. 1. de Generat. disp. 6. quæst. 45. Sect. 3. ac Titus in Cælesti Philosophia, lib. 3 cap 1. Docentes id repugnare, & neque per divinam potentiam fieti posse, vt, idem corpus, nisi replicetur, ad duos oppositos terminos moueatur. Quod igitur sidera singulis diebus vniformiter moveantur ad partes Occidentaliores, & insuper statis temporibus, vt sol integro anno, Mars in duobus, &c. Moveantur ad partes Orientaliores perficientes integrum Zodiacum, id procedit, vt dictum est, à maiori, & maiori ipsorum resistentia ad impulsum illi datum à primo mobile: quod adhuc tali pacto luculentius explicabimus. Rapit primum mobile, siue alios cælos, siue alias eiusdem cæli partes in quibus sidera fixa sunt; sed quoniam virtus impulsua, quò tendit in aliquid remotius eò remissior est,

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LEXICON 300 lies, and always the same distance between them, and the motion of all the celestial bodies from East to West, and moreover of the lower ones, the more they are removed from the first mobile, the greater the resistance, unless we say: above the fixed stars themselves there is truly some part of the heaven which moves very swiftly, and completes its revolution in the span of 24 hours, returning to the same point from which it had departed, the part where the fixed stars stand, because the lower part moves somewhat more slowly, yet in such a way that we imagine all the fixed stars at the same distance from the earth, and the planets successively placed in the farther regions, and moving together with them, either more slowly or more quickly, according as they are more or less removed from the first mover. But that the stars we see moving not over the poles of the world, as the parts of the heaven move, in which, as in a container, we say they move, but over the poles of the Zodiac, since that alone can prove a particular motion in each star (& Clavius makes much of this), does not interfere; but I say this arises from the arrangement of their orbits, and from the relation they have to different poles, as may be somewhat conceived in the wheels of some chariot, which although all are carried by one motion, all are governed by one pole, yet imprint different paths and strive toward different goals, which can be conceived much more readily in the stars themselves, which although they are carried along, are nevertheless not so bound to the heaven as the wheels of a chariot. 77. However, this opinion about a single motion of the stars is not so new that many of the older writers did not also agree with it, especially Averroes and Alpetrasius: afterwards followed Alexander Achillinus, book 1 of De Orbibus , Franciscus Patri- tius, Io: Antonius Delphinus, and most recently Paulus Are- lius, book 1 of De Generatione , disputation 6, question 45, section 3, and Titus in Cælestis Philosophia , book 3, chapter 1. Teaching that this is repugnant, and that not even by divine power can it happen that the same body, unless it be duplicated, moves toward two opposite termini. Therefore that the stars each day move uniformly toward the western parts, and moreover at fixed times, as the sun in one whole year, Mars in two, etc., move toward the eastern parts, completing the entire Zodiac, this proceeds, as was said, from the greater and greater resistance of the stars themselves to the impulse given to them by the first mobile: which we shall explain even more clearly in this way. The first mobile carries along either the other heavens, or the other parts of the same heaven in which the fixed stars are; but since the impelling force, the farther it extends to something more remote, the weaker it is,

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MATHEMATICVM. 301 non potest orbis solis, exempli gratia tantâ velocitate mo- neri, quantâ partes, & orbis superiores, ipsumque primum mobile: hinc est, vt ipse, sol non possit in vna circulatio- tione adequare motum primi mobilis, sed post ipsum re- manet retrò ferè vnum gradum. At enim primum mobile, & partes superiores non expectant cursum solis compleri, sed expleta vna integra circulatione incipiunt mox secundam: & cum etiam in ea seriùs moueatur sol, in hac secunda primi mobilis circulatione ipse remanet retro duos gra- dus; in tertia tres, & sic de reliquis, ita vt quo tempore sol facit 365. circulationes circà tellurem spatio vnius an- ni, inueniatur primum mobile perfecisse 366. circulationes, vnâ plus ipso sole, quam vt iste adæquet requiritur adhuc spatium vnius anni. Hinc motus ille directorius, quo si- dera occursantia ad moderatores feruntur tanto temporis spatio, quantum interest æquatoris inter vtrumque; itavt motus solis in æquatore singulis diebus, sit mensura dire- ctionum vnius anni, vt suo loco diximus. Cæterum, vt ad rem nostram reuertamur, qui primi obseruarunt, so- lem, & alia sidera magis, ac magis, & successiuè semper remanere post primum mobile, dixerunt, ipsa moueri pro- priis motibus in partes oppositas, cum sanè id non sit verè in oppositam partem moueri, sed potius lentiùs ad eandem partem ad quam primum mobile nititur ferri. Nihilominus cum in re parum referat, an hic Planetarum motus sit vns, & lentior, an potius duplex, isque al- ter alteri contrarius, præstat in hoc morem gerere antiquo, & communi loquendi vsui, quo facilius res astronomicæ explicantur; sicque vt ratum supponere, duobus motibus moneri sidera, iuxta duplicem situum permutationem quam reuerà in dies singulos faciunt, altera quidem circà Mun- dum, quam Primam lationem nominat Aristoteles 2. de Generat text. 56. altera in Zodiaco, quam Secundam la- tionem dicit; atque ad has refert causam perpetuitatis ortus, & interitus rerum. Quinimò, vt benè aduertit Titus, dici potest, tot esse motus in cælo, quot modis astræ per- mutant respectus ergà partes telluris; qui tamen respectus habent relationem ad modum pariendi rerum: Nihilomi- nus ex authoritate Ptolemæi, traditione Antiquorum, ob- seruatione, & ratione Philosophica quatuor tantum motus possunt constitui, qui sint præcipui. Motus solis, qui di- rectorius appellatur: Motus Lunæ qui Progressio: Motus quotidiamus siderum respectiùs ad loca directionum, & progressionum, quem ingressum nominat Ptolemæus; &

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MATHEMATICVM. 301 the sphere of the sun cannot, for example, be moved with so great a velocity as the parts and the higher spheres, and indeed the first movable; hence it is that the sun itself cannot, in one revolution, equal the motion of the first movable, but after it remains backward by nearly one degree. But the first movable, and the higher parts, do not wait for the course of the sun to be completed; rather, after one entire revolution has been completed, they immediately begin a second. And since in that too the sun moves more slowly, in this second revolution of the first movable it remains two degrees behind; in the third, three; and so on for the rest, so that in the time in which the sun makes 365 revolutions around the earth in the space of one year, the first movable is found to have completed 366 revolutions, one more than the sun itself, for which there is still required the space of one year in order that it may equal it. Hence that direct motion, by which the stars meeting in their course are carried to the regulators through so much time as there is difference of the equator between the two; so that the motion of the sun in the equator on each day is the measure of the directions of one year, as we said in its place. Moreover, to return to our subject, those who first observed that the sun and the other stars remain more and more, and always successively, behind the first movable, said that they are moved by their own motions into opposite parts, when indeed this is not truly to be moved into the opposite part, but rather more slowly toward the same part toward which the first movable strives to be carried. Nevertheless, since in the matter it makes little difference whether this motion of the planets is one and slower, or rather two, and one contrary to the other, it is preferable in this to follow the ancient and common usage of speech, by which astronomical matters are more easily explained; and thus it may be safely supposed that the stars are moved by two motions, according to the double change of positions which in truth they make each day, one indeed around the World, which Aristotle in 2 De Generatione, text 56, calls the First Motion; the other in the Zodiac, which he calls the Second Motion; and to these he refers the cause of the perpetuity of generation and corruption of things. Indeed, as Titus well notes, it can be said that there are as many motions in the heavens as there are ways in which the stars change their relations toward the parts of the earth; yet those relations have reference to the manner of the generation of things. Nevertheless, from the authority of Ptolemy, the tradition of the Ancients, observation, and philosophical reason, only four motions can be established as principal. The motion of the sun, which is called the direct motion: the motion of the moon, which is progression: the daily motion of the stars with respect to the places of directions and progressions, which Ptolemy calls the ingress; and

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LEXICON 301 Motus quotidianus respectiuus ad loca Natalis siue inceptionis rerum, quem similiter transitum vocat; de quibus omnibus suo loco. 79. MòTLATVM seù MTLATVM, teste Kirchero Arabice dicitur Triangulum sidus in cælo constans stellis 4. vel vt placet Baiero 5. de natura Mercurij, cuius in horoscopo est afferte sublime ingenium. Hebraicè dicitur Humoschlusch. id est, tri partitus. 80. MOZNAIM, seù MOZNAIM, apud Hebræos idem sonat ac Bilanxe, denotatque Libræ sidus, seù signum in cælo septimum ab Ariete, illique directè oppositum, vnde incipit australis semicirculus signorum. 81. MVNDVS, appellatur Vniuersum hoc constans ex regione elementari & ætherea complectens quidquid in rerum natura existit, suoque loco disponitur: Vnde Cicero lib. 2. de Natura Deorum. Mundus, inquit, est quasi communis Deorum, atque hominum Domus, atque vtrorumque Vrbs. Et author lib. de Mundo ad Alex. Est compages inquit, à cælo, terraque coagmentata, & ex iis naturis, quæ inter ea continentur. Græci Cosmon appellant, ab ornatu; est enim hæc Mundi machina perfecta, & absoluta rerum omnium dispositio, & ornamentum. Hinc etiam à Latinis abortu, & mundo muliebri dictus est, eoquod nil sit eo mundus, & ornatius; vt aduertit Plin. lib. 2. cap. 4. Quandoquidem secundum omnes sui partes tam perfectus est, tam suis omnibus numeris absolutus, vt, neque eo perfectiorem fieri posse; afferat D. Th. prima parte quast. 25. art 6. neque minimum quid addi possit, quod non eius ordinem, & proportionem corrumpat; vt in Cythara corrumptitur melos, si vel vna chorda plus debito intendatur. In eo enim videre est rerum omnium genera suis quæque locis aptè disposita, & ordinata: Cælos ob materiæ nobilitatem, ob luminis claritatem, molis immensitatem super omnia constitutos: Terram vtpote elementum omnium grauius, & vilius in centro sitam: mox aquam, mox aërem, inde ignem. In eo omne genus viuentium: Corporea, Incorrea, Mixta. In eo inanimata; in eo tertij ordinis entia, quæ sensu prædita sint, necne, iure ambigeres. Videmus in eo entia per se stantia, quæ idcircò vocitamus substantias; in eo substantiæ inhærentia accidentia. Habet insuper ad gignendum nunquam deficientem materiam, elementa: in iis ipsis, quæ generantur admirabilem connexionem, varietatem, vt vel ipsa cuiuis Atheo faris sit ad Conditoris sui notitiam ingerendam, cum nullo pacto credendum

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LEXICON 301 Periodic motion relative to the places of the birth or inception of things, which he likewise calls a transit; concerning all of which, in their proper place. 79. MòTLATVM or MTLATVM, according to Kircher, in Arabic is called the constellation Triangulum, standing in the sky with 4 stars, or, as Baier prefers, 5, of the nature of Mercury; in whose horoscope it gives eminent talent. In Hebrew it is called Humoschlusch, that is, “three-parted.” 80. MOZNAIM, or MOZNAIM, among the Hebrews has the same meaning as Bilanxe, and denotes the constellation Libra, or the seventh sign in the sky from Aries, and directly opposite to it, from which begins the southern semicircle of the signs. 81. MVNDVS is called the Universe, consisting of the elemental and ethereal regions, embracing whatever exists in the nature of things, and disposed in its proper place. Hence Cicero, book 2 On the Nature of the Gods: “The world,” he says, “is as it were the common house of gods and men, and the city of both.” And the author of the book On the World to Alexander says: “It is,” he says, “a structure joined together from heaven and earth, and from those natures which are contained between them.” The Greeks call it Cosmos, from ornament; for this machine of the world is the perfect and complete arrangement and ornament of all things. Hence also by the Latins it is called “mundus,” from cleanliness and the feminine toilet, because nothing is more clean and elegant than it, as Pliny notes, book 2, chapter 4. Since according to all its parts it is so perfect, so complete in all its measures, that, as St. Thomas states in the first part, question 25, article 6, neither can anything more perfect be made, nor can even the smallest thing be added that would not corrupt its order and proportion; as in a cithara the melody is ruined if even one string is stretched more than is due. For in it one sees all kinds of things suitably arranged and ordered in their own places: the heavens, because of the nobility of matter, the brightness of light, and the vastness of their bulk, set above all things; the earth, as the heaviest and most base of all the elements, placed in the center; then water, then air, then fire. In it is every kind of living being: corporeal, incorporeal, mixed. In it are the inanimate; in it the beings of the third order, whether endowed with sense or not, you might rightly hesitate. We see in it beings existing in themselves, which for that reason we call substances; in it, accidents inhering in substances. It also has, for generating, matter that never fails, namely the elements; in those very things that are generated, an admirable connection and variety, so that even the wise man himself may be a witness to reveal the knowledge of his Creator to any atheist, since it is in no way to be believed

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MATHEMATICVM. 309 sit, tam concinnam rerum omnium seriem casu è nihilo emersisse, sed esse supremam quandam mentem, quæ cuncta crearit, ordinet, & gubernet. Quare sine optimo Trismegistus: Tora, inquit, Mundi conspiratio, & rerum pulcherrimus ordo contemplandi Dei suggerit materiam: Est enim Orbis velus Liber Diuinitate plenus, & speculum Diuinorum. < 81.> Porrò eius immensitatem quis explicare poterit? cum eius gyrus sola Empyrei cæli extima superficie definiatur, & huius amplitudo tanta sit, vt vix ex comparatione ad Firmamentum, cuius solum notitiam habemus, concipi possit; & primi mobilis crassities, quæ ex proportionne ad alias sphæras, perè in infinitum protensa credenda est, nos prorsus lateat? Blacanus in sua Sphæra existimat totum gyrum Mundani Orbis ex conuexo tantum Firmamenti consideratum continere adminus semidiametros terræ 14000. & consequenter milliar. 301412000. Hinc Primi Mobilis, hinc Cæli Empyrei conuexum lieet conijcere, cum Firmamentum ad Cælum Empyreum comparatum se habeat vt Terra ad ipsum Firmamentum, proindeque vt punctum. < 83.> Mundos plurimos eosque perfectiores, & perfectiores in infinitu à Diuina omnipotentia, quæ infinita est creari posse vt satis constat, ita & vnum tantum de facto conditum esse, certum est ex fide. In eo autem adhuc duplicem mundum considerare est, magnum, quem Græci Macrocosmum appellant, quo nomine veniunt creata omnia, Cælum, terra, Cælestesque, terrenæque naturæ, sicque etiam Angeli, vt obseruat Possidonius. & paruum, hoc est hominem, quem Philosophus 8. Physic. Microcosmum dixit, eo quod sit in omnibus Macrocosmo similis: sicut & iste Deo, qui propterea Mundus Archetypus appellatus est, quod ad eius similitudinem mundus vterque sensibilis est formatus. Qua etiam ratione Mundum hunc magnum sphærica figura præditum aduertit Io: de Sacrobosco, vt Creatoris sui specimen, exhiberet, quem definit Trismegistus, esse Circulum, enius centrum ubique est, circumferentia nusquam. Vnde Boëth. 3. de Consol. metr. 9. sit eum interpellando canit. Tu cuncta superno Ducis ab exemplo, pulchrum pulcherrimus ipse Mundum mente gerens similique in imagine formans. Existimavit Philosophus Mundum fuisse ab æterno eo < 84.> quod nullam viderit rationem, cur in vna potiùs differentia temporis condi debuerit, quam in alia. Debi facè

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MATHEMATICVM. 309 it is, that so well-ordered a sequence of all things should have emerged by chance from nothing, but that there is a supreme mind which created, orders, and governs all things. Wherefore sine optimo Trismegistus: The whole, he says, conspiracy of the world, and the most beautiful order of things suggests matter for contemplating God: for it is an old book full of Divinity, and a mirror of divine things. < 81.> Moreover, who will be able to explain its immensity? since its circuit is bounded only by the outermost surface of the Empyrean heaven, and since its extent is so great that it can scarcely be conceived by comparison with the Firmament, of which alone we have knowledge; and since the thickness of the primum mobile, which in proportion to the other spheres must be believed to extend almost into infinity, is utterly hidden from us? Blacanus in his Sphere thinks that the whole circuit of the Mundane Sphere, considered only from the convexity of the Firmament, contains at least 14,000 semi-diameters of the earth, and consequently 301,412,000 miles. Hence the convexity of the Prim um Mobile, hence also of the Empyrean Heaven, may be inferred, since the Firmament compared with the Empyrean Heaven stands as the Earth does to the Firmament itself, and therefore as a point. < 83.> That many worlds, and more perfect worlds, and more perfect worlds without end, can be created by divine omnipotence, which is infinite, is sufficiently clear; and that in fact only one was made, is certain from faith. But in it we must still consider a twofold world: the great one, which the Greeks call the Macrocosm, by which name are included all created things, heaven, earth, and celestial and earthly natures, and thus also the angels, as Possidonius observes; and the little one, that is, man, whom the philosopher in Phys. 8 called the Microcosm, because he is in all things like the Macrocosm; just as the latter is like God, who for that reason has been called the Archetypal World, because in likeness to Him both visible worlds were formed. For this reason also John of Sacrobosco observed that this great world was endowed with a spherical figure, so that it might display the likeness of its Creator, whom Trismegistus defines as a Circle, whose center is everywhere and circumference nowhere. Hence Boethius in Consol. 3, meter 9, singing to him in prayer says: You lead all things from the highest model, most beautiful yourself, bearing the beautiful world in mind and shaping it in a similar image. The philosopher thought that the world had existed from eternity, because he < 84.> had seen no reason why it should have been made in one rather than another difference of time. Debi facè

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304 LEXICON argumentum: cum ad id satis esse potuerit simplex Conditoris voluntas. Sed nec ab æterno extitisse, aut fieri potuisse, conuine ipsa æternitatis ratio, quæ nulli enti creato connaturalis esse potest, ac successimus motus competens cælis, qui necessariò initium habere debet. Sanè ex iugi terrestris Globi corrosione, aquarumque alluuione putat Blancaus euidenter probari posse Mundum aliquando initium habuisse: alias Oceanus debuisset iam terram operuisse. Sed quidquid sit de hoc; certum est de fide, Mundum fuisse creatum in tempore, ex Gen. 1, In principio creavit Deus calum, & terram. In qua tamen differentia temporis, ignoramus. D. Hieronymus, Ambros. Basil. aliique Patres existimant illum conditum fuisse in verè, sole existente in primo gradu Arietis, atque in Cæli culmine, cuius Naturalitium Thema affert Petrus Aliacensis constituens omnes planetas in suis domiciliis. Hebræi, Chaldæi, Arabes opinantur Mundum in Autumno creatum in ipsa media nocte, ascendente primo gradu Cancri. Ægyptii, cum quibus Nicepso, & Petosyris ipsorum reges sapientissimi tradunt, ipsum in Æstate creatum sole in medio Leonis signo, locato; atque in cuspide secundæ domus, ascendentibus totidem gradibus Cancri, & cum ipsis Luna eius signi Domina, cæterisque Planetis in centris domiciliorum suorum constitutis. Vt cumque sit, certum est diuinare omnes, nec certò ad metam collineare. lib. 3. cap. 1. Neque enim (vt rectè Firmius) aliquis interfuit eo tempore, quo Mundus Diuina mentis, & prouidi Numinis ratione formatus est; nec eousque se intentio potuit humana fragilitatis extendere, vt originem Mundi facili posset ratione concipere. aut explicare. < 5.> Quanrò etiam tempore duraturus sit, pariter ignoramus. Et hoc sapientissimè nos latere voluit Diuina Numinis prouidentia, vt sollicitudo teneret anxios, semperque paratos. Sanè (vt varios hæreticorum errores præteream, quos refert, & confutat optimè Bellarminus de Romano Pont. lib. 3. cap. 3.) ab Apostolorum vsque temporibus instare extremum diem, constans opinatio fuit; Ioannes in Apo cal. tempus probe esse, ait, & in Epist. 1. nouissimam horam esse, & Antichristum iam venisse testatur. Hieronymus Iustinus Martyr, Irenæus, Hilarius, aliique Patres Mundum sex mille annis duraturum dixere: Chrysostomus, Cyrillus, & Hippolytus his addunt quingentos adhuc annos, quorum fundamenta & congruentias affert Sixtus Senensis in Biblioth. sancta lib. 5. to. 2. annot. 190. addens hanc eandem

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304 LEXICON argument: since the simple will of the Creator could have been sufficient for that. But neither could it have existed from eternity, nor could it have come to be, for this is contrary to the very nature of eternity, which cannot be connatural to any created being, as is the successive motion proper to the heavens, which must necessarily have a beginning. Certainly, from the continual erosion of the terrestrial globe and the overflowing of the waters, Blancaus thinks it can be clearly proved that the world once had a beginning: otherwise the Ocean would already have covered the earth. But whatever may be said about this, it is certain from the faith that the world was created in time, from Gen. 1: In the beginning God created the heaven and the earth. Yet in what difference of time this was, we do not know. St. Jerome, Ambrose, Basil, and other Fathers judge that it was created in spring, the sun being in the first degree of Aries and at the summit of the heavens, the natural theme of which Petrus Aliacensis gives, assigning all the planets to their own domiciles. The Hebrews, Chaldeans, and Arabs think the world was created in autumn, at midnight, with the first degree of Cancer rising. The Egyptians, with whom Nicepso and Petosiris, the wisest of their kings, are said to agree, hold that it was created in summer, the sun being placed in the middle of the sign of Leo; and at the cusp of the second house, with so many degrees of Cancer ascending, and with the Moon, mistress of that sign, together with the other planets placed in the centers of their own domiciles. However it may be, all are certain in divination, yet do not certainly aim at the mark. lib. 3. cap. 1. For no one was present at that time when the world was formed by the reason of the divine mind and providence of God; nor could the intention of human frailty extend so far as to conceive or explain the origin of the world with ease. < 5.> And as to how long it will endure, we are likewise ignorant. And divine providence very wisely wished us to be unaware of this, so that concern might keep us anxious and always ready. Certainly, to pass over the various errors of the heretics, which Bellarmine excellently refutes and recounts, de Romano Pont. lib. 3. cap. 3., from the time of the Apostles until now it has been the settled opinion that the last day was imminent; John in the Apocalypse says that the time is at hand, and in his 1st Epistle testifies that it is the last hour, and that Antichrist has already come. Jerome, Justin Martyr, Irenaeus, Hilary, and other Fathers said that the world would last six thousand years: Chrysostom, Cyril, and Hippolytus add to these another five hundred years, the foundations and correspondences of which Sixtus Senensis gives in Biblioth. sancta lib. 5. to. 2. annot. 190, adding this same

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MATHEMATICVM. 305 eandem opinionem de sex mille annis inualuisse etiam apud Gentiles Hydaspes, Trismegistum, & Sybillas: apud Hebræos autem extare antiquissimam traditionem Eliæ cu- iusdam magni nominis Rabini in libris Talmudicis, quæ La- tinè sic se habet. Sex millia annorum erit mundus, & ito- rum destruetur: Duo millia inanitatis, duo millia legis, duo millia dierum Messia, vt taceam quæ in 14. cap. 4. Esdix habentur adesse iam finem mundanæ durationis, & è duodecim partibus, iam ab eius tempore decimam, & dimidium excessisse, nam præterquam liber iste inter Apo- cryphos ab Ecclesia computatur, si id verum esset, opor- tebar iam Mundum desisse ab hinc mille sexcentis annis Alij ex motu octauæ sphæræ, qui non completur, nisi in 36000. annis colligunt mundi ætatem totidem annorum esse, vt nos alibi obseruauimus. Sed enim verò quicquam certi hac in re definire temerarium foret, quippe vt ait Do- minus Marci 16. Non est nostrum nosse tempora vel momen- ta, qua Pater posuit in sua potestate. Expectemus igitur cum timore, sollicitudine, & tremore diem Domini, ne fortè cum minus credimus veniens nos inueniat impa- ratos. Cæterum ex rerum mirabili connexione Mundum esse < 861> animatum, non anima tantum sensitiua, sed & rationali opinati sunt Plato in Philælo, Trismagistus, Pithagoras aliique Philosophi, neque enim aliter saluari posse puta- bant hanc ord natissimam creaturarum seriem, & partium quantumuis etheroganearum perinde atque in humano corpore harmoniam, sine magna quadam anima intrinse- cùs informante, quæ omnia benè ordinet, disponat, ac nectat, quo sensu loquutus est Poëtarum princeps dum ce- cinit. Omnesque infusa per artus Mens l agitat molem, & magno se corpore miscet. & alibi. Luna lucentem globum, Titaniaque astra Spiritus intus alit. In hac etiam sententia fuere olim Philo Iudæus in libro de somniis, & Origenes 1 Periarchon. cap. 7. quoad mundi nobiliorem partem, quales sunt Cæli, & Astra: nec ab ea abhorret D. Aug. lib. 2. in Genes. cap 18. & Caier. explicans illud, Psal. 135. Fecit calos in intellectu, hoc est, inquit, in- tellectuales: quod est verum, vel quantum ad substantiam calorum, si sunt animati: vt multi philosophi rationabi- liter putant, vel quoad motum, quia motus eorum pro- V.

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MATHEMATICVM. 305 The same opinion about six thousand years having prevailed even among the Gentiles, in Hydaspes, Trismegistus, and the Sibyls; among the Hebrews, however, there exists an ancient tradition of a certain Elijah, a Rabbi of great name, in the Talmudic books, which in Latin runs thus: The world shall last six thousand years, and then be destroyed again: two thousand of emptiness, two thousand of the law, two thousand of the days of the Messiah; not to mention what is found in 14. chapter 4. of Esdras concerning the end of the world’s duration, and that out of the twelve parts, by his time the tenth and a half had already passed; for besides the fact that this book is reckoned among the Apocrypha by the Church, if that were true, the world ought already to have ended sixteen hundred years ago. Others, from the motion of the eighth sphere, which is not completed except in 36,000 years, infer that the age of the world is to be reckoned at so many years, as we have observed elsewhere. But indeed it would be rash to define anything certain in this matter, since, as the Lord says in Mark 16, It is not for us to know the times or moments, which the Father has placed in his own power. Let us therefore await the day of the Lord with fear, anxiety, and trembling, lest perhaps, when we believe it least, he come and find us unprepared. Furthermore, from the marvelous connection of things, they thought that the World is animated, not only by a sensitive soul, but also by a rational one: Plato in the Phaedrus, Trismegistus, Pythagoras, and other philosophers, for they believed that otherwise this most orderly series of creatures, and the harmony of its parts however heterogeneous, just as in the human body, could not be preserved without some great soul informing it inwardly, which orders, disposes, and binds all things well; in this sense the prince of poets spoke when he sang: And through all the limbs infused Mind moves the mass, and mingles with the great body. And elsewhere: The spirit within nourishes the shining globe and Titanian stars. In this opinion too were formerly Philo Judaeus in the book On Dreams, and Origen in the first book of Periarchon, chapter 7, as far as the nobler part of the world is concerned, such as the heavens and the stars; nor does St. Augustine in book 2 On Genesis, chapter 18, and Cæterus, explaining that passage, Psalm 135, “He made the heavens in understanding,” differ from it; that is, he says, in intelligences: which is true, either with regard to the substance of the heavens, if they are animated, as many philosophers reasonably think, or with regard to their motion, because their motion pro- V.

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LEXICON cui dubio intellectualis est, hoc est ab intellectu. Hæc Caie- tanus. 87. Verum, etsi id non ineptè, falsò tamen assertum, con- stat modò ex Concilio Constantinopolitano V. vbi anathemate feriuntur quotquot dixerint, Calum, & Solem, & Lunam, & Stellas animatas quasdam esse, & mobiles virtutes. An autem ibi Anima in vniuersum remoueatur à cælis, atque sideribus, an verò solum rationalis, dubium magnum est. Certè D. Thomas, etsi hanc materiam ex in- stituto pertractans in pag. 1. quæst. 70 art. 3. dicat paruam, vel nullam differentiam inueniri in re; sed in voce tantum in hac controuersia, concludatque corpora cælestia non nisi æquiuocè animata dici ab iis inferioribus, quibus conjungitur anima vt forma, illis verò, vt motor tantum, nihilo- minus in 2. contra Gentes cap. 7t. vult ex Arist. necessariò ponendam esse in cælis aliquam animam, quæ illis intrinsecè vniatur vt forma; atque parum spectare ad Catholica veritatem disquirere num cæli animati sint, an non. Ad auctoritatem verò Concilij supra allatam respondet, eam vel non esse authenticam, vel sanè intelligendam esse de Anima rationali, secùs autem de alia specie omninò diuersa. Et quidem aliquam mundi formam substantialem, quæ hanc rerum compagem intrinsecùs nectat, diffuteri non possimus, ni velimus Vniuersum hoc aggregatum per accidens nominare, quo nihil ineptius: ipse ordo, & consensus partium clarè indicat esse aliquid interiùs, quod omnia vniat, & substantialiter compleat: Ipsa Macrocosmi ad Microcosmum analogia id apertè suadet: quandoquidem, vt aduertit Picus in Epsaplo ipse Mundus à Moïse magnus homo appellatur; Nam si homo, inquit, est paruus Mundus; vtique Mundus est magnus homo. Præiereà cælos ab intrinseca forma moueri, absque vlla temeritatis nota doceri posse, asserit Raynaudus in Theologia naturali, disput. 2 quæst. 1. art. 1 id olim plures Philosophi atque insignes Astronomi docuerunt; & ex recentionibus Longomontanus, Keplerus, Bulliardus, Tycho, Nierembergensis, Baranzanus, & alij: ex quibus Tycho, Keplerus, & Baranzanus adhuc illis vitam attribuunt, sed longè ab aliis viuenribus differentem, homine quidem inferiorem, cum in hoc Anima à Deo immediatè veniat, & creetur, reliquis autem absoluè perfectiorem, & in superiori ordine. Si ergò cælis vitam concedunt isti, cur non potiùs eandem nos toti Mundo impertiamur? Si illis animam quamdam specie ab rationali, ac sensitiva diuersam, quam iure dixe-

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LEXICON in which there is no doubt, is intellectual, that is, from the intellect. This is Caietanus. 87. Yet, although that is not ineptly said, it is nevertheless falsely asserted, as is now evident from the Fifth Council of Constantinople, where those are struck with anathema who said that the Heaven, the Sun, the Moon, and the Stars were certain animated things and moving powers. Whether there a Soul is removed altogether from the heavens and the stars, or only the rational soul, is a very great doubt. Certainly St. Thomas, although treating this matter expressly in p. 1, q. 70, art. 3, says that a small or no difference is found in the thing itself, but only in the wording in this controversy, and concludes that heavenly bodies are said to be animated only equivocally by those inferior beings with which the soul is joined as form, but with them only as mover; nevertheless, in 2 Contra Gentiles, ch. 7, he holds that, according to Aristotle, some soul must necessarily be posited in the heavens, which is intrinsically united to them as form; and that it matters little for Catholic truth to inquire whether the heavens are animated or not. As for the authority of the Council cited above, he answers that it is either not authentic, or certainly is to be understood of the rational soul, but otherwise of a wholly different kind. And indeed we cannot deny some substantial form of the world, which inwardly binds together this structure of things, unless we are willing to call this whole aggregate a mere accident, than which nothing could be more absurd: the very order and harmony of the parts clearly indicate that there is something within which unites all things and brings them to substantial completion. The analogy of the Macrocosm to the Microcosm plainly suggests this: for, as Picus notes in the Epsaple, the world itself is called by Moses a great man; for, he says, if man is a little world, then the world is a great man. Moreover, that the heavens may be moved by an intrinsic form, without any mark of rashness, can be taught, says Raynaud in the Natural Theology, disputation 2, question 1, article 1. This was formerly taught by many philosophers and distinguished astronomers; and among the more recent, Longomontanus, Kepler, Bulliardus, Tycho, Nierembergensis, Baranzanus, and others; among whom Tycho, Kepler, and Baranzanus still attribute life to them, but one far different from that of other living beings, indeed inferior to man, since in man the soul comes immediately from God and is created, but in the others absolutely more perfect and of a higher order. If, then, these men grant life to the heavens, why should we not rather bestow the same on the whole World? If we assign to them some kind of soul, different from the rational and the sensitive soul, which with good reason we have called...

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MATHEMATICVM. 107 xis locomotricem, assignant, cur non eadem prorsùs anima totum mundum debeat informare; proindeque habeat cælis conferre motum, brutis animantibus vitam, cæteris partibus connexionem, atque consensum, quando vide- mus, hæc omnia vnam animam rationalem in homine, hoc est in mundo paruo præstare? Et mirum est quam acriter Recensiores fere omnes in hanc Mundi formam conspitent: & quando nouis formis effectis, nouorumque entium varietate Mundum istum exornant, hunc ipsum propria forma exutum planè audeant deformare. Enimuerò quæ maior deformitas, quam in tam grandi corpore incomplexio? quid absurdius, quam Vniuersum hoc aggregatum per accidens dicere? Etenim si ex consensu, & connexion, quam habent inter se partes vnius corporis, arguimus illud corpus naturale esse sua forma substantiali præditum; quæ verò si- bi accidentaliter tantum adhærent, hanc consensus societatem minimè admittere; si ex vnitate per se, perfectionem alicuius entis colligimus, qua ratione debeamus affirmare mundum, cætetoqui adeò perfectum vt dicatur in se genere perfectionem fieri non potuisse, hæc præcipua & maxima perfectione eatere, vt non sit quid per se existens, sed aggregatum per accidens, cuius partes sine forma substantiali intrinsecus inhærente, temanerent naruraliter incompactæ perindè ac parres domus, cui non habet artifex tribuere vnitatem, nisi tantum incomplexam, atque accidentalem; & alias maiorem consensum, & sympathiam videmus inter cælum, & terram, quam inter partes vnius corporis naturalis? Si autem stante tali consensu & sympathia inter partes istius vasti corporis dicimus eas non habere vnam formam communem, non est tarjo cur non dicamus lapides, plantas, cætera omnia esse vnam quid aggregatum per accidens. Quis autem hæc cogitans sibi persuadeat Auctorem Naturæ, qui perfectissimè omnia operatur, quique singulis rebus peculiarem indidit formam, Naturam ipsam, hoc est rerum omnium congeriem, & suum opus maximum effecisse eum accidentali tantum vnione inter partes, easque reliquisse substantialiter inconnexas? Ex his igitur, aliisque permultis, quæ abundè congerit Resta, lib. 2. tract 2. cap. 5 de Meseoris, concludendum est, aliquam mundi formam necessariò admittendam esse: An autem ea adhuc vitalis sit, id ipse affirmare non audet; sed tamen ex iis, quæ huc vsque diximus, tum etiam ex mox infra dicendis manifestè conuincitur. Equidem Vita, ex communi omnium Philosophorum, V ij

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MATHEMATICVM. 107 ...they assign a locomotive soul; why then should not the same soul altogether inform the whole world, and therefore have the power to impart motion to the heavens, life to brute animals, and to the other parts connection and harmony, since we see all these things performed by one rational soul in man, that is, in the little world? And it is astonishing how sharply almost all the moderns spit against this form of the World; and when, by the production of new forms and the variety of new beings, they adorn this world, they dare quite openly to deform this same world, stripped of its proper form. For indeed what greater deformity than lack of composition in so great a body? What is more absurd than to say that this Universe is a mere accidental aggregate? For if from the agreement and connection which the parts of one body have among themselves we argue that that body is natural and endowed with its substantial form; and if what adheres to itself only accidentally does not at all admit this society of harmony; if from unity in itself we infer the perfection of some being, by what reasoning ought we to affirm that the world, which otherwise is so perfect that it is said in its kind to have been unable to be made more perfect, should lack this chief and greatest perfection, namely, that it is not something existing per se, but an accidental aggregate, whose parts, without an inwardly inhering substantial form, would remain naturally unconnected, just as the parts of a house, to which the builder cannot impart unity except only an incomplex and accidental one; and do we not see a greater agreement and sympathy between heaven and earth than between the parts of one natural body? But if, while such agreement and sympathy exists between the parts of this vast body, we say that they do not have one common form, there is surely no reason why we should not say that stones, plants, and everything else are one certain accidental aggregate. But who, thinking these things over, would persuade himself that the Author of Nature, who works all things most perfectly and who has given to each thing its peculiar form, should have made Nature itself, that is, the assemblage of all things and his greatest work, by a merely accidental union among the parts and have left them substantially unconnected? From these things therefore, and from many others which Resta abundantly collects, book 2, treatise 2, chapter 5, de Meseoris, it must be concluded that some form of the world must necessarily be admitted: but whether it is still a vital one, he himself does not dare to affirm; yet from what we have said thus far, and also from what will be said immediately below, it is manifestly proved. Indeed, life, according to the common view of all philosophers, V ij

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308 LEXICON 89. Theologorumque acceptione definitur esse Principium intrinsecum sui motus. Ea enim ex Aristotele dicuntur viuere, quæ constituta in sua naturali dispositione sese ab intrinseco principio mouent: & in 2. de Anima distinguit viuere in quatuor genera: scilicet alimento vti, sentire, moueri secundum locum, & intelligere, Quod assumens D. Thomas, 1 part quæst. 18 art. 2 in responso ad primum ait, ideo Philosophum id egisse, quia in istis inferioribus quatuor sunt genera viuentium, quædam, quæ habent naturam solum ad vtendum alimento, & ad consequentia, quæ sunt augmentum, & generatio: hæc ad conseruationem speciei illud ad indiuidui: quædam ad sentiendum vt patet in animalibus immobilibus secundum locum, sicut sunt ostrea, & conchilia: quædam verò cum his vlteriùs ad se mouendum secundum locum vti sunt animalia perfecta, quadrupedia, volatilia, &c. quædam verò vlterius ad intelligendum, sicut homines. Lia tamen, vt solus motus ab intrinseco sit ratio vitæ, & ex solo motu intrinseco, siue imperfectè sumatur, provt dicit operationem intrinsecam, qualia sunt intelligere, & sentire, siue perfectè pro motu locali ab intrinseca virtute proueniente, vita manifestetur: quemadmodum idem D. Thomas explicat quæst. 1. art. 1 in corpore. Porrò ex singulis speciebus motus scorsim diuersæ viuentium species constituuntur, & ex singulis vita argui potest. Non quod plures rationes vitæ in vno eodemque subiecto reperiri non possint, vt patet in animalibus perfectis, & in homine, sed quod singulæ ad rationem vitæ sufficiant: Sic sola inrellectio in Angelis constituit rationem vitæ intellectualis, sola sensatio in conchiliis rationem vitæ sensitivæ; sola vegetatio in plantis vitæ vegetatiuæ, & sola demum in cælis, (si ab intrinseco mouentur) vitæ loco motivæ. Quemadmodum etiam in anima ibus perfectis datur triplex ratio vitæ, vegetabilis, sensitivæ, & loco motiuvæ, & in homine adhuc etiam intellectiua, quæ omnes ab vna anima rationali tanquam à principio intrinseco actuante corpus ad vitam, originem trahunt. Quod autem ex singulis speciebus motus arguatur ratio vitæ, manifestè ostendit S. Doctor loco citato art. 1. in corpore. Ait enim. Ex his, quæ manifestè viuunt, accipere possumus quorum sit viuere. Viuere autem manifestè animalibus conuenit: dicitur enim in lib. de vegetabilibus quod vita in animalibus manifesta est. Vnde secundum illud oportet distinguere viuentia à non viuentibus (aduertas Lector) secundum quod animalia dicuntur viuere. Hoc autem est in quo

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308 LEXICON 89. In the acceptation of the theologians, it is defined to be the intrinsic principle of its own motion. For those things are said by Aristotle to live which, being established in their natural disposition, are moved from an intrinsic principle: and in book 2 of De Anima he distinguishes living things into four classes: namely, to use nourishment, to sense, to be moved according to place, and to understand. Taking this up, D. Thomas, in 1 part, question 18, art. 2, in the response to the first, says that the Philosopher did this because in these lower things there are four kinds of living beings: some, which have a nature only for using nourishment, and for the consequences, which are increase and generation: the former for the preservation of the species, the latter for that of the individual; some for sensing, as is clear in animals immobile in respect of place, such as oysters and shellfish; some, moreover, with these, further, for moving themselves according to place, such as perfect animals, quadrupeds, birds, etc.; and some, finally, for understanding, such as men. Life, however, is said to be the motion alone from within, and life is manifested from intrinsic motion alone, whether taken imperfectly, inasmuch as it denotes an intrinsic operation, such as understanding and sensing, or perfectly, as local motion proceeding from an intrinsic power is understood: as the same D. Thomas explains in question 1, art. 1 in the body of the article. Moreover, from individual species of motion, separately, diverse species of living beings are constituted, and from each one life can be inferred. Not that several notions of life cannot be found in one and the same subject, as is evident in perfect animals and in man, but because each one is sufficient for the notion of life: thus, understanding alone in Angels constitutes the notion of intellectual life, sensation alone in shellfish the notion of sensitive life; vegetation alone in plants the life of the vegetative kind, and finally in the heavens alone, (if they are moved from within) the life of local motion. Likewise also in perfect animals there is given a threefold notion of life, vegetative, sensitive, and local motion, and in man also intellectual, which all derive their origin from one rational soul as from an intrinsic principle actuating the body for life. But that from individual species of motion the notion of life is inferred, the holy Doctor clearly shows in the place cited, art. 1 in the body. For he says: From those things which manifestly live, we can learn whose it is to live. But to live manifestly belongs to animals: for it is said in the book De Vegetabilibus that life in animals is manifest. Hence according to that it is necessary to distinguish living things from non-living things (notice, Reader) according to the way in which animals are said to live. But this is in which

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MATHEMATICVM. 309 primò manifestatur vita, & in quo ultimò remanet. Primò autem dicimus animal viuere, quando incipit ex se motum habere, & tamdiu iudicatur animal viuere, quandùs talis motus in eo apparet: quando verò iam ex se non habet aliquem motum, sed mouetur tantum ab alio, tunc dicitur animal mortuum per defectum vita: Ex quo patet illa propriè sunt viuentia, quæ seipsa secundum aliquam speciem mouent, siue accipiatur motus propriè, sicut motus dicitur actus imperfecti id est existentis in potentia. siue motus accipiatur communiter provt dicitur actus perfecti, provt intelligere, & sentire, (in iis profectò quæ motum localem non habent) dicitur moueri. Huc vsque D. Thomas. Ex quibus manifestè liquet, solum motum intrinsecum esse de ratione vitæ, quia sine intellectione, sine sensatione, sine vegetatione, sine motu locali, non autem sine vllor prorsus motu, siue provt est actus perfecti, siue provt imperfecti potest, dari aliquod viuens. His igitur constitutis manifestè euincitur vita Mundi: < 90.> habet enim duplicem rationem motus, & provt est actus perfecti scilicet ab intrinseco operari, & provt est actus imperfecti hoc est motus localis, atque ad hunc ab intrinseco se moueri. Agunt enim coelestia corpora in ista inferiora ea producendo, corrumpendo alterando viuificando, agunt singulæ partes adinuicem in ordine ad conseruationem totius. Item mouentur cæli motu ipsis maximè proprio, & connaturali, & non est ratio cur ad intelligentias recurramus, cum motus extrinsecus & violentus non sit mobilium perfectius: exlorum autem motus est eorum maxima perfectio, seù potiùs totius Mundi, ex quo retum ordo seruatur & Mundus ipse consistit: & si demum minimum motus iste cessaret, Mundus ipse mox confestim desideret, vt Philosophi omnes conueniunt, & probat Abulensis in cap. 10. Iosue. vel ex eo ostendens magnitudinem Imperij Iosue, quo simul, & solem stetisse fecit, & Naturæ ordinem præteruertit, occurrents miraculo, ne orbis provt res postulauerat, deperiret, Mouentur elementa contrà propriam naturam, nulla exteriori vi adhibita, ad repleendum vacuum, atque ad conseruandam rerum connexionem, quæ perinde atque in animantibus vitam sustentat, cum alioqui discontinuatio partium vitæ discrimen inducat, & mortem: quod nisi in ipsis seorsim vitam non arguat, vt benè infert D. Th. loco cis. atquit tamen in toto quatenus habet intrinsecam virtutem suas partes mouendi, quæ si non essent connexæ, si non in vnam vitam mundi, conseruandam conf- V ijj

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MATHEMATICVM. 309 first life is manifested, and in which it finally remains. First, however, we say that an animal lives when it begins to have motion from itself, and so long is an animal judged to live as such motion appears in it; but when it no longer has any motion from itself, but is moved only by another, then the animal is said to be dead through the loss of life. From which it is clear that those things are properly living which move themselves according to some species, whether motion be taken properly, as motion is said to be the act of the imperfect, that is, of that which exists in potency, or whether motion be taken more generally, insofar as it is called the act of the perfect, insofar as to understand and to sense (in those things, certainly, which do not have local motion) is said to be moved. Thus far St. Thomas. From these things it is manifestly clear that intrinsic motion alone belongs to the nature of life, because without intellection, without sensation, without vegetation, without local motion, but not without motion of any kind whatever, whether as the act of the perfect or as of the imperfect, some living thing can exist. These things therefore being established, the life of the World is clearly proved: for it has a twofold notion of motion, both insofar as it is the act of the perfect, namely to operate from within, and insofar as it is the act of the imperfect, that is, local motion, and through this to move itself from within. For the heavenly bodies act upon these lower things by producing, corrupting, altering, and giving life; the individual parts also act upon one another in order to preserve the whole. Likewise the heavens are moved with a motion most proper and connatural to them, and there is no reason why we should have recourse to intelligences, since an external and violent motion is not more perfect than the things moved; but the motion of the heavens is their greatest perfection, or rather that of the whole World, from which the order of things is preserved and the World itself consists: and if at length this motion should cease even a little, the World itself would straightway fail, as all philosophers agree, and Abulensis proves in chapter 10 of Joshua, or by that same passage showing the greatness of Joshua’s dominion, by which at one and the same time he made the sun stand still and overturned the order of nature, with the miracle intervening, lest the globe, as the case required, should perish. The elements are moved contrary to their proper nature, no external force being applied, in order to fill the vacuum and to preserve the connection of things, which in the same way as in living beings sustains life; since otherwise the discontinuity of the parts brings about danger to life and death: which, although it does not argue life in the parts taken separately, as St. Thomas rightly infers in the place cited, nevertheless it does in the whole, insofar as it has an intrinsic power of moving its own parts; and if these were not connected, if they were not united in one life of the world, to be preserved… V iij

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LEXICON piraret, frustrà contenderent contra insitam cuique naturam, perinde & reliqua membra in homine ad conseruationem torius. Atqui, vt auctor est idem D. Thomas 2. 2. qu. 1. 9. art. 1. Illa decuntur viuentia, qua ex seipsis mouentur, seu operantur, illud autem maximè conuenit alicui per seipsum, quod est proprium ei, & ad quod maximè inclinatur. Prætereà motus cæli, vt idem S. Doctor ait, 1. part. quast. 18. art. 1. est in vniuerso corporalium naturarum; sicut motus cordis in animali, quo conseruatur vita. Et in opusc. 35. de motu cordis in Animali sic ait: Forma autem nobilissima in Inferioribus est anima quia maximè accedit ad similitudinem motus cæli: vnde & motus ipsam consequens similimus est motui cæli: sic enim est motus cordis in animali sicut motus cæli in mundo. Ergò sicut in animali vita præcipuè est in corde, ità in vniuerso vita præcipuè est in corporibus cælestibus: sicut à corde vita est originatiuè in animali, & ad reliqua mebra diffunditur, ita ex accessu, & recessu corporu[m] cælestiu[m] imponitur rebus initiu[m], & finis essendi: & sicut cessate motu cordis in animali hoc illico deperiret, ita cessante motu cæli, vniuersum naturaliter, & ipsum desiceret. Et hic tandem est Alexandri gladius tot gordianos nodos in vniuersa Philosophia rescindens: hoc Ariadnæ filum nos manuducens ad tot difficultarum inextricabiles aditus superandos: hæc inquam Mundi vitæ; quâ semel admissâ statim vniuersa Naturæ arcana intelliguntur, qua demptâ in mille errorum lapsus inpingimus. Qui enimverò intelligi poterit sol vitalis potentiæ author, & viuentium omnium fons, & origo, quamdiu in ipso, seù in vniuerso vitam negabimus? Quomodo ex accessu, & recessu siderum in Zodiaco generatio, & corruptio rerum in inferioribus hisce causetur? Vnde insectis, aliisque impefectis animantibus, quæque non per generationem ab alio eiusdem speciei viuenre, sed ex putti prosiliunt, vita communicatur, si non è cælis, sideribusque hauritur? Profecto, aut ad causam primam recurrendum, quod turpe est Philosopho, quando ad causas secundas potest confugere, easque quæ in omnium opinione ad rerum productiones} concurrunt, aut ad species separatas Platonis, aut ad vitam mundi superiorem; ni velimus aliud absurdum maius admittere, posse, inquam, cælos vitam, quam in se non haberent, alteri communicare; proindeque effectum se nobiliorem producere. Quonam igitur pacto sol omnium vita esset omnia suo accessu viuificaret, quando ipse vita careret? At enim inquies, ex hoc iam Mundus magnum quoddam

Transcription: Translated (English)

LEXICON they were contending, in vain, against the nature implanted in each thing, just as the other members in man are for the preservation of the whole. But, as the same Doctor Thomas says, 2. 2. qu. 1. 9. art. 1. Those are called living things which are moved, or act, from themselves; and that especially belongs to a thing by itself which is proper to it, and to which it is most inclined. Moreover the motion of the heavens, as the same holy Doctor says, 1. part. quast. 18. art. 1. is in the universe of bodily natures like the motion of the heart in an animal, by which life is preserved. And in opusc. 35. de motu cordis in Animali he says thus: But the most noble form in inferior things is the soul, because it most closely approaches the likeness of the motion of the heavens; hence also the motion following it is most like the motion of the heavens: for thus the motion of the heart in an animal is as the motion of the heavens in the world. Therefore, just as in an animal life is chiefly in the heart, so in the universe life is chiefly in the heavenly bodies: just as from the heart life is originally in the animal, and is diffused to the other members, so from the approaching and withdrawing of the heavenly bodies there is imposed on things the beginning, and the end of being: and just as, if the motion of the heart in an animal should cease, this would immediately perish, so if the motion of the heavens should cease, the universe naturally would fail, and it itself would perish. And here at last is Alexander’s sword, cutting through the countless Gordian knots in all philosophy: this is the thread of Ariadne guiding us to overcome the many inextricable entrances of difficulties: this, I say, is the life of the world; once it is admitted, at once all the secrets of Nature are understood, but if it is removed we are driven into a thousand errors. For how indeed can it be understood that the sun is the author of vital power, and the source and origin of all living things, as long as we deny life in it, or in the universe? How is generation and corruption in these lower things caused from the approach and withdrawal of the stars in the Zodiac? Whence is life communicated to insects and other imperfect animals, which are not by generation from another living being of the same species, but spring from putrefaction, if not drawn from the heavens and the stars? Surely, either we must recur to the first cause, which is shameful for a philosopher when he can take refuge in secondary causes, especially those which, in everyone’s opinion, concur in the production of things; or to Plato’s separate species, or to a higher world-soul; unless we wish to admit yet another and greater absurdity, namely, that the heavens can communicate life to another, when they would not have it in themselves; and consequently produce an effect nobler than themselves. By what manner, then, would the sun be the life of all things and vivify all things by its approach, when it itself would lack life? But, you will say, from this already the World is some great

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MATHEMATICVM. < 93.> animal foret: Sol, Luna, sideraque omnia Animantia fo- rent sensu, & vegetatione prædita, quando ipsa ad animalium vegetabilium, ac sensitiuorum productionem, tanquam causæ immediatæ, ac principales concurrerent, quod nemo vnguam dixerit, & manifestè reiicitur à Concilio Constantinopolitano supra relato: & insuper nullum gradum sensationis, aut vegetationis in ipsis videmus. < 94.> Fateor, hoc maximum, ac difficillimum in tota hac controversia argumentum. At non tanti apud me est, vt præponderet aliis; cæteroqui euidentibus demonstrationibus modò allatis, euincentibus Mundi vitam. Scio equidem Thomam Campanellam lib. de sensu, & Magia rerum, totum in eo esse, vt contendat, Mundum esse viuam Dei statuam, omnesque illius partes sensu, alias clariore, alias obtusiore præditas: Et in Epilogo Operis in fine, post quam elementa, lapides, plantas, suo modo sentire dixit, in hæc verba coucludit. Mundus ergò totus est sensus, vita, anima, corpus, statua, et altissimi ad ipsius condita gloriam. Verum, etsi ego Mundum viuere vita propriè dicta, quæ sit omni vita, (excepta intellectuali, quæ est per intellectum, ac voluntatem, qua viuit etiam homo per animam rationalem à Deo immediat infusam) superior, detque omnibus viuentibus, etiam homini quoad vitam animalem, qua nutritur, & sentit, viuere, & moueri, constanti animo affirmem; tamen non per hoc, ipsum vastum aliquod animal dicere audeo, nec si adhuc ausim, concessero. Etenim, Animal, propriè denotat viuens sensu, & cognitione præditum: iuxta quam acceptionem Arist. lib. de Vita, & Mortem, ait, Plantam viuere quidem, sed non esse Animal. Plante enim, inquit, viuunt quidem, non habent autem sensum: per sentire autem, animal à non animali determinamus. Sic igitur, viuit cælum, viuunt sidera, viuit vniuersus Orbis, sed animantia non sunt, quia sensu, & ratione carent. Nec, quia hos gradus viuendi non habent, dicenda sunt cæteris viuentibus imperfectiora: Quandoquidem vegetatio, & sensatio sunt imperfectiones quædam viuentium, sine quibus melius quidem in suo genere vita fruerentur: at enim vegetatio in inferioribus hisce necessaria est ad speciei, atque indiuidui conservationem; sensus autem in animalibus ad sibi conducensia prosequenda, & incommoda fugienda. Vnde ex hoc tantum rationem animalitatis excludere videtur D. Thomas à cælis, atque ab vniuerso Mundo, ait enim loco cit. art. 3. ad 3. Vita in istis inferioribus recipitur in natura corruptibili, qua indiget & generatione V iiiij

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MATHEMATICVM. <93.> If it were an animal: the Sun, Moon, and all the stars would be living beings, endowed with sense and vegetation, since they themselves would concur in the production of animal, vegetative, and sentient things as immediate and principal causes; which no one has ever said, and it is manifestly rejected by the Constantinopolitan Council cited above. And besides, we see in them no degree of sensation or vegetation. <94.> I confess that this is the greatest and most difficult argument in this whole controversy. But in my judgment it is not so great as to outweigh the others; for otherwise the evident demonstrations now set forth would prevail, proving the life of the world. I certainly know that Thomas Campanella, in his book De sensu et Magia rerum , is wholly intent on maintaining that the world is the living statue of God, and that all its parts are endowed with sense, some clearer, others more obscure; and in the Epilogue of the work at the end, after saying that the elements, stones, and plants feel in their own way, he concludes with these words: Therefore the whole world is sense, life, soul, body, statue, and is made for the glory of the Most High. Yet although I firmly affirm that the world lives with a life properly so called, which is above every life, except intellectual life, which is through intellect and will, by which man also lives through the rational soul immediately infused by God, and that it gives life to all living things, even to man as to animal life, by which he is nourished and feels, and that it moves; nevertheless I do not venture, nor should I even if I dared, to call it some vast animal. For animal properly denotes a living being endowed with sense and cognition; according to which meaning Aristotle, in De Vita et Morte , says that a plant does indeed live, but is not an animal. For, he says, plants do live, but they do not have sense; and by sense we distinguish an animal from a non-animal. Thus, the heaven lives, the stars live, the whole universe lives, but they are not living creatures, because they lack sense and reason. Nor, because they do not have these degrees of living, should they be called more imperfect than other living things. Indeed, vegetation and sensation are certain imperfections of living things, without which life would indeed be better in its own kind; but vegetation is necessary in these lower things for the preservation of the species and the individual; and sensation in animals for pursuing what is useful to them and avoiding what is harmful. Hence Saint Thomas seems by this alone to exclude from the heavens, and from the whole world, the notion of animality, for he says in the cited place, art. 3 ad 3: Life in these lower things is received in a corruptible nature, which needs both generation and ... V iiiij

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ad conseruationem species, & alimento ad conseruationem indiuidui: & propter hoc in istis inferioribus non inuenetur vita sine anima vegetabili, sed hoc non habet locum in in- corruptibilibus: & art. 1. in responsione ad primum argu- mentum, quo inferebatur omnium rerum naturalium pro- prium esse viuere; vltrò facetur, quod si totum vniuersum corporale esset unum animal, ita quod isto motus esset amo- uente intrinseco, vt quidam posuerunt, sequeretur, quod motus esset vita omnium naturalium corporum. Similiter ratio sensus impertinens est ad vitam, & potius passio imperfectio, quam perfectio. Ait enim Philosophus, in lib. de Semno, & Vigilia, quod iis conuenit sensus, in qui- bus est tristari, & gaudere, contupiscere, & odisse: plantis autem nihil horum inesse, vnde conuenienter iis à Natura inditus non est sensus: supra quod D. Thomas in commen- to. Complexio, inquit, plantarum in nutrimento, & aug- mento, & his similia melius fiunt sine sensu, quam cum sensu: ergo planta non habent sensum, cum naturæ semper faciat quod melius est. Cum igitur isti gradus vitæ potius sint imperfectiones, & defectus naturæ, quam perfectio- nes, & Sol, Astra, & mundus non indigeant generatione, & nutritione ad conseruationem speciei vel indiuidui, & adhuc non habeant aliquod ad sui esse conducens, vel ad sui esse contrarium, quod amore prosequi debeant, aut odio; iure illis à Natura neque sensu, neque vegetatione prouisum, sed solum vitâ quadam superiore, quæ omnem vitam inferiorum eminenter contineat, & colligitur ex motu perfectissimo, qui est circularis, & ab intrinseco, po- tens naturaliter in æuum protrahi, & motum cæteris viuen- tibus participare. Alloquin si gradus huiusmodi vitæ, vege- tatio inquam & sensatio absoluè, & simpliciter dicerent rationem vitæ perfectiorem, quæ non in aliquo eminenter conrineretur, posset etiam dici, quod vita hominis est per- fectior vita Angeli, quia viuit, nedum intellectualiter, vt ille, sed adhuc vita sensitiva; & vegetabili. Sicut igitur vita Angeli est perfectior vita hominis, etiamsi non sit ve- getabilis, & sensibilis, ita etiam vita Muudi est perfectior omnibus viuentibus inferioribus, atque adeo plantis, & animalibus, etiamsi sensum, & vegetationem non habear. Qui quidem gradus vitæ in talibus viuentibus dicunt per- fectionem, at non in superioribus, quæ tali modo viuendi non indigent. Igitur pro coronide huius nobilissimæ Controuersiæ, concludendum est, vniuersum hoc vnum quid esse, per se

Transcription: Translated (English)

for the preservation of the species, and nourishment for the preservation of the individual; and for this reason among these lower things life is not found without the vegetative soul, but this does not apply to incorruptible beings; and in article 1, in the response to the first argument, by which it was inferred that it belongs to all natural things to live, it is further stated that if the whole corporeal universe were one animal, so that its motion were by an intrinsic mover, as some have maintained, it would follow that motion would be the life of all natural bodies. Likewise, sense is irrelevant to life, and is rather a passion and an imperfection than a perfection. For the Philosopher says, in the book De Somno et Vigilia , that sense belongs to those in whom there is sorrow and joy, desire and hatred; but plants have none of these, so that it is not fitting that sense was naturally given to them. On this point St. Thomas in the commentary says: The constitution of plants in nourishment and growth, and similar things, is better effected without sense than with sense; therefore plants do not have sense, since nature always does what is better. Since, then, these degrees of life are rather imperfections and defects of nature than perfections, and the Sun, the stars, and the world do not need generation and nutrition for the preservation of the species or the individual, and still have nothing conducive to their being, or contrary to their being, which they should pursue by love or avoid by hatred, it was rightly provided for them by Nature neither with sense nor with vegetation, but only with a certain higher life, which eminently contains every lower life, and is gathered from the most perfect motion, which is circular and from within, naturally capable of being extended through eternity, and of participating in motion with other living things. Otherwise, if such degrees of life, namely vegetation and sensation, were said absolutely and simply to be a more perfect notion of life, not eminently contained in something else, it could also be said that the life of man is more perfect than the life of an Angel, because he lives not only intellectually, as the Angel does, but also with a sensitive and vegetative life. Just as, therefore, the life of an Angel is more perfect than the life of man, although it is not vegetative or sensitive, so also the life of the World is more perfect than all inferior living things, and therefore than plants and animals, even if it does not possess sense or vegetation. Indeed, these degrees of life in such living things signify perfection, but not in higher beings, which do not need to live in such a way. Therefore, as the crowning conclusion of this most noble controversy, it must be concluded that this universe is one thing, in itself

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MATHEMATICVM. 313 subsistens, sua vniuersali forma præditum, eâque substantiali, & perfectissimâ, quæ det quidem toti, cunctisque eius partibus, atque animantibus vitam, non tamen ipsum mundum, aut præcipuas eius partes, nempe cælum, sidera, elementa, animantes denominet: & quia sensu, & vegetatione carent, proindeque, vt ait Conc. Constantinop. omninò animantes non sunt, Non tamen ex hoc sequitur vitam Mundi præcipuarumque eius partium non esse cæteris viuentibus, etiam ipso homine secundum gradus vegetationis, nutricationis, & sensationis, superiorem, atque vniuersaliorem; non autem secundum gradum intellectiui, in quo homo spiritualis est; ac minimè à cælorum influxibus pendet. Viuit ergo Mundus, cælum, sidera, gradu quodam vitæ superiore, cui profecto parem, aut similem in inferioribus hisce non sit inuenire: sed omnis ipsorum vitæ ratio, & gradus eminenter in vita mundi est, & ab ipsa tanquam vniuersali, & æquiuoca causa deriuat; vnde est etiam virtus ad causandam hanc retum varietatem. Et hoc, vt benè habet D. Th. 1. part. 9. 105. art. 3 inquantum hac (scilicet cælestia corpora) vniuersali virtute co[n]tinet in se quidquid in inferioribus generatur & quia (vt paulo antedixerat, quidquid in istis inferioribus generat, & mouet ad speciem, est instrumentu[m] cælestis corporis. Igitur cælestia corpora sunt causæ superiores, ac principales vitæ, omnisque motionis inferiorum ad certas species: & quà talia in se ipsis eodem, sed longè nobiliore gradu vitæ prædita sint, necesse est. <96.> MvNIR, seù, vt alij legunt, Mumir, Arabicè dicitur quasi pupilla lucida Coronæ Gnostiæ, stella fixa secundæ magnitudinis de natura veneris, & Mercurij, quà ob sui pulchritudine[m] verisque apperitionem quam ortu suo facit cæli pupillam, sertum aperitionem que dixerunt. Vide fusiùs in V. Corona. <97.> MVSATOR, dicitur à Cicerone sagitta fidus apud Aquilam constans stellis quinque de quibus vide in V. Sagitta. <98:> MVSCA, seù, Apis fidus in cælo ad polum Antarcticum nobis inuisum, & nuper à nouis Astronomis ad Australes plagas appulsis cum aliis vndecim obseruatum, continens quatuor stellas infimæ noxæ: Est nunc in longitudine sub signo Scorpij incidens in ipsum Antarcticum circulum: Apud Indos Muis. <99.> MVSIDA Eqvi, Arabicè Alpheraiz, vulguò dicitur stella fixa tertia magnitudinis in dictu Pegasi existens, de natura mixta Martis, Iouis, & Veneris de qua vide iam dicta in V. Alpheraiz. <100> MVSCA, vna est ex quatuor præcipuis Mathesis diuisio-

Transcription: Translated (English)

MATHEMATICVM. 313 subsisting, endowed with its universal form, and with that substantial and most perfect one, which indeed gives life to the whole and to all its parts, and to living things, yet does not denominate the world itself, or its principal parts, namely heaven, the stars, the elements, and living creatures: and because they lack sense and vegetation, and therefore, as the Council of Constantinople says, they are by no means living things. Nevertheless, from this it does not follow that the life of the World and of its principal parts is not superior and more universal than that of other living things, even man himself, according to the degrees of vegetation, nutrition, and sensation, though not according to the intellectual degree, in which man is spiritual; and he depends very little on the influxes of the heavens. Therefore the World, heaven, and the stars live by a certain higher degree of life, to which surely no equal or similar thing among these lower beings can be found: but the whole account of their life, and degree, eminently exists in the life of the world, and derives from it as from a universal and equivocal cause; whence also comes the power for causing this variety of things. And this is, as well says St. Thomas, 1st part, q. 105, art. 3, inasmuch as this (namely the heavenly bodies) by a universal virtue contains in itself whatever is generated in the lower things; and because (as he had said a little before) whatever in these lower things generates and moves to species, is an instrument of the heavenly body. Therefore the heavenly bodies are higher and principal causes of life and of all motion of the lower things to certain species: and as such, it is necessary that in themselves they too are endowed with the same life, but on a far nobler degree. <96.> MVNIR, or, as others read, Mumir, is called in Arabic, as it were, the bright pupil of the Gnostic Crown, a fixed star of the second magnitude, of the nature of Venus and Mercury; because of its beauty and the opening of true appearances which it makes by its rising, they called it the pupil of the sky, and the opening of the garland. See more fully in V. Corona. <97.> MVSATOR, is called by Cicero the faithful arrow under the Eagle, standing firm among five stars; see about these in V. Sagitta. <98:> MVSCA, or the Bee, a faithful one in the sky near the Antarctic pole, invisible to us, and recently observed by the new astronomers who arrived in the southern regions together with eleven others, containing four stars of the lowest brilliance: it is now in longitude under the sign of Scorpio, falling into the Antarctic circle itself. Among the Indians, Muis. <99.> MVSIDA Eqvi, in Arabic Alpheraiz, commonly called a fixed star of the third magnitude existing in the said Pegasus, of a mixed nature of Mars, Jupiter, and Venus, concerning which see what has already been said in V. Alpheraiz. <100> MVSCA is one of the four principal divisions of Mathematics-

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314 LEXICON nibus Arithmeticæ subalterna, facultas nempe, vt inquit Boëthius, quæ multitudine ad aliud relata rationes nume- rales concretas habet ad sonos & voces. Dicta est à Græ- co verbo Mos, quod æquam rationem, atque harmoniam sonat; vel potiùs à Musis, quibus olim familiaris erat. Ha- bet pro obiecto numerum seu quantitatem discretam provt ad alteram relatam: confert enim temporis momenta ad sonorum modules, & inde eos artificiosè nectit, & copu- lat, vt dulcissima harmonia, atque ordinatissimum melos auribus nostris insonet. Eius nobilitatem vel inde licet colligere, quod in diuinis laudibus decantandis, Numine- que propitlando, ab ipso religionis exordio ad hæc vsque tempora religio è sit semper adhibita: vnde sibi 38. dicitur: Vbi eras quado ponebam fundamenta terra: cum me lau- darent simul astramatina, et subilarent omnes Filij Dei? Adeovt de ipso Dite referant Fabulæ Poëtarum, quod sit Orphei cantibus emollitus: Nec mirum, cum eius ordo vt cælestis Hierarchiæ symbolum est, ita & inferis illatus vbi nullus ordo est, sed confusio, eorum conditionem anteuer- tere satis est. Porrò quanta sit Musices efficacia in immu- tandis affectibus, ac passionibus animi mitigandis, lucu- lenter explicat Seneca: Cassiodorus, & Augustinus, qui lib. contra Iulianum, Ciceronis testimonium adducens, refer[en]t Pithagoram spondeum in sono canentem tarditate modo- rum, & grauitate cantus furentem aliquorum iuuenum pe- rulantiam abegisse: & iure quidem, nam ars hæc ita ani- mas sibi reddit intentas, vt quemadmodum loquitur Cassio- dorus,) nil aliud cogitare possint; sed deposita omni cura mentis induant grauitatem. Hinc ob diuersas animorum commotiones, quas suis mo- <101> dulis suscitare potest Diuina isthæc facultas, quatuor melo- diæ species distinxit Philosophus ad diuersos affectus ten- dentes- Mistolidiscam, quæ ad compassionem mouet; Li- discam, quæ animos emollit ad concupiscentiam: Doriscam, quæ mentem erigit ad fortitudinem, atque virilitarem: & Frigiscam, quæ rigidior cæteris incitat ad dura consilia, pro- mouetque seuerirarem. Habet etiam tonos, diuersasque consonantiarum dissonantiarumque rationes, quas Dia- tesseron, Diapente, Diapason appellant: ac similiter tria melorum genera Diatonicum, Chromaticum, Enharmoni- cum, de quibus omnibus, aliisque Musices diuisionibus, vide Ficinum in Platonis Conuiuio Orat. 3. cap. 1. Guidonem, & Iacobum Fabrum in Elemen. Music. lib. 3. ß 4 Nobis eas tetigisse sufficiat.

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314 LEXICON ...in the subordinate parts of Arithmetic, namely that faculty, as Boethius says, which, through quantities related to another, has numerical ratios applied to sounds and voices. It was so called from the Greek word mos , which signifies an equal ratio and harmony; or rather from the Muses, with whom it was once familiar. Its object is number, or discrete quantity, insofar as it is related to another: for it brings moments of time to the measures of sounds, and from this it artfully joins and binds them together, so that sweetest harmony and a most orderly melody may sound in our ears. Its nobility may be gathered from the fact that, in singing divine praises and appeasing God, from the very beginning of religion to the present time, religion has always been accustomed to use it: hence it is said in Psalm 38: “Where were you when I laid the foundations of the earth, when the morning stars praised me together, and all the sons of God shouted for joy?” So much so that the poets’ fables relate even of Dis himself that he was softened by Orpheus’ songs. Nor is this surprising, since its order is a symbol of the heavenly hierarchy; and thus also, when introduced into the underworld, where there is no order but confusion, it is enough to overcome their condition. Moreover, how great the power of music is in changing emotions and calming the passions of the mind is clearly explained by Seneca, Cassiodorus, and Augustine, who, in the book against Julian, adducing Cicero’s testimony, report that Pythagoras, playing a spondean strain, by the slowness of the measures and the gravity of the song drove away the raging wildness of certain youths: and rightly indeed, for this art so captures souls that, as Cassiodorus says, they can think of nothing else; rather, putting aside every care, their minds assume seriousness. Hence, because of the various motions of the mind which this divine faculty can arouse through its measures, the Philosopher distinguished four kinds of melody tending toward different affections: the Mixolydian, which moves to compassion; the Lydian, which softens minds toward desire; the Dorian, which lifts the mind to courage and manliness; and the Phrygian, which, being harsher than the rest, stirs up hard counsels and promotes severity. It also has tones and various relations of consonances and dissonances, which they call Diatesseron, Diapente, and Diapason; and similarly three kinds of melodies: Diatonic, Chromatic, Enharmonic. For all these, and other divisions of music, see Ficino in Plato’s Convivium , Oration 3, chapter 1; Guido; and Jacobus Faber in the Elementa Musica , book 3, section 4. It is enough for us to have touched upon them.

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MATHEMATICVM. MVTA SIGNA sunt quæ præseferunt figuram Animalium 102 voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raucâ dicuntur, brutorum videlicet vocalium formam habentiæ, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio habetur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. MVTATIT arab. idem sonat ac latinè agglutinatus; cum vi- 103 delicet Planeta iia est alteri iunctus, vt nec in minuto qui- dem aberrer. Hoc vocabulo frequenter vtitur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. MVTLVM arab. Vide in V. Motlatum. 104 MVTLATA SIGN. sunt quæ membrum aliquod seu etiam corpus mutilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruat Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt ferè semper inducant membrorum incisio- nem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem posteà misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agir, in signis mutilis, inquit, aut quorum figuræ sunt imperfe- cta, aut circà caput Medusa Mars significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opusc. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. NABLON SCHALIAF seu etiam Nescussackas teste schie- 1. chardo Chaldaicè diciur Lyra sidus in Cælo, de quo sæ- pius dictum est. NAASCH LAAZAR hoc est Feretrum Lazari dictur apud 2. Christianos arabes Plaustrum, vt testatur Kircherus in Oc- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Vr- sa, quæ quatuor plaustri totas efftingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, atque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. NADIR apud Arabes significat punctum Cæli sub terra 3. oppositum diamcraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant: itavt ambo sint

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MATHEMATICVM. There are mute signs which present the figure of animals 102 that are without voice, such as Cancer, Scorpio, and Pisces; just as, on the contrary, those that have voice are said to be both human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, and feral, which are also called hoarse, namely those having the form of vocal beasts, as Aries, Taurus, Leo, Capricorn. The greatest consideration of these is found in Genethliacs, so far as defects and impediments of speech are concerned; on which matter Ptolemy, lib. 3. Quadrip. cap. 17. MVTATIT, Arabic; it sounds the same as the Latin agglutinatus ; namely, when a planet is joined to another in such a way that it does not err even by a minute. Ptolemy often uses this word in the Quadripartitum from the Arabic version, and Haly, his commentator, likewise. MVTLVM, Arabic. See under V. Motlatum. 104 MVTLATA SIGNS are those which represent some limb, or even a mutilated body, such as Taurus, the section of the Horses, the Head of Medusa, which indeed, as Titus observes well in Celestial Philosophy lib. 2. cap. 3, have this nature and power of influence, that they almost always cause the cutting off of limbs, if, with the rulers of life in an unhappy condition in the nativity, they are afterwards mingled by direction. Hence Ptolemy, in Quadrip. lib. 4. cap. 10, where he treats of the kind of death, says that in mutilated signs, or those whose figures are imperfect, or around the Head of Medusa, Mars signifies that one is to be beheaded, or mutilated in the limbs. Which St. Thomas observed in the Opuscula 28, art. 3, saying that such stars are funeral, and indicate a monstrous ending of life. See what we said under V. Gorgonis caput. N. NABLON SCHALIAF, or also Nescussackas, according to Schiechard, is said in Chaldean to be the constellation Lyra in the heavens, of which much has already been said. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among Arab Christians the Wagon, as Kircher testifies in the Oedipus , because the four more conspicuous stars in the Bear seem to represent no less a wagon than a bier, and the four wheels of the wagon are completed by them. Schiller, however, who took this as an occasion for transforming all the celestial images and naming them from the names of saints, calls this very star Peter’s Little Boat. NADIR among the Arabs signifies the point of heaven beneath the earth, diametrically opposite to the vertex of our head, which they likewise call by their own native term, Zenith; so that both are

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LEXICON 316 veluti poli horizontis, & distent ab eodem hinc inde gr. 90. ac proinde necessario incidant in ipsum meridianum, Zenith quidem supra tertam, Nadir autem sub terra. Et quam propositionem vnvem eorum habeat ad æquatorem & alterum polorum Mundi, eandem vice versa habeat alterum ad oppositum polum, & aduersam æquatoris partem. 4. NAHAR, ALCHARNER teste Kirchero in Oedipo arabice dicitur Fluuius Eridanus sidus ad australem plagam constans stellis triginta tribus, de quo plura diximus suo loco. 5. NAEIS CETI teù etiam Mandibula Ceti vulgò dicitur steila sira secundæ magnitudinis valdè præsignis, de natura Saturni, existens in rictu Ceti, atque in longitudine sub gr. 10. Tauri arab. dicta Menchar. 6. NATIVITAS, Natalitium thema, seù etiam Natiuitatis figura dicitur vulgò apud Astrologos constitutio Cæli erecta ad punctum Natiuitatis alicuius hominis, aut etiam initium alicuius rei. Quale autem dicendum sit verum punctum Natiuitatis, disputatum est luculenter in V. Genesis. 7. NATURA, eisi secundum varias acceptiones plura significet, quæ ad nostrum institutum non pertinem, primo tamen loco, & ex sui notione appellat generationem viuendum ex insita sibi à Creatore vi naturaliter, hoc est nullatenus alterata, constituto sibi primitùs ordine prodeuntium: vnde dicta est Natura quasi Nascitura, græcis autem expressiore vocabulo Physis & naturale dicitur quidquid non violentè, non casu, non artificiosè, non denique præter naturæ cursum emanat. Adeo vt iam Naturæ nomine proprie, & vniuersalissimè veniat congeries illa causarum secundarum, ex indita sibi à Creatore virtute necessatio operantium, quæ sui varietate pulcherrimum hunc rerum ordinem constituunt, atque à Deo ita præordinatæ sunt, vt nulla vi, nullo planè artificio, nullo humanæ voluntatis adminiculo ex se suos effectus promant, ac naturali ordine progrediantur: cuius admirabilem cursum demirans D. August. lib. 8. in Genesim. Quod enim, inquit mains, mirabiliusque spectaculum est, aut vbi magis cum rerum natura humana ratio quodammodo loqui potest, quam cumpositis seminibus, plantatis surculis, translatis arbustulis, insitis malleolis, tanquam interrogatur quæque v[er]s radicis & germinis, quid possit, quidve non possit; vnde possit, vnde non possit? quid in ea valeat numerorum inuisibilis, interiorque potentia, quid extrinsecùs adhibita diligentia, inque ipsa consideratione perspicere, quia neque qui plantat est aliquid, neque qui rigat, sed qui incrementum dat Deus: quia & illud

Transcription: Translated (English)

LEXICON 316 as the poles of the horizon, and are distant from the same on either side by 90 degrees; and therefore they necessarily fall upon the meridian itself, the Zenith indeed above the earth, but the Nadir beneath the earth. And whichever proposition one of them has toward the equator and one of the poles of the World, the other in turn has the same toward the opposite pole and toward the opposite part of the equator. 4. NAHAR, ALCHARNER, according to Kircher in the Oedipus, is called in Arabic the river Eridanus, a star in the southern region consisting of thirty-three stars, of which we have spoken more fully in its place. 5. NAEIS CETI, also commonly called the Whale’s Jaw, is a very notable second-magnitude star, of the nature of Saturn, existing in the mouth of the Whale, and in longitude under 10 degrees of Taurus; in Arabic it is called Menchar. 6. NATIVITY, the natal theme, or also the figure of nativity, is commonly called among astrologers the constitution of the heavens erected for the point of someone’s nativity, or also the beginning of some thing. But what should be said to be the true point of nativity has been discussed at length in Genesis V. 7. NATURE, although according to various meanings it signifies many things that do not pertain to our purpose, in the first place, and by its notion, it denotes generation for living according to the natural power implanted in it by the Creator, that is, in no way altered, with the order of things first established for it from the beginning; whence it is called Nature, as it were, Nascitura; but with a more exact Greek term Physis, and natural is called whatever does not flow violently, not by chance, not artificially, not finally beyond the course of nature. So much so that now under the name of Nature, properly and most universally, there comes that assemblage of secondary causes, operating necessarily from the power imparted to them by the Creator, which by their variety constitute this most beautiful order of things, and have been so preordained by God that by no force, by no artifice at all, by no aid of human will do they of themselves produce their effects, and proceed in natural order: admiring whose wondrous course St. Augustine, book 8 on Genesis, says: For what, he says, is a more wondrous spectacle, or where can human reason more, in a manner, speak with the nature of things than when seeds have been set, shoots planted, little shrubs transplanted, cuttings grafted, as though each is asked concerning the root and the sprout, what it can do, and what it cannot; whence it can, whence it cannot? what in it is the invisible and inward power of numbers, what the diligence applied from without, and in the very consideration to perceive that neither he who plants is anything, nor he who waters, but God who gives the increase: because even that

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MATHEMATICVM. 317 operis, quod accedit extrinsecus, per illum accedit, quem nihilominus creauit, & quem regit atque ordinat inuisibilitex Deus? Hinc iam in ipsum mundum velut in quamdam magnam arborem rerum oculus cogitationis attollitur, atque ipso quoque gemina operatio prouidentia reperitur partim Naturalis, partim Voluntaria. Naturalis quidem per occultam Dei administrationem, quæ etiam lignis, & herbis dat incrementum, voluntaria verò per angelorum opera, & hominum. Secu[n]dum illam primam cælestia superiùs ordinari, inferiùsq[ue] terrestria, luminaria, sideraque fulgere, diei, nectisque vices agitari, aquis terram fundatâ interlui, atque circumlui, aërem altiùs superfundi, arbusta, & animalia concipi, & nasci, crescere, & senescere, occidere, & quidquid aliud in rebus interiori, naturalique motu geritur: In hac autem altera signa dari, docepi, & discere, agros coli, societates administrari, artes exercevi, & quoque alia, siue in superna societate aguntur, siue in hac terrena atque mortali, ita- ut bonis consulatur, & per nescientes malos: inque ipso homine eandem geminam prouidentia vigere potentiam: primò erga corpus naturale scilicet eo motu quosit, quo crescit, quo senescit; voluntarium vero quoad victum, tegumentum, curationemque consulitur. Hucusque D. August. Ex quibus liquet, duo esse rerum principia; naturam, & voluntatem; eaque ambo à Diuina prouidentia regi, promoueri, disponi, atque etiam superiori potentia impediri posse: Verum in suo cursu relicta Naturam necessariò operari, Voluntatem liberè, ac naturæ cursum disponere posse, coadiuare, & aliquatenus impedire hinc quæ à natura pure & absque voluntatis adminiculo prodeunt, naturalia; quæ à sola voluntate nihil subfæculante Natura, purè voluntaria: quæ verò à voluntate provt applicat actiua passuis, impedimenta remouet, naturam ipsam ad operandum disponit artificialia dicuntur Quod, & obseruauit ipsemet Augustinus paulò post subde[n]s: Sicut autem in arbore id quod agit agricultura forinsecus, ut illud proficiat, quod geritur (à natura) intrinsecus; sic in homine secundum corpus, ei quod intrinsecus agit natura, seruit extrinsecus medicina: quod autem ad arborem celendi negligentiâ, hoc ad corpus medendi incuria, hoc adanimam discendi seenitia. Et quod ad arborem humor inutilis, hoc ad corpus victus exitiabilis, hoc ad animam persuasio iniquitatis. Porrò inter naturales causas principem sibi locum vendi- cant corpora cælestia, quæ sua vniuersali potentia in omnia isthæc sublunaria agunt, suis induxibus producunt, 8.

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MATHEMATICVM. 317 of the work, which comes in from outside, it comes through Him whom nonetheless He created, and whom God governs and orders invisibly? Hence now the eye of thought is raised to the world itself, as to a kind of great tree of things, and in that too a twofold operation of providence is found, partly natural, partly voluntary. Natural, indeed, through the hidden administration of God, who also gives increase to trees and plants; voluntary, however, through the works of angels and of men. According to that first mode, the heavenly things are ordered above, and the earthly below; the lights and stars shine forth; the alternations of day and night are driven on; the waters flow beneath and around the earth, the air is spread more widely above, shrubs and animals are conceived and born, grow and age, die, and whatever else is carried on in things by an inward and natural motion. But in this other mode signs are given, fields are cultivated, communities are administered, arts are practiced, and likewise other things, whether in the higher society they are carried on or in this earthly and mortal one, so that provision is made for the good, and through the ignorant for the bad. And in man himself the same twofold power of providence is active: first, in relation to the body, namely by that motion by which it grows and by which it grows old; but in a voluntary way, as to food, clothing, and care, provision is made. Thus far St. Augustine. From these things it is clear that there are two principles of things: nature and will; and that both are ruled, advanced, and ordered by Divine providence, and can even be hindered by a higher power. Yet, being left in its own course, Nature necessarily works, while Will works freely and can arrange the course of nature, assist it, and to some extent hinder it. Hence those things which proceed from nature purely and without the aid of will are called natural; those which come from will alone, with Nature adding nothing, purely voluntary; but those which come from the will insofar as it applies active things to passive, removes impediments, and disposes nature itself to act, are called artificial. This the same Augustine himself observed shortly afterward, adding: “As in a tree that which agriculture does from outside is for the advancement of that which is carried on from within by nature; so in man, with respect to the body, medicine from outside serves that which nature does within. What neglect in cultivating does to a tree, carelessness in healing does to the body, and sloth in learning does to the soul. And what harmful moisture does to a tree, destructive food does to the body, and persuasion to injustice does to the soul.” Moreover, among natural causes, the heavenly bodies claim for themselves the chief place, which by their universal power act upon all these sublunary things, and by their influences produce them, 8.

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318 LEXICON conseruant, immutant, alterant, perdunt: neque eorum actiuitas tolli vel impediri potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo, atque adeò vel ob id cæteris omnibus præstant. Benè verò potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Centiloquio Verbo 8, Sapiens anima, inquit, confert calesti operationi, quemadmodum optimas Agrico a arando, expurgandoque confert Natura. Igitur non potest homo facere, vt Astra suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuertere. 9. Sic non potest homo vll modo Eclipsim futurum impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Martis sequuturum præuertere, nives, pluuias, ventos, aëris infectiones, &c. potest autem in naturis inferioribus, vt ædificando supersolum, ne herbas getminet, exsiccando stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subfamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt fecit Ioseph Patriarcha) magnam frumenti vim in hortea comportare, in bonis siderum configurationibus terram excolere, maria exsulcare; in malis domi consistere, atque à labore inutili abstinere, &c. Concludam igitur cum iis quæ appositè ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, actus virtutum aut vitiorum: alia mixta, vt facere iter, comedere, &c. Verum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpori nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu certo

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318 LEXICON preserve, change, alter, destroy: neither can their activity be taken away or impeded by human will, or by any lower causes, but only by the First Cause, God, and therefore for that reason too they excel all other things. Yet man can skillfully cultivate their nature, qualities, effects, and unchangeable power of acting in lower things, apply, avert, divert them, as Ptolemy said in the Centiloquy, Word 8: “A wise soul,” he says, “contributes to the celestial operation, just as good farmers contribute to Nature by plowing and clearing.” Therefore man cannot cause the stars not to exercise their natural powers, not to produce their proper effects, to cast off the harmful or beneficial qualities with which they are intrinsically endowed, and to put on contrary ones; but he can in some measure, in lower causes, alter, impede, or even destroy them, and thus entirely avert their effects. 9. Thus man can in no way prevent a future eclipse, nor the effects which will naturally flow from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, nor snow, rains, winds, diseases of the air, etc. But he can in lower natures, as by building a cover over the ground so that weeds do not sprout, by drying up ponds so that they do not corrupt the air; by cutting down trees so that they do not bear fruit. So also, by assisting the stars, he can contribute to their operation, as by supplying matter, or removing it; by guarding himself against the evil influences of the stars, supporting the good ones, disposing things, and applying the susceptible subject at the time of a foreseen sterility (as the Patriarch Joseph did), by storing up a great quantity of grain in the barns, by cultivating the land in good configurations of the stars, by sailing the seas; in bad ones by staying at home, and abstaining from useless labor, etc. I will therefore conclude with what Kircher aptly has on this matter in the Great Art of Light & Shadow, book 6, part 3, chapter 2: “Nature,” he says, “is governed by two principles, nature, and will: Nature is subject to the stars, will is free, and therefore effects and operations that are purely natural obey the stars completely as necessary causes, as health or sickness; the long or short life of men, etc. Others are purely voluntary, such as contemplating, teaching, acts of virtues or vices; others are mixed, such as making a journey, eating, etc. Yet whether a journey will be convenient or not depends on the stars, and on the constitution of the air. Therefore if anyone perfectly knew the influences of the stars suitable or unsuitable to our body, he would no doubt certainly know the fortunate or unfortunate state of the journey”

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MATHEMATICVM. 519 judicare posset: item desanitate, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAUBARACH, siue Naubahàr arab. idem sonat, ac No-10; uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans 11. stellis 64. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Mar- cheb in medio scuti posita. Hoc sidus à schillero immutatum fuit in Arcam Noë. Hebraicè autem dicitur se- phina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, 13. pallenti, & suboscuro micantes: eô dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt dux magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebulosum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequitur aculeum scorpij. Idque, vt obseruat Titus lib. 1. cap. 12. quia earum nebulositas parem, & consimilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vi- tium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum lucem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos derivatur congressu fiant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIUM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Ciceroni, & aliis idem est, ac Scorpij fidus fortè à 16.

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MATHEMATICUM. 519 judge: likewise concerning health, concerning sickness, etc. Likewise concerning the success of business with a prince. But since these things can be difficult to accomplish, and to know, hence the knowledge of these elections, unless supported by experience, is for the most part fallacious. Thus Kircher. From which it is clear what art, or human ingenuity, can do, what Nature can do, and what a man, having properly known the nature of things, can undertake, and finally what he may undertake in vain, and what even rashly he may undertake. NAUBARACH, or Naubahàr in Arabic, means the same as the Lord of Noah's- hunting. See under V. Anaubarach. NAVIS is commonly called the constellation in the southern region consisting of 11. stars, 64 in number, as is clear from the most accurate observations of the new Astronomers, all for the most part of the nature of Saturn and Jupiter, whose chief star is Canopus, standing in the rudder, of the first rank in Arabic, Rubail, to which closely follows the star called Mar- cheb, placed in the middle of the shield. This constellation was changed by Schiller into the Ark of Noah. In Hebrew, however, it is called se- phina. NEBOLASSID, among the Fetzans, Moroccans, and the rest of the 12. Nubian astrologers, is called the Tail of the Lion, a fixed star of first magnitude, concerning which enough has been said in its proper place. NEBULOUS STARS are certain fixed stars shining with a dull, pale, and rather dim light: so called either because they present certain clouds by their appearance, (such as especially are the two great and quite conspicuous ones near the Antarctic pole) or indeed, because they generate clouds, and when setting with the sun they make the air cloudy, as Ptolemy and Pliny observed, in the Manger, which is in the breast of Cancer, in that which is in the eye of Sagittarius, but especially it is seen in that which follows the stinger of Scorpio. And this, as Titus observes, lib. 1. cap. 12. because their nebulosity produces a similar and equivalent effect in these lower regions. Hence experience has also shown that whenever they come together with the Luminaries in anyone's nativity, they always bring spots, clouds, or some other defect in the eyes; which natural reason itself suggests, for their light is very faint and weak, and therefore it is no wonder if they take away or dull the light of the eyes, when they become hostile by conjunction with the luminaries themselves, from which light is conveyed into the eyes. NEMER, that is, Pardus in the Hebrew tongue, is called the Wolf 14. a constellation of which elsewhere mention has been made. NEOMENIUM in Greek has the same meaning as New Moon, of which 15. presently below. NEPA, in Cicero and others, is the same as the sign of Scorpio, perhaps from 16.

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520 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum lingua dicitur Cancer aliud sudus, quod in nominibus sæpe eum Scorpione confunditur. 19. NESCHER, Hebraicè dicitur Aquila. 20. NIGEAR, (teste Iunctino in Sphætam Io: de Sacrobofco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & conceipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboseuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Ad ducit etiam nebulas, nimbos, glacies, nives, & in hominibus Saturninis solitudinis, austeritatis, invidiæ, obstinationis, auaritix incitamentum, & incrementum. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach; id est circulus signorum diuiditur in duodecim partes æquales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus 23. NITVRA, pro Genitura, seù Natalitio Themare per Apocopen sæpissimè ab aliquibus vsurpatur. Vide Isidorum. 24. NOCTRNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiuæ, quales sunt humiditas, & sceitas: sicut è contrà Diurna dicuntur signa & planetæ in quibus abundant qualitates actiuæ: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclypticam in duobus punctis oppositis, & Nodus quidem boreus dicitur punctum in quo Planeta è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euehens; arque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porrò Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibilites mouentur: inferiorum verò non

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520 LEXICON Chelis dictum; for the same reason also. 18. NEPA is said in the African tongue to mean Cancer, or another scorpion, because in names it is often confused with Scorpio. 19. NESCHER is said in Hebrew to mean Eagle. 20. NIGEAR, (as testified by Iunctinus in the Sphaera of Ioannes de Sacrobosco) is said by Arab writers to mean the axis of the world, which terminates at its poles, and is conceived to pass through the center of the earth; see under V. Axis. 21. NIGRA, or Niger, is the name given to a certain kind of comet of black color, or rather leaden and somewhat dark, of the nature and condition of Saturn, and therefore, as in color, so also in qualities, altogether like him. For it signifies, when it appears, scarcity of the year, long-lasting locusts and other harmful animals of that kind, pestilence, chronic fevers, etc. It also brings fogs, heavy rains, ice, snow, and in Saturnine men an incitement and increase of solitude, severity, envy, obstinacy, and greed. NITACH, in Arabic, or rather in Chaldaic, signifies the Zodiac and the circle of the signs. Hence Alchabitius begins his book thus: Nitach; that is, the circle of the signs is divided into twelve equal parts, etc. See what is to be said more fully under V. Zodiacus. 23. NITVRA is very often used by some in place of Genitura, or Natal Theme, by apocope. See Isidore. 24. A NOCTURNAL sign, or also planet, is one in which passive qualities predominate, such as humidity and dryness; just as, on the contrary, those signs and planets are called Diurnal in which active qualities abound: on this matter see what we said under V. Diurnus. 25. NODES are called by astronomers the intersections of the orbits of the sun and of the individual planets having latitude, namely where the orbits of the planets intersect the ecliptic at two opposite points; and the northern node is the point at which a planet passes from southern latitude into northern; the southern node, where it descends from north to south. They are also so called from the shape they bear, resembling the head and tail of the Dragon; likewise the ascending, or lifting, and the descending. But where the planets have their greatest latitude it is called the belly of the Dragon, because this too is broader in the belly than at the extremities. Moreover, these nodes change their place in the Zodiac, just as the planets themselves do, but they proceed contrary to the succession of the signs. And indeed the nodes of the three superior planets move imperceptibly; but those of the inferior do not

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MATHEMATICVM. 127 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliacis nodi maximam significationem quoad formam corporis, quam plerumque deturpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis, vel euruis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, contorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. NUNA SPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem eursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalicatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltrò eitróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgato illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Qua de re vide Clauium, & Blancanum in sphæra mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem nobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnico tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis 13. X

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MATHEMATICUM. 127 not so, but rather to each individual one minute, indeed even the lunar nodes to their own minutes, as appears in the Ephemerides and in tables of secondary motions. In genethliacal astrology the nodes have the greatest significance with respect to the form of the body, which they usually disfigure if they are found with the Luminaries or with the malefics, especially in the Angles and in the mutilated or oblique signs, such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Hence those born will turn out hunchbacked, cross-eyed, lame, twisted, or in some way debilitated, as Ptolemy has in book 3, chapter 17. The ninth sphere is commonly called the Primum Mobile, which is placed above the eighth sphere, or the heaven of the stars, which carries along with it all the lower spheres from east to west, accomplishing its revolution with the swiftest course in a space of about 24 hours. Others, however, admit this ninth sphere as distinct from the Primum Mobile, and even a tenth, which they call spheres of libration, or trepidation, which they see in the firmament; for they observed that it, in addition to its universal motion and its proper motion, moves irregularly from north to south and from south to north under the colure of the first mobile's solstices, back and forth; again it moves from east to west and from west to east under the ecliptic and over its poles. Wherefore, since so many motions are found in the firmament and in the planets, and since they say that the two motions just explained cannot be had in themselves or from the first mobile, according to that common axiom that one simple body by its nature can be moved inwardly by only one simple motion, but from without by several, consequently they also admit this ninth sphere, which is said to move from east to west and from west to east over the poles of the Zodiac by 14 minutes in a span of 1716 years, as they say, and again a tenth, which is said to move from north to south under the colure of the solstices by 24 minutes in a span of 3432 years. On this matter see Clavius and Blancanus in Sphaera Mundi book 18, chapter 7. But I, for my part, can by no means admit these distinct motions, and therefore distinct spheres, because it is contrary for one and the same noble body to be moved by two contrary motions, by which token such motions of trepidation would exist, which are altogether fictitious, and the appearances of the stars, irregularities, etc., are most excellently preserved in the mere fluidity of the heavens and in only one motion from east to west, yet regularly irregular according to all parts of the heavens, farther and farther removed from the first motive power. See what we have explained at length in V. Motus. NOTE: Peliotes is a wind, one of the four intermediate winds. 13. X

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326 LEXICON æquè spirans inter meridiem, & ortum, aliis Euronotus dictus à nostris vulgò Syrouus, eo quod per mediam syriam transeat, opponiut directè Borrolybico, seu Magistrali. Eius qualitas est valdè debilis, & silens, humidior tamen quam in Euro, & sæpè in austri naturam degenerat; qui licet pluuiam non afferat, facit tamen tempus valdè turbidum, aquosum, & repletaërem caligine, atque obscuritate. Excitari solet hic ventus à sole ex oriente cum stellis fixis sitis in cornu, & cauda Arietis, in nexu, & Ventre Piscium, Fornaham, Vmbilico Andromedæ, & quæ sunt in Cæto. Similiter à Mercurio, (qui ventorum generalis est motor) congridiente cum dictis stellis, atque insuper cum Lyra, Scheat, Pleiadibus, Lucida Hidræ, Hebulosa in oculo Sagirrarij, ac denique tribus stellis existentibus in fronte Scorpij. Plura de eius natura, & qualitatibus vide apud Vitruuium lib.1 cap.6. NOTOLIBICVS est item Ventus alius intermedius spirans <29.> ex æquo inter meridiem, & occasum, oppositus Mese, seu Borrhapeliosi: apud nos vulgò Libeuius, seù Garbinus dicitur, eo quod acersit, & peruersæ naturæ, tum etiam quia tempus serenum in turbidum, ac pluuiosum semper conuerit. Natura sua est humidus, morbosus, tempestuosus præsertim verò Ligustico mari infensus. <30.> Nôrvs græcè idem quod Auster Ventus vnus ex quatuor cardinalibus spirans à puncto meridiei oppositus directè septentrioni. Est de natura sua calidus, & humidus morbosus, noxius (vnse & nomen à nocendo hausit) & soler morbos multos excitare, vt febres putridas, pleuritides, &c. & si diu absque interpolatione spirauerit inducere solet pestilentiam, vt sæpius obseruatum est, & refert Abraham Gorlnitz in compendio Geographico. Ratio autem naturalis est, quia corpora per ipsum efficiuntur humida, & calida, atque ob id putredini maximè obnoxia: vnse exurgit pestis, quæ aliud planè non est quam corruptio sanguinis circa cor. Hinc Ouidius. Letiferis calidi spirarunt astibus austri. Flare solet potissimum in occasu vespertino Arcturi, Pleiadum, atque Sirij; nec non in occasu marutino Hyadum, & Coronæ Gnossiæ: quo tempore, inquit Plinius lib.18. c.33. Materiam, vineamque, agricola ne tractes: humidus, æstuosus Italia est: Africa quidem incendia cum serenitate affert, cuius rei rationem reddidimus in V. Auster. Idem testatur in lib.2.cap.45. huic vento esse rupem quamdam in Cyrenaica provincia sacram, quam profanum sit attrectare ho-

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326 LEXICON blowing equally between the south and the east, called by others Euronotus, and by our people commonly Sirocco, because it passes through the middle of Syria, directly opposite to the Boreal, or Magistral wind. Its quality is very weak and silent, yet more humid than the Euro, and it often degenerates into the nature of the south wind; which, although it does not bring rain, nevertheless makes the weather very stormy, watery, and filled with haze and darkness. This wind is usually stirred up by the sun in the east together with the fixed stars situated in the horn and tail of Aries, in the knot and Belly of Pisces, Fornax, the Umbilicus of Andromeda, and those that are in Cetus. Likewise by Mercury, (who is the general mover of the winds) when in conjunction with the said stars, and moreover with Lyra, Scheat, the Pleiades, the bright star of Hydra, Hebulosa in the eye of Sagittarius, and finally the three stars existing in the forehead of Scorpio. For more on its nature and qualities see Vitruvius, book 1, chapter 6. NOTOLIBICUS is also another intermediate wind blowing <29.> equally between the south and the west, opposite to the Mese, or Borrhapelios: among us commonly called Libeccio, or Garbino, because it calls up and is of a perverse nature, and also because it always turns fair weather into stormy and rainy weather. By its nature it is humid, unhealthy, stormy, especially indeed hostile to the Ligurian sea. <30.> North, in Greek, the same as Auster, one of the four cardinal winds blowing from the point of the south, directly opposite to the north. By nature it is hot and humid, unhealthy, harmful (and its very name is derived from harming), and it is accustomed to stir up many diseases, such as putrid fevers, pleurisy, etc.; and if it blows for a long time without interruption it is usually said to bring pestilence, as has often been observed, and as Abraham Gorlinitz relates in the Geographical Compendium. The natural reason is that bodies become humid and warm through it, and for that reason are especially liable to putrefaction: whence pestilence arises, which is nothing other than corruption of the blood around the heart. Hence Ovid. The warm south winds blew with deadly breaths. It usually blows especially at the evening setting of Arcturus, the Pleiades, and Sirius; as well as at the morning setting of the Hyades and the Gnossian Crown: at which time, says Pliny, book 18, ch. 33, do not handle materials or vines, farmer: Italy is humid and oppressively hot; Africa indeed brings fires together with clear weather, the reason for which we have given in V. Auster. He likewise testifies in book 2, chapter 45, that this wind has a certain rock in the Cyrenaican province that is sacred, which it is sacrilegious to touch-ho

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MATHEMATICVM. 327 minis manu, confestim austro voluente arenas. Vide adhuc quæ diximus in dicto verbo Auster. NOTIVS PISCI, seu Aurinus dicitur fidus in coelo ad Au- < 314> stralem plagam piscis magni figuram præseferens atque am- bitu suo complectens stellas duodecim omnes ferè de natura Saturni, vel Veneris, quarum præcipua est quæ in ore, & est eadem quæ in vltima effusione aqvæ Aquarij dicta Forna- hand primæ magnitudinis de natura Veneris, & Mercurij. Hoc fidus in Horoscopo, inquit Pontanus; facit eximiura natatorem & venatorem. In occasu verò mottem indicit in aquis, aut per belluarum ingluuiem. Propè ipsum sunt ali- quot sporades de natura item Saturni. NOVENARIÆ quid sint, & quis earum Dominus Vide in V. < 325> Anaubarach. NOVELVNIUM dicitur tempus illud, quo Luna silet, est- < 330> que in coniunctione solis, eo quia vetere decedente, noua quasi succedit. Eius momentum si quis obseruare volet, vi- debit planè in lixluio, vel etiam in aqua cuius plenum sit vas vitreum, aut argenteum, atque in fundo vasis consi- stant quieti cineres oleæ, vel vitis: Nam cum primum Lu- na Solis diametrum intrat, mox cineres ex seipsis exiliunt, turbant aquam, & in gyrum vertuntur, nec ad pristinam quietem redeunt, quoad vsque Luna perfectè de disco solis exierit: quod ego semel & iterum obseruaui. Dies etiam Nouilunij artificiosè per numeros, & Epa- < 340> etam facile internosci poterit. Quandoquidem, si Epactæ currenti numerum Calendarum ac dierum qui à Martio præ- teriro vsque ad præsentem diem effluxerunt, adieceris; at- que à 30. (quæ integra Lunario est) numerum productum detraxeris, relinquetur numerus dierum, post quos cele- brabitur Luminarium synodus. Quodsi productus numerus tricenarium excesserit, tunc deme ab eo triginta, & quod su- perest tursus à triginta subtrahe, & mox Nouilunij dies emerget. NOX dicitur tempus illud, quo sol inferius hemisphæ- < 351> rium lustrat à cardine occidentis per Imum Cæli ad Cardi- nem Orientis tendens: sicut econtrà dies est cum sol emer- git ex horizonte, & graditur per Medium Cæli ad Occi- dentem, quovsque in ipsum mergatur. Eius porrò quanti- tatem metitur arcus æquatoris nocturnus, sicut & dici diur- nus, qui inter vtrumque cardinem intercipitur, aut sub ter- ra, aut suprà terram, accepta pro singulis quindemis gra- dibus integra hora. Et nox quidem diuiditur in septem spa- tia, quæ sunt Vesper, Crepusculum, Conticinium, In- X ij

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MATHEMATICVM. 327 by a slight hand, the sands being immediately whirled about by the south wind. See further what we said under the word Auster. NOTIVS PISCI, or Aurinus, is said to be a constellation in the heaven toward the southern quarter, bearing the figure of a great fish and enclosing within its circuit twelve stars, all or nearly all of the nature of Saturn or Venus, the chief of which is that in the mouth; and it is the same as that in the last pouring forth of the water of Aquarius, called the Fornax; of the first magnitude, of the nature of Venus and Mercury. This constellation in the horoscope, says Pontanus, makes an excellent swimmer and hunter. In setting, however, it brings death in the waters, or by the swallowing of beasts. Near it are some more little clusters, likewise of the nature of Saturn. NOVENARIÆ, what they are, and who is their lord, see under V. Anaubarach. NOVELVNIUM is said of that time when the Moon is silent, and is in conjunction with the Sun, because as the old Moon departs, the new one, as it were, succeeds. Whoever wishes to observe its moment will clearly see it in lye, or also in water in a glass or silver vessel full of it, with ashes of olive or vine lying quiet at the bottom of the vessel; for as soon as the Moon enters the diameter of the Sun, the ashes at once leap up of themselves, disturb the water, and whirl in a circle, nor do they return to their former stillness until the Moon has completely passed out from the disk of the Sun: which I have observed once and twice. The day of New Moon may also be easily recognized by numbers and the Epact. For if you add to the current Epact the number of the Calends and the days which have elapsed from the preceding March up to the present day; and then subtract from 30, which is the full lunar month, the resulting number, there will remain the number of days after which the conjunction of the luminaries will be celebrated. But if the resulting number exceeds thirty, then subtract thirty from it, and from what remains subtract thirty again, and the day of New Moon will immediately appear. NOX is said of that time when the sun traverses the lower hemisphere, moving from the western cardinal point through the bottom of the sky toward the eastern cardinal point: just as, on the contrary, day is when the sun rises from the horizon and travels through the middle of the sky toward the west, until it sinks into it. Its quantity is measured by the nocturnal arc of the equator, just as also by the diurnal arc, which lies between the two cardinal points, either under the earth or above the earth, a full hour being taken for every fifteen degrees. And night is indeed divided into seven parts, which are Vesper, Crepusculum, Conticinium, In- X ij

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101 LEXICON nibus Arithmeticæ subalterna, facultas nempe, vt inquit Boëthius, quæ multitudine ad aliud relata rationes nume- rales concretas habet ad sonos & voces. Dicta est à Græ- co verbo Mos, quod æquam rationem, atque harmoniam sonat; vel potiùs à Musis, quibus olim familiaris erat. Ha- bet pro obiecto numerum seù quantitatem discretam p[ro]ovt ad alteram relatam: confert enim temporis momenta ad sonorum modulos, & inde eos artificiosè nectit, & copu- lat, vt duleissima harmonia, atque ordinatissimum melos auribus nostris insonet. Eius nobilitatem vel inde licet colligere, quod in diuinis laudibus decantandis, Numine- que propitlando, ab ipso religionis exordio ad hæc vsque tempora religio è sit semper adhibita: vnde Iobi 38. dicitur: Vbi eras quado ponebam fundamenta terra: cum me lau- darent simul atra matutina, & subilarent omnes Filij Dei? Adeovt de ipso Dite referant Fabulæ Poëtarum, quod sit Orphei cantibus emollitus: Nec mirum, cum eius ordo vt celestis Hierarchiæ symbolum est, ita & inferis illatus vbi nullus ordo est, sed confusio, eorum conditionem antuer- tere satis est. Porrò quanta sit Musices efficacia in immu- tandis affectibus, ac passionibus animi mitigandis, lucu- lenter explicat Seneca. Cassiodorus, & Augustinus, qui lib. contra Iulianum, Ciceronis testimonium adducens, refer[en]t Pithagoram spondeum in sono canentem tarditare modo- rum, & grauitate cantus furentem aliquorum iuuenum pe- tulantiam abegisse: & iure quidem, nam ars hæc ita ani- mas sibi reddit intentas, vt quemadmodum loquitur Cassio- dorus,) nil aliud cogitare possint; sed deposita omni cura mentis induant grauitatem. Hinc ob diversas animorum commotiones, quas suis mo- dulis suscitare potest Diuina isthæc facultas, quatuor melo- diæ species distinxit Philosophus ad diversos affectus ten- dentes. Mistolidiscam, quæ ad compassionem mouet; Li- discam, quæ animos emollit ad concupiscentiam: Doriscam, quæ mentem erigit ad fortitudinem, atque virilitarem: & Frigiscam, quæ rigidior cæteris incitat ad dura consilia, pro- mouetque seueritatem. Habet etiam tonos, diuersasque consonantiarum dissonantiarumque rationes, quas Dia- tesseron, Diapente, Diapason appellant: ac similiter tria melorum genera Diatonicum, Chromaticum, Enharmoni- cum, de quibus omnibus, aliisque Musices diuisionibus, vide Ficinum in Platonis Conuiuio Orat.3.cap.3. Guidonem, & Iacobum Fabrum in Elemen. Music. lib.3. & 4 Nobis eas terigisse sufficiat.

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101 LEXICON Music is an auxiliary branch of arithmetic, namely, as Boethius says, the faculty which, by relating many things to something else, has numerical ratios applied to sounds and voices. It is called from the Greek word mos , which signifies equal proportion and harmony; or more properly from the Muses, with whom it was once familiar. Its object is number, or discrete quantity, as related to another. For it brings the moments of time into relation with the patterns of sounds, and thus ingeniously joins and binds them together, so that sweetest harmony and the most orderly melody may sound in our ears. Its nobility may be gathered from the fact that, in singing divine praises and propitiating the Deity, it has been employed from the very beginning of religion down to these times; whence Job 38 says: “Where were you when I laid the foundations of the earth, when the morning stars praised me together, and all the sons of God shouted for joy?” So much so that the poets’ fables relate of Dis himself that he was softened by the songs of Orpheus. Nor is this surprising, since its order, as it is a symbol of the heavenly hierarchy, when brought even into the underworld, where there is no order but confusion, is enough to alter their condition. Moreover, how great music’s power is in changing emotions and soothing the passions of the mind is clearly explained by Seneca, Cassiodorus, and Augustine, who, in the book against Julian, citing Cicero’s testimony, report that Pythagoras, singing a spondean melody, by the slowness of the notes and the gravity of the song drove away the wantonness of certain young men in a fit of fury. And rightly so; for this art so holds souls intent upon itself that, as Cassiodorus says, they can think of nothing else, but laying aside every care of the mind, assume a serious demeanor. Hence, on account of the various stirrings of the mind which this divine faculty can excite through its modes, the Philosopher distinguished four kinds of melody tending to different affections. The Mixolydian, which moves one to compassion; the Lydian, which softens souls toward desire; the Dorian, which raises the mind to fortitude and manliness; and the Phrygian, which, being sterner than the others, incites to harsh counsels and promotes severity. It also has tones and various relations of consonances and dissonances, which they call Diatesseron, Diapente, and Diapason; and likewise the three kinds of melodies, Diatonic, Chromatic, and Enharmonic, concerning all of which, and other divisions of music, see Ficino in Plato’s Symposium , Oration 3, chapter 3, and Guido and Jacobus Faber in Elements of Music , books 3 and 4. It is enough for us to have touched on these matters.

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MATHEMATICVM. 102 MVTA SIGNA sunt quæ præseferunt figuram Animalium voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raueà dicuntur, brutorum videlicet vocalium formam habentia, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio habetur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. 103 MVTATIL arab. idem sonat ac latinè agglutinatus; cum vi- delicet Planeta ita est alteri iunctus, vt nec in minuto qui- dem aberret. Hoc vocabulo frequenter vtitur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. 104 MVTLATVM arab. Vide in V. Motlatum. 105 MVTLATA SIGNA sunt quæ membrum aliquod seù etiam corpus mutilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruat Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt ferè semper inducant membrorum incisio- nem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem postea misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agit, in signis mutilis, inquit, aut quorum figurà sunt imperfe- cto, aut circà caput Medusa Mare significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opus. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. 1. NABION SCHALIAF seù etiam Nescussackat teste schie- chardo Chaldaicè dicitur Lyra sidus in Cælo, de quo sæ- pius dictum est. 2. NAASCH LAAZAR hoc est Feretrum Lazari dicitur apud Christianos arabes Plaustrum, vt testatur Kircherus in Oe- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Vr- sa, quæ quatuor plaustri totas efftingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, atque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. 3. NADIR apud Arabes significat punctum Cæli sub terra oppositum diametraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant: itavt ambo sint

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MATHEMATICVM. 102 MUTA SIGNA are those which present the figure of animals lacking voice, such as Cancer, Scorpio, and Pisces; just as, on the contrary, those said to have voice are both human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, and also feral, which are likewise called rough-voiced, namely those having the form of vocal beasts, as Aries, Taurus, Leo, Capricornus. Their chief consideration is had in Genethliacs, as regards vices and impediments of the tongue, concerning which matter Ptolemy, lib. 3. Quadrip. cap. 17. 103 MVTATIL in Arabic sounds the same as in Latin, agglutinatus; namely, when a planet is so joined to another that it does not even depart by a minute. Ptolemy frequently uses this word in the Quadrip. from the Arabic version, and Hali, his commentator. 104 MVTLATVM Arabic. See under V. Motlatum. 105 MVTLATA SIGNA are those which represent some member, or even a mutilated body, such as Taurus, the cutting of the Horses, the Head of Medusa, which indeed, as Titus observes well in Cælestis Philosophia lib. 2. cap. 3, have this nature and influence, that they almost always bring about the cutting off of members, if the rulers of life are unfortunately placed in the Nativity and are later mingled by direction. Hence Ptolemy in the Quadrip. lib. 4. cap. 10, where he treats of the kind of death, says, in mutilated signs, or those whose figure is imperfect, or around the Head of Medusa, the sea signifies that they are to be beheaded, or mutilated in the limbs. Which St. Thomas noted opus. 28. art. 3, saying that that star is funerary, and indicates a monstrous ending of life. See what we said under V. Gorgonis caput. N. 1. NABION SCHALIAF, or also Nescussackat, according to Schiechard, is called in Chaldaic the constellation Lyra in the sky, of which much has been said. 2. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among the Arab Christians Plaustrum, as Kircher testifies in Oedipus, because the four more conspicuous stars in the Bear seem to represent no less a bier than a cart, the four wheels of which they make up entirely. Schiller, however, who took from this the occasion to transform all the celestial images and to name them from the names of the Saints, calls this same star Peter’s little ship. 3. NADIR among the Arabs signifies the point of the sky under the earth diametrically opposite to the vertex of our head, which they likewise call by their native word Zenith: so that both are

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LEXICON 316 veluti poli horizontis, & distent ab eodem hinc inde gr. 96. ac proinde necessario incidant in ipsum meridianum, Zenith quidem suptà tertam, Nadir autem sub terra. Et quam propositionem vnm eorum habeat ad æquatorem & alterum polorum Mundi, eandem vice versa habeat alterum ad oppositum polum, & aduetiam æquatoris partem. 4. NAHAR, ALCHARNER teste Kirchero in Oedipo arabice dicitur Fluuius Eridanus sidus ad australem plagam constans stellis triginta tribus, de quo plura diximus suo loco. 5. NAKIS CETI seù etiam Mandibula Ceti vulgò dicitur steila fixa secundæ magnitudinis valdè præsignis, de natura Saturni, existens in rictu Ceti, atque in longitudine sub gr. 10. Tauri arab. dicta Menchar. 6. NATIVITAS, Natalitium thema, seù etiam Natiuitatis figura dicitur vulgò apud Astrologos constitutio Cæli erecta ad punctum Natiuitatis alicuius hominis, aut etiam initium alicuius rei. Quale autem dicendum sit verum punctum Natiuitatis, disputatum est luculenter in V. Genesis. 7. NATURA, eisi secundum varias acceptiones plura significet, quæ ad nostrum institutum non pertinem, primo tamen loco, & ex sui notione appellat generationem viuentium ex insita sibi à Creatore vi naturaliter, hoc est nullatenus alterata, constituto sibi primitùs ordine p[ro]todeuntium: vnde dicta est Natura quasi Nascituræ, græcis autem expressiore vocabulo Physis & naturale dicitur quidquid non violentè, non casu, non artificiosè, non denique præter naturæ cursum emanat. Adeo vt iam Naturæ nomine proprie, & vniuersalissimè venjat congeries illa causarum secundarum, ex indita sibi à Creatore virtute necessariò operantium, quæ sui varietate pulcherrimum hunc rerum ordinem constituunt, atque à Deo ita præordinatæ sunt, vt nulla vi, nullo planè artificio, nullo humanæ voluntatis adminiculo ex se suos effectus promant, ac naturali ordine progrediantur: cuius admirabilem cursum demirans D. August. lib. 8. in Genesim. Quod enim, inquit mains, mirabiliusque spectaculum est, aut vbi magis cum rerum natura humana ratio quodammodo loqui potest, quam cùmpositis seminibus, plantatis surculis; translatis arbustulis, insitis malleolis, tanquam interrogatur quæque v[er]s radicis & germinis, quid possit, quidve non possit; vnde possit, vnde non possit? quid in ea valeat numerorum inuisibilis, interiorque potentia, quid extrinsecùs adhibita diligentia, inque ipsa consideratione perspicere, quia neque qui plantat est aliquid, neque qui rigat, sed qui incrementum dat Deus: quia & illud

Transcription: Translated (English)

LEXICON 316 like the poles of the horizon, and are distant from it on either side by 96 degrees. and therefore necessarily fall upon the meridian itself, the Zenith indeed being beneath the earth, and the Nadir beneath the earth. And in what proposition one of them has in relation to the equator and to the other pole of the World, the other in turn has the same in relation to the opposite pole, and also to the other part of the equator. 4. NAHAR, ALCHARNER, as Kirchero testifies in the Oedipus, is called in Arabic the River Eridanus, a star standing on the southern side, consisting of thirty-three stars, of which we have spoken more fully in its place. 5. NAKIS CETI, or also the Jaw of Cetus, is commonly called a fixed star of the second magnitude, very notable, of the nature of Saturn, situated in the mouth of Cetus, and in longitude under 10 degrees of Taurus, called in Arabic Menchar. 6. NATIVITY, the natal theme, or also the figure of Nativity, is commonly called among astrologers the configuration of the heavens erected for the point of someone’s nativity, or also the beginning of something. But what should be said to be the true point of Nativity has been clearly discussed in V. Genesis. 7. NATURE, although according to various acceptations it signifies many things, which do not concern our purpose, in the first place, and by its own notion, it denotes the generation of living things from the power implanted in them by the Creator, naturally, that is, in no way altered, proceeding from the order first established for them: whence it is called Nature, as it were from nascitura; and among the Greeks, by a more exact term, Physis; and natural is said of whatever arises not violently, not by chance, not artificially, not finally contrary to the course of nature. So much so that now under the name of Nature, properly and most universally, comes that collection of secondary causes, which, from the virtue implanted in them by the Creator, necessarily act; by their variety they constitute this most beautiful order of things, and are so preordained by God that from themselves they produce their effects by no force, by no artifice whatsoever, by no aid of human will, but proceed according to the natural order: at whose admirable course Saint Augustine marvels. lib. 8. in Genesis. For what, he says, is a more wonderful spectacle, or where can human reason speak, as it were, more with the nature of things, than when, seeds having been laid, shoots planted; saplings transferred, grafts inserted, as though every root and sprout were being questioned, what it can do and what it cannot; from where it can, from where it cannot? what in it is made effective by the invisible, inward power of numbers, what by diligence applied from without, and in the very consideration itself to perceive, because neither he who plants is anything, nor he who waters, but God who gives the increase: because also that

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MATHEMATICVM. 317 operis, quod accedit extrinsecus, per illum accedit, quem nihilominus creauit, & quem regit atque ordinat inuisibiliter Deus? Hinc iam in ipsum mundum velut in quamdam magnam arborem rerum oculus cogitationis attollitur, atque in ipso quoque gemina operatio prouidentia reperitur partim Naturalis, partim Voluntaria. Naturalis quidem per occultam Dei administrationem, quæ etiam lignis, & herbis dat incrementum, voluntaria verò per angelorum opera, & hominum. Secu[n]dum illam primam cælestia superiùs ordinari, inferiùsque terrestria, luminaria, sideraque fulgere, diei, noctisque vices agitari, aquis terram fundatâ interlui, atque circumlui, aërem altiùs superfundi, arbusta, & animalia concipi, & nasci, cresce, & senescere, occidere, & quidquid aliud in rebus interiori, naturalique motu geritur: In hac autem altera signa dari, doceri, & discere, agros coli, societates administrari, artes exerceri, & quaque alia, situe in superna societate aguntur, siue in hac terrena atque mortali, ita- vt benis consulatur, & per nescientes malos: inque ipso homine eandem geminam prouidentia vigere potentiam: primò erga corpus naturale scilicet eo motu quo fit: que crescit, quo senescit; voluntarium vero quoad victum, tegumentum, curationemque consulitur. Hucusque D. August. Ex quibus liquet, duo esse rerum principia; naturam, &c voluntatem; eaque ambo à Diuina prouidentia regi, promoueri, disponi, atque etiam superioti potentia impediri posse: Verum in suo cursu relicta Naturam necessariò operari, Voluntatem liberè, ac naturæ cursum disponere posse, coadiuare, & aliquatenus impedire hinc quæ à natura pure & absque voluntatis adminiculo prodeunt, naturalia; quæ à sola voluntate nihil subfamulante Natura, purè voluntaria: quæ verò à voluntate provt applicat actiua passuis, impedimenta remouet, naturam ipsam ad operandum disponit artificialia dicuntur Quod, & obseruauit ipsemet Augustinus paulò post subdèns: Sicut autem in arbore id quod agit agricultura forinsecus, ut illud proficiat, quod geritur (à natura) intrinsecus; sic in hemine secundum cerpus, ei quod intrinsecus agit natura, seruit extrinsecus medicina: quod autem ad arborem colendi negligentia, hoc ad corpus medendi incuria, hoc ad animam discendi sevnitia. Et quod ad arborem humor inutilis, hoc ad corpus victus exitiabilis, hoc ad animam persuasio iniquitatis. Porrò inter naturales causas principem sibilocum vendi. 8. cant corpora cælestia, quæ sua vniuersali potentia in omnia isthæc sublunaria agunt, suis influxibus producunt,

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MATHEMATICVM. 317 of a work which comes from outside comes through that which it has nevertheless created, and which God invisibly governs and orders? Hence now the gaze of thought is lifted up into the world itself, as into a certain great tree of things, and in it too a twofold operation of providence is found, partly natural, partly voluntary. Natural, indeed, through the hidden administration of God, which also gives increase to trees and herbs; voluntary, however, through the works of angels and of men. According to that first, the heavenly things are ordered above, and below the earthly things; lights and stars shine forth; the alternations of day and night are brought about; the waters, having the earth as their foundation, flow through and around it; the air is spread above; shrubs and animals are conceived, brought forth, grow, and grow old, die, and whatever else is done in things by an inward and natural motion. But in this other, signs are given, teaching and learning take place, fields are tilled, societies are governed, arts are practiced, and whatever other things, whether in the heavenly society or in this earthly and mortal one, are carried on so that the good may be cared for, and through the ignorant, the evil; and in man himself the same twofold power of providence is at work: first with respect to the body, naturally, namely in that motion by which it comes about that it grows, and by which it grows old; but voluntarily, inasmuch as food, clothing, and healing are provided for it. Up to this point St. Augustine. From these things it is clear that there are two principles of things: nature and will; and that both are governed, promoted, arranged, and even able to be hindered by a higher power, by divine providence. Yet, when left to their own course, Nature operates necessarily, Will freely, and can direct the course of nature, assist it, and in some measure hinder it; hence those things which proceed from nature purely and without the aid of will are called natural; those which come from will alone, with Nature serving nothing at all, are purely voluntary; but those which come from will insofar as it applies active to passive things, removes impediments, and disposes nature itself to act, are called artificial. This Augustine himself also observed a little later, adding: “As in a tree, that which agriculture does from outside works so that that may thrive which is produced within by nature; so in man, according to the body, medicine from outside serves that which nature does within: what neglect of cultivation is to a tree, that lack of care in healing is to the body; what bad watering is to a tree, that pernicious diet is to the body; what persuasion of wickedness is to the soul.” Moreover, among natural causes the heavenly bodies are reckoned in the first place, 8. which by their universal power act upon all these sublunary things, and by their influences produce them.

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318 LEXICON conseruant, immutant, alterant, perdunt: neque eorum actiuitas tolli vel impediri potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo, atque adeò vel ob id cæteris omnibus præstant. Benè verò potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Centiloquio Verbo 8, Sapiens anima, inquit, confert cælesti operations, quemadmodum optimus Agrico'a arando, expurgandoque confert Natura. Igitur non potest homo facere, vt Astras suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuertere. 9. Sic non potest homo vllò modo Eclipsim futuram impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Martis sequuturum præuertere, nives, pluuias, ventos, aëris infectiones, &c. potest autem in naturis inferioribus, vt ædificando super solum, ne herbas getminet, exsiccan- do stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subfamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt fecit Ioseph Patriarcha) magnam frumenti vim in horrea comportare, in bonis siderum configurationibus terram excolere, matia exsulcare; in malis domi consistere, atque à labore inutili abstinere, &c. Concludam igitur cum iis quæ appositè ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, actus virtutum aut vitiorum: alia mixta, vt facere iter, comedere, &c. Vtrum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpore nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu serio

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318 LEXICON preserve, change, alter, destroy: nor can their activity be taken away or hindered by human will, or by any inferior causes, but only by the First Cause, God; and therefore for that reason also they excel all others. Yet man can indeed, by understanding their nature, qualities, effects, and unchangeable power of acting, cultivate them in inferior things, apply them, anticipate them, and turn them aside, as Ptolemy said in the Centiloquium, Saying 8: “The wise soul,” he says, “contributes to celestial operations, just as the best farmer does by ploughing and clearing the ground to Nature.” Therefore man cannot make his stars fail to exercise their natural powers, not produce their proper effects, or divest themselves of the harmful or beneficial qualities which they intrinsically possess and take on contrary ones; but he can in some measure, in inferior causes, by altering, hindering, or even destroying them, altogether avert their effects. 9. Thus man cannot in any way prevent a future eclipse, nor the effects naturally flowing from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, nor snow, rain, winds, infections of the air, etc. But he can, in inferior natures, by building over the ground so that grass does not sprout, by drying up ponds so that they do not corrupt the air, by cutting down trees so that they do not bear fruit. So too, by cooperating with the stars, he can contribute to their operation, as by supplying matter or removing it; by guarding himself against the evil influences of the stars, by preparing for good ones, arranging matters, and making himself susceptible at the time of foreseen sterility (as the Patriarch Joseph did), by storing up a great quantity of grain in granaries; in good configurations of the stars, by cultivating the land, by dredging the sea; in bad ones, by staying at home and refraining from useless labor, etc. I shall therefore conclude with what Kircher aptly says on this matter in his Magnes sive de Arte Magna Lucis et Umbrae, book 6, part 3, chapter 2. Nature, he says, is governed by two principles: nature and will. Nature is subject to the stars; will is free. And therefore effects and operations that are purely natural obey the stars entirely as necessary causes, such as health or sickness; the long or short life of men, etc. Others are purely voluntary, such as looking, teaching, acts of virtues or vices; others are mixed, such as making a journey, eating, etc. But whether a journey will be convenient or not depends on the stars and on the constitution of the air. If anyone therefore perfectly knew the influences of the stars as they agree with or disagree with our body, he would undoubtedly seriously

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MATHEMATICVM. 519 iudicare posset: item desanitare, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAVBARACH, siue Naubahar arab. idem sonat, ac No- 10. uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans 11. stellis 63. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Mar- cheb in medio scuti posita. Hoc sidus à schillero immutatum fuit in Arcam Noë. Hebraicè autem dicitur Se- phina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, 13. pallenti, & suboscuro micantes: eò dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt duæ magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebulosum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequi- tur aculeum scorpij. Idque, vt obseruat Titus lib.1. cap.12. quia earum nebulositas parem, & consumilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vi- tium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum lucem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos deri- uatur congressu fiant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIUM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Ciceroni, & aliis idem est, ac Scorpij fidus fortè à 16.

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MATHEMATICVM. 519 one could judge; likewise to heal, concerning illness, &c. Likewise concerning the success of a business with a prince. But since these things can scarcely be done, and knowing them from this, the knowledge of these elections, unless supported by experience, is for the most part deceptive. Thus Kircher. From which it is clear what art, or human ingenuity, can do, what Nature can do, what man, having properly learned the nature of things, may undertake, and finally what he undertakes in vain, and what even rashly. NAVBARACH, or Naubahar in Arabic, has the same meaning as “Lord of the Nine Villas.” See in V. Anaubarach. NAVIS, commonly called the constellation situated on the southern side, consisting of 63 stars, as is clear from the most accurate observations of the new astronomers, almost all of Saturnian and lunar nature, the chief of which is Canopus, standing in the rudder of the first magnitude, Arabic Rubail, to which very near is the said Marcheb, placed in the middle of the shield. This constellation was changed by Schiller into Noah’s Ark. In Hebrew, however, it is called Sephina. NEBOLASSID, among the Fezzans, Moroccans, and other Nubian astrologers, is called the Tail of the Lion, a fixed star of the first magnitude, of which enough has been said in its place. NEBULOUS STARS are certain fixed stars shining with a dim, pale, and somewhat obscure light: so called either because they present by their appearance certain mists, as are especially the two large and quite conspicuous ones near the Antarctic pole, or indeed because they generate mists, and when setting with the sun make the air cloudy, as Ptolemy and Pliny observed, in the Praesepe, situated in the breast of Cancer, in that which is in the eye of Sagittarius, but especially one may see it in that which follows the sting of Scorpio. And this, as Titus observes, lib. 1, cap. 12, because their nebulousness produces a similar and like effect in these lower regions. Hence it has also been learned by experience that whenever they come together with the Luminaries in anyone’s nativity, they always bring redness, mist, or some other defect in the eyes; which natural reason itself suggests, for their light is very slight and weak, and therefore it is no wonder if they take away or dull the light of the eyes, when they become hostile to the very luminaries from which light is conveyed into the eyes. NEMER, that is, Pardus, in the Hebrew tongue, is called the Wolf-star, of which elsewhere mention has been made. NEOMENIUM in Greek means the same as New Moon, of which below at once. NEPA, in Cicero and others, is the same as the star of Scorpio, perhaps from ...

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520 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum lingua dicitur Cancer aliud sidus, quod in nominibus sæpe cum Scorpione confunditur. 19. NESCHER, Hebraicè dicitur Aquila. 20. NIGEAR, (teste lunctino in Sphætam Io: de Sacrobosco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & concipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboscuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Adducit etiam nebulas, nimbos, glacies, niues, & in hominibus Saturninis solitudinis, austeritatis, inuidiæ, obstinationis, auaritæ incitamentum, & incrementum. 22. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach, id est circulus signorum diuiditur in duodecim partes æquales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus 23. NITVRA, pro Genitura, seù Natalitio Themate per Apocopen sæpissimè ab aliquibus vsurparur. Vide Isidorum. 24. NOCTURNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiux, quales sunt humiditas, & siccitas: sicut è contrà Diurna dicuntur signa & planetæ in quibus abundant qualitates actiæ: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclipticam in duobus punctis oppositis, & Nodus quidem boreus dicitur punctum in quo Planera è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euehens; atque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porrò Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibiliter mouentur; inferiorum verò non

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520 LEXICON Chelis dictum; for the same reason also. 18. NEPA, in the African language, is said of Cancer, another star, which is often confused in names with Scorpio. 19. NESCHER, in Hebrew, means Eagle. 20. NIGEAR, (according to Iunctinus in the Sphere of Io. de Sacrobosco) is called by Arabic writers the axis of the world, which ends at its poles, and is conceived to pass through the center of the earth. See under V. Axis. 21. NIGRA, or Niger, is the name given to a certain kind of comet of black color, or rather leaden and somewhat dim, by nature and condition Saturnine, and therefore, in color as well as in qualities, wholly like him. For when it appears it signifies scarcity of the year, long-lasting locusts, and other harmful animals of that kind, pestilence, chronic fevers, etc. It also brings fogs, storms, ice, snow, and in Saturnine men an incitement and increase of solitude, austerity, envy, obstinacy, and avarice. 22. NITACH, in Arabic, or rather in Chaldean, signifies the Zodiac and the circle of the signs. Hence Alchabitius thus begins his book: Nitach, that is, the circle of the signs, is divided into twelve equal parts, etc. See what is to be said more fully under V. Zodiacus. 23. NITVRA is very often used by some, by apocope, for Genitura, or Nativity figure. See Isidore. 24. A NOCTURNAL sign, or even a planet, is one in which passive qualities predominate, such as humidity and dryness: just as, on the contrary, signs and planets in which active qualities abound are called diurnal; on this matter see what we have said under V. Diurnus. 25. NODES are called by astronomers the intersections of the orbits of the sun and of each of the planets having latitude, namely where the orbits of the planets cut the Ecliptic at two opposite points; and the northern node is indeed called the point at which a planet passes from southern latitude into northern, but the southern one where it descends from north to south. They are also so called from the form they resemble, the head and tail of the Dragon; also the ascending, or lifting, and the descending. Moreover, where the planets have the greatest latitude it is called the belly of the Dragon, because there too it is broader in the belly than at the extremities. Furthermore, these nodes change their place in the Zodiac, just as the planets themselves do, but they move contrary to the succession of the signs. And indeed the nodes of the three superior planets move imperceptibly; but those of the inferior do not

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MATHEMATICVM. 127 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliæis nodi maximam significationem quoad formam corporis, quam plerumque deturpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis, vel curuis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, contorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. N NASPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem cursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalitatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltró citróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgare illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re vide Clauium, & Blancanum in sphæra mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem mobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnco tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Mores. NOTA PELIOTES ventus est vnsus ex quatuor intermediis 13. X

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MATHEMATICVM. 127 not likewise, but about each single one, nearly a minute; indeed the lunar nodes, as to their own minutes, as is clear in Ephemerides and tables of second movable bodies. In genethliacal matters the nodes have the greatest significance with regard to the shape of the body, which they usually disfigure, if they are found with the luminaries or the unfortunate planets, especially in the angles and in the truncated or curved signs, such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Whence the natives will turn out hunchbacked, squint-eyed, lame, twisted, or in whatever way weakened, as Ptolemy has in book 3, chapter 17. N NASPHÆRA is commonly called the Primum Mobile, which is situated above the eighth sphere, or the heaven of the stars, which carries along with itself all the lower spheres from east to west, completing its revolution with the swiftest course in a space of nearly 24 hours. Others, however, admit this ninth sphere as distinct from the Primum Mobile, and indeed also a Tenth, which they call of libration or trepidation, which they see in the firmament. For they observed that it, besides the motion of the whole and its proper motion, moves irregularly from north to south and from south to north under the solstitial colure of the first mobile, back and forth; again moving from east to west and from west to east under the ecliptic and over its poles. Therefore, since so many motions are found in the firmament, and also in the planets, and since they say that not even the two motions just explained can be had from themselves or from the first mobile, by that common axiom that one simple body by its nature can be moved inwardly by only one simple motion, but externally by several, consequently they also admit this ninth sphere, which causes motion from east to west, and from west to east over the poles of the Zodiac in 14 minutes over a span of 1716 years, as they say; and again the Tenth, which they say causes motion from north to south under the colure of the solstices by 24 minutes in a span of 3432 years. On this matter see Clavius and Blancanus in the Sphere of the World, book 18, c. 7. But I for my part cannot in any way admit these distinct motions, and therefore distinct spheres, since it is repugnant for one and the same mobile to be moved by two contrary motions, in which case motions of this sort would be trepidations, which are altogether fictitious, and the appearances of the stars, irregularities, etc., are excellently preserved in the mere fluxibility of the heavens, and in a single motion only from east to west, though regularly irregular according to all the parts of heaven, farther and farther removed from the first moving virtue. See what we have discussed at length in V. Mores. NOTE PELIOTES is a wind, one of the four intermediate ones 13. X

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ad conseruationem species. & alimento ad conseruationem indiuidui: & propter hoc in istis inferioribus non inuenitur vita sine anima vegetabili, sed hoc non habet locum in incorruptibilibus: & art. 1. in responsione ad primum argumentum, quo inferebatur omnium rerum naturalium proprium esse viuere; vltrò facetur, quod si totum vniuersum corporale esset unum animal, ita quod iste motus esset amouente intrinseco, vt quidam posuerunt, sequeretur, quod motus esset vita omnium naturalium corporum. Similiter ratio sensus impertinens est ad vitam, & potius passio de imperfectio, quam perfectio. Ait enim Philosophus, in lib. de Somno, & Vigilia, quod iis conuenit sensus, in quibus est tristari, & gaudere, contupiscere, & odisse: plantis autem nihil horum inesse, vnde conuenienter iis à Natura inditus non est sensus: supra quod D. Thomas in commento. Complexio, inquit, plantarum in nutrimento, & augmento, & his similia melius fiunt sine sensu, quam cum sensu: ergo planta non habent sensum, cum naturæ semper faciat quod melius est. Cum igitur isti gradus vitæ potius sint imperfectiones, & defectus naturæ, quam perfectiones, & Sol, Altra, & mundus non indigeant generatione, & nutritione ad conseruationem speciei vel indiuidui, & adhuc non habeant aliquod ad sui esse conducens, vel ad sui esse contrarium, quod amore prosequi debeant, aut odio; iure illis à Natura neque sensu, neque vegetatione prouisum, sed solum vitâ quadam superiore, quæ omnem vitam inferiorum eminenter contineat, & colligitur ex motu perfectissimo, qui est circularis, & ab intrinseco, potens naturaliter in æuum protrahi, & motum cæteris viuentibus participare. Alloquin si gradus huiusmodi vitæ, vegetatio inquam & sensatio absolutè, & simpliciter dicerent rationem vitæ perfectiorem, quæ non in aliquo eminentet conrineretur, posset etiam dici, quod vita hominis est perfectior vita Angeli, quia viuit, nedum intellectualiter, vt ille, sed adhuc vita sensu sua; & vegetabili. Sicut igitur vita Angeli est perfectior vita hominis, etiamsi non sit vegetabilis, & sensibilis, ita etiam vita Muudi est perfectior omnibus viuentibus inferioribus; atque adeo plantis, & animalibus, etiamsi sensum, & vegetationem non habeat. Qui quidem gradus vitæ in talibus viuentibus dicunt perfectionem, at non in superioribus, quæ tali modo viuendi non indigent. Igitur pro coronide huius nobilissimæ Controversiæ, concludendum est; vniuersum hoc vnum quid esse, per se

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for the preservation of the species, and nourishment for the preservation of the individual; and for this reason, in these lower things, life is not found without a vegetative soul; but this does not hold in incorruptible things. And art. 1, in the response to the first argument, by which it was inferred that it belongs to all natural things to live; it will be answered further that, if the whole corporeal universe were one animal, so that this motion were from an intrinsic mover, as some have held, it would follow that motion would be the life of all natural bodies. Likewise, the notion of sense is irrelevant to life, and rather a passion, of an imperfection than a perfection. For the Philosopher says, in book De Somno et Vigilia, that sense belongs to those in whom there is sadness and joy, desire and hatred; but plants have none of these things, whence consequently sense was not imparted to them by Nature. On this D. Thomas in the commentary: The constitution, he says, of plants in nourishment and growth and things of that sort is better accomplished without sense than with sense; therefore plants do not have sense, since nature always does what is better. Since, then, these degrees of life are rather imperfections and defects of nature than perfections, and the Sun, Altra, and the world do not need generation and nourishment for the preservation of species or individual, and still have nothing conducive to their being, or contrary to their being, which they ought to pursue with love, or hate; by right, therefore, Nature has provided for them neither sense nor vegetation, but only some higher life, which eminently contains every life of lower things, and is gathered from the most perfect motion, which is circular, and from within, naturally able to be prolonged into eternity, and to share motion with other living things. Otherwise, if such grades of life, I mean vegetation and sensation, were said absolutely and simply to constitute a more perfect life, which were not eminently contained in something else, it could also be said that the life of man is more perfect than the life of an Angel, because he lives, not only intellectually, as the Angel does, but still by life through sense and vegetation. Therefore, just as the life of an Angel is more perfect than the life of man, even though it is not vegetative and sensitive, so also the life of the World is more perfect than all lower living things; and therefore than plants and animals, even though it does not have sense or vegetation. These grades of life in such living things signify perfection, but not in higher beings, which do not need to live in such a way. Therefore, as the crown of this most noble controversy, it must be concluded: that this universe is one thing, by itself

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MATHEMATICVM. 313 subsistens, sua vniuersali forma præditum, eâque substan- tiali, & perfectissimâ, quæ det quidem toti, cunctisque eius partibus, atque animantibus vitam, non tamen ipsum nun- dum, aut præcipuas eius partes, nempe cælum, sidera, ele- menta, animantes denominet: & quia sensu, & vegera- tione carent, proindeque, vt ait Conc. Constantinop. om- ninò animantes non sunt, Non tamen ex hoc sequitur vi- tam Mundi præcipuarumque eius partium non esse cæteris viueniibus, etiam ipso homine secundum gradus vegeia- tionis, nurrieationis, & sensationis, superiorem, atque vni- uersaliorem; non autem secundum gradum intellectui, in quo homo spiritualis est; ac minimè à cælorum Influxibus pender. Viuit ergo Mundus, cælum, sidera, gradu quodam vitæ superiore, cui profectò parem, aut similem in inferio- ribus hisce non sit inuenire: sed omnis ipsorum vitæ ratio, & gradus eminenter in vita mundi est, & ab ipsa tanquam vniuersali, & æquiuoca causa deriuat; vnde est etiam vir- tus ad causandam hanc rerum varietatem. Et hoc, vt benè habet D. Th. 1. part. 9. 10. art. 3 inquantum hac (seilicet cælestia corpora) vniuersali virtute co[n]tinet in se quidquid in inferioribus generatur & quia (vt paulo ante dixerat) quid- quid in istis inferioribus generat & mouet ad speciem, est in- strumentu cælestis corporis. I girur cælestia corpora sunt causæ superiores, ac principales vitæ, omnisque motionis infe- riorum ad certas species: & quà talia in se ipsis eodem, sed longè nobiliore gradu vitæ prædita sint, necesse est. MVNIR, seù, vt alij legunt, MUMIR, Arabicè dicitur quasi pu- <96.> pilla lueida Coronæ Gnostiæ, Stella fixa secundæ magnitudi- nis de natura veneris, & Mercurij, quâ ob sui pulchritudine verisque apperitionem quam ortu suo facit cæli pupillam, serium aperitionem que dixerunt. Vide fusiùs in V. Corona. MVSATUR, dicitur à Cicerone sagitta sidus apud Aquilam <97.> constans stellis quinque de quibus vide in V. Sagitta. MVSCA, seù, Apis sidus in cælo ad polum Antarcticum no- <98:> bis inuisum, & nuper à nouis Astronomis ad Australes pla- gas appulsis cum aliis vndecim obsecuarum, continens qua- tuor stellas infimæ notæ: Est nunc in longitudine sub signo Scorpij incidens in ipsum Antarcticum circulum: Apud In- dos MUA. MVSCIDA EQVR, Arabicè Alpheratz, vulgò dicitur stella <99.> fixa ictiæ magnitudinis in dictu Pegasi existens, de natura mixta Marris, Iouis, & Veneris de qua vide iam dicta in V. Alpheratz. MVSTCA, vna est ex quatuor præcipuis Mathesis diuisio- <100>

Transcription: Translated (English)

MATHEMATICVM. 313 subsisting, endowed with its universal form, and that substantial and most perfect form which indeed gives life to the whole and to all its parts and living creatures, yet does not thereby denote the heavens themselves, or their principal parts, namely the sky, stars, elements, and living creatures: and because they lack sense and growth, and therefore, as the Council of Constantinople says, are altogether not living creatures, this does not however follow, namely that the life of the World and of its chief parts is not superior to all other living things, even to man himself according to the degrees of growth, nourishment, and sensation, and more universal; though not according to the degree of intellect, in which man is spiritual; and least of all dependent on the influences of the heavens. Therefore the World, the heaven, the stars, live by a certain higher degree of life, to which indeed no equal or similar thing is to be found in these lower things: but all the account and degree of their life is eminently in the life of the world, and derives from it as from a universal and equivocal cause; whence also comes the power for causing this variety of things. And this is, as St. Thomas rightly has it, 1 part. 9. 10. art. 3, insofar as these things (namely the heavenly bodies) contain in themselves by a universal power whatever is generated in the lower things; and because (as he had said a little before) whatever in these lower things generates and moves toward species is the instrument of the heavenly body. Therefore the heavenly bodies are higher causes, and principal causes of life, and of all movement of inferior things toward certain species; and as such, it is necessary that in themselves also they be endowed with the same life, but in a far nobler degree. MVNIR, or, as others read, MUMIR, is said in Arabic to mean, as it were, the bright pupil of the Gnostic Crown, a fixed star of the second magnitude, of the nature of Venus and Mercury; because of its beauty and the true openings which it makes by its rising, they called it the pupil of the sky, and also the opening of the “serium.” See more fully under V. Corona. MVSATUR, Cicero calls the star in Sagittarius, standing by Aquila, consisting of five stars; see under V. Sagitta. MVSCA, or Apis, is a constellation in the sky near the Antarctic pole, invisible to us, and recently, when new astronomers arrived at the southern regions along with eleven other obscure ones, containing four stars of the lowest magnitude. It is now in longitude under the sign of Scorpio, falling upon the Antarctic circle itself. Among the Indians: MUA. MVSCIDA EQVR, in Arabic Alpheratz, is commonly called a fixed star of the second magnitude, existing in the so-called Pegasus, of mixed nature of Mars, Jupiter, and Venus; see what was said above under V. Alpheratz. MVSTCA is one of the four principal divisions of mathematics. <100>

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LEXICON 314 nibus Arithmeticæ subalterna, facultas nempe, vt inquit Boëthius, quæ multitudine ad aliud relata rationes nume- rales concretas habet ad sonos & voces. Dicta est à Græ- co verbo Mos, quod æquam rationem, atque harmoniam sonat; vel potiùs à Musis, quibus olim familiaris erat. Ha- bet pro obiecto numerum seu quantitatem discretam provt ad alteram relatam: confert enim temporis momenta ad sonorum modules, & inde eos artificiosè nectit, & copu- lat, vt dulcissima harmonia, atque ordinatissimum melos auribus nostris insonet. Eius nobilitatem vel inde licet colligere, quod in diuinis laudibus decantandis, Numine- que propitlando, ab ipso religionis exordio ad hæc vsque tempora religio è sit semper adhibita: vnde Iobi 38. dicitur: Vbi eras quado ponebam fundamenta terra: cum me lau- darent simul astra matutina, et iubilarent omnes Filij Dei? Adeo vt de ipso Dite referant Fabulæ Poëtarum, quod sit Orphei cantibus emollitus: Nec mirùm, cum eius ordo vt ælestis Hierarchiæ symbolum est, ita & inferis illatus vbi nullus ordo est, sed confusio, eorum conditionem anteuer- tere satis est. Porrò quanta sit Musices efficacia in immu- tandis affectibus, ac passionibus animi mitigandis, lucu- lenter explicat Seneca: Cassiodorus, & Augustinus, qui lib. contra Iulianum, Ciceronis testimonium adducens, refer[en]t Pithagoram spondeum in sono canentem tarditate modo- rum, & grauitate eantus furentem aliquorum iuuenum pe- tulantiam abegisse: & iure quidem, nam ars hæc ita ani- mas sibi reddit intentas, vt quemadmodum loquitur Cassio- dorus,) nil aliud cogirare possint; sed deposita omni cura mentis induant grauitatem. Hinc ob diversas animorum commotiones, quas suis mo- <101> dulis suscitare potest Diuina isthæc facultas, quatuor melo- dix species distinxit Philosophus ad diuersos affectus ten- dentes- Mistolidiscam, quæ ad compassionem mouet; Li- discam, quæ animos emollit ad concupiscentiam: Doriscam, quæ meniem erigit ad fortitudinem, atque virilitarem: & Frigiscam, quæ rigidior cæteris incitat ad dura consilia, pro- mouetque seueritatem. Habet etiam tonos, diuersasque consonantiarum dissonantiarumque rationes, quas Dia- tesseron, Diapente, Diapason appellant: ac similiter tria melorum genera Diatonieum, Chromaticum, Enharmoni- cum, de quibus omnibus, aliisque Musices diuisionibus, vide Ficinum in Platonis Conuiuio Orat. 3. cap. 4. Guidonem, & Iacobum Fabrum in Elemen. Music. lib. 3. ß 4 Nobis eas tetigisse sufficiat.

Transcription: Translated (English)

MUSIC is a subalternate science of Arithmetic, namely, as Boethius says, that faculty which, by relation to another thing, has numerical ratios applied to sounds and voices. It is called from the Greek word mos , which signifies an equal ratio and harmony; or rather from the Muses, with whom it was once familiar. It has for its object number, or discrete quantity, as related to another thing; for it combines the moments of time with the measures of sounds, and thence skillfully joins and unites them, so that the sweetest harmony and the most ordered melody may sound in our ears. Its nobility may also be gathered from the fact that, in chanting divine praises and appeasing the Godhead, it has been used from the very beginning of religion down to these times; hence in Job 38 it is said: “Where wast thou when I laid the foundations of the earth, when the morning stars praised me together, and and all the sons of God shouted for joy?” So much so that the poets’ fables tell of Dis himself, that he was softened by Orpheus’ songs. Nor is this surprising, since its order, as a symbol of the heavenly hierarchy, is also brought into hell, where there is no order but confusion, and is enough to overcome their condition. Moreover, how great Music’s power is in changing the emotions and calming the passions of the mind is clearly explained by Seneca, Cassiodorus, and Augustine, who in the book against Julian, adducing Cicero’s testimony, relate that Pythagoras, singing the spondean mode, by the slowness of the measures and the gravity of the song drove away the rashness of certain young men in a frenzy; and rightly so, for this art so draws souls to itself that, as Cassiodorus says, they can think of nothing else, but, having laid aside every care, they put on seriousness. Hence, because of the various movements of the mind which this divine faculty can excite by its measures, the Philosopher distinguished four kinds of melodic modes tending to different affections: the Mixolydian, which moves to compassion; the Lydian, which softens minds toward desire; the Dorian, which raises the mind to fortitude and manliness; and the Phrygian, which, being harsher than the others, incites to stern counsels and promotes severity. It also has tones and various relations of consonances and dissonances, which they call Diatesseron, Diapente, and Diapason; and likewise the three kinds of melodies, Diatonic, Chromatic, and Enharmonic. Concerning all these, and other divisions of Music, see Ficino in Plato’s Symposium , Oration 3, chapter 4; Guido; and Jacobus Faber in Elementa Musicae , book 3, section 4. It is enough for us to have touched upon them here.

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MATHEMATICVM. MVTA SIGNA sunt quæ præseferunt figuram Animalium 102 voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raucâ dicuntur, brutorum videlicet vocalium formam habentia, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio habetur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. MVTAII arab. idem sonat ac larinè agglutinatus; cum vi- 103 delicet Planeta ita est alteri iunctus, vt nec in minuto qui- dem aberret. Hoc vocabulo frequenter vtitur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. MVTLVM arab. Vide in V. Motlatum. 104 MVTLATA SIGN. sunt quæ membrum aliquod seù etiam 105 corpus murilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruar Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt ferè semper inducant membrorum incisionem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem posteà misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agit, In signis mutilis, inquit, aut quorum figurà sunt imperfe- cta, aut circà caput Medusa Mars significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opus. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. NABLON SCHALIAE seù etiam Nescussackat teste schie- 1. chardo Chaldaicè dicitur Lyra sidus in Cælo, de quo sæ- pius dictum est. NAASCH LAAZAR hoc est Feretrum Lazari dicitur apud 2. Christianos arabes Plaustrum, vt testatur Kircherus in Oe- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Vr- sa, quæ quatuor plaustri totas effingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, atque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. NADIR apud Arabes significat punctum Cæli sub terra 3. oppositum diametraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant; itavt ambo sint

Transcription: Translated (English)

MATHEMATICVM. MUTE SIGNS are those which present the figure of voiceless animals, such as Cancer, Scorpio, and Pisces; whereas, on the contrary, those having a voice are said to be either human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, or feral, which are also called hoarse, namely those having the form of vocal beasts, as Aries, Taurus, Leo, Capricornus. The greatest consideration of these is had in Genethliacs, with regard to defects and impediments of the tongue, concerning which see Ptolemy, lib. 3 of the Quadripartitum, cap. 17. MUTAAI, in Arabic, sounds the same as larinè agglutinatus; namely when a planet is so joined to another that it does not depart even by a minute. Ptolemy frequently uses this word in the Quadripartitum from the Arabic version, and also Haly, his commentator. MUTLVM, Arabic. See under V. Motlatum. MUTLATA SIGNS are those which represent some limb or even a mutilated body, as Taurus, the division of the Horses, the Head of Medusa; these, as Titus has well observed in Cælestial Philosophy, lib. 2, cap. 3, have this nature and power of influence, that they almost always bring about cutting off of limbs, if, with the rulers of life unfortunately positioned in the Nativity, they are afterward joined by direction. Hence Ptolemy in the Quadripartitum, lib. 4, cap. 10, where he treats of the kind of death, says: In mutilated signs, or those whose figure is imperfect, or around the Head of Medusa, Mars signifies that men shall be beheaded or mutilated in their limbs. This St. Thomas observed, opus. 28, art. 3, saying that that star is funereal and indicates a monstrous termination of life. See what we have said under V. Gorgon's head. N. NABLON SCHALIAE, or also Nescussackat, according to Schiechard, is in Chaldaic called the constellation Lyra in the sky, of which much has already been said. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among the Christian Arabs the Wagon, as Kircher testifies in Oedipus, because the four most conspicuous stars in the Bear seem no less to represent a wagon than a bier, and they form the entire wagon. Schiller, however, who took from this the occasion to transform all the heavenly figures and to name them after the names of saints, calls this same star Peter's Boat. NADIR among the Arabs signifies the point of the sky beneath the earth, diametrically opposite the vertex of our head, which they likewise call by their own gentile word Zenith; so that both are

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316 LEXICON veluti poli horizontis, & distent ab eodem hinc inde gr. 90. ac proinde necessario ineidant in ipsum meridianum, Zenith quidem supra terram, Nadir autem sub terra. Et quam propositionem vnmineorum habeat ad æquatorem & alterum polorum Mundi, eandem vice versa habeat alterum ad oppositum polum, & aduersam æquatoris partem. 4. NAMAR, ALCHARNER teste Kirchero in Oedipo arabice dicitur Fluuius Eridanus sidus ad australem plagam constans stellis triginta tribus, de quo plura diximus suo loco. 5. NAEIS CETI teù etiam Mandibula Ceti vulgò dicitur steila fixa secundæ magnitudinis valdè præsignis, de naturæ Saturni, existens in rictu Ceti, atque in longitudine sub gr. 10. Tauri arab. dicta Menchar. 6. NATIVITAS, Natalitium thema, seù etiam Natiuitatis figura dicitur vulgò apud Astrologos constitutio Cæli erecta ad punctum Natiuitatis alicuius hominis, aut etiam initium alicuius rei. Quale autem dicendum sit verum punctum Natiuitatis, disputatum est lueulenter in V. Genesis. 7. NATURA, etsi secundum varias acceptiones plura significet, quæ ad nostrum institutum non pertinem, primo tamen loco, & ex sui notione appellat generationem viuendum ex insita sibi à Creatore vi naturaliter, hoc est nullatenus alterata, constituto sibi primitùs ordine prodeuntium: vnde dicta est Natura quasi Nascitura, græcis autem expressiore vocabulo Physis & naturale dicitur quidquid non violentè, non easu, non artificiosè, non denique præter naturæ cursum emanat. Adeo vt iam Naturæ nomine proprie, & vniuersalissimè veniat congeries illa causarum secundarum, ex indita sibi à Creatore virtute necessariò operantium, quæ sui varietate pulcherrimum hunc rerum ordinem constituunt, atque à Deo ita præordinatæ sunt, vt nulla vi, nullo planè artificio, nullo humanæ voluntatis adminiculo ex se suos effectus promant, ac naturali ordine progrediantur: cuius admirabilem eursum demirans D. August. lib. 8. in Genesim. Quod enim, inquit manus, mirabiliusque spectaculum est, aut ubi magis cum rerum natura humana ratio quodammodo loqui potest, quam cùmpositis seminibus, plantatis surculis; translatis arbustulis, insitis malleolis, tanquam interrogatur quæque v[er]s radicis & germinis, quid possit, quidve non possit; vnde possit, vnde non possit? quid in ea valeat numerorum inuisibilis, interiorque potentia, quid extrinsecùs adhibita diligentia, inque ipsa consideratione perspicere, quia neque qui plantat est aliquid, neque qui rigat, sed qui incrementum dat Deus: quia & illud

Transcription: Translated (English)

316 LEXICON like the poles of the horizon, and are distant from it on either side by 90 degrees; and therefore necessarily fall upon the very meridian, the Zenith indeed above the earth, but the Nadir beneath the earth. And as the same proposition has with the equator and the other poles of the world, so conversely the other has with the opposite pole and the opposite part of the equator. 4. NAMAR, ALCHARNER, according to Kircher in Oedipus, is said in Arabic to be the River Eridanus, a constellation on the southern side consisting of thirty-three stars, of which we have spoken more fully in its place. 5. NAEIS CETI, or also commonly called the Jaw of Cetus, is a very notable fixed star of the second magnitude, of the nature of Saturn, existing in the mouth of Cetus, and in longitude under 10 degrees of Taurus; in Arabic it is called Menchar. 6. NATIVITY, the natal figure, or also the figure of the birth is commonly called among astrologers the constitution of the heavens erected for the point of the nativity of some man, or also the beginning of some thing. What, however, should be called the true point of nativity has been discussed at length in V. Genesis. 7. NATURE, although according to various meanings it signifies many things, which do not concern our present purpose, nevertheless in the first place, and from its own notion, it denotes generation by means of the natural power innate in itself from the Creator, that is, in no way altered, proceeding according to the order first established for it: whence it is called Nature as if Nascitura, but in Greek by the more exact term Physis; and natural is called whatever does not proceed violently, not by chance, not artificially, nor finally beyond the course of nature. So that now under the name of Nature there properly and most universally comes that assemblage of secondary causes, operating necessarily by the power indited to them by the Creator, which by their variety constitute this most beautiful order of things, and have been so preordained by God that by no force, by no artifice whatever, by no assistance of human will do they of themselves bring forth their effects, but proceed in a natural order: at whose admirable course Saint Augustine marvels, book 8 on Genesis. For, he says, what more wonderful spectacle is there, or where can human reason more suitably in some manner speak with the nature of things, than when, after seeds are placed, slips planted; saplings transplanted, cuttings grafted, as though each thing is asked concerning the power of root and shoot, what it can do and what it cannot; whence it can, whence it cannot? what the invisible and inner power of numbers has in it, what the diligence applied from without, and in that very consideration perceive, because neither he who plants is anything, nor he who waters, but God who gives the increase: because also that

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MATHEMATICVM. 317 operis, quod accedit extrinsecus, per illum accedit, quem nihilominus creauit, & quem regit atque ordinat inuisibiliter Deus? Hinc iam in ipsum mundum velut in quamdam magnam arborem rerum oculus cogitationis attollitur, atque in ipso quoque gemina operatio prouidentia reperitur partim Naturalis, partim Voluntaria. Naturalis quidem per occultam Dei administrationem, quæ etiam lignis, & herbis dat incrementum, voluntaria verò per angelorum opera, & hominum. Secundum illam primam cælestia superiùs ordinari, inferiùsque terrestria, luminaria, sideraque fulgere, diei, noctisque vices agitari, aquis terram fundatâ interlui, atque circumlui, aërem altiùs superfundi, arbusta, & animalia concipi, & nasci, crescere, & senescere, occidere, & quidquid aliud in rebus interiori, naturalique motu geritur: In hac autom altera signa dari, doceri, & discere, agros coli, societates administrari, artes exerceri, & quoque alia, situe in superna societate aguntur, siue in hac terrena atque mortali, ita- vt bonis consulatur, & per nescientes malos: inque ipso homine eandem geminam prouidentia vigere potentiam: primò erga corpus naturale scilicet eo motu quo fit, quo crescit, quo senescit; voluntarium vero quoad victum, tegumentum, curationemque consulitur. Hucusque D. August. Ex quibus liquet, duo esse rerum principia; naturam, & voluntatem; eaque ambo à Diuina prouidentia regi, promoueri, disponi, atque etiam superiori potentia impediri posse: Verum in suo cursu relicta Naturam necessariò operari, Voluntatem liberè, ac naturæ cursum disponere posse, coadiuare, & aliquatenus impedire hinc quæ à natura pure & absque voluntatis adminiculo prodeunt, naturalia; quæ à sola voluntate nihil subfamulante Natura, purè voluntaria: quæ verò à voluntate provt applicat actiua passuis, impedimenta remouet, naturam ipsam ad operandum disponit artificialia dicuntur Quod, & obseruauit ipsemet Augustinus paulò post subdens: Sicut autem in arbore id quod agit agricultura forinsecus, vt illud proficiat, quod geritur (à natura) intrinsecus; sic in homine secundum corpus, ei quod intrinsecus agit natura, seruit extrinsecus medicina: quod autem ad arborem colendi negligentiâ, hoc ad corpus medendi incuria, hoc ad animam discendi segenitia. Et quod ad arborum humor inutilis, hoc ad corpus victus exitiabilis, hoc ad animam persuasso iniquitatis. Porrò inter naturales causas principem sibilocum vendi- cant corpora cælestia, quæ sua vniuersali potentia in omnia isthæc sublunaria agunt, suis influxibus producunt,

Transcription: Translated (English)

MATHEMATICVM. 317 of a work that comes from outside, does it come through the one whom nonetheless God created, and whom He rules and orders invisibly? From this the eye of thought is now lifted up to the world itself, as to some great tree of things, and in it too a twofold operation of providence is found, partly natural, partly voluntary. Natural, indeed, through the hidden administration of God, who even gives increase to trees and herbs; voluntary, however, through the works of angels and of men. According to the first, the heavens are ordered above, and the earthly things below; the lights and stars shine; the alternations of day and night are carried on; the earth is laid under and washed around by the waters; the air is poured out above; shrubs and animals are conceived and born, grow and grow old, die, and whatever else is done in things by an inward and natural motion: in this other, signs are given, instruction is taught and learned, fields are cultivated, societies are governed, arts are exercised, and also other things, whether they are carried on in the higher society or in this earthly and mortal one, so that provision is made for the good, even through the ignorant and evil; and in man himself the same twofold power of providence is at work: first with regard to the body, namely the natural one, by that motion by which it is formed, by which it grows, by which it grows old; but with regard to the voluntary, provision is made for food, clothing, and healing. Thus far St. Augustine. From these things it is clear that there are two principles of things: nature and will; and that both are governed, advanced, and ordered by Divine providence, and can even be hindered by a higher power. Yet, when left in its own course, Nature operates necessarily, Will freely, and can direct the course of nature, assist it, and in some measure impede it: hence things that proceed from nature purely and without the aid of will are natural; those that arise from will alone, with Nature serving nothing at all, are purely voluntary; but those that arise from will insofar as it applies active things to passive ones, removes obstacles, and disposes nature itself to operate, are called artificial. This, St. Augustine himself also observed a little later, adding: But just as in a tree, that which agriculture does from outside, is for the advancement of that which is brought forth (within) by nature; so in man, with respect to the body, medicine from outside serves that which nature acts upon within. But what neglect in cultivating is to a tree, that carelessness in healing is to the body, and slothfulness in learning is to the soul. And what harmful moisture is to trees, that destructive food is to the body, and that persuasive wickedness is to the soul. Moreover, among natural causes, the foremost place is claimed by the heavenly bodies, which by their universal power act upon all these sublunary things, by their influences produce them,

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LEXICON conseruant, immutant, alterant, perdunt: neque eorum actiuitas tolli vel impediti potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo, atque adeò vel ob id cæteris omnibus præstant. Benè verò potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Centiloquio Verbo 8, Sapiens anima, inquit, confert cælesti operationi, quemadmodum optimus Agrico'a arando, expurgandoque confert Natura. Igitur non potest homo facere, vt Astra suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuertere. 9. Sic non potest homo vllò modo Eclipsim futuram impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Martis sequuturum præuertere, nuius, pluuias, ventos, aëris infectiones, &c. potest autem in naturis inferioribus, vt ædificando super solum, ne herbas germinet, exsiccan- do stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subfamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt secit Iosephi Patriarcha) magnam frumenti vim in horrea comportare, in bonis siderum configurationibus terram excolere, maria exsulcare; in malis domi consistere, atque à labore inutili abstinere, &c. Concludam igitur cum iis quæ appositè ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, actus virtutum aus vitiorum: alia mixta, vt facere iter, comedere, &c. Vtrum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpori nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu certo

Transcription: Translated (English)

LEXICON conserving, mutating, changing, destroying: neither can their activity be removed or hindered by human will, or by any inferior causes, but only by the First Cause, God; and indeed on that account they excel all other things. But rightly man can cultivate their nature, qualities, effects, immutable power of action in the lower things, applying, averting, diverting them, as Ptolemy said in the Centiloquy, Word 8: the wise soul, he says, contributes to celestial operation, just as the best farmer does by ploughing and clearing Nature. Therefore man cannot cause the stars not to exercise their natural virtues, not to produce their proper effects, to cast off the harmful or beneficial qualities by which they are inwardly possessed, and to put on contrary ones; but he can to some extent, in inferior causes, by altering, impeding, or even destroying them, and thus completely avert their effects. 9. Thus man cannot in any way prevent a future eclipse, nor the effects that will naturally flow from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, or hail, rains, winds, corruptions of the air, etc. But in inferior natures he can, for instance by building over the ground so that herbs do not sprout, by drying up ponds so that they do not corrupt the air; by cutting down trees so that they do not bear fruit. In this way also, by subordinating himself to the stars, he can contribute to their operation, for example by supplying matter, or removing it, by guarding himself against evil stellar influences, by preparing good ones beneath him, by disposing things, and applying what is capable of suffering in a time of foreseen sterility (as Joseph the Patriarch did), by bringing a great quantity of grain into the storehouses, by cultivating the earth under favorable stellar configurations, by ploughing the seas; under bad ones by staying at home, and abstaining from useless labor, etc. I shall conclude therefore with what Kircher appositely has on this matter in the Ars Magna Lucis & Umbrae, book 6, part 3, chapter 2: Nature, he says, is governed by two principles, nature, and will: Nature is subject to the stars, will is free, and therefore effects and purely natural operations plainly obey the stars as necessary causes, such as health or illness; the long or short life of men, etc. Others are purely voluntary, such as to contemplate, to teach, acts of virtues or vices: others mixed, such as to travel, to eat, etc. Whether, however, a journey will be convenient or not depends on the stars, and on the state of the air. Therefore, if anyone were to know perfectly the influences of the stars agreeable or disagreeable to our body, he would undoubtedly know with certainty the fortunate or unfortunate condition of the journey

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MATHEMATICVM. 519 iudicare posset: item desanitate, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAVBARACH, siue Naubahàr arab. idem sonat, ac No-10; uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans stellis 65. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Marcheb in medio scuti posita. Hoc sidus à schillero immutatum fuit in Arcam Noë. Hebraicè autem dicitur sephina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, 13. pallenti, & suboseuro micantes: eò dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt dux magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebulosum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequitur aculeum scorpij. Idque, vt obseruat Titus lib.1. cap.12. quia earum nebulositas parem, & consimilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vitium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum lucem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos derivatur congressu fiant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIVM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Cicetoni, & aliis idem est, ac Scorpij ludus fortè à 16.

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MATHEMATICVM. 519 would be able to judge: likewise concerning health, disease, etc. Also concerning the success of an undertaking with a prince. But since these things can scarcely be done, and known from this source, the knowledge of these elections, unless supported by experience, is for the most part deceptive. Thus Kircher. From which it is clear what art, or human ingenuity, can do, what Nature can do, what a man, having properly known the nature of things, can undertake, and finally what he undertakes in vain, and what even rashly. NAVBARACH, or Naubahàr in Arabic, sounds the same as No-10; the Lord of the hunt. See in V. Anaubarach. NAVIS, commonly called the constellation on the southern side consisting of 65 stars, as is evident from the most accurate observations of the newer Astronomers, almost all of them of the nature of Saturn and Jupiter, whose chief star is Canopus, situated in the rudder, of the first Arabic magnitude, Rubail, to which is very near the aforementioned Marcheb placed in the middle of the shield. This constellation was changed by Schiller into Noah’s Ark. In Hebrew it is called sephina. NEBOLASSID is what among the Fetzans, the Moroccans, and the other 12. Nubian astrologers is called the Tail of the Lion, a fixed star of the first magnitude, of which enough has been said in its place. NEBULOUS STARS are certain fixed stars shining with a dull, pale, and somewhat obscure light: they are so called either because they display in their appearance certain nebulae, such as especially the two large and quite conspicuous ones near the Antarctic pole, or indeed because they generate nebulae, and when setting with the sun make the air cloudy, as Ptolemy and Pliny observed, in the Praesepe, located in the breast of Cancer, in that which is in the eye of Sagittarius, but especially it is seen in that which follows the sting of Scorpio. And this, as Titus observes in lib. 1, cap. 12, because their nebulosity produces a similar and like effect in these lower regions. Hence also experience has shown that whenever they come together with the Luminaries in someone’s nativity, they always bring inflammation, cloudiness, or some other defect in the eyes; which natural reason itself suggests, for their light is very faint and weak, and therefore it is no wonder if they take away or dim the light of the eyes, when they become hostile through contact with the luminaries, from which light is derived into the eyes. NEMER, that is, Pardus in the Hebrew tongue, is called the Wolf 14. a constellation, of which something has been said elsewhere. NEOMENIUM in Greek is the same as New Moon, of which 15. presently below. NEPA, with Ciceto and others, is the same as the sport of Scorpio, perhaps from 16.

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320 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum linguâ dicitur Cancer aliud sidus, quod in nominibus sæpe cum Scorpione confunditur. 19. NESCHER, Hebraicè dicitur Aquila. 20. NIGEAR, (teste Iunctino in Sphætam Io: de Sacrobosco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & concipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboscuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Adducit etiam nebulas, nimbos, glacies, niues, & in hominibus Saturninis solitudinis, austeritatis, inuidiæ, obstinationis, auaritiæ incitamentum, & incrementum. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach; id est circulus signorum diuiditur in duodecim partes æquales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus. 23. NITVRA, pro Genitura, seù Natalitio Themate per Apocopen sæpissimè ab aliquibus vsurpatur. Vide Isidorum. 24. NOCTRNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiuæ, quales sunt humiditas, & siccitas: sicut è contrà Diurna dicuntur signa & planetæ in quibus abundant qualitates actiuæ: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclypticam in duobus punctis opposiris, & Nodus quidem boreus dicitur punctum in quo Planeta è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euchens, atque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porrò Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibiliter mouentur; inferiorum verò non

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320 LEXICON Chelis dictum; for the same reason as well. 18. NEPA, in the language of the Africans, means Cancer, another star, which is often confused in names with Scorpio. 19. NESCHER, in Hebrew, means Eagle. 20. NIGEAR, (as testified by Iunctinus in the Sphere of Io: de Sacrobosco) is called by Arab writers the axis of the world, which terminates at its poles, and is conceived to pass through the center of the earth. See under V. Axis. 21. NIGRA, or Niger, is the name of a certain kind of comet of black color, or rather leaden and somewhat dark, of the nature and condition of Saturn, and therefore, just as in color, so also in qualities, altogether like it. For when it appears it signifies scarcity of the year, prolonged locusts, and other destructive animals of that kind, pestilence, chronic fevers, &c. It also brings mists, storms, ice, snow, and in Saturnine men an incitement to and increase of solitude, austerity, envy, obstinacy, and greed. NITACH, in Arabic, or rather in Chaldean, signifies the Zodiac and the circle of the signs. Hence Alchabitius begins his book thus: Nitach; that is, the circle of the signs is divided into twelve equal parts, &c. See more fully what must be said under V. Zodiacus. 23. NITVRA is very often used by some for Genitura, or Natal Figure, by apocope. See Isidore. 24. NOCTURNAL sign, or also planet, is called that in which passive qualities predominate, such as humidity and dryness; just as, on the contrary, signs and planets in which active qualities abound are called Diurnal: on which matter see what we have said under V. Diurnus. 25. NODES are what astronomers call the intersections of the orbits of the sun and of each of the planets having latitude, namely where the orbits of the planets cut the Ecliptic at two opposite points; and the northern node is the point at which a planet passes from southern latitude into northern; the southern node, where it descends from the north to the south. They are also so called from the shape they resemble, namely the head and tail of the Dragon; likewise the ascending, or earthen, and the descending. Where the planets have their greatest latitude it is called the belly of the Dragon, because this too is broader in the belly than at the extremities. Moreover, these nodes change their place in the Zodiac, just as the planets themselves do, but they proceed contrary to the succession of the signs. And indeed the nodes of the three superior planets move imperceptibly; but those of the inferior do not

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MATHEMATICVM. 327 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, actabulis secundorum mobilium. Habent in Genethliacis nodi maximam significationem quoad formam corporis, quam plerumque deturpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis, vel curuis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, contorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. NONA SPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem cursu concitatissimo revolutionem suam persiciens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalitatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltrò citróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgato illo axiomatico corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re uide Clauium, & Blan[n]eanum in sphæra mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem mobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnco tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis X

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MATHEMATICVM. 327 not so; but to individual points, almost to a single minute; indeed the lunar nodes, to their own almost-minutes, as appears in the Ephemerides, and tables of the moving seconds. In Genethliacs the nodes have the greatest significance as regards the shape of the body, which they for the most part disfigure, if they are found with the Luminaries, or with the infortunes, especially in the Angles, and in truncated or crooked signs, such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Whence the newborn will turn out hunchbacked, squint-eyed, lame, twisted, or weakened in whatever way, as Ptolemy has in book 3, chapter 17. THE NINTH SPHERE is commonly called the Primum Mobile, because it is placed above the eighth sphere, or the heaven of the fixed stars, which draws along with itself all the lower spheres from east to west, accomplishing its revolution in a very swift course in a space of almost 24 hours. Others however admit this ninth sphere as distinct from the Primum Mobile, indeed, and a Tenth also, which they call of libration, or trepidation, which they see in the Firmament; for they have observed that, apart from the motion of the universe, and its proper motion, it moves irregularly from north to south, and from south to north, under the colure of the solstices of the Primum Mobile, back and forth: again, it moves from east to west, and from west to east under the ecliptic, and over its poles. Wherefore, since so many motions are found in the firmament; and also in the planets, and since they say that not even the two motions just explained can be had in themselves, or from the Primum Mobile, from that well-known axiom, that a single simple body by its nature can be moved intrinsically by only one simple motion, but extrinsically by several; consequently, they also admit this ninth sphere, which is said to move from east to west, and from west to east over the poles of the Zodiac by 14 minutes in the space, as they say, of 1716 years; and again a Tenth, which is said to move from north to south under the colure of the solstices by 24 minutes, in the space of 3432 years. Concerning this matter see Clavius and Blan[n]eanus in De sphaera mundi , book 18, ch. 7. But I for my part can by no means admit these distinct motions, and therefore distinct spheres, because it is repugnant for one and the same movable to be moved by two contrary motions, under which concept there would be motions of this kind, namely trepidation, which are utterly fictitious, and the appearances of the stars, irregularities, etc., are best preserved in the mere fluidity of the heavens, and by a single motion from east to west, though regular yet irregular according to all parts of the heavens, as they are farther and farther removed from the first motive power. See what we have said at length in V. Motus. NOTE: PELIOTES is a wind, one of the four intermediate winds X

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320 LEXICON Chelis dictum; eandem etiam ob rationem. 18. NEPA, Afrorum linguâ dicitur Cancer aliud sidus, quod in nominibus sæpe cum Scorpione confunditur. 19. NESCHER, Hebraïcè dicitur Aquila. 20. NIGEAR, (teste lunctino in Sphætam Io: de Sacrobosco) apud Arabes scriptores dicitur axis Mundi, qui ad eiusdem polos terminatur, & concipitur transire per centrum terræ, Vide in V. Axis. 21. NIGRA, seù Niger, appellatur species quædam Cometæ nigri coloris, seù potiùs plumbei, & suboscuri de natura, & conditione Saturni, ac proinde vt in colore, ita & in qualitatibus ei omninò persimilis. Significat enim cum apparuerit anni inopiam, diuturnas locustas, & alia id genus animalia perniciosa, pestilentiam, febres chronicas, &c. Adducit etiam nebulas, nimbos, glacies, niues, & in hominibus Saturninis solitudinis, austeritatis, inuidiæ, obstinationis, auaritix incitamentum, & incrementum. 22. NITACH, Arab. seù potius Chaldaicè significat Zodiacum, & circulum signorum. Vnde Alchabitius ita incipit librum suum, Nitach; id est circulus signorum diuiditur in duodecim partes aequales, &c. Vide quæ fusius dicenda sunt in V. Zodiacus 23. NITVRA, pro Genitura, seù Natalitio Themate per Apocopen sæpissimè ab aliquibus vsurpatur. Vide Isidorum. 24. NOCTURNVM signum, vel etiam Planeta denominatur in quo præponderant qualitates passiux, quales sunt humiditas, & siccitas: sicut è contrà Diurna dicuntur signa & planetæ in quibus abundant qualitates actiux: qua de re vide quæ diximus in V. Diurnus. 25. NODI vocantur ab Astronomis intersectiones orbitarum solis, & singulorum planetarum latitudinem habentium, vbi videlicet orbitæ planetarum incidunt in Eclypticam in duobus punctis oppositis, & Nodus quidem boreus dicitur puhetum in quo Planeta è latitudine australi transit in borealem; Austrinus verò vbi à borea descendit ad Austrum. Qvi etiam ex forma quam referunt caput, & cauda Draconis dicuntur; Item Attollens, seu euehens; atque deprimens. Vbi autem Planetæ maximam latitudinem habent appellatur venter Draconis, quia & hic in ventre latior est, quam in extremitatibus. Porrò Nodi isti permutant locum in Zodiaco, quemadmodum ipsi Planetæ sed gradiuntur contrà successionem signorum. Et trium quidem superiorum Nodi insensibiliter mouentur; inferiorum verò non

Transcription: Translated (English)

320 LEXICON Chelis dictum; for the same reason also. 18. NEPA, in the African language means Cancer, another star, which in names is often confused with Scorpio. 19. NESCHER, in Hebrew, means Eagle. 20. NIGEAR, (according to Iunctinus in the Sphere of Io: de Sacrobosco) among Arab writers means the axis of the world, which ends at its poles, and is conceived to pass through the center of the earth; see under V. Axis. 21. NIGRA, or Niger, is the name given to a certain kind of Comet of black color, or rather leaden and somewhat dark, of the nature and condition of Saturn, and therefore as like him in qualities as it is in color. For when it appears it signifies scarcity for the year, long-lasting locusts, and other harmful animals of that kind, pestilence, chronic fevers, etc. It also brings fogs, heavy rains, ice, snow, and in Saturnine men an incitement and increase of solitude, austerity, envy, stubbornness, and greed. 22. NITACH, in Arabic, or rather in Chaldean, signifies the Zodiac and the circle of the signs. Hence Alchabitius begins his book thus, Nitach; that is, the circle of the signs is divided into twelve equal parts, etc. See more fully what must be said under V. Zodiacus. 23. NITVRA is very often used by some instead of Genitura, or the natal figure, by apocope. See Isidore. 24. A NOCTURNAL sign, or also a planet, is called one in which passive qualities predominate, such as humidity and dryness: just as, on the contrary, signs and planets in which active qualities abound are called diurnal; on this matter see what we have said under V. Diurnus. 25. NODES are called by astronomers the intersections of the orbits of the sun and of individual planets having latitude, where, namely, the orbits of the planets meet the ecliptic at two opposite points; and the northern node is indeed called the point at which a planet passes from southern latitude to northern; the southern node, however, where it descends from the north to the south. They are also so called from the shape which they bear, the head and tail of the Dragon; likewise the ascending, or raising one; and the descending, or lowering one. But where the planets have their greatest latitude it is called the belly of the Dragon, because here too it is broader in the belly than at the extremities. Moreover, these nodes change their place in the Zodiac, just as the planets themselves do, but they move contrary to the succession of the signs. And indeed the nodes of the three superior planets move imperceptibly; those of the inferior, however, not

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MATHEMATICVM. 325 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliæis nodi maximam significationem quoad formam corporis, quam plerumque deurpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis; vel curuis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, eontorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. cap. 17. NUNA SPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem cursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis; quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalitatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltrò citróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dieant ex se, aut à primo mobili, ex vulgato illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenrer, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam; quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re vide Clauium, & Blancanum in sphara mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem mobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnico tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis X

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MATHEMATICVM. 325 not so, but to each one, almost a minute; indeed the lunar nodes to their own minutes, as is evident in the Ephemerides and tables of the second mobiles. In nativities the nodes have very great significance with regard to the shape of the body, which they usually mar, if they are found with the Luminaries or the infortunes, especially in the Angles and in mutilated or crooked signs, such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Hence the natives will come out humpbacked, cross-eyed, lame, twisted, or weakened in whatever way, as Ptolemy has in book 3, chapter 17. The NUNA SPHÆRA is commonly called the Primum Mobile, which is constituted above the eighth sphere, or the heaven of the fixed stars, which carries along with it all the lower spheres from east to west, accomplishing its revolution in the course of almost 24 hours with most rapid motion. Others, however, admit this ninth sphere as distinct from the Primum Mobile, and even a Tenth, which they call of libration, or trepidation, which they see in the Firmament; for they have observed that it, besides the motion of the totality and its proper motion, moves irregularly from north to south and from south to north under the colure of the solstices of the Primum Mobile, hither and thither; and again it moves from east to west, and from west to east under the Ecliptic and above its poles. Therefore, since so many motions are found in the firmament and among the planets, and since they say that neither of the two motions just explained can be had from itself or from the Primum Mobile, according to that common axiom that one simple body by its nature can be moved intrinsically by only one simple motion, but extrinsically by several, consequently they admit also this ninth sphere, which causes motion from east to west and from west to east over the poles of the Zodiac by 14 minutes in the space of 1716 years, as they say; and again the Tenth, which causes motion from north to south under the colure of the solstices by 24 minutes in the space of 3432 years. On this matter see Clavius and Blancanus, in the Sphere of the World, book 18, chapter 7. But I, for my part, can by no means admit these distinct motions, and therefore distinct spheres, since it is repugnant for one and the same mobile thing to be moved by two contrary motions; in which way there would be motions of this kind of trepidation, which are altogether fictitious, and the appearances of the stars, irregularities, etc., are most excellently preserved in the mere fluidity of the sky, and in a single motion only from east to west, though regularly irregular according to all the parts of heaven, farther and farther removed from the first moving power. See what we have discussed at length in V. Motus. NOTE. PELIOTES is a wind, one of the four intermediate winds. X

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LEXICON ad conseruationem species, & alimento ad conseruationem indiuidui: & propter hoc in istis inferioribus non inuenitur vita sine anima vegetabili, sed hoc non habet locum in in- corruptilibilius: & art. 1. in responsione ad primum argu- mentum, quo inferebatur omnium rerum naturalium pro- prium esse viuere; vltrò fatetur, quod si totum vniuersum corporale esset unum animal, ita quod iste motus esset amo- uente intrinseco, vt quidam posuerunt, sequeretur, quod motus esset vita omnium naturalium corporum. Similiter ratio sensus impertinens est ad vitam, & potius passio imperfectio, quam perfectio. Ait enim Philosophus, in lib. de Somno, & Vigilia, quod iis conuenit sensus, in qui- bus est tristari, & gaudere, contupiscere, & odisse: plantis autem nihil horum inesse, vnde contenienter iis à Natura inditus non est sensus: supra quod D. Thomas in commen- to. Complexio, inquit, plantarum innutrimento, & aug- mento, & his similia melius fiunt sine sensu, quam cum sensu: ergo planta non habent sensum, cum natura semper faciat quod melius est. Cum igitur isti gradus vitæ potius sint imperfectiones, & defectus naturæ, quam perfectio- nes, & Sol, Astra, & mundus non indigeant generatione, & nutritione ad conseruationem speciei vel indiuidui, & adhuc non habeant aliquod ad sui esse conducens, vel ad sui esse contrarium, quod amore prosequi debeant, aut odio; iure illis à Natura neque sensu, neque vegetatione prouisum, sed solum vitâ quadam superiore, quæ omnem vitam inferiorum eminenter contineat, & colligitur ex motu perfectissimo, qui est circularis, & ab intrinseco, po- tens naturaliter in æuum protrahi, & motum cæteris viuen- tibus participare. Alloquin si gradus huiusmodi vitæ, vege- tatio inquam & sensatio absolutè, & simpliciter dicerent rationem vitæ perfectiorem, quæ non in aliquo eminentet conrineretur, posset etiam dici, quod vita hominis est per- fectior vita Angeli, quia viuit, nedum intellectualiter, vt ille, sed adhuc vita sensitiva; & vegetabili. Sicut igitur vita Angeli est perfectior vita hominis, etiamsi non sit ve- getabilis, & sensibilis, ita etiam vita Muudi est perfectior omnibus viuentibus inferioribus; atque adeo plantis, & animalibus, etiamsi sensum, & vegetationem non habeat. Qui quidem gradus vitæ in talibus viuentibus dicunt per- fectionem, at non in supetiotibus, quæ tali modo viuendi non indigent. Igitur pro coronide huius nobilissimæ Controversiæ, concludendum est, vniuersum hoc vnum quid esse, per se

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LEXICON for the preservation of the species, and food for the preservation of the individual: and for this reason among these lower things life is not found without a vegetative soul; but this does not apply to the incorruptible beings: and in art. 1, in the response to the first argument, by which it was inferred that it is proper to all natural things to live, he freely admits that if the whole corporeal universe were one animal, so that this movement were from an intrinsic mover, as certain men have held, it would follow that motion would be the life of all natural bodies. Likewise, sensation is irrelevant to life, and rather a passion is an imperfection than a perfection. For the Philosopher says, in the book On Sleep and Waking, that sensation belongs to those in whom there is being saddened and rejoicing, desiring and hating: but plants have none of these things in themselves, whence fittingly sensation was not imparted to them by Nature. On this point St. Thomas says in his commentary: The constitution, he says, of plants in nourishment, and growth, and such things is better effected without sense than with sense: therefore plants do not have sense, since nature always does what is better. Since therefore these degrees of life are rather imperfections and defects of nature than perfections, and the Sun, the Stars, and the world do not need generation and nourishment for the preservation of the species or the individual, and still have nothing conducive to their being, or contrary to their being, which they ought to pursue with love or hate; by right Nature has provided them neither with sense nor with vegetation, but only with a certain higher life, which eminently contains every life of lower things, and which is gathered from the most perfect motion, which is circular and from within, naturally able to be carried through eternity, and to participate in motion with the rest of living things. Otherwise, if such degrees of life, I mean vegetation and sensation absolutely and simply, were to be called a more perfect notion of life, which would not be eminently contained in anything, it could also be said that the life of man is more perfect than the life of an Angel, because he lives not only intellectually, as that one does, but still with sensitive and vegetative life. Just as therefore the life of an Angel is more perfect than the life of man, even though it is not vegetative and sensible, so also the life of the World is more perfect than all lower living things; and therefore than plants and animals, even if it does not have sense and vegetation. Which degrees of life in such living things indeed signify perfection, but not in the superiors, which do not need to live in such a way. Therefore, as the crowning of this most noble Controversy, it must be concluded that this universe is one thing, by itself

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MATHEMATICVM. 313 subsistens, sua vniuersali forma præditum, eâque substan- tiali, & perfectissimâ, quæ det quidem toti, cunctisque eius partibus, atque animantibus vitam, non tamen ipsum mun- dum, aut præcipuas eius partes, nempe cælum, sidera, ele- menta, animantes denominet: & quia sensu, & vegeta- tione carent, proindeque, vt ait Conc. Constantinop. om- ninò animantes non sunt, Non tamen ex hoc sequitur vi- tam Mundi præcipuarumque eius partium non esse cæteris viuensibus, etiam ipso homine secundum gradus vegeta- tionis, nutricationis, & sensationis, superiorem, atque vni- uersaliorem; non autem secundum gradum intellectiui, in quo homo spiritualis est; ac minimè à cælorum Influxibus pendet. Viuit ergo Mundus, cælum, sidera, gradu quodam vitæ superiore, cui profectò parem, aut similem in inferioribus hisce non sit inuenire: sed omnis ipsorum vitæ ratio, & gradus eminenter in vita mundi est, & ab ipsa tanquam vniuersali, & æquiuoca causa deriuat; vnde est etiam vir- tus ad causandam hanc rerum varietatem. Et hoc, vt benè habet D. Th. 1. part. 9. 105. art. 3 inquantum hæc (scilicet cælestia corpora) vniuersali virtute cōtinêt in se quidquid in inferioribus generatur & quia (vt paulò antedixerat) quid- quid in istis inferioribus generat. & mouet ad speciem, est in- strumentu[m] cælestis corporis. Igitur cælestia corpora sunt causæ superiores, ac principales vitæ, omnisque motionis infe- riorum ad certas species: & quà talia in se ipsis eodem, sed longè nobiliore gradu vitæ prædita sint, necesse est. MVNIR, seù, vt alij legunt, Mumir, Arabicè dicitur quasi pu- <96.> pilla lucida Coronæ Gnostiæ, Stella fixa secundæ magnitudi- nis de natura veneris, & Mercurij, quâ ob sui pulchritudine[m] verisque apperitionem quam orru suo facit cæli pupillam, sertum aperitionem que dixerunt. Vide fusiùs in V. Corona. MVSATOR, dicitur à Cicerone sagitta sidus apud Aquilam <97.> constans stellis quinque de quibus vide in V. Sagitta. MVSCA, seù, Apis sidus in cælo ad polum Antarcticum no- <98.> bis inuisum, & nuper à nouis Astronomis ad Australes pla- gas appulsis cum aliis vndecim obseruatum, continens qua- tuor stellas infimæ noxæ: Est nunc in longitudine sub signo Scorpij incidens in ipsum Antarcticum circulum: Apud In- dos Muia. MVSIDA Eqvi, Arabicè Alpheratz, vulgò dicitur Stella <99.> fixa tertiæ magnitudinis in rictu Pegasi existens, de natura mixta Martis, Iouis, & Veneris de qua vide iam dicta in V. Alpheratz. MVSICA, vna est ex quatuor præcipuis Mathesis diuisio- <100>

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MATHEMATICVM. 313 subsisting, endowed with its universal form, and with that substantial and most perfect one, which indeed gives life to the whole and to all its parts and living beings, yet does not name the world itself, nor its principal parts, namely the heavens, stars, elements, and living creatures: and because they lack sense and vegetation, and consequently, as the Council of Constantinople says, they are by no means living beings. Nevertheless, it does not follow from this that the life of the World and of its principal parts is not superior and more universal than that of the other living things, even than man himself according to the degrees of vegetation, nutrition, and sensation; though not according to the intellectual degree, in which man is spiritual, and depends least of all on the influences of the heavens. Therefore the World, the heaven, and the stars live by a certain higher degree of life, to which, indeed, no equal or similar one can be found in these lower things: but every reason and degree of their life is eminently in the life of the world, and flows from it as from a universal and equivocal cause; whence also comes the power of causing this variety of things. And this, as St. Thomas rightly has it, 1. part. 9. 105. art. 3, insofar as these things (namely the heavenly bodies) by a universal power contain in themselves whatever is generated in the lower things; and because (as he had said a little before) whatever in these lower things generates and moves toward a species is an instrument of a heavenly body. Therefore the heavenly bodies are the higher and principal causes of life, and of all motion in lower things toward certain species: and as such, it is necessary that in themselves they too be endowed with the same, but by a far nobler degree of life. MVNIR, or, as others read, Mumir, is said in Arabic to mean, as it were, the bright pupil of the Corona Gnostiae, a fixed star of second magnitude, of the nature of Venus and Mercury, because of its beauty and the true opening which it makes in its rising; they called it the pupil of the sky, and also the opening of the garland. See more fully under V. Corona. MVSATOR, Cicero calls the star under the Eagle, consisting of five stars; see under V. Sagitta. MVSCA, or Apis, is a constellation in the sky near the Antarctic pole, invisible to us, and recently observed by the new astronomers who sailed to the southern regions along with eleven others, containing four stars of the lowest magnitude: it is now in longitude under the sign of Scorpio, falling upon the Antarctic circle itself: among the Indians, Muia. MVSIDA Eqvi, in Arabic Alpheratz, is commonly called a fixed star of the third magnitude, situated in the mouth of Pegasus, of a mixed nature of Mars, Jupiter, and Venus; see what has already been said under V. Alpheratz. MVSICA is one of the four principal divisions of Mathematics.

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LEXICON 314 nibus Arithmeticæ subalterna, facultas nempe, vt inquit Boëthius, quæ multitudine ad aliud relata rationes nume- rales concretas habet ad sonos & voces. Dicta est à Græ- co verbo Mos, quod æquam rationem, atque harmoniam sonat; vel potiùs à Musis, quibus olim familiaris erat. Ha- bet pro obiecto numerum seù quantitatem discretam provt ad alteram relatam: confert enim temporis momenta ad sonorum modules, & inde eos artificiosè nectit, & copu- lat, vt dulcissima harmonia, atque ordinatissimum melos auribus nostris insonet. Eius nobilitatem vel inde licet colligere, quod in diuinis laudibus decantandis, Numine- que propitlando, ab ipso religionis exordio ad hæc vsque tempora religio è sit semper adhibita: vnde Iobi 38. dicitur: Vbi eras quado ponebam fundamenta terra: cum me lau- darent simul astra matutina, & iubilarent omnes Filij Dei? Adeovt de ipso Dite referant Fabulæ Poëtarum, quod sit Orphei cantibus emollitus: Nec mirum, cum eius ordo vt ælestis Hierarchiæ symbolum est, ita & inferis illatus vbi nullus ordo est, sed confusio, eorum conditionem anteuer- tere satis est. Porrò quanta sit Musices efficacia in immu- tandis affectibus, ac passionibus animi mitigandis, lucu- lenter explicat Seneca: Cassiodorus, & Augustinus, qui lib. contra Iulianum, Ciceronis testimonium adducens, refer[en]t Pithagoram spondeum in sono canentem tarditare modo- rum, & grauitate cantus furentem aliquorum iuuenum pe- tulantiam abegisse: & iure quidem, nam ars hæc ita ani- mas sibi reddit intentas, vt quemadmodum loquitur Cassio- dorus,) nil aliud cogitare possint; sed deposita omni cura mentis induant grauitatem. Hinc ob diuersas animorum commotiones, quas suis mo- <101> dulis suscitare potest Diuina isthæc facultas, quatuor melo- dix species distinxit Philosophus ad diuersos affectus ten- dentes- Mistolidiscam, quæ ad compassionem mouet; Li- discam, quæ animos emollit ad concupiscentiam: Doriscam, quæ mentem erigit ad fortitudinem, arque virilitarem: & Frigiscam, quæ rigidior cæteris incitat ad dura consilia, pro- mouetque seueritatem. Habet etiam tonos, diuersasque consonantiarum dissonantiarumque rationes, quas Dia- tesseron, Diapente, Diapason appellant: ac similiter tria melorum genera Diatonicum, Chromaticum, Enharmoni- cum, de quibus omnibus, aliisque Musices diuisionibus, vide Ficinum in Platonis Conuiuio Orat.3. cap.1. Guidonem, & Iacobum Fabrum in Elemen. Music. lib.3. & 4 Nobis eas tetigisse sufficiat.

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LEXICON 314 Music is a subordinate branch of arithmetic, namely, as Boethius says, that faculty which, by relating multiplicities to something else, has numerical ratios applied to sounds and voices. It is said to derive from the Greek word Mos , which signifies an equal proportion and harmony; or more properly from the Muses, with whom it was once familiar. Its object is number, or discrete quantity, insofar as it is related to another; for it brings together the moments of time with the measures of sounds, and thus skillfully joins and combines them, so that the sweetest harmony and the most orderly melody may sound in our ears. Its nobility may be gathered from this also: that in singing divine praises and appeasing the Deity, it has been employed in religion from the very beginnings of religion down to the present time; whence in Job 38 it is said: “Where were you when I laid the foundations of the earth, when the morning stars sang together, and all the sons of God shouted for joy?” So much so that the poets’ fables relate that even Dis was softened by the songs of Orpheus. Nor is this surprising, since its order is a symbol of the heavenly hierarchy; and likewise, when introduced even into the underworld, where there is no order but confusion, it is enough to overcome their condition. Moreover, how great is music’s power in changing emotions and calming the passions of the mind is clearly explained by Seneca, Cassiodorus, and Augustine, who in his book against Julian, citing Cicero’s testimony, reports that Pythagoras, by singing the spondean mode in sound, by the slowness of the measures and the gravity of the chant drove away the unruliness of some young men. And rightly so, for this art so fixes minds upon itself that, as Cassiodorus says, they can think of nothing else; instead, laying aside all care, they assume gravity of mind. Hence, because of the various movements of the spirit which this divine faculty can arouse by its modes, the Philosopher distinguished four kinds of melody tending toward different affections: the Mixolydian, which moves to compassion; the Lydian, which softens minds toward desire; the Dorian, which raises the mind to courage and manliness; and the Phrygian, which, being harsher than the others, stirs men to severe counsels and promotes severity. It also has tones, and different relations of consonance and dissonance, which they call Diatesseron, Diapente, and Diapason; and likewise three kinds of melody, Diatonic, Chromatic, and Enharmonic. For all these, and other divisions of music, see Ficino in Plato’s Symposium , Orat. 3, chap. 1; Guidone; and Jacobus Faber in Element. Music. books 3 and 4. It is enough for us to have touched on these matters.

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MATHEMATICVM. 311 MVTA SIGNA sunt quæ præseferunt figuram Animalium 102 voce carentium, qualia sunt Cancer, Scorpio, & Pisces: sicut econtrà vocem habentia perhibentur esse tum humana, Gemini, Virgo, Libra, Sagittarius, & Aquarius, tum ferina, quæ etiam raucâ dicuntur, brutorum videlicet vocalium formam habentia, vt Aries, Taurus, Leo, Capricornus. Horum maxima consideratio haberur in Gene- thliacis, quoad vitia, & impedimenta linguæ, de qua re Ptolemæus lib. 3. Quadrip. cap. 17. MVTA T it arab. idem sonat ac latinè agglutinatus; cum vi- 103 delicet Planeta ita est alteri iunctus, vt nee in minuto qui- dem aberret. Hoc vocabulo frequenter vtitur Ptolemæus in Quadrip. ex versione arabica, & Hali eius commen- tator. MVTLVM arab. Vide in V. Moslatum. 104 MVTLATA SIGN. sunt quæ membrum aliquod seu etiam 105 corpus mutilum repræsentant, vt Taurus, Equi sectio, Caput Medusæ, quæ quidem, vt benè obseruat Titus in Cælesti Philosophia lib. 2. cap. 3. hanc habent naturam & in- fluendi vim, vt fer semper inducant membrorum incisio- nem, si Vitæ moderatoribus infeliciter se habentibus in Natali, per directionem postea misceantur. Hinc Ptole- mæus in Quadrip. lib. 4. cap. 10 vbi de genere mortis agit, in signis matilis, inquit, aut quorum figura sunt imperfe- cta, aut circà caput Medusa Mars significat capite truncan- dos, aut membris mutilandos. Quod D. Thomas obseruauit opus. 28. art 3. dicens, quod stella illa funerea sunt, & mon- struosam indicant vita terminationem. Vide quæ diximus in V. Gorgonis caput. N. NABLON SCHALIAF seu etiam Nescussackat teste schie- 1. chardo Chaldaicè dicitur Lyra sidus in Cælo, de quo sæ- pius dictum est. NAASCH LAAZAR hoc est Feretrum Lazari dicitur apud 2. Christianos arabes Plaustrum, vt testatur Kircherus in Oe- dipo, eo quod non minus plaustrum, quam Feretrum re- præsentare videantur stellæ quatuor magis conspicuæ in Ve- sa, quæ quatuor plaustri totas effingunt. Schillerus autem, qui ex hoc occasionem sumpsit omnes coelestes imagines transmutandi, æque ex Diuorum nominibus appellandi, hoc ipsum Astrum vocat Petri Nauiculam. NADIR apud Arabes significat punctum Cæli sub terra 3. oppositum diametraliter vertici capitis nostri, quod ipsi pari- ter gentili suo vocabulo Zenith appellant: itavt ambo sint

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MATHEMATICVM. 311 MUTE SIGNS are those which present the figure of animal 102 lacking voice, such as Cancer, Scorpio, and Pisces; just as, on the contrary, those having voice are said to be both human, Gemini, Virgo, Libra, Sagittarius, and Aquarius, and feral, which are also called hoarse, namely those having the form of vocal brutes, as Aries, Taurus, Leo, Capricorn. The greatest consideration of these is had in Genethliacs, with regard to faults and impediments of the tongue, on which matter Ptolemy, lib. 3. Quadrip. cap. 17. MUTE T in Arabic sounds the same as in Latin, agglutinatus; that is, when a planet is so joined to another that it does not even deviate by a minute. Ptolemy frequently uses this word in the Quadrip., from the Arabic version, and Hali, his commentator. MUTLUM, Arabic. See under V. Moslatum. 104 MUTILATED SIGNS are those which represent some limb or even a mutilated body, such as Taurus, the cut-off Horse, the Head of Medusa; and these indeed, as Titus well observes in Celestial Philosophy, lib. 2. cap. 3, have this nature and influence, that they always bring about the cutting off of limbs, if, with the rulers of life being unfavorably situated in the Nativity, they are afterward joined by direction. Hence Ptolemy in Quadrip., lib. 4. cap. 10, where he treats of the kind of death, says that in mutilated signs, or those whose figure is imperfect, or around the Head of Medusa, Mars signifies that they will be beheaded, or mutilated in the limbs. St. Thomas noted this, opus. 28. art. 3, saying that such stars are funereal, and indicate a monstrous end of life. See what we have said under V. Gorgon’s head. N. NABLON SCHALIAF, or also Nescussackat, according to Schichard, is in Chaldaic the name of the constellation Lyra in the sky, of which much has already been said. NAASCH LAAZAR, that is, the Bier of Lazarus, is called among the Arabic Christians the Wain, as Kircher testifies in the Oedipus, because the four more conspicuous stars in the Wain seem to represent no less a wain than a bier, and they make the whole of the four-wheeled wagon. Schiller, however, who took occasion from this to transform all heavenly images, and likewise to name them from the names of the saints, calls this very star Peter’s Little Ship. NADIR among the Arabs signifies the point of the sky beneath the earth, diametrically opposite the zenith of our head, which they likewise call by their own vulgar term Zenith: so that both are

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316 LEXICON veluti poli horizontis, & distent ab eodem hinc inde [mercur]ij. ac proinde necessario incidant in ipsum meridianum, Zenith quidem supra tertiam, Nadir autem sub terra. Et quam propositionem vnm eorum habeat ad æquatorem & alterum polorum Mundi, eandem vice versa habeat alterum ad opposium polum, & aduersam æquatoris partem. 4. NAHAR, ALCHARNER teste Kirchero in Oedipo arabice dicitur Fluuius Eridanus sidus ad australem plagam constans stellis triginta tribus, de quo plura diximus suo loco. 5. NÆSIS CETI teu etiam Mandibula Ceti vulgò dicitur steila sixa secundæ magnitudinis valdè præsignis, de natura Saturni, existens in rictu Ceti, atque in longitudine sub [mercur]ij. Tauri arab. dicta Menchar. 6. NATIVITAS, Natalitium thema, seu etiam Natiuitatis figura diciur vulgò apud Astrologos constitutio Cæli erecta ad punctum Natiuitatis alicuius hominis, aut etiam initium alicuius rei. Quale autem dicendum sit verum punctum Natiuitatis, disputatum est luculenter in V. Genesis. 7. NATURA, eisi secundum varias acceptiones plura significet, quæ ad nostrum institutum non pertinem, primo tamen loco, & ex sui notione appellat generationem viuentium ex insita sibi à Creatore vi naturaliter, hoc est nullatenus alterata, constituto sibi primitùs ordine prodeuntium: vnde dicta est Natura quasi Nascitura, græcis autem expressiore vocabulo Physis & naturale dicitur quidquid non violentè, non casu, non artificiosè, non denique præter naturæ cursum emanat. Adeo vt iam Naturæ nomine proprie, & vniuersalissimè veniat congeries illa causarum secundarum, ex indita sibi à Creatore virtute necessariò operantium, quæ sui varietate pulcherrimum hunc rerum ordinem constituunt, atque à Deo ita præordinatæ sunt, vt nulla vi, nullo planè artificio, nullo humanæ voluntatis adminiculo ex se suos effectus promant, ac naturali ordine progrediantur: cuius admirabilem cursum demirans D. August. lib. 8. in Genesim. Quod enim, inquit manus, mirabiliusque spectaculum est, aut vbi magis cum rerum natura humanæ ratio quodammodo loqui potest, quam cumpositis seminibus, plantatis surculis, translatis arbustulis, insitis malleolis, tanquam interrogatur quæque v[er]s radicis & germinis, quid possit, quidve non possit; vnde possit, vnde non possit? quid in ea valeat numerorum inuisibilis, interiorque potentia, quid extrinsecùs adhibita diligentia, inque ipsa consideratione perspicere, quia neque qui plantat est aliquid, neque qui rigat, sed qui incrementum dat Deus: quia & illud

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316 LEXICON as the poles of the horizon, and are distant from it on either side [of Mercury]. and therefore necessarily fall upon the meridian itself, the Zenith indeed above the third, but the Nadir beneath the earth. And as one proposition of them bears to the equator and the other pole of the World, so in turn the other bears to the opposite pole, and to the opposite part of the equator. 4. NAHAR, ALCHARNER, according to Kircher in Oedipus, is called in Arabic the River Eridanus, a star in the southern quarter, consisting of thirty-three stars, of which we have spoken more in its proper place. 5. NÆSIS CETI or also the Jaw of Cetus is commonly said to be the fixed star of the sixth magnitude, very notable, of the nature of Saturn, existing in the mouth of Cetus, and in longitude under [Mercury]. In Arabic it is called Menchar. 6. NATIVITY, a natal theme, or also the figure of the Nativity, is commonly said by astrologers to be the constitution of the heavens erected to the point of the Nativity of a certain man, or even the beginning of some thing. But what should be said to be the true point of the Nativity has been clearly discussed in V. Genesis. 7. NATURE, although according to various acceptations it signifies many things, which do not pertain to our subject, in the first place, and from the force of the word itself, it denotes the generation of living things proceeding by the natural force implanted in them by the Creator, that is, by an order established for them at the beginning which has in no way been altered: whence it is called Nature, as if Nascitura; and among the Greeks, by a more expressive term, Physis, and natural is said of whatever does not flow forth violently, by chance, artificially, or finally beyond the course of nature. So much so that now under the name of Nature, properly and most universally, comes that collection of secondary causes, operating necessarily by the virtue implanted in them by the Creator, which by their variety constitute this most beautiful order of things, and are so foreordained by God that no force, no artifice whatsoever, no assistance of human will, can of itself bring forth their effects, but they proceed in natural order: marvelling at whose admirable course, St. August. lib. 8 in Genesis. For what, he says, is a more wondrous spectacle, or where can human reason more, as it were, speak with the nature of things, than when, seeds having been laid, shoots planted, saplings transplanted, grafts inserted, as though each one is questioned concerning the power of root and sprout, what it can do, what it cannot do; from where it can, from where it cannot? what in it is the invisible, inward power of numbers, what the diligence applied from outside, and to discern in the very consideration that neither he who plants is anything, nor he who waters, but God who gives the increase: because even that

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MATHEMATICVM. 317 operis, quod accedit extrinsecus, per illum accedit, quem nihilominus creauit, & quem regit atque ordinat inuisibilitex Deus? Hinc iam in ipsum mundum velut in quamdam magnam arborem rerum otulus cogitationis attollitur, atque in ipso quoque gemina operatio prouidentia reperitur partim Naturalis, partim Voluntaria. Naturalis quidem per occultam Dei administrationem, quæ etiam lignis, & herbis dat incrementum, voluntaria verò per angelorum opera, & hominum. Secu[n]dum illam primam cælestia superius ordinari, inferiusque terrestria, luminaria, sideraque fulgere, diei, noctisque vices agitari, aquis terram fundatam interlui, atque circumlui, aërem altiùs superfundi, arbusta, & animalia concipi, & nasci, crescere, & senescere, occidere, & quidquid aliud in rebus interiori, naturalique motu geritur: In hac autem altera signa dari, docepi, & discere, agros coli, societates administrari, artes exerceri, & quoque alia, siue in superna societate aguntur, siue in hac terrena atque mortali, ita- ut bonis consulatur, & per nescientes malos: in quo ipso homine eandem geminam prouidentia vigere potentiam: primò erga corpus naturale scilicet eo motu quo fit, quo crescit, quo senescit; voluntarium vero quoad victum, tegumentum, curationemque consulitur. Hucusque D. August. Ex quibus liquet, duo esse rerum principia; naturam, & voluntatem; eaque ambo à Diuina prouidentia regi, promoueri, disponi, atque etiam superiori potentia impediri posse: Verum in suo cursu relicta Naturam necessariò operari, Voluntatem liberè, ac naturæ cursum disponere posse, coadiuare, & aliquatenus impedire hinc quæ à natura pure & absque voluntatis adminiculo prodeunt, naturalia; quæ à sola voluntate nihil subfamulante Natura, purè voluntaria: quæ verò à voluntate provt applicat actiua passuis, impedimenta remouet, naturam ipsam ad operandum disponit artificialia dicuntur Quod, & obseruauit ipsemet Augustinus paulò post subdens: Sicut autem in arbore id quod agit agricultura forinsecus, ut illud proficiat, quod geritur (à natura) intrinsecus; sic in homine secundum corpus, ei quod intrinsecus agit natura, seruit extrinsecus medicina: quod autem ad arborem colendi negligentia, hoc ad corpus medendi incuria, hoc ad animam discendi seenitia. Et quod ad arborem humor inutilis, hoc ad corpus victus exitiabilis, hoc ad animam persuasio iniquitatis. Porrò inter naturales causas principem sibilocum vendicant corpora cælestia, quæ sua vniuersali potentia in omnia isthæc sublunaria agunt, suis influxibus producunt, 8.

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MATHEMATICVM. 317 of the work, which comes from outside, comes through that which, nevertheless, He has created, and which God governs and orders invisibly? From this the mind is now lifted up into the world itself, as into a great tree of things, and in it too a twofold operation of providence is found, partly Natural, partly Voluntary. Natural, indeed, through the hidden administration of God, who also gives increase to trees and herbs; voluntary, however, through the works of angels and of men. According to the first, the heavenly things are ordered above, and the earthly things below; lights and stars shine, the turns of day and night are carried on, waters flow around and through the earth laid upon them, the air is spread above, plants and animals are conceived, and are born, grow, and grow old, die, and whatever else in things is carried on by an inner and natural motion. But in the other, signs are given, teaching and learning, fields are cultivated, societies are administered, arts are practiced, and likewise other things, whether they are carried on in the heavenly society or in this earthly and mortal one, so that provision is made for the good, and by the ignorance of the wicked; in which very man the same twofold power of providence is active: first with respect to the body, namely by the motion by which it is made, by which it grows, by which it grows old; but with respect to the voluntary, provision is made for food, clothing, and healing. Thus far St. Augustine. From which it is clear that there are two principles of things: nature and will; and that both are governed, promoted, ordered, and even able to be hindered by a higher power by Divine providence. But in their own course, nature is left to operate necessarily, will freely, and to dispose the course of nature, to help it, and to hinder it to some extent; hence those things that from nature purely and without the aid of will proceed are called natural; those that from will alone, with Nature contributing nothing, are purely voluntary; but those that from will, as it applies the active to the passive, removes impediments, and disposes nature itself to act, are called artificial. This, Augustine himself also observed, a little later adding: As in a tree that which agriculture does externally, so that that may thrive which is wrought inwardly by nature; so in man, with respect to the body, to that which nature does inwardly, medicine serves from without: what neglect of cultivation is to a tree, that carelessness in treatment is to the body, and sluggishness in learning is to the soul. And what unwholesome moisture is to a tree, that deadly food is to the body, and that persuasion of wickedness is to the soul. Moreover, among natural causes the heavenly bodies claim the foremost place, which, by their universal power, act upon all these sublunary things, produce them by their influences,

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LEXICON conseruant, immutant, alterant, perdunt: neque eorum activitas roli vel impedi potest ab humana voluntate, aut ab vllis causis inferioribus, sed tantum à Causa prima Deo; atque adeò vel ob id cæteris omnibus præstant. Benè vero potest homo eorum naturam, qualitates, effectus, inalterabilem agendi vim callens excolere in ipsis inferioribus, applicare, præuertere, declinare, sicut dixit Ptolemæus in Cenriloquio Verbo 8, Sapiens anima, inquit, confert cælesti operationi, quemadmodum optimus Agrico a arando, expurgandoque confert Natura. I Girur non potest homo facere, vt Astras suos naturales virtutes non exerant, effectus sibi proprios non producant, qualitates maleficas, aut beneficas, quibus intrinsecus potiuntur exuant, & contrarias induant, potest verò aliquatenus in causis inferioribus eas alterando, impediendo, aut etiam destruendo, sicque totaliter eorum effectus præuerrere. 9. Sic non potest homo vllor modo Eclipsim futuram impediire, neque effectus, inde naturaliter emanaturos: non potest, exempli gratia, æstum nimium ex congressu solis, & Marris sequuturum præuertere, nives, pluuias, venros, aëris infectiones, &c. potest aurem in naturis inferioribus, vt ædificando super solum, ne herbas germinet, exsiccan- do stagna, ne aërem corrumpant; recidendo arbores ne fructus proferant. Sic etiam astris subsamulando eorum operationi conferre, vt subministrare materiam, vel remouere, sese contrà prauas siderum influentias præmunire, bonis substernere, disponere, & passibilem applicare tempore præuisæ sterilitatis (vt fecit Ioseph Patriarcha) magnam frumenti vim in horrea comporrare, in bonis siderum configurationibus tertam excolere, maria exsulcare; in malis domi consistere, arque à labore inutili abstinere, &c. Concludam igirut cum iis quæ apposire ad hanc rem habet Kircherus in Arte Magna Lucis & Vmbra lib. 6. part. 3. cap. 2. Natura, inquit, duobus principiis regitur, natura, & voluntate: Natura subiecta est sideribus, voluntas libera, & ideò effectus, & operationes purè naturales sideribus planè obediunt tanquam causis necessariis, vt sanitas, vel infirmitas; longa, vel breuis hominum vita, &c. alia qua purè voluntaria, vt speculari, docere, ætus virtutum aut vitiorum: alia mixta, vt facere iter, comedere, &c. Vtrum autem iter commodum futurum sit, necne, à sideribus pendet, aërisque constitutione. Si quis igitur perfectè cognosceret influxus siderum corpori nostro congruum, vel incongruum, haud dubiè de fortunato, vel infortunato itineris statu certò

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LEXICON preserving, changing, altering, destroying: neither can their activity or operation be impeded by human will, or by any lower causes, but only by the First Cause, God; and therefore on that account too they surpass all the others. Yet indeed man can cultivate in the lower things their nature, qualities, effects, and immutable power of acting, knowing how to apply, turn aside, and divert them, as Ptolemy said in the Centiloquium, Word 8: “The wise soul,” he says, “contributes to the celestial operation, just as the best farmer does by ploughing and clearing the ground.” But man cannot make the stars not exercise their natural virtues, not produce their proper effects, or divest themselves of the harmful or beneficial qualities with which they are intrinsically endowed, and put on contrary ones; yet he can in some measure, in the lower causes, alter them, hinder them, or even destroy them, and thus entirely avert their effects. 9. Thus man cannot in any way prevent an eclipse to come, nor the effects naturally flowing from it: he cannot, for example, avert the excessive heat that will follow from the conjunction of the sun and Mars, nor snow, rains, winds, infectious airs, etc. But he can in lower natures, as by building over the soil so that grass may not sprout, drying up ponds so that they do not corrupt the air, cutting down trees lest they bear fruit. In this way too he can, by co-operating with the stars in their operation, contribute, as by supplying matter or removing it; he can guard himself against evil stellar influences, prepare for the good ones, dispose and render passible matter fit at the time of foreseen sterility (as the patriarch Joseph did), store up a great supply of grain in barns, cultivate the fields in favorable stellar configurations, sail the seas; in unfavorable ones remain at home, and abstain from useless labor, etc. I shall conclude therefore with what Kircher has aptly stated on this matter in the Ars Magna Lucis & Umbrae, book 6, part 3, chapter 2. “Nature,” he says, “is governed by two principles, nature and will: nature is subject to the stars, will is free, and therefore effects and operations that are purely natural plainly obey the stars as necessary causes, such as health or illness; the long or short life of men, etc. Others are purely voluntary, such as to contemplate, to teach, to exercise virtues or vices; others mixed, such as to take a journey, to eat, etc. Whether the journey will be convenient or not depends on the stars and on the constitution of the air. If therefore someone perfectly knew the influences of the stars agreeable or disagreeable to our body, he would doubtless be able to know with certainty the fortunate or unfortunate state of the journey”

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MATHEMATICVM. 51. iudicare posset: item de sanitate, de morbo, &c. Item de successu negotij cum principe. Verum cum hæc difficulter fieri possint, & scire, hinc electionum harum notitia, nisi experientiis fulciatur, vt plurimum fallax est. Hæc Kircherus. Ex quibus patet quid ars, seu humanum ingenium, quid Natura possit, quidve homo ex rerum natura probè cognita aggredi possit, quid demum frustrà, quid etiam temerè ag- grediatur. NAVBARACH, siuè Naubahàr arab. idem sonat, ac No-10. uenariæ Dominus. Vide in V. Anaubarach. NAVIS vulgò audit sidus ad australem plagam constans 11. stellis 63. vt liquet ex accuratissimis nouorum Astronomorum obseruationibus, omnibus ferè de natura Saturni, & Louis, quorum præcipua est Canopus in temone consistens primi honoris arab. Rubail, cui proximè accedit dicta Marcheb in medio scuti posita. Hoc sidus à schillero immutatum fuit in Arcam Noë. Hebraicè autem dicitur Sephina. NEBOLASSID apud Fetzanos, Maroccenses, cærerosque 12. Nubianos astrologos appellatur Cauda Leonis, stella fixa primæ magnitudinis, de qua satis dictum est suo loco. NEBVLOSÆ STELLÆ sunt fixæ quædam obtuso lumine, pallenti, & suboscuro micantes: eò dictæ vel quia nebulas quasdam specie sua præseferunt, (quales præcipuè sunt dux magnæ & satis conspicuæ ad polum Antarcticum) vel sanè, quia nebulas generant, & cum sole occidentes aerem nebulosum reddunt, vt obseruarunt Ptolemæus & Plinius, in Presepi, existente in pectore Cancri, in ea, quæ est in oculo Sagittarij, sed præsertim videre est in ea, quæ sequitur aculeum scorpij. Idque, vt obseruat Titus lib. 1. cap. 12. quia earum nebulositas parem, & consimilem effectum parit in hisce inferioribus. Hinc etiam experientia compertum est, vt quandocumque cum Luminaribus in alicuius genesi congredientur, semper excitatem, nebulas, aut aliud vitium in oculis importent; quod ipsa naturalis ratio suadet, Nam earum lux valdè exilis, ac debilis est, ac proinde non mirum, si oculorum lucem adimant, aut obtundant, quando ipsis luminaribus, à quibus lumen in oculos derivatur congressu stant infensæ. NEMER hoc est Pardus hæbreorum lingua dicitur Lupus 14. sidus de quo alibi dictum. NEOMENIUM græcè idem valet, ac Nouilunium, de quo 15. mox infrà. NEPA Ciceroni, & aliis idem est, ac Scorpij sudus fortè à 16.

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MATHEMATICVM. 51. could judge: likewise about health, disease, etc. Likewise about the success of a business with a prince. But since these things can hardly be done, and known, the knowledge of these elections, unless supported by experience, is for the most part deceptive. Thus Kircher. From these things it is clear what art, or human ingenuity, can do, what Nature can do, and what a man, having properly understood the nature of things, may undertake, and finally what he undertakes in vain, and what even rashly he undertakes. NAVBARACH, or Naubahàr in Arabic, signifies the same as Lord of the hunting grounds. See under V. Anaubarach. NAVIS, commonly called the constellation in the southern region consisting of 11. stars 63., as is clear from the most accurate observations of the new Astronomers, almost all of the nature of Saturn and Jupiter, the chief of which is Canopus, situated in the rudder, of the first Arab honor, Rubail, to which the said Marcheb, placed in the middle of the shield, comes next. This constellation was changed by Schiller into Noah’s Ark. In Hebrew it is called Sephina. NEBOLASSID, among the Fetzans, Moroccans, and the rest of the 12. Nubian astrologers, is the name given to the Tail of the Lion, a fixed star of the first magnitude, of which enough has been said in its place. NEBULOUS STARS are certain fixed stars gleaming with a dull, pale, and somewhat dark light: so called either because they present a sort of nebula in their appearance, (such are especially the two great and quite conspicuous ones near the Antarctic pole) or truly because they generate mists, and, when setting with the sun, make the air misty, as Ptolemy and Pliny observed, in the manger, situated in the breast of Cancer, in that which is in the eye of Sagittarius, but especially to be seen in that which follows the sting of Scorpio. And this, as Titus observes, book 1, chap. 12. because their nebulousness produces an equal and similar effect in these lower regions. Hence experience has also shown that, whenever they come together with the Luminaries in anyone’s nativity, they always bring redness, mists, or some other defect in the eyes; which natural reason itself suggests, for their light is very slight and weak, and therefore it is no wonder if they take away or dim the light of the eyes, when they stand in hostile conjunction with those luminaries, from whose encounter light is conveyed into the eyes. NEMER, that is, Pardus, in the Hebrew tongue, is called the Wolf 14. a constellation of which mention has been made elsewhere. NEOMENIUM in Greek means the same as New Moon, of which 15. presently below. NEPA, in Cicero and others, is the same as the sign of Scorpio, perhaps 16.

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MATHEMATICVM. 327 non item, sed ad singulos ferè minutum vnum, quinimò nodi Lunares ad sua ferè minuta, vt patet in Ephemeridibus, ac tabulis secundorum mobilium. Habent in Genethliacis nodi maximam significationem quoad formam corporis, quam plerumque deurpant, si cum Luminaribus, vel infortunis fuerint reperti, præsertim in Angulis, & in signis detruncatis, vel curuis; qualia sunt Aries, Taurus, Cancer, Scorpio, & Capricornus. Vnde Nati euadent gibbi, strabi, claudi, consorti, vel quouis modo debilitati, vt habet Ptolemæus lib. 3. eap. 17. N [N]AS [N]ASPHÆRA communiter dicitur Primum Mobile, quod constituitur supra octauam sphæram, seu Cælum stellarum, quod secum trahit omnes inferiores sphæras ab oriente in occidentem eursu concitatissimo revolutionem suam perficiens spatio ferè 24. horarum. Alij autem hanc nonam sphæram admittunt distinctam à Primo mobili, quin, & Decimam, quas vocant librationis; seu trepidationis, quam in vident in Firmamento; obseruarunt enim ipsum præter motum vniuersalisatis, & proprium, moueri irregulariter ab septentrione in Austrum, & ab Austro ad Septentrionem sub coluro solstitiorum primi mobilis, vltrò eitróque: rursus moueri ab ortu in occasum, & ab occasu in ortum sub Ecliptica, & super polos eiusdem: Quare cum tot motus comperiantur in firmamento; atque in planetis, nec duos modò explicatos posse haberi dicant ex se, aut à primo mobili, ex vulgato illo axiomate corpus vnum simplex natura sua vno tantum simplici motu moueri posse intrinsecè, ab extrinseco verò pluribus, consequenter, & hanc nonam sphæram admittunt, quæ dat moueri ab ortu in occasum, & ab occasu in ortum super polos Zodiaci per minuta 14. annorum 1716. vt dicunt spatio, & rursus Decimam, quæ det moueri à septentrione in Austrum sub coluro solstitiorum per minuta 24. spatio annorum 3432. Quæ de re vide Clauium, & Blancanum in sphara mundi lib 18. c.7. Ego vero hos motus distinctos, proindeque distinctas sphæras admittere nullatenus possum, quoniâ repugnat vnum & idem nobile duobus motibus contrariis moueri, quo pacto essent huiusmodi motus trepidationis, qui prorsus fictitij sunt, & optimè saluantur apparentiæ siderum, irregularitates, &c. in sola cæli fluxibilitate, & vnco tantum motu ab oriente in occidentem regulariter tamen irregulari secundum omnes cæli partes remotiores, & remotiores à prima virtute motrice. Vide quæ fusè diximus in V. Motus. NOTA PELIOTES ventus est vnsus ex quatuor intermediis 18. X

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MATHEMATICVM. 327 not in the same way, but to individual minutes, or even to the lunar nodes to their own minutes, as appears in ephemerides and tables of secondary motions. In genethliacs the nodes have the greatest significance with regard to the form of the body, which they usually deform, if they are found with the luminaries or the infortunes, especially in the angles, and in truncated or crooked signs, such as Aries, Taurus, Cancer, Scorpio, and Capricorn. Hence those born will turn out hunchbacked, cross-eyed, lame, deformed, or weakened in some way, as Ptolemy has in book 3, chap. 17. The sphere [N]AS [N]ASPHÆRA is commonly called the Primum Mobile, which is placed above the eighth sphere, or the heaven of the fixed stars, and which carries along with itself all the lower spheres from east to west, completing its revolution in a very rapid course in a space of about 24 hours. Others, however, admit this ninth sphere as distinct from the Primum Mobile, and even a Tenth, which they call the sphere of libration, or trepidation, which they see in the firmament; for they observed it, besides the universal and proper motion, to move irregularly from north to south, and from south to north under the colure of the solstices of the Primum Mobile, back and forth; again to move from east to west, and from west to east under the ecliptic, and over its poles: wherefore, since so many motions are found in the firmament, and in the planets, and since they say that not only the two explained motions can arise of themselves, or from the Primum Mobile, according to that common axiom that a simple body by its own nature can be moved intrinsically by only one simple motion, but extrinsically by many, they consequently admit this ninth sphere also, which causes motion from east to west, and from west to east over the poles of the Zodiac by 14 minutes in a space of 1716 years, as they say, and again a Tenth, which causes motion from north to south under the colure of the solstices by 24 minutes in a space of 3432 years. For this matter see Clavius and Blancanus in the sphere of the world, book 18, c. 7. But I myself cannot in any way admit these motions as distinct, and therefore distinct spheres, because it is contradictory for one and the same noble body to be moved by two contrary motions, by which account such motions of trepidation would be entirely fictitious, and the appearances of the stars, irregularities, etc., are most excellently preserved in the mere fluidity of the heavens, and by one single motion from east to west, yet regularly irregular according to all the parts of heaven, farther and farther removed from the first motive virtue. See what we have discussed at length in V. Motus. NOTE: PELIOTES is a wind, one of the four intermediate ones, 18. X

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326 LEXICON æquè spirans inter meridiem, & ortum, aliis Euronotus dictus à nostris vulgò Syrouus, eo quod per mediam syriam transeat, opponitur directè Borrolybico, seu Magistrali. Eius qualius est valdè debilis, & silens, humidior tamen quam in Euro, & sæpè in austri naturam degenerat; qui licet pluuiam non afferat, facit tamen tempus valdè turbidum, aquosum, & repletaërem caligine, atque obscuritate. Excitati solet hic ventus à sole ex oriente cum stellis fixis sitis in cornu, & cauda Arietis, in nexu, & Ventte Piscium, Fornaham, Vmbilico Andromedæ, & quæ sunt in Cæto. Similiter à Mercurio, (qui ventorum generalis est motor) congetdiente cum dictis stellis, atque insuper cum Lyra, Scheat, Pleiadibus, Lucida Hidræ, Hebulosa in oculo Sagittarij, ac denique tribus stellis existentibus in fronte Scorpij. Plura de eius natura, & qualitatibus vide apud Vitruuium lib.1 cap.6. NOTOLIBICVS est item Ventus alius intermedius spirans <29.> ex æquo inter meridiem, & occasum, oppositus Mese, seu Borthapeliosi: apud nos vulgò Libeuius, seu Garbinus dicitur, eo quod acer sit, & peruersæ naturæ, tum etiam quia tempus serenum in turbidum, ac pluuiosum semper convertit. Natura sua est humidus, morbosus, tempestuosus præsertim verò Ligustico mari infensus. <30.> Nórvs græcè idem quod Auster Ventus vnus ex quatuor cardinalibus spirans à puncto meridiei oppositus directè septenirioni. Est de natura sua calidus, & humidus morbosus, noxius (vnde & nomen à nocendo hausit) & solet morbos multos excitare, vt febres putridas, pleuritides, &c. & si diu absque interpolatione spirauetit inducere solet pestilentiam, vt sæpius obseruatum est, & refert Abraham Gorlnitz in compendio Geographico. Ratio autem naturalis est, quia corpora per ipsum efficiuntur humida, & calida, atque ob id puiredini maximè obnoxia: vnde exurgit pestis, quæ aliud planè non est quam corruptio sanguinis circa cor. Hinc Ouidius. Letiseris calidi spirarunt astibus austri. Flare solet potissimum in occasu vespertino Arcturi, Pleiadum, atque Sirij; nec non in occasu matutino Hyadum, & Coronæ Gnostiæ: quo tempore, inquit Plinius lib.18. c.33. Materiam, vineamque, agricola nstractes: humidus, & astuosus Italia est: Africa quidem incendia cum serenitate affert. cuius rei rationem reddidimus in V. Auster. Idem testatur in lib.2.cap.45. huic vento esse rupem quamdam in Cyrenaica provincia sacram, quam profanum sit attrectare ho-

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326 LEXICON A wind blowing equally between the south and the east, by others called Euronotus, by our people commonly Syrouus, because it passes through the middle of Syria, is directly opposite to the Borrolybicus, or Magistral. Its quality is very weak and silent, though more humid than the Euro, and it often degenerates into the nature of the Auster; and although it does not bring rain, it nevertheless makes the weather very cloudy, watery, and filled with mist and darkness. This wind is usually stirred up by the sun in the east together with the fixed stars situated in the horn and tail of Aries, in the knot and belly of Pisces, Fornaham, the navel of Andromeda, and those in Cetus. Likewise from Mercury, who is the general mover of the winds, when conjoined with the said stars, and moreover with Lyra, Scheat, the Pleiades, Lucida Hydrae, the nebulous star in the eye of Sagittarius, and finally the three stars situated in the forehead of Scorpio. See more about its nature and qualities in Vitruvius, book 1, chapter 6. NOTOLIBICVS is likewise another intermediate wind blowing <29.> equally between the south and the west, opposite to Mese, or Borthapelios: among us it is commonly called Libeuius, or Garbinus, because it is sharp and of perverse nature, and also because it always turns clear weather into cloudy and rainy. By nature it is humid, unhealthy, stormy, and especially hostile to the Ligurian sea. <30.> Nórvs, in Greek, means the same as Auster. It is one of the four cardinal winds, blowing from the point of the south directly opposite to the north. By nature it is hot and humid, unhealthy, harmful—whence it also took its name from harming—and it usually excites many diseases, such as putrid fevers, pleurisy, etc.; and if it blows for a long time without interruption, it usually brings pestilence, as has often been observed and as Abraham Gorlnitz relates in his Geographical Compendium. The natural reason is that bodies are made humid and hot by it, and are therefore especially liable to putrefaction; whence arises pestilence, which is nothing other than corruption of the blood around the heart. Hence Ovid: Letiferis calidi spirarunt astibus austri. It is most commonly wont to blow at the evening setting of Arcturus, the Pleiades, and Sirius; and also at the morning setting of the Hyades and the Crown of Gnosia: at which time, says Pliny, book 18, chapter 33, the farmer should store his materials and vineyard. Italy is humid and stormy; Africa indeed brings fires together with clear weather. We have given the reason for this in the section on Auster. The same author testifies in book 2, chapter 45, that in the province of Cyrenaica there is a certain rock sacred to this wind, which it is profane to touch ho-

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MATHEMATICVM. 327 minis manu, confestim austro voluente arenas. Vide adhuc quæ diximus in dicto verbo Auster. NOTIVS PISCI, seu Aurinus dicitur sidus in coelo ad Au- < 328> stralem plagam piscis magni figuram præsefecens atque am- bitu suo complectens stellas duodecim omnes fetè de natura Saturni, vel Veneris, quarum præcipua est quæ in ore, & est eadem quæ in vltima effusione aquæ Aquarij dicta Forna- hand primæ magnitudinis de natura Veneris, & Mercurij. Hoc sidus in Horoscopo, inquit Pontanus; facit eximium nativorem & venatorem. In occasu verò mortem indieit in aquis, aut per belluarum ingluuiem. Propè ipsum sunt ali- quot sporades de natura irem Saturni. NOVENARIÆ quid sint, & quis earum Dominus Vide in V. < 329> Anaubarach. NOVELVNIUM dicitur tempus illud, quo Luna silet, est- < 330> que in coniunctione solis, eo quia vetere decedente, noua quasi succedit. Eius momentum si quis obseruate volet, vi- debit planè in lixiuo, vel etiam in aqua cuius plenum sic vas vitreum, aut argenteum, atque in fundo vasis consi- stant quieti cineres oleæ, vel vitis: Nam cum primum Lu- na Solis diametrum intrat, mox cineres ex seipsis exiliunt, turbant aquam, & in gyrum vertuntur, nec ad pristinam quietem redeunt, quoad vsque Luna perfectè de disco solis exierit: quod ego semel & iterum obseruaui. Dies etiam Nouilunij attificiosè per numeros, & Epa- < 331> etam facile internosci poterit. Quandoquidem, si Epactæ currenti numerum Calendarum ac dierum qui à Martio præ- teriro vsque ad præsentem diem effluxerunt, adieceris; at- que à 30. (quæ integra Lunario est) numerum productum detraxeris, relinqueur numerus dierum, post quos cele- brabitur Luminarium synodus. Quodsi productus numerus tricenarium excesserit, runc deme ab eo triginta, & quod su- perest tursus à triginta subtrahe, & mox Nouilunij dies emerget. NOX dicitur tempus illud, quo sol inferius hemisphæ- < 332> rium lustrat à cardine occidentis per Imum Cæli ad Cardi- nem Orientis tendens: sicut econtrà dies est cum sol emer- git ex horizonte, & graditur per Medium Cæli ad Occi- dentem, quovsque in ipsum mergatur. Elus porrò quanti- tatem metitur atcus æquatoris nocturnus, sicut & diei diur- nus, qui inter vttumque cardinem intercipitur, aut sub ter- ta, aut suprà terram, accepra pro singulis quind-nis gra- dibus integra hora. Et nox quidem diuiditur in septem spa- ria, quæ sunt Vesper, Crepusculum, Conticinium, In- X ij

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MATHEMATICVM. 327 with the hand of the diminutive, at once the south wind whirling the sands. See further what we said under the word Auster. NOTIVS PISCI, or Aurinus, is said to be a constellation in the heavens toward the southern quarter, presenting the shape of the great Fish and enclosing within its circuit twelve stars, all almost of the nature of Saturn or Venus, the chief of which is that in the mouth, and this is the same as the one in the final outpouring of water of Aquarius, called Fornax, of first magnitude, of the nature of Venus and Mercury. This constellation, says Pontanus, makes an excellent native and hunter. At its setting, however, it signifies death in waters, or by the appetite of beasts. Near it are several star-clusters of the nature of Saturn's wrath. NOVENARIÆ: what they are, and who is their Lord, see under V. Anaubarach. NOVELVNIUM is called that time when the Moon is silent, and is in conjunction with the sun, because the old one departing, the new seems to succeed. If anyone wishes to observe its moment, he will clearly see it in lye, or even in water, if you fill such a glass vessel, or silver one, and let quiet ashes of olive or vine settle at the bottom of the vessel; for as soon as the Moon enters the Sun's diameter, the ashes immediately leap up of themselves, disturb the water, and turn in a circle, nor do they return to their former stillness until the Moon has completely come out from the disk of the sun: which I myself have observed once and twice. The day of the New Moon may also be easily recognized artificially by numbers and the Epact. For if you add to the current Epact the number of the Calendar days and the days that have elapsed from the previous March up to the present day; and subtract the product from 30, which is the full lunar cycle, there will remain the number of days after which the conjunction of the luminaries will be celebrated. But if the resulting number exceeds thirty, then subtract thirty from it, and what remains subtract again from thirty, and immediately the day of the New Moon will appear. NOX is called that time when the sun traverses the lower hemisphere, moving from the western cardinal point through the bottom of the sky toward the eastern cardinal point: just as, on the contrary, day is when the sun rises from the horizon and goes through the middle of the sky toward the west, until it sinks into it. Its quantity is measured by the nocturnal arc of the equator, just as also that of the day, which is intercepted between either cardinal point, either beneath or above the earth, taking fifteen degrees as one hour. And night is divided into seven intervals, which are Vesper, Crepusculum, Conticinium, In- X ij

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LEXICON 328 tempestum, Gallicinium, Matutinum, & diluculum, siue Aurora. Vesper est ea pars, quæ complectitur modicum illud tempus, quo sol horizontem occiduum radit, & adhuc in aliqua sui parte conspicuus est. Crepusculum est totum illud tempus quo sol consistit citra lineam crepusculinam, quod spatium se extendit ad 18. gradus infra horizontem, & hac linea crepusculina claudiur, in quo proinde spatio lucem illam subobscuram transmittit ad superius hemisphærium quam nos crepusculum vocamus. Inde sequitur Conticinium, & est obscurum noctis in quo solent omnes conticescere, & cubare. Post conticinium sequitur Intempestum, quod est medium noctis, quando sol possidet Cardinem Imi Cæli: Intempestum subsequitur Gallicinium quod est spatium temporis, quo galli gallinacei primum cantare incipiunt. Deinde instat Matutinum seu Matutinum Crepusculum, quando sol intrat lineam crepusculinam, & facit iterum subobscuram lucem. Tandem subintrat Diluculum quando est iam clara dies, & Aurora; sed tamen sol adhuc ex inferiori hemisphærio non emersit, 36. Nybes aliud planè non est, quam vapor vi siderum ex inferioribus hisce in secundam aeris regionem attractus, atque addensatus vt habet Arist. 1. Meteor. c. 9 qui si in aquas resoluatur dicitur pluuia, nimbus, imber, pro qualitate decidentium guttarum: si vero terris incubet, nec ob ratitatem, vel exhaltationum admixtarum multitudinem, valeat in pluuiam resolui dicitur nebula, & caligo, quæ postea a solis radiis, vel a ventis dissoluitur, & dissipatur. 37. Numeris definiti solet communiter esse Vnitatum collectionem, seu ex vnitatibus compositam multitudinem: ita vt vnitas ipsa numerus non dicatur, sed initium numeri. Est obiectum Arithmeticæ, quatenus eius passiones, proportiones, ordinem, atque vnius ad alterum habitudinem considerat. Hinc apud græcos rythmus appellatur, quod proportionem, & harmoniam sonat: Apud veteres non nisi ad summam centum millium pertingebat, vt author est Plinius lib. 33. cap 10. Verum hodie vsque in infinitum protrahi potest arte, & præceptis huius verè Angelicæ disciplinæ, quæ Angelorum hierarchico numero primum inuenta credimur, atque Angelorum ministerio, vt ex sacris paginis habetur, passim hominibus insinuata. Egit de numerorum mysteriis sparsim in suis operibus Augustinus, præsertim tom. 3. & 4. Eorumque miram proportionem, processum, vim, qualitatem, diuisionem luculenter explicat Marsilius Dicinus in expositione numeri nuptialis Reipubli-

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LEXICON 328 tempestum, Gallicinium, Matutinum, and diluculum, or Aurora. Vesper is that part which includes that brief time when the sun grazes the western horizon and is still visible in some part of itself. Crepusculum is that whole time during which the sun remains this side of the twilight line; this space extends to 18 degrees below the horizon, and is bounded by this twilight line, in which space it therefore transmits that dim light to the upper hemisphere, which we call twilight. Then follows Conticinium, the dark part of night in which all usually cease speaking and go to bed. After conticinium follows Intempestum, which is the middle of the night, when the sun occupies the Cardinal of the lower heaven: Intempestum is followed by Gallicinium, which is that span of time in which cocks first begin to sing. Then comes Matutinum, or Morning Twilight, when the sun enters the twilight line and again makes a dim light. Finally comes Diluculum when it is already broad day, and Aurora; but yet the sun has not yet emerged from the lower hemisphere, 36. A cloud is nothing other than vapor, by the force of the stars drawn from these lower regions into the second region of the air, and condensed, as Aristotle has in Meteor. 1, c. 9. If it is resolved into waters it is called rain, nimbus, shower, according to the quality of the falling drops: but if it lie upon the earth, and by reason of rarity, or of the multitude of mixed exhalations, cannot be resolved into rain, it is called mist and fog, which afterwards are dissolved and dispersed by the rays of the sun, or by the winds. 37. Number is commonly defined as a collection of units, or a multitude composed of units: so that unity itself is not called a number, but the beginning of number. It is the object of Arithmetic, insofar as it considers its properties, proportions, order, and the relation of one to another. Hence among the Greeks it is called rhythm, because it suggests proportion and harmony: among the ancients it reached no further than the sum of one hundred thousand, as the author Pliny says, book 33, chapter 10. But today it can be extended even to infinity by the art and precepts of this truly angelic discipline, which, we believe, was first invented for the hierarchical number of the Angels, and, by the ministry of Angels, as is found in the sacred pages, was everywhere communicated to men. Augustine dealt with the mysteries of numbers here and there in his works, especially in vols. 3 and 4. And Marsilius Ficinus, in the exposition of the nuptial number of the Republi-

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MATHEMATHICVM. 329 ex Platonis; atque integro volumine idem argumentum prosequitur Petrus Bongus diligentissimus scriptor. Nobis hæc tetigisse sufficiat. Vide quæ de numerorum proportio- nalitate dicemus in Verbo Proportionalitas. O. 1. OBDIENTIA SIGNA communiter apud Astronomos appellatur ea Antisciorum genera, quæ cum alias æqualiter distent ab æquatore, atque eande numero declinationem habeant, ipsa nihilominus deflectunt ad Austrum aliis sibi pari potentia respondentibus, ad boream declinantibus, quæ proinde imperantia audiunt, eo quia ratione situs & regionis, qua super alia eleuantur ista videntur quodammodo imperare, illa obedire, atque istis subfamulari. Vide quæ fusius de hac re diximus in V. Imperantia signa. 2. OBIAC LARI, teste Valla, dicitur apud Astronomos stella aliam stellam sibi succedentem secundum ordinem signorum respiciens aliquo radio; cum videlicet in tanta ab ea distantia ponitur, vt inde à sinistris aliquem radium immittere ac iaculari possit in aliam: vt stella, quæ verbi gratiâ est in Ariete fetit eam quæ in Sagittario triangulari aspectu: eam quæ in Capricorno, quadrato, eam quæ in Aquario sextili, &c. 3. OBLIQVA ASCENSIO, sphara, &c. Vide in VV. Ascensio, Sphara, &c. 4. OBLIQVUS ANGVLVS apud Geometras audit qui constat ex duabus lineis curuis, aut sanè vna recta aut altera curua. Qua de re vide Clauium in Elementa Euclidis. 5. OBLIQVUS CIRCULVS vide Zodiacus. 6. OBLIQVA SIGNA dicuntur quæ obliquè emergunt ex horizonte hoc est, quibuscunt minor portio æquatoris ascendit: vnde consequens est, vt obliquiùs quam æquator ascendat ille arcus Zodiaci, qui talia signa complectitur. Recta verò appellantur quæ ascendunt rectè, rectiùs inquam quam æquatoris arcus illis respondens, quæ profecto maiori semper cum graduum portione quam ipse æquator ascendant necesse est. Porrò quæ signa obliquè ascendunt, rectè postea cadunt, quia minor portio æquatoris cum illis descendit: quæquè rectè ascendunt, descendunt postea obliquè. Qua de re extant versiculi id breuiter explicantes. Rectà meant, obliquè cadunt à Sidere Cancri Donec finitur Chiron: sed cætera signa X iij

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MATHEMATHICVM. 329 from Plato; and with an entire volume, Petrus Bongus, a most diligent writer, pursues the same subject. It will suffice for us to have touched on these matters. See what we shall say about the proportionality of numbers in the word Proportionalitas. O. 1. OBEDIENT SIGNS is the name commonly given by astronomers to those kinds of antiscia which, although they are equally distant from the equator and have the same number of degrees of declination, nevertheless incline toward the south when others, answering them with equal force, incline toward the north; and thus they are said to obey and to be subject, because, by reason of position and region, in which they are raised above the others, these seem in some sense to rule, and those to obey, and to serve them. See what we have said more fully on this matter in V. Imperantia signa. 2. OBLIQUELY LOOKING AT, according to Valla, is said among astronomers of a star that looks by some ray at another star succeeding it in the order of the signs; that is, when it is placed at such a distance from it that from there, on its left side, it can cast and shoot a ray into another: as a star which, for example, is in Aries looks at the one in Sagittarius with a triangular aspect; the one in Capricorn with a square aspect; the one in Aquarius with a sextile aspect, and so on. 3. OBLIQUE ASCENSION, etc. See in the words Ascensio, Sphara, etc. 4. OBLIQUE ANGLE, among geometers, is the name given to that which is made up of two curved lines, or indeed one straight line and another curved one. On this matter see Clavius on the Elements of Euclid. 5. OBLIQUE CIRCLE, see Zodiacus. 6. OBLIQUE SIGNS are those which rise obliquely from the horizon, that is, those with which a smaller portion of the equator ascends: hence it follows that the arc of the zodiac which includes such signs ascends more obliquely than the equator. Those signs are called straight, however, which rise straight, that is, more straightly than the arc of the equator corresponding to them, which certainly must ascend with a greater portion of degrees than the equator itself. Moreover, the signs which ascend obliquely afterward set straight, because a smaller portion of the equator descends with them; and those which ascend straight afterward descend obliquely. On this matter there are verses briefly explaining it. They move straight, they set obliquely from the star of Cancer Until Chiron ends: but the remaining signs X iij

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LEXICON Nascuntur prono, descendunt tramite recto. 7. OBLIQV TO PLANETA, teste Abraham Auenarre, & infirmitas, & defectio virium illi accidens in situ Mundi, cum videlicet repertus fuerit in domibus cadentibus, Nona, Tertia Sexta, & Duodecima; sed in his postremis longè grauiùs debilitatur: quod quidem in Infortunis bonum est, minus quippe noxiæ sunt; Et inde forte cuasit, vt Saturnus dicatur gaudere in Duodecima, Mars in Sexta, ibi siquidem benè quoad nos locaniur. 8. OBSC RÆ STELLAe au[n]diunt, quæ lumine obtuso, & sub- oscuro præditæ sunt; quales in Sectione equi quatuor, toti- dem circa Helicon, & vna antecedens caput Medulæ. Ha- rum esse & us, vt diximus cum de Nebulosis, suis causis assi- milantur; atque adeò prodibunt obscuri, tenebrosi, &c. Cum enim Astra agant per lumen, qualis erit huius affectio, tale etiam esse dabunt effectibus. 9. OBSSESSIO est passio contingens Planetæ quando à duobus præsertim contrariæ naturæ, Medius intercipitur, & val- latur, absque aliorum aspectu, & fulcimenio Quæ qui- dem passio, si bonis planetis ab infortunis obuenerit, pessima est, si à fortunis optima: si demum malefico à fortu- nis contigerit, eius vires funditus infringuntur, absque tamen, vel saltem leui beneficiarum repassione, ac ia- ctura. 10. OBTVSVS ANGULVS. Vide in V. Angulus. 11. OCCIDENS apud Astronomos dicitur ea horizontis pars, vbi cadit æquator, aut stella in æquatore consistens in in- sertus hemisphærium, vnde spirat Zephyrus ventus: im- propriè verò complectitur totum illum horizontis arcum, qui stellarum occiduam amplitudinem definit. Quemadmo- dum oriens locus illi directè oppositus nominatur, vnde spi- rat subsolanus, & emergunt sidera ex horizonte. Hinc septi- ma Domus ab horoscopo Occidens, & Cardo occiduus ap- pellari consueui. Apud Geographos verò, quoniam Oriens, & Occidens variantur secundum varietatem Regionum, & horisonis, computari solet verum occidens ab Insulis for- tunatis æquarori subiectis, à quibus Ptolemæus, vtpore ab extremis finibus terræ habitabilis incipit computare lon- gitudines Ciuiarum versus Orientem, qui consequenter concipiendus est in parte terræ habitabilis, quæ distat ab In- sulis fortunatis medietate Circuli, hoc est gr. 180. Vnde sunt qui ponunt veru Orienté in Civitate Arym quam dicut esse sub Æquatore. Verum id falsum esse vel ex eo liquet, quod neque a Ptolomæo neq[ue] ab alio insigni Comosgrapho

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LEXICON They are born with a downward slant, they descend in a straight path. 7. OBLIQUE TO THE PLANETS, according to Abraham Avenarre, and weakness, and the loss of strength occurring to it in the situation of the world, namely when it is found in cadent houses, the Ninth, Third, Sixth, and Twelfth; but in these latter it is weakened far more severely: which indeed is good in infortunes, since they are less harmful; and from this perhaps it came about that Saturn is said to rejoice in the Twelfth, Mars in the Sixth, since there they are well placed with respect to us. 8. OBSCURE STARS are understood to be those which are endowed with a dull and somewhat dark light; such as in the Section of the four Horses, four around Helicon, and one preceding the head of Medusa. These, as we said when speaking of Nebulous stars, are assimilated to their causes; and thus they will come forth obscure, dark, and so on. For since the stars act by means of light, whatever the quality of this condition may be, such also will the effects that it produces. 9. OBSESSION is a passion affecting a planet when, especially by two of contrary nature, it is intercepted and surrounded, without the aspect and support of others. This passion, if it happens to good planets from the infortunes, is worst; if to the fortunes, best: if at last it happens to a malefic from the fortunes, its powers are utterly broken, though without, or at least with slight, repercussion and loss from the benefics. 10. OBTUSE ANGLE. See in V. Angle. 11. OCCIDENT among astronomers is said to be that part of the horizon where the equator falls, or where a star placed on the equator enters the hemisphere, whence the west wind, Zephyrus, blows: but improperly it includes the whole arc of the horizon which marks the setting amplitude of the stars. Just as the opposite place is called the Orient, whence the subsolanus wind blows and the stars emerge from the horizon. Hence the seventh House from the horoscope is customarily called the Occident, and the western angle. Among geographers, however, because the East and West vary according to the variety of regions and horizons, the true west is usually reckoned from the Fortunate Islands subject to the equator, from which Ptolemy, as from the extreme boundaries of the habitable earth, begins to compute the longitudes of cities toward the East, which consequently is to be conceived as lying in that part of the habitable earth which is distant from the Fortunate Islands by half the circle, that is, 180 degrees. Hence there are those who place the true East in the city of Arym, which they say is under the Equator. But that this is false is clear even from the fact that neither by Ptolemy nor by any other distinguished cosmographer

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MATHEMATICVM. 331 ponitur vlla Ciuitas immediatæ æquatori subiecta, distans ab Insulis fortunatis medietate Circuli, sed solum inuenitur in vndecima Asiæ tabula Ciuitas nomine Arisabium, quæ tamen in longitudine non excedit summam grad. 158. vt videre est in Ptolemæi Geographia ab Magino recusa, recognita, & castigata, cum alias vlterius versus Orientem totum spatium, quod inter est, Mare alluat. Deinde, vt alibi obseruauimus, Verum Occidens computari debeat non ab Insulis fortunatis (Ptolemæus enim vlteriorem terræ habitabilis notitiam non habuit sed ab ea parte sinus Hesperici, quæ subiacet æquatori secundum Meridianum Azorum, non longè à Promontorio Hieron: ibi enim acus nautica se vertit rectè ad polos Mundi, diuidens æquatorem ad angulos rectos; vt qui nauigiis Indiæ occidentalis, seu Noui Orbis prouincias peragrarunt, scriptis suis testarum liquerunt: quam quidem lineam Diametri, seu Diametrum Mundi ipsi appellant: & hic situm esse contendunt verum occidens. Ergò similiter verum Oriens accipiendum est in ea parte, quæ subest æquinoctiali, & distat ab hoc occidentis puncto medietate circuli: quod ferè incidit in Sarapam Asiæ ciuitatem insensibiliter tendentem ad Tropicum Capricorni non longè à Promontorio Satyrorum, vt videre est in Mappis Mundi, ac Tabulis Geograficis titè delincatis. 11. OCCIDENTALES DOMVS, seu quadrantes dicuntur ab Astronomis tres Domus, & consequenter Quadrans interceptus inter Medicum Coeli, & Occasum; atque etiam alius, qui est inter Imum Coeli, & Horoscopum: Eaque fæminina sunt, quippe quæ præponderant in qualitatibus passiuis. Econtrà orientales Domus, & Quadrantes vocantur quæ intercipiuntur inter occasum, & Imum, atque inter Horoscopum, & Culmen, quæ proinde masculina sunt, & abundant in qualitatibus actiuis: Equidem eadem ratio, & discursus de ipsis est, ac de signis, & quadrantibus Zodiaci, ac temporibus Anni, itavt primus quadrans ab horoscop[us] ad culmen correspondeat Veri, & tribus signis Arieti, Tauro, & Geminis: Secundus à Culmine ad occasum, Æstati, atque adeò Cancaro, Leoni, & Virgini: Tet- tius ab occasu ad Imum, Autumno, & sic Libræ, Scorpio, Sagittario, Quartus denique ab Imo ad horoscopum, Hyemi, ac signis Capricorni, Aquarij, & Piscium. 13. OCCIDENTALIS dicitur Planeta, cum Vespere post solis occasum supra horizontem conspicitur, vnde & Vespertinus etiam appellatur; Orientalis verò cum solem præcedit, X iiiij

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MATHEMATICVM. 331 no city is placed directly under the equator, distant from the Fortunate Islands by half a circle, but only on the eleventh map of Asia is found a city by the name of Arisabium, which nevertheless in longitude does not exceed the total of 158 degrees, as may be seen in Ptolemy’s Geography, reprinted by Maginus, revised and corrected; for otherwise farther toward the East the entire space between is washed by the sea. Then, as we have observed elsewhere, the true West ought to be reckoned not from the Fortunate Islands (for Ptolemy had no knowledge of the more distant inhabited earth), but from that part of the Hesperian Gulf which lies under the equator according to the meridian of the Azores, not far from Cape Hieron: for there the nautical needle turns directly to the poles of the world, dividing the equator at right angles, as those who have traversed by ships the provinces of Western India, or of the New World, have left in writing in their charts; and they call this line the Diagonal, or the Diameter of the World itself, and contend that the true West is situated there. Therefore likewise the true East must be taken in that part which lies under the equinoctial and is distant from this point of the West by half a circle: and this nearly falls upon the Asian city of Sarapa, tending imperceptibly toward the Tropic of Capricorn, not far from Cape of the Satyrs, as may be seen in World Maps and carefully drawn Geographical Tables. 11. WESTERN HOUSES, or quadrants, are called by astronomers the three houses, and consequently the quadrant intercepted between the Midheaven and the Descendant; and also another, which lies between the Imum Coeli and the Horoscopos: and these are feminine, since they predominate in passive qualities. On the other hand, Eastern Houses and quadrants are called those intercepted between the Descendant and the Imum Coeli, and between the Horoscopos and the Midheaven, which therefore are masculine and abound in active qualities. Indeed the same reason and discourse concerning them applies as concerning the signs and quadrants of the Zodiac, and the seasons of the year, so that the first quadrant from the Horoscopos to the Midheaven corresponds to Spring, and to the three signs Aries, Taurus, and Gemini; the second from the Midheaven to the Descendant to Summer, and thus to Cancer, Leo, and Virgo; the third from the Descendant to the Imum Coeli to Autumn, and thus to Libra, Scorpio, and Sagittarius; the fourth finally from the Imum Coeli to the Horoscopos to Winter, and to the signs Capricorn, Aquarius, and Pisces. 13. A planet is called WESTERN when in the evening, after sunset, it is seen above the horizon, and therefore it is also called Vespertine; Eastern, however, when it precedes the sun, X iiiij

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332 PHYSIO-THEOLOGIA, & manè ante ipsius exortum videur; vnde & Matutinus. Porro orientalitas respectu superiorum, & Occidentalitas respectu inferiorum est fortitudo, & accessus virium: illi enim orientales, & isti occidentales à sole magis recedunt, vnde & lumine augentur: sicut e contra superiores occidentales, & Inferiores orientales ad so em magis, magisque accedunt, ac proinde lumine minuuntur. Augmentum autem luminis magna est virtutis accessio, & fortitudo, vt alibi obseruauimus, quippe Astra non agunt nisi mediante lumine. 34. Occrantes vocari passim solent à plerisque Astronomiæ professoribus, qui Promissorum communiori etiam vocabulo appellantur, Planetæ omnes, eorumque a pectus, sixæ, quin & nova Phænomena & Cometæ in Cælo apparentes, quatenus habent virtutem causæ efficientis secundum qualitates actiuan, quibus pollent, & afficiunt Prorogatores, seu rerum significatores, quibus directione occurrunt. 35. Porrò sicut prorogatores duplicem virtutem passiuam constituuunt, quarum vna consistit immobilis in situ Mundi, mouentur autem motu ipsorum proprio in Zodiaco, si in eo moueri habeant: altera verò consistat immobilis in Zodiaco, & mouentur motu primi mobilis circa mundum; ita etiam Occursantes duplicem virtutem actiuan constituuunt secundum diuersam rationem immobilem, vnam in Mundo, alteram in Zodiaco: in Mundo quidem cum consistunt immobiles in suo circulo posirionis, & expectant Prorogatores, qui motu primi mobilis ad ipsos deuoluan, & eorum qualitatibus afficiantur, in Zodiaco verò cum consistentes immobiles in eo gradu Zodiaci in quo sunt in radice, vel rapiuntur ipsi motu primi mobilis ad situm Prorogatorum, vel sanè expectant Prorogatores, qui proprio motu in Zodiaco pergunt ad gradum illum quem obtinebant ipsa sidera occursantia in radice. Et sic pro ratione huius triplicis motus constituitur triplex genus Directionum: vnum quidem in Zodiaco, quo prorogator per suam orbitam realiser incedens, impingit tandem in locum siderum occursantium vbi ab his in radice virtus eorum propria impressa est, concipiturque restare immobiliter: reliqua verò duo persiciantur in Mundo, & alterum quidem directo, inoru, quo sidera occursantia, seu loca Zodiaci suis qualitatibus effecta moueantur vna cum ipso Zodiaco raptu primi mobis, ac deferantur ad situm, seu virtutem impressam à Prorogatoribus in situ mundi: alterum per motum con-

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332 PHYSIO-THEOLOGIA, & is seen even before its rising; whence it is also called Matutinus. Moreover, orientalness with respect to the upper parts, and occidentalness with respect to the lower parts, is strength and an accession of powers; for those oriental, and these occidental, recede more from the sun, whence they are also increased in light: just as, on the contrary, the upper occidental and the lower oriental approach more and more to the sun, and therefore are diminished in light. But an increase of light is a great accession of virtue and strength, as we have observed elsewhere, since the stars act only by means of light. 34. Those are commonly called Occrantes by most professors of Astronomy, who are also called by the more common name of Promissors: all the Planets, and their aspects, fixed stars too, and even new Phenomena and Comets appearing in the heavens, inasmuch as they have the power of an efficient cause according to the active qualities which they possess, and affect the prorogators, or significators of things, with which they encounter by direction. 35. Furthermore, just as the prorogators constitute a twofold passive virtue, of which one consists as immobile in the position of the World, yet they are moved by their own proper motion in the Zodiac, if they have to be moved in it; the other truly remains immobile in the Zodiac, and is moved by the motion of the primum mobile around the world; so also the Occursants constitute a twofold active virtue according to a different immobile relation, one in the World, the other in the Zodiac: in the World indeed when they stand immobile in their circle of position, and await the prorogators, who by the motion of the primum mobile are carried down to them, and are affected by their qualities; in the Zodiac truly when, remaining immobile in that degree of the Zodiac in which they are in the radix, either they themselves are carried by the motion of the primum mobile to the position of the prorogators, or else they await the prorogators, who by their own motion proceed in the Zodiac to that degree which the very stars encountering in the radix occupied. And thus, according to the reason of this threefold motion, a threefold kind of directions is constituted: one indeed in the Zodiac, whereby the prorogator, advancing really through his own orbit, finally strikes the place of the encountering stars, where in the radix their own proper virtue was impressed upon them, and is conceived to remain immovably: the other two are completed in the World, and one indeed by direct motion, the other by retrograde motion, whereby the encountering stars, or the places of the Zodiac affected by their qualities, are moved together with the Zodiac itself by the carrying force of the primum mobile, and are conveyed to the position, or virtue impressed by the prorogators in the position of the world: the other by motion con-

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MATHEMATICVM. 333 uersum, quo videlicei Prorogatores motu conuerso, hoc est, vt explicat Ptolemæus contra ordinem signorum rapiantur vnà cum partibus Zodiaci, in quibus eorum qualitas passiua fuit impressa, idque motu primi mobilis ad situm Mundi, in quo fuit impressa qualitas actiua sidetum occursumium; ita vt hæc nullo pacto moueri concipiantur. Quæ omnia fortè clatiùs explicata sunt in V. Directio. OCEANVS. Vide quæ diximus in V. Aqua. De eius autem 16. æstu, & ratione dictum est in V. Amposim. OCTAEDRVM est figura Geometrica, quam definit Euclides < 17.> lib. 11. esse figuram solidam sub octo triangulis æqualibus, & æquilateris contentam: cuius speciem exibet oculis inspiciendam Clauius in dictum locum Euclidis. OCTANGVLVS est item figura Geometrica, sed plana octo < 18.> angulis constans, de quo vide Euclidem lib. 6. OCTAVA SPHARA, communiter dicitur Firmamentum, seu < 19.> Orbis stellarum in cuius crassitie, vt ego ctedo, seu vt alij volunt concaua superficie sidera quæque inerrantia fixa sunt, & in certas imagines colligata, atque ab inuicem disperrita. Cuius distributionis non casu, & oscitanter factæ < 19.> ab antiquis illis Astronomis, sed magno consilio, matura deliberatione, & summa prudentia rationem dedimus in V. Imagines Cælestes. Et alias pulchras addit Lucius Bellantius, qu 6. art. 1. quarum potissima ratio est, vt memoria retineantur natura, locus, ordo, & qualitates stellarum: si enim ipsæ absque vllo ordine, proprio nomine, loci designatione, aut naturæ distinctione relinquuerentur magna esset confusio, nec tam facilè quod prisci illi sapientes post tot exantlos labores, post tot sæculorum indefessam observationem compararunt, possemus nos vnico intuitu comprehendere, nisi huius veluti localis memoriæ, ac mutorum stemmatum subsidio leuaremur. Porrò non ita huiuscemodi Imaginum, ac stellarum conglomeratio < 20.> efficta est, vt non melius efformari potuerit, aut deinceps possit per eum, qui probè nouerit stellarum naturam, singularesque proprietates, atque iis nomina quibusque propria, & naturæ earum conuenientia aptare sciuerit. Qua in re tria aduerienda esse notat ipse Bellantius. Primò propinquitatem stellarum ad inuicem, qua in vnam, eandemque imaginem comprehendi debeant: & ob hoc stellarum nimium ab se dissanium non est formanda figura. Secundò, vt quantum fieri potest proprietas, & similitudo < 20.> naturæ, tum stellarum ad inuicem, tum eamndem cum nomine, vel figura appieta secuetur. Tertiò tandem

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MATHEMATICVM. 333 reversed motion, that is, as Ptolemy explains, they are carried against the order of the signs together with the parts of the Zodiac in which their passive quality was impressed, and that by the motion of the first mover, to the position of the world, in which the active quality of the stars was impressed; so that these are in no way conceived to be moved. All these things may perhaps have been explained more clearly in V. Directio. OCEANVS. See what we said in V. Aqua. But concerning its 16. ebb and flow, and the reason, see in V. Amposim. OCTAEDRVM is a geometric figure, which Euclid defines <17.> in book 11 as a solid figure contained under eight equal, and equilateral triangles: the appearance of which Clavius presents for inspection in the said place of Euclid. OCTANGVLVS is likewise a geometric figure, but a plane one, consisting of eight <18.> angles; see Euclid, book 6. OCTAVA SPHARA is commonly called the Firmament, or <19.> the sphere of the stars, in whose substance, as I believe, or, as others wish, in its concave surface, each of the fixed stars is established, and bound together into certain figures, and separated from one another. The reason for this distribution was not made by chance and carelessly <19.> by those ancient astronomers, but by great judgment, mature deliberation, and the highest prudence, we have given the explanation in V. Imagines Cælestes. And Lucius Bellantius adds other beautiful ones, qu 6, art. 1, the chief reason for which is that the nature, place, order, and qualities of the stars may be remembered: for if they were left without any order, proper name, designation of place, or distinction of nature, there would be great confusion, nor could we so easily comprehend at a single glance what those ancient wise men, after so many toilsome labors, after so many centuries of unwearied observation, collected, unless we were aided by this kind of local memory and by the help of mute emblems. Moreover, such a conglomeration of images and stars was not fashioned <20.> so that it could not be better formed, or thereafter be formed by anyone who rightly knows the nature of the stars, and their individual properties, and who knows how to assign to them names both proper and fitting to their nature. On this matter Bellantius himself notes three things to be observed. First, the proximity of the stars to one another, by which they ought to be comprehended in one and the same image: and for this reason a figure must not be formed from stars too far separated from one another. Second, that as far as possible the property and similarity <20.> of nature, both among the stars in relation to one another, and likewise with the name or the figure applied, should be followed. Third, finally

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LEXICON figura imaginata compleatur, & nullæ relinquantur stellæ informes præsertim notabilis magnitudinis, & speciali nota dignæ; quod ab antiquis Astronomis prætermissum est: Arcturus enim stella tam insignis primæ magnitudinis non est in vllam imaginem colligatur, sed iacet informis inter crura Bootis; duæ secundæ magnitudinis circa Lances, & aliæ non paræ, nec contemnendæ: quare, & ipsæ in ordinem reducendæ forent. Scio non neminem opus aggressum, sed difficultate rei territum, ac stellarum multitudine dissuaque natura pressum ab eius prosequutione alioqui optimè cepta destitisse. <21.> Sed & Iulius quidam Schillerus I. C. Augustanus alio fine ductus imagines cælestes ab antiquis variis Poëtarum figmentis depictas, in alias Diuorum nomine insignitas commutasse. Neque enim, inquit, Christiana fidei, rectaque rationi congruit Damones, bestias, & probrosos homines nominibus stellarum designare, cum stella sit hieroglyphicum verorum sanctitate illustrium, iuxta illud l'anel. 11. Qui autem docti fuerint, fulgebunt, quasi splendor Firmamenti, & qui ad iustitiam erudiunt multos, quasi stella in perpetuas æternitates. Atque adeo ipse cælum Christianum molitus est, duodecim signa Zodiaci ab duodecim Apostolorum nominibus appellans, aliisque characterismis ex instrumentis martyriorum ipsorum designans. Planetarum verò, relictis antiquis characterismis, (quos tamen inuerso ordine præcipit denotari) ab Adam, Moïse, Iosue, Elia, Christo, B. Virgine, & Ioanne appellatorbes, & Astra, Quod ne memoriâ excidat in sequentes versiculos redegit Iacobus Barschius. Adam Saturno; Moses Ioue; Iosua Marte, Solus Sole micat Christus; Venere ipsa Ioannes. Mercurio Elias; Lunâque Beata Maria. <22.> Similiter alia sidera extrà Zodiacum alijs Sanctis, & Patriarchis noui & veteris Testamenti dedicauit, vt Perseum Paulo Apostolo, Cepheum S. Stephano, Bootem S. Syluestro, &c. vt ex sequentibus versibus à Barschio, item compositis videre licebit: quorum tamen aliquos Alstedius, nosque metri causa non nihil inmutauimus. CONSTELLATIONES BOREALES. Vrsa minor Michael: Petri ratis Vrsaque Maior: Innocui Pueri deturbant sede Draconem: Dat Stephano Palmam Cepheus: pellitque Bootem

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LEXICON the imagined figure may be completed, and no stars be left unformed, especially those of notable magnitude, and worthy of special notice; a matter neglected by the ancient astronomers: for Arcturus, a star so remarkable and of first magnitude, is not included in any image, but lies shapeless between the legs of Bootes; two of second magnitude about the Scales, and others not equal to, nor to be despised: wherefore, these too ought to be reduced to order. I know that more than one has taken up the work, but, terrified by the difficulty of the matter, and pressed down by the multitude and diverse nature of the stars, has otherwise abandoned the continuation of what had been well begun. <21.> But a certain Julius Schiller, a jurist of Augsburg, moved by another purpose, changed the heavenly figures, depicted by the ancients from various poetic fictions, into others distinguished by the names of the Saints. For neither, he says, does it accord with the Christian faith and right reason to designate by the names of stars demons, beasts, and shameless men, since a star is a hieroglyph of those truly illustrious in sanctity, according to that passage, Dan. 11. But those who are wise shall shine as the brightness of the firmament, and those who instruct many unto justice, as a star for ever and ever. And so he himself devised a Christian sky, calling the twelve signs of the Zodiac by the names of the twelve Apostles, and designating them by other distinguishing marks taken from the instruments of their martyrdoms. But for the planets, having set aside the ancient characters, (which nevertheless he orders to be denoted in reverse order), he named the globes and stars after Adam, Moses, Joshua, Elijah, Christ, the Blessed Virgin, and John. Lest this escape memory, Jacob Barschius reduced it into the following verses. Adam for Saturn; Moses for Jupiter; Joshua for Mars, Christ alone shines with the Sun; John with Venus itself. Elijah with Mercury; and Blessed Mary with the Moon. <22.> In like manner he dedicated other stars outside the Zodiac to other Saints and Patriarchs of the New and Old Testament, as Perseus to the Apostle Paul, Cepheus to St. Stephen, Bootes to St. Sylvester, etc., as from the following verses, likewise composed by Barschius, it will be possible to see: some of which, however, Alsted, and we too, for the sake of meter, altered somewhat. NORTHERN CONSTELLATIONS. The Lesser Bear: Michael; Peter’s bark and the Great Bear: The Innocent Children drive the Dragon from its seat: Cepheus gives the palm to Stephen; and drives away Bootes

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MATHEMATICVM. 331 Syluester: Christi scuticam Comacalica signat: Spinea sed Iesu borea stellata Corona: Tres Sancti Reges gaudent nunc Herculis Astro: Vertitur in præsepe Dei Lyra: Crux sacra Olorem: Magdala Cassiopem pellit: sic Persea Paulus: Auriga est Hieronymus; Anguitenens Benedictus: Eius spinetum est Anguis: sed Lancea Christi, Cum claus Telum est: Aquilam Catherina repellit: Hydria fit Cana Delphin: Rosa mistica parui Sectio Equi: Gabriel fit Pegasus: Andromedeque Fit tumulus Christi: Petridat Miera Trigonum. CONSTELLATIONES IN PLAGA Australi. Exornant Austrum Ioachim, & Anna parentes Virginis Augusta pro Ceto: Per Mare rubrum Transitus Israel fluvium tegit Eridanumque: Sponsus Maria Ioseph est clarus Orion: Expellit Leporem Graeonis nobile vellus: Quaque columba olim fuerat, nunc ipsa Noachi est. Sirus est Dauid: Procyon Paschal: & Agnus. Ast Argonautis Noachi est Arca; sed Hydram Iordanis pellit: pellit quoque Fæderis Arca Craterem, & Corvum: Centaurum Abramus, & Isaac. Atque Lupum Iacob: Altare sacrum fugat Aram. Et Salomon cinetus diademate tollit ad Austrum Sertum: sic piscem fugat Hydria plena Sarepta: Aroni cedunt Phoenix, Grus, Pauoq; & Indus: Iobo Apes: Indica Musca, Camaleon, & quoque cedunt Eua: Tau signum nunc est Australe Trigoum: Iustus Abel nubes maior: Dorado volansque Piscis & hinc Toucan, cum nube minore colubrum, Victor detrudit Raphael Archangelus almus. Signa Zodiaci per duodecim Apostolos distributa. Petrum Aries: Taurusque Fratrem: Geminique Iacobum: Cancer Ioannem: te Leo Thoma notat. Virgine Iacobus gaudet: Librâque Philippus: Et tibi respondet Bartholomae Nepa: Signat Matthaum Chiron: Caper atque Simonem: Iudam Vrna: At Pisces sorte delectus habet,

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Sylvester marks Christ’s Comacalica shield: But the thorny Crown of Jesus, starry in the north: The Three Holy Kings now rejoice in Hercules’ star: Lyra is turned into the manger of God: the holy Cross, the Swan: Magdala drives away Cassiopeia: so Paul [drives away] Perseus: Hieronymus is the Charioteer; Benedict the Serpent-Bearer: His thorn-bush is the Snake: but the spear of Christ, With the nail, is the Weapon: Catherine drives back the Eagle: The Water-Jar becomes the Dolphin at Cana: the mystical Rose, the small Section of the Horse: Gabriel becomes Pegasus: and Andromeda Then becomes the tomb of Christ: Peter gives Miera the Triangle. CONSTELLATIONS IN THE Southern Hemisphere. Joachim and Anna, parents of the August Virgin, adorn the south in place of Cetus: through the Red Sea the passage of Israel covers the river Eridanus as well: Joseph, spouse of Mary, is the shining Orion: He drives away Lepus, the noble fleece of Graeon: And where once there was the dove, now the ark itself is Noah’s. Sirius is David: Procyon is Paschal, and the Lamb. But the Ark of Noah is for the Argonauts; and the Ark of the Covenant drives away Hydra from the Jordan: it also drives away the Crater and the Raven; Abraham and Isaac, the Centaur. And Jacob, the Wolf: the sacred Altar drives away the Altar. And Solomon, girded with a diadem, lifts to the south the garland: thus the full Water-Jar drives away the fish from Sarepta; to Aaron yield the Phoenix, the Crane, the Peacock, and the Indian bird: to Job, the Bees: the Indian Fly, the Chameleon, and also yield to Eve: now Taurus is the southern Trigon: Righteous Abel, a greater cloud: the flying Dorado and Fish, and here the Toucan, with a lesser cloud, the serpent, the gracious Archangel Raphael drives back as victor. Signs of the Zodiac distributed among the twelve Apostles. Aries is Peter; Taurus, Brother [Andrew]; and Gemini, James: Cancer is John: Leo marks you, Thomas. In Virgo James rejoices; and Philip in Libra: And Bartholomew answers you in Scorpio: Sagittarius marks Matthew: Capricorn, Simon: Aquarius, Judas: but Pisces, chosen by lot, has,

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LEXICON Item Characteres Signorum sunt. 1. 2. 3. 4. 5. Claus: Crux: 6. cea: 7. 8. 9. 10. 11. Crux: Culter: 12. que Hoc est instrumenta, quibus Apostoli ab inuicem distin- guuntur, ac prænotatur: vt S. Petrus per claues illi à Domi- no traditas; Andreas per crucem, cui infixus fuit; Iacobus Maior per Dolonem, seù baculum suæ peregrinationis; Ioannes Euangelista per Calicem veneno plenum, quem innocuè propinasse ferunt; S. Thomas per lanceam, qua fuit transuerberatus; Iacobus Minor per fullonis pectem, quo caput eius fuit percussum; Philippus per crucem cui similiter affixus est; Bartholomæus per cultrum, quo fuit ex- coriatus; Matthæus per hastam, qua fuit appetitus; Simon per serram, qua medius fuit sectus; Iudas per fustem quo fuit illisus; Denique Mathias per securim, qua fuit occisus. <23.> Atque hæ sunt sacræ Imagines à Schillero sideribus ap- plicatæ. Cuius sanè pietas, & eruditio summoperè vene- randa est; Verum eius opera non multo cum plausu fuit re- cepta, neque à pristina stellarum Nomenclatura eatenus quisquam abhorruit, aut destitit. Et verò, si religionis ze- lum excipias, omnia frigida, omnia intulsa, omnia è ce- rebro facta comperientur: quæ enim proportio, exempli gratia, Innocentium cum Dracone? Vrsæ cum Nauicula D. Petri, signorum Zodiaci cum Apostolis? vbi, sexus diffe- rentiâ? quæ ranro iudicio apposita est ab antiquis, tum Pla- netis, tum signis? vbi qualitatum conbinatio, & distinctio? vbi natura siderum explicata? vbi denique partitio illa si- gnorum ex affectibus comprobata, in humana, ferina: vo- cem habentia, muta, sterilia, foecunda, pulchra, defor- mia, &c. De quibus hæc quanto cum pondere dicta sint, suis locis non obscurè tradidimus. Quapropter, nisi me- liùs res instituatur, vt benè monet Keplerus, ab antiqua siderum nomenclatura, Imaginumque affixione non recedendum. Neque enim temporibus hisce quicquam Reli- gioni obest, quod ea ab inanium Deorum nomine, fictis-

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LEXICON The items are the characters of the signs. 1. 2. 3. 4. 5. Claus: Cross: 6. cea: 7. 8. 9. 10. 11. Cross: Knife: 12. que These are the instruments by which the Apostles are distinguished from one another and marked beforehand: thus St. Peter by the keys handed down to him by the Lord; Andrew by the cross to which he was affixed; James the Greater by the pilgrim’s staff, or walking-stick of his pilgrimage; John the Evangelist by the cup filled with poison, which they say he drank harmlessly; St. Thomas by the spear with which he was pierced through; James the Less by the fuller’s bat, with which his head was struck; Philip by the cross to which he was likewise affixed; Bartholomew by the knife with which he was flayed; Matthew by the spear with which he was attacked; Simon by the saw with which he was cut in half; Judas by the club with which he was beaten; lastly Matthias by the axe with which he was killed. <23.> And these are the sacred images which Schiller applied to the stars. His piety and learning must indeed be highly revered; yet his work was received with no great applause, nor did anyone thereby depart from the former nomenclature of the stars or cease to prefer it. And indeed, if you set aside religious zeal, everything will be found cold, everything tasteless, everything contrived: for what relation, for example, is there between the Innocents and the Dragon? Between the Bear and St. Peter’s Ship, between the signs of the Zodiac and the Apostles? Where is the difference of sex, which the ancients, with great judgment, assigned both to the planets and to the signs? Where is the combination and distinction of qualities? Where is the nature of the stars explained? Where, finally, is that division of the signs, confirmed by their influences, into human, beastly; speaking, mute, barren, fruitful, beautiful, ugly, etc.? We have elsewhere set forth with no little force what should be thought of these matters. Therefore, unless the matter is arranged better, as Kepler rightly advises, we must not depart from the ancient nomenclature of the stars and the affixing of images. For in these times nothing harms religion that is removed from the name of idle gods, from fictitious...

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MATHEMATICVM. 337 que Poëtarum fabulis appellantur, quippe hæ sunt destru- ctæ superstitionis exuuiæ, sideique nostræ trophæa cælo affixa: quare inseruiunt ad ingerendum nobis non tam pristinæ religionis inanitatem, quam veram sideræ qualitatis notitiam, non secus ac modò in Templorum aditis extant Idola ad ornatum, gentiumque superstitionis derisionem. Et hæc quidem de Schilleri molitione. 24. Cæterum mouetur octaua Sphæra, seù potius præpeditur, vt non assequi possit velocitatem Primi Mobilis ferè gradum vnum in singulis 70. annis ad partes Orientaliores secundum successionem signorum. Alij triplicem dant ei motum: vnum sibi proprium in Zodiaco super eiusdem polos, qui est modo explicatus, itavt cursum suum perficiat in annis 36000. alterum raptus quem habet à primo mobili. Tertium item violeutum sibi impressum à nona Sphera (quam ad saluandas apparentias de nouo cælo appingunt) trepida- tionis, seù accessus, & recessus vocatum, qui similiter est secundum successionem signorum, & super polos Zodiaci, tam lentus, vt in singulis ducentis annis non plus quam gradum vnum, & 28. ferè minuta progrediatur. Qua de re re. Vide Georgium Peurbachium in Theoricis Planetarum. 25. OCULVS TAVRI antonomasticè appellatur stella fixa Martia, primæ magnitudinis, in oculo australi Tauri con- sistens dicta, à nostris Palilitium, atque ab Arabibus Alde- baram; cum aliàs in oculo dextro & boreo sit altera stella tertiæ magnitudinis dicta Oculus boreus. De quibus vide in V. Hyades. 26. OLOR, GAILINA, &c. Sidus in cælo ad borealem plagam intrà Galaxiam, de quo vide in Verbo Cygnus. OLYMPIADES olim apud Græcos audiebat certùm tem- poris spatium, quod quadriennio complebatur; (eo prorsùs pacto, quo suprà diximus lustrum quinquennio, & in- dictionem tribus lustris, hoc est quindennio terminari:) itavt quinto quoque anno nouæ succederent, & ordine cens- cetentur; quarum ratio in distinguendis, notandisque tem- pocibus seruabatur, atque in Annalibus, Chronieis, scrip- tutisque publicis notabatur. Erat enim tempus hoc maximè notum, fixum, & immutabilè: è cuius exordio. Chrono- logiæ ratio haberi coepit, & Historiam Græcam fidem apud posteros inuenisse narrat Eusebius in Chronico: & Marcus Varro apud Censorinum, totum illud tempus, quod Olym- piades antecessit, fabulosum appellat. Vnde meritò Iulius Africanus, & Iustinus Martyr, hoc de Olympiacæ Chro-

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MATHEMATICVM. 337 which are called in the fables of the Poets; for these are the remains of destroyed superstition, and trophies of our faith fixed to the sky: wherefore they serve to impress upon us not so much the emptiness of the ancient religion as the true knowledge of the nature of the stars, not otherwise than now in the entrances of Temples Idols are displayed for ornament, and for the derision of the superstition of the nations. And these things indeed are about Schiller’s undertaking. 24. Furthermore, the eighth Sphere is moved, or rather hindered, so that it cannot reach the velocity of the Primum Mobile by nearly one degree in every 70 years toward the eastern parts according to the succession of the signs. Others assign it a threefold motion: one proper to itself in the Zodiac around its own poles, which has just been explained, so that it completes its course in 36,000 years; another, the rapts, which it has from the first mover; and a third, likewise violent, impressed upon it by the ninth Sphere (which, in order to save appearances, they newly paint in as a new heaven), called trepidation, or access and recession, which likewise is according to the succession of the signs and around the poles of the Zodiac, so slow that in every 200 years it advances no more than one degree and nearly 28 minutes. On this matter see Georgius Peurbachius in the Theoricae Planetarum. 25. OCULUS TAVRI is antonomastically called the fixed Martian star of first magnitude, so named because it stands in the southern eye of Taurus; by our writers Palilitium, and by the Arabs Aldebaran; while in the right and northern eye there is another star of third magnitude called the northern eye. See under V. Hyades. 26. OLOR, GAILINA, etc. A constellation in the sky toward the north within the Galaxy; see under the word Cygnus. OLYMPIADES among the Greeks once denoted a certain span of time, completed in four years; (in precisely the same way as above we said that a lustrum ends in five years, and an indiction in three lustra, that is, in fifteen years:) so that every fifth year new ones succeeded, and were counted in order; the method of them was preserved in distinguishing and marking times, and was noted in Annals, Chronicles, and public writings. For this time was very well known, fixed, and unchangeable: from its beginning the method of chronology began to be reckoned, and Eusebius in the Chronicle relates that Greek history found credibility among later ages; and Marcus Varro, apud Censorinus, calls all that time which preceded the Olympiads fabulous. Whence rightly Julius Africanus and Justin Martyr, this of the Olympian Chron-

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LEXICON 338 nologiæ certitudine elogium protulerunt. Ante Olympiades, inquiunt, nihil in Græcorum Historia explorarum inueniri, sed esse omnia confusis scripia temporibus: post Olympiades autem quoniam quadriennio diligentissimè omnia notabantur, nullam temporum confusionem excitisse. Nomen, Originem, authoritatem, & famam compararunt ex Ludis illis Olympicis toto Orbe celeberrimis, quinto quoque anno in Elide fieri solitis, quos ob Solis quadriennalem cursum, in quo dies vns adijciur, ob sex illas horas singulis annis ad 365. die residuas, institutos esse docet D. Cyrillus Episcopus Hierosolimitanus Catechisi 12. atque ab Hercule primùm inuentos testantur Strabo, Clemens Alexandrinus, Eusebius aliique sequuti Plutarchum, Plinium, Solinum, Pausaniam, Diodrorumque Sicutum. Incipiebant autem numerari ab solstitio Æstuiali, quo tempore, Ludi illi celebrabantur: Vnde & initium anni, & primi mensis quem Hecatonbæon vocabant ab eo die fiebat, vt refert Simplicius in explanatione, lib. 5. Physic. sext. 25. & fusè probat Theodorus Gaza in libro, quem de Mensibus, Atticis scripsit. Quamquam Io: Lucidus Samotheus in emendatione temporum cap. 8. & in lib. cui titulus de vero die Passionis Domini, Hyppotehi 7 & 8. contentiosè velit, initium Ludorum Olympicorum, & Olypiadum fuisse circà æquinoctium Autumnale. Sed quidquid sit de hac re, certum est, quod, licet Olympiades ab Ludis Olympicis fuerint denominatæ, non tamen cum illis & ab eorum initio computari cæperunt, sed multo post tempore, Etenim Ludos Olympicos, etiam ante bellum Troianum fieri solitos apud omnes ferè Græcarum rerum scriptores inuenimus: Olympiadum antem vsum, non nisi post quadringenitos annos ab excidio Troix legimus introductum, vt pia cæteris aduertit Pererius. De communibus rerum omnium Principiis lib. 4. sap. 3 Nisi fortè vellimus dicere, eos, qui vsum, idemque viriusque rei initium extitisse opinati sunt, loquutos fuisse de Ludorum illorum, qui iam diu intermissi fuerant, restauratione facta ab Iphito Elio, qui certamen Olympicum longè celebriùs renouauit, in quo certamine victor eusit Coræbus Elæus, & ab eo tempore prima Olympias numerari cæpit. Igitur Olympiadum ratio haberi cæpit annis anre Christum natum 774. & consequenter ab origine Mundi, anno 4425. iuxta sepruaginta interpretum supputationem, quam sequitur, & amplexa est Romana Ecclesia in Martyrologia Romano. Cæterum, quia vera ætatis Mundi notitia haberi

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The authors of chronology have spoken of it as certain. Before the Olympiads, they say, nothing in Greek history can be found that is securely established, but everything is in confused writings of times; after the Olympiads, however, since everything was noted very diligently every four years, no confusion of times arose. It derived its name, origin, authority, and fame from those Olympic Games, celebrated throughout the world, held every fifth year in Elis, which the blessed Cyril, Bishop of Jerusalem, teaches in Catechesis 12, were instituted because of the four-year course of the sun, in which one day is added, on account of those six hours remaining each year to make 365 days; and Strabo, Clement of Alexandria, Eusebius, and others following Plutarch, Pliny, Solinus, Pausanias, and Diodorus Siculus testify that they were first invented by Hercules. They began, however, to be reckoned from the summer solstice, at which time those Games were celebrated; whence the beginning of the year, and of the first month, which they called Hecatombaeon, was made from that day, as Simplicius relates in his explanation of Book 5 of the Physics, section 25, and Theodorus Gaza proves at length in the book he wrote On the Attic Months. Although Ioannes Lucidus Samotheus, in the correction of times, chapter 8, and in the book entitled On the True Day of the Passion of the Lord, hypotheses 7 and 8, contends obstinately that the beginning of the Olympic Games and of the Olympiads was around the autumnal equinox. But whatever may be said about this matter, it is certain that, although the Olympiads were named from the Olympic Games, they did not begin to be reckoned with them and from their origin, but much later. For we find that the Olympic Games were even held before the Trojan War among almost all writers on Greek affairs; but the use of Olympiads we read was introduced only after four hundred years from the fall of Troy, as Pererius more piously than the others notes, in De communibus rerum omnium principiis, book 4, question 3. Unless perhaps we wish to say that those who thought the use, and likewise the beginning of both matters, had existed, were speaking of the restoration of those Games, which had long been interrupted, made by Iphitus of Elis, who renewed the Olympic contest far more famously, in which contest Coroebus of Elis was victor, and from that time the first Olympiad began to be reckoned. Therefore the reckoning of the Olympiads began in the year 774 before Christ was born, and consequently from the origin of the world, in the year 4425, according to the computation of the Seventy interpreters, which the Roman Church follows and has adopted in the Roman Martyrology. But because a true knowledge of the age of the world can be had

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MATHEMATICVM. 339 nequit, &, vt supra nota uimus, ante Olympiades, omnia Cræcorum monumenta confusa erant, vt potius ab ipsis lumen acceperint, quas lumen impertire potuerint; ideò nil mirum, si quo tempore ab origine mundi Olympiades iniium sumpserint, auspicari non possit. Certe citatus Pe- rerius à consequentibus computat, atque ad tria temporà, quæ maximè illustria, & memorabilia fuerunt, referre niti- tur; nempe ad Excidium Troiæ, ad Vrbem Romam condi- tam, & ad sacram Chronologiam, ad ea videlicet tempo- ra, quæ in sacris Paginis describuntur: atque ab omnibus idem tempus earum institutionis deducit, anno, inquam, post euersam Troiam quadringeniesimo octauo, & conse- quenter viginti quatuor annis priusquam Roma ædificare- tur: & ex sacris literis regnante apud Iudæos Achaz, anno regni eius octauo. Et quoniam idem Pererius in Commentariis super Danielem lib. 11. quast. ex iisdem monumen- tis probat, Christum Dominum natum esse quaternilles mo vigesimo secundo anno post Orbem, conditum, profectò ex iisdem monumentis liquet Olympiades expisse anno mundi termillesimo, ducentesimo quadragesimo octauo. Et hæc demùm de Olympiadum raione, institutione, & com- modis dicta sint. OPHTVEVS Græcè, Larinè Serpentarius fidus item in cælo < 27.> ad borealem plagam propè æquarorem constans stellis 4. secundum antiquorum obseruationem, at secundum Baie- rum 30. & adhuc iuxta Keplerum 37. qui tamen inter eas connumerant aliquor informes à Ptolomæo prætermissas. Omnes autem hæ stellæ sunt de natura Veneris, & Saturni, proindeque humorum corruptrices, ac venenosæ: inter quas primò venir vna fulgens in capite, Arab. Ras Alangue, secundæ magnitudinis existés tunc temporis in gr. 18. Sagit- tarij cum gr. ferè 13. declinationis borealis: Secundò al- tera in sinistra manu, nomine Red, seu corrupto vocabulo ex Latino, & Arabicæ idiomate Colubramet, hoc est cor- pus Serpentis, in quod incidit manus Serpentarii, tertij ho- noris existens in gr. 16. Scorpij cum gr. 3. declinationis australis: stella quidem perniciosa nimis, ad quam directus vitæ moderator adducit sæpe veneni, vel venenatorum mor- sus periculum. In hoc sidere apparuit anno 1604. nona stella, quæ du- < 28.> ravit ad annos duos, ac postea euanuit, nihil post se re- linquens, ne vllum quidem vestigium; vt sanè fecit altera quæ quatuor, ante, annis apparuit in pectore Cygni, & postea discedens reliquit quendam hiatum etiam num cons-

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cannot, and, as we noted above, before the Olympiads all the monuments of the Greeks were confused, so that they received light rather than imparted it; hence it is no wonder if, at the time when the Olympiads began from the origin of the world, it cannot be determined with certainty. Certainly the cited Pererius computes from the consequences, and strives to refer it to three times that were most illustrious and memorable; namely, to the destruction of Troy, to the founding of the city of Rome, and to sacred chronology, that is, to those times which are described in the Sacred Pages: and from all these he deduces the same time of their institution, namely, in the year four hundred and eight after the overthrow of Troy, and consequently twenty-four years before Rome was built; and from the sacred writings, when Achaz was reigning among the Jews, in the eighth year of his reign. And since the same Pererius in his Commentaries on Daniel, book 11, question ..., proves from the same monuments that Christ the Lord was born in the two thousand and twenty-second year after the founding of the world, it is certainly clear from the same monuments that the Olympiads began in the three thousand two hundred and forty-eighth year of the world. And let this finally be said concerning the nature, institution, and advantages of the Olympiads. OPHIUCHUS, in Greek; in Latin, Serpentarius, also faithful in the sky <27.> toward the northern region near the equator, consisting of 4 stars according to the observation of the ancients, but according to Bayer 30, and according to Kepler 37; though among these they also count some unformed stars omitted by Ptolemy. But all these stars are of the nature of Venus and Saturn, and therefore corrupters of humors and poisonous. Among them first comes one shining in the head, Arab. Ras Alangue, of second magnitude, then at that time in 18 degrees of Sagittarius, with almost 13 degrees of northern declination. Second, another in the left hand, by the name Red, or by a corrupted word from the Latin and Arabic idiom Colubramet, that is, the body of the Serpent, into which the hand of the Serpentarius falls; it is of third magnitude, in 16 degrees of Scorpio with 3 degrees of southern declination: indeed a most harmful star, toward which the directed ruler of life often brings the danger of poison or poisonous bites. In this constellation there appeared in the year 1604 a ninth star, which lasted for two years, and then vanished, leaving nothing behind, not even any trace; as indeed the other one did, which appeared four years before in the breast of Cygnus, and then departing left a certain gap even now visible.

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LEXICON 340 picuum: qua propter de ijs multi multa scripserunt, ac præcæteris Tycho; & Keplerus: de qua nos etiam aliquid dicemus in V. Phanomena, & in V. Serpentarius. 29. Cæterum Ophiucus in Horoscopo, inquit Firmicus, Facit marsos, qui pestiferos angies sopitis, ac mitigatus aculeis opprimant. In occasu verò, & cum aspectu quocumque maleficarum, subdit: Serpentis ide venenati infeliciter moriuntur. Oritur Ophiucus Romæ cum gr. ferè 20. Scorpij, & occidit cum tosisdem Sagitarij. 30. OPORA Græcè proptè dicitur vltima pars æstatis post Canis exortum vsque ad ortum Atcturi, qui incidit nunc in ferè Calendas Octobris: sed ante correctionem Gregorianam decem ante diebus, quo tempore subintrabat Autumnus: Vnde postea Opora licet improptè audiebat pro toto Autumnali tempore; & oporinum dicebatur quidquid ad Autumnum pertinebat: quo sensu Martial. ludens eecinit. Si daret Autumnus mihi nomen Oporinus essem. Et Varro de re rustica locum Autumnali tempore fructibus seruandis destinatum Oporothecam dixit. Hinc etiam. OPORINVM S I D V S promiscuè audit tam Canis maior 31. initium Oporæ faciens, quam Atcturus finem adducens. 32. OPPOSITIO apud Astronomos est species quædam familiaritatis contracta inter duo sidera in distantia semicirculi, & gr. 180. itavt ex diametro se respiciant; qui profectò radius, & aspectus habet consonantium, & proportionem in modis musicis ad octauam, quæ cum prima facit tonum vnisonum, vt Musicæ peritis notum est. Æstimatur radius hostilis, & perfectæ inimicitæ eoquia per ipsum sidera opponantur, atque adeo inuicem se oppugnent: Verum ad Cardines proiectus (qui passiuis tanum qualitatibus pollent) est de natura siderum à quibus proiicitur, atque inter beneficas præsertim conuenientis naturæ bonus euadit: Vt proptereà Ptolemæus ipse Cap de Moderanda vita, Quadratum, Trinum, Oppositionem si à beneficis ad Vitz Moderatorem ciaculentur, æqui felices appellet, atque impedire dicit effectum directionis Prorogatoris ad locum Anæreticum. Semper enim per quemcunque radium transmittitur virtus benefici maior, aut minor, provt est validitas radij, ad locum prorogatorium: qua proinde iste ita afficitur, vt ab insultu sideris occursandis, & Anerææ aliquatenus subleuetur. At verò hic radius inter infortunas; aut ab infortunis ad fortunas proiectus, eadem ratione semper maleficus est. OPTICA

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LEXICON 340 picuum: wherefore many have written much about these things, and above all Tycho; & Kepler: about which we shall also say something in V. Phanomena, & in V. Serpentarius. 29. Moreover, Ophiucus in the horoscope, says Firmicus, makes Marsi, who, when the poisonous snakes are lulled and subdued, crush them with their stings. In the setting, however, and with any aspect of the malefics, he adds: those born under the venomous serpent die unhappily. Ophiucus rises at Rome with about 20 degrees of Scorpio, and sets with the same degrees of Sagittarius. 30. OPORA is properly said in Greek to be the last part of summer, after the rising of the Dog Star until the rising of Arcturus, which now falls around the Kalends of October: but before the Gregorian correction ten days earlier, at which time autumn began to enter: whence afterwards Opora, though improperly, was heard to mean the whole autumn season; and whatever belonged to autumn was called oporinus: in which sense Martial, playing, sang. If Autumn gave me a name, I would be Oporinus. And Varro, in his work On Agriculture, called the place assigned in autumn for preserving fruit the Oporotheca. Hence also. OPORINVM S I D V S is heard indiscriminately both as the Greater Dog, 31. making the beginning of Opora, and as Arcturus bringing the end. 32. OPPOSITION among astronomers is a certain kind of familiarity formed between two stars at a distance of a semicircle, and 180 degrees, so that they face one another diametrically; which indeed has a radius and an aspect of consonances, and in musical modes the proportion of the octave, which with the first makes a unison tone, as is known to experts in music. It is judged to be a hostile ray, and one of perfect enmity, because through it the stars are opposed to one another and thus attack one another mutually: but when projected to the angles (which possess only passive qualities), it is of the nature of the stars from which it is projected, and among benefics, especially of a suitable nature, it becomes good: so that therefore Ptolemy himself, in Cap. de Moderanda vita, calls the square, trine, and opposition, if cast from benefics to the governor of life, equally fortunate, and says they hinder the effect of the direction of the prorogator to the anaretic place. For through whatever ray the power of the benefic is transmitted, greater or lesser, according to the strength of the ray, to the prorogatory place: whereby that place is accordingly affected, so that it is somewhat shielded from the assault of the incoming star, and from the destructive point. But on the other hand, this ray, when projected among the infortunes, or from the infortunes to the fortunes, is for the same reason always malefic. OPTICA

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MATHEMATICVM. 341 < 35.> OPTICA scientia est, quæ per radios visuales, vnabrasque radiis terminatas rerum distantias, magnitudines, corpo- rumque cælestium, adhuc parallaxes, refractiones, & vm- bras accipit, ac dimesitur: idque siue directè, siue reflexè radij ipsi ab obiecto ad oculum transmittantur: ita tamen, vt si directè id fiat per foramina aut rimas alicuius instru- menti excipiendo siderum radios, appellerur Dioptrica: si verò reflexè ex superficie aliqua partim opaca partim Dia- phana, dicatur Catoptrica, vel Anacamptica: si autem per lineas refractas in medio diuersæ densitatis Anaclastica audiat, de quibus omnibus suo loco. < 34.> ORBIS propriè dicitur de deferentibus singulorum plane- tarum quæ vulgò Sphæræ appellantur. Differt verò Orbis à sphæra, quod hæc propriè globum significer vnica superficie contentum, atque vsque ad centrum eousque solidum; Or- bis autem dicit corpus sphæricum duabus superficiebus sini- tum, vna exteriore conuexa, altera interiore concaua: & ideo, quot cæli tot orbes inuicem contigui, & immediati, itavt superior includat inferiorem, & quanta est superficies concaua superioris, tanta etiata sit conuexa inferioris, non secus ac vnius cæpæ tunicæ. Quia autem vnsquisque orbis, seu cælum intrà se alios etiam orbes continet, vt, pro exem- plo, orbis solis habet tres alios orbes à se inuicem diuisos, ac sibi contiguos, quorum duo sunt excentrici secundum quid; tertius simpliciter excentricus; ideò ad euitandam vo- cabulorum confusionem vsus obtinuit, vt ipsi cæli iam non orbes sed spæræ appellitentur: & sic sphæra omnium maxi- ma sit primum mobile quod omnes alias suo ambitu com- plectitur, & secum rapit: Post (si dantur) decima, & nona sphæra trepidationis dictæ. Inde octaua, seu Firmamen- tum: mox cælum Saturni, posteà Louis, & sic deinceps vs- que ad Lunam, itavt sphæra Lunæ sit omnium minima tam circuitu, quam crassitie, & ambius quidem concaui ipsius su millariorum 758250. crassities verò, hoc est intercapedo inter concauum & conuexum illius sit milliar. 109056. am- bitus autem conuexi, qui vt dixi est idem cum concauo su- perioris, & sic Mercurij est milliar. 1443750. Crassities Orbis Mercurij lata est milliar. 370480. Ambitus < 35.> superficiei eius conuexæ est milliar. 3772500. Crassities Orbis Veneris est milliar. 3413756. ambitus ve- ro conuexi 25230375. Crassities deferendis solis, est milliar. 339102. ambitus verò extimæ superficii conuexæ est milliar. 27361875. Crassities Orbis Martis est lata milliar. 27339375. ambitus V

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MATHEMATICVM. 341 < 35.> OPTICS is the science which, by means of visual rays and the shadows bounded by rays, takes account of the distances, magnitudes, parallaxes of celestial bodies, refractions, and shadows, and measures them: and this whether the rays themselves are transmitted directly or reflected from the object to the eye; yet in such a way that if this is done directly through holes or slits of some instrument receiving the rays of the stars, it is called Dioptrics; if, however, by reflection from some surface partly opaque and partly diaphanous, it is called Catoptrics, or Anacamptics; but if through refracted lines in a medium of different density, it is called Anaclastic; of all which in their proper place. < 34.> ORBIT properly is said of the deferents of the individual planets, which are commonly called spheres. Orbit, however, differs from sphere, because this latter properly signifies a globe contained by a single surface, and solid all the way to the center; but orbit says a spherical body bounded by two surfaces, one exterior convex, the other interior concave: and therefore, as many heavens, so many orbits contiguous to one another and immediately adjacent, so that the superior encloses the inferior, and as great as is the concave surface of the superior, so great also is the convex of the inferior, just as in the tunic of a single onion. But because each orbit, or heaven, contains within itself other orbits as well, so that, for example, the orbit of the sun has three other orbits separated from one another and contiguous to itself, of which two are eccentric in a certain respect; the third simply eccentric; therefore, to avoid confusion of terms, usage has prevailed that the heavens themselves are now called not orbits but spheres: and thus the greatest sphere is the first mobile, which embraces all the others within its circuit and carries them along with itself: after it the tenth and ninth sphere, called of trepidation, if such there be. Then the eighth, or Firmament: next the heaven of Saturn, then of Jupiter, and so on down to the Moon, so that the sphere of the Moon is the smallest of all both in circuit and thickness, and indeed the circumference of its concavity itself is 758250 miles, but its thickness, that is, the interval between its concave and convex, is 109056 miles; the circumference of the convex, however, which, as I said, is the same as the concave of the superior, is thus for Mercury 1443750 miles. The thickness of the orbit of Mercury is 370480 miles. The circumference of its convex surface is 3772500 miles. The thickness of the orbit of Venus is 3413756 miles; the circumference of the convex surface 25230375. The thickness of the deferent of the sun is 339102 miles; the circumference of the outermost convex surface is 27361875 miles. The thickness of the orbit of Mars is 27339375 miles. Circumference V

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LEXICON verò conuexi est 199209375. Crassities Orbis Louis protenditur ad milliar. 19775497. ambitus autem conuexi est milliar. 323512500. Crassities orbis Saturni est milliar. 29474574. ambitus verò conuexi eiusdem, & consequenter superficii concauæ Firmamenti, est milliar. 5c8781250. Crassities Firmamenti, seu cæli stellati est milliariorum 8094 471. cum dimidio Ambitus conuexi 1017561500. Et hic est etiam circuitus extimæ superficii Primi Mobilis, cuius tamen crassities auspicari non potuit, cum nec potuerit ipsa eius conuexi amplitudo: non enim per quid sensibile potest dignosci, ex comparatione tamen aliisque congruentiis deducitur haud temere tantam esse superficiem conuexam Primi Mobilis, adeoque & concauam cæli Empyrei, vt ipse orbis stellatus comparatus ad illam partem se habeat vt punctum, non secus ac se babet terra ad ipsum Firmamentum relata. Qui plura volet de hac re, adeat clauium in spæram Io: de Sacrobosco cap. 1. p. mihi 214. ex quo nos etiam ista ex cerpsimus. ORBITA, Plinio auctore; dicitur vestigium currentis rotæ in viis impressum (siquidem ipsa rota quandoque Orbis dicirur.) Hinc apud Astronomos vsurpatur ad significandam viam solis, & singulorum planearum per circulum suæ latitudinis realiter incedentium; nec sanè absque ratione, atque experimento: Quandoquidem per eam Planeta transiens imprimit nescio quod suæ qualitatis vestigium, qua locus ille afficitur, ac proinde eandem pænè induit sui incessoris naturam; eo prorsus pacto ac limaces, & alia eiusmodi insecta relinquunt post se suæ tabificæ qualitatis impressiones in via per quam incedunt. Sed id præcipuè fit in intersectionibus orbitæ planetarum cum orbita solis, quæ proprièra vocatur eclipsa, eo quod in ea accidant luminarium Eclipses, vt in loco admonuimus. ORICRATOR, teste Valla, apud Astronomos olim dicebatur finium Dominus: qua de re vide in V. Fines. ORIENS appellatur vniuersaliter punctum illud in horizontis circulo vnde sol emergit quocumque anni tempore, imò & loca vnde emergunt sidera: propriè verò vnum ex quatuor punctis cardinalibus horizontis, per quod semper ascendit æquator, atque adeò, vnde oritur sol, quando est in punctis æquinoctialibus Arietis, & Libræ. Et locus diametraliter oppositus dicitur occidens, per quæ duo puncta concipitur transire circulus qui intersecet Meridianum ad angulos rectos, & cum eo diuidat horizontem in qua-

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LEXICON indeed its convexity is 199209375. The thickness of the orb of the Moon extends to 19775497 miles. but the circumference of the convexity is 323512500 miles. The thickness of the orb of Saturn is 29474574 miles; but the circumference of its convexity, and consequently of the concave surface of the Firmament, is 5c8781250 miles. The thickness of the Firmament, or starry heaven, is 8094 471 miles and a half. The circumference of the convexity is 1017561500. And this is also the circuit of the outer surface of the Primum Mobile, whose thickness, however, could not be conjectured, since the extent of its convexity itself could not be ascertained: for it cannot be recognized by anything sensible; nevertheless, from comparison and other congruities it is inferred without rashness that the convex surface of the Primum Mobile, and thus also the concave one of the Empyrean heaven, is so great that the starry orb itself, compared with that part, is as a point, just as the earth stands in relation to the Firmament itself. Whoever wishes to know more about this matter should consult the keys to the sphere of Io: de Sacrobosco, chap. 1, p. 214 in my copy, from which we also extracted these things. ORBITA, according to Pliny; is said to be the track impressed in roads by a running wheel (since the wheel itself is sometimes called an Orbis). Hence among astronomers it is used to signify the path of the sun, and of the individual planets moving actually through the circle of their own latitude; and not without reason, and by experience: for as a planet passes through it, it impresses, I know not what, a trace of its own quality, by which that place is affected, and therefore it almost takes on the nature of the body moving over it; just as snails and other such insects leave behind them on the path they travel impressions of their destructive quality. But this happens especially in the intersections of the orbit of the planets with the orbit of the sun, which is properly called an eclipse, because the eclipses of the luminaries occur in it, as we noted in the place. ORICRATOR, as Valla testifies, was once said among astronomers to be the Lord of the bounds: see on this matter in V. Fines. ORIENS is universally called that point in the circle of the horizon from which the sun emerges at whatever time of year, and also the places from which stars emerge; properly, however, one of the four cardinal points of the horizon, through which the equator always ascends, and therefore from which the sun rises when it is in the equinoctial points of Aries and Libra. And the place diametrically opposite is called the west, through which two points is conceived the circle to pass which intersects the Meridian at right angles, and with it divides the horizon into a-

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MATHEMATICVM. 343 tuor partes æquales, Septentrionalem, Orientalem, Meridianam, & Occidentalem, à quarum initiis spirant quatuor Venti cardinales, Septentrio, qui & Boreas, Subsolanus, Auster, & Fauonius, de quibus suo loco. Porrò Oriens apud Geographos dicitur illa pars orbis terrarum ad dexteram sita, quam sol primò lustrat in nostrum Hemisphærium se attollens, & vniversaliter ea loca, quæ solem priùs Orientem vident dicuntur Orientaliora, quam, quibus Sol seriùs oritur; quæ proptereà respectu illorum vocantur Occidentiora. Verum autem Oriens, (vt diximus eum de Occidente sermo incidit) computari debet in eo tractu terræ habitabilis, quæ diametraliter opponitur vero Occidenti, quod non iam est in insulis fortunatis, sed in insulis Azorum, vbi acus magnetica se vertit recti ad polos mundi, diuidens æquatorem ad angulos rectos, vnde consequenter erit in Sarapa, Asiæ Ciuitate, provt latè in loco probauimus. ORIENTALES DOMVS, & Quadrantes. Vide in V: Occidentales. 40. ORIENTALIS PLANETA. Vide item in V. Occidentalis Planeta. 41. ORION, qui & Iugula, sidus est in octaua sphæra ad australem plagam hinc inde ad æquatorem, (in quem incidit eius cingulus habens stellas 38. conspicuas sub signo Geminorum, omnes serè de natura Iouis & Saturni, præter duas de natura Martis, & Mercurij, quarum altera primæ magnitudinis, in dextro humero, altera adhuc rubore, & actiuitate præsignior, licet corpore minor, & secundæ magnitudinis est in sinistro humero, & vocatur bellatrix à bello ad quod mirè animos incitat, & impellit. Est item in sinistro pede altera insignis stella nomine Rigel communis fluuo, nec non aliæ tres in ciugulo supra memorato valde lucidæ, & secundæ magnitudinis stantes ad rectam, & aliæ multæ præsertim in ense, & in scuto: quippe non est in cælo sidus tam latum, tam conspicuum, tam multiplici stellarum varietate ornatum, & in eo quidem Galilæus tot stellas minutiores suo Telescopio obseruauit, vt pænè in numerando defecerit, vt refert in Nuncio sidereo. Porrò Orion sidus maximè tempestatuosum est, quod & Virgilius obseruauit 7. Æneid. Quam multi Lybico voluntur marmore fluctus, Sauus vbi Orion Hybernis conditus vndis! Cum sole enim eongrediens, siue in ortu, siue occasu ventos ciet, turbat aërem, mare tempestatibus quarit, imbres Y ij

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MATHEMATICVM. 343 the four equal parts, Northern, Eastern, Southern, and Western, from whose beginnings blow the four cardinal Winds, Septentrio, who is also Boreas, Subsolanus, Auster, and Favonius, concerning which in their proper place. Moreover, the East among Geographers is said to be that part of the world placed on the right hand, which the sun first illuminates as it rises into our Hemisphere, and universally those places which first see the rising sun are called more Eastern, than those to which the sun rises later; which therefore, in relation to the former, are called more Western. But truly the East, (as we said when the discourse turned to the West) must be reckoned in that tract of habitable earth which is diametrically opposite to the true West, which is now no longer in the Fortunate Islands, but in the Azores Islands, where the magnetic needle turns itself directly to the poles of the world, dividing the equator at right angles, whence consequently it will be in Sarapa, a city of Asia, as we have at length proved in the place. ORIENTAL HOUSES, and Quadrants. See in V: Western. 40. ORIENTAL PLANET. See also in V. Western Planet. 41. ORION, also called Iugula, is a constellation in the eighth sphere on the southern side, extending on both sides to the equator, (into which its belt falls, having 38 conspicuous stars under the sign of Gemini, almost all of the nature of Jupiter and Saturn, except two of the nature of Mars and Mercury, one of which, of the first magnitude, is on the right shoulder, the other still more notable for redness and activity, though smaller in body, and of the second magnitude, is on the left shoulder, and is called Bellatrix from the battle to which it wondrously incites and impels the mind. There is also on the left foot another notable star named Rigel, of common yellow colour, and likewise three others in the above-mentioned belt, very bright, and of the second magnitude, standing in a straight line, and many others, especially in the sword, and in the shield: indeed there is not in the heavens a constellation so broad, so conspicuous, so adorned with so many varieties of stars, and Galileo in fact observed so many smaller stars in it with his Telescope, that he almost failed in counting them, as he relates in the Sidereal Messenger. Moreover Orion is a constellation extremely stormy, as Virgil also observed, Aeneid 7. How many waves roll on Lybic marble, when fierce Orion is sunk beneath the wintry waters! For when it rises with the sun, whether at its rising or setting, it stirs up winds, disturbs the air, seeks the sea with storms, rains Y ij

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LEXICON 344 facit, fulgura & tonitrua: quod & cum Saturno, & cum Mercurio facit, & eò maximè si omnes vnà conueniant. At si eo ex oriente Iupiter soli, aut Mars permisceatur, eius sideris vehementia longè lateque dignoscitur: quippe tempestatem sub ortu Sirij producit, & Aquilo magnis flatibus aërem quauis corruptione purgabit: Inde exurgent Etesiæ, & Autumnus salubris erit. In Genethliacis etiam, inquit Maternus: Ss Orson in horoscopo partilicer fuerit, faciet homines velocis corporis mobilitate conspicuos, & quorum animus variis solicitudinibus implicatus perui-gili cogitatione semper exastuet. Hi enim variabuntur, sæpè domicilia & domos, sedesque mutabunt, ac per omnium limina matutinis semper salutationibus discurrant. Si verò in occasu fuerit, subdit: Tales nascentur homines, quorum animos varia solicitudo semper exagitet. Hi quoque à ciuibus suis in legationem missi, ac in ipso munere constituti peregrè morientur, leue quoddam solatium ad inferos afferentes quod illis à ciuibus suis datum fuerit. Iis quoque honores perpetui, imagines, tituli, & honorabilium statuarum cernuntur insignia. Hucusque Firmicus. Vide in V. In-gula. 43. ORIZON. Vide Horizon. 44. ORNITHIAS ventus est ex genere Ethesiarum, nomen ex Græco ab auium aduentu sortitus, quod potissimum Veris tempore quando illæ ad nos aduentant exsufflare soleat circà vespertinum Arcturi exortum. Fertur humilis circà terræ latera: vnde & omnium commodissimus est: qui vt plurimùm vertitur in Fanonium; ob idque à Plin. Zephi-rus appellatur. 45. OROASER in sphæra Barbarica, ditur primus Decanus Aquarij manens sub dominatu Veneris: significator ærum-narum pro lucro, inquietudinis, laboris, paupertatis, &c. 46. ORTHOGONIVS Græcè idem sonat, ac rectus angulus: significat enim apud Geometras figuram, quæ rectis angulis constet, & omnium partium æqualitatem habeat. Vnde & Columella, lib.5. Orthogonium agrum appellauit. 47. ORTHOGRAPHIA est descriptio frontis, erectæque ma-gnitudinis, quam ædificium construendum habiturum est, facta ex regulis Geometricis, ad cuius posteà idæam tota moles consurgit. Quapropter est ars Architecturæ mini-stra, illique subseruiens. Vide Vitruuium lib.1.cap.2. 48. ORTVS, & occasus siderum, Achronicus, Cosmicus, He-liacus, Matutinus, Vespertinus, &c. Vide in propriis cu-

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LEXICON 344 causes lightning and thunder: which it does also with Saturn, and with Mercury, and especially if all come together at once. But if Jupiter alone, or Mars, be mixed with it from the east, the force of that star is recognized far and wide: for it brings on storms at the rising of Sirius, and the North Wind with great blasts will cleanse the air from any corruption: then the Etesian winds will arise, and Autumn will be healthy. In Genethliacs also, says Maternus: If Orion in the horoscope shall be partly there, it will make men notable for the agility of a swift body, and whose mind, entangled with various anxieties, is always made feverish by sleepless thinking. For these will be changeable, often altering their dwellings and houses, and seats, and will run through all doorways with morning greetings. But if he shall be in the west, he adds: Such men will be born, whose minds constant anxiety will always disturb. These too, sent by their fellow-citizens on an embassy, and set in that very office will die abroad, bringing to the underworld a certain slight consolation from what had been given them by their fellow-citizens. For them also are seen perpetual honors, images, titles, and insignia of honorable statues. Thus far Firmicus. See in V. In-gula. 43. ORIZON. See Horizon. 44. ORNITHIAS is a wind of the Etesian kind, taking its name from the Greek from the arrival of birds, because it is accustomed especially in springtime, when they arrive here from there, to blow around the rising of Arcturus in the evening. It blows low along the sides of the earth: whence it is also the most agreeable of all winds: and it usually turns toward Fanonium; and for that reason Pliny calls it Zephyrus. 45. OROASER in the Barbaric sphere is said to be the first Decan of Aquarius, remaining under the dominion of Venus: signifying gains for profit, restlessness, labor, poverty, etc. 46. ORTHOGONIVS in Greek sounds the same as a right angle: for among geometers it signifies a figure that consists of right angles, and has equality of all its parts. Whence Columella also, in book 5, called a field orthogonium. 47. ORTHOGRAPHIA is a description of the front and the upright magnitude which the building to be constructed will have, made according to geometric rules, from which afterwards the whole structure rises up to its idea. For this reason it is a helper in the art of Architecture, serving beneath it. See Vitruvius, book 1, chapter 2. 48. The rising and setting of the stars, Achronic, Cosmic, He-liac, Morning, Evening, etc. See under the proper headings.

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MATHEMATICVM. 343 iisque locis, de ea re fusè agit Plin. lib. 18. cap. 25. OSTENSOR, Latinè dicitur quæ Græcè Dioptra, apud < 49.> Arabes verò Alhidada: Index videlicet in Astrolabio, aut alio consimili instrumento lineæ diametralis vices gerens, & ostendens horas, gradus ventos & alia circum in Limbo descripta. Vide in V Alhidada. Os Piscis vulgò dicitur Fomahand stella fixa insignis ex- < 50.> stens in ore Piscis notij, estque vltima in effusione aquæ < 51.> Aquarij, cuius naturam, & influxus vide in V. Foma- hand. OVALIS figura, dicitur apud Geometras, quæ oui spe- < 52.> ciem præsefert, rotunda quidem sed oblonga, ita vt lineæ ab extima superficie ad centrum ductæ non sint æquales, benè verò à lateribus sibi inuicem ex opposito responden- tibus. Differt ab Ellipsi, quod hæc plana sit, & vnicam tan- tum linea circumscribatur, illa autem intelligatur solida, & superficie vndequaque finita, eo pacto ac globus, qui tamen est perfectè rotundus. OXYGONIUM est figura item Geometrica triangularis ha- < 53.> bens necessario omnes tres angulos acutos: in quo differt ab Amblygonio, quod necessariò constare debet ex duo- bus angulis acutis, & vno obtuso. Quare omne triangulum Oxygonium potest esse aut æquilaterum, quod necessariò, non erit rectangulum, & constabit tribus acutis angulis; aut Iosceles, si videlicet duo æqualia habeat latera, ea- demque maiora, quam tertium: aut etiam scalenum, quod omnia latera habere debet inæqualia: At verò Amblygo- < 54.> nium potest quidem esse Iosceles, & Scalenum, minimè verò æquilaterum, cum figura, quæ æqualia omninò la- tera habet in obtusangulum terminare nullatenus possit. Qua de re vide Clauium in lib. 1. Elem. Euclidis num. 18. & in Commentar. ad propos. 15. libri 4. P PALILITIVM, Arab. Aldebaram stella fixa primæ magni- < 1.> tudinis vna ex Hyadibus in oculo australi Tauri consi- stens, de natura Martis valde rutila, vnde & Lampas, & Facula dicta est. Nomen obtinuit à Paliliis, quæ Romæ eo die celebrabantur, quo ipsa oriens serenitatem adducebat, vnde & ab hoc clarior fieri coepit, cùm alioqui reliquæ Hyades pluuiosæ sint: Quod & Plinius obseruauit, lib. 18. cap. 26. Hoc est, inquit, appellatum fidus Palilitium: quo- < 2.> niam XI. Kalend. Maij Vrbis Roma natalis, quo ferè fere- Y iii

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MATHEMATICVM. 343 and at those places Pliny discusses the matter at length, lib. 18, cap. 25. OSTENSOR, in Latin is called what in Greek is Dioptra, among the Arabs, however, Alhidada: namely, the index in the astrolabe, or in some similar instrument, serving in place of the diametral line, and showing the hours, degrees, winds, and other things described around the limb. See under V. Alhidada. The Fish’s Mouth is commonly called Fomahand, a notable fixed star extending in the mouth of the Northern Fish, and the last in the water-pouring of Aquarius, whose nature and influence see under V. Fomahand. OVAL figure is said by geometers of that which presents the appearance of an egg, round indeed but oblong, so that the lines drawn from the outer surface to the center are not equal, but are equal on the sides opposite to one another. It differs from the ellipse, because this is a plane figure and is circumscribed by only one line, whereas that is understood to be solid, and bounded on every side by a surface, in that way as a globe is, which nevertheless is perfectly round. OXYGONIUM is likewise a geometrical figure, triangular, necessarily having all three acute angles: in this it differs from an Amblygonium, which must necessarily consist of two acute angles and one obtuse angle. Therefore every oxygonial triangle may be either equilateral, which necessarily will not be right-angled, and will consist of three acute angles; or isosceles, if it has two equal sides, and those greater than the third; or even scalene, which must have all its sides unequal. But an Amblygonium can indeed be isosceles and scalene, but by no means equilateral, since a figure that has absolutely equal sides cannot in any way terminate in an obtuse angle. On this matter see Clavius in lib. 1, Elem. Euclidis, num. 18, and in the commentary on proposition 15 of book 4. P PALILITIVM, Arab. Aldebaran, a fixed star of the first magnitude, one of the Hyades, situated in the southern eye of Taurus, of a nature very like Mars, whence it is also called Lampas and Facula. It received its name from the Palilia, which were celebrated at Rome on the very day when its rising brought clear weather; from which it likewise began to shine more brightly, whereas the rest of the Hyades are rainy. This too Pliny observed, lib. 18, cap. 26. “It is called,” he says, “the star Palilitium, because on the eleventh day before the Kalends of May the birthday of the city of Rome, on which almost all things are brought- Y iii

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LEXICON nitas redditur, claritatem observationi dedit, nimboru[m] argumento Hyadas appellantibus Gracis has stellas, quod no- stri à similitudine cognominis Graci propter suos impositum arbitrantes, imperita appellauere succulas. Cum hoc fidere exoriens sol cõmouet ventos, fulmina facit, & tonitrua: Cum Marte calorem magnum, cum Mercurio itidem ventos im- petuosos: est enim maximè violentum, intemperatè cali- dum, & siccum; vnde & in Genethliacis facit animum ela- tum, iracundum ad iixas, & bella proclivem cum quadam grauitate, & prudentia ob communicationem cum Ioue. Vide quæ diximus in V. Aldebaran. PALMA S R P E N T A R I L Fixa insignis Vide in V. Cela- bramet. 2. PANSELENE Græcè dicitur Luna plena, cum est in solis oppositione ex Pan quod significat aggregationem, & Se- lene, quæ dicitur Luna: nos eâdem ratione Plenilu- nium appellamus. 3. PAARAB LA, seu Parabole, apud Geomeiras dicitur figu- ra plana, seu area, quæ duabus lineis, alterâ recta, altera curua circumscribatui. De hac multa habet Archimedes, qui etiam eam multis argumentis, ac demonstrationibus quadrare primus, nec sanè irritio conatu aggressus est. 4. PARADISVS TERRESTRIS est locus aincænissimus in Edi- tiori Orbis parte constitutus ad Orientem; Dei manu con- sirus, & plantatus ad humani generis iucundissimam habi- tationem: in quo quidem Diu vitam traduxisset, ni primi parentis lapsus fuisset in causa, vt & ipse inde eijcerétur, & posteri omnes perpetuò exularent, posito ad custodiam Cherubim, & flammeo gladio, atque versatili, vt habetur Gen. 3. ad omnem eius viam intercludendam. De eius situ, varix sunt, innumeræ, sibique prorsus contrariæ SS. PP. alio- rumque Doctorum Sententix, quas omnes accuratè cen- sent, & expendunt Augustinus; ac Thomas Maluenda in peculiari libro de Paradiso. Communior tamen, & quæ vulgi plausum, fidemque promeruit, est eum fuisse situm in partibus Orientis, circà Mesopotamiam, & Armeniam. Tum quia Sacræ Paginę referunt cum fuisse placatum à prin- cipio, hoc est (vt explicat Abulensis) à prima parte rectæ habitabilis Orientalis: cui explicationi consonat Hebraica dictio Miqueden, scilicet ab Oriente, quod est Principium Mundi: Necnon versio septuaginta interpretum, quæ sic habet. Et plantauit Deus Paradisum in Eden ad Orientem, & posuit ibi hominem, quem psalmauerat. Tum etiam, quia ex illo loco dicitur, quod egrediebatur magnus qui-

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nitas is restored; he gave clarity to observation. Because of the argument of the clouds, the Greeks called these stars Hyades, which our people, thinking the name was given from their resemblance to a Greek cognomen, ignorantly called succulae. When the sun rising with this sign stirs up the winds, it produces lightning and thunder; with Mars, great heat; with Mercury, likewise stormy winds. For it is most violent, excessively hot and dry; hence also in genethliacs it makes the mind elevated, prone to anger, to quarrels, and inclined to war, with a certain gravity and prudence through its association with Jupiter. See what we said in V. Aldebaran. PALMA S R P E N T A R I L, a notable fixed star. See in V. Celabramet. 2. PANSELENE is said in Greek of the full moon, when it is in opposition to the sun, from Pan, which signifies aggregation, and Selene, which means moon; on the same principle we call it plenilunium. 3. PARABOLA, or Parabole, among geometers is said to be a plane figure, or area, bounded by two lines, one straight, the other curved. Archimedes has much to say about this, and he was the first to attempt to square it by many arguments and demonstrations, and certainly not in vain. 4. PARADISE TERRESTRIAL is a most beautiful place established in the most excellent part of the world toward the East; constructed and planted by the hand of God for the most delightful habitation of the human race: in which man would indeed have spent his life, had not the fall of the first parent been the cause that he too was cast out from it, and all his posterity were exiled forever, with a Cherub placed there to guard it, and a flaming, revolving sword, as is found in Gen. 3, to block every way to it. Concerning its location, there are various, countless, and utterly contradictory opinions of the Holy Fathers and other Doctors, all of which Augustine and Thomas Malvenda in a special book on Paradise carefully examine and weigh. The more common view, however, and the one that has won popular approval and belief, is that it was situated in the eastern regions, around Mesopotamia and Armenia. First, because the Sacred Pages say that it was planted from the beginning, that is (as Abulensis explains), from the first part of the eastern habitable world; to which explanation the Hebrew term Miqueden agrees, namely, “from the East,” which is the beginning of the world. Likewise the version of the seventy interpreters, which reads thus: And God planted paradise in Eden toward the east, and placed there the man whom he had formed. Then also, because from that place it is said that there went out a great which-

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MATHEMATICVM. 347 damfons, qui irrigabat vniuersum Paradisum; quique postea diuidebatur in quatuor capita, seu magnos fluuios Orbi notissimos, ac celebres, Gehon, hoc est Gangem; Phison, quem volunt esse Nilum; Tigrim, & Euphratem: qui omnes, vt constat, ad Orientem positi sunt. Cuius rei consonam etiam rationem affert D. Th. 1. parte quest. 1. 2. art. 1. in corpore Quia, inquit, creuendum est, quod in nobilissimo loco terra sit constitutus. Cum autem Oriens sit dextera Cali vt per Philosophum 2 de Calo: dextera autem nobilior est, quam sinistra, conveniens fuit, vt in Orientali parte Paradisus Terreus institueretur à Deo. Hæc S. Doctor. Verum (vt hinc tandem exordiamur) non videtur hæc ratio sufficiens ad probandum dictum Paradisum situm esse in Oriente: & adhuc si in Oriente; vbinam locorum sit: quia, vt benè subinfert Abulensis, quilibet punctus horizontis est Oriens respectu alicuius alterius, ob reiæ rotunditatem, & solis iugem circà ipam circulationem. Vnde Palæstina nobis dicitur Orientalis, Indis verò Occidentalis. Econtra Alia tota; licet ad dexteram sit Europæ, atque ipsa Orientalior, est tamen ad sinistram Americæ, ex eâ præsertim parte; vnde incipit Amana Regnum ad polum Arcticum, cui succedit Quiuira, Noua Albion, inde Noua Hispania, & ad Meridiem Noua Andalusia, Guiana, mox Prouincia Peruana, ac tandem vltra Tropicum Capricorni per Regnum Chisi, Chicam & Pantagonum regionem, vsque ad eam insulam seu potius reliqui continentis partem nondum detectam extenditur, quam ab igne circumambiente vulgò appellant, La tierra del Fuego, ad latitudinem gr. 55. Quod ideò nil mirum, si eo scripturæ testimonio non obstante, Patres nihilominus dissident: & alij in hac noui Orbis parte, alij in insula Taptobana, quam Sumatram esse multi autumant sub Æquatore (licet peritiores Cosmographi eam insulam non Sumatram, sed Ceilan esse censeant) alij demum verosimiliùs in modo memorata terra ab igne circumambiente dicta, proindeqne inaccessibili, Paradisum hunc inaccessum & flammeo gladio, hoc est muro igneo, vt volunt intelligi circumseptum velint constitui. Sed & illud omnibus indubitatum est, ac pro fundamento omnium maximo statuendum, locum illum debere esse omnium florentissimum, atque amoenissimum, vbi ex naturali soli dispositione potuissent homines diù vitam p[er]tetrare: vt notat etiam Abulensis in cap. 2. Gen. quod non icredibile esse ait. Quia in Hybernia, subdit, quædam insula sunt, in quibus homines Y iiiij

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MATHEMATICVM. 347 that fountain which watered the whole Paradise; and which afterward was divided into four heads, or great rivers well known and celebrated throughout the world, Gehon, that is, the Ganges; Phison, which they hold to be the Nile; Tigris, and Euphrates: all of which, as is clear, are situated toward the East. For this reason also D. Th. 1. part, quest. 1. 2. art. 1. in the body gives a corresponding reason, because, he says, it must be believed that the earth was placed in the most noble region. But since the East is the right side of the heaven, as the Philosopher says in 2 De Caelo; and the right is more noble than the left, it was fitting that the Terrestrial Paradise should have been established by God in the Eastern part. These are the words of the Holy Doctor. Yet, in truth, from this point we must finally begin: this reason does not seem sufficient to prove that the said Paradise was located in the East; and even if in the East, where exactly it was: because, as Abulensis well adds, every point of the horizon is East in relation to some other, on account of the roundness of the earth, and the sun’s continual circuit around it. Hence Palestine is called Eastern to us, but Western to the Indians. Conversely, all America, though to the right of Europe, and indeed more Eastern than it, is nevertheless to the left of America, especially from that part where the Kingdom of Amana begins toward the Arctic pole, to which succeed Quivira, New Albion, then New Spain, and to the south New Andalusia, Guiana, then the Peruvian Province, and finally beyond the Tropic of Capricorn through the Kingdom of Chisi, Chicam, and the region of Pantagono, extending to that island, or rather part of the continent not yet discovered, which, from the fire surrounding it, is commonly called La tierra del Fuego, at latitude 55 degrees. For this reason it is no wonder if, despite the testimony of Scripture, the Fathers nevertheless disagree: and some place it in this part of the New World, others on the island of Taptobana, which many suppose to be Sumatra under the Equator (though more learned cosmographers judge that island to be not Sumatra, but Ceylon), and others finally, more plausibly, in the aforesaid land called from the fire surrounding it, and therefore inaccessible, wishing this inaccessible Paradise, enclosed with the flaming sword, that is, with a wall of fire, as they would have it understood, to be situated there. But this also is beyond doubt to all, and must be set down as the greatest foundation of all: that that place ought to be the most flourishing and the most delightful of all, where, from the natural disposition of the soil, men could have prolonged life for a long time: as Abulensis also notes on chapter 2 of Genesis, which he says is not unbelievable. For in Ireland, he adds, there are certain islands in which men Y iiiij

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LEXICON numquam moriuntur; quia tanta est aëris s[an]t[us] ubritas, quod vita humana valdè protenditur, & cum ad magnam senectutem homines perucnerint; paulisper deficiente per calorem naturalem humido radicali, & anima propter bonitatem complexionis recedere non potest, fiunt magni dolores in corpore: & ideò homines illis regionis post diuturnos labores vitam fastidientes extrà illam terram longè se deportari faciunt, vbi faciliter moriuntur. Locus autem adeò salubris, ac temperatus, qui cæteris omnibus anrecellat, vix in toto terræ tractu excogitari potest, cui non sit alius compar, siue Periæcus, siue Antæcus, siue etiam diamerrariter oppositus: quippe est in eadem cæli posizione; vbi eosdem aut pares effectus contingere, necessum est affirmare. At enim sub Æquatore conveniunt omnes, esse temperatissimum Clima: quod obseruauit etiam S. Th. vbi suprà art. 2. in respons. ad 4. antequam adhuc id Hispanorum experientia compertum esset, ob iugem dierum, ac noctium æqualitatem: quod porissimum de supradicto Guaianæ Regno sub Æquatore sito asseuerant. Vnde ob id contrarià ratione dici non potest, Paradisum hunc esse in ea orbis parre ob ignem hactenus inaccessa; quandoquidem ibi ob maximam latitudinem australem, nimium frigus esse naturaliter deduci debear. Prærerquam, cum locus ille primis parenribus ad habirandum datus sit cum omnibus suis posteris, ni peccassent, consequenter non in definito spario circiter leucarum in longitudine, (vt vult Abulensis qu. 98. in Gen. cap. 13.) in ea amplitudine concipiendus est, quam non facilè exequare possit vna regio, aut insula, qualis est terra illa ab igne denominata. Quod ideo Abraham Ortelius in tabula Sacra Geographia, Io: Nouiomagus in Schol. ad lib. 5. Beda de Natura rerum, Pineda de Monarchia Ecclesiast. lib 1 cap 6. aliique quos referr Maluenda de Paradiso cap. 8. dixerunt, Paradisum hunc â Moyse descriptum, totam terram fuisse. Iacobus vero Episcopus Christopolitanus in expositione ps. 71. opinatus est, totam regionem australem vltrà tropicum Capricorni, fuisse datam primis parentibus in regnum hæredirarium: adeoque in toto eius tractu constituendum esse Paradisum terrestrem; quem dicit gladio igneo, & versatili circumseptum, tropico videlicet Capricorni, qui ob solis ardorem iugiter per Zonam torridam diuaganiis, igneus gladius, & versatills, quem Deus inter nos, & Paradisum illum posuit, dictus est. Sed audiamus illum de hac loci amoenitate sic discurrentem. Quomodocunque, ait, Philosophi diuidant terram, & totum Calum in-

Transcription: Translated (English)

LEXICON never die; because such is the wholesomeness of the air, that human life is greatly prolonged, and when men have reached great old age; as the natural heat gradually fails, the radical moisture being diminished, and the soul unable to withdraw because of the goodness of the complexion, great pains arise in the body: and therefore the men of those regions, after long labors, being wearied of life, have themselves carried far outside that land, where they easily die. But a place so healthy, and temperate, surpassing all others, can scarcely be conceived in the whole extent of the earth, to which there is no other comparable, whether Periæcus, or Antæcus, or even diametrically opposite: since it is in the same position of the heavens; where the same or similar effects must necessarily be said to occur. But indeed under the Equator all agree that there is the most temperate climate: which even S. Th. observed there above, art. 2. in response to 4, before this was yet known by Spanish experience, because of the continual equality of days and nights: which they especially affirm of the aforesaid Kingdom of Guiana situated under the Equator. Wherefore, for that reason, by contrary reasoning it cannot be said that this Paradise is in that part of the world made inaccessible hitherto by fire; since there, because of the greatest southern latitude, excessive cold must naturally be inferred. Besides, since that place was given to the first parents to dwell in, together with all their descendants, if they had not sinned, consequently it is not to be conceived as confined to a definite space of about leagues in length, (as Abulensis wishes, q. 98. in Gen. cap. 13.) but in such a vast extent as cannot be easily matched by a single region or island, such as is that land so named from fire. For this reason Abraham Ortelius in the map of Sacred Geography, Io: Nouiomagus in the Schol. to lib. 5. of Bede On the Nature of Things, Pineda On Ecclesiastical Monarchy, book 1, cap. 6, and others whom Maluenda refers to in On Paradise, cap. 8, have said that this Paradise described by Moses was the whole earth. But James, Bishop of Christopolis, in the exposition of ps. 71, was of the opinion that the entire southern region beyond the Tropic of Capricorn had been given to the first parents as an hereditary kingdom: and therefore that earthly Paradise ought to be established throughout its whole extent; which, he says, is surrounded by a fiery and turning sword, namely the Tropic of Capricorn, which, because of the sun’s heat continually raging through the Torrid Zone, was called the fiery and revolving sword which God placed between us and that Paradise. But let us hear him speaking thus concerning the pleasantness of this place. However, he says, the philosophers divide the earth, and the whole heaven in-

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MATHEMATICVM. 349 men omnes in hoc conueniunt, quod pars Australis vltrà tropicum hyemalem est nobilior, & fauorabilior, & fertilior, & felicior: eo quod est sub nobilioribus astris; & per consequens recipit nobiliores influentias, & maiores virtutes quam ista pars nostra Aquilonaris, & quam tota mensa solis (Mensam solis cum Philosophis, ac Poëtis appellat Zonam torridam quæ clauditur duobus tropicis, Cancri videlicet, & Capricorni.) & sic fructus, & omnia nascentia, qua ibi germinantur sunt perfectiora & maioris virtutis. His habitis ponitur prima conclusio: quod Paradisus deliciarum, unde Adam expulsus est, est assignandus in illa parte Australi, vltrà mensam solis, & ambos tropicos: nam nobilissima pars terra debet collocari sub nobiliore parte Cali: sed ille Paradisus deliciarum est huiusmodi: ergo. Maior est nota: quia bonitas, & fertilitas terra inest ibi ex nobili influentia astrorum, & aspectu cali. Minor autem probatur ex dictis Sacra scriptura, & sacrorum Docterum. Nam illa terra spontè absque omni labore humano prefert fructus suauissimos pro vitahumana conseruanda; & inter cætera profert lignum vita, cuius fructus potest vitam hominum in æternum perpetuare, ut patet Gen. 2. & 3 prove bodie nutrit Eliam, & Enoch, ergò sequitur, quod illa terra est cæteris nobilior, & foecundior, & magis vbertosa, & amana, & delectabilis in omni genere deliciarum: quod ideò dicitur Paradisus deliciarum. Quod autem terra illa australis sic cæteris nobilior & stellarum benignicare foecundior, iam suprà probauerat, & confirmat hic ex responsione ad quoddam argumentum tibi factum. Quia, subdit, omnia astra Cali, tam illa, qua sunt in Zodiaco quam illa, qua sunt extrà, habent suas proprietates, & qualitates quadam bonas, & quadam malas sicut habent & planeta: & ideo quando planeta mittit radios suos ad astra nostra, qua sunt extrà Zodiacum causat effectus diuersos apud nos, secundum diuersitatem qualitatum astrorum: & sic planeta malitiosus ex mixtione sua influentia cum influentia astri malitiosi causat pestilentias, aut sterilitates, aut bella, & discordias, aut tempestates, & cætera infortunia. apud nos, secundum dispositionem aspectus: hoc idem facit Sol secundum mixtionem radiorum cum aliis astris, quoad calorem & aliis influentias: & sic patet, quod non solum accessus, & recessus planetarum ad nos, aut coniunctio eorum inter se est præcisa causa variorum effectuum, sed mixtio influentiarum eorum cum nostris astris, qua sunt suprà nos. Sed quia omnia illa astra, qua sunt in hem. sphario australi sunt bona, & fauorabilia, & magna virtutis, provt di-

Transcription: Translated (English)

MATHEMATICVM. 349 men all agree in this, that the southern part beyond the winter tropic is more noble, and more favorable, and more fruitful, and happier: because it is under more noble stars; and consequently it receives more noble influences, and greater virtues than this our northern part, and than the whole “table of the sun” (with the philosophers and poets Zonaras calls the torrid zone, which is enclosed by the two tropics, namely Cancer and Capricorn). And thus the fruits, and all things born there, which germinate there, are more perfect and of greater virtue. Having set these things forth, the first conclusion is laid down: that the Paradise of delights, from which Adam was expelled, is to be assigned in that southern part, beyond the table of the sun and both tropics. For the noblest part of the earth ought to be placed under the nobler part of the sky; but that Paradise of delights is of this kind; therefore. The major premise is evident: because the goodness and fertility of the earth are found there from the noble influence of the stars and the aspect of the sky. The minor premise, however, is proved from the sayings of Sacred Scripture and of the holy Doctors. For that land of its own accord, without any human labor, brings forth sweetest fruits for the preservation of human life; and among other things it produces the tree of life, whose fruit can perpetuate the life of men forever, as is clear from Gen. 2 and 3, and to this day nourishes Elijah and Enoch; therefore it follows that that land is nobler than the others, and more fruitful, and more abundant, and pleasant, and delightful in every kind of delights: for which reason it is called the Paradise of delights. That that southern land is thus nobler than the others and more fruitful by the benignity of the stars, he had already proved above, and here he confirms it from the reply to a certain argument made to you. For, he says, all the stars of the sky, both those which are in the Zodiac and those which are outside it, have their own properties and qualities, some good and some bad, just as the planets do; and therefore when a planet sends its rays to our stars, which are outside the Zodiac, it causes different effects among us according to the diversity of the qualities of the stars: and thus an evil planet, by mixing its influence with the influence of an evil star, causes pestilences, or sterilities, or wars and dissensions, or storms, and other misfortunes among us, according to the disposition of the aspect. The sun does this same thing according to the mixing of its rays with the other stars, with regard to heat and other influences: and thus it is clear that not only the approach and recession of the planets to us, or their conjunction among themselves, is the precise cause of various effects, but also the mixture of their influences with our stars, which are above us. But because all those stars which are in the southern hemisphere are good, and favorable, and of great virtue, as in the case of di-

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LEXICON etumest; ideò nullam possunt recipere malam influentiam à planetis; immò resistunt malitia eorum; instarum quod nullum possunt facere nocumentum in toto hemisphario vltrà Capricornum, propter virtutes illarum stellarum prohibentium maliam planetarum. Et ita est dicendum de radiis solaribus, quia non possunt causare intensum, & inordinarum calorem, & estum cum illis attvis, sicut cum nostris, per eandem rationem, propter nobilitatem, & temperantiam illorum. Et sic planeta nullum possunt causare nocumentum, nec disproportionem in illis partibus propter benignitatem, & fauorem, & virtutem illorum astrorum resistentium malitia planetarum. Tandem concludit Sic pates, quod nullum inconueniens sequitur ex ista positione, sed multa, & plura inconuenientia sequerentur, si Paradisus deliciarum collocaretur, sub linea aquinoctiali inter tropicos, prout quidam dicunt, aut circa tropicos in parte orientali, sicut alij autumant: quia vtraque istarum partium est subiecta multis miseris vt pates Verum, vtcumque sit de ista assertione, in qua multa gratis assumuntur, multa effinguntur profus veritati, & experientiæ Hispanorum contraria; illud vnum ei maximè officit, quod Paradisus ille dicitur omninò inaccessibilis, atque à cognitione hominum remotissimus. Ista autem terra australis (excepta forsitam ea parte, quam diximus ab igne denominari) non modò est permeabilis, sed adhuc tota inhabitata, atque à nostris magna ex parte detecta. Ex quo etiam manifestè conuincitur, neque in partibus orientalibus, præsertim circà Mesopotamiam, & Armeniam, vt multi pro certo autumnant, posse constitui; vel ex eo id approbantes, quod illa quatuor sumina, quæ dicuntur ex fonte in medio Paradisit collocato exire, præsertim Tigris, & Euphrates in Asia ortum habent: & hi quidem in Armenia; vnde postea per Mesopotamiam & Assyriam transeuntes in sinum Persicum exonerantur. Ganges autem ex Caucaso Indiæ Monte prosilit, vt author est strabo: & Nilus ex quodam Monte Mauritianæ inferioris non longè ab Oceano, stagnante ibi lacu, quem vocant Nolidem: deinde se condit itinere plurium dieru[m]; rursumque erumpit alio maiore lacu in Mauritania Cæsariensi, iterumque arenis receptus per desertum, viginti dierum spatio fertur ad proximos Æthiopas, & denuò proslit fonte qui Nigris dicitur: Mox Africam ab Æthiopia disterminans, medtosque Æthiopas secans, in Ægyptum venit; ac tandem septem ostiis in Mare Ægyptium se exonerat. Ex quo eludere conantur obiectionem illam, quod heiusmodi fontes non ab eodem loco originem

Transcription: Translated (English)

LEXICON and so they cannot receive any evil influence from the planets; rather, they resist their malice, just as they can do no injury in the whole hemisphere beyond Capricorn, because of the virtues of those stars that prevent the evil of the planets. And the same must be said of the solar rays, because they cannot cause intense and irregular heat and warmth in those activities, as with ours, for the same reason, because of their nobility and temperance. And so the planets can cause no injury, nor disproportion in those parts, because of the benignity and favor and virtue of those stars resisting the malice of the planets. Finally he concludes thus, that no inconvenience follows from this position, but many and more inconveniences would follow if the Paradise of delights were placed under the equinoctial line between the tropics, as some say, or around the tropics in the eastern part, as others suppose: because each of those parts is subject to many miseries, as you see. But however it may be with this assertion, in which many things are assumed without basis, many things are invented quite contrary to truth and to the experience of the Spaniards; one thing especially militates against it, namely that that Paradise is said to be utterly inaccessible, and most remote from the knowledge of men. But this southern land (except perhaps that part which we said is called from fire) is not only passable, but still entirely uninhabited, and in great part discovered by our people. From this it is also clearly proved that it cannot be established in the eastern parts, especially around Mesopotamia and Armenia, as many confidently suppose; and they support this by saying that the four rivers which are said to issue from a source placed in the middle of Paradise, especially the Tigris and Euphrates, have their origin in Asia: and these indeed in Armenia; whence later, passing through Mesopotamia and Assyria, they are discharged into the Persian Gulf. The Ganges, however, springs from Mount Caucasus of India, as Strabo is witness: and the Nile from a certain mountain of lower Mauritania not far from the Ocean, with a stagnant lake there, which they call Nolidem: then it hides itself in a journey of several days; and again bursts out by another larger lake in Mauritania Caesariensis, and once more received by the sands through the desert, for a span of twenty days it is carried to the neighboring Ethiopians, and again it springs from a fountain that is called Nigris: then, marking off Africa from Ethiopia and cutting through the middle Ethiopians, it comes into Egypt; and finally it discharges itself by seven mouths into the Egyptian Sea. From this they try to evade that objection, namely that such springs do not have origin

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MATHEMATICVM. 351 trahunt, sed ab valdè dissitis regionibus. Quippe, in- quiunt, ex Nili eruptionibus deduci etiam potest, tam ip- sum, quam Gangem, reliquosque duos, ab vno, eodem- que loco, Paradiso inquam illo hominibus inaccesso pri- mam suam scaturiginem acceptam ferre; postmodum sub terras condi, ac demum post longos tractus, foras, vbi pri- mum hominibus patet accessus, erumpunt: cum alioqui Paradisus variis impedimentis, vel montium, vel marium, vel sanè æstuosæ alicuius regionis, quæ pertransiri non po- test, sic hominibus interclusus: vt author est D. Th. in res- pens. ad 3. Cæterum id non modo non euacuat difficultatem, sed < 6.> eam maioribus difficultatibus implicat; maiusque dubium facit; vbi tandem locorum constituendus sit Paradisus ter- restris. Siquidem inter Tigrin Euphratemque (qui ex Ar- menia, vt dictum est, primò se spectabiles reddunt) ac Gangem fluuium, intercedit spatium septuaginta graduum; hoc est iuxta Ptolemæum, plusquam quatuor millium ac trecentorum milliariorum: maiusque etiam inter eosdem, & Nilum. Vt proptereà non tam de istorum origine, incer- ta res sit, quam de illorum; atque etiam, nùm omnes, aut eorum aliquis non tam ex India, quam ex alio quouis vel dissito loco, ad vltimas Occidentis oras proctenso originem trahat: ac per longissimos tractus, occultosque terræ mea- tus, tandem hic apud Indos, ille in Mauritania, reliqui circa Armeniam foras erumpant. Deinde (vt id etiam eui- dentiùs cadat) hoc ipsum, quod modò diximus clarissimè conuellamus. Nam cum flumen aliquod per occultos terræ meatus permeat, erumpere possea solet magno impetu, & nisu, & eò maiore, quo maior exciterit occultatio: quod & ratio suades, & euin s it experientia, præsertim in Ana Fluuio, qui per quinque leucas subtus terram occultus per- meat, totusque deinde quasi renascens rapidissimus erum- pit. Id etiam videre est in ipso Nilo, vbi in Mauritania Cæsariensi denuò nascitur, ac tertiò apud Æthyopas: quod non facit in Mauritania inferiori. Vt proinde id argumento sit, eum hîc prima incunabula obtinere, illic adultum viri- bus, per motum, atque arctos terræ meatus auctum, foras violenter erumpere. Sicque etiam Gangem in India, Ti- grim, & Euphratem in Armenia, vbi quies & placidè oriuntur, primas scaturigines acceptas ferre. Quare cum ista loca, vt dictum est, inter se longè disiecta; neque vnus quidam sic sons toto terrarum orbe, ex quo verosimi- liter conjectari possit, omnes hos fluuios realiter deriuare;

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MATHEMATICVM. 351 they draw, but from very distant regions. For, they say, from the overflowing of the Nile it can also be inferred that both it and the Ganges and the other two derive their first source from one and the same place, namely from that Paradise inaccessible to men; afterward they are hidden under the earth, and at length, after long courses, they burst forth outside, where access first lies open to men. Otherwise Paradise would be shut off from men by various impediments, whether of mountains, or seas, or indeed some torrid region that cannot be traversed, as D. Th. author says in the response to 3. But this not only does not remove the difficulty, but also entangles it with greater difficulties; and it makes the doubt greater still: where, at last, is the earthly Paradise to be placed? For between the Tigris and the Euphrates (which, as has been said, first become visible from Armenia) and the river Ganges there lies a distance of seventy degrees; that is, according to Ptolemy, more than four thousand three hundred miles; and even more between the same rivers and the Nile. Thus the question is not so much uncertain as to the origin of those rivers, as of these; and also whether all of them, or any one of them, may not have taken origin not so much from India as from some other, even distant, place, stretched out to the farthest shores of the West; and whether, through very long courses and hidden channels of the earth, one may finally burst forth here among the Indians, another in Mauretania, and the rest around Armenia. Then, too, to make this still clearer, let us very plainly overturn what we have just said. For when some river passes through hidden channels of the earth, it is accustomed to burst out afterward with great force and effort, and all the more so the greater the hiddenness it has undergone; which both reason suggests and experience proves, especially in the river Ana, which for five leagues flows hidden beneath the earth, and then, as if born again whole, bursts forth most rapidly. This can also be seen in the Nile itself, where it is born again in Mauretania Caesariensis, and a third time among the Ethiopians; but it does not do so in lower Mauretania. So that this may serve as an argument that it has its first cradle here, and there, grown with strength by motion and narrow passages of the earth, it bursts violently forth. And so also the Ganges in India, and the Tigris and Euphrates in Armenia, where they arise in quiet and gently, bear their first sources there. Therefore, since these places, as has been said, are far apart from one another, and there is not one single source somewhere throughout the whole world from which it may be reasonably conjectured that all these rivers actually derive;

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LEXICON 352 vel dicendum est cum. Damasceno lib. 1. de fide Orthodoxa cap. 1. pro fonte illo, vnde quatuor ista sumina exire dicuntur, intelligendum esse Oceanum; vel cum Vgone Carensi in cap. 2. Genel. id quod sacræ paginæ de his quatuor aluminibus ex vno Paradisi fonte prodeuntibus refertunt, non videri purè ad litteram dici, sed aliquantò aliiùs & figura- tè, vt mox infra subiiciam. Postremò iam modò debite valdè est argumentum, Paradisum illum fieri vel montium, vel Marium immensitate inaccessibilem. Tum quia in scripturis manifestè dicitur Paradisus ille muro igneo circum- septus eoque tanium, non alio quouis impedimento fieri inaccessibilis: Tum quia, iam nostro æuo tellus ferè omnis Orbis istius penetrata est, omnis vel maxima pars habi- tatoribus culta, Oceanus totus sæpissimè excursus, Montes omnes lustrati, descripti, altitudo emensa, & ne minimus quidem terræ angulus relictus est, qui non sit penitissimè obseruarius: excepta vix ad polum Antarticum despectibili parte, longitudinis vix quinque graduum, nec ea qui- dem, vt creditur prorsus inaccessibili, sed hactenus, ob subterraneos ignes exilientes inaccessa: in qua num homines degant, iure etiam dubitari potest, licet forte ob cli- matis asperitatem, rudes admodum, si vlli sint, esse de- beant, & inculti, vt de sinitimis populis compertum est, utque etiam de sitis ad borealem polum, his de quibus lo- quimur Aniæcis; vbi ob solis obliquitatem, nimiumque frigus omnia rigent, & algent, mare perpetua glacie con- cretem est, tellus germen nullum profert, &c. vt incredi- bile planè sit, Paradisum deliciarum, quem tam amænum, tam floridum, tam fructibus omnibus redundante sacræ pagi- næ sancti[us]; Patres describunt, in frigidissima zona, sub incle- menti adeò cælo, posse naturaliter, aut potuisse consistere. Accedit, quod vbique tandem locorum huius terræ habi- tabilis Paradisus terrestris constituatur, is debuisset iam aquis diluuij obrui, ac diffipari. Quippe legimus Gen. 7. omnem terram fuisse aquis inundatam: imò aquas maximis, & altissimis montibus aliores quindecim cubitis extitisse. Nec valet aliquorum effugium dicentium eò aquas peculiari Dei privilegio minimè penetrasse; aut, quod assumit Abulensis circumstetisse vndique ad morem fornicis, eo pacto, quo Mare rubrum transeunibus Israelitis sterisse vtrinque pro muro. Tum quia id sacræ paginæ non enunciant, immò potius contrarium, cùm absolutè dicant terram omnem fuisse aquis cooperiam: Tum quia, vt benè aduertit Viega in Apocal. cap. 11. sol. 5. num 6. Si locus iste in terris à ge-

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or it must be said with Damascene, book 1, On the Orthodox Faith, chapter 1, that by that source, from which these four streams are said to come forth, the Ocean should be understood; or with Hugo of Car, in Genesis chapter 2, that what the sacred page relates about these four rivers issuing from one source of Paradise does not seem to be said purely according to the letter, but somewhat more broadly and figuratively, as I shall immediately note below. Finally, the argument is now very well established that that Paradise would be inaccessible either because of the immensity of the mountains or of the seas. First, because in the Scriptures it is plainly said that that Paradise was surrounded by a wall of fire, and made inaccessible by that alone, not by any other obstacle whatsoever. Second, because in our age almost the whole earth of this world has been traversed, almost the whole or very great part inhabited and cultivated by people, the whole Ocean has very often been sailed over, all the mountains have been explored, described, their height measured, and not even the smallest corner of the earth has been left that has not been most thoroughly observed: except for scarcely a small part near the Antarctic pole, scarcely five degrees in longitude, and even that not believed to be absolutely inaccessible, but thus far inaccessible because of subterranean fires bursting forth. In that region, whether men dwell there may also rightly be doubted, though perhaps because of the severity of the climate, if any are there, they must be very rude and uncultivated, as has been found among neighboring peoples, and as also among those near the northern pole, among those of whom we are speaking, the Aniæci; where, because of the obliquity of the sun and the excessive cold, everything is rigid and frozen, the sea is congealed with perpetual ice, the earth produces no sprout, and so forth; so that it is plainly incredible that the Paradise of delights, which the holy page and the Fathers describe as so pleasant, so flourishing, and overflowing with every kind of fruit, could naturally have existed, or could have existed, in the very cold zone, beneath so severe a sky. Added to this is the fact that wherever on this habitable earth the terrestrial Paradise is placed, it ought by now to have been overwhelmed and dispersed by the waters of the flood. For we read in Genesis 7 that the whole earth was inundated with waters; indeed, the waters stood fifteen cubits above the highest mountains. Nor is the evasion of some valid, who say that the waters did not penetrate there by a special privilege of God; or that, as Abulensis assumes, they surrounded it everywhere like the arch of a vault, in the same way as the Red Sea stood on both sides like a wall for the Israelites passing through. For the sacred page does not state this; rather, it says the contrary, since it says absolutely that the whole earth was covered by waters. Moreover, as Viegas correctly observes in Apocalypse chapter 11, section 5, number 6, if this place in the earth were of ge-

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MATHEMATICVM. 331 nerali alluutione cuasit immunis; vtique in eo potuisset Noe cum suis, & animantibus asseruari, nec opus habuisset ex Dei præscripto centum annos insumere in Arcæ fabricatio- ne: nec Deus id sanè præcepisset, si locum vllum in terra à Diluuo immunem conseruare decreuisset. Dicere autem cum eodem Viega, Genebrando, Oleastro, Eugubino, Iansenio, & aliis paucis quos ipse Viegas refert loco citato, Paradisum nempe terrestrem iam modo nul- lum extare, sed fuisse aquis diluuij dissipatum planeque destructum; præterquam quod est contrà communem sen- sum SS. Patrum, fereque omnium scholasticorum, vt ipse- met Viegas obseruat; immò & contrà fidem, vt opinatur D. Augustinus lib.8 in Genes. cap.3. dieens: Esse Paradisum illum fides Christiana non dubitat. Hoc etiam aduersariis dato, non euacuant difficultatem: Nam etiam si aquis diluuij Paradisus ille fuisset iam dissipatus; adhuc tamen locus exta- ret; montes, fontes, solique illius saltem non obseura ve- stigia; præsertim sons ille è medio Paradisi erumpens, at- que in quatuor illa superiùs enumerata flumina diuisus. Aquæ enim, arbores; ædificia, solique ad tempus vberta- tem potuerunt quidem dissipare, vt de cæteris orbis parti- bus fecisse, eompertum est, minimè autem montium situs, aquarum intimas scaturigines, fluminum alueos deflexisse: & quod his omnibus præstat, eælestem positionem, ac temperiem climatis præteruertere minimè valuerunt; vt non mox tellus aquis libera pristinam vbertatem, eæli ele- mentiam, aërisque iucunditatem reassumere debuisset, sicut reliquæ orbis partes, pro suæ quæque positionis gradu re- assumpsere, iugiterque recuperant in fluviorum alluutione, igniumque è sumnis montibus eruptione, ac devastatione, experientia id sæpiùs attestante. At enim neque in Palæsti- na, neque in armenia, neque in Taprobana insula, neque in America, neque vllibi tandem locorum vllum Paradisi vestigium fuit hactenus obseruatum, præsertim quatuor il- lorum fluminum vna, & eadem seaturigo, vt omnes scriptores tradunt: cum tamen modò iam tota tellus sit vn- dique peruagata, diligentissimè conquisita. Denique nec etiam, absolutè loquendo subsistere modo 8. potest quod alij ad hanc aquarum diluuij vniuersalem allu- tionem euadendam effinxerunt. Nempe Paradisum terre- strem in editissima terræ parte situ esse, adeò à communi hac terreni orbis planitie elatum, vt lunæ orbem pertingat eam- que ob causam, neque hodie permeari posse, neque olim aquas diluuij illùc pertingere potuisse. Cuius sententiæ

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generally by a universal overflowing rendered immune; and certainly in it Noah, with his own, and the living creatures, could have been preserved, and he would not have needed, by God’s command, to spend a hundred years in the building of the Ark: nor would God truly have commanded this, if He had decreed to preserve any place on earth immune from the Flood. But to say, with the same Viegas, Genebrard, Oleaster, Eugubinus, Jansenius, and a few others whom Viegas himself cites in the passage mentioned, that the earthly Paradise no longer exists at present, but was dispersed by the waters of the Flood and completely destroyed; besides the fact that this is contrary to the common sense of the Holy Fathers, and of almost all the scholastics, as Viegas himself observes; indeed, and contrary to the faith, as St. Augustine thinks, lib. 8 in Genesis, cap. 3, saying: “The Christian faith does not doubt that that Paradise exists.” Granted even this to the adversaries, they still do not remove the difficulty. For even if that Paradise had already been destroyed by the waters of the Flood, still the place would remain; the mountains, springs, and at least not obscure traces of that soil; especially that spring bursting forth from the middle of Paradise, and divided into the four rivers mentioned above. For waters indeed, trees, buildings, and the fertility of the soil for a time could certainly be dispersed, as is known to have happened in the other parts of the world, but by no means could they have altered the situation of the mountains, the hidden sources of waters, the channels of rivers; and, what is greater than all these, they were in no way able to overturn the heavenly position and climate of the region; so that as soon as the land was freed from the waters it ought to have reassumed its former fertility, the mildness of the sky, and the pleasantness of the air, just as the remaining parts of the world have reassumed, each according to the degree of its own position, and are continually recovering in the overflowing of rivers and the eruption and devastation of fires from the highest mountains, experience testifying to this very often. But in Palestine, or in Armenia, or in the island of Taprobana, or in America, or anywhere at all, no trace of Paradise has until now been observed, especially no one and the same source of those four rivers, as all writers relate; though now the whole earth has been traversed everywhere and most diligently searched. Finally, nor can even, speaking absolutely, what others have contrived to escape this universal overflow of the waters of the Flood now stand. Namely, that the earthly Paradise is situated in the highest part of the earth, raised so far above this common level of the terrestrial globe that it reaches the orbit of the moon, and for that reason can neither now be traversed, nor in former times could the waters of the Flood have reached it. Of this opinion

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LEXICON author est Beda in explanat. cap. 2. Genes. quem sequuti sunt strabo, Isidorus Rabbanus, Magister, Alensis, Caiet. & alij, quos refert Maluenda cap. 11. Hoc, inquam, nequit subsistere: tum quia id planè officeret terræ globositati, & figuræ sphæricæ, quam Mathematici omnes mille obseruationibus adacti admittere compulsi sunt: & licet montium, & vallium inæqualitates huic globositati aliquatenus videantur obstare; tamen ob terreni orbis amplitudinem, vt aliàs dictum est, hæc perinde se habent, ac in aurantij pomo tuberculi: quod de tam sublimi monte, qui vsque ad Lunæ orbem pertingeret autumari nequaquam posset. Tum quia si vllibi terrarum daretur tam altus mons, sanè foret omnibus notus, ac celebris propter summam altitudinem, solis radios exorientis diutissimè impediret, facileque posset & oculis cerni, & pedibus inuestigari: cum tamen hoc vnum memoria proditum sit, solum Olympum esse cæteris omnibus altiorem, quippe qui, seù verè, seù hyperbolicè dieitur nubes ipsas excedere. D Thomas, id alia ratione confutat. Quia inquit, ea Regio neque commoda esset habitationi hominum, neque salubritati. Verum ea ratio non conuincit: quia possent ibi homines affuescere, fierique aër ille tenuissimus iugiter, & ab incunabilis habitantibus oppido opportunus, atque connaturalis, eo planè modo, quo Lusitanis primo ad Indias orientales appulis aër ille longè diuersus euadebat incongruus; itavt ob climatis nouitatem mox extinguuerentur: at postmodum eò destinatis adolescentulis, qui paulatim aëri affuescerent factus tandem sui connaturalis, & proprius. Sic igitur diei posset de hac editissima regione, quæ ad Lunæ orbem pertingeret. Sed, vt diximus, obstat experientia, quod neutiquam talis regio comperta sit, nunquam talis mons oculis tentus, qui vertice suo aliquando Lunam attingeret, aut eius cursum impediret, faciemve saltem seù sui corporis densitate opposita, seù vmbrae suæ proiectione aliquatenus obuelaret: Cum tamen ad nostra tempora vniuersus penè Orbis sit penitissimè inuestigatus, cælestium corporum affectiones, Lunæque, vel minimæ quæuis defectiones exquisitissimè obseruatæ. 9. Constituto itaque dari verè Paradisum terrestrem, arque etiam nùm extare in rerum natura; ibique asseruari sanctos illos Heroas Henoch, & Eliam, (& vt aliqui volunt etiam S. Ioannem Euangelistam) vbi, loco depositi sistant, quoadvsque finis Mundi aduenerit, quando ex Dei ordinatione inde huc remeare debent, & finem suum prædicatio-

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LEXICON author is Beda in his explanation of chapter 2 of Genesis, whom followed Strabo, Isidore, Rabbanus, Master, Alensis, Caietan, and others, as Maluenda relates in chapter 11. This, I say, cannot stand: first, because it would plainly be contrary to the roundness of the earth, and the spherical figure which all the Mathematicians, driven by a thousand observations, have been compelled to admit: and although the inequalities of mountains and valleys may seem in some measure to hinder this roundness; yet, on account of the vastness of the terrestrial globe, as has elsewhere been said, these are to be reckoned in the same way as the little knobs on an orange; which could by no means be supposed of so lofty a mountain as one that should reach as far as the orb of the Moon. Then because if anywhere on earth there were given so high a mountain, it would surely be known to all and celebrated on account of its immense height; it would for a very long time hinder the rays of the rising sun, and could easily be both seen by the eyes and traced by foot: whereas this alone has been handed down by memory, namely that Olympus alone is higher than all the rest, inasmuch as, whether truly or hyperbolically, it is said to surpass the clouds themselves. St. Thomas refutes this by another argument. Because, he says, that region would be neither convenient for human habitation nor for health. But that reason does not convince: because men there could become accustomed, and that very thin air could become continually, and from the cradle for those dwelling there, most suitable and natural, in the very same way as for the Portuguese, when first they came to the East Indies, that air, altogether different, became unsuitable; so that on account of the novelty of the climate they would soon be destroyed: but afterwards, for youths sent there, who gradually became accustomed to the air, it finally became their own natural and proper air. Thus therefore it could be said of this most lofty region, which would reach the orb of the Moon. But, as we have said, experience is against it, because no such region has been discovered, never has such a mountain been found by sight, which with its summit would at any time touch the Moon, or impede its course, or at least obscure its face, either by the density of its body set opposite, or by the projection of its shadow. Yet down to our times the whole nearly of the world has been most thoroughly explored, the conditions of the heavenly bodies, and of the Moon, and even the least eclipses whatsoever, have been most exactly observed. 9. Therefore, once it has been established that the earthly Paradise truly exists, and also whether it is to be found in the nature of things; and that those holy Heroes Enoch and Elijah are preserved there, (& as some will have it also St. John the Evangelist) where, in place of deposit, they remain, until the end of the world shall have come, when by God's ordinance they must return from there to here, and bring their preaching to an end-

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ne sunt, & martyrio completuri, vt omnes ferè SS. Pa- tres affirmant, atque ex scripturis sanctis euincitur. Et ex alia parre cum planè euidenter probatum sit nullibi terra- rum esse, sed nec consistere posse, quando is prorsus dici- tur inaccessibilis, & iam modò omnis tetrae angulus detectus est, & nusquam apparent vlla Paradisi vestigia: iam clarè videtur euinci, eum extrà rerrarum orbem constituendum, in regione quidem habitationi hominum congrua; verum naturali potentia impermeabili, atque vt scriptura refert, igne, vndique circumsepta. Id quod olim aliquibus durum videri potuisset, sed tamen ex tunc B. Ephrem Syro, Moysi Barcephæ, aliisque Patribus aliquatenùs innotuit, arque à Moyse ipso non obscurè litteris tradirum Sic enim loquitur lib. de Paradiso cap. 9. Illud insuper asserimus eam terram, in quæ est Paradisus, altiorem multò sublimioremque existio- re hac quam, nos colimus: id enim ità se habere, in dicio sunt quatuor illa grandia flumina, quæ orta in Paradisi terra, per hanc nostram ab illa diuersam feruntur. Nisi enim illa terra altior extaret, fieri non posset, vt illa flumina illinc præcipiti cursu sub mare magnum delata, tandem per hanc à nobis cultam regionem spargerentur, &c. & clariùs cap. 8. Cæterum statuimus, inquit, terram in qua Paradis sus existebat diuersam quidem esse ab hac nostra; verum non natura, ipsaque sui materia, sed raritate, & densitudine. Diuidamus ergò terram in duas maximas partes quarum al- tera Paradisi terra, altera extrà Paradisum vocetur: illa subtilis, sincera, pura: hac qua à nobis colitur crassa, ma- teriata, impura, confusa sit. Hæc Moses, tum ex sua, tum ex aliorum Patrum, præsertim Ephrem Syri senrentia, à qua licet B. Ephrem immunem facere conrendar Maluenda lib. de Paradiso cap. 9 eamque vti falsam, ineptamque de- rideat; non tamen quidquam solidi affert, quod saltem tunc temporis in tanta rerum notitia, & reiectis modò reli- quis aliorum opinationibus, hanc in sua probabilitate non linquat. Quod enim ait, hoc temdore clarissimis Hispano- rum navigationibus, toto orbis ambitu immenso sulcato, Oceano circumnavigato euidenti experientia manifestum sit, neque totam terram ab Oceano cingi, neque vltrà Oceanum aliam esse tellurem, nisi forsan iaceat in aëre. Id, inquam, nobis potiùs fauer dicentibus, nusquam in toto hoc terræ marisque ambitu inueniri Paradisum deliciarum. At enim ei vel nolenti è calamo excidir verus Paradisi locus. Nisi forsan, inquit, iaceat in aëre. Vere quidem dixisti, ad scopum, nesciens, collineasti: nempè in aëre iacet Para-

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they are, and are to be completed by martyrdom, as almost all the holy Fathers affirm, and as is proved from the sacred Scriptures. And on the other hand, since it has been very clearly proved that it is nowhere on the earth, but also cannot exist there, because it is said to be altogether inaccessible, and now every corner of the earth has been explored, and nowhere are any traces of Paradise seen: it now clearly seems to be proved that it must be placed outside the orbit of the earth, indeed in a region fit for the habitation of men; yet surrounded on all sides by a natural, impassable power, and, as Scripture relates, by fire. This might once have seemed harsh to some, but nevertheless from that time it became somewhat known to B. Ephrem the Syrian, Moses Barcepha, and other Fathers, and was plainly handed down in writing by Moses himself. For thus he speaks in book On Paradise, chapter 9: “We further affirm that the land in which Paradise is is much higher and more elevated than this one which we inhabit; for that it is so is shown by those four great rivers, which, having risen in the land of Paradise, are carried through our own land, which is different from it. For unless that land stood higher, it would not be possible that those rivers, rushing down from there, should be borne beneath the great sea, and at length be spread through the region inhabited by us,” etc. And more clearly in chapter 8: “Moreover, we state,” he says, “that the land in which Paradise existed is indeed different from this of ours; not however in nature, or in the matter itself, but in rarity and density. Let us therefore divide the earth into two great parts, of which one shall be called the land of Paradise, the other outside Paradise: that one subtle, pure, clean; this, which is inhabited by us, coarse, material, impure, confused.” These are Moses’ words, both from his own opinion and from that of other Fathers, especially Ephrem the Syrian, from which although Maluenda in book On Paradise, chapter 9, strives to free B. Ephrem, and derides it as false and foolish, nevertheless he brings forth nothing solid which would at least not leave this opinion in its probability, at a time when so much was known. For what he says, that in this age, with the most famous Spanish navigations, the entire circumference of the world traversed, the ocean sailed around, it is manifest by evident experience that the whole earth is not surrounded by Ocean, nor is there any other land beyond Ocean, unless perhaps it lies in the air. This, I say, rather favors us who say that nowhere in this whole expanse of land and sea is Paradise of delights to be found. But indeed from his pen there slipped, even against his will, the true place of Paradise. “Unless perhaps,” he says, “it lies in the air.” Truly you have spoken, unknowingly you have aimed at the mark: namely, Paradise lies in the air.

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LEXICON 356 radisus tertestris, hoc est in liquidissimo illo Lunaris regionis æthere, quod ipsissimum aerem, seu eiusdem substantiæ, licet purioris alibi satis aperte monstrauimus. Et vt iam, detecto velo, elariùs & fidentiùs loquar, in ipsa superficie Lunæ (quam Beatarum mentium sedem Veteres non omninò extra aleam, alteram terram Plato, Pythagoreique omnes apud Tullium, stobeamque dixere quamque habitabilem, arboribus consitam, vitæque hominum opportunam nedum ex versibbus, sed ex neothericis multi, variis obseruationibus edocti probabiliter astruunt) in ipsa inquam superficie lunaris globi Paradisus ille est constitutus; quam & olim primi parentes nostri incoluerunt, & nunc sancti illi secundi saluatoris aduentus prodromi diuinitùs translati, illi finem mundi expectantes, loco depositi detinentur. 10. Fateor, id nouum, singulare, & hactenus inauditum: at non per hoc temerarium, atque intolerabile dixeris; quia & id Antiquiores divissent, si eam rerum notitiam habuissent, quam nos longo vsu, experientiateste, nouis obseruationibus, & eorum qui nos præcesserunt, detectis, reuulsisque erroribus comparauimus. Equidem olim temporibus Augustini, Antipodas affirmare, non absimili ratione; vt alias dictum est, hæreticum habebatur. Verùm postea Orbis peragrarione, & ipsâ experientiâ, ita res firmata fuit, vt iam modò eosdem non admittere erroneum, ac ridiculum foret. Ita planè: olim Paradisum terrestrem extrà terreni Orbis ambitum sistere, error intolerabilis, ac censurâ dignus meritò habebatur, præsertim eum nomen ipsum oppositum videatur euincere: at modò partâ tanta rerum noririâ, Lunæ facie Telescopio penitissimè obseruata, veterum dictis expensis, locis inuestigatis, Paradisum in Lunæ superficie collocare, ratio ipsa compellit. Siquidem, vt dixi, nouis obseruationibus compertum est Lunæ globum esse alteram veluti terram, Montibus, vallibus, syluis, arque aliis id genus præditam, adeò vt eam terram cælestem; ac terram hanc nostram Lunam terrestrem, cælesti lumine afflatus appellarit Diuinus Plato: vt David fabritius apud Argolum: nec nostris temporibus absuerunt, qui ausi sint affirmare, Lunam esse habitatoribus culram, se juc inibi homines & iumenra discurrere Telescopio obseruasse, vt nos in V. Luna litteris consignauimus, (quod tamen nimis audenter, minùs verè dictum existimauerim, fideique prorsus contrarium, cum exinde planè deduceretur, homines esse non à primo homine naturali propagine deriuetos, proindeque

Transcription: Translated (English)

LEXICON 356 radisus tertestris, that is, in that very liquid ether of the lunar region, which we have shown quite plainly to be the same air, or of the same substance, though purer there. And now, with the veil removed, I speak more clearly and confidently: on the very surface of the Moon (which the Ancients did not think altogether outside the bounds of possibility as the seat of blessed minds, the second earth, as Plato and all the Pythagoreans call it in Tully and Stobaeus, and which they and others plausibly maintain to be habitable, planted with trees, and suited to human life, proving this not only from verses, but from later writers and from various observations) — on the very surface, I say, of the lunar globe that Paradise is situated; which our first parents once inhabited, and now those holy forerunners of the second coming of the Savior, translated by divine power, are kept there in the place appointed for them, awaiting the end of the world. 10. I confess, this is new, unusual, and until now unheard of: but for that reason do not call it rash or intolerable; because the Ancients too would have divided on it, if they had had that knowledge of things which we have acquired by long use, the witness of experience, new observations, and by discoveries and the removal of errors made by those who went before us. Indeed, in the time of Augustine, to affirm Antipodes, on no very different grounds, as has elsewhere been said, was considered heretical. But afterwards, by travel around the globe, and by experience itself, the matter was so firmly established that nowadays not to admit the same would be erroneous and ridiculous. So too, certainly: formerly, to place the earthly Paradise outside the bounds of the terrestrial world was rightly thought an intolerable error and worthy of censure, especially since the very name itself seems to prove the contrary. But now, with so much knowledge of things acquired, the face of the Moon most carefully observed with a telescope, the sayings of the ancients weighed, the places investigated, reason itself compels us to place Paradise on the surface of the Moon. For, as I said, it has been discovered by new observations that the globe of the Moon is as it were another earth, endowed with mountains, valleys, forests, and other such things, so that the Divine Plato called it a heavenly earth; and this earth of ours a lunar earth, inspired by heavenly light, as David Fabrizius says with Argolus: nor have there been lacking in our own times those who have dared to affirm that the Moon is inhabited, and who claim to have observed with a telescope that men and animals move about there, as we recorded in the fifth book of the Lunar Letters (though I should judge that to have been said too boldly and not very truly, and altogether contrary to the faith, since from it it would plainly follow that men are not derived by natural propagation from the first man, and therefore...

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MATHEMATICVM. 317. deque non à Christo redemptos.) At verò locum illum esse habitationi hominum congruum, ibique tantùm vitam suam agere sanctos illos Hæroas miraculosè illuc translatos, non ità incredibile est, non multum à plurimorum Patrum dictis aberrans, nec demùm Fidei dogmatibus repugnans, Consonant sacræ Paginæ attestantes Eliam sublimè elatum, & curru igneo raptum in cælum, non vtique Empyreum, neque in aëra, vt constat, sed in Paradisum voluptatis, vt omnes Patres affirmant, in Cælo, hoc est in Lunæ globo situm. Et de Henoch dicitur Gen. 5. quod tulit eum Deus, & amplius non apparuit; translatus vtique in Paradisum: vti Ecclesiast. 44. apertè dicitur. Consonant SS. Patres id, etsi non clarè affirmantes, tamen aliqualiter innuentes, atque ad metam propè collineantes. Etenim Iustinus martyr in respons. ad orthodoxor. quæst. pluribus in locis præsertim quæst. 75. 76. & 85. clarè docet, Paradisum illum etiamnùm extare, & permansurum vsque ad diem Iudicij, in'eoque loco versari Henoch, & Eliam, & D. Ioannem Euangelistam. Ambrosius lib. de Paradiso, eum testatur in terra non esse, sed in tertio Cælo. Irenæus lib. 5. aduersus Hareses, addit, hunc Paradisum esse illum, ad quem raptus est Paulus; eiusdemque sententiæ suffragatores laudat Asiæ Presbyteros Apostolorum discipulos. Cæterùm Paradisum ab hacterra non quidem discontinuum, ac disiunctum, sed ex ipsa insurgere, atque ad orbem vsque Lunæ pertingere Rupertus Abbas lib. 1. de Trin. cap. 37. Damasc. lib. 2. de fide cap. 11. Basil. Orat. de Paradiso, Glossa in cap. 14. Gen. aliique Patres, quos suprà retulimus, docuerere: quibus indubitanter subscribit etiam Augustinus ad Orsium scribens in hæc verba. Paradisus in Oriente situs est, interiecto Oceano, & à nostro Orbe longe remotus in altissimo loco constitutus, vertingens vsque ad lunarem circulum: unde illuc aqua diluuij minimè peruenisse dicuntur. Quin & eiusdem sententiæ primus author fuisse dicitur Thomas Apostolus, vt proinde eam ob causam ei contradicere non audent Albertus Magnus 2 part. Summa Theolog. tr. 13. q. 29. ac Dionys. Carthus. in 2. sentent. dist. 17. quæst. 5. qui de hac sententia, hæc reuerenter habent. Hoc tamen dico sine praiulicio sententia melioris; quoniam in quibusdam libris antiquissimis inuenitur, quod gloriosus Thomas Apostolus fuit illius sententia author, quæ Beda & strabo in ascribitur, quod scilicet Paradisus sua altitudine tendat vsque ad sphæram Luna. Quis igitur damnare audebit sententiam, quam tantus Apostolus primus docuit, quamque experimenta Z

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MATHEMATICVM. 317. and not redeemed by Christ.) But that that place is suitable for the dwelling of men, and that the holy heroes, miraculously transferred there, live their life only there, is not so incredible, nor does it depart much from the sayings of the majority of the Fathers, nor is it finally contrary to the dogmas of the Faith. The sacred pages agree, attesting that Elijah was carried aloft and borne away in a chariot of fire into heaven, not indeed into the Empyrean, nor into the air, as is clear, but into the Paradise of delight, as all the Fathers affirm, in Heaven, that is, situated in the globe of the Moon. And of Enoch it is said, Gen. 5, that God took him, and he appeared no more; assuredly transferred into Paradise, as is plainly said in Ecclesiasticus 44. The holy Fathers agree with this, though not clearly affirming it, nevertheless hinting at it somewhat and drawing close to the goal. For Justin the Martyr, in his response to the questions of the orthodox, in many places, especially questions 75, 76, and 85, clearly teaches that that Paradise even now exists, and will remain until the day of Judgment, and that in that place dwell Enoch, and Elijah, and St. John the Evangelist. Ambrose, in book On Paradise, testifies that it is not on earth, but in the third Heaven. Irenaeus, book 5, Against Heresies, adds that this Paradise is the one to which Paul was caught up; and he praises the Presbyters of Asia, disciples of the Apostles, as supporters of the same opinion. Moreover, that Paradise is not indeed discontinuous from this earth, nor separated from it, but rises from it and extends as far as the orbit of the Moon Rupert the Abbot teaches, book 1, On the Trinity, ch. 37; Damascene, book 2, On the Faith, ch. 11; Basil, Oration On Paradise; the Gloss on Gen. ch. 14; and other Fathers, whom we cited above: to whom Augustine also undoubtedly subscribes, writing to Orosius in these words: Paradise is situated in the East, with the Ocean intervening, and far removed from our world, placed in the highest place, extending up to the lunar circle; whence it is said that the waters of the Flood by no means reached there. Moreover, Thomas the Apostle himself is said to have been the first author of this same opinion, so that for that reason Albert the Great, 2nd part of the Summa Theologiae, tract. 13, q. 29, and Dionysius the Carthusian, on the 2nd Sentences, dist. 17, q. 5, do not dare to contradict it, who concerning this opinion speak thus respectfully: Yet this I say without prejudice to a better opinion; for in certain very ancient books it is found that the glorious Apostle Thomas was the author of that opinion, which is attributed to Bede and Strabo, namely that Paradise in its height extends up to the sphere of the Moon. Who then will dare to condemn an opinion which so great an Apostle first taught, and which experiments Z

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358 LEXICON multa, plurimæ coniecturæ, SS. Parrum non interrupta series probabilissimam faciunt? Porrò è re non multum esse videtur, si locus ille, aut terræ coniunctus, vt isti volunt, aut ab eiusdem planitie segregarus, atque in ipsa Lunæ superficie constituatur, vt nos dicimus, modo in eodem situ, altitudine, ac distan[n]ia astruatur. Accedit; quod Paradisus deliciarum nusquam in Sacris paginis inuenitur in hac nostra terrâ plantatus; quemadmodum obseruauit etiam Franciscus Georgius tom. 1. probl. 31. Et si demùm Terrestris nomen promeruit, id est quia cum reuerà Luna sit arboribus consua, Monribus, & Vallibus formata, vt cuique Telescopio obseruare licet, perinde est, vti diximus, ac Terra quædam Cælestis. 11. Quod aurem in Scripturis Sanctis dicatur è medi Paradisi fons crumpere, qui postea diuidatur in quauor illa flumina, Tygrim & Euphratem, Phison, & Gehon (quos duos postremos, vt suprà annoraui, communiter Interpretes pro Gange, & Nilo accipiunt) id vel non ad litteram accipiendum, prout suprà cum Vgone meminimus, vel de Oceano, cum Damasceno: vel sanè quod à Luna, quæ humorum, & aquarum mater est, originem & incrementa hæc præsertim celebriora Orbis flumina sumunt; vi & Oceanus ipse, qui ad Lunæ motum, & normam minuitur, & augerur. Idque eò maximè dixerim, quod non minus ægrè de aliquo fonte in terrâ constituro, è quo æquè omnes isti amnes originem trahant, interpretari poest; vt fusè suprà probauimus. 12. Denique nil magis nostram sententiam confirmare potest, quam romphæa illa flammea, & versatilis, quam scriptura referr circa Paradisum constitutam ad custodiendam viam ligni Viræ: hoc est, murus igneus, & versatilis, (vt explicant D. Thomas, Hugo Victorinus, Rupertus Abbas, Tostatus, & alij.) Paradisum vniuersum ambiens, & circumuallans: quod licet aliqui explicare nitantur de Zona torrida, asserenies, Paradisum istum esse in ea parte australi, quæ extenditur vltrà tropicum Capricorni, vt suprà dictum est, & saris abundè reiectum: tamen minus ægrè, immò longè conuenientius explicari poest cum Vgone Carbonello in Paradoxis Quadragesimal. Sabbat. post Dom. 1. Quadragesim. de sphæra ignis inter nos, & Lunarem circulum constituta. Is enim, poët relatas multorum opiniones de vero situ Paradisi terrestris, concludit, eum esse circà orbem Lunæ, ac sphæra ignis, quæ nomine flammei gladij venit, vallari. En ipsius verba. Paradisus, in-

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358 LEXICON many arguments, and the unbroken series of the holy Fathers make it most probable? Moreover, it seems not very important whether that place is joined to the earth, as those men wish, or separated from its surface and set upon the very surface of the Moon, as we say, so long as it is shown to be in the same position, altitude, and distance. It is also the case that the Paradise of delights is nowhere found in the Sacred pages planted in this our earth, as Francis Georgius also observed, vol. 1, probl. 31. And if in the end it has deserved the name “terrestrial,” that is because, since the Moon is truly furnished with trees, mountains, and valleys, as anyone may observe with a telescope, it is all the same, as we have said, as a certain heavenly earth. 11. And when in the Holy Scriptures it is said that a spring bursts forth from the middle of Paradise, which is afterward divided into those four rivers, the Tigris and Euphrates, the Pison and Gihon (the last two of which, as I noted above, interpreters commonly take to be the Ganges and the Nile), this either is not to be taken literally, as above we remembered with Hugo, or it refers to the Ocean, with Damascenus; or indeed because from the Moon, which is the mother of moisture and waters, these origins and increases of the world’s most famous rivers are derived; and likewise the Ocean itself, which according to the Moon’s motion and rule is diminished and increased. And I would say this especially because it is no less difficult to interpret it of some spring set on earth, from which all those rivers should equally draw their origin, as we have shown at length above. 12. Finally, nothing can more strongly confirm our view than that fiery and revolving sword which Scripture says was placed around Paradise to guard the way of the tree of life: that is, a wall of fire and revolving flame (as St. Thomas, Hugh of St. Victor, Abbot Rupert, Tostatus, and others explain), surrounding and encircling the whole of Paradise. Although some try to explain this as referring to the Torrid Zone, asserting that this Paradise is in that southern part which extends beyond the Tropic of Capricorn, as was said above, and sufficiently refuted, nevertheless it is far easier, indeed far more fitting, to explain it with Hugo Carbonellus in Paradoxes of Lent, Saturday after the First Sunday of Lent, concerning the sphere of fire set between us and the lunar circle. For he, after citing the opinions of many about the true location of the earthly Paradise, concludes that it is encompassed by the orb of the Moon and the sphere of fire, which is called by the name of the flaming sword. Here are his words. Paradise, in-

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MATHEMATICVM. 359 quit, terrestris ascendit vsque ad globum Lunarem, vnde aqua diluuij eluc minimè peruenerunt: ex quo patet, quod eras altior media regione aëris, & nullaeras nox in illo Pa- radiso. Sed quaritur, cur à sphæra ignis non consumebatur attingens concauum Luna? Respondetur, quod priuilegio spe- ciali fuit locus isto conditus; vnde circumquæque erat sphæra ignis, non tamen intrans eum, dono Dei: & hoc innuitur Gen 2. vbi gladius igneus, & versatilis sphæra ignis intelli- genda est. Hucusque prædictus auctor: & quidem valdè ad rem, nam non nisi de sphæra ignis verificari magis propriè possunt quæ de flammea illa romphæa à Scripturis, & Pa- tribus dicuntur. Benè autem versatilis dicitur quia, vt ali- bi dictum est, & ipsa cum cæteris sphæris, ac regione aëris pro sua quæque à primo motore distantia, alia citiùs alia lentius circà terrarum orbem motu vniuersitatis rotatur. Constat igitur in hac celeberrima, ac difficili admodum quæstione non esse adeò intolerabile, nec rationi, aut Sacris Saginis repugnans, affirmare Paradisum Terrestrem, in quo primi parentes fuerunt, & nunc temporis vitam suam degunt Henoch, & Elias esse in Lunari globo situm, romphæa ignea, hoc est sphæra ignis vndique circum- feptum. Cæterùm hæc disputandi gratia dicta sint, non vt noui quicquam hactenùs inauditum è meo capite audeam affir- mare. Cùm aliàs Quæstio hæc ex earum genere sit, quas Augustinus lib. 2. contrà Pelagium, & Celestium cap. 23. præter fidem esse ostendit. In quibus, inquit, salua fide Christianismus, aut ignoratur quid verum sit, & senten- tia definitiua suspenditur, aut aliter, quam est, humanâ, & infirma suspicione coniicitur. Veluticum quaritur QV A- LIS, VEL VBI SIT PARADISVS, vbi con- stituit Deus hominem quem formauerat ex puluere, cum tamen ESSE ILLVM PARADISVM, Fides Christianæ nou dubites. Vel cùm quaritur, vbi sint nunc Elias, & He- noch, an ibi, an alicubi; quos tamen non dubitamus in qui- bus nati sunt corporibus, viuere, &c. & post pauca. Quis enim non sentias, subdit, in his, atque huiusmodi variis, & innumerabilibus quæstionibus, siue ad obscurissima opera Dei, siue ad Scripturarum abditissimas latebras pertinentibus, quas certo aliquo genere complecti, ac definire difficile est, & multa ignorari, salua Christiana fide, & alicubi errari, si- ne aliquo heretico dogmatis crimine? Hæc Augustinus. Cui consonat Theodorus quæst. 45. in Genes. cap. 23 Cyprianus Lib. de montibus Sina, & Sion, & alij vltrò affirmantes, Z ij

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MATHEMATICVM. 359 which, having ascended from the terrestrial world up to the lunar globe, the waters of the flood did not reach at all: from which it is clear that it was higher than the middle region of the air, and there was no night in that Paradise. But it is asked, why was he not consumed by the sphere of fire when he reached the hollow of the Moon? It is answered that, by a special privilege, that place was established in this condition; whence on every side there was the sphere of fire, yet it did not enter it, by the gift of God: and this is intimated Gen. 2, where the fiery sword, and the revolving sphere of fire, are to be understood. Thus far the aforesaid author; and indeed very much to the point, for only of the sphere of fire can more properly be verified the things which are said in the Scriptures and by the Fathers about that flaming rhomphaea. It is rightly called revolving, because, as has been said elsewhere, it also, with the other spheres and the region of the air, according to each one’s distance from the first mover, some more quickly, others more slowly, is rotated by the motion of the universe around the orb of the earth. It is therefore established in this most celebrated, and very difficult question, that it is not so intolerable, nor contrary to reason or Holy Scripture, to affirm that the Earthly Paradise, in which our first parents were, and in which now Enoch and Elijah pass their life, is situated in the lunar globe, surrounded on all sides by the fiery rhomphaea, that is, the sphere of fire. Moreover, let these things be said for the sake of argument, not that I should dare to affirm anything new or hitherto unheard-of from my own head. Since otherwise this question is of that kind which Augustine, book 2 against Pelagius and Celestius, chapter 23, shows to be beyond the faith. In such matters, he says, while Christian faith is preserved, either one does not know what is true, and a definitive judgment is suspended, or one conjectures otherwise than it is, by human and weak suspicion. As when it is asked what kind of place or where Paradise is, where God placed the man whom he had formed from dust, when nevertheless the fact that that Paradise exists you do not doubt from the Christian faith. Or when it is asked where Elijah and Enoch are now, whether there or somewhere else; yet we do not doubt that they live in the bodies in which they were born, etc. And after a few lines. For who, he adds, would not think that in these and similar various and countless questions, whether they pertain to the most obscure works of God or to the most hidden recesses of the Scriptures, which it is difficult to gather into any certain class and define, many things may be unknown, while the Christian faith remains safe, and one may err in some point, without any crime of heretical doctrine? These are Augustine’s words. To which Theodore agrees, question 45 in Genesis chapter 23, Cyprian in the book On the Mountains of Sinai and Zion, and others freely affirming, Z ij

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i69 LEXICON hæc, & similia Naturæ arcana per scrutari, de iisque in al- terutram partem disputare, ac noui aliquid in medium fer- re, salua side, liberum cuique esse, cum ea ad fidem mi- nimè pertineant. Quod si demùm nostra hæc opinatio ali- quibus displiceat, velintque omnino Paradisum terrestrem in terra constituendum, locum inueniant, & subscribam. Certè ex his, quæ hactenus diximus, nullus aptior, & conuenientior videri poterir, quam terra illa in australi orbis parte ob ignem circumambientem hactenus inaccessa, quam idcircò appellant la Terra del fuego. Et hæc satis di- cta sint de Paradiso terrestri, eâ parte, qua eius sirum con- siderare, peritum Astronomum Geographumque con- cernit. 14. PARALLAGE, teste Va-la, diciùr apust Astronomos cer- tus stellarum ad inuicem positus, & constitutio, iravt in figura efforment triangulum Isoceles, hoc est vt sint ita in- ter se constitutæ duæ stellæ ad inuicem, vt respectu ad ali- quod punctum, vel aliam terriam stellam, si ducerentur li- neæ efformantes triangulum, duæ ex illis essent æquales, ad inuicem, tertia verò minor. Talis est constitutio Arcturi cum spica Virginis, & Cauda Leonis efformantes perfe- ctum triangulum Isoceles, facta basi in Arcturo, & Cau- da, Angulo verò in Spica: talis est etiam forma Trianguli sideris dicti, Delteton. Hanc ipsam Ptolemæus in Lumina- ribus cum inforrunis vocat figuram æquicuriam: de quâ fusè egimus suo loco 15. PARALLAXIS est deuiatio visus facta ex distantia termini lineæ visualis proiectæ à superficie terræ ad sidus, vel aliud Phænomenon in Cælo apparés à termino alterius lineæ pro- iectæ à centro telluris ad corpus eiusdem sideris in loco vbi reuerà consistit. Pro cuius rei intelligentiæ sciendum est, quod omnia loca superiora à telluris centro moderationem sumant: cu enim nos conspiciamus sidera à superficie terræ, quæ distat à centro milliar. ferè 3033. quanta est ipsius ter- ræ semidiameter, consequenrer necesse est vt diuersus sit locus designatus per lineam rectam à centro telluris, ac ab eiusdem superficie, & in diuerso etiam situ consistere vi- deatur stella à superficie terræ prospecta, ac si ab eius cen- tro conspireremr, vt ex opticis perspicuum est. Hanc au- tem aspectus diuersitatem dicimus Parallaxim: quæ maior aut minor est, pro maiore vel minore propinquitate, quam habersidus ad terram. Porrò id locum habet in radio obli- què immisso, seu quando stella cum non sit verticalis pro- ijcit radium ex aduerso, atque à latere ad centrum, & su-

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i69 LEXICON these and similar secrets of Nature to investigate, and to debate about them on either side, and to bring something new into the middle, without prejudice to the faith, is free for everyone, since they do not concern faith at all. But if at last some dislike this opinion of ours, and wish the earthly Paradise to be placed altogether on the earth, let them find a location, and I shall subscribe to it. Certainly from what we have said so far, no place could seem more suitable and fitting than that land in the southern part of the world, hitherto inaccessible because of the surrounding fire, which for that reason they call la Terra del fuego . And enough has been said about the earthly Paradise, in so far as it concerns the skilled astronomer and geographer to consider its location. 14. PARALLAGE, according to Valla, is said by astronomers to be a certain arrangement and position of the stars among themselves, and a configuration whereby they form an isosceles triangle; that is, the two stars are so positioned relative to each other, with respect to some point or another star, that if lines were drawn forming a triangle, two of them would be equal to each other, and the third smaller. Such is the arrangement of Arcturus with the Spica of Virgo and the Tail of Leo, forming a perfect isosceles triangle, with the base made in Arcturus and the Tail, but the angle in Spica; such also is the form of the star-shaped triangle called Delteton. Ptolemy himself calls this same figure, in the Luminaries with the infortunates, an equilateral figure: of which we have spoken at length in its proper place. 15. PARALLAXIS is a deviation of vision caused by the distance of the end of the visual line projected from the surface of the earth to a star, or to some other phenomenon appearing in the sky, from the end of another line projected from the center of the earth to the body of the same star in the place where it really lies. For understanding this matter, it should be known that all higher places take their measure from the center of the earth; since we observe the stars from the surface of the earth, which is about 3033 miles distant from the center, as much as the semidiameter of the earth itself, it is consequently necessary that the place marked out by a straight line from the center of the earth, and from its surface, should be different, and that the star seen from the surface of the earth should appear to stand in a different position than if we were looking from its center, as is clear from optics. We call this difference of aspect Parallax, which is greater or smaller according to the greater or lesser nearness which the star has to the earth. Moreover, this applies in an obliquely admitted ray, or when the star, since it is not vertical, sends forth the ray from opposite and lateral points toward the center, and from its

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MATHEMATHICVM. 361 perficiem terræ: Nam verticalis cum proiiciat radium rectâ ad superficiem terræ, necessariò cum is transeat per superficiem, quæ vertici subest, nullam patitur parallaxim: ideoque quo magis à vertice elongantur, & ad horizontem appropinquant eo maiorem habent parallaxim, & econtra cum ex horizonte ad Verticem accedunt, semper minuitur parallaxis pro ratione situum. Patiuntur parallaxim Cometæ, seù nova phænomena in 16. aërea regione producta, maximam: Post Luna, Planetæ & reliqua Phænomena in ea æthereæ regionis parte genita, in cuius distantia telluris corpus aliquam retinet proportionem sensibilem: nam vbi terra se habet ad instar puncti insensibilis, vt in sphæra fixarum, nulla omninò est parallaxis. Et ideo noua stella, quæ apparuit in Sede Cassiopææ anno 1572. & quæ in Cygno anno 1600. creditæ fuerunt non in regione elementari, neque in lunari, aut alterius planeræ productæ, sed in ipso cælo & regione fixarum, quia profectò vt reliquæ stellæ fixæ nullam recipiebant parallaxim. Regio Saturni, & Iouis, eorumque corpora nullam habent sensibilem parallaxim; ferè enim coincidit locus designatus per Lineas rectas â centro telluris, atque à superficie: sic stellæ eorum comites à Galilæo nuper observatæ. Mars ex Tychonis observationibus, constitutus in Perigæo, vbi sit terræ proximior magis quam sol, habet parallaxim minutorum quatuor: in Apogæo ferè nullum. Sol siue in Apogæo, siue in Perigæo minut. fere trium: Venus, & Mercurius paruam: Luna, & quæ in eius regione generantur phænomena, experiuntur parallaxim vnius ferè gradus circa horizontem, quæ, vt dixi, proportionaliter semper minuitur pro maiori approximatione ad verticem. Et cum radius visualis intersecare necessario: debeat lineam rectam à centro telluris in corpus stellæ protensam, consequenter humilior apparebit, quam reuera sit, & exigat calculus Astronomicus. Parallaxis ope nouimus ordinem planetarum inter se, ac singulorum tum ad inuicem, tum à terra distantiam: noscimus tempus veræ coniunctionis, præcipuè verò Eclipsium verum momentum ab apparente discernimus: aliaque permulta, quæ apud auctores videri possunt, in quibus etiam extant Tabulæ parallaxium, tum planetarum, tum Cometarum in quacunque aëris regione apparentium. PARALLELI dicuntur circuli, seu lineæ æquè distantes ab inuicem, seu ab aliquo puncto. Potissimè vero accipiuntur pro circulis æquidistantibus ab æquarore, tam in Z iij

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MATHEMATHICVM. 361 the surface of the earth: for when a vertical line projects its ray straight to the surface of the earth, necessarily, since it passes through the surface which lies beneath the zenith, it suffers no parallax; and therefore the more they are removed from the zenith and approach the horizon, the greater parallax they have, and conversely, when they approach the zenith from the horizon, parallax is always diminished in proportion to their position. Comets, or new phenomena produced in the 16. aerial region, suffer the greatest parallax: after the Moon, the Planets and the other phenomena generated in that part of the ethereal region, in whose distance the body of the earth retains some sensible proportion: for where the earth is like an insensible point, as in the sphere of the fixed stars, there is absolutely no parallax. And therefore the new star which appeared in the seat of Cassiopeia in the year 1572, and that which in Cygnus in 1600, were believed not to have been produced in the elemental region, nor in the lunar region, nor in that of any other planet, but in heaven itself and in the region of the fixed stars, because indeed, like the other fixed stars, they received no parallax. The region of Saturn and Jupiter, and their bodies, have no sensible parallax; for the place indicated by straight lines from the center of the earth and from the surface almost coincides: thus the stars accompanying them, recently observed by Galileo. Mars, from Tycho’s observations, placed at perigee, where it is nearer the earth than the sun, has a parallax of four minutes; in apogee, almost none. The Sun, whether in apogee or in perigee, about three minutes; Venus and Mercury, a small one. The Moon, and the phenomena generated in its region, experience a parallax of almost one degree around the horizon, which, as I said, always decreases proportionally with greater approximation to the zenith. And since the visual ray must necessarily intersect the straight line extended from the center of the earth to the body of the star, consequently it appears lower than it really is, and this requires astronomical calculation. By means of parallax we know the order of the planets among themselves, and the distance of each both from one another and from the earth; we know the time of the true conjunction, and especially we distinguish the true moment of eclipses from the apparent one; and many other things, which may be seen in the authors, among which there are also tables of parallaxes, both of planets and of comets appearing in whatever region of the air. PARALLELS are called circles, or lines equally distant from one another, or from some point. But they are chiefly taken for circles equidistant from the equator, both in Z iij

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56. LEXICON superficie terræ quàm in regione ætherea consideratis: ita v[er]e qui habitant in eadem distantia ab æquatore versus eundem polum, dicantur esse in eodem parallelo: Quæ item sidera eandem habent declinationem & numero, & regione, eandemque ab æquatore distantiam, dicantur esse in eodem parallelo: quæ eandem quidem declinationem, sed non eandem distantiam ab æquatore, benè verò ab alterutro ex duobus tropicis dicantur esse in parallelis intuentibus, quæ nos communiter Antiscia vocitamus: Quæ tandem sunt in eadem distantia hinc inde ab æquatore, suntque profecto in eadem numero declinatione, sed regione diuersa, ea dicantur esse in Conrantisciis seu antisciis Imperamibus, & obedientibus, quoniam vnum necessariò debet esse in signis borealibus, alterum in australibus, quæ sanè ob situs humilitatem dicuntur borealibus obedire. Hinc iure Tius hoc familiaritatis genus inter astra contractum in æqualibus parallelis, non communi Antisciorum; Sed expressiore vocabulo Parallelorum declinationis, ad differeniam eorum, quæ in mundo fiunt (de quibus mox infræ) voluit appellare, & eos quidem qui ab eodem Tropico æquè distant, Parallelos primarios, qui verò ab æquatore hinc inde, secundarios, imperantes, aut obedientes. 58. Quoniam autem, vt diximus in Verbo Familiaritas, duplicem familiaritatem, ad rationem duplicis morus, contrahere possunt sidera, & in Zodiaco, in proportionalibus, scilicet, distantiis ab inuicem in partibus Zodiaci, & in Mundo, in proportionalibus distantiis à cardinibus mundi sumptis in partibus suorum arcuum; ideò duplex etiam genus Antisciorum, seu Parallelorum, & in Zodiaco, & in Mundo. Et sicut qui in Zodiaco computantur sunt æquidistantiæ à quatuor punctis cardinalibus Zodiaci, atque attendi debent in siderum declinatione eadem: ita & isti (quos cosinicos placuit appellare) computari debent in æquidistantia siderum à Cardinibus, Mundi sumpta in partibus proportionalibus suoru[m] arcu[m], ita vt sicut duo sidera, ex. gr. quorum alterum sit in gr. 30. Tauri, alterum in gr. 1. Leonis dicuntur se mutuò intueri, & esse in parallelis primariis seu Antisciis, quia sunt in eadem declinatione, & æquidistantia à Tropicis: ita etiam, si eadem sidera in situ Mundi tali modo disponantur, vt alterum sit in cuspide Vndecimæ Domus, alterum in cuspide Nonæ, vel vnum in Duo decima, alterum in octava, vel sanè in proportionalibus distantiis à Culmine; eadem ratione se dicantur intueri in Mundo, & esse in Parallelis, seu Antisciis, cosmicis, quia

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56. LEXICON surface of the earth, than when considered in the ethereal region: thus truly those who dwell at the same distance from the equator toward the same pole are said to be in the same parallel: likewise those stars which have the same declination, both in number and in region, and the same distance from the equator, are said to be in the same parallel: those which have the same declination indeed, but not the same distance from the equator, yet truly from either of the two tropics, are said to be in the parallels of the beholders, which we commonly call Antiscia: those at last which are at the same distance on this side and that from the equator, and are indeed in the same numerical declination, but in a different region, are said to be in Conrantiscia or antiscia of imperants and obedients, because one must necessarily be in the northern signs, the other in the southern; and the latter, indeed, by reason of the lowness of its position, is said to obey the northern. Hence Tius by right wished to call this kind of familiarity contracted among the stars in equal parallels, not by the common term of Antiscia, but by the more explicit term of parallels of declination, in distinction from those things which happen in the world (of which below shortly), and indeed to call those who are equally distant from the same Tropic primary Parallels, but those who are on this side and that from the equator secondary, imperants, or obedients. 58. But since, as we said in the word Familiarity, stars can contract a double familiarity, according to a double motion, both in the Zodiac, in proportional distances from one another in the parts of the Zodiac, and in the World, in proportional distances taken from the cardines of the world in the parts of their own arcs; therefore there is also a double kind of Antiscia, or Parallels, both in the Zodiac and in the World. And just as those computed in the Zodiac are equidistant from the four cardinal points of the Zodiac, and must be regarded in the same declination of the stars: so also these (whom it has pleased us to call cosinical) must be computed in the equidistance of the stars from the Cardines of the World, taken in the proportional parts of their arcs, so that just as two stars, for example, of which one is at 30° of Taurus, the other at 1° of Leo, are said to look upon one another, and to be in primary parallels or Antiscia, because they are in the same declination, and equidistant from the Tropics: so also, if the same stars in the situation of the World are disposed in such a way that one is in the cusp of the Eleventh House, the other in the cusp of the Ninth, or one in the Twelfth, the other in the Eighth, or indeed in proportional distances from the Midheaven; by the same reasoning they are said to look upon one another in the World, and to be in cosmic Parallels, or Antiscia, because

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MATHEMATICVM. 363 videlicet æqualiter distant à Cardinibus Mundi. Et si quidem ea distantia sit ab eodem cardine, & ambo sint suprà terram, dicantur esse in Parallelis primariis, & intuentibus; si verò æterum sit suprà, alterum infra; ita tamen, vt quam distantiam habet vnum à Culmine, eandem prorsus habeat alterum ab imo; ea dicantur esse in Parallelis secundariis, seu Contrarisciis Imperantibus, & obedientibus, (quod enim est in superiori hemisphærio imperat ei quod in inferiori cosmicis tamen ad differentiam eorum qui in Zodiaco attenduntur. Quod quidem familiaritatis genus eandem ferè habet poteniam, ac Antiscia communi calculo admissa, & in Zodiaco considerata: siquidem, vt benè aduertit Titus ingeniosissimus huius familiaritatis inuictor in suo Primo mobilium. 13, plures reperiuntur similitudines inter parallelos in Mundo, & parallelos, seu Antiscia in Zodiaco. Primò in verisque efficacia familiaritatis consistit in paritate, seu æquipollentia virtutis actiux: Secundò, sicut in Zodiaco exhibetur à duobus punctis antisciis eadem quantitas ascensionis signorum, vt exempli gratia, in pari differentia remporis ascendit primus gradus Piscium, & postremus Arietis, &c. ita similiter in Mundo exhibetur eadem quantitas Ascensionum, & Descensionum à duobus punctis æquè distantibus à Culmine: vt Domus Vndecima parem efficit Ascensionem Descensioni Domus Nonæ, proindeque & sidera in ipsis constituta; duodecima parem Octauæ, &c. Tertio, vt dictum est sicur Paralleli in Zodiaco sunt pares distantiæ à punctis Cardinalibus Zodiaci sumptæ in partibus æquatoris, ita paralleli in Mundo sunt pares distantiæ à punctis cardinalibus Mundi, meridiano videlicet & horizonte, sumptæ in partibus proportionalibus suorum arcuum Quarto sicut in Zodiaco exhibent pares temporales horas ita in mundo exhibent paretèporeles horas distantiaru à Cardinibus. Quintò paralleli in Zodiaco sunt æquales distatiæ à polis mundi: & paralleli in mundo æqualem seruât poli elevationem. Et si quis mentem diutius applicauerit, inueniet profectò plures similitudines & conueniemias inter vtrosque parallelos, vnde consequens etia est, vt similem habeant gradum actiuitatis. Quippe eorum efficacia in eo sira est, vt astra in iis reperta eandem habeant qualitatis intentionem, alterum quidem ad puncta cardinalia progrediendo, & qualitatem intendens; alterum vero recedendo, & qualitatem remittens, quod proportionaliter in parallelis quoque secundariis considerandum. Contingit etiam sæpè, vt licet duo astra non sint in radice 19. Z iiiij

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MATHEMATICUM. 363 namely, equally distant from the Cardinals of the World. And if indeed that distance be from the same cardinal point, and both be above the earth, they are said to be in primary Parallels, and in sight; but if one be above and the other below, yet in such a way that the distance which one has from the Midheaven, the other has exactly the same from the Imum Coeli; these are said to be in secondary Parallels, or in opposing governing and obeying Contrariscia, (for that which is in the upper hemisphere rules over that which is in the lower, though in cosmic matters, to distinguish them from those which are observed in the Zodiac. And indeed this kind of familiarity has almost the same power as Antiscia, admitted by common calculation, and considered in the Zodiac: since, as Titus, the most ingenious discoverer of this familiarity, well notes in his Primo mobilium, 13, there are found more similarities between parallels in the World and parallels, or Antiscia, in the Zodiac. First, in truth, the efficacy of this familiarity consists in parity, or equivalence of active force: second, just as in the Zodiac the same quantity of rising of the signs is shown by two antiscia points, as for example, at an equal difference of time there rises the first degree of Pisces and the last of Aries, etc., so likewise in the World the same quantity of Ascensions and Descensions is shown by two points equally distant from the Midheaven: thus the Eleventh House produces an equal Ascension to the Descension of the Ninth House, and therefore also the stars placed in them; the Twelfth, an equal one to the Eighth, and so on. Third, as has been said, just as the Parallels in the Zodiac are equal distances taken from the Cardinal points of the Zodiac in parts of the equator, so the parallels in the World are equal distances from the cardinal points of the World, namely the meridian and the horizon, taken in proportional parts of their arcs. Fourth, just as in the Zodiac they show equal temporal hours, so in the world they show equal temporal hours of distances from the Cardinals. Fifth, parallels in the Zodiac are equal distances from the poles of the world: and parallels in the world preserve an equal elevation of the poles. And if anyone should apply his mind more closely, he will certainly find many more similarities and agreements between the two kinds of parallels, whence it also follows that they have a similar degree of activity. For their efficacy lies in this, that the stars found in them have the same intention of quality, one indeed advancing toward the cardinal points and intensifying the quality; the other receding and diminishing the quality, which is likewise to be considered proportionally in secondary parallels. It also often happens that, although two stars are not in the radix 19. Z iiiij

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LEXICON in eadem distantia à cardinibus Mundi, eam tamen acqui- sant directione, & motu primi mobilis, quod duplici modo sieri concipi potest: altero, vt significaror existens immo- bilis in suo circulo positionis expectes, vt Promissor motu primi mobilis feratur ad situm æquè distanrem à cardini- bus Mundi, ac erat significaror in radice constitutus; & tunc emanat effectus huius directionis: altero, vt ambo motu primi mobilis rapiantur, tam Promissor, quam si- gnificator (ab vtroque enim imprimitur virtus in Primo mobili seù in gradibus Zodiaci in quibus tempore radicis reperiebantur) & tunc quando ambo motu primi mobilis sapti ponuntur in proportionali distantia hinc inde ad ali- quem cardinem, iunc intelligitur compleri directio, & emanat profecto idem, vel sanè consimilis effectus, ac in parallelis modo explicatis; & sicut illi Paralleli Cosmici simpliciter appellantur; ita isti ad differentiam illorum Pa- alleli Ascensionales iure appellari poterunt; quoniam am- bo tam significator, quam Promissor pariter supponuntur ascendere, & suum suum murando æquidistantiam istam à cardine acquirere. Quorum omnium dirigendi methodum docet Titus in Primo Mobili Canon: 35. PARALLELI etiam, vt supra tactum est, vocantur apud Geographos circuli in superficie terræ descripsi æquè distan- tes à circulo immediatè æquatori subiecto, de quibus supra in V. Climæ pertractauimus. Qui profecto infiniti concipi possunt: de facto tamen tot concipiuntur, quot satis sunt ad faciendam notabilem diei maximi varietatem. At- que hac ratione Antiqui cum Prolemao sentem climata constituebant, quorum singula tribus parallelis definie- bant, singulis parallelis singulos horæ æquinoctialis quadrantes assignando Quoniam vero experientia comper- tum est, non solum partem aliquam vnius, vel etiam cu- jussiber quadrantis habitabilem esse, sed totam ferè terræ molem; vbique enim Insulæ sunt, vel etiam terræ conti- nentes, quocunque versus nauigandi instituatur, nec vlla planè regio est tam calida, aut frigida, in qua degere non possint homines; quin immò vbique ferè terrarum tam ho- mines, quam bruta animania reperta sunt: idcircò Re- centiores multo plura Climata adeoque plures etiam paral- lelos numerant, quam Antiqui, totum sparium quod est ab æquatore ad polos in tot parallelos dividendes, quot horæ quadrantes accresionis diei maximæ ab locis æquareti sub- iectis ad ea quæ immediatè polo subsunt. Adeoque insi- stentes nihilominus Ptolemæi præceptis viginti-tria Clima-

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in the same distance from the cardinal points of the world, yet they acquire it by the direction and motion of the first movable, which can be conceived to happen in two ways: the first, when the significator, remaining immobile in its circle of position, is expected, by the motion of the first movable, to be carried to a place equally distant from the cardinal points of the world as the significator was when fixed in the radix; and then the effect of this direction emanates. The second, when both are carried by the motion of the first movable, both the Promissor and the significator (for from both is impressed the virtue in the first movable, or in the degrees of the Zodiac in which they were found at the time of the radix), and then, when both, snatched along by the motion of the first movable, are placed in proportional distance on either side from some cardinal point, then the direction is understood to be completed, and the same, or at least a very similar, effect certainly emanates as in the parallels explained above; and just as those are simply called Cosmic Parallels, so these, to distinguish them from the others, may rightly be called Ascensional Parallels; since both the significator and the Promissor are equally supposed to ascend and, by changing their position, acquire that equidistance from the cardinal point. Titus teaches the method of directing all of these in Primo Mobili, Canon 35. Parallels are also, as noted above, called by geographers circles described on the surface of the earth, equally distant from the circle immediately subject to the equator, concerning which we treated above in the V. Climes. These can certainly be conceived as infinite; in fact, however, as many are conceived as are sufficient to produce a notable variation in the length of the longest day. And for this reason the ancients, with Ptolemy, established so many climates, defining each by three parallels and assigning to each parallel a quadrant of the equinoctial hour. But since experience has shown that not only some part of one quadrant, or even of any quadrant whatsoever, is habitable, but almost the whole mass of the earth; for everywhere there are islands, or even continents, whichever way navigation is undertaken, and there is plainly no region so hot or so cold in which human beings cannot live; indeed, in almost every part of the world both men and brute animals have been found: therefore more recent writers count far more climates, and consequently also more parallels, than the ancients, dividing the whole space from the equator to the poles into as many parallels as there are quarter-hours by which the longest day increases from places subject to the equator to those which are immediately under the pole. Thus, nevertheless adhering to Ptolemy’s precepts, twenty-three climates...

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MATHEMATICVM. 361 ta constituunt, atque intrà 49. Parallelos includunt. Qua de re vide quæ diximus in Veibo Clima. PARALLELOGRAMMVM definitur ab Euclide lib. 1. propos. 21. 35. Est figura quadrilatera, cuius bina opposita latera sunt parallela, seu æquidistantia. Adeoque si duo parallelogramma super æquales bases, & in eisdem parallelis constituantur necessario æqualia debent esse: Si vero cum triangulo eandem basum habuerit Parallelogrammum, fueritque in eisdem parallelis, ipsum erit duplum illius trianguli, vt habet idem Euclides, propos. 41. Porrò omne Parallelogrammum est in quadruplici differentia. Primum quod perfectum quadratum dicitur, haberque omnes angulos rectos, & omnia latera inter se æqualia. Secundum, quod habet quidem omnes angulos rectos, verum non omnia latera æqualia, sed omnis angulis constat duobus latetibus inæqualibus, quorum vnum est longius altero; ita tamen, vt bina opposita latera æqualia inter se sint. Tertium, quod habet quidem omnia latera æqualia, sed anguli sunt inæquales, quorum duo necessariò acuti sunt, duo etiam inuicem oppositi, obtusi, quod à piscis nomine, cuius similiu-dinem refert, Rhombum appellauere. Quartum denique quod neque angulos rectos habet, neque omnia latera æqualia, sed est quadrato omnino opposium; itavt constet quatuor lateribus, quorum duo opposita sint reliquis longiora, atque efforment quatuor angulos, duos acutos inuicem opposuos, & duos obtusos item oppositos ex diametro: & hæc Rhomboides dicitur. Atque ad has quatuor species reduciuor omne parallelogrammum, & omnis figura quadrilatera; quæ aliquam proportionem, & regularitatem habeat. Cæterum aliæ figuræ quadrilateræ irregulares, quæ quidem infinitis modis variari possunt, sub generali Trapeziorum nomine veniunt: de quibus, vt de speciebus Parallelogrammi suo loco. 22. PARALLELOPEVRA sunt Parallelogrammorum, vt ita dicam abortiones, arque irregulares correspondentiæ angulorum, aut laterum, quibus constituuntur: Sunt enim in genere Trapeziorum, quia inæquales habent angulos, & inæqualia lateta, sed non omnia; seruant enim alicubi saltem aliquam regulariatiem, & parallelorum proportionem: Vnde minùs latè patent, quam Trapezia, quæ omnem figuram quous modo irregularem includunt. Possunt nihilominus, vt ista multiplicari, & diuersificari pænè in Infinitum. Qua de re vide Clauium in Euclidem. 23. PARALLELOGIPIDVM est figura solida sex planis quadri-

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MATHEMATICVM. 361 These are set up, and enclosed within 49 parallels. On this matter see what we said in the entry Clima . PARALLELOGRAM is defined by Euclid, book 1, proposition 21. 35. It is a quadrilateral figure, whose two opposite sides are parallel, or equidistant. Hence, if two parallelograms are constructed on equal bases and in the same parallels, they must necessarily be equal: but if a parallelogram has the same base as a triangle, and is in the same parallels, it will be double that triangle, as the same Euclid has in proposition 41. Moreover, every parallelogram is of four different kinds. The first, which is called a perfect square, has all its angles right, and all its sides equal to one another. The second has indeed all right angles, but not all equal sides; rather, every angle is made up of two unequal sides, of which one is longer than the other; yet in such a way that the two opposite sides are equal to each other. The third has indeed all its sides equal, but the angles are unequal, two of which are necessarily acute, and the other two, opposite one another, obtuse; from the name of a fish, whose likeness it resembles, it was called a rhombus. The fourth, finally, has neither right angles nor all equal sides, but is altogether opposite to the square, so that it consists of four sides, of which two opposite are longer than the others, and form four angles, two acute opposite one another, and two obtuse also opposite across the diagonal; and this is called a rhomboid. And to these four species is reduced every parallelogram, and every quadrilateral figure which has some proportion and regularity. Other irregular quadrilateral figures, which can indeed vary in infinite ways, come under the general name of trapezia: of which, as of the species of parallelogram, in its proper place. 22. PARALLELOPEVRA are, so to speak, the abortions of parallelograms, and irregular correspondences of angles or sides, by which they are constituted. For they belong to the genus of trapezia, because they have unequal angles and unequal sides, though not all; for they preserve somewhere at least some regularity and the proportion of parallels. Hence their scope is narrower than that of trapezia, which include every kind of irregular figure. Nevertheless, like these, they can be multiplied and diversified almost to infinity. On this matter see Clavius on Euclid. 23. PARALLELOGIPID is a solid figure with six quadr...

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LEXICON 366 lateris constans, quorum quodlibet æquale est, & paralle- lum opposito. Cuius ea conditio est, vt super æquales ba- ses constitutæ plures huiuscemodi figuræ, & in eadem altitudine, æquales etiam sint inter se. Differt à Parallelogrammo, quod hoc dicit vnum tantum planum quadrilaterum, constans quatuor tantum angulis: illud autem inuoluit plura plana, nempè sex in superficie, & consequenter octo angulos ex aduerso sibi inutem respondentes, ita- vt non vnam figuram superficialem, sed vnum corpus solidum omnis dimensionis capax præseferat: huiusmodi sunt taxilli, quibus in aluceolo luditur. Cæterum Parallelopipedum, habet omnes conditiones parallelogrammi, cum aliud non sit, quam multa parallelogramma in vnum conuenientia. Vnde etiam est, vt non nisi in quatuor differentias parallelogrammo etiam communis diuidi possit. Si enim continet sex parallelogramma æquilatera, & rectangula, correspondet quadrato in planis figuris, & dicitur Cubus, qualis est, vt modò dixi, taxillus. Si sex illa parallelogramma fuerint quidem rectangula, sed non omnia æquilatera sed duobus æqualibus, & minoribus existentibus, reliqua sint longiora, vocabitur parallelopipedum altera parte longius. Si fuerit quidem omni ex parte æquilaterum, sed non æqualibus angulis respondentibus, & omnibus rectis, cor- respondebit Rhombo. Si demum neque omnia parallelogramma æquilatera, neque omnes anguli recti erunt, quam- uis duo ex iis rectangula fuerint, & æquilatera; vel re- tangula tantum, vel æquilatera tantum; fuerint nihilo- minus verè parallelogramma; ita vt tam plana, seu latera, quam anguli ex aduerso æqualia sint, correspondet Rhomboidi. Porrò quodcumque parallelopipedum vocari etiam poterit Prisma; sed non omne Prisma, parallelopipedum: vt ex definitione Prismatis, quam infra trademus, constabit. 24. PARELIA sunt reflexiones solarium radiorum in nube rotida, sed benè compacta; quæ quasi speculum in se recipiat, & referat imaginem solis, ita vt quasi sol alter appareat, & ferè nescias quisnam sit verus, & quis fictitius. Di- cuntur autem Parelia, quasi pares Elio, hoc est Soli, vocabulo ex duplici idiomate Græco, & Latino compacto: & quandoque duo, quandoque etiam tres soles apparere solent, vt videre accidit Romæ anno 1621. die 11. Februarij ferè in meridie, & duravit per duas circiter horas, vt refert Raphaël Auersa quæst. 42. sect. 5. & ante Saluatoris orium tres item soles apparuisse omnes pænè illius temporis scri- ptores testantur: quod olim pro ostento habitum, postea

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LEXICON 366 having sides equal, each of which is equal, and parallel to the opposite. Its condition is such that, if several figures of this kind are placed upon equal bases and at the same height, they are also equal among themselves. It differs from the Parallelogram, because this denotes only one plane quadrilateral, consisting of only four angles; whereas that includes more planes, namely six on the surface, and consequently eight angles corresponding oppositely to one another, so that it presents not one superficial figure, but one solid body capable of every dimension: such are dice, with which one plays at the aluceolus. Moreover, the Parallelopiped has all the conditions of a parallelogram, since it is nothing other than many parallelograms coming together into one. Hence also it is that it can be divided only into four differences, common even to the parallelogram. For if it contains six equilateral and rectangular parallelograms, it corresponds to the square among plane figures, and is called a Cube, such as, as I just said, a die. If those six parallelograms are indeed rectangular, but not all equilateral, but two being equal and smaller, and the rest longer, it will be called a parallelopiped longer on one side. If it is indeed equilateral in every respect, but with the corresponding angles not equal and not all right angles, it will correspond to a Rhombus. If finally neither all the parallelograms are equilateral, nor are all the angles right, although two of them are rectangular and equilateral; or rectangular only, or equilateral only; nevertheless they are truly parallelograms, so that both the planes, or sides, and the opposite angles are equal, it corresponds to a Rhomboid. Moreover, whatever parallelopiped may also be called a Prism; but not every Prism is a parallelopiped, as will be clear from the definition of the Prism, which we shall give below. 24. PARELIA are reflections of the sun’s rays in a round cloud, but well compacted; which, as if a mirror, receives into itself and reflects the image of the sun, so that another sun seems to appear, and one can scarcely know which is the true one and which the fictitious one. They are called Parelia, as it were equal to Helios, that is, to the Sun, a word formed from a double idiom, Greek and Latin: and sometimes two, sometimes also three suns are accustomed to appear, as happened to be seen at Rome in the year 1621, on February 11, about midday, and it lasted for about two hours, as Raphael Auersa reports, question 42, section 5; and before the sunrise of the Savior, likewise three suns appeared, as nearly all writers of that time testify: which was formerly regarded as a portent, afterward

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MATHEMATHICVM. 367 tamen agnita eius causa, non iam cum tanta admiratione conspicitur: Quamquam ego quæ ante Salvatoris exortum apparuere miraculosa crediderim ad explicandum Sanctissimæ Trinitaris Mysterium; eò maximè quod postea in e vnum confluxisse scribantur. Porrò Parelia sunt pluuix mox sequuturæ indubirata si- <25> gna, quam promissum fidelius quam Virgæ, quia inquit Arist. magis denorant aërem efficienser se habere ad ge- neraionem aquæ, eoquod parelium sit in materia omninò consimili, & æqualiter densa: Virgæ autem denotant inæ- qualem materiam, & nubes non vndequaque densas. Theo- phrastus de signis pluuix air: Si duo parelij sint, & simul <26.> corona celebrem imbrem expectandum esse. Addit Arist. Pa- relium australe cerrius quam boreale significare propin- quam pluuiam; eo quia facilius in aquam constringitur aër austrinus, quæm boreus. Alias significaciones Astrolo- gicas Pareliorum, vide apud Restam . . . . . . PARASELENE irem ex Græco, & Larino dicitur ad instar <27.> Parælij Lunæ replicatio in nube causa se reflectentis eodem pacto, ac Sol. Freqventer id accidisse canit Pontanus in sua Vrania: Verum apud scriprores rarissimè id factum le- gimus: & Plinius vnam tantum commemorat. Luna, in- <28.> quit, trina vt C. Domitio & C. Fannio Consulibus apparue- <29.> re, quas plerique appellauere soles nocturnos. PARMA apud Azophum egregium Persarum Mathemati- <27.> cum dicitur Lucida Coronæ Gnostiæ, quasi pupilla: siqui- dem, vt sæpè meminimus, Cæli pupilla vulgò apud Astro- <28.> nomos audir hæc fulgentissima stella. PARSFORTVNÆ. Vide in V. Fortunæ pars. <29.> PARTES aliæ nempè Viiæ, Mortis, Matris, Vxoris, &c. <30.> ab Arabibus excogitatæ planè inanes sunt, nisi ad ratio- dem reuocentur. Vide quæ diximus sub eodem verbo in <30.> fine. PARTILIS RADIVS, seù aspectus apud Astronomos diciunt <30.> familiariras à duobus, vel pluribus astris se mutuò intuen- ribus perfectè, & exquisiè contracta à loco, & determina- ta ad ynguem distania, tot præcisè partiù, quot requiuntur ad aspectum illum efformandum, & ad hoc, vt fidus proij- <30.> ciat radium ad ipsum corpus alterius sideris: quod habita ratione quantitatis diamerri singulorum, sit intrà latitudi- nem vnius gradus tam per longum, quam per latum. Quod <30.> etiam intelligendum est de congressu, & coniunctione; itavr duo sidera, quæ haberi eundem gradum longitudinis, eademque sint prædita latitudine, dicantur esse in coniun-

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MATHEMATHICVM. 367 Yet once its cause is recognized, it is no longer viewed with such wonder: although I would believe that those things which appeared miraculous before the coming of the Savior were given to explain the Mystery of the Most Holy Trinity; especially because afterward they are said to have converged into one. Moreover, parelia are certain signs of rain soon to follow, more dependable than rods, because, as Aristotle says, they indicate that the air is more effectively disposed for the generation of water, since the parhelion is in a matter altogether similar and equally dense; but rods indicate matter that is uneven and clouds not dense in every part. Theophrastus, on the signs of rain, says: if there are two parhelia, and at the same time a crown, a celebrated shower is to be expected. Aristotle adds that a southern parhelion signifies nearer rain more than a northern one; because the southern air is more easily condensed into water than the northern. For other astrological meanings of parhelia, see Resta ... PARASELENE, from Greek and Latin, is so called by analogy, the reflection of the Moon in a cloud, reflecting itself in the same way as the Sun. Pontanus in his Urania sings that this happened frequently; but in the writers we read that it happened very rarely, and Pliny mentions only one instance. The Moon, he says, appeared thrice when C. Domitius and C. Fannius were consuls, which most called nocturnal suns. PARMA, according to Azophus, an excellent Persian mathematician, is said to be the bright star of the Gnostic Crown, as it were the pupil: for, as we have often noted, this most brilliant star is commonly called among astronomers the pupil of heaven. PARS FORTUNÆ. See under V. Fortunæ pars. PARTES, namely those of Life, Death, Mother, Wife, etc., invented by the Arabs, are altogether empty unless they are brought back to reason. See what we said under the same word at the end. PARTILIS RADIUS, or aspect, is said by astronomers to be a familiarity, exactly and carefully contracted from a place and determined at a proper distance, between two or more stars mutually looking at one another, precisely in as many parts as are required to form that aspect, and so that the star may cast a ray upon the body of the other star; which, having regard to the size of each diameter, lies within the breadth of one degree, both in length and in width. The same must also be understood of conjunction and meeting; so that two stars which are taken to have the same degree of longitude and are endowed with the same latitude are said to be in conjun-

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168 LEXICON ctione partili: At si vnum eorum deflectat ad boream, al rerum ad austrum, coniunctio non erit partilis: si demum tanta sit deuiatio hincinde, vt excedat quantitatem orbis singulorum, nec erit dicenda coniunctio aut familiaritas etiamsi fuerint in eodem gradu, & minuto longitudinis. Vt esset si Venus reperiretur in primo gradu Arietis, cum maxima latitudine boreali, quam possit habere, & Mars in eodem quidem gradu longitudinis, sed cum quinque aut etiam plus, gradibus latitudinis meridianæ. In oppositione verò, ad hoc vt sit partilis, quia est ex diametro, oportet etiam vt latitudo sit oppositæ regionis, vt quod Luna exempli gratia sit in primo gradu Arietis cum latitudine boreali gr. 5. Venus in primo gradu Libræ cum totidem latitudinis australis. <31.> In radiis intermediis definiendis, contendit Blanchinus, quem sequuntur Maginus, Argolus, & Rationales communiter, accipiendam esse partem proportionalem latitudinis: Ducit enim circulum maximum per centrum stellæ latitudine præditæ ad eius opposirum, inclinatum super Eclipticam; atque ab hoc circulo sumit proportionem, atque æquationem omnium aspectuum intermediorum; ostendisque Quadratum fieri semper in Eclipria, Sextilem inciderre in medietatem latitudinis, quam habet stella; Trinum verò in dimidium latitudinis oppositæ, cuius schema affert Argolus in Astronomicis, atque in Primo Mobili. Sed enim hanc considerationem spreuit Ptolemæus in sine libri primi Quadrip. & reuera fictitius est hic circulus maximus à Blanchino excogitatus, in quo radij computari debeant, vt benè aduertit Titus in Cælesti Philosophia lib. 1. cap. 4. Nam stella est potius centrum radiorum, qui sunt circuli ducti in orbem circa stellam, qui maiores, & minores sunt, provt partes, vnde proijciantur radij, à stella ipsa elongantur: vnde ex latitudine stellarum attendenda potius esset ea proportio, ac differentia quæ prouenit à circulis minoribus, quorum centrum remouetur à circulo maiori, in quo sumuntur radij; quò enim magis centrum minoris circuli elongatur à maiore, eò maior accidit differentia distantiæ in loco sectionis, id est minor semper pars accipitur de circulo maiori. Vnde falsum est, quod air Blanchinus in quadratis nullam seruandam esse latitudinem, benè verò in sextili, vt ex schemate radiorum ad stellam, (quod affert Titus initio sui operis ex ære delineatum) obseruari potest. Hinc Regiomontanus vult in directionibus hanc proportionem variationis aspectus ob latitudinem stellæ ser-

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168 LEXICON tione partili: But if one of them turns toward the north and the other toward the south, the conjunction will not be partile; and if finally the deviation on either side is so great that it exceeds the extent of the individual orbs, then it will not even be called a conjunction or familiarity, even if they are in the same degree and minute of longitude. As would be the case if Venus were found in the first degree of Aries, with the greatest northern latitude she could have, and Mars in the same degree of longitude, but with five or even more degrees of southern latitude. In opposition, however, in order for it to be partile, because it is diametrically opposite, it is also necessary that the latitude be of the opposite region, so that, for example, the Moon may be in the first degree of Aries with north latitude of 5 degrees, and Venus in the first degree of Libra with the same amount of south latitude. <31.> In defining intermediate rays, Blanchinus contends, whom Maginus, Argolus, and the Rationales generally follow, that a proportional part of the latitude must be taken: for he draws a great circle through the center of the star endowed with latitude to its opposite, inclined over the Ecliptic; and from this circle he takes the proportion and the equivalence of all intermediate aspects; and he shows that the Square is always made in the Ecliptic, the Sextile to fall into the half of the latitude which the star possesses, and the Trine into the half of the opposite latitude, whose diagram Argolus presents in the Astronomica and in Primo Mobili. But Ptolemy despised this consideration at the end of the first book of the Quadripartite; and indeed this circle, invented by Blanchinus, in which the rays are supposed to be calculated, is fictitious, as Titus properly observes in the Celestial Philosophy, book 1, chapter 4. For the star is rather the center of the rays, which are circles drawn in a sphere around the star, circles greater and smaller according as the parts from which the rays are thrown out are farther from the star itself: whence, from the latitudes of the stars, that proportion and difference ought rather to be considered which arises from the smaller circles, whose center is moved away from the greater circle, in which the rays are taken; for the more the center of the smaller circle is displaced from the greater, the greater is the difference of distance at the point of intersection, that is, a smaller part is always taken from the greater circle. Whence it is false what Blanchinus says, that in squares no latitude need be observed, but in the sextile, as can be seen from the diagram of rays to the star, (which Titus presents engraved in brass at the beginning of his work) it is to be observed. Hence Regiomontanus wants in directions this proportion of variation of aspect on account of the latitude of the star to be ser-

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MATHEMATICVM. 369 uandam esse: Verum quia ea modica est, & planè insensibilis, vt ex dicto schemate patet, omninò negligi potest: Quoniam autem duplex est genus familiaritatis, quam < 32.> sidera possunt ad inuicem contrahere, vt sæpius dictum est, & in Zodiaco, & in Mundo: ideo à duplici etiam ratione distantiæ computari debent aspectus, ad hoc vt partiles euadant: Et in Zodiaco quidem sit semper in determinata distantia, vt puta sextilis in distantia 60. graduum; Quintilis 71. Quadratus 90. Trinus 120. Sesquiquadratus < 33.> 135. & sic de reliquis: In mundo verò secundum partes proportionales arcus sideris visti, atque à domibus: Vt quæ sidera reperiuntur in eadem cuspide domus, vel sanè in eodem circulo positionis horatio; etiamsi per longum, & latu[m] in Zodiaco longè distiterint, dicantur nihilominus esse in mundo partiliter coniuncta, qualis est congressus Sirij cumjsole in linea Orientis, qui Romæ accidir circa secundu[m] diem Augusti, cum tamen in Zodiaco longè lateque absint, & ultra sphæram sui orbis. Quæ verò quoad situm mundi ita inter se sunt disposita, vt alterum sit in cuspide ori[n]tis alteru[m] in cuspide vndecimæ decimæ, nonæ domus, aur in spatio intermedio inter octauam & nonam dicantur esse in partili aspectu Mundano, Sextili, Quadrato, Trino, Sesquiquadrato, etiam si non tot gradibus distent, quot in Zodiaco requiruntur ad huiusmodi aspectus formandos. Si verò tam in Zodiaco, quam in Mundo, hæc proportionalis radiorum distantia non sit exquisita, neque in corpore stellæ proijciatur ad corpus stellæ, siue diametrum, sed ad sphæram suæ lucis, iam non erit aspectus patrilis, sed platicus: de quo mox suo loco dicemus. PASSER, Piscis volans sidus in cælo nouiter ab Astronomis < 33.> recensiotibus obseruatum propè polum antarcticum, habens stellas septem, in longitudine, sub Libra, & Scorp. similiter. PAVO aliud sidus australe vnum ex duodecim de nouo < 34.> aliis 48 antiquis adiunctum, constans stellis 16. aliis verò 23. omnibus sub Capricorno, quarum præcipua est quæ in oculo secundæ magnitudinis. PATERA sidus, alias Crater, Vas. Arab. Alphum Hebreis < 35.> autem Kus id est poculum. Vide in V. Crater. PEGASVS sidus in cælo ad borealem plagam propè æquarorem < 36.> constans stellis 20. Arabicè Alpharax. de quo fusè egimus in Verbo Equus alatus. Is si fuerit in Horoscopo, inquir Iulius Firmicus, Nati erunt metallorum inventores,

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MATHEMATICVM. 369 to be so: but since that is slight and quite insensible, as is clear from the said diagram, it can altogether be neglected: Moreover, since there is a twofold kind of familiarity, which the stars can contract with one another, as has been often said, both in the Zodiac and in the World: therefore aspects must also be computed by a twofold measure of distance, so that they may become partile: And in the Zodiac indeed let it always be at a determined distance, as for example the sextile at a distance of 60 degrees; Quintile 71. Square 90. Trine 120. Sesquiquadrate 135. and so of the rest: In the world, however, according to the proportional parts of the arc of the seen star, and from the houses: So that those stars which are found in the same cusp of a house, or indeed in the same horoscopic circle of position; even if in length and breadth in the Zodiac they be far apart, are nevertheless said to be partilely conjoined in the world, such as the conjunction of Sirius with the Sun on the line of the East, which occurred at Rome about the second day of August, although in the Zodiac they are far apart in length and breadth, and beyond the sphere of their orbit. But those which, as to the position of the world, are so disposed among themselves that one is in the cusp of the ascendant, another in the cusp of the eleventh, tenth, ninth house, or in the intermediate space between the eighth and ninth, are said to be in a partile Mundane aspect, Sextile, Square, Trine, Sesquiquadrate, even if they are not separated by as many degrees as are required in the Zodiac for forming aspects of this kind. But if in both the Zodiac and the World this proportional distance of the rays is not exact, nor is it projected on the body of the star to the body of the star, or its diameter, but to the sphere of its light, then it will no longer be a partile aspect, but a platick: about which we shall speak shortly in its proper place. PASSER, the Flying Fish, a constellation in the sky newly observed by Astronomers in recent observations, near the antarctic pole, having seven stars, in longitude, under Libra and likewise Scorpio. PAVO another southern constellation, one of the twelve newly added to the other 48 ancient ones, consisting of 16 stars, and indeed 23 in all, all under Capricorn, the chief of which is that in the eye of second magnitude. PATERA a constellation, otherwise Crater, Vas. Among the Hebrews however Kus, that is, a cup. See under V. Crater. PEGASVS a constellation in the sky toward the northern region near the equator consisting of 20 stars, in Arabic Alpharax. Concerning which we have spoken at length under the word Winged Horse. If this is in the Horoscopo, inquires Julius Firmicus, they will be born inventors of metals,

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170 LEXICON qui latentes auri, & argenti venas, ac cæterarum specierum solertibus inquisitionibus persequantur. Si vero in occasio fuerit inuentus, & Mars in ipso loco fuerit, vel in diametro, vel quadrato; hi aut incensa domo conflagrabunt, aut publica Iudicis sententia flammis vltricibus cremabuntur. Hæc Firmicus. 37. PENTAGONVS apud Geometras dicitur figura quinque angulos habens, siue ea æquilatera sit, siue non: Et si quidem ea fuerit æquilatera dicetur etiam regularis Isoperimetra, quæ in cælo constituit radium quintilem: Si verò fuerit inæqualium laterum, ea absolutè irregularis dicitur, quæ multis modis variari potest, eo pacto, ac Trapezia, de quibus suo loco. 38. PEREGRINVS apud Astronomos dicitur Planeta repertus in loco, vbi nullam habet dignitatem, ex quinque essentialibus, Domicilio nempè, Exaltatione, Trigono, Terminis & Facie, vt Sol in Virgine, Luna in Geminis, &c. Quod si stat mutua receptio cum alio Planeta ex domibus, aut Exaltatione, itavt permutent domos, ac dignitates; sitque ideo vns in domo vel exaltatione alterius, & hic in domo, vel exaltatione illius; tunc perinde est ac si reperirentur in propriis domiciliis, aut exaltationibus, & mutuò confortantur, nec p[ro]tioinde amplius dici poterunt peregrini. Talis esset Sol in Virgine, Mercurius in Leone, vel Iupiter in Libra, Saturnus in Cancro, &c. Cæterum in Genethliacis Planete peregrini maiorem fortunam afferunt extrà Patriam, quam in Patria ob similem rationem, quam supra tetigimus: sicut è contrà in domibus suis, fortunam in Patria, ni fortè à malescis, aut alio quouis casu infortunentur: Nam malè constituti nullibi omninò boni quicquam largiuntur, sed vix ea, quæ à virtute, & laboribus proficiscuntur, permittunt. Nec sine ætumnis, vt benè ex Philosophicis principiis aduertit Titus lib 3. cap. 17. 39. PERIGEVM Græcè dicitur oppositum Augis, seu infima absis Eccentrici, & Epicycli Planetarum, in qua humiliores apparent & terræ viciniores, vt quando sol est in gr. 6. Capricorni: sicut è contra Apogæum est locus à tetra remotior in suprema abside Epicycli, de qua re vide iam dicta in V. Apogaum, & in V. Absis. 40. PERIMETRVM Græcè idem ac apud nos circumferentia. 41. PERIOECT apud Geographos vocantur populi omnes, qui habitant sub eodem meridiano; eodemque parallelo, sed in locis oppositis eiusdem paralleli, quales sunt populi

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170 LEXICON which, by diligent inquiry, seek out hidden veins of gold and silver, and of the other kinds. But if they are found in the occasion, and Mars be in the very place, or in the diameter, or in the square, they will either perish with the house set on fire, or by the public sentence of the Judge be burned in avenging flames. Thus Firmicus. 37. PENTAGON is called among geometers a figure having five angles, whether it be equilateral or not: and if it is equilateral it is also called regular, Isoperimetral, which in the heavens establishes the quintile ray: but if it be of unequal sides, it is absolutely called irregular, which can be varied in many ways, in the same manner as the Trapezia, of which in their place. 38. PEREGRIN is called among astronomers a planet found in a place where it has no dignity, out of the five essential ones, namely Domicile, Exaltation, Trine, Terms, and Face, as the Sun in Virgo, the Moon in Gemini, etc. But if there is a mutual reception with another planet from houses or from exaltation, so that they exchange houses and dignities; and one is thus in the house or exaltation of the other, and the other in the house or exaltation of that one; then it is as if they were found in their own domiciles or exaltations, and they mutually strengthen one another, nor can they any longer properly be called peregrine. Such would be the Sun in Virgo, Mercury in Leo, or Jupiter in Libra, Saturn in Cancer, etc. Moreover, in genethlialogical matters peregrine planets bring greater fortune outside their country than in their country, for a similar reason as we touched on above: just as, on the contrary, in their own houses, fortune is in their country, unless perhaps they are made unfortunate by malefics or by some other accident: for planets badly placed grant no good thing anywhere at all, but scarcely even those things which proceed from virtue and labors. Nor without anxieties, as Titus rightly observes from philosophical principles, lib. 3, cap. 17. 39. PERIGEE in Greek is said of the opposite of the apogee, or the lowest apsis of the eccentric and epicycle of the planets, in which they appear lower and nearer to the earth, as when the sun is in the 6th degree of Capricorn; just as, on the contrary, Apogee is the place farthest from the earth in the highest apsis of the epicycle, concerning which see what has already been said under V. Apogaum and V. Absis. 40. PERIMETER in Greek is the same as among us, circumference. 41. PERIOECT among geographers are called all peoples who inhabit under the same meridian and the same parallel, but in opposite places of that same parallel, such as the peoples

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MATHEMATICVM. 371 Virginæ in America, & qui sunt in India intrà Gangem; quoniam sunt ambo in eodem meridiano, & in eodem ferè parallelo, sed in parte opposita: habent enim ambo latitudinem ferè gr. 40. sic Mexico Vrbs celebertima in India Occidentali, eiusque sinus, eum Insulis Cambæ in Asia; sic populi nouæ Hispaniæ cum Persarum Regno, &c. Vt aurem Periœci vnius loci facilè inueniantur, longitudini dicti loci adde gr. 180. atque in eodem parallelo ad æquatorem inquire; & qui sub dicta longitudine & parallelo reperiuntur erunt Periœci loco aut ciuitati de qua disquirimus. Sic Castellæ Regnum in Hispania habet longitudinem gr. 10. latitud. gr. ferè 42. additis igitur eius longitudini gr: 180. prosilient gr. 190. in quo metidiano inquire parallelum latum gr. 42. & videbitur ei esse Periœca celebris Vrbs Quinsai in Regno Chinensium. PERIODVS apud Astronomos propriè significat spatium temporis; quod quilibet Orbis insumit ad perficiendum suum cursum in Zodiaco; vt Saturnus in annis ferè 30. Iupiter in 22. Mars in duobus; Sol, Venus, Mercurius in vno, Luna in diebus 27. & horis 8. Hæ igitur sunt periodi motuum Planerarum: quæ quidem intelligi debent non de orbibus, seu Cælis totalibus, sed vel de ipsis corporibus Planetatum, quatenus feruntur per ipsum cæli expansum: vel de propriis orbibus deferentibus, qui sunt Eccentrici in medio cælorum collocati: in his namque Planetæ, vel eorum Epicycli infici deferuntur temporibus p[er]tædictis. Totales enim cæli (saltem in sententia communi) mouentur ab Occidente in Orientem eadem prorsus tarditate, qua mouetur octava sphæra; licet ego, vt dixi in V. Motus aliter sentiam. Hinc periodicum dicitur quod ecrtâ, statâque recurrit periodo; quales sunt annuæ revolutiones, Anni, diesque climacterici, &c. quæ cum cælestium motuum periodis quandam connexionem, & affinitatem habent. PERIPHERIA Græcè idem, ac Latinè circumferentia propriè significat extremum in quod terminat circulus, seu lineam illam circularem, quæ totam circularis figuræ aream ambit, & circumplectitur, cuius proportio ad diametrum ipsius circuli est ferè tripla sesquiseptima, vt habet Archimedes de dimensione circuli, hoc est 12. ad septem. Quandoque etiam accipitur pro tota superficie terræ, aut pro conuexo, & extima parte cuiusuis sphæræ cælestis. PERISCIT apud Geographos vocantur accolæ frigidarum regionum intrà ambitum circulorum Arctici, & Antartici, qui constituunt Zonas frigidas: sic dicti, quasi Contraum-

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MATHEMATICVM. 371 Virgins in America, and those who are in India beyond the Ganges; since both are in the same meridian, and in almost the same parallel, but in opposite parts: for both have a latitude of about 40 degrees. thus Mexico, a most celebrated city in Western India, and its gulf, with the islands of Camba in Asia; likewise the peoples of New Spain with the Kingdom of Persia, etc. But in order that the Perioeci of a place may be easily found, add 180 degrees to the longitude of the said place, and in the same parallel, up to the equator, inquire; and those who are found under the said longitude and parallel will be the Perioeci of the place or city about which we are investigating. Thus the Kingdom of Castile in Spain has a longitude of 10 degrees, latitude of about 42 degrees; therefore, adding to its longitude 180 degrees, there will result 190 degrees, in which meridian inquire the parallel of latitude 42 degrees. and it will appear to be Perioecic to it the famous city of Quinsai in the Kingdom of the Chinese. PERIOD, among Astronomers, properly signifies the span of time that any orbit takes to complete its course in the Zodiac; as Saturn in about 30 years, Jupiter in 22, Mars in two; the Sun, Venus, Mercury in one, the Moon in 27 days and 8 hours. These therefore are the periods of the motions of the Planets: which indeed must be understood not of the orbits, or of the total Heavens, but either of the planets’ own bodies, insofar as they are carried through the very expanse of heaven; or of their proper conveying orbits, which are eccentric, placed in the middle of the heavens: for in these the planets, or their epicycles, are carried along imperceptibly in the aforesaid times. For the total heavens (at least in the common view) move from West to East with exactly the same slowness as the eighth sphere is moved; although I, as I said in V. Motus, think otherwise. Hence something is called periodic which returns with a certain, fixed period; such as annual revolutions, climacteric years and days, etc., which have with the periods of celestial motions a certain connection and affinity. PERIPHERY in Greek means the same as in Latin, circumference; properly it signifies the outer boundary at which the circle ends, that is, that circular line which surrounds and encloses the whole area of the circular figure, whose proportion to the diameter of the circle itself is about triple sesquiseptimal, as Archimedes has it in the measurement of the circle, that is, 12 to 7. Sometimes also it is taken for the whole surface of the earth, or for the convex and outer part of any celestial sphere. PERISCIT, among Geographers, are called the inhabitants of the cold regions within the bounds of the Arctic and Antarctic circles, which constitute the frigid zones; so called, as if Contraum-

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LEXICON 372 braciles: quia vmbra illis est versatilis, & fertur in orbem molarum more in plano horizontis. Antiqui existimabant has regiones ob nimium frigus esse inhabitabiles, quæ tamen reuera habitantur, licet homines sint omninò syluestres, & rudes, vt testantur Hollandi, qui eò sæpè navigationes suas instituerunt. Ad huius Zonæ iniium sub circulo Arctico posita est celebris insula Thule, de qua Virgilius. Tibi serviat ultima Thule. Vide quæ diximus in V. V. Amphiscij, & Heteroscij. 46. PERPENDICVLVM: Instrumentum notum Mathematicum ac Mechanicis omnibus familiare nimis, librandisque aliter tudinibus aptum: Cuius inuentorem fuisse Dædalum testatur Plinius lib.7 cap.56 Hinc perpendiculare vocant Geometræ quodcumque ex superiore loco ad imum dimittim[en]ta rectitudine, qua plumbum pendet ex perpendiculo. Quæ etiam ratione Astronomi solem, aut stellas, quæ sunt verticales, perpendiculares appellant; quia profectò eorum radij tectà admodum perpendiculi supra nostrum verticem cedunt. Porrò ad longitudinis, latitudinis atque profunditatis cognitionem habendam nulla melior mensura excogitari potest quam linea perpendicularis; Quandoquidem mensura debet esse maximè certa, & determinata: Atqui, vt habet Clau. in sphæram cap.1. Sola linea perpendicularis inter alias lineas certam, determinatamque longitudinem habet. 47. PERSEVS dictus etiam Inachides, Cyllenius, &c. Arab. Chelub, vel Chelub. hoc est ferens caput diaboli: sidus in octaua sphæra ferens caput Medusæ, consistensque in via lactea ad partem borealem, in quo ex Ptolemao numerantur stellæ 26. at in Bayeri Vranometria 18. omnes ferè de natura Saturni, & Iouis in longitudine sub signo Tauri. Quarum potissima, & malignitate suas satis nota est, quæ Caput Medusæ dicitur, secundi honoris: proximè accedit Fulgens in dextro latere Arabicè Alchenib, seu Elgenab. inde dux nebulosæ, altera in extremo dextræ manus, altera in sinistra antecedens Caput Medusæ. De eo horoscopante sic cecinit Pontanus in sua Vrania. Fera vincula semper, Semper torturas agitat crudelia Perseus Funera, sunt enses illi, sunt vulnera, cura, Gorgonei capitis semperque insignia præfert. Quo surgente aliquis veniens in luminis arcus Si Phœbus quoque Gorgoneo sese extulit ortu, Si

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LEXICON 372 braciles: because the shadow in them is variable, and is carried around in a circle, like millstones, in the plane of the horizon. The ancients thought that these regions were uninhabitable on account of excessive cold; yet they are in fact inhabited, although the people are entirely savage and rude, as the Dutch testify, who often undertook voyages there. At the beginning of this Zone, under the Arctic Circle, is situated the famous island of Thule, concerning which Virgil says: Tibi serviat ultima Thule. See what we said in V. V. Amphiscij, & Heteroscij. 46. PERPENDICVLVM: A well-known mathematical instrument, and one most familiar to all mechanics, suited for measuring heights: Pliny testifies that Daedalus was its inventor, lib. 7 cap. 56. Hence geometers call perpendicular whatever is let down from a higher place to a lower one by a straight line, as a plumb line hangs from the plumb. For this reason astronomers also call the sun or stars perpendicular when they are vertical; because indeed their rays fall very nearly perpendicularly over our zenith. Moreover, for obtaining knowledge of length, breadth, and depth, no better measure can be devised than the perpendicular line; since a measure ought to be as exact and determinate as possible. But, as Claudius has in his Sphaera, cap. 1, only the perpendicular line among all lines has a fixed and determinate length. 47. PERSEVS, also called Inachides, Cyllenius, etc. Arab. Chelub, or Chelub, that is, bearing the head of the devil: a star in the eighth sphere bearing the head of Medusa, and situated in the Milky Way toward the northern part, in which, according to Ptolemy, 26 stars are counted; but in Bayer’s Uranometria, 18. Nearly all are of the nature of Saturn and Jupiter in longitude under the sign of Taurus. The principal among them, and well known enough by its malign influence, is that which is called the Head of Medusa, of the second magnitude. Next comes the bright one on the right side, in Arabic Alchenib, or Elgenab. Then the leader of the nebulous ones, one at the extreme of the right hand, the other on the left preceding the Head of Medusa. Concerning this constellation when rising, Pontanus sang in his Urania: Fera vincula semper, Semper torturas agitat crudelia Perseus Funera, sunt enses illi, sunt vulnera, cura, Gorgonei capitis semperque insignia præfert. Quo surgente aliquis veniens in luminis arcus Si Phœbus quoque Gorgoneo sese extulit ortu, Si

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MATHEMATICVM. 373 Si Maurs telo infelix rucilante lacessat, Quo sol, aut quo Luna loco, Dominumque locorum, Nec felix stella occurset, calove cadenti Sese agat occasum versus regione secunda. Huic caput auulsum collo violenta bipennis Auferet, & media truncus spectatur arena. Hucusque Pontanus. Quæ omnia in funeream Gorgonis stellam recidunt; quam alibi authoritate etiam D[ominum] Thomæ, violentæ nimis, ac luctuosæ naturæ fuisse semper, aduer- timus. PERSONA Astronomis idem valet, quod Facies: Vnde < 49.> Planetæ dicuntur personas suas gerere, quandocumque se facie ad faciem intuentur; præsertim verò cum luminatibus, hoc est, vt eo modo configurentur cum Sole, aut Luna (ita tamen vt sint Orientales ab illo, Occidentales ab ista) quo eorum domicilia cum domibus luminarium. Hanc familiaritatis, scù dignitatis speciem Arabes Almugeam vocant: de qua vide quæ fusiùs diximus suo loco. PERSPECTIVA vna est, ex Mathematicis disciplinis, quam < 50.> Geometriæ filiam vocant: Facultas est, quæ iuxtà principia Geometrica per radios visuales, tamquam lineis, & angulis res longè ab oculis dissitas speculatur, siue ea cælestia corpora sint, siue quæcumque colorata; (inquo latiùs paret quam Optica) atque ad rationem emissarum specierum in modum Pyramidis dimetitur. Est in triplici differentia: Alia enim est, quæ absolutè, & anthonomasticè dicitur Perspectiua, & in eo consistit, vt rationem reddat earum apparentiarum, quæ aliter, ac res sunt, nostris obtutibus sese offerre solent, ob diuersam rerum situationem, atque distantiam; qua ratione videmus circulos rectos tamquam lineas, quadrata tamquam circulos, &c. Alia est, quæ versatur circa varias, ac multiplices refractiones; quæ profecto ab speculis, ex quibus eas potissimum exquirit, specularia, siue specularia appellatur. Alia demum, quæ circa vmbras versatur; atque ostendit qua ratione fieri queat, vt ea, quæ in picturis apparent confusa & inordinata, ex diversitate situs concinna & ordinata, & è contrà quæ aliàs benè disposita, è longinquo, aur è latere deformia, & inconcinna videantur: Et hæc dicitur Sciacoptrica, de quibus omnibus eruditè admodum scripsit Alaazel in sua Perspectiua, Vitellion, Guidobaldus è Marchionibus Montis, ac nouissimè Kircherus in Arte Magna lucis, & vmbræ. A a

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MATHEMATICVM. 373 If ill-starred Mars, brandishing his weapon, should assail you, where the sun is, or where the moon, and the Lord of places, and no fortunate star is encountered, or the sky is falling; let him drive himself toward the setting in the second region. The violent two-edged axe will cut off his head from his neck, and the trunk will be seen in the middle of the arena. Thus far Pontanus. All these things refer to the funeral star of Gorgo; which elsewhere we note, on the authority also of Lord Thomas, to have always been of a very violent and mournful nature, and too sorrowful. PERSONA among astronomers has the same meaning as Facies: hence <49.> the planets are said to bear their persons whenever they look face to face; especially indeed when they are with the luminaries, that is, when they are configured with the Sun or the Moon in that manner (provided however that they are Oriental from the former and Occidental from the latter) in which their domiciles are with the houses of the luminaries. This kind of familiarity, or rather dignity, the Arabs call Almugeam: on which see what we have said more fully in its proper place. PERSPECTIVA is one of the mathematical disciplines, which <50.> they call the daughter of Geometry: it is a faculty which, according to geometrical principles, through visual rays, as through lines and angles, contemplates things far removed from the eyes, whether those things are heavenly bodies or any colored objects; (in which it is broader than Optics) and it measures them according to the ratio of emitted species in the form of a pyramid. It is of three kinds: for one is that which is absolutely, and by antonomasia, called Perspectiva, and in this it consists, that it gives an account of those appearances which otherwise, than the things are, are wont to present themselves to our sight, because of the different situation and distance of things; by which means we see straight circles as lines, squares as circles, etc. Another is that which deals with various and manifold refractions; which indeed, from the mirrors from which it especially investigates them, is called specularia, or specularia. A third, finally, is that which deals with shadows; and it shows by what means it can happen that those things which appear in paintings confused and disordered, by difference of position may seem neat and ordered, and conversely that which otherwise is well arranged may, from afar or from the side, appear deformed and ill-arranged: and this is called Sciacoptrica, concerning all of which Alaazel wrote very learnedly in his Perspectiva, Vitellion, Guidobaldus of the Marquises of Montis, and most recently Kircher in the Great Art of Light and Shadow. A a

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374 LEXICON PERTICA dicitur Cometa crinitus longus valdè, plus eo, qui dicitur Veru, minus tamen latus Tenaculo: (de quibus suo loco) Quando apparet, videtur semper ex aduerso solis habens caudam densam, crassam, & rotundam: & viuersaliter portendit siccitatem, sterilitatem, & aquarum defectum, vnde consequenter caritatem annonæ, & quæ his consequentur. Si adhuc cum Planetis appareat coniunctus, denunciat mala secundum naturam eius, vt si fuerit iu[n]ctus corporaliter Saturno, timenda erit mortalitas, & detrimentum in hominibus & rebus quibus præest Saturnus: si cum Ioqe, mala affert Iouialibus: cum Marte indicit bella, & occisiones innumeras: & sic de reliquis, Planetis iuxta eorum proprias significationes discurrendum, excepto sole, cum quo numquam congreditur. PERSELE Barbarum, seu potius Chaldaicum Vocabulum, sed frequens inter Astronomos: quo significatur Nebulosa stella in pectore Cancri consistens dicta communiter Præsepe, de qua paulò infra. PHARMAZ Arab. Latinè Crater, sidus supra dorsum Hydræ consistens, de quo suo loco. PHAES Græcè dicuntur variæ Cælestium corporum, præsertim Lunæ, affectiones, & apparentiæ pro diuerso ad solem, telluremque positu: Vnde & obscura, cotniculata, dimidiata, plena, nunc cornibus ad solem inuersis, nunc ab eodem auersis conspicitur, quod & in Venere, & in Marte nuper Telescopij ope obseruatum est. PHOENICE olim dicebatur Stella polaris, & Cynosura in extremo caudæ Vræ minoris propè polum arcticum posita, eo quod Phoenices populi nondum reperta magneticæ acus virtute, cuius beneficio hodie totus Oceanus peragratur, ad hanc respicientes nauigiorum suorum cursum dirigebant: maximè enim illis accommoda veniebat ad explorandum in qua Mundi plaga consisterent, quantum fuerint à termino vnde discesserint, elongati, quantum vltra progressi. Quippe semper in eodem situ, non sicut alia stellæ circumactu coeli volutabatur. PHOENIX, seu Phoenicias ventus Meridionalis, qui & Euro Auster lateralis Austro, medius inter ipsum, & Notapeliotem, directeque oppositus Circio: qualitate calidus, & humidus, ac morbosus Eo flante subinde apparent altè radiantia fulmina, & nubes in vnum coguntur. PHOENIX etiam dicitur in coelo sidus ad polum antarcticum, vnum ex duodecim nuper detectis, Stellas habet

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374 LEXICON PERTICA is the name given to a very long hairy comet, larger than that which is called Veru, but narrower than Tenaculum: (of which in its place.) When it appears, it is always seen opposite the sun, having a thick, dense, and round tail: and universally it portends dryness, barrenness, and a lack of waters, whence consequently dearth of grain, and whatever follows from these. If it appears still joined with the Planets, it announces evils according to their nature; thus if it be corporally joined with Saturn, mortality and loss in the things and persons over which Saturn presides are to be feared: if with Ioue, it brings evils to Jovial things: with Mars it proclaims wars and innumerable slaughters: and so with the rest, one must proceed according to the proper significations of the Planets, except the sun, with which it never comes together. PERSELE, a barbarous, or rather Chaldaic, word, but frequent among Astronomers: by which is signified the nebulous star in the breast of Cancer, commonly called Præsepe, of which a little below. PHARMAZ, Arabic; in Latin, Crater, the star situated above the back of Hydra, of which in its place. PHAES, in Greek, are called the various affections and appearances of heavenly bodies, especially of the Moon, according to their different position with respect to the sun and the earth: whence it is seen now obscure, now horned, now half, now full, now with horns turned toward the sun, now turned away from it; which has also lately been observed in Venus and in Mars by means of the Telescope. PHOENICE was once the name given to the polar star, and Cynosura, placed at the extremity of the tail of Ursa Minor near the arctic pole, because the Phoenician people, before the virtue of the magnetic needle was discovered, by whose benefit today the whole Ocean is traversed, directing their course by looking to this star, steered the paths of their ships: for it was especially suited to them for discovering in what region of the World they were situated, how far they had been separated from the point from which they set out, and how far they had advanced beyond it. Indeed it always remained in the same position, not turning like the other stars by the revolution of the heavens. PHOENIX, or the Phoenician wind, a southern wind, which is also the side-wind Euro Auster, midway between it and Notapeliotes, and directly opposite Circius: in quality hot and humid, and unhealthy; when it blows, lightning shining high above appears from time to time, and clouds are gathered into one. PHOENIX is also the name of a star in the heavens near the antarctic pole, one of the twelve recently discovered. It has stars

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MATHEMATICVM. 375 14. secundum alios 15. omnes in longitudine sub signo Piscium. PHOENICOPTERVS aliud fidus ab Hispanis nouissimè obseruatum extrà numerum duodecim primitùs detectorum ab iis suo idiomate El Flamengo vocatum. Exprimit autem auem expansis alis Piscem notium, qua in arcum curuatur, rostro appetentem: tredecim ei assignant stellas, inter quas vnam in capite secundæ magnitudinis, quam alij priùs in Piscem notium reducebant. PHOENOMENA, Græcè, Latinè Apparentiæ interpre- tari possunt, dicuntur promiscuè noua sidera in cælo appa- rentia, siue ea in regione elementari, siue in ætherea cons- piciantur. Et ea quidem in aëre generantur ex quadam ex- halatione crassa, & viscosa constante ex partibus bene co- agmentatis, quæ virtute Astrorum sursum euehitur, ibique accenditur, ac tamdiù durat quousque materia illa ab igne concepto absummatur; ac pressius Cometæ dicti sunt. Isti autem retento Phoenomenum nomine in cælo verè consi- stunt, ibique aut de nouo generantur, aut saltem alias ge- niti de nouo apparent, & ex maiori approximatione ad nos aut alia quauis ratione sunt visibiles. De illis satis copiosè dictum in V. Cometes: de his modò hic sermo instituendus. Nasci autem interdum in cælo noua hæc sidera, nulli dubium; cum ipsa testetur experientia id sæ- pissimè euenire; atque in isto sæculo, quod adhuc transa- ctum non est, tres omninò stellas in ipso orbe fixarum vi- sas referunt omnes pænè scriptores. Vnam in pectore Cy- gni, alteram in genu Serpentarij, tertiam longè pulchrio- rem, & clariorem in Cathedra Cassiopæ, corpore ipsum ferè Veneris fidus exxquantem, quas non fuisse de genere cometarum ipsa tatio parallaxis, qua nulla præditæ erant, ipse motus idem prorsus ac cæterarum fixarum, ipsa tem- poris duratio, aliaque multa manifestè suadent, Sed & olim etiam huiusmodi stellas in cælo apparuisse testatur Plinius lib. 2. cap. 24. Namque, inquit, & in ipso calo stella repente nascuntur. & cap. 16 de quadam stella tempore Hipparchi visa sic ait. Hipparchus numquam satis laudatus, vt quo nemo magis approbauerit cognationem cum homine siderum, animasque nostras calo dignas esse nouam stellam, & aliam suo auo genitam deprehendit, eiusque motu, quo die fulxit ad dubitationem est adductus, anno hoc sapius fieret, no- uerenturq[ue] eodem ac ea, quasputamur affixas: idemque ausut rem etiam Deo improbam annumerare posteris stellas side- raque ad normam expandere. Quid autem sibi velit per Aa ij

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MATHEMATICVM. 375 14. according to others 15. all in length under the sign of Pisces. PHOENICOPTERVS, another fixed star, recently observed by the Spaniards outside the number of twelve first discovered by them, and in their own idiom called El Flamengo. It represents a bird with its wings spread, the Southern Fish, which it bends into an arch, reaching forward with its beak: they assign thirteen stars to it, among which one in the head of second magnitude, which others formerly referred to the Southern Fish. PHOENOMENA, in Greek, can be translated in Latin as Apparitiones, and the name is used indiscriminately for new stars appearing in the sky, whether they are seen in the elemental region or in the ethereal one. Those in the air are generated from a certain thick and viscous exhalation, composed of well-coagulated parts, which by the power of the stars is carried upward, there is kindled, and lasts until that matter is consumed by the fire it has taken up; and more properly these are called comets. But those which retain the name of phenomena truly exist in the sky, and there either are generated anew, or at least, having been generated elsewhere, appear anew, and are visible from a closer approach to us or for some other reason. Of those enough has been said in V. Cometes; now the discussion here is to be about these. That such new stars are sometimes born in the sky is beyond doubt, since experience itself testifies that this happens very often; and in this century, which has not yet passed, almost all writers report that three stars at all were seen in the very sphere of the fixed stars. One in the breast of Cygnus, another in the knee of Serpentarius, a third, far more beautiful and brighter, in the Chair of Cassiopeia, nearly equalling the body of Venus itself; and that they were not of the kind of comets is clearly shown by the very parallax, which they lacked, by their very same motion as the other fixed stars, by the duration of time itself, and by many other things. But Pliny also testifies that stars of this kind once appeared in the sky, book 2, chapter 24. For, he says, stars are suddenly born even in the very heaven. And in chapter 16, concerning a certain star seen in the time of Hipparchus, he says thus: “Hipparchus, never praised enough, as the man who more than anyone approved the kinship of the stars with mankind, and that our souls are worthy of the sky, discovered a new star and another born in his age, and by its motion, which shone on a certain day, he was brought into doubt whether this too might happen more often, and whether they might be renewed in the same manner as those which are thought to be fixed: and he even ventured to number this matter among things displeasing to God, that stars should be handed down to posterity and the constellations extended to a rule.” What, however, he means by Aa ij

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376 LEXICON hoc quod dicit Deo rem improbam fore annumetate nouas stellas, atque ad formam expandere, quod ausum esse di- cit Hipparchum, non satis intelligo. 60. Cæterum de istis stellis varia fuit tum antiquorum, tum recensiorum Astronomorum opinio. Democritus, cuius sen- tentiam amplecti videtur Bodinus lib. 2. Theatri, somnia- uit, eas esse illustrium virorum mentes, quæ postquam in- numerabilibus seculis viguerunt in terris, tandem obituræ extremos peragunt triumphos, aut in cælum stellatum, quasi splendida sidera reuocanrur, ac propterea sequuntur fames, morbi populares, ac ciuilia bella, quasi Ciuitates & populi ducibus illis optimis, & gubernatoribus, qui di- uisos furores placabant, desererentur. Aristoteles minus absurdè dixit eas omnes gigni ex materia elementari, ferri- que aliquando ad ipsam regionem ætheream: Sequuntur eum non pauci recensiores, eo maximè, quod posita cæloru[m] fluxibilitate, iam nil obstare videtur, quin ijsdem Cometæ, qui in regione aërea generantur, si subtilioris materiæ sint, possint orbes planetarum transcendere, atque etiam ad ipsum Firmamentum peruenite, vbi postea perinde ac astra refulgeant, quoadusque eorum materia penitùs absumatur. Quod, præcæteris, actiter sustinet Christophorus Roth- mannus. 61. Verum etsi fortè huic rei non obstet ipsa cælorum sub- stantia, quæ sit fluxibilis, & per consequens facillimè etiam attrahi à sideribus possint huiusmodi ignitæ exhilarationes; attamen non videtur credibile, eas tanto tempore durare posse, cum Stella Cassiopææ duos integros durarit annos, & de ea quæ apparuit anno 1600. in pectore Cygni testatur Blancanus adusq[ue] suum tempus hoc est anno 1616. fuisse vi- sibilem, quando Cometæ in aëre apparentes vix ad mensem durare solent. Deinde vnde emanat tanta exhalationum co- pia, quæ ad cælum vsque fixarum possit ascendere, ibique accensa, sint probè visibilis? non certè è terra, quæ si tota ad sidera evolaver è loco vbi modo consistit, videri ob sui tenuitatem minimè posset cum ipsa terra ad Firmamentum relata se habeat vt punctum, & minima Stella visibilis Fir- mamenti, bis nouies sit terra maior. Non ergo noua phæno- mena suprà orbem Saturni visa esse possunt ex mareria ele- mentari coagmentata, sed necessario debent esse ex ipsare- gone ætherea. Melius philosophatur Pythoras putans eas non esse de nouo genitas, sed ex perpetuo recurso terris approximari, fierique visibiles, cuius opinionem minimè absurdam existimat Blancanus, dicens ideo eas nouiter, ac

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376 LEXICON that which he says is an improper thing for God to do, to create new stars every year and to expand them into a form, which he says Hipparchus dared to do, I do not sufficiently understand. 60. Moreover, concerning those stars there was a varied opinion both among the ancients and among more recent astronomers. Democritus, whose view Bodin seems to embrace in book 2 of the Theatrum, dreamed that they were the minds of illustrious men, which, after they had flourished for countless ages on earth, at last, when about to die, perform their final triumphs, or are recalled into the starry heaven, as if into bright constellations; and that therefore famines, pestilences, and civil wars follow, as though cities and peoples were abandoned by those best of leaders and governors who were calming divided rages. Aristotle said less absurdly that they are all generated from elemental matter and are sometimes carried up into the very ethereal region. A number of more recent writers follow him, especially because, once the fluxibility of the heavens has been posited, it now seems that there is nothing to prevent those same comets, which are generated in the air, if they are of subtler matter, from being able to pass beyond the spheres of the planets and even reach the Firmament itself, where afterwards they shine like stars until their matter is completely consumed. This is especially maintained by Christophorus Rothmannus. 61. But although perhaps the very substance of the heavens, which is fluxible, does not hinder this matter, and consequently such fiery exhalations may very easily be drawn by the stars, nevertheless it does not seem credible that they could last for so long a time, since the star of Cassiopeia lasted two full years, and Blancanus testifies that the one which appeared in the year 1600 in the breast of Cygnus was visible up to his own time, that is, the year 1616, whereas comets appearing in the air are scarcely accustomed to last a month. Then, whence comes such a great abundance of exhalations, able to ascend all the way to the heaven of the fixed stars and, being ignited there, become clearly visible? Surely not from the earth; for if the whole earth were to fly up to the stars from the place where it now stands, it could by no means be seen because of its subtlety, since the earth itself, when carried up to the Firmament, would stand in relation to it as a point, and the smallest visible star of the Firmament is eighteen times nine times greater than the earth. Therefore the new phenomena seen above the orbit of Saturn cannot have been formed from elemental matter compacted together, but must necessarily be from the ethereal region itself. Pythagoras philosophizes better, thinking that they were not newly generated, but become visible by perpetual return when approaching the earth; Blancanus judges this opinion not at all absurd, saying that therefore they newly...

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MATHEMATICVM. 377 statis temporibus apparere, quia cum sint in Firmamento ob vastitatem expansi, ob rarditatem motus, & amplitudinem Epicycli quamdiu sunt in Apogæo minime conspici possunt, at verò cum descendunt ad Perigæum paulatim fieri conspicuas, ac durare quoadusque ab illo notabiliter recedunt: quod & accidisse credendum est in Stella Cassiopeæ, quæ anno 1522. descendit ad suum Perigæum, in locum longè cæteris fixis humiliorem, at verò cum sensim minui cæpit, ac tandem facta est inuisibilis, tunc ab eo paulatim recessit ac tantum elongara est, vt iam amplius conspici non potuerit. Sed iam multum inualuit apud Recensiores opinio Anaxagoræ existimantis huiusmodi stellas aliud planè non esse, quam coitum plurium stellularum discurrentium per tenuissimum illud expansum, quæ in tanta distantia vnam & eandem stellam repræsentent, vt iam perspicuum est de stellis nebulosis, atque ipsa Galaxia; eo maximè quod huiusmodi stellæ semper, & non nisi in Galaxia apparuerunt: quæ postea euanescunt, quia ab inuicem elongantur. Vrcumque sit certum est, eas magnum quid, & insolita semper portendere: quorum qualitas ex earum qualibus, motu, situ, regione, & tempore apparitionis eruenda est: vt ex intensione lucis qualitatum activarum intensio, extensione passiarum commotio, colore natura planetis consimilis: figura, & imagine species, & similitudo rerum, tempore demum apparitions duratio effectuum, &c. provt innui Ptolemæus lib 2. cap. 9. < 62.> Et quidem quoad naturam, arimet, ex cæsi pro qualitate coloris, intensione, & extensione lucis modò vnius, modò alterius Planetæ naturam referant semper tamen quæcumque sint habent nescio quid ex Martis, & Mercurij natura mixtum: quod etiam ex Ptolemæo obseruat Titus de tls agens lib. 1. cap. 16. idque eo quod ex materia vstibili, ac transmutabili eoagmentantur, qua naturam Martis præseferunt; & insuper cum talis materia inconstans sit, & ex humida transeat in calidam & siccam naturæ M reuri quodammodo assimilantur. Et hic est quod semper siccitates adducant, vredines, corruptiones, ac violenta quæque, siue bella, & occisiones, siue animalia perniciosa, siue pestilentias, aliaque id genus mala, & quò magis in sublimi apparenr, eò vniuersaliores effectus progignunt. < 63.> Quoad situm in cælo, & loci permutationem, sciendum, quod à ratione loci, & imaginis in qua apparent, sumitur coniectatio effectuum resultantium, personarum, & regionum, in quibus dictos effectus præsignant. Si enim ex iis A a iii

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MATHEMATICVM. 377 at stated times appear, because, since they are in the Firmament, on account of the vastness of the expanse, the slowness of their motion, and the amplitude of the epicycle, so long as they are at Apogee they can scarcely be seen; but when they descend to Perigee, they gradually become visible and remain so until they notably recede from it: and this too must be believed to have happened in the Star of Cassiopeia, which in the year 1522 descended to its Perigee, to a place much lower than the other fixed stars; but when it began gradually to diminish, and at length became invisible, then it slowly receded from that point and was so greatly carried away that it could no longer be seen. Yet now the opinion of Anaxagoras has greatly prevailed among later writers, who thought that stars of this kind are nothing other than the meeting of several little stars running through that very thin expanse, which at such a distance represent one and the same star, as is now clear in the case of nebulous stars, and in the Milky Way itself; especially because stars of this kind have always appeared, and only in the Milky Way: and then they vanish, because they are drawn apart from one another. However this may be, it is certain that they always foretell something great and unusual; and their quality is to be inferred from their qualities, motion, position, region, and the time of appearance: thus from the intensity of the light, the intensity of active qualities; from the extension, the stirring of passive ones; from the color, a nature similar to the planets; from the shape and image, the species and likeness of things; from the time of appearance, finally, the duration of effects, etc., as Ptolemy indicates, Book 2, chapter 9. < 62.> And indeed, as to nature, because from the quality of color, and the intensity and extension of light they sometimes resemble the nature of one planet, sometimes of another, nevertheless whatever they are, they always have something mixed of the nature of Mars and Mercury; which Titus also observes from Ptolemy, treating of comets, Book 1, chapter 16, and this because they are formed from combustible and changeable matter, by which they show the nature of Mars; and moreover, since such matter is inconstant, and passes from a humid to a hot and dry condition, they are in a way assimilated to the nature of Mercury. And this is why they always bring droughts, dampnesses, corruptions, and all violent things, whether wars and killings, or harmful animals, or pestilences, and other evils of that kind; and the more they appear in the higher regions, the more universal are the effects they produce. < 63.> As to their position in the sky, and the changing of place, it must be known that from the position of the place and the figure in which they appear is taken the conjecture of the resulting effects, the persons, and the regions in which they foretell said effects. For if from these A a iii

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578 LEXICON quas hucusque memorauimus fuerint, atque in fixatum re- gione apparuerint, itavt ipsæ non permutent locum in Zo- diaco, sed tantum motu ipsius circumagantur, afficient eam Prouinciam, quæ sub tali signo crit: quod si, & ipsæ lo- cum permutent, atque ab vno signo in aliud transeant, transferunt suos effectus etiam ad alias provincias huic si- gno subiectas, aut subsunt verticaliter imagini, in qua illæ apparuerint. At si fuerint pseudostellæ in aëris regio- ne progenitæ non exercent suas vites nisi in eas provincias in quibus apparebit, aut in quas motu suo perueniens eos- dem deriuabit effectus. 64. Quoad tempus denique effectuum ab istis Phoenomenis præsignatorum, eodem ferè modo discurrendum, ac de Eclypsibus, aliisque terminis directionum, ac progressio- num Solis, & Lunæ. Nam quot diebus, & binis horis fulse- rint à regione æterea, & partibus superioribus, tot annos, & menses indicant, si in regione aërea præsertim inferiori, quot horis, tot annos, vel menses præsignant, & tunc qui- dem maximè intendetur effectus, quando luminatia misce- banitur, vel fuerint in locis astrorum, quæ causæ fuerunt huiusmodi portentorum. Hæc omnia ex Tito loco sitato. Plura qui volet videat ipsum Titum, Argolum in Astrono- micis, & iunctinum in tractatu de Cometis. 65. PHOENON, Græcè dicitur Saturnus à Fulgore: sicut etiam. 66. PHOETON Iupiter, nec non stella lucida Acarnat in extremo Eridani sita, à luce qua prædita est, & ob simili- tudinem, quam habet cum Ioue: teste Blancano in sphæra Mundi. 67. PHOSPHOROS etiam dicitur Venus matutina, quasi lucis prodroma & ferens diem, vnde Mart. lib. 8. Phosphore rede diem; quid gaudia nostra moraris? 68. PHOLFK AEBARVGI apud Arabes, teste Kirchero in Oedi- po Ægyptiaco vocatur Zodiacus hoc est sphæra duodecim arcium. 69. PHTHINYSA dicitur apud quosdam Luna decrescens. Au- ctor est Laurent. in Amalthea. 70. PHVONISIE in sphæra Barbarica audit terrius Deca- nus Leonis, manens sub Dominio Martis, significator societatis, non decedendi de iure suo pro rixis vi- tandis. 71. PICA brasilica. Vide Toncan. 72. PICATAPHORA, Octaua domus ab Horoscopo. Vide Epi- cataphora.

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578 LEXICON as many as we have hitherto mentioned may have been, and may have appeared in the fixed region, so that they themselves do not change place in the Zodiac, but are only carried around by the motion of the Zodiac itself, they affect that Province which shall be under such a sign; but if they too change place, and pass from one sign into another, they transfer their effects also to other provinces subject to that sign, or vertically beneath the image in which they appeared. But if they were pseudo-stars generated in the region of the air, they exercise their influence only in those provinces in which they appear, or into which, as they move, they carry the same effects. 64. As for the time of the effects foretold by these phenomena, the same course is to be followed almost as in eclipses and the other terms of the directions and progressions of the Sun and Moon. For for as many days, and in two-hour intervals, as they have shone from the ethereal region and the upper parts, so many years and months do they signify; if in the airy region, especially the lower one, they indicate so many years or months as hours. And then indeed the effect will be most strongly aimed at when the luminaries are mixed, or were in the places of the stars which were the causes of such portents. All these things are from Titus, in the place cited. Whoever wants more, let him see Titus himself, Argolus in the Astronomics, and Juntinus in the treatise On Comets. 65. PHOENON, in Greek, is said of Saturn from its brightness; as also. 66. PHOETON, Jupiter, and also a bright star in Acarnat, situated at the end of Eridanus, from the light with which it is endowed, and because of the similarity it has with Jupiter: witness Blancanus in the sphere of the world. 67. PHOSPHOROS is also called the morning Venus, as the forerunner and bringer of light, whence Mart. lib. 8. Phosphore, bring back the day; why do you delay our joys? 68. PHOLFK AEBARVGI among the Arabs, as Kircher testifies in the Egyptian Oedipus, is called the Zodiac, that is, the sphere of the twelve signs. 69. PHTHINYSA is called by some the waning Moon. Laurent. is the authority in Amalthea. 70. PHVONISIE in the barbarian sphere is called the third decan of Leo, remaining under the dominion of Mars, signifying companionship, not departing from one’s right for the sake of avoiding quarrels. 71. PICA brasilica. See Toncan. 72. PICATAPHORA, the eighth house from the horoscope. See Epicataphora.

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MATHEMATICVM. 379 FINNÆ vulgò Astronomorum dicuntur duo spicilla in 73. extremis Dioptræ partibus constituta ad excipiendos stella- rum radios, aliaque speculanda per quadrantem, Astrola- bium, & alia similia instrumenta PINACIM KOELASMENON in tabulis persicis dicitur Lucida 74. Coronæ Gnostiæ, hoc est discus paruus contractus. PIOTHANATOS. Vide Biothanatos 75. PISCES duodecimum, ac postremum Zodiaci signum in 76. australi semicircuio, sed conterminum Arieti, adeoque commune, aequum, frigidum, & humidum, domicilium Iouis, & Exaltatio Veneris, sic dictum eoquod Sole il- lud intrante omnia in aquis natare videntur. Arabicè vero Haut, & cum articulo Elhaut, & quoniam signum Bicor- poreum est, piscis, qui ad boream infectit dicitur Haut Elschemali; qui verò ad austrum Haut Elgenubi. Qui sub hoc signo nascuntur, inquit Ptolemæus erunt 77. colore albo, capite paruo, maxillis amplis, pectore ma- gno, membris omnibus inæqualiter, & malè dispositis, & vt plurimum cum aliquo vitio inseparabili, qualis esset claudicatio, & gibbositas. Piscium sidus in octaua sphæra habet stellas 34. secundum Ptolemæum, sed iuxta Keplerum 59. sed non admodum nobiles, quippequæ non excedunt[ur] quartam vel quintam magnitudinem præter vnam tertij ho- moris de natura Iouis, & Mercurij quæ est in nodo lini vtrosque pisces nectentis. Eius initium nunc est in gr. 15. Piscium primi mobilis, & protenditur vsque ad gr. 27. Arietis. Pars prior frigida est, media humiditate abundans, vl- tima ob communicationem cum stellis in capite Arietis con- sistentibus caliditate. Quæ ad boream spectit, ventosa; quę. ad Austrum, humida, & aquosa. PISCIS NOTIVS. Vide in V. Notius Piscis. 78. PISCIS VOLANS. Vide Passer. 79. PISTRIX, Cætus, Balena sidus in octaua sphæra, de quo 80. alibi dictum. Hoc vocabulo sæpè vtitur Cicero in Atati Phoenom. PITHETIS Cometæ genus ad formam Dolij vnde & Do- 81. liaris dicitur, habens in concauo fumidæ lucis obscuros quosdam radios, de quo Plin. lib. 2. cap. 25. ad hunc etiam reducitur Tenaculum, PLANETÆ dicuntur ex Græco stellæ non in Firmamento, 81. vt fixæ, sed in propriis cuiusque orbibus fixæ, atque erran- tes singularibus motibus in Zodiaco contra motum primi mobilis ab Occidente in Orientem secundum successionem signorum; vnde & ab errando sunt dicti, nedum apud Græ- A a itij

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MATHEMATICVM. 379 FINNÆ are commonly called by astronomers the two little spikes placed at the 73 extremities of the Diopter, for receiving the rays of stars and for observing other things through the quadrant, astrolabe, and other similar instruments. PINACIM KOELASMENON is called in Persian tables the Lucida 74. of the Gnostic Crown, that is, a small contracted disc. PIOTHANATOS. See Biothanatos 75. PISCES, the twelfth and last sign of the Zodiac in 76. the southern semicircle, but bordering on Aries, and therefore common, equal, cold, and humid; the domicile of Jupiter, and the Exaltation of Venus, so called because when the Sun enters it all things seem to swim in waters. In Arabic, however, Haut, and with the article Elhaut; and since it is a bicorporeal sign, the fish which stretches toward the north is called Haut Elschemali; but the one toward the south, Haut Elgenubi. Those who are born under this sign, says Ptolemy, will be 77. of white color, with a small head, broad jaws, a large chest, all the limbs unevenly and badly formed, and for the most part with some inseparable defect, such as lameness and humpback. The constellation of Pisces in the eighth sphere has 34 stars according to Ptolemy, but according to Kepler 59, but not very noble ones, since they do not exceed the fourth or fifth magnitude except for one of the third ho- moris, of the nature of Jupiter and Mercury, which is in the knot of the line binding the two fishes together. Its beginning is now at 15 degrees of Pisces in the first mobile, and it extends as far as 27 degrees of Aries. The first part is cold, the middle abundant in humidity, the last warm because of its communication with the stars situated in the head of Aries. That which faces the north is windy; that which faces the south is humid and watery. PISCIS NOTIVS. See under V. Notius Piscis. 78. PISCIS VOLANS. See Passer. 79. PISTRIX, Cetus, the constellation Balena in the eighth sphere, concerning which 80. something has been said elsewhere. Cicero often uses this word in Atati Phoenom. PITHETIS, a kind of comet in the shape of a Dolium, whence it is also called Doliaris, having in the hollow of its smoky light certain dark rays, of which Pliny speaks in book 2, chapter 25. To this also belongs Tenaculum, PLANETÆ are so called from the Greek for stars not in the Firmament, like the fixed stars, but fixed in their own orbits and wandering with singular motions in the Zodiac against the motion of the first mobile from West to East according to the succession of the signs; whence they are also called wanderers, not only among the Gre- A a itij

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cos, sed etiam, apud Latinos, qui eos errores, seu erraticas stellas appellauere. Hi septem omninò sunt; (vt taceam de stellulis comitibus Louis, & Saturni: quas non ita pridem Galilæus detexit, & circa illos, & cum illis duplici motu rotari) Saturnus, Iupiter, Mars, Sol, Venus, Mercurius, Luna. Ex quibus primum locum, hoc est summum, proximum Firmamento obtinet Saturnus, mox Iupiter; inde Mars, posteà Sol, Venus, Mercurius, & Luna per ordinem, itavt hæc vltimum locum teneat, adeoque minimum orbem terræ propinquum, vt ex paralaxi singulorum, aliisque obseruationibus euidenter deductum est. Porrò multa sunt in quibus planetæ à reliquis astris discordant: Primò in motu, qui vt dixi in singulis est peculiaris, & proprius nullique alteri communis: quando astris vns est omnium, qui propriè illorum non est, sed orbis, in quo fixa sunt. Secundò in Luce, cum alia sit fixarum lux, alia errantium siderum: Etsi enim ambo mutuentur lumen à Sole fixa tamen habent nescio quam primigeniam, & insitam lucem, quæ posteà à Sole intenditur, & vt ita dicam viuificatur, vnde est scintillatio illæ ipsis propria, & intuentium oculos præstringens: Planetæ verò hoc non habent, vt etiam Aristoteles obseruauit, sed sunt corpora densa, in seipsis obscura (quod videre maximè est in Luna, cum Solis corpore copulata in Eclipsi.) Tertio color, & diuersus influendi modus, & alia, quæ recensuimus cum de fixis. Vt proinde maxima altercatio sit inter Astronomos, quinam primas teneant, fixæ ne, an planetæ. De horum natura, loco, magnitudine, aliisque proprietatibus. Vide in propriis locis. 83. PLANISPHÆRIVM, vt ex etymo nominis constat, dicitur sphæra in plano descripta Est enim instrumentum planum totam in se doctrinam primi mobilis continens, circulos, polos, sidera, ascensiones, descensiones, parallelos, aliaque ex perspectiuæ præceptis delineata oculis exhibens, vnde directiones probè perfici queunt, arcus diurni & nocturni omnium siderum indagari ad quamcumq[ue] poli elevationem. Est in triplici differenria: Alterum Gemmæ Frisij cuius diameter æquatorem præsignat, & puncta cardinalia Arietis, & Libræ incidunt in ipsum centrum, quem linea recta secans refert axem mundi ad vtrumque polum terminans à quibus ellipses parallelæ ductæ transeunt per singulas diuisiones Zodiaci: ipso etiam Zodiaco per alias etiam ellipses æquatori parallelas abvno ad alium Tropicum designato, ac definito. Alterum Io: Royas, huic, prorsus affine, nisi quod hic paralleli ad

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not only, but also among the Latins, who called them errors, or wandering stars. These seven are altogether: (not to say anything of the little companion stars of Jupiter and Saturn, which not long ago Galileo discovered, and which revolve around them and with them in a double motion) Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon. Of these, Saturn holds the first place, that is, the highest, nearest to the Firmament; then Jupiter; after him Mars; then the Sun, Venus, Mercury, and the Moon in order, so that the Moon holds the last place, and consequently the smallest orbit, closest to the earth, as has been clearly deduced from the parallax of each and from other observations. Moreover, there are many things in which the planets differ from the remaining stars: First, in motion, which, as I said, in each is peculiar and proper, and common to no other; whereas the motion of the stars is one for all, which is not properly theirs, but that of the sphere in which the fixed stars are placed. Second, in light, since the light of the fixed stars is one thing and that of the wandering stars another: for although both borrow light from the Sun, the fixed stars nevertheless have, I know not what, a primordial and inherent light, which is afterwards intensified by the Sun and, so to speak, given life, whence comes that scintillation proper to them and dazzling to the eyes of those who look at them; but the planets do not have this, as Aristotle also observed, but are dense bodies, dark in themselves (this is seen most clearly in the Moon, when joined to the body of the Sun in an eclipse). Third, color, and a different mode of influencing, and other things which we have listed when speaking of the fixed stars. Hence there is the greatest controversy among astronomers as to which have the first rank, the fixed stars or the planets. See in their proper places for the nature, position, size, and other properties of these. 83. PLANISPHÆRIUM, as the etymology of the name shows, is so called because it is a sphere described on a plane. It is a flat instrument containing within itself the whole doctrine of the first mobile, displaying to the eyes circles, poles, stars, ascensions, descensions, parallels, and other things drawn according to the precepts of perspective, by which directions may be properly carried out, and the diurnal and nocturnal arcs of all the stars may be investigated for any elevation of the pole. It is of three kinds: the first, that of Gemma Frisius, whose diameter marks the equator, and the cardinal points of Aries and Libra fall into the very center, which a straight line cutting through represents the axis of the world, ending at either pole, from which drawn parallel ellipses pass through the individual divisions of the Zodiac; the Zodiac itself is also marked by other ellipses parallel to the equator from one Tropic to the other, and defined. The second, that of Io: Royas, is wholly akin to this, except that here the parallels to

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MATHEMATICVM. 381 æquatorem non per ellipses, sed per lineas rectas designantur. Tettium tandem, quod vulgò dicitur Astrolabium, in quo centrum refert polum Arcticum, diameter horizontem rectum, linea secans Meridianum; Retè primum mobile, ac cælum stellarum, cum principalioribus fixis in ea longitudine, & latitudine, in qua nunc temporis sunt: tandem tabulæ ad singulas poli eleuationes constructæ situm mundi, & singula horizonta obliqua, cum suis circulis parallelis, seu altitudinum quos vocant almicantarath, nec non circulis verticalibus parallelis ad meridianum dictis Azimuth, quorum ope cuiusque stellæ positus in situ mundi facillimè nosci poterit. De huius fabrica & vsu scripsit Io: Stophlerinus Latinè, & Ignatius Dantes italicè: de illis Auctores, à quibus denominantur. PLANVM apud Geometras dicitur superficies recta, seu < 85.> corpus habens superficieni rectam hoc est vt definit Euclides lib. 1. prop. 7. quæ ex æquo suas intetiacet lineas: per quod opponitur corpori sphærico, & circulo, quæ linea, aut supersicie curua circumscribuntur. Vnde vulgatum illud Axioma, quod corpus sphæricum non tangit planum, nisi in puncto. PLATICVS ASPICTVS dicitur ad differentiam Partilis. Est < 86.> enim radius proiectus à planeta non quidem ad corpus alterius planetæ, cum non sit in exquisita distantia, sed ad orbem sphæræ lucis illius: vt ad Saturnum intrà spatium decem graduum ante, & rettò; ad Iouem 12. ad Martem gr. 7. min. 30. ad Solem gr. 17. ad Venerem gr. 8. ad Mercurium gr. 12. ad Lunam gr. 12. min. 30. tanta est enim quantitas Orbis ipsorum, ad quam lux, & activitas lateraliter se extendit. Quemadmodum etiam fixæ primæ magnitudinis habent Orbem hinc inde latum ad gr. 7. min. 30. Secundæ magnitudinis gr. 5. min. 30 Tertiæ gr. 3. m. 40. Quartæ gr. 1. min. 30. Portò vel iste aspectus plaricus proijcitur citrà, vel ultrà corpus Planetæ; si citrà, dicitur Applicatio, applicat enim planeta aspiciens, ac se disponit ad habendum cum altero familiaritatem, & aspectum partitem: Vel iam fuit in partili, & inde per motum suum ab eo separatur, ita tamen, vt adhuc sit intrà fines orbis illius, & hæc dicitur Separatio, seu Defluxus, vt dictum est suo loco. Quæ quidem in Luna maximè attenditur: & quo aspectus erit partili vicinior, eo efficacior: sicut etiam potentior qui ad partitem se disponit, quam qui à partili recedit. Vide quæ ibi diximus, similiter ad aspectum platicum applicanda. PLAVSTRVM fidus in cælo ad borealem plagam intra He- < 87.>

Transcription: Translated (English)

MATHEMATICVM. 381 are marked not by ellipses, but by straight lines. The third is finally what is commonly called the Astrolabe, in which the center represents the Arctic pole, the diameter the horizon, the secant line the Meridian; the Rete the first mobile, and the heaven of the stars, with the principal fixed stars in the longitude and latitude in which they are at present: finally, plates constructed for each elevation of the pole show the position of the world, and each oblique horizon, with its parallel circles, or altitude circles called almicantarath, as well as the vertical circles parallel to the meridian called Azimuth, by means of which the position of any star in the arrangement of the world can most easily be known. Of its construction and use Io: Stophlerinus wrote in Latin, and Ignatius Dantes in Italian: of those, the authors from whom they are named. PLANE among geometers is called a straight surface, or < 85.> a body having a straight surface, that is, as Euclid defines it, book 1, proposition 7, which interposes its lines evenly; by which it is opposed to a spherical body, and to a circle, which are enclosed by a curved line or surface. Hence the common axiom, that a spherical body touches a plane only at a point. PLATIC ASPECT is called, as distinct from Partile. For < 86.> the ray projected from a planet is not indeed to the body of another planet, since it is not at an exact distance, but to the orb of that planet's sphere of light: thus to Saturn within the space of ten degrees before, and exactly; to Jupiter 12; to Mars 7 deg. 30 min.; to the Sun 17 deg.; to Venus 8 deg.; to Mercury 12 deg.; to the Moon 12 deg. 30 min.; for so great is the quantity of their orb, to which light and activity extend laterally. Just as the fixed stars of first magnitude also have an orb extending on either side to 7 deg. 30 min.; of second magnitude 5 deg. 30 min.; of third 3 deg. 40 min.; of fourth 1 deg. 30 min. Moreover, this platic aspect is projected either short of or beyond the body of the planet; if short, it is called Application, for the planet looking on applies itself and prepares to have familiarity and a partile aspect with the other: or it has already been in the partile aspect, and from there by its motion is separated from it, yet so that it is still within the bounds of that orb, and this is called Separation, or Defluxion, as was said in its place. This is especially considered in the Moon: and the nearer the aspect is to partile, the more effective it is: just as also the stronger is one who is preparing himself toward partility than one who recedes from the partile. See what we said there, likewise to be applied to the platic aspect. PLAVSTRVM a fixed star in the sky toward the northern region within He- < 87.>

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LEXICON licem, seu Vrsam maiorem vel ipsis bubulcis & plaustri du- ctoribus notum (à quibus fortè ei nomen est inditum) quip- pe quod formatur septem claris, & satis conspicuis stellis per ordinem sic dispositis, vt quaruot borealiores abeant in figuram parallelogrammi rectanguli repræsentantis qua- tuor plaustri rotas, tres verò reliquæ australiores repræsen- tent temonem, seu etiam equos vnum post alium positum ad illud trahendum; vide, & Equi primus, secundus, & ter- tius dicti sunt. Arab dicitur Alrunabach, quod promiscuè vsurpatur tam de maiori quam de minori plaustro, quod est Vrsa minor, quæ in eandem prorsus figuram abit, nisi quod sunt ad inuicem obuersa 11. Referta utem Kircherus in Odipo Ægyptiaco hoc fidus ab Christianis Arabibus Naasch Laazar, hoc est Feretrum La- zari vocitari, ac tres lucidiores caudæ modo dictas, quæ in Plaustro efformant temonem appellari Benach Naasch, id est, Filias Feretri, quæ sunt prima caudę Maria Magdalene, media Martha, vltima earum ancilla. Porrò Omnes hæ stellæ sunt secundæ magnitudinis, prærer eam que est prima in eductione caudæ, fingiturque esse secunda rota, quæ est tertij honoris, ac de natura Saturni, & Mercurij, cum aliè sex sint de narura Martis. Romæ hoc fidus num- quam occidit, sed postrema solum in cauda dicta Equus primus Arab. Elkerd Bennenaz radit horizontem. Nihilo- minus eosdem ferè parit effectus quando est in parte cæli ascendente, vel descendente, ac si foret in Ortu, vel in oc- casu. Itaque exoriens, inquit Pontanus, facir domitores ferarum, & vrsorum, & qui Elephantos ducant in scenam, ac gesticulare doceant, vel mansuecant. Occidens verò minatur dilaniationem ab Vrso, vel aliis feris, præsertim si Mars male aspexerit. 19. PLEIADES septem item stellæ sunt in pectore Tauri consi- stentes, conglomeraræ tamen & minores prædictis, sic di- ctæ ex Græco à quod ortu suo navigationis tem- pus ostendant. Latini eas dixere Vergilias à Verè, quia cit- câ æquinoctium vernum oriuntur. Ortu suo Fauonium ex- citant, occasu Austrum. Cum occidunt matutino tempore, quod accidit citcâ initium Aurumni, si cadant nubilo cælo hyemen pluuiosam decernunt, si sereno, hyemis asperita- rem. Cum Saturno congredientes turbant aërem, replent illum caligine, pluuias, & niues faciunt: cum Mercurio etiam ventos: id ipsum præstant occidentes cum sole. Cæte- rum Pleiades vniuersaliter sunt stellæ pluuiosæ nimis, tem- pestuosæ, ac Nautis intensa. Oriuntur autem Romæ ferè

Transcription: Translated (English)

LEXICON the Great Bear, or the one known even to ox-drivers and wagon-drivers (from whom perhaps it received its name), since it is formed of seven bright and quite conspicuous stars arranged in order in such a way that the four more northerly form the figure of a rectangular parallelogram representing the four wheels of the wagon, while the three remaining more southerly stars represent the pole, or even the horses placed one after another to draw it; see also the first, second, and third Horse. The Arabs call it Alrunabach, a name used indiscriminately both for the Great and for the Little Wagon, which is Ursa Minor, and which falls into exactly the same figure, except that the parts are turned opposite to each other. 11. Kircher reports in his Oedipus Aegyptiacus that this constellation is called by the Christian Arabs Naasch Laazar, that is, the Bier of Lazarus, and that the three brighter stars, just mentioned as forming the pole in the Wagon, are called Benach Naasch, that is, the Daughters of the Bier, namely the first the star of Mary Magdalene, the middle one Martha, the last their maidservant. Moreover, all these stars are of the second magnitude, except the one that is first in the extension of the tail; and it is imagined to be the second wheel, which is of the third order, and of the nature of Saturn and Mercury, while the other six are of the nature of Mars. At Rome this constellation never sets, but only the last star in the tail, called by the Arabs the first Horse, Elkerd Bennenaz, brushes the horizon. Nevertheless, it produces almost the same effects when it is in the ascending or descending part of the sky as if it were at rising or setting. Thus, when rising, says Pontanus, it makes tamers of wild beasts and bears, and those who lead elephants on stage and teach them tricks, or tame them. When setting, however, it threatens dismemberment by a bear or other wild beasts, especially if Mars looks upon it unfavorably. 19. THE PLEIADES are likewise seven stars situated in the breast of Taurus, though more clustered together and smaller than the foregoing. They are so called from the Greek because their rising indicates the season for navigation. The Latins called them Vergiliae, from ver, spring, because they rise around the vernal equinox. Their rising brings about the west wind; their setting, the south wind. When they set in the morning, which happens around the beginning of autumn, if they fall under a cloudy sky they foretell a rainy winter; if under a clear sky, a severe winter. When they come together with Saturn they disturb the air, fill it with gloom, and cause rain and snow; with Mercury they also bring winds. The same effects do they produce when they set with the sun. In general, the Pleiades are stars that are excessively rainy, stormy, and troublesome to sailors. They rise at Rome about

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MATHEMATICVM. 183 cum gr. 18. Tauri, & occidunt cum 17. In Genethliacis, si cum luminaribus reperiantur, aut omninò cæcitatem inducunt, aut sanè visus acumen obtundunt: quod & portendunt horoscopantes, præsertim cum prauo Mattis radio aut Saturni. Sed præstat hic apponere quæ de pleiadibus exorientibus in alicuius Natiuitate cecinit Pontanus in sua Vtania. Sic enim habet lib. 3. Oblectant & adhuc artes, studiumque colendi Oris, & antiqui reuocantur pectora sensus Et cura molles, & grata pocula mensa, Luxusque illecebraque & olentia tempora fertis Hos Nati mores referant, quibus aurea crinem Fibula subnectis, roseo quibus enitet ore Purpura, quasitusque decor, similisque puella Cultus, & Assyriam redolent lita pectora myrrham. Vina placent, hilaresque ioci, & petulantia lir. qua. Mordacesque sales, intinctaque verba veneno. Semper amant, & cura nouos ex suscitat ignes Ac domito regnat victrix in corde libido. Nec minus ambitio tenet, & certamen honorum: Poeniteat generis samen, & se Coena malint, Aut in foemineam penitus transire figuram. Hucusque prolixè nimis Pontanus. De iis verò in occasu repertis ait, quod portendunt mortem ex naufragio, aut inter epulas, atque ebrietates. PLENILUNIVM quid significet, sat suo etymo præfert: 90. denotat enim tempus cum Luna in solis oppositione luminibus plena est: Vnde Plin. lib. 18 cap 12. Quùm Sole, inquit, occidente Luna orietur ex aduerso, itavit pariter aspiciantur tunc eris Plenilunium. Græci Panselene vocant, vt nos paulò antè adnotauimus. Plenilunij tempore quid fieri iiceat, quidue non explicat idem Plin. cod. lib. 18. c. 28. PLINTIS, seu Quadra Instrumentum Mathematicum mensurandis rebus idoneum. Hiuc Plintides olim dicebantur quadrati læterculi, quibus Romani quæstorios agros in centurias diuidebant, easdem in quinquagenis iugeribus quadratas limitibus claudentes, atque ita aliis vendentes. De qua re vide quæ habet Hyginus in lib. de limitibus. POGONIAS Græcæ, Latinè Barbatus dicitur Cometæ genus habens radios ex parte profilientes, quibus caput hominis barbatum præfert. De eo Plin. lib. 2. cap. 25. POLLVX aliter Geminorum dictus etiam Hercules fidus 93.

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MATHEMATICUM. 183 with 18° of Taurus, and they set with 17°. In nativities, if they are found with the luminaries, they either bring on blindness altogether, or certainly blunt the keenness of sight: and so the astrologers also foretell, especially when there is the evil ray of Mars or Saturn. But it is better here to add what Pontanus sang about the rising Pleiades in someone’s nativity, in his Utania. For thus he has it, book 3. They delight even now in the arts, and in the study of cultivation; the care of old customs is recalled to their hearts, and gentle concern, and the pleasant cup at table, and luxury and allurements, and perfumed seasons they bring. These born under them will have such manners, with a golden clasp binding the hair, with purple shining on the rosy face, with sought-after grace, and a maiden-like adornment, and their breasts scented with Assyrian myrrh. Wine pleases them, and cheerful jests, and wanton speech. They always love, and care for new fires is awakened; and desire, once mastered, reigns victorious in the heart. No less does ambition hold them, and rivalry for honors: let them be ashamed of their race, and they would rather dine, or even pass entirely into the form of a woman. Thus far Pontanus, excessively at length. But of those found in the setting he says that they portend death by shipwreck, or at banquets and drunken revels. PLENILUNIUM, what it signifies, the etymology itself sufficiently shows: 90. for it denotes the time when the Moon is full, in opposition to the Sun. Hence Pliny, book 18, chapter 12: when, he says, the Sun is setting, the Moon rises opposite, so that they are seen at the same time; then it is the Full Moon. The Greeks call it Panselene, as we noted a little above. What may or may not be done at the time of the full moon is explained by the same Pliny, book 18, chapter 28. PLINTIS, or Quadra, a mathematical instrument suitable for measuring things. Hence plintides were formerly called the square blocks by which the Romans divided the quaestorian lands into centuriae, enclosing them in square plots of fifty iugera by boundary lines, and then selling them to others. On this matter, see what Hyginus has in his book on boundaries. POGONIAS, Greek; in Latin, “bearded” is the name of a kind of comet, having rays projecting from one part, by which it presents the head of a bearded man. On this, Pliny, book 2, chapter 25. POLLUX, otherwise also called one of the Twins, and also Hercules fidus 93.

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LEXICON in octava sphæra constans stellis 18. quas ferè pari numero sibi diuidunt cum Castore altero geminorum ipsum præcedente. In capite Pollucis est stella subrufa, nix, violenta de natura Martis, de qua pluries dictum est præsertim in V. Hercules. 94. POLI dicuntur duo cardines ex diametro oppositi, seu duo puncta axem terminantia, circà quem mobile aliquod rotatur, & circumuoluitur. Quoniam autem in cælo est præcipuè huiusmodi motus circularis regulatus, & numquam intermissus, & in cælo plura mobilia sunt, quorum quodlibet incedit per suam orbitam, quæ est circulus magnus sphæram in duas partes æquales secans, ideò Poli in celo potissimum attenduntur, & quot orbitæ ac mobilia sunt, tot etiam concipiuntur geminati poli, circa quos singula voluantur, qui necessariò debent distare hinc inde à dictis circulis per gradus 90 Immò vt benè aduertit Clauius, quilibet sphæræ circulus, siue paruus, siue magnus duos concipitur habere polos, circà quos, si moueretur, vniformiter volueretur: Nam polus aliud non est, quam punctum illud in conuexa superficie sphæræ existens, & correspondens in axe centro eiusdem circuli, à quo omnes lineæ recta ad circulum ductæ æquales sunt: Sicque poli Horizontis intelliguntur esse Zenit, & Nadir: Poli Meridiani duo puncta ortus & occasus æquatoris in horizonte: Poli coluri solstitiorum sunt duo puncta æquinoctialia Aretis, & Libræ: Poli coluri æquinoctiorum sunt, duo puncta solstitialia Cancri, & Capricorni: oli Æquatoris & circulorum ipsi parallelorum sunt Poli Mundi Arcticus, & Antarcticus: tandem Zodiaci & Eclipticæ sunt poli Zodiaci, qui describunt duos circulos minores Arcticum & Antarcticum distantes 13. gradibus, & semis à polis Mundi. Nihilominus polorum nomine, quando absolutè, & sine adjuncto dicuntur, antonomasticè veniunt Poli Mundi quoniam ipsi soli consistunt omninò immobiles, & circà ipsos omnes quæcumque sphæræ spatio 24. horarum motu primi mobilis raptè rotantur. Inde poli Zodiaci, circà quos voluuntur omnes secundi mobiles ab Occidente in Orientem statis temporibus, cum propriè poli in ordine ad mobilia dicantur: Vnde deriuatum nomen habent à Græco verbo πολις, quod idem sonat, ac verbo, & circumago. Et quotus quisque cuiusuis sphæræ motus est, totidem bini poli concipiendi sunt circà quos illæ voluntur. Hinc poli Zodiaci propriè solius solis, & Orbitæ eius, seu mavis dicam Eclipticæ sunt: reliquorum planetarum, seu Orbium

Transcription: Translated (English)

LEXICON in the eighth sphere, consisting of 18 stars, which are distributed in almost equal number with the other of the Twins, Castor, preceding him. In the head of Pollux there is a reddish star, of snowy, violent nature, of Mars, concerning which much has been said, especially in V. Hercules. 94. POLES are called the two diametrically opposite pivots, or the two points terminating the axis, around which some moving body turns and revolves. But since in the heavens there is especially this kind of regulated circular motion, and one never interrupted, and since in the heavens there are several moving bodies, each of which proceeds along its own orbit, which is a great circle dividing the sphere into two equal parts, therefore the poles in heaven are chiefly considered, and as many orbits and moving bodies as there are, so many paired poles are also conceived, around which each revolves, which must necessarily be distant on either side from the said circles by 90 degrees. Indeed, as Clavius well notes, every circle of a sphere, whether small or large, is conceived to have two poles, around which, if it were moved, it would turn uniformly: for a pole is nothing other than that point existing on the convex surface of the sphere, corresponding on the axis to the center of that same circle, from which all straight lines drawn to the circle are equal. And thus the poles of the Horizon are understood to be the Zenith and Nadir; the poles of the Meridian, the two points of sunrise and sunset of the equator on the horizon; the poles of the colure of the solstices are the two equinoctial points, Aries and Libra; the poles of the colure of the equinoxes are the two solstitial points, Cancer and Capricorn; the poles of the Equator and of the circles parallel to it are the Arctic and Antarctic poles of the World; finally, those of the Zodiac and the Ecliptic are the poles of the Zodiac, which describe two smaller circles, Arctic and Antarctic, distant 13 degrees and a half from the poles of the World. Nevertheless, by the name of poles, when they are said absolutely and without any addition, the poles of the World are understood by antonomasia, since they alone remain entirely immovable, and around them all things whatsoever, in the space of 24 hours, are whirled by the motion of the first mobile. Hence the poles of the Zodiac, around which all the second mobiles revolve from West to East at stated times, when poles are properly spoken of in relation to moving bodies: whence they have a name derived from the Greek verb πολις, which has the same meaning as the verb, and move round. And however many the motions of any sphere may be, so many pairs of poles must be conceived around which they are turned. Hence the poles of the Zodiac properly belong to the Sun alone, and to its orbit, or, if you prefer, to the Ecliptic: of the remaining planets, or orbits

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MATHEMATICVM. 385 roridem etiam singulis proprij concipiendi sunt tantum- dem ab Eclipticæ polis distantes, quantum orbitæ singulo- rum in maxima latitudine ab orbita Solis exorbitant. Porrò cum poli isti puncta sint in cælo, vt dixi tantum < 95.> concepta, neque oculis petua, ex situ, & pro ratione mo- tus dehiniuntur. Et polus quidem Arcticus Mundi hoc rem- pore ad hoc vt internoscatur, arque adeo, vt vbique loco- rum eiusdem supra horizontem elevatio dignosci possit; imaginari debemus lineam rectam ab stella polari ad aliam sibi proximam in cauda Vrsæ minoris, super qua posteâ li- nea constituatur triangulum æquilaterum versus caput Vrsæ maioris; nam vbi definit apex dicti trianguli, ibi situ est polus; cuius postea altitudo facilè per quadrantem, aut aliud simile instrumentum inuestigari poterit. Circà finem verò præsentiis sæculi non erit opus hac diligentia, nam stella polaris, quæ nunc temporis habet declinationes gr. 88. tunc habebit declinationem gr. 90 ac proinde in ipsum polum incidet, vt diximus in V. Alruchabak. POLYCHRONIVM ex Græco propriè dicitur quod est lon- < 96.> geum, diuturnum & multi temporis. Hinc apud quosdam Astronomos vsus inoleuit, vt planetæ ponderosi, quales maximè sunt Saturnus, & Iupiter Polychronij appellaren- tur; quoniam tardi motus sunt, & multum temporis insu- munt in perficienda revolutione sua in Zodiaco. POLYDRVM apud Geometras dicitur corpus multis pla- < 97.> nis faciebus constans. POLYGONVS, seu Polygonius, item apud Geometras signi- < 98.> ficat figuram multis angulis constantem. Sicut etiam. POLYGRAMMVS figura dicitur multis lineis interstincta. < 99.> Hinc gemma quædam smaragdo petsimilis, quæ pluribus lineis albis distincta est, ac toti Orienti (vt author est Pli- nius lib. 37 cap. 9.) pro amuletho inseruit, Polygrammos appellatur. PONDEROSVS apud Astronomos audit Planeta, qui velut < 100> graui pondere pressus tardè, & cunctanter incedit, quales sunt Saturnus, Iupiter, & Mars, qui ex natura sua tales di- cuntur, quia numquam motu suo diurno acquirere valent gradum vnum in Zodiaco: licet aliàs Ponderosus in toto rigore dicatur respectivè ad alium, qui sit velocioris mo- tus: Vnde Iupiter Saturno comparatus dicitur leuis, non ponderosus: è contrà Ponderosus respectu Martis & alio- rum; Mars respectu Solis, &c. Verum ex accidente fieri po- test, vt qui natura sua Ponderosi sunt, per alterius postea retrogradatione, aut etiam directionem, qua sunt stationa-

Transcription: Translated (English)

MATHEMATICVM. 385 The poles likewise of each proper orbit are to be conceived as being as far from the poles of the Ecliptic as the orbit of each, in its greatest latitude, departs from the orbit of the Sun. Moreover, since these poles are points in the heavens, as I said, merely conceived, and not perceived by the eyes, they are defined by their position and in accordance with motion. And indeed the Arctic Pole of the World at this time, in order that it may be recognized, and thus that the elevation of its position above the horizon in each place may be known, we must imagine a straight line from the pole star to another star near it in the tail of Ursa Minor; then upon that line let there be established an equilateral triangle toward the head of Ursa Major; for where the apex of said triangle ends, there is the pole situated; whose altitude afterward can easily be sought by means of a quadrant, or some similar instrument. Near the end, however, of the present age there will be no need of this diligence, for the pole star, which at present has a declination of 88 degrees, will then have a declination of 90 degrees and will therefore fall upon the pole itself, as we said in V. Alruchabak. POLYCHRONIVM is properly said, from the Greek, of that which is long-lived, long-lasting, and of much time. Hence among certain astronomers the usage has arisen that the ponderous planets, such as especially Saturn and Jupiter, are called Polychronia; because they are slow in motion and take a great deal of time to complete their revolution in the Zodiac. POLYDRVM is said by geometers of a body consisting of many plane faces. POLYGONVS, or Polygonius, likewise among geometers signifies a figure consisting of many angles. POLYGRAMMVS is a figure distinguished by many lines. Hence a certain gem, akin to emerald, which is marked off by several white lines and was used by all the East as an amulet, as Pliny is author of in book 37, chapter 9, is called Polygrammos. PONDEROSVS among astronomers is the name of a planet which, as though pressed down by a heavy weight, advances slowly and with reluctance, such as Saturn, Jupiter, and Mars, which are said to be such by nature, because by their diurnal motion they can never gain one degree in the Zodiac; although otherwise Ponderosus is said in full rigor relatively to another that is of swifter motion: whence Jupiter, compared with Saturn, is called light, not ponderous; by contrast ponderous in respect of Mars and others; Mars in respect of the Sun, etc. But by accident it can happen that those which by nature are ponderous, by another’s retrogradation afterward, or even by direction, during which they are stationary—

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386 LEXICON rij, & lentè nimis, imò etiam quandoque insensibiliter mo- uentur, dicantur leues, & illi Ponderosi, qui alioqui natura sua sunt leues. 101 PRÆSPE Stella est Nebulosa, in pectore Cancri de natura Martis, & Lunæ existens nunc temporis in gr. 3. Leonis cum vno ferè gradu latitudinis borealis: Stella, in- quam, infensa nimis, & pessimæ qualitatis; quippe cum So- le, aut Saturno repentinis motibus turbat aërem, ventos in- festissimos ciet, pluuias, & imbres impetuosos ex repenti- no affert, fulgura facit, & tonitrua, atque suo tempore ni- ues. In Genethliacis verò cum luminaribus affert cæcitatem aut debilitatem in oculis: in horoscopo autem reperta ho- minem violentum facit, seditiosum, vagum, inconstantem, & etiam oculorum affectionibus laborantem. In eo sidere ope Telescopij Galilæus obseruauit stellas omnino 36 eo ordine, quo ipse exponit in Nuncio sidereo. Oritur Romæ cum gr. 2. Leonis, occidit verò cum quatuor. De ea Plin. lib. 16, cap. ultim. Hæc, inquit, cum sereno calo appa- rere desserit, atrox hyems sequitur. 102 PRÆSTER. Græcè, Latinè Turbo: ventus est impetuo- sissimus, ac vorticosus, ex eorum genere, qui de fundo at- que ex hiatibus terræ desiliunt, atque in superna elati irre- gulariter perflant, omnia sibi obuia violento nisu detur- bantes: quales sunt etiam Ecnephias Typhon, ac Vortex, necnon alij, (qui tamen in istos recidunt) de quibus lo- quitur Arist. in Meteoris. Ab Ecnephia antem eatenus diffe- re Præstera inquit Plin. lib. 1. cap. 48. quatenus eo fuit ar- dentior, & contactu amburit pariter, ac prosternit. Et cap. 49. addit eum eodem modo à Typhone differre, quo flam- ma ab igne. Hic latè, inquit, funditur statu, illud con glo- batur impetu. 103 PRÆVENTIONALIS apud Astrologos vocatur ea Natiui- tas, Anni initium, aut aliud quodvis rerum exordium, quod proxime præuenit luminarium opposicio: sicut coniunctio- nalis dicitur Genesis, quæ subsequitur coniunctionem. A loci enim dispositore, in quo celebrata fuit alterutra, auspicari solent statum illius rei, & etiam in Natiuitatibus verum gradum horoscopantem, quem Arabes Annimodat dixere. Vide sub hoc verbo. 104 PRIMVM MOBILE. Vide in V. Motus. 105 PRINCIPATVS, teste Abraham Auenarre, in suo introdu- ctorio, idem est, ac Orientalitas à Sole respectu Superio- rum, & Occidentalitas respectu Inferiorum. Sic enim in- quit cap. 7. propè finem. Principatus est, vt sint, tres Superio-

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386 LEXICON are said to be light, and those ponderous which, otherwise by their nature, are light. 101 PRÆSPE. A nebulous star in the Breast of Cancer, of the nature of Mars and the Moon, now in 3 degrees of Leo, with nearly one degree of northern latitude: a star, I say, exceedingly hostile, and of the worst quality; for when it is with the Sun or Saturn, by its sudden motions it disturbs the air, stirs up the most violent winds, brings sudden showers and heavy rains, makes lightning and thunder, and at its proper season snow. In genethliacal figures, however, when joined with the luminaries, it brings blindness or weakness in the eyes; in a horoscope, if it is found there, it makes a man violent, seditious, wandering, inconstant, and also afflicted with disorders of the eyes. In that constellation Galileo observed, by means of the telescope, 36 stars altogether, in the order in which he himself sets them out in the Sidereal Messenger. It rises at Rome with 2 degrees of Leo, but sets with four. Of it Pliny, book 16, ch. last, says: When this appears in a serene sky, a severe winter follows. 102 PRÆSTER. In Greek, in Latin Turbo: it is a very violent and whirling wind, of the kind that spring from the depths and from the chasms of the earth, and, lifted up into the upper regions, blow irregularly, violently driving down everything in their path: such also are Ecnephias, Typhon, and Vortex, as well as others, which however fall into these kinds, of which Aristotle speaks in the Meteors. But Præster differs from Ecnephias in this respect, says Pliny, book 1, ch. 48, that it was the more ardent, and by contact both scorches and overthrows. And ch. 49 he adds that it differs from Typhon in the same way that flame differs from fire. This, he says, spreads broadly in its state; that is gathered into a mass by its violence. 103 PRÆVENTIONALIS, among astrologers, is called that nativity, the beginning of a year, or any other commencement of events, which immediately precedes the opposition of the luminaries: just as that which follows the conjunction is called conjunctional genesis. For from the dispositer of the place in which either was celebrated, they are accustomed to foretell the state of that matter, and also in nativities the true degree horoscoping, which the Arabs called Annimodat. See under that word. 104 PRIMUM MOBILE. See under V. Motus. 105 PRINCIPATVS, according to Abraham Avenarr in his Introductory Work, is the same as Orientality with respect to the superior planets, and Occidentality with respect to the inferior. For thus, he says at chapter 7 near the end: Principatus is, that there are three superio-

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MATHEMATICVM. 107 Orientales à Sole ab hora, qua visione incipiunt oculari videri; tanequesunt in eius principatu sublimi, donec inter eos, & Solem interueniat aspectus sextilis, & ab inde vsque ad quadratam aspectum minuetur principatus eorum sublimitas: & deinde ad stationem secundam non est ipsorum principatus; etsi fuerint huiusmodi planeta à Sole Orientales, & Occidentales à Luna, non erit isto sublimior principatus. Trium verò inferiorum planetarum incipiet principatus ab hora visionis in Occidente post solis coniunctionem; & principatus elatio Veneris, & Mercurij permanet donec retrogradentur, & si fuerint Occidentales à Sole, à Lunaque Orientales, nullus isto sublimior principatu. Luna autem vsque ad mensis dimidium principatur. Huc vsque Abraham Quare autem Orientalitas in superioribus, & Occidentalitas in inferioribus faciat huiusmodi principatum, seu faciat planetas validiores dictum est in V. Occidentalis Planeta. PRISMA definitur ab Euclide lib 10. defin. 13. quo! sit si- 106 gura solida, quæ planis continetur, quorum aduersa duo sunt, & æqualia, & similia, & parallela; alia verò parallelogramma. Ex qua definitione aperiè colligitur ipsum aliud planè non esse, quam columnam quamdam lateratam æqualis crastitudinis, cuius bases oppositæ æquales sunt, similes, & parallelæ, siue sint triangulares, siue quadrangulares, siue pentagonæ, &c. Vnde tot parallelogramma continebit quodlibet Prisma, quot latera, vel etiam anguli in vnoquoque oppositorum planorum reperiuntur. Vide quæ diximus in verbo Parallelopipedum. PROCELLÆ nomine veniunt genericè omnes pseudouenti, qui videlicet è fundo, vel hiatibus terræ exiliunt, & cum magno impetu siue in mare proripiuntur, ac tempestates exsuscitant, siue ad superna conscendunt, & vt, inquit Apuleius in lib. de Mundo: Sursum tormentum illud ire pergit, densasque & tumidas nubes præ se agit, coactusque collidit, fit sonitus & intonat calum; non secus ac si commotum ventis mare cum ingenti fragore vndas littoribus impingat. Huiusmodi sunt Ecnephias, Turbo, Typhon, Vortex, & alij de quibus diximus suo loco. Græci Anaphysemata vocant. PRO YON Græcè, Arabicè Algomeysa, Canis minor, seù 108 Antecanis: fidus in octaua sphæra, duas tantummodo habens stellas; alteram in femore grandem, primi honoris, de natura Martis, & Mercurij; alteram quartæ magnitudinis de natura solum Mercurij. Oritur Romæ circa diem 24. Iulij

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MATHEMATICVM. 107 The planets that are oriental of the Sun begin from the hour when they begin to be seen in vision; and they remain in their exalted dominion until the sextile aspect intervenes between them and the Sun, and from then on, up to the quadrate aspect, the height of their dominion is diminished; and afterwards, at the second station, their dominion is no more. Although planets of this kind are oriental of the Sun and occidental of the Moon, there will not be a dominion higher than this. But for the three inferior planets, their dominion begins from the hour of appearance in the West after conjunction with the Sun; and the exaltation of Venus and Mercury remains until they retrograde; and if they are occidental of the Sun and oriental of the Moon, there will be no dominion higher than this. The Moon, however, rules up to the middle of the month. Thus far Abraham. But why orientalness in the superior planets, and occidentalness in the inferior ones, makes such dominion, or makes the planets more powerful, has been said in Book V, under Occidental Planet. PRISM is defined by Euclid in book 10, definition 13, as a solid figure contained by planes, of which the opposite two are equal, similar, and parallel, while the others are parallelograms. From this definition it is clearly gathered that it is nothing other than a kind of many-sided column of equal thickness, whose opposite bases are equal, similar, and parallel, whether they be triangular, quadrangular, pentagonal, etc. Hence every prism will contain as many parallelograms as there are sides, or even angles, in each of the opposite planes. See what we said under the word Parallelopipedum. By the name PROCELLÆ are understood generically all pseudowinds, that is, those which spring forth from the ground or from openings in the earth, and with great force are either rushed into the sea, and stir up storms, or ascend upward, and, as Apuleius says in his book On the World: “That force keeps going upward, driving before it thick and swollen clouds, and, being driven together, they clash, there is a sound, and the sky thunders; no differently than when the sea, stirred by winds, with great crash beats its waves against the shores.” Such are Ecnephias, Turbo, Typhon, Vortex, and others about which we spoke in their place. The Greeks call them Anaphysemata. PROYON, in Greek; in Arabic Algomeysa; Canis Minor, or Antecanis: a fixed star in the eighth sphere, having only two stars, one large one on the thigh, of first magnitude, of the nature of Mars and Mercury; the other of fourth magnitude, of the nature of Mercury alone. It rises at Rome around July 24.

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LEXICON cum gr. 2. Leonis, & occidit cum totidem Cancri: quo tempore æstus himis intenditur. Hinc aduettit Hippocrates morbos eo tempore esse difficilis cutationis, adeoque à medicamentis validis, ac purgationibus abstinendum. Naves etiam litrore soluere malum est hoc sidere cum Luna exorient; aut etiam cum Mercurio, quicum ventos producit impetuosos, turbines, ac procellas. Quoad Agriculturam etiam, inquit Plinius lib. 18. cap. 18. Hoc temporis interuailo res summa vitium agitur, decretorio vnis sidere illo, quod Caniculam appellauimus; (paulò antè Procyonem Latino nomine vrentem Caniculam appellauit) vnde carbunculare dicuntur, vt quodam vredinis carbone exusta. Non comparantur huic malo grandines, procella, qua numquam annona intulere caritatem. Agrorum quippe mala sunt illa, carbunculus autem regionum latè parentium non difficili remedio nisi calumniari naturam rerum homines, quam sibi prodesse mallent. Huc vsque, Quod, vt obseruauit Stadius potiùs in occasu vespertino accidit, præsertim si tunc temporis concurat etiam interlunium quia tunc, viti, & oleæ germinanti iniutiam ex vredine affert. 109 Hinc olim Rustici in die S. Vibani de vindemix qualitate pronunciabant. At verò in Genethliacis Procyon, quemadmodum reliquæ stellæ adurentes Syrius, Hircus, Regulus, Antares, habet vim Aneræticam, si ad eum directione vitæ moderator feratur. Si autem in horoscopo partiliter inuentus fuerit, inquit Pontanus in Vrania facit cunctis gratum, venatorem, cutscelerem, &c. In occasu verò indicit mortem per morsus ferarum, dum illas capere gestit natus, maximè si Mars malo radio affulsetit; aut affert periculum dilaniationis, & membrorum concisionis, aut sanè mortem ex morsu canis rabidi. 110. PROFECTIONES, seu Progressiones apud Astronomos dicuntur esse æquales, ac regulares incessus solis, aliorumque significatorum per signa Zodiaci secundum successione signorum, tribuendo cui ibet profectioni integrum circulum, & adhuc signum vnum. Triplicis generis ab antiquis constituuntur: Annuæ, Menstruæ, ac Diurnæ. Annua Profectio complectitur signum vnum distribuendum per anni solaris dies; ita vt si Sol v. g. initio primi anni fuerit in gr. 24. Arietis, initio secundi anni sit in 24. Tauri, & sic deinceps, donec singulis duodecim annis reuertatur ad locum, quem tenebat initio primi anni. Cumque in hac profectione adsit quantitas vnius signi distri- buenda

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LEXICON with 2 degrees of Leo, and it sets with the same amount of Cancer: at which time the summer heat is increased. Hence Hippocrates advised that diseases at that time are difficult to cure, and therefore that strong medicines and purgations must be avoided. It is also bad for ships to put out from the shore under this star when the Moon is rising; or also when Mercury is with it, because it produces violent winds, whirlwinds, and storms. As to Agriculture also, says Pliny, lib. 18, cap. 18, in this interval of time the chief business of the vine is being done, under that single decisive star which we have called Canicula; (a little before he called Procyon by the Latin name the burning Canicula) whence they are said to become carbuncular, as though burned with a sort of firebrand. Hailstorms and tempests are not to be compared with this evil, since they never brought dearness in provisions. For those are evils of fields, but carbuncle is an evil of regions lying far and wide; not hard to remedy, unless men would calumniate the nature of things, which they would rather that it should help them. Thus far, which, as Stadius observed, happens rather at the evening setting, especially if at that time also the interlunium occurs; because then it brings injury by burning to vines and to olive trees in growth. 109 Hence in former times rustics on the day of St. Viban used to pronounce judgment on the quality of the vintage. But in Genethliacs Procyon, just like the other burning stars, Sirius, Hircus, Regulus, Antares, has an anaretic power, if the ruler of the life is directed toward it. But if it is found partilely in the horoscope, Pontanus says in Urania, it makes one acceptable to all, a hunter, a cook, etc. In the setting, however, it signifies death by the bites of beasts, when the native seeks to catch them, especially if Mars shines with an evil ray; or it brings danger of being torn apart and of the cutting off of limbs, or indeed death from the bite of a mad dog. 110. PROFECTIONS, or Progressions, are said by astronomers to be equal and regular courses of the sun and of the other significators through the signs of the Zodiac according to the succession of the signs, assigning to each profection a whole circle, and one sign besides. They are established by the ancients of three kinds: Annual, Monthly, and Daily. The Annual Profection comprises one sign to be distributed through the days of the solar year; so that if the Sun, for example, at the beginning of the first year were at 24 degrees of Aries, at the beginning of the second year it would be at 24 degrees of Taurus, and so on thereafter, until every twelve years it returns to the place it occupied at the beginning of the first year. And since in this profection there is the quantity of one sign to be distributed

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MATHEMATHICVM. 389 buenda per totum annum, sit, vt singulis gradibus competant duodecim dies: & significator singulis mensibus proficiscatur in consequentiam signorum duos gradus, cum dimidio. In Profectione Menstrua singulis mensibus tribuitur signum vnum, itavt singulis diebus competat gr. 1. min. 4. secund. 4. quomodo annus solaris integer dieum 365. diuiditur in tredecim partes æquales, & sic in toto anno perficiatur integer circulus. In Profectione demum Diurna tribuitur signum vnum binis diebus, hor. 3. min. 52, itavt in hac profectione singulis diebus competant gr. 13. min. 51, sicque mensis profectionalis subdiuiditur etiam in 13. partes æquales; quo expleto significator regreditur ad idem signum, in quo erat initio mensis. Plura apud Auctores, & ealeulatores Ephenieridum in suis introductoriis, de hac regulari processione: De quarum singulis speciebus claritatis gratia afferunt tabulas expansas profectionum omnium locorum hÿegialium, Annuarum videlicet, menstruarum, ac Diurnarum. Verum nouissimè Titus in cælesti Philosophia lib. 7. cap. 9. rem altiùs indagando, pluribus ingeniosè commonstrat, hanc æqualem significatorum processionem, provt modo explicatum est, naturalem non esse. Siquidem notat ipse, quod profectionum mensura constituitur per singulos Lunæ reditus ad eandem cum sole faciem, quam habebat in radice Natalis. Nam quemadmodum per directionis motum præordinatur in potentia calor vitalis cum suis coeffectibus; sic per motum profectionis, inquit, præordinatur in potentia humidum radicale cum suis coeffectibus: ergò, sieur motus directionis non instituitur vniformis, & æqualis in Zodiaco, sed mensuratur ex motu solis successivo à die Natalis insequentis, vt alibi monstratum est; ita & motus progressionis instituendus est ex quotidianis lationibus Lunæ per signa Zodiaci suis assiduis circulationibus, ac rediribus ad eandem cum sole faciem, & illuminationem, seu distantiam, quam habebat initio anni: itavt singuli reditus, & circuitus Lunæ ad eandem cum Sole faciem referantur, ac respiciant tanquam causa, ad singulos annos subsequentes, & peragrario Lunæ per singula signa referatur ad singulos ferè menses. Quandoquidem circuitus hic Lunæ erga Solem ad viuum demonstrat anni circuitum: eo enim temporis spatio, quo Luna post discessum à Sole ad ipsum redit, & Sol vice versa signum ferè vnum perambulat, ascendunt in singulis mundi cardinibus tot signa, quot sunt anni dies ad vnguem: quod sic euidenter ostenditur. Bb

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MATHEMATHICVM. 389 provided for the whole year, so that twelve days correspond to each degree; and the significator, each month, proceeds through the signs by two degrees and a half. In the Monthly Profection one sign is assigned to each month, so that each day corresponds to 1 degree 4 min. 4 sec. in such a way that the entire solar year of 365 days is divided into thirteen equal parts, and thus in the whole year the complete circle is accomplished. In the Daily Profection at last, one sign is assigned for two days, 3 hours, 52 minutes; so that in this profection each day corresponds to 13 degrees 51 minutes, and thus the profectional month is likewise subdivided into 13 equal parts; when this is completed the significator returns to the same sign in which it was at the beginning of the month. More is found in the authors and calculators of ephemerides in their introductions concerning this regular progression: and for each of these kinds, for the sake of clarity, they present expanded tables of all the profections of places according to climate, namely annual, monthly, and daily. But most recently Titus, in Celestial Philosophy , book 7, chap. 9, investigating the matter more deeply, ingeniously shows in many ways that this equal progression of the significators, as has now been explained, is not natural. For he notes that the measure of profections is constituted by the Moon’s repeated returns each time to the same face with the Sun that it had at the radix of the nativity. For just as by the motion of direction the vital heat with its coeffects is preordained in potency; so by the motion of profection, he says, the radical moisture with its coeffects is preordained in potency. Therefore, just as the motion of direction is not established as uniform and equal in the zodiac, but is measured from the successive motion of the Sun from the day following the nativity, as has been shown elsewhere; so also the motion of progression must be instituted from the daily courses of the Moon through the signs of the zodiac, with its constant revolutions and returns to the same face with the Sun and illumination, or distance, which it had at the beginning of the year; so that the Moon’s several returns and circuits to the same face with the Sun are referred to and regarded as the cause for the several following years, and the Moon’s passage through the several signs is referred to the several months almost. Since this circuit of the Moon with respect to the Sun clearly shows the circuit of the year: for in that span of time in which the Moon, after departing from the Sun, returns to it, and the Sun in turn traverses almost one sign, there rise in each of the world’s angles as many signs as there are days in the year down to the very point; which is thus clearly shown. Bb

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LEXICON 112. Annus Lunaris constat diebus 354. hos diuide per duodecim lunationes, & remunbunt 29. dies cum dimidio, quibus Luna ad Solem redit; & est spatium mensis lunaris medium: hos dies adhuc produc per duodecim signa quæ ascendunt singulis diebus in quouis mundi cardine, & fiunt signa 354. quæ successiuè ascendunt tempore vnius Lunationis; quibus adde signum vnum, quod transiui Sol, & consequenter etiam cardines hisce diebus, & fiunt signa 355. Quia verò non integrum signum, sed quid minus, hoc est spatium, quod progressus est Sol in vna integra Lunatione indicat annum in profectionibus, ideò etiam aliquid minus signo indicat diem nam supersunt in fine anni de duodecim Lunationibus vndecim ferè gradus; itavt de singulis lationibus signiferi circà Mundum, detractis duodecim portionibus pro duodecim Lunæ circulationibus supersint adhuc vndecim gradus. Produc ergò 11. per 29. dies, in quorum singulis ascendunt duodecim signa & fiunt gr 319. qui ad signa reducti constituent decem signa cum residuo quæ iterum addita suppradictis 355. efficiunt suminam 365. signorum cum residuo. Vel sic facilius discurramus. Mensis lunaris medius est dierum 29. cum ferè duodecim horis: hos produc per 360. quot sunt gradustorius signiferi, & constituent sumam grad. 10620. quibus adde 29. alios gradus, quos Sol, & Anguli progressi sunt tempore inegræ revolutionis Lunæ, & fiunt gr. 10649. qui ascendunt in singulis cardinibus in singulis integris circuitionibus Lunæ erga Sole: hos diuide per tot gradus, quot deambulat Sol medio motu tempore circuitus Lunæ; quod sic habebis. Diuide per 12. lunationes omnes gradus, quos perambulat sol tepore duodecim lunationum: sunt autem gr. 349. & fiunt 29. gradus cum duodecima parte: per hanc igitur mensuram diuide summam illam omnium graduum ascendentium in Angulis tempore vnius lunationis, & remanent ferè 366. quot videlicet sunt circiter dies anni: Vnde patet, quod tot signa ascendunt in quolibet cardine tempore vnius integræ lunationis, quot sunt dies anni ad anguem vi admiratione digna sit hæc dierum correspondentia, & regularis incessio. Igitur vnum ferè signum habet relationem ad annum, & ad diem: sicque circuitus Lunæ circa Solem in mense ad vinum repræsentat circuitum Anni. Hæc, & alia multa habet Titus eodem loco: & in Primo Mobili exemplis plurimis confirmat hanc suam doctrinam, methodumque facilem tradit supputandi huiusmodi progressiones. 113. PROHIBITIO LVMINIS secundum Abraham Auenar, sit id

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LEXICON 112. A lunar year consists of 354 days. Divide these through twelve lunations, and there will remain 29 days and a half, which is the time in which the Moon returns to the Sun; and this is the middle span of the lunar month. Carry these days further through the twelve signs, which ascend each day in every quarter of the world, and there result 354 signs, which successively ascend during the time of one lunation; to these add one sign, which the Sun has passed, and consequently also the quarters on these days, and there result 355 signs. But because it is not a whole sign, but something less, that is, the space which the Sun has progressed in one complete lunation indicates a year in profections, therefore something less than a sign also indicates a day; for at the end of the year from the twelve lunations there remain almost eleven degrees. Thus, of the zodiacal parts around the world, after subtracting twelve portions for the twelve circulations of the Moon, there still remain eleven degrees. Therefore multiply 11 by 29 days, in each of which twelve signs ascend, and there result 319 degrees, which, reduced to signs, will make ten signs with a remainder; these, again added to the above-mentioned 355, make a total of 365 signs with a remainder. Or let us proceed more easily thus. The mean lunar month is 29 days with almost twelve hours: multiply these by 360, which is the number of degrees of the whole zodiac, and they will make 10,620 degrees; to these add 29 other degrees, which the Sun and the angles have advanced during the time of a complete revolution of the Moon, and there result 10,649 degrees, which ascend at each quarter in each complete circuit of the Moon with respect to the Sun. Divide these by as many degrees as the Sun traverses by its mean motion during the circuit of the Moon; which you will have thus. Divide by 12 lunations all the degrees which the Sun traverses during the time of twelve lunations: these are 349 degrees, and there result 29 degrees with a twelfth part. By this measure, therefore, divide that sum of all the degrees ascending at the angles during the time of one lunation, and there remain almost 366, which are, namely, about the days of the year. Whence it is clear that as many signs ascend in each quarter during the time of one complete lunation as there are days of the year. Truly admirable is this correspondence of the days, and its regular course. Therefore one sign almost has relation to the year and to the day; and thus the circuit of the Moon around the Sun in a month represents the circuit of the Year. Titus has these things, and many others, in the same place; and in the Prima Mobilia he confirms this doctrine with many examples, and gives an easy method for calculating such progressions. 113. PROHIBITION OF LIGHT according to Abraham Auenar, let it be

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MATHEMATICVM. 39r planetis duobus modis: Primò si fuerint tres planetæ in vno signo, sed in gradibus diuersis, fueritque ponderosus in pluribus gradibus, leuior in paucioribus; tunc qui est medius inter ipsos prohibet lumen inter illos communicari donec leuior ipsum transferit. Sic posiro Saturno in gr. 20. Arietis, Venere in 11. Mercurio in 15. eiusdem signi; Mercurius prohibet lumen Saturni communicari Veneri, donec ipsum Venus pertransferit. Secundo modo sic prohibitio per aspectus: vt si duo planetæ sint in vno signo, coniungaturque leuior ponderosiori, & alius planeta ponderosiorem aspiciat, quocumque tandem aspectu; tunc sibi planeta coniunctus prohibet aspicientem, & eius esse dissipabit; ita tamen, vt gradus sint æquales; sin autem gradus fuerint aspicientes propinquiores aspectui, non valebit se coniungens aspicientem prohibere. < 114> PROMISSORES apud Astronomos dicuntur communiter si- gna, & alia loca in cælo, quæ habent virtutem causæ efficientis ergà moderatores, & motu directionis deducta ad eos, suis qualitatibus afficiunt. Huiusmodi sunt omnia corpora planetarum, ne ipsis quidem exclusis luminaribus, (licet alia ratione considerata fiant moderatores, & se habeant ad modum subiecti) eorum radij, fixæ, & noua Phænomena, quæ in cælo apparent; de quibus abunde dictum est in V. Occursantes. Dicuntur autem promissores, quia profectò promittunt in radice aliquid tempore expletæ directionis compleendum; hoc est quando motu primi mobilis feruntur ad situm moderatorum, qui etiam ob eandem causam significatores dicuntur, eo quia significant aliquid generaliter adimplendum tempore expletæ directionis, ab ipsis promissoribus: ac proidde, vt dixi, se habent tamquam subiectum passiuum respectu aliorum siderum. Plura de ipsis vide in dicto loco & in Verbo Directio < 115.> PROPORTIONALITAS, quam Græci Analogiam vocant, definitur ab Euclide lib. 5. def. 4. quod sit similitudo, & comparatio duarum, vel plurium rationum interse: Dicitur etiam attributio, & relatio, quia facit vnm referri ad aliud, tamquam ad subiectum attributionis. Ea est basis, suprà quam totius Matheseos structura fundatur, quinimmo & scopus, ad quem omnia eius præcepta collineant: quippe quæ ex comparatione vnius quantitatis ad alteram, alias innumeras proportionaliter facit, atque exinde venit in cognirionem planè euidentissimam rerum cæteroqui, abditissimatum sensusque hominum fugientium. Sunt igitur Mathematicæ rationes, vt probè aduertit Virruius lib. 1. cap. 1. B b ij

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MATHEMATICVM. 39r planets in two ways: First, if there are three planets in one sign, but in different degrees, and the heavier one be in more degrees, the lighter in fewer; then the one that is middle between them prevents the light from being communicated among them until the lighter one transfers it. Thus, with Saturn placed in 20 degrees of Aries, Venus in 11, Mercury in 15 of the same sign; Mercury prevents the light of Saturn from being communicated to Venus, until Venus carries it across. Secondly, prohibition is made by aspects: as if two planets are in one sign, and the lighter one is joined to the heavier, and another planet looks at the heavier one, by whatever aspect at last; then the planet conjoined with it prevents the one aspecting, and will dissipate its influence; yet so that the degrees be equal; but if the degrees of the aspecting body are nearer to the aspect, the one that joins itself will not be able to prevent the aspecting body. < 114> PROMISSORES among astronomers are commonly called those sig- ns, and other places in the sky, which have the virtue of an efficient cause toward the rulers, and, brought by the motion of direction to them, affect them with their qualities. Of this kind are all the bodies of the planets, not even excluding the luminaries, (though considered in another way they become rulers, and behave as a subject does) their rays, fixed stars, and new phenomena that appear in the sky; concerning which enough has been said in V. Occursantes. They are called promissors, however, because they truly promise in the radix something to be completed at the time of the completed direction; that is, when by the motion of the first mover they are carried to the position of the rulers, who also for the same reason are called significators, because they signify something generally to be fulfilled at the time of the completed direction, from the promissors themselves: and therefore, as I said, they behave as a passive subject with respect to the other stars. See more about them in the said place and in the word Direction < 115.> PROPORTIONALITY, which the Greeks call Analogy, is defined by Euclid, book 5, def. 4, as the likeness and comparison of two, or more, ratios among themselves. It is also called attribution and relation, because it makes one thing referred to another, as to the subject of attribution. It is the basis upon which the whole structure of Mathematics is founded, indeed also its aim, toward which all its precepts are directed: for from the comparison of one quantity to another, it makes many others in proportion, and from this comes the most clearly evident knowledge of things otherwise hidden, and escaping human senses. Mathematical reasonings, therefore, are, as Virruvius notes well, book 1, ch. 1. B b ij

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LEXICON proportionis, mensuræque rationes, quatenus considerant quantum, vt est extensum, proindeque vt mensura quædam est aptum per suam extensionem, vt per ipsum alia <116> quanta mensuremus, & ipsum vicissim per alia quanta mensuretur. Et quoniam duplex est quantum continuum, & discretum, ita & duplex proportio, Geometrica quæ attenditur in quantis continuis, & Arithmetica, quæ versatur in numeris conferendo vnum cum alio, & exinde aliorum ignotorum inducendo notitiam. Nihilomtnus vtraque per numeros expeditur & adhuc retento tuo nomine ad quantum alterius considerandum se exendir pro diuersa proportionum ratione, & habitudine vnius quanti ad alterum; applicando postea ad quantitatem continuam quod per discretam deductum est: & è contrà fingendo in numeris passiones omnes quætitatis continuæ, vt quod in quantitate continua perspicuum est, in discreta etiam fac clarum, per eandem habitudinis rationem. Sic in quantitate discreta perinde est assignare ac in continua, totum & partes, puncta indiuisibilia, quæ sunt vnitates componentes eandem quantitatem discretam, & ad quæ terminatur, Angulos, & latera. Sic datur numerus planus, & solidus; Quadratus, & cubus; simplex, & compositus: rationalis, & irrationalis, &c. Sicque suo modo, in quantitate discreta est assignare omnes figuras quantitatis continuæ, triangulares, quadrangulares, trilateras quadrilateras, pentagonas, exagonas, parallelogramma, trapezia, &c. vt latè explicat Clauius in Elem. Euclid. lib. 7. <117> Igitur proportio Arithmetica est cum tres, vel plures numeri per eandem differenriam progrediunrur, vt 4. 7. 10. 13. 16. 22. & sic procedendo per reliqua, quorum quilibet numerus se proximè præcedenté ternario superat. Proportio Geometricà est cum tres, vel plures numeri eandem rationem habent: vt numeri 2. 6. 18. 54. 162. &c. quilibet enim ad suum antecedentem eandem proportionem habet, seu rationem triplam. Vnde porest, vt supra dicebam eadem proportionalitas Arithmetica, atque Geomerrica, & continua esse, & discreta: Continua quidem, quando idem numerus, qui consequens est respectu numeri præcedentis est etiam antecedens respectu numeri subsequentis: vt proportionalitas, quæ est inter 1. 6. 28. 54. continua est, discreta autem, cum numerus, qui consequens est non est idem antecedens respectu alterius numeri consequentis, sed rursum assumitur alius numerus antecedens, & alius nume-

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LEXICON the relations of proportion and measure, insofar as they consider quantity, as it is extended, and therefore as some measure is suited by its own extension, so that by it we may measure other quantities, and it in turn may be measured by other quantities. And since quantity is twofold, continuous and discrete, so also proportion is twofold: Geometrical, which is regarded in continuous quantities, and Arithmetical, which deals with numbers by comparing one with another, and thereby introducing knowledge of other unknown things. Nevertheless both are worked out by means of numbers, and, still retaining your name, it extends to considering the quantity of another according to the different relation of proportions and the habit of one quantity to another; afterwards applying to continuous quantity what has been deduced through the discrete: and conversely inventing in numbers all the properties of continuous quantity, so that what is clear in continuous quantity, make clear also in discrete, by the same relation of proportion. Thus in discrete quantity it is just as much necessary to assign as in continuous: the whole and the parts, indivisible points, which are the units composing the same discrete quantity, and to which it is terminated, angles, and sides. Thus plane and solid number are given; square and cube; simple and composite: rational and irrational, etc. And in the same way, in discrete quantity it is necessary to assign all the figures of continuous quantity: triangular, quadrangular, trilateral, quadrilateral, pentagonal, hexagonal, parallelograms, trapeziums, etc., as Clavius explains at length in the Elements of Euclid, book 7. Therefore Arithmetical proportion is when three or more numbers proceed by the same difference, as 4, 7, 10, 13, 16, 22, and so on by the rest, each number exceeding the one immediately preceding it by three. Geometrical proportion is when three or more numbers have the same ratio: as the numbers 2, 6, 18, 54, 162, etc.; for each has the same proportion to its predecessor, that is, a triple ratio. Whence it may be, as I was saying above, that the same proportionality, both Arithmetical and Geometrical, may be continuous and discrete. Continuous indeed, when the same number, which is consequent with respect to the preceding number, is also antecedent with respect to the following number: as the proportionality which is between 1, 6, 28, 54 is continuous; but discrete, when the number which is consequent is not the same antecedent with respect to another consequent number, but another antecedent number is taken again, and another nume-

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MATHEMATICVM. 393 tus consequens. Ita hi numeri bini se habent: 2. 3. & 11. 18. & 20. 30. eandem habentes proportionem sesqualiteram. < 119.> Datur etiam Proportionalitas, quæ dicitur Harmonica, seu Musica ex miro ordine, & correspondentia, quam habent sibi inuicem numeri: Vt cum tres numeri ità ordinantur, vt eadem sit proportio maximi ad minimum, quæ est differentiæ inter maiores duos ad differentiam inter duos minores: sic hi numeri 3. 4. 6. harmonicam proportionatatem constituunt, quia profectò eadem est proportio maximi, nempe 6. ad minimum nempe 3. quæ est proportio differentiæ inter maximum 6. & medium 4. nimirum numero 2. ad differentiam inter medium 4. & minimum 3. id est ad 1. cum vtrobique proportio sit dupla. Denominator autem proportionis dicitur ille numerus, qui distinctè, apertèque exprimit habitudinem vnius quantitatis ad alteram At verò illæ multitudines dicuntur habere proportionem inter se, quæ possunt multiplicatæ sese inuicem superare: vt habet Euclid. lib. defin. 5. Porrò proportionum, quas inter se possunt habete duo < 120> quanta, siue continua, siue discreta, alia est rationalis, alia irrationalis. Rationalis est, quam habent inter se duo quanta commensurabilia: irrationalis, quam duo incommensurabilia. Illæ autem quantitates dicuntur commensurabiles, quæ habent vnam communem partem aliquotam, seu quas vna mensura communis meritur, vt sunt lineæ 10. & 8. palmorum, quarum pars est aliquota linea tum 4. tum 2. palmorum. Quantitates verò incommensurabiles dicuntur quæ nullam partem habent aliquotam hoc est, quarum nulla datur mensura communis; cuiusmodi sunt diameter, & latus eiusdem quadrati. Similiter alia est proportio æqualitatis, quæ est inter duo quanta æqualia, vt 20. ad 10. alia inæqualitatis inter duo quanta inæqualia, vt inter 20. & 10. vel 8. & 40. quæ rursus alia est maioris inæqualitatis, quando maior cum minore quantitate confertur, alia minoris inæqualitatis, quando confertur minor quantitas cum maiore, vt in supra posito exemplo 8. ad 40. Huius autem proportionis minoris inæqualitatis quinque sunt genera, Primum, quam dicunt multiplicem. 2. superparticularem 3. superpartientem, 4. Multiplicem superparticularem. 5. Multiplicem superpartientem. Prima est quæ dicit habitudinem maioris quantitatis ad minorem, quando maior continet aliquoties minorem, vt his, ter quater, &c. ita vt maiorem quantitatem metiatur Bb iii

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MATHEMATICVM. 393 that which follows. Thus these pairs of numbers stand in this relation: 2. 3. and 11. 18. and 20. 30. having the same sesquialter proportion. <119.> There is also given a Proportionality, which is called Harmonic, or Musical, from the marvelous order and correspondence which numbers have with one another: as when three numbers are so arranged that the same ratio exists between the greatest and the least as there is between the difference of the two greater and the difference of the two lesser: thus these numbers 3. 4. 6. constitute a harmonic proportion, because indeed the same ratio exists between the greatest, namely 6, and the least, namely 3, as between the difference of the greatest 6 and the middle 4, namely the number 2, and the difference between the middle 4 and the least 3, that is, to 1, since in both cases the ratio is double. The denominator, however, of a proportion is called that number which distinctly and plainly expresses the relation of one quantity to another. But those multitudes are said to have proportion among themselves, which can, when multiplied, exceed one another: as Euclid says, lib. defin. 5. Moreover, of the proportions which two quantities, either continuous or discrete, can have between themselves, one is rational, another irrational. Rational is that which two commensurable quantities have between themselves; irrational, that which two incommensurable quantities have. And those quantities are called commensurable which have one common aliquot part, or which a common measure measures, as are lines of 10 and 8 palms, whose aliquot part is a line both of 4 and of 2 palms. But quantities are called incommensurable which have no aliquot part, that is, of which no common measure is given; such as the diameter and the side of the same square. Likewise there is one proportion of equality, which is between two equal quantities, as 20 to 10; another of inequality, between two unequal quantities, as between 20 and 10 or 8 and 40; which again is either of greater inequality, when the greater is compared with the lesser quantity, or of lesser inequality, when a lesser quantity is compared with a greater, as in the above example, 8 to 40. And of this proportion of lesser inequality there are five kinds: First, that which they call multiple. 2. submultiple? 3. superparticular, 4. multiple superparticular. 5. multiple superpartient. The first is that which indicates the relation of a greater quantity to a lesser, when the greater contains the lesser a certain number of times, as in these: three times, four times, etc., so that it measures the greater quantity Bb iii

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LEXICON 394 minor, qualis est proportio tripla 12 ad 4. quadrupla 16. ad 4. &c. Secunda est habitudo maioris quantitatis ad minorem, cum maior semel tantum minorem continet, sed adhuc eius aliquam partem aliquotiam vt dimidiam, tertiam, quartam, &c. vt est proportio sesqualtera 3. ad 2. sesquitertia 12. ad 9. Tertia est habitudo talis maioris quantitatis ad minorem, vt maior minorem semel duntaxat contineat, & insuper aliquot eius partes aliquotas non efficientes vnam aliquotam, vt est 8. ad 5, Quarta constata ex multiplici, & superparticulari est cum maior quantitas minorem aliquoties continet, vt bis, ter; quater, & insuper vnam eius partem aliquotam, vt est proportio 9. ad 4. quæ numerum quaternarium bis continet, & prætereà vnitatem. Quinta demum composita ex multiplici, & superpartiente est habitudo maioris quantitatis ad minorem, quâ maior minorem complectitur aliquoties, & insuper aliquas eius partes aliquotas non valentes conficere vnam, vt est proportio 11. ad 3. vbi numerus 11. ter continet numerum ternarium, & adhuc duas vnitates non sufficientes conficere quartum ternarium. < 121> Tandem alia dicitur proportio ordinata, quæ in eo consistit; vt quemadmodum fuerit antecedens ad consequens, ita antecedens ad consequens, fuerit etiam vt consequens ad aliud quippiam, ita consequens ad aliud quippiam. Perturbata verò est cum positis tribus magnitudinibus, & aliis quæ sint his magnitudine pares, vt in primis quidem magnitudinibus se habet antecedens ad consequentem, ita in secundis magnitudinibus antecedens ad consequentem; vt autem in primis magnitudibus consequens ad aliud quippiam, ita in secundis magnitudinibus aliud quippiam ad antecedentem. Plura qui volet videat Euclidem lib. 1. & lib. 7. vbi latè agit de proportionibus, quæ intercedunt tam inter duas magnitudines, seu quantitates continuas, quam inter duas quantitates discretas, Teu numerorum quamlibet multitudinem. < 122> Propus dicitur stella fixa quartæ magnitudinis de natura Veneris, & Mercurij in extremo pede sinistro præcedentis Geminorum consistens, sic dicta quasi propes, hoc est ante pedem, seu vt habet Proclus, quia p[ro]pè est conversioni æstius, & initio Cancri: est enim in longitudine in gr. ferè 1, Cancri. Quæ tamen oritur Romæ cum gr. 25. eius-

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LEXICON 394 minor, as is the ratio triple 12 to 4, quadruple 16 to 4, etc. The second is the relation of the greater quantity to the lesser, when the greater contains the lesser only once, but still some part of it, as the half, third, fourth, etc., as is the ratio sesquialter 3 to 2, sesquitertian 12 to 9. The third is the relation of such a greater quantity to the lesser, so that the greater contains the lesser only once, and besides certain aliquot parts of it not making up one whole aliquot, as is 8 to 5. The fourth, composed of multiplicative and superparticular, is when the greater quantity contains the lesser several times, as twice, three times, four times, and besides one aliquot part of it, as is the ratio 9 to 4, which contains the number four twice, and moreover unity. The fifth at last, composed of multiplicative and superpartient, is the relation of the greater quantity to the lesser, whereby the greater embraces the lesser several times, and besides certain aliquot parts of it not amounting to one whole, as is the ratio 11 to 3, where the number 11 contains the ternary number three times, and still two units not sufficient to make a fourth three. < 121> Finally another ratio is called ordered, which consists in this: just as the antecedent has been to the consequent, so the antecedent to the consequent has also been to something else, and so the consequent to something else. Disturbed ratio, however, is when three magnitudes are set down, and others which are equal to these in magnitude, so that in the first magnitudes the antecedent is to the consequent, thus in the second magnitudes the antecedent is to the consequent; but as in the first magnitudes the consequent is to something else, so in the second magnitudes something else is to the antecedent. Whoever wishes may see Euclid, book 1 and book 7, where he treats at length of proportions which intervene both between two magnitudes, or continuous quantities, and between two discrete quantities, or any multitude of numbers. < 122> Propus is called a fixed star of the fourth magnitude, of the nature of Venus and Mercury, standing in the extreme left foot of the preceding Gemini; so called as it were propes, that is, before the foot, or, as Proclus has it, because it is near the turning of summer, and the beginning of Cancer: for it is in longitude at nearly 1 degree of Cancer. Yet it rises at Rome with 25 degrees of its-

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MATHEMATICVM. 395 dem signi, & occidit cum gr. 19. Geminorum. De ea me- minit lunctinus in Catalogo stellarum fixarum, qui est in Commentar. ad sphæram lo: de Sacrobolco. PROROGATOR s apud Astronomos vocantur iidem, qui 123 moderatores, ac significatores: Sunt enim Planetæ, & alia ioca in exlo, quæ rerum moderandarum dispositionem sub- intrant; De quibus paulò antè dictum in V. Promissores: afficiuntur enim horum qualitatibus, & provt benè, vel ma- lè fuerint ab istis affecta, benè vel malè, de re ab ipsis signi- ficata denunciant. Sunt autem quinque ex Ptolemao: Sol, Luna, Ascendens, Medium cæli, & Pars Fortunæ: & insu- per Sole, Luna, vel Parte Fortunæ existentibus in locis non idoneis ad Vitæ p[er]torogationem ineundam, Planeta, qui cum reperiatur in loco hylegiali, plurimas dignitates ha- buerit in locis luminarium ascendentis, partis fortunæ & præcedentis luminarium coniunctionis, aut oppositionis, cui profectò tunc competet ius moderandæ vitæ ac præroga- tiua hylegii. 124 H ne moderatoris nomen, meo iudicio lariùs patet, quam prorogatoris: Moderator enim comprehendit significato- res quoscumque rerum; Prorogator autem, vt nominis etymon præsefert, aliquid speciale significat, quod proro- gari possit, & in longum protrahi, qualis est potissimum vi- ta: Vnde iis solis conuenit hoc nomine insigniri, qui mode- randam vitam, & prærogatiuam hylegialem sortiti fuerint. Rursus significatoris nomen adhuc vniuersalius est, quam moderatoris aut prorogatoris: Quantum enim ad etymon, dicit tantum rei alicuius significationem habere; sicque etiam comprehendere potest loca minùs principalia, quæ certarum rerum significationem habent, vt secunda diui- tiarum, tertia fratrum, &c. similiter reliqui quinque Plane- tæ Saturnus, Iupiter, Mars, Venus, & Mercurius, quos ali- liqui in significatores assumunt (vt dictum est in V. Mode- ratores) ad quos dirigunt corpora & radios aliorum plane- tarum, aliaque sidera occursantia, nec sanè sine fructu. Hæc autem dixerim, vt aliquam diuersorum nominum significationis diuersitatem tradam; cum alias non me lateat, apud omnes Professores, ipsumque Ptolemæum hæc vocabula indiscriminatim, ac sine delectu aliquo vsurpari. PROSCATHETON apud Græcos idem valet quod perpendi- 125. culum, instrumentum librandis planis, aliisque Geome- tricis operationibus perficiendis factum. Vide in V. Per- pendiculum. PROSTHAPHÆRISIS Græcè, Latinè idem sonat ac impletio, 126 Bb iiiij

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MATHEMATICVM. 395 of the sign, and it sets with 19 Gemini. Lunctinus makes mention of it in the Catalog of fixed stars, which is in the Commentary on the Sphere, book 10, of Sacrobosco. PROROGATORS among astronomers are called the same as moderators and significators. For they are the planets and other places in the sky which enter into the arrangement of things to be governed. Of these mention was made a little before in V. Promissores. For they are affected by the qualities of these, and according as they have been well or badly affected by them, they declare concerning the thing signified by them, whether well or badly. Now according to Ptolemy there are five: the Sun, the Moon, the Ascendant, the Midheaven, and the Part of Fortune; and furthermore, if the Sun, Moon, or Part of Fortune exist in places not suitable for undertaking the prorogation of life, the planet which is found in a hylegial place, and has the greatest dignities in the places of the luminaries, the Ascendant, the Part of Fortune, and the preceding conjunction or opposition of the luminaries, to that planet assuredly then belongs the right of governing life and the prerogative of the hyleg. The name moderator, in my judgment, is broader than that of prorogator. For a moderator comprehends all significators of things; but a prorogator, as the derivation of the word itself suggests, signifies something special that can be prorogued and extended into length, of which life is especially such a thing. Hence only those deserve to be distinguished by this name who have received the governance of life and the hylegial prerogative. Again, the name significator is still more universal than that of moderator or prorogator. For as far as the etymology goes, it means only that something has the signification of some thing; and thus it can also include less principal places which have the signification of certain things, such as the second house of riches, the third of brothers, etc. Likewise the remaining five planets, Saturn, Jupiter, Mars, Venus, and Mercury, which some likewise take as significators (as was said in V. Moderatores), toward which they direct the bodies and rays of the other planets and other stars encountered, and certainly not without profit. I have said these things, however, in order to set forth some difference in the meanings of the various names; since otherwise I am not unaware that, among all professors and Ptolemy himself, these terms are used indiscriminately and without any distinction. PROSCATHETON among the Greeks means the same as a perpendicular, an instrument made for balancing planes and for carrying out other geometrical operations. See in V. Perpendiculum. PROSTHAPHÆRISIS in Greek sounds in Latin the same as addition, 126 Bb iiij

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396 LEXICON seu adæquario: estque pars illa Eclipticæ, quæ addenda est, vel minuenda à motu medio Planerarum, vt habeatur verus, aut à verò, vt habeatur medius. Vide in V. Æquatio. < 127 > PROTHANATOS (alij Prothanatos) aq[ui]d Campanilam est Planeta vel locus in cælo mortis qualitatem decernens, qui videlicet in cælesti figura locum Anereticum aut præcedit, aut sequitur, aut etiam eidem applicat. Item Dominus termini, in quem incidit mortalis directio < 128 > PROTRIGETES item Græcè dicitur Vindemiator, stella fixa tertiæ magnirudinis de natura Saturni, & Mercurij, ab Arabibus dicta Alasaph existens in ala septentrionali Virginis, quæ tempore Vindemiæ oritur. Plinius lib.16.cap. cap. 31. eam vocat Astyriæ stellam. Vide in V. Vindemiator. < 129 > PSEVDOSTELLA communiter dicitur quicunque cometa, siue nouum Phænomenon de novo apparens in cælo, siue in regione elementari, siue in ætherea: pressus tamen accipitur pro iis qui in suprema aëris regione generantur, vnde pseudostellæ quasi falsæ, & veluti supposititiæ appellantur, ad differentiam earum quæ perpetuò in regione ætherea micant, & nullam mutationem subeunt. Nihilominus istæ sublunares, vii æthereas in luce, atque in coloribus imitantur, ita & qualitatibus imbuuntur, & secundum naturam Planerarum, quibus assimilantur, & quos credendum est in ipsarum productione magis concurrere Fausta vel in fausta obnunciant; ita tamen, vt quia adulterina est earum actiuitas, atque ex cælorum partim, partim è nulluris pravis qualitatibus confarcinata, semper portemosa sit, ac timenda huiusmodi Phænomenon appariti. Et quidem, cum eorum materia sit exhalatio quædam spissa, pinguis, & crassa in vnum coiens, quæ siue ab ignis sphæra illis proxima, siue à sideribus; ex motu quo ignem concipit accenditur, & tantum durat quovsque eius crassities absumatur, vt habet Arist. 1. Meteor. cap. 7. ideò eorum materia iam resoluta, consequens est, vt reliqua exhalatio, in ventros conueriatur, sicque maris tempestates, terræ motus, terræ sterilitatem, aëris intemperiem, aliaque id genus mala denuncient: Vnde Pontanus in Vrania: Ventorum quoque certa dabunt tibi signa Cometa. < 130 > Placet autem hic ex Iunctino in tractatu de Cometis particulares eorum significationes afferre siue ex natura Planetarum quos referunt, siue à qualitatibus signorum, in qui-

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396 LEXICON its equation: and it is that part of the Ecliptic which must be added to, or subtracted from, the mean motion of the Planets, so that the true may be obtained, or from the true that the mean may be obtained. See in V. Æquatio . < 127 > PROTHANATOS (others Prothanatos), or, as it were, Campanilam, is the Planet or place in the sky determining the quality of death, which in a celestial figure either precedes, or follows, or even applies to the Anaretic place itself. Likewise the Lord of the term into which a mortal direction falls. < 128 > PROTRIGETES is also called in Greek Vindemiator , a fixed star of the third magnitude, of the nature of Saturn and Mercury, called by the Arabs Alasaph , situated in the northern wing of Virgo, which rises at the time of the vintage. Pliny, book 16, ch. 31, calls it the Astyrian star. See in V. Vindemiator . < 129 > PSEVDOSTELLA is commonly called any comet, or any new phenomenon appearing anew in the sky, whether in the elemental region or in the ethereal. Strictly, however, it is taken for those generated in the highest region of the air, whence they are called pseudostars, as it were false and spurious, in distinction from those which perpetually shine in the ethereal region and undergo no change. Nevertheless, these sublunary ones imitate the ethereal in light and in colors, and are likewise imbued with qualities; and according to the nature of the Planets to which they are assimilated, and which it is to be believed concur more in their production, they prognosticate good or ill fortune. Yet because their activity is adulterous, and compounded partly from the heavens and partly from noxious qualities, it is always dangerous and to be feared when such a phenomenon appears. And indeed, since their matter is a certain thick, fatty, and dense exhalation coalescing into one, which is kindled either by the sphere of fire near them, or from the stars by the motion with which it receives fire, and lasts only until its thickness is consumed, as Aristotle says, Metaph. 1, ch. 7, therefore, when their matter has now been dissolved, it follows that the remaining exhalation is turned into winds, and thus they announce storms at sea, earthquakes, barrenness of the earth, unhealthy air, and other evils of that kind. Hence Pontanus in Urania : You too shall receive sure signs of winds from the comet. < 130 > It is also pleasing here, from Iunctinus in his treatise on Comets, to present their particular significations, either from the nature of the Planets which they resemble, or from the qualities of the signs, in whi-

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MATHEMATICVM. 137 bus apparuerint, quoniam eius rei notitia multum iuuare potest ad ea, quorum signa extiterint declinanda, nosque per contraria communiendos. itaque Cometæ, Pseudostellæ de natura Saturni, quales sunt quæ 132. referunt colorem plumbeum, liuidum, suboscurum, in quo genere veniunt Pithetes, Tenaculum, Hircus, &c. in Ho- roscopo mundi repertæ, obnunciant multorum perniciem, famem, pestem, exilia, inopiam, angustias, luctus, terrores; & brutis animantibus vsui hominum accommodatis detri- menta: Prætereà afferunt frigora suo tempore intensissima, glaciosa, & nebulosa; niuium magnam vim, ventos vali- dissimos, tempestates, naufragia, piscationis iacturam, frugum ab erueis, ac locustis devastationem, inundationes, grandines, & similia. In hominibus insuper denotant varia accidenia, & pericula, quicque adhuc erunt plus solito tri- stes, inuidi, solitarij, laboriosi, &c. Phænomenon de natura Iouis, qualis est Argenteus, signi- 133. ficat anni fertilitatem, salutares pluvias suis temporibus con- gruentes, aëris serenitatem, præsertim si in signis aereis: Verum corporibus ad morbos dispositis, iis maximè qui Iouis complexionem habent, pleuritides, aliasque ægri- tudines, quas Iouem facere diximus suo loco. Martius Cometes dictus Veru, seù Pertica indicat aridita- 134. tem fontium, & fluuiorum exsiccationem, Ventos morbi- ficos, fructuum, & satorum dissipationem: Ad hæc frequen- tissima sequentur tonitrua, coruscationes, & fulmina: Mare præter solitum agirabitur, & crebriora contingent naufragia. Et quia Mars naturaliter accendit bilem, ideo frequentes rixæ, contentiones, bella, seditiones, &c. ex- citabuntur. Ex morbis etiam grassabuntur disenteriæ, fe- bres ardentes; hæmorrhagia, & his similia. Cometa de natura Solis, qualis est qui communiter diei- 135. tur Rosa, si vitus fuerit in regionis alicuius horoscopo por- tendit Regis, aut alicuius viri præpotentis mortem, aut se- ditiones, & tumultus eum rerum mutatione, sed qui- bus meliora forte succedent. Item bella, contentiones, æstus, & siceitates. Homines etiam solares, cuiusmodi sunt magnanimi, prudentes, hilares, generosi, graues, multis afflictabuntur incommodis. Veneris Pseudostella colore flauo, & valdè rutilans mina- 135. tur mala de ipsius natura, stomachi, renum, spermatico- rumque valorum affectiones, quibus potissimum laborabunt mulieres, sacra Virgines, adolescentes delicatuli, vo- luptuosi & similes. Adducit etiam fructuum corruption-

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MATHEMATICVM. 137 appear, since knowledge of this matter can greatly help us to avoid those things whose signs have emerged, and to fortify ourselves against them by contraries. Thus Comets, pseudostars of the nature of Saturn, such as those which 132. show a leaden, livid, somewhat dark color, among which kind come Pithetes, Tenaculum, Hircus, &c., found in the horoscope of the world, proclaim the destruction of many, famine, pestilence, exiles, poverty, hardships, sorrows, terrors; and damage to brute animals useful to men. Moreover they bring intense cold in due season, icy and foggy weather; a great quantity of snow, very strong winds, storms, shipwrecks, loss of fishing, devastation of crops by worms and locusts, floods, hail, and the like. In human beings they moreover indicate various accidents and dangers; and everyone will be more sad than usual, envious, solitary, laborious, &c. A phenomenon of the nature of Jupiter, such as the Silvery one, 133. signifies the fertility of the year, salutary rains falling in due season, and the serenity of the air, especially if in airy signs. But to bodies disposed to disease, especially those that have a Jovial complexion, it signifies pleurisies and other illnesses, which we said Jupiter causes in their place. The Martian comet called the Spear, or Staff, indicates 134. dryness of springs and drying up of rivers, harmful winds, scattering of fruits and seed; to these will be added very frequent thunderings, flashes, and lightnings. The sea will be stirred more than usual, and shipwrecks will happen more often. And because Mars naturally kindles bile, frequent quarrels, contentions, wars, seditions, &c. will be stirred up. Diseases also will spread, such as dysenteries, burning fevers, hemorrhage, and the like. A comet of the nature of the Sun, such as the one commonly called the Rose, if it has appeared in the horoscope of some region 135. portends the death of a king, or of some very powerful man, or seditions and tumults with a change of affairs, though perhaps better things will follow. Likewise wars, contentions, heat, and droughts. Solar men too, such as the magnanimous, prudent, cheerful, generous, grave, will be afflicted by many misfortunes. A pseudostar of Venus, yellow in color and very bright, threatens evils from her own nature, afflictions of the stomach, kidneys, and seminal organs, with which women, sacred virgins, delicate youths, the pleasure-loving, and the like will chiefly suffer. It also brings corruption of fruits-

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398 LEXICON nem, aquarum inundationes, rerum publicarum, legumque murationes. 136. Comeres Mercurialis colore ceruleus, dictus Dominus Ascone præter ventos plus solito ituenses adducit famem, bellum, & pestilentiam, cum magni viri alicuius morte, ac personis Mercurialibus præsertim ingeniosis phrænesim lethargum, epilepsiam, & similia. 137 Tandem lunaris muliebri statui, & populatibus aliquid mali semper obnunciat, iis præsertim qui sub Lunæ gubernaculo sunt, vt Phlegmatici, inconstantes, albi, mobiles, pusillanimes, meticulosi, &c. quibus ingerit morbos ex nimia humiditate, hidropem catarrhos, paralyses, epylepsias. In vniuersum autem significat sterilitates, legum, rituumque innouaiones, ac leuiabella. 138 Porrò si Cometa suprà dictos planetas exaltabitur augebit supra modum significara: si super Saturnum infirmitates validas, ac diuturnas adducit: Si super Iouem, morientur homines eximij, nobiles, insignibus, ac laude conspiciui: Si suprà Martem homines litigabunt, & bella gerent: Si suprà solem, deprimentur Reges, ac potentes, & viles exaltabuntur: Si suprà Venerem, aquatum diminuiones cum siccitate denunciantur: Si suprà Mercurium, rixæ, & iuuenum morbi: Si suprà Lunam, in substantiis multorum derrimenta: Si suprà Draconis caput, interficientur nobiles, & qui in pretio erunt: Si suprà Caudam, denotar, quod in fructibus arborum erit iactura. 139 Addit prætereà Georgius Valla, quod si Crinita caudam ad Saturnum conuerterit, fructuum inopiam, & annonæ caritatem portendit; si ad Iouem, regias domos euertendas si ad Martem, ægritudines, interitus, & bella atrocia cum immutatione status rerum publicarum; si ad Venerem magnarum mulierum, Reginarumq[ue] mortem; si ad Mercurium multitudini suspendia, & infamiam. 140 Denique pro qualitate signorum, in quibus hæc Phænomena apparuerint habent diuersa significata. Nam si in Ariere fulserint, indicant futuros armorum strepitus, sanguinis effusionem, ac potentium virorum mortem: item siccitatem insignem, morbos vulgares, oculorum, & capitis affectiones, lucem pecudum, nobilium, summorumque virorum deiectionem, & ignobilium exaltationem, non sine magno æstu, & apprimè noxio. Si in Tauro: significant messis, & fructuum corruptelam, terræmotus hotrendos, ventos validos; item & frigora suo tempore ingentia: Hinc erunt ægritudines vehementes, do-

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398 LEXICON nem, inundations of waters, changes in republics and laws. 136. A Mercurial comet, blue in color, called by Lord Ascone, besides the winds brings, more than usual, famine, war, and pestilence, together with the death of some great man, and to Mercurial persons, especially the ingenious, frenzy, lethargy, epilepsy, and the like. 137. Finally, the lunar one always foretells something evil for the female condition and for the people, especially for those who are under the governance of the Moon, such as phlegmatic, inconstant, white, mobile, faint-hearted, timid, and the like, to whom it brings diseases from excessive humidity, dropsy, catarrhs, paralyses, epilepsies. In general, however, it signifies sterilities, innovations in laws and rites, and trifles. 138. Moreover, if the comet is exalted above the aforesaid planets, it will increase beyond measure what it signifies: if above Saturn, it brings strong and lasting illnesses. If above Jupiter, distinguished men, nobles, and those conspicuous for their honors and praise will die: if above Mars, men will quarrel and wage war: if above the sun, kings and powerful men will be brought low, and the lowly will be exalted: if above Venus, decreases of water with dryness are announced: if above Mercury, quarrels and diseases of the young: if above the Moon, losses in the goods of many: if above the Dragon's Head, nobles and those held in esteem will be killed: if above the Tail, it is indicated that there will be loss in the fruit of trees. 139. Moreover, Georgius Valla adds that if the Crinite turns its tail toward Saturn, it portends scarcity of fruits and dear prices of provisions; if toward Jupiter, the overthrow of royal houses; if toward Mars, illnesses, deaths, and savage wars together with a change in the state of republics; if toward Venus, the death of great women and queens; if toward Mercury, hangings for many, and infamy. 140. Lastly, according to the quality of the signs in which these phenomena have appeared, they have different meanings. For if they have shone in Aries, they indicate future clashing of arms, shedding of blood, and the death of powerful men: also an extraordinary drought, common diseases, afflictions of the eyes and head, the downfall of cattle, nobles, and the greatest men, and the exaltation of the lowly, not without great heat, and highly harmful. If in Taurus: they signify corruption of the harvest and of fruits, terrible earthquakes, strong winds; likewise great cold in its season: hence there will be violent illnesses, do-

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MATHEMATICVM. 399 lores sicci, vt scabies, impetigines, pruritus, &c. Si in Geminis: significant rixas, belli seminatia, ægritudines & ex his mortes puerorum, & adolescentium, prægnantium aborsiones, auium interitum, famem, tonitrua, & corruscationes cum ventorum tanta vi, vt arbores eradicare valeant Item lasciviam, & fornicationis licentiam, proborumque hominum deiectionem. Si in Cancro; indicant multitudinem locustarum ingruentium, ac deuastantium messem, adeoque frumentis & aliarum frugum paucitatem, vel ab iis corrosarum, vel sanè à vermibus in eis productis: Item præagiunt bella, discordias, submersiones, direptiones, famem, & quam plurima mala. Si in Leone denorant destructionem ædificiorum, infestationem luporum, & ex ipsis impedimenta multa in hominibus, productionem vermium in frugibus, canum rabiem, oculorum affectiones, & bella Si in Virgine: significant labores multos, dolores, ac febres, tremores, vlcera, & postulas, præsertim in fœmineo sexu, in quo abortus valde erunt timendi. Item hominum proborum vexationes, ac malorum viuendi licentiam. Si in Libra: denotant pluviarum paucitatem, ventorum imperium, fluuiorum desiccationem, frugum inopiam, reræmotus horribiles. Item mortem Principum, cædes, proditiones, & alia huiusmodi. Si in Scorpion: portendunt multitudinem bellorum inter Principes viros, contentiones, & regnorum revolutiones. Insuper labores, & ægritudines in omni hominum genere: parturientium pericula dolores, & affectiones partium generarioni inseruientium, & fructuum terræ certissimam corruptelam. Si in Capricorno: præsignant magnam viuendi licentiam in hominibus pravis, fornicationes, adulteria, bella, rixas, venena principibus propinata. Item hyemis asperitatem, grandines, niues; vnde fructuum catitas, & penuria. Si in Aquatio: afferunt infirmitates populares, bella longo tempore duratura; aëris obscuritatem cum ventorum, tonitundrum, & fu'minum impetu. Insuper pestem luctuosam, & summorum præsertim virorum inopinatam mortem. Si denique in Piscibus apparuerint indicant plebis calamitosum statum, bella atrocia, rebelliones, ac proditiones.

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Dry diseases, such as scabies, impetigo, itching, etc. If in Gemini: they signify quarrels, seeds of war, illnesses, and from these the deaths of boys and youths, miscarriages among pregnant women, the death of birds, famine, thunder, and lightning with such force of winds that they can uproot trees. Likewise, wantonness and license in fornication, and the casting down of good men. If in Cancer: they indicate a multitude of locusts descending and devastating the harvest, and thus scarcity of grain and of other crops, either gnawed by them or indeed ruined by worms produced in them. Likewise, they foretell wars, discord, shipwrecks, plundering, famine, and very many evils. If in Leo: they portend the destruction of buildings, infestations of wolves, and from them many hindrances among men, the production of worms in crops, madness in dogs, eye afflictions, and wars. If in Virgo: they signify many labors, pains, and fevers, tremors, ulcers, and pustules, especially in the female sex, in whom miscarriages will be greatly to be feared. Likewise, vexations of good men, and the license of evil men in living. If in Libra: they denote scarcity of rain, the rule of winds, drying up of rivers, shortage of crops, terrible earthquakes. Likewise the death of princes, killings, betrayals, and other such things. If in Scorpio: they portend a multitude of wars among princes and men, contentions, and revolutions of kingdoms. Moreover, labors and illnesses in every kind of person: dangers and pains of women in childbirth, afflictions of the parts serving generation, and the most certain corruption of the fruits of the earth. If in Capricorn: they foreshadow great license in living among wicked men, fornications, adulteries, wars, quarrels, poisons given to princes. Likewise the severity of winter, hail, and snow; hence scarcity and lack of crops. If in Aquarius: they bring popular illnesses, wars lasting a long time; darkness of the air with the violence of winds, thunder, and lightning. Moreover, a mournful pestilence, and the unexpected death especially of men of the highest rank. If finally they appear in Pisces, they indicate the calamitous condition of the common people, savage wars, rebellions, and betrayals.

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LEXICON 400 iteru periculosa etit nauigatio, & detrimentum patietur ars piscatoria. 141 Ad hæc adueriendum, quod si in Oriente fuerit appari- tio, res indicata velocius accider, si verò in Occidente se- riùs. Loca autem quæ maximè his incommodis laborabunt sunt in quæ cauda Phoenomeni inclinabit, vel sanè subiecta signis, in quibus fieri conspicuum. Hæc ex Iunctino, cui s è cæteri scriptores de Comeris astipulantur. Vincentius tamen Guinitius è Societate I & v, in Oratione habita de Cometa anni 1648. viso in Romano hemisphærio conten- dit, eos non minus felicitatem quam infelicitatem afferre, cum tamen homines ob inditum à natura genium infor- tunia magis obseruent, quam prospera. Cæterum Ricciolus in Almagesto nouo lib. 8. sett. 1. cap 2. post longam huius rei vencilationem concludit, quod si Cometæ elementates sint, vniuersaliter, & ex natura sua habent obnunciare in- signem aliquam rerum mutationem in natura sublunati factam, cuius effectus nondum desierint, sed haud ita mul- tò post sint prodieri, iuxta dispositionem materiæ, & con- cursum aliarum causarum. Si verò cælestes sint, & ex ma- teria ætherea producti, à Deo ordinatos esse tum vt morta- les oculos ad cælum erigant; tum vt inde magnum aliquid expectent, vel in se, vel in suis regionibus quasi Dei lingua sint: maximè verò in iis quibus fuerint perpendicula- res, aut multum in horoscopo morabuntur. 142 PVTSATIO apud Astronomos est commissio dispositionis suæ, quam facit Planeta alteri ad quem proijcit radium, aut in cuius dignitatibus reperitur: tunc enim communicat esse suum, ac naturam ipsi, quem pulsat. Sicut econira Re- ceptio dicitur acceptatio, quam facit planeta pulsatus dispo- sitionis ab aliosibi commissæ. Ea autem est in triplici dif- ferentia, provt aduersù Abraham Auenarre in suo intro- ductorio; Virtutis, Potestatis, & Naturæ. Pulsatio virtutis est cum planeta fuerit in eius Domino, Exaltatione, Tripli- cite, aut Termino, & coniungatur alteri planetæ, aut il- lum respiciat: tunc enim suam virtutem dicetur alteri com- mittere. Pulsatio potestatis est cum planeta alium respici- cit radio perfectæ amicitiæ, qualis est Trinus, aut imper- fectæ, qualis est sextilis; tunc enim inter ipsos erit perfecta commixtio, & potestatis pulsatio. Pulsatio naturæ pluribus etiam modis sit. Primò cum planeta jungitur alteri planetæ existenti in suo domicilio, vel exaltatione. Secundò cum jungitur alteri de sua conditione, & natura, vt si masculus masculo, diurnus copuletur diutno, ac nocturnus noctur-

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LEXICON 400 there will be a dangerous voyage, and the fishing trade will suffer loss. 141 It should also be noted that if the apparition is in the East, the matter indicated will happen more quickly; if in the West, more slowly. The places that will especially suffer from these inconveniences are those toward which the tail of the phenomenon inclines, or certainly those lying beneath the signs in which it is seen. This is from Junctinus, to whom most other writers on comets agree. Vincentius Guinitius, however, of the Society of Jesus, in an oration delivered on the comet seen in the Roman hemisphere in the year 1648, argues that they bring happiness no less than misfortune; yet men, because of the tendency implanted by nature, observe misfortunes more than prosperous events. Moreover, Ricciolus, in the New Almagest, book 8, sect. 1, chap. 2, after a long discussion of this matter, concludes that if comets are elemental, in general and by their nature they announce some remarkable change in things occurring in sublunary nature, the effects of which have not yet ceased, but are to appear not long afterward, according to the disposition of the matter and the concurrence of other causes. But if they are celestial, and produced from ethereal matter, they have been ordered by God, both that mortals may raise their eyes to heaven, and that from there they may expect something great, either in themselves or in their regions, as though they were the language of God; especially in those places to which they are perpendicular, or where they remain a long time in the horoscope. 142 PULSATION, among astronomers, is the commission of its own disposition, which one planet makes to another at which it projects a ray, or in whose dignities it is found; for then it communicates its being and nature to the one it strikes. Likewise Reception is called the acceptance that the struck planet makes of the disposition entrusted to it by another. This, however, is of three kinds, according to Abraham Avenar in his introductory work: of Virtue, of Power, and of Nature. Pulsation of virtue is when a planet is in its domicile, exaltation, triplicity, or term, and joins another planet, or regards it; for then it is said to entrust its virtue to the other. Pulsation of power is when a planet regards another by a ray of perfect friendship, such as the trine, or imperfect friendship, such as the sextile; for then there is a perfect mixture between them, and a pulsation of power. Pulsation of nature also occurs in several ways. First, when a planet is joined to another planet existing in its own domicile or exaltation. Second, when it is joined to another of its own condition and nature, as if a masculine planet were coupled with a masculine one, a diurnal with a diurnal, and a nocturnal with a nocturnal.

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MATHEMATICVM. 401 no. Tertiò cum planeta velox existens in suis dignitatibus respicit tardiorem nullam dignitatem habentem in loco ipsius velocioris; nam tunc velox dicetur propriam naturam tardiori transmiserê. PUNCTVM definitur ab Euclide, Cuius pars nulla est: Est enim minima pars quantitatis, seu illud extremum, quod in vlteriores partes diuidi nullo modo potest saltem conceptu, licet non re: Quandoquidem Philosophi ferè omnes cum Arist. 6. Physic. text. 1. & 1. Gener. text. 8. non admirunr puncta indiuisibilia in continuò, sed partes, & partes in infinitum diuisibiles, ac distinctas, eo quia punctum, provt indiuisibile considerarum, nullam habeat extensionem, deberet enim tangere aliud secundum se totum, alioquin non esset indiuisibile: Nihilominus tamen hoc Mathematici non atendunt, sed minimam quantitatem, quæ sensibus obuiet, & concipiarur esse incapax omnis dimensionis, longitudinis nempe, latitudinis, & profunditatis, quarum, vel omnes, vel aliquam saliem reperire est in qualibet quantitate extensa, punctum appellant. Vnde Plin. lib 1. cap. 68. Non aliud terra uniuersa, inquit, quin Mundi punctum: Quia videlicet Terra in comparatione totius Machinæ Munda[n]næ, & Orbium superiorum est instar puncti indiuisibilis, inextensi, neque longi, neque lati, neque profundi: & ideò nulla est differentia radij proiecti à stella in Firmamento per lineam rectam in centrum, & in superficiem terræ; quia profectò terra in anta distantia, & respectu ad Firmamentum planè insensibilis est, proindeque se habet vt punctum. Corpus igitur, quod concipitur esse neque longum, neque latum, neque profundum, dieitur punctum, perindeque est in quantitate continua, ac in discreta vnitas, vel in successiva, quale est tempus, instans. Quod, vt aliquo modo concipiamus, debemus imaginari extremum alicuius subtilissimè acus, vel minimum foramen, aur characterem per ipsam, vel calamum in papyro signarum: qui rursus, si vlterius producatur, lineam efformet, longam quidem, sed nec latam, nec profundam, duobus in extremitaribus punctis terminatam. Si verò concipiaur idem character indiuisibilis & in longum & in latum productus, vel duæ, aut plures lineæ parallelæ se inuicem, & lateraliter constringentes, constituerent superficiem: si demum producatur ram in longum, quam in latum, & in profundum, cuiusmodi esset si plures superficies super alias concipia-

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MATHEMATICVM. 401 no. Thirdly, when a swift planet, existing in its dignities, looks to a slower one that has no dignity in the place of the swifter; for then the swift is said to have transmitted its own nature to the slower. POINT is defined by Euclid as that of which there is no part: for it is the smallest part of quantity, or that extreme which can in no way be divided into further parts, at least in conception, though not in reality. Since, however, almost all the Philosophers, with Aristotle, Phys. 6, text. 1, and Gen. 1, text. 8, do not admire points as indivisible in a continuum, but rather as parts, and parts divisible into infinity and distinct, because a point, considered as indivisible, has no extension; for it would have to touch another by its whole self, otherwise it would not be indivisible. Nevertheless, Mathematicians do not attend to this, but call a point the smallest quantity that meets the senses, and is conceived as incapable of all dimension, namely length, breadth, and depth, one or all of which are found in every extended quantity. Hence Pliny, lib. 1, cap. 68: “No other thing,” he says, “is the whole earth than a point of the world.” For the Earth, in comparison with the whole fabric of the world and the higher spheres, is like an indivisible, unextended point, neither long, nor broad, nor deep; and therefore there is no difference between a ray projected from a star in the Firmament in a straight line to the center and to the surface of the earth, because truly the earth at so great a distance, and in relation to the Firmament, is altogether imperceptible, and so behaves as a point. A body, then, which is conceived as neither long, nor broad, nor deep, is called a point; and likewise, in continuous quantity as in discrete, unity, or in successive quantity, such as time, an instant. In order to conceive this in some way, we must imagine the extreme point of the finest needle, or the smallest hole, or a mark made by a pen upon paper; which again, if carried farther, will form a line, indeed long, but neither broad nor deep, bounded at both ends by points. But if the same indivisible character is conceived as extended both in length and in breadth, or if two or more parallel lines, constraining one another laterally, are taken together, they would constitute a surface; if finally it is extended both in length and in breadth and in depth, such as it would be if several surfaces are conceived one upon another,

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LEXICON 402 mus, tunc habebimus corpus solidum omnis dimensionis capax. Et hæc sunt tria genera quanti, secundum trinam dimensionem, circa quæ voluitur omnis Geometriæ labor, & speculatio. Porrò punctum, etsi quantum non sit, nihilo- minus eius prima, & potissima est consideratio in Geometria: sine enim ipso quantitas vlla percipi haud posset, eo prorsus pacto, ac numerus sine vnitare, cum tamen vnitas numerum non constituat, sed tamen in numero sit eius initium, eius & finis. Vnde anguli omnes in figuris tam planis, quam solidis, quæ tamen angulos habeant, & circulares non sint in puncta necessariò terminari concipendi sunt. 144 PVTEVS ab aliquibus diciur in exlosidus, quod aliàs Ara, Lar, Thuribulum appellatur. Vide sub his dictionibus. 145 PVTEALE: GRADVS, vide in V. Gradus. 146 PYRAM s apud Geometras est figura solida, quæ definitur ab Euclide lib.11. propos. 2. esse eam, qua sub p'uribus planis consterta, ab vno plato, ad vnum punctum constituitur. Ex qua definitione intelligimus figuram pyramidalem ex pluribus planis ad minus tribus in longum protractis constare; quæ enim vno vel duobus planis constituitur, non pyramis, sed superficies triangularis existat necesso est. Item omnia plana, quæ pyramidem constituunt, triangularia debere esse, excepta tamen basi, vel plano, à quo omnia plana pyramidem efformantia, incipiunt, & in idem punctum desinunt, quod vel triangulum, vel quadrangulum, vel pentagonum, vel exagonum, &c. potest esse: & quale est istud planum seu basis, talis tota pyramidalis figura denominabitur; tot enim triangulis quælibet pyramis construitur, & finitur, quot angulos, & laiera planum dictum habet. 147 Porrò omne corpus seu opacum, seu luminosum, lumen suum, vel vmbram in aliud transmittit in formam pyramidalem, vt præ aliis notat Vitellio in Perspectiua lib.2. nisi quod corpus luminosum ita transmittit, vt vertex pyramidis efformatæ sit in puncto eiusdem corporis, vnde prosilit lumen, & basis cadat in superficiem corporis illuminati: corpus autem opacum ita vmbram suam transmittit, vt basis pyramidis efformatæ sit in superficie ipsius corporis vmbram suam diffundentis, & vertex in puncto corporis euiscumque ad quod vmbra protenditur. Plura apud ipsum Vitellionem, nec non apud Clauium, in Commentar. ad Elem. Euclidis.

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LEXICON 402 If we have it, then we shall have a solid body of every dimension, capable. And these are the three kinds of magnitude, according to the threefold dimension, around which all the labor and speculation of Geometry revolves. Moreover, a point, although it is not a magnitude, nevertheless is the first and most important consideration in Geometry: for without it no magnitude could be perceived, just as number could not exist without unity, although unity does not constitute number, but in number is its beginning and its end. Hence all angles in figures, both plane and solid, which nevertheless have angles and are not circular, must necessarily be conceived as terminating in points. 144 PUTEUS is called by some in exlosidus, which elsewhere is called Ara, Lar, Thuribulum. See under these words. 145 PUTEALE: GRADUS, see under V. Gradus. 146 PYRAMIS among geometers is a solid figure, which Euclid defines in Book 11, proposition 2, to be that which, being made up of several planes, is formed from one plane to one point. From this definition we understand that a pyramidal figure consists of several planes, at least three, drawn out in length; for that which is composed of one or two planes is not a pyramid, but must rather be a triangular surface. Likewise, all the planes that make up a pyramid ought to be triangular, except for the base, or plane from which all the planes forming the pyramid begin and in the same point end, which may be a triangle, or square, or pentagon, or hexagon, etc.: and as is such a plane or base, such also will the whole pyramidal figure be named; for each pyramid is constructed and finished with as many triangles as the plane in question has angles and sides. 147 Moreover, every body, whether opaque or luminous, transmits its light or shadow to another in a pyramidal form, as Vitellio particularly notes in Perspectiva, Book 2, except that a luminous body transmits it in such a way that the vertex of the formed pyramid is at the point of that body from which the light springs, and the base falls upon the surface of the illuminated body: but an opaque body transmits its shadow in such a way that the base of the formed pyramid is on the surface of the very body spreading its shadow, and the vertex at the point of whatever body toward which the shadow extends. More on this in Vitellio himself, and also in Clavius, in the Commentary on Euclid’s Elements.

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MATHEMATICVM. 401 PYROIS Græcè dicitur Martis astrum ab ignea natura, co- lore, & fulgore dictum. Vide in V. Mars. PYTHETES. Vide Pithetes. 149 PYTHON ab aliquibus dicitur serpens sidus in exlo ad 150 manus Ophiuci. Nomen à fabulis derivatum à Pythone quodam serpente ex putredine terræ producto, quem postea ab Apolline telis confossum, exlo inuexerunt, atque in eius figuram stellas quasdam veneficæ naturæ sapientes Astronomi colligarunt. Q QVADRA Græcè Plinthis, apud Geometras dicitur quodlibet instrumentum planum in quadratam figuram abiens: vnde ab aliis ex figura quam referebat Quadra appellabatur mensa illa parua, & portatilis, super qua carnes & cibaria in partes tribui consueuerunt: item &c panes olim in quadratam figuram efformatos, quadras dicebant: vnde est illud Virgilij 7. Æneid. Patulis, nec parcere quadris. Nune tamen pressius audit Quadra instrumentum Mathematicum rectangulum, quo quælibet figura plana in quatuor partes secatur, ex ea constituens quadratum, eubum vnde, & QVADRANTAL, & Cubus, & Quadrata figura dicitur quæ 2 omni ex parte sit quadra, seu quæ sex planis quadrilateris, & rectangulis constat, & in quancumque partem incubuerit, semper æqualis in omni dimensione erit, & immotam seruans stabilitatem, quales sunt taxailli, & resseræ, quibus in alueolo luditur. Quadrantal etiam dicitur mensuræ genus, de qua nihil ad nos. QVADRANGVLVS dicitur figura Geometria quatuor angulis constans, vr Parallelogrammum, Rhombus, Romboides, &c. de quibus omnibus suo loco. QVADRANS GEOMETRICVS est instrumentum Mathematicum, quod iure inter omnia Mathematica instrumenta principatum obtinet: siquidem eius ope omnia ferè Geometriæ, Astronomiæ, aliarumque Mathematicarum disciplinarum operationes, & eomplentur, & facilè percipiuntur: sed præcipuè deseruit ad inquirendam poli elevationem, Solis, aliorumque siderum, tam de die, quam de nocte altitudinem supra horizontem, declinatio- nem, ab inuicem distantiam, locum in Zodiaco, aliaque permulta, quibus tota Astronomia, ae Geometria ad praxim reducitur, & completur. Est igitur Quadrans Geome-

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MATHEMATICVM. 401 PYROIS is called in Greek the star of Mars, so named from its fiery nature, color, and brightness. See Mars in the letter V. PYTHETES. See Pithetes. 149 PYTHON by some is called the serpent star in the sky near the hands of Ophiuchus. The name is derived from a fable, from a certain serpent Python produced from the corruption of the earth, whom Apollo later pierced with arrows; and they placed it in the sky, and to its figure wise astronomers gathered certain stars of a venomous nature. Q QVADRA, in Greek Plinthis, is called by geometers any flat instrument taking a square form: whence, from the shape it represented, that little and portable table was also called by others Quadra, on which meat and provisions used to be divided into portions: likewise also loaves formerly fashioned into a square shape were called quadras: whence is that of Virgil, Aenid 7, “Patulis, nec parcere quadris.” Now however, more strictly, Quadra is understood to mean a rectangular mathematical instrument, by which any plane figure is cut into four parts, making from it a square, a cube, whence also QVADRANTAL, and Cube, and a square figure is said to be one that is square on every side, or that consists of six quadrilateral and rectangular planes, and whichever way it may be laid, it will always be equal in every dimension, and preserving unmoving stability; such are dice, and the game pieces with which one plays in a small board. Quadrantal is also said to be a kind of measure, concerning which nothing is our concern. QVADRANGVLVS is called a geometric figure consisting of four angles, such as the parallelogram, rhombus, rhomboid, etc., all of which are treated in their proper place. QVADRANS GEOMETRICVS is a mathematical instrument, which rightly holds the chief place among all mathematical instruments: for by its aid almost all operations of geometry, astronomy, and the other mathematical disciplines are both carried out and easily understood: but it is especially useful for investigating the elevation of the pole, the height of the sun and of the other stars above the horizon, their declination, their distance from one another, their place in the zodiac, and many other things, by which the whole of astronomy and geometry is reduced to practice and completed. Therefore the Geometric Quadrant is...

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tricus corpus solidum, & planum quartam partem circuli referens, atque in area sua descriptos continens per gyrum grad. 90. qui omnes per lineam rectam conueniunt in puncto, quod incidit in eius angulum, & est centrum totius circuli, & quadrantis, & ex hoc centro dependet perpendiculum aliquod ex filo, quo mediante in limbo, gradus, eorumqueque fractiones metimur. Ad vnum autem laterum eius affixa sunt duo pinnacidia, seu spicillæ, cum foraminibus rese per lineam rectam respicientibus, non quidem amplis, sed taliter fabricatis, vi per ea res quidem mensurabilis probè conspici queat, & oculus nimio astri fulgore non præstringatur, sed rectà in ipsum, innoxieque possit intendere ipso quidem in ea quadrantis parte, quæ limbo sinitur constituto, astro verò, vel alia quavis re mensurabili ex aduersa, iuvt ex centro quadrantis radium suum in oculum possit prolicere. 5. Eius vsus hic est: Visa Solis de die, vel Lunæ aut alterius insignis stella de nocte altitudine supra terram; si vis præcisè indagare, quanta sit eius eleuatio supra terram, declinatio ab æquatore, &c. vel etiam quota sit hora diei vel noctis, id per quadrantem duplici via assequi poteris. Primò per distantiam eius à vertice in cordis subiensis. Secundò per adminiculum sphæræ, quam præstat in hoc negotio eligere solidam. Nam posito, quod tantum eleuetur Sol, siue aliud Astrum supra horizontem, quantum abscindit in gradibus perpendiculi filum ex cento quadrantis pendens, computa gradus illos, & transfer ad sphæram collocatam ad elevationem poli suprà tuum horizonte, atque ibi in tali distantia graduum ex Meridiano computandorum constituere debes solem, aut aliud Astrum in sphæra, in quanta ipsum in cælo esse ex quadrante inuestigasti. At quorsum, inquies, metiri potero talem aliudinem, atque ab quadrante ad sphæram meam transferre? Sanè id facillimè poteris. Accipe igitur circinum, atque in sphæra tot gradus in æquatore enumera (ipse enim, vt alibi dictum est, totius sphæræ, totiusque motus regula est, & mensura tot inquam gradus enumera & circino comprehende, quot gradus siue ab horizonte, siue à vertice elongatur illa stella, quam per quadrantem vidisti: deinde circino inuariato pone pedem eius in contactu horizontis, & alio sursum è regione verticis eleuato, tandiu spæram voluas, quandiu locus solis eo die cadat subtus pedem alterum circini, & sic habebis elevationem Solis. Quo præstito reuerrere cum Sole, & constitue eum ad contactum horizontis, ac si tunc oriretur, & nota gradum

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A solid, flat body representing a quarter of a circle, containing in its surface a circumference marked with 90 degrees, all of which meet by a straight line in a point that falls on its angle, and is the center of the whole circle and quadrant; and from this center hangs a certain plumb-line by means of a thread, through which we measure in the limb the degrees and their fractions. To one of its sides are affixed two pinnacidia, or sighting vanes, with holes looking along a straight line, not indeed large, but so fashioned that the measurable object may be properly seen through them, and the eye may not be dazzled by the excessive brilliance of the star, but may safely look straight at it; the quadrant itself being in that part where the limb is placed, while the star, or any other measurable object, is on the opposite side, so that, from the center of the quadrant, it may cast its ray into the eye. 5. Its use is this: when the altitude of the sun by day, or of the moon or another notable star by night, has been observed above the earth, if you wish precisely to investigate how great is its elevation above the earth, its declination from the equator, etc., or even what hour of day or night it is, you can achieve this by means of the quadrant in two ways. First, by the distance from the zenith in the suspended cord. Second, by the aid of the sphere, which it is best in this matter to choose solid. For once it is assumed that the sun, or some other star, is elevated above the horizon by as many degrees as the thread of the plumb-line hanging from the center of the quadrant cuts off, count those degrees and transfer them to the sphere set at the elevation of the pole above your horizon; and there, at such a distance of degrees to be reckoned from the meridian, you ought to place the sun or other star in the sphere, in the same position as you have investigated from the quadrant that it is in the heavens. But, you will ask, how can I measure such an altitude and transfer it from the quadrant to my sphere? Surely you can do this very easily. Take therefore a pair of compasses, and on the sphere count so many degrees on the equator (for it, as has been said elsewhere, is the rule and measure of the whole sphere and of the whole motion), and, I say, count and grasp with the compasses as many degrees as the star is distant, either from the horizon or from the zenith, which you saw by means of the quadrant. Then, keeping the compasses open, place one leg of it in contact with the horizon, and with the other raised upward opposite the zenith, turn the sphere until the place of the sun on that day falls beneath the other leg of the compasses; and thus you will have the elevation of the sun. This done, return with the sun and place it at the contact of the horizon, as if it were then rising, and note the degree

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MATHEMATICVM. 401 gradum æquatoris; qui tunc cum sole oritur: postea volue solem ad locum prioris elevationis, quam per circinum ob- seruasti, ac vide quot gradus æquatoris intercipiuntur in- ter locum illum prius inuentum, cum quo Sol oriebatur, & alium, qui tunc emergit ex horizonte, sole in tanta altitu- dine constituto, nam quot quindenis gradibus emersit æqua- tor ex horizonte, à puncto exortus Solis, tot horæ ab eius- dem exortu effluxerunt, quot gradum minutæ, vel resi- dua, tot horæ excessus similiter transferunt, dando singulis gradibus æquatoris singula quatuor minuta temporis, & singulis quindenis minutis æquatoris, singula minuta tem- poris. Quod etiam præstari poterit de nocte computando tempus intermedium inter ortum æquatoris cum Stella ali- qua & ortum alterius gradus eiusde æquatoris, Stella interim in certa aliqua a terra altitudine constituta, qua per quadrantem vidisti. Sit pro exemplo. Solem primum gradum Cancri permeantem in aliqua hora diei supra horizontem eleuatum contemplatus es, & ex quadrante gradus etiam quibus su- pra horizontem erigitur adnotasti. Cum his igitur gradibus perge ad æquatorem sphæræ, & extenso circino loca alterum eius pedem in contactu horizontis, alterum per rectam li- neam ad verticem supra primum gradum Cancrisinde sphæ- ram voluês, quo vsque gradus iste ad horizontem sit consti- tutus, & obserua gradum æquatoris coascendentem, qui profectò erit circiter gr. 70. pro ratione elevationis poli tuæ regionis: & notatis ex parte his gradibus, siste solem in tanta altitudine quantam per quadrantem vidisti, verbi gra- tia in gr. 64. computatis in limbo meridiani, & aspice quis- nam gradus æquatoris supra horizontem emergat, seu con- stituatur in contactu ipsius horizontis, videbis esse gr. 185. Subtractis igitur ex hoc cumulo grad. 70. illis nempe, qui tunc oriebantur cum sole in horizontis contactu posito (quandoquidem ij iam intelliguntur exorti) remanebunt gr. 115. quibus diuisis per 15. prouenient horæ 7. & insuper min. 40. temporis, hoc est duæ tertiæ partes vnius horæ, eo- quia ad integras graduum per 15. diuisiones supersunt adhuc gr. 10. qui 40. temporis minuta appellant: quod quidem tempus computatum ab exortu solis in illa die, dabit horas præcisas quas explorare volueris ferè circa meridiem. Quod ità exactè per horologia, siue Mechanica, siue Solaria præ- stare nullatenus possumus. Et hæc est certa, ac tutissima via indagandi horam præcisam alicuius differentiæ tempo- ris, ad quam Coe estem Figuram ad amussim erigere vo- lumus. C c

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MATHEMATICVM. 401 degree of the equator; which then rises with the sun: afterward turn the sun to the place of the former elevation, which you observed by the circle, and see how many degrees of the equator are intercepted between that place previously found, with which the Sun was rising, and the other, which then emerges from the horizon, the sun being set in so great a height; for as many fifteenths of degrees as the equator has emerged from the horizon, from the point of the Sun’s rising, so many hours have passed since its rising; and as many degrees and minutes, or the remainder, so many excess-hours likewise transfer, giving to each degree of the equator four minutes of time, and to each fifteen minutes of the equator, one minute of time. This also may be done by night, by calculating the intermediate time between the rising of the equator with some star and the rising of another degree of the same equator, the star meanwhile being set at some definite altitude above the earth, which you observed by the quadrant. Let it be as an example. You have observed the Sun passing the first degree of Cancer elevated above the horizon at some hour of the day, and from the quadrant you have also noted the degrees by which it is raised above the horizon. With these degrees then proceed to the equator of the sphere, and with the compass extended, placing one foot in contact with the horizon, the other by a straight line to the zenith above the first degree of Cancer, then turn the sphere until that degree is placed at the horizon, and observe the coascending degree of the equator, which certainly will be about gr. 70, according to the elevation of the pole in your region; and having noted these degrees in part, place the sun at so great an altitude as you saw by the quadrant, for example at gr. 64, counted on the limb of the meridian, and see which degree of the equator emerges above the horizon, or is placed in contact with the horizon itself; you will see it to be gr. 185. Therefore, subtract from this total 70 degrees, namely those which were then rising when the sun was placed in contact with the horizon (since indeed these are already understood to have risen), there will remain 115 degrees, which, divided by 15, produce 7 hours, and moreover 40 minutes of time, that is, two thirds of one hour, because to the complete divisions of the degrees by 15 there remain still 10 degrees, which are called 40 minutes of time: and this time, computed from the sunrise on that day, will give the precise hours you wish to determine, almost at midday. This we cannot in any way perform so exactly by clocks, whether mechanical or solar. And this is the sure and safest way of investigating the precise hour of some difference of time, to which we wish to erect the Coe estem Figure exactly. C c

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LEXICON Eodem modo operari poteris & de nocte, sed cum hoc addito. Nam visa altitudine stellæ, vel Lunæ per quadrantem & ea in sphæra postea inuenta, inspice qui gradus æquatoris in tali positu ex horizonte emergat, & seorsim nota: deinde volue sphæram ad contactum loci Solis in horizonte, & numera quot gradus intersint inrer hunc & illum, qui emergebat in tali altitudine stellæ, computando tot horas ab oriente, vel occidente Sole, quot quindecim gradus interim emetserunt (subducendo, vt supra, partes, quæ iam ante intelligui tur elapsæ) nam habendo noxitiam diei, ac noctis habebis, etiam quot horæ noctis transierint, quot etiam supertint expositu sideris in tali altitudine supraterram. Alia etiam munia, & vtilitates Quadrantis geometrici vide apud Clauium in Geometria pract. alioque authores qui de eius vsu ex professo scripserunt. 7. QVADRANTES dicuntur in sphæra quatuor præcipuæ ipsius intersectiones tam in Mundo, quam in Zodiaco consideratæ: duo quidem Orientales, & masculini, qui computantur ab ortu solis vsque ad meridiem, & ab occasu vsque ad Imum in Mundo, atque ab Ariete vsque ad initium Cancri, nec non ab initio libræ vsque ad finem Sagittarij in Zodiaco; duò vero occidentales, & fæminini in Mundo, à culmine vsque ad occasum, & ab Imo vsque ad ortum, atque in Zodiaco ab initio Cancri vsque ad Libram, & ab initio Capricorni vsque ad finem piscium. Ab his enim sidera incipiunt influere & successivè continenter intendunt primas qualitates, & quia ab oriente, & ab ariete vsque ad Meridiem, vel Initium Cancri incipiunt sidera influere calorem, & continenter intendunt, & calor est qualitas maximè actiua, ideo appellantur hi quadrantes masculini: quia ab Culmine vsque ad occasum & à Cancro vsque ad libram incipit remitti calor, & successivè introduci siccitas, quæ est qualitas passiua, ideo dicuntur hi quadrantes fæminini: similiter quia ab occasu ad imum, & à Libra ad Capricornum cedit paulatim siccitas, & incipit intendi frigiditas, qualitas item actiua, & masculina, ideò hi quadrantes etiam masculini: quia demum ab imò ad ortum, atque ab Capricorno ad Arietem sensim cedit frigiditas, & paulatim introduciur, & augescit humiditas, qualitas fæmina & passiua, ideò hi reliqui duo quadrantes dicuntur etiam fæminini. Pari etiam ratione Ptolemæus quatuor hominis ætates his quatuor quadrantibus assimilat lib. 1. Quadrip. c. 8. sic inquiens. Omnia animansia prima ætate dum tenera sunt & molia, vt ver humore abundans (in Vere etenim

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LEXICON In the same way you can work by night as well, but with this addition: for after observing the altitude of a star or of the Moon with the quadrant, and then finding that position on the sphere, look to see which degree of the equator in such a position rises above the horizon, and note it separately; then turn the sphere to the point where the Sun touches the horizon, and count how many degrees lie between that and the point which was rising at such an altitude of the star, computing, from sunrise or sunset of the Sun, as many hours as fifteen degrees have meanwhile traversed (subtracting, as above, the parts which are already understood to have elapsed); for by having the day and the night together you will also know how many hours of the night have passed, and how many remain from the exposure of the star at such an altitude above the earth. See also other duties and uses of the geometric quadrant in Clavius, in Practical Geometry, and other authors who have written specifically on its use. 7. QUADRANTS are called, in the sphere, the four principal intersections of it considered both in the World and in the Zodiac: two indeed eastern and masculine, which are reckoned from sunrise to midday, and from sunset to the nadir in the World, and from Aries to the beginning of Cancer, and also from the beginning of Libra to the end of Sagittarius in the Zodiac; but two western and feminine, in the World from the zenith to sunset, and from the nadir to sunrise, and in the Zodiac from the beginning of Cancer to Libra, and from the beginning of Capricorn to the end of Pisces. For from these the stars begin to influence and successively and continuously intensify the primary qualities, and because from the east, and from Aries to midday, or the beginning of Cancer, the stars begin to influence heat and continually strengthen it, and heat is the most active quality, therefore these quadrants are called masculine; because from the zenith to sunset and from Cancer to Libra heat begins to diminish, and dryness is successively introduced, which is a passive quality, therefore these quadrants are called feminine: similarly because from sunset to the nadir, and from Libra to Capricorn, dryness gradually gives way, and coldness begins to increase, likewise an active and masculine quality, therefore these quadrants are also masculine: because finally from the nadir to sunrise, and from Capricorn to Aries, coldness slowly gives way and humidity is gradually introduced and increases, a feminine and passive quality, therefore these remaining two quadrants are also called feminine. By a similar reason Ptolemy, in book 1 of the Quadripartite, chapter 8, likens the four ages of man to these four quadrants, saying thus: All living things in their first age, while they are tender and soft, are like spring, abounding in moisture (for in spring indeed

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MATHEMATICVM. 407 maxima est humiditas, iam per præcedentem anni quadrantem intensa, quæ interim transacta hyeme paulacima incipit remitti, & introduci successiuè calor, ita vt ista sic propria huius tempestatis qualitas, quam ipsa adducit) Deinde secundam ætate donec maneat vigor magis calent, vt a[n]tas. Tertia cum vigor languesit, & initium est consumptiones siccitas maior est, vt in autumno. Postrema frigidior est, vt hyems, q[uæ] a proxima est, morti. De hac re plura diximus etiam in VV. Masculinum, & Fæmininum, & alibi passim. < 8.> QVADRATVS, vt paulò antè antè dictum est apud Geometras est figura quatuor larera æqualia omnino habens inter se, & item in æquales angulos eosque rectos definens, vt proinde quadratus perfectus, & Orthogonius audiat, ad differentiam Parallelogrammi, Rhombi, & Rhomboidis, quæ aut non omnes angulos, aut non omnia latera, aut etiam neutra habent æqualia, vt suo loco dictum est. Apud Astronomos verò pari ratione dicitur aspectus, seu familiaritas à sideribus contracta per quartam circuli partem, hoc est per gr. 90. in Zodiaco, & per totum arcum semidiurnum, vel seminocturnum in Mundo. Ab his enim punctis ductæ ad inuicem lineæ perfectum quadratum æquilaterum, & rectangulum efformant. Et hic quidem aspectus infaustus est, & hostilis, imperfectæ tamen inimicitæ, vt asserit Ptolemæus lib. 1. c. 12. Quemadmodum Oppolitio est aspectus perfectæ inimicitæ. Cuius rei rationem, sicur & qualitatis aliorum aspectuum ex consonantiis musicis expiscatam afferunt Keplerus, & Titus in Cælesti Philosophia, vt nos alibi adnotauimus. Nihilominus tamen directio Aphetæ ad suum quadratum est omnium pessima, & vitæ exitialis. Quod & Nicepso, & Petoxyris antiquissimi Astronomi atque Arabum reges mistice docuerunt, dicentes neminem posse transgredi Trimorion hoc est congeriem trium signorum, quam importat quadratus radius, qui profectò secundum rationem locorum directione extendi potest vsque ad annos 120. vt ex iis quæ diximus cum de directionum mensura, colligi potest. Quod & concordat cum termino à Creatore post diluvium vitæ hominis constituto, vt habetur Genes. 6. cum dixit. Non permanebit spiritus meus in hominem æternum, quia caro est, eruntque dies illius centum viginti annorum. Quod, etsi de termino poenitendi illis hominibus dato, intelligant Hioronymus, Augustinus, Abulensis, & alij: Philotamen Ludæus, Ioseph, Rupertus, & alij magis ad literam explicant dictum de termino vitæ C c ij

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MATHEMATICVM. 407 the greatest is moisture, which is now already intensified by the preceding quarter of the year, and which, meanwhile, after the winter that has passed, begins little by little to abate, and heat is gradually introduced, so that this is the proper quality of this season, which it itself brings on) Then the second age, while vigor remains, is warmer, as in spring. The third, when vigor begins to fail and consumption begins, is drier, as in autumn. The last is colder, as winter, which is next to death. More on this matter we have also spoken elsewhere under the headings Male and Female, and elsewhere throughout. < 8.> A SQUARE, as was said a little before among geometers, is a figure having four sides entirely equal to one another, and likewise defining equal angles, and those right angles; and therefore it is called a perfect square and orthogonius, in distinction from the parallelogram, rhombus, and rhomboid, which either do not have all their angles equal, or not all their sides equal, or even neither, as was said in its place. Among astronomers, however, it is likewise called an aspect, or familiarity contracted by the stars through a fourth part of the circle, that is, through 90 degrees in the Zodiac, and through the whole semi-diurnal or semi-nocturnal arc in the world. For from these points lines drawn to one another form a perfect square, equilateral and rectangular. And this aspect is indeed inauspicious and hostile, though nevertheless of imperfect enmity, as Ptolemy asserts in book 1, chapter 12. Just as opposition is an aspect of perfect enmity. The reason for this matter, and likewise the quality of the other aspects, is drawn from musical consonances by Kepler and Titus in the Cælestial Philosophy, as we have noted elsewhere. Nevertheless, the direction of the hyleg to its square is the worst of all, and destructive of life. This also the most ancient astronomers, Nicepsos and Petosiris, and the kings of the Arabs, mystically taught, saying that no one can pass beyond the Trimorion, that is, the heap of three signs, which the square ray signifies; and indeed this, according to the relation of places, can be extended by direction as far as 120 years, as may be gathered from what we have said concerning the measure of directions. And this also agrees with the limit of human life appointed by the Creator after the Flood, as is found in Genesis 6, where he said: My spirit shall not remain in man forever, because he is flesh; and his days shall be a hundred and twenty years. Which, although Jerome, Augustine, Abulensis, and others understand as referring to the term of repentance given to those men, Philotamen the Jew, Josephus, Rupertus, and others explain more literally as referring to the term of life. C c ij

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LEXICON hominis constituto, Fortè quia cum prius Apheta suum quadratum impunè transgredi poterat, saltem sine abscissione, & progredi illæsus vsque ad oppositionem, & eo amplius; vt euenit, & concessum fuit Patriarchis antiquis; postmodum Deus constituit vt prima occurstatio Aphetæ ad Anaretam, nempe ad suum quadratum, vitam abscinderet. Sed de hæc re iterum redibit sermo in V. Trimorion. 9. QVADRATRA CIRCVIT, quæ à Græcis dicitur Tetragonismus, nil aliud est, vt ipsum nominis erymon præsefert, quam circulum quadratum red lere; hoc est cuilibet circulo exhibere quadratum æquale illi ex amussi respondens. Quod vti facile est intelligere, ità difficile admodum facto exequi, ac pethiere, & hactenus quod sciam à nullo est præstitum, licet quamplurimi, iique sapientissimi Mathematici, ac Principes ipsi pluribus annis in hoc negotio detenti, vsque ad defectionem spiritus desudarint. Etenim Circulum quadrare olim conati sunt apud Veteres, Antiphon, Bryso, & Hyppocrates Chius, quorum meminit Arist. 1. Physic. text. 11. & 1 Poster. text. 21. & 1. Elench cap. 10. Apud Recensiores verò Orontius Finçus, Campanus, & Nicolaus Cardinalis Cusanus, qui omnes Circuli Quadraturam inuenisse se iactant: & Cardinalis quidé Cusanus, scripto ad Georgium Peurbachium libro, duplicem à se inuentam profert: Prima autem in eo consistebat, vt, si ex semidiametro Circuli dati, & chorda quadrantis eiusdem, directè coniunctis, diameter alteri circulo constitueretur, triangulus æquilaterus posteriori circulo inscriptus, priori circulo Isoperimeter foret. Alia circuli quadrandi ratio ab Cusano excogitata, hæc erat. Si in circulo ductis duabus ad angulos rectos diametris una hinc inde producatur, & alteri ab uno extremo sic accommodetur sublensa trientis circuli, vt facto centro, qua in alia diametri parte desinit, circumducatur, & transiens per dictum extremum, secet hinc inde productam diametrum, recta intercepta his sectionibus erit circuli semicircumferentia æqualis. Verum hæc quadrandi circuli ratio, de qua controuertebatur, non erat. Nam circuli quadratura non consistit in eo quod conuerti debeant lineæ arcuales in rectas, aut econtrà: sed quod area circuli, seù superficies illa circularis, æqualis omninò sit, neque excedat neque excedatur ab area superficiesi quadratæ: ita vt Circulum quadrare aliud planè non sit, quàm reperire aream alicuius quadrati parem, & æqualem areæ cuiuspiam circuli, vt proinde areæ veriusque figuræ sint æque capaces. Non enim id sic intelligi debet, vt areæ istæ inter se congruant, & planè coapten-

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LEXICON of a person constituted, perhaps because before, Aphæta could pass his square boundary with impunity, at least without being cut off, and proceed unharmed even to the opposition, and beyond it; as happened, and was granted to the ancient Patriarchs; afterwards God ordained that the first encounter of Aphæta with Anareta, namely with his square, should cut off life. But on this matter the discussion will return again in the V. Trimorion. 9. QVADRATRA CIRCVIT, which among the Greeks is called Tetragonismus, is nothing else, as the very etymology of the name suggests, than to square the circle; that is, to furnish any circle with a square equal to it and corresponding by exact measure. This, though easy to understand, is very difficult in practice to carry out, and to this day, as far as I know, has been accomplished by no one, although very many, and those most wise mathematicians, and even princes themselves, having been occupied for many years in this business, have toiled to the exhaustion of their spirit. For indeed people formerly attempted to square the circle among the ancients: Antiphon, Bryso, and Hippocrates of Chios, whom Aristotle mentions in 1 Physic. text. 11, and 1 Poster. text. 21, and 1 Elench. cap. 10. Among the more recent authors, however, Orontius Finaeus, Campanus, and Nicolaus Cardinalis Cusanus, all of whom boast that they have found the squaring of the circle; and Cardinal Cusanus certainly, in a book written to Georgius Peurbachius, sets forth a twofold method discovered by himself: The first consisted in this: if from the semidiameter of a given circle, and the chord of its quadrant, directly joined, a diameter were formed for another circle, then the equilateral triangle inscribed in the latter circle would be isoperimetric with the former circle. Another method of squaring the circle, devised by Cusanus, was this. If in a circle, two diameters being drawn at right angles, one be extended on this side and that, and to the other, from one end, there be fitted a raised line measuring a third part of the circle, so that, the center being fixed, from the point where the other diameter ends, it may be carried around, and passing through the said end, cut the diameter extended on this side and that, the straight line intercepted by these sections will be equal to the semicircumference of the circle. But this method of squaring the circle, about which controversy was raised, was not the true one. For the squaring of the circle does not consist in this, that curved lines should be turned into straight ones, or vice versa: but that the area of the circle, or that circular surface, should be altogether equal, and neither exceed nor be exceeded by the area of a square surface: so that to square the circle is nothing other than to find the area of some square equal and comparable to the area of any circle, so that therefore the surfaces and more properly the figures may be equally capacious. For this is not to be understood as though those areas should agree with one another and fit perfectly together, and

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MATHEMATICVM. 409 vut ad invicem: quod certè est impossibile, non tam in areis, quam in lineis ipsis, atque in quibuslibet figuris forma & specie diversis, cum ratio figuræ consistat in indivisibili: vnde in nullo vquam casu potest triangulum coagtrari quadrangulo, nec linea curua lineæ rectæ, nam si rectum congrueret vquam curuo, iam non esset rectum, sed indueret rationem curui, vt ostendit Arist. 7. Physi. text. 23. et 10 Metaph. commens. 10. Consistit igitur Circuli Quadratura in area quadrati reperienda, quæ in æquè capax, ac circularis. Neque verò, ex hoc, quod reperiantur quatuor lineæ arcuales, quæ in longitudine tantæ sint, vt in rectum protensæ congruanti, & adaptari possint quatuor lineis rectis quadrangulum efformantibus, (quod sanè difficile admodum non est, & fortè assecutus est, Cusanus) sequitur eo ipso inuentam esse quadrationem circuli, hoc est aream huius æqualem esse areæ quadrati eo modo, quo verè æquales sunt lineæ ipsas viriusque areas terminantes; Nam, vt benè Euclides, semper forma circularis amplior est, & capacior, cæteris paribus, aliis non circularibus: quod ideo, vel ex hoc dicitur perfectissima, & diuidior. Hoc posito, Circuli quadraturam non modò inueniri posse, sed adhuc post Aristotelem, inueniam fuisse, ac tradidiam à Sexto Pythagonio, Archimede, Apollonio, Nicomede & Carto, affirmat Iambicus apud Simplicium, in 1. Physic. text. 11. Certè Archimedes, etsi perfectè circulum non quadrarit, dedit tamen certissimam viam quadrandi, ac docuit ea quibus cognitis, & compertis necessariò circulus ipse venit quadrandus: si enim quadrauit Parabolam, quæ est area, duabus lineis, alterâ rectâ, arcuali alterâ, intercepta, eur non etiam circulus ipse duabus parabolis constans, æquè quadrari poterit; Deinde Hippocrates Chius quadrauit Lunulas, vt manifestum est; at si omnes quadrasset quas in sua demonstratione, qua circuli quadraturam possibilem asseruit, in medium fert, absque dubio circulum quadrauisset, vt fatentur etiam ipsi, qui eiusmodi demonstrationem redarguunt. Cur igitur si vnam, aut alteram Lunulam quadrare potuir, non potuisset, & reliquas, cum omnium par ratio sit, & omnium quadratio circuli quadraturam perfecisset? Non ergò impossibilis est quadratura Circuli, licet fortè nemo fuerit, qui eum actu quadraverit. Et hæc de Quadratura Circuli saris, superque sint dicta: qui plura volet videat Simplicium vbi supra, Zimaram in Concordantiis super 10. librum Metaphysic. Alexandrum Aphrodisæum, super primum librum Physic. ac C e iij

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MATHEMATICVM. 409 one to another: which is certainly impossible, not so much in areas as in the lines themselves, and in any figures differing in form and shape, since the ratio of a figure consists in the indivisible; whence in no case whatever can a triangle be made equal to a quadrangle, nor a curved line to a straight line; for if the straight ever agreed with the curved, it would no longer be straight, but would take on the nature of the curved, as Aristotle shows, 7 Physic. text. 23, and 10 Metaph. comm. 10. Therefore the squaring of the circle consists in finding the area of a square, which is of equal capacity with the circular one. Nor, indeed, from the fact that four arcual lines are found, which in length are so great that, when extended into a straight line, they may agree and be adapted to four straight lines forming a quadrangle, (which is truly very difficult, and perhaps Cusanus achieved it) does it follow for that very reason that the squaring of the circle has been found, that is, that the area of this is equal to the area of a square in the way in which the lines themselves are truly equal, which terminate the one and the other areas; for, as Euclid well says, the circular form is always broader and more capacious, ceteris paribus, than other non-circular forms: and for this reason it is called, either because of this, most perfect and more divided. Granted this, Iamblichus, apud Simplicius, on 1. Physic. text. 11, affirms that the squaring of the circle can not only be found, but that even after Aristotle it was found and handed down by Sextus Pythagoreus, Archimedes, Apollonius, Nicomedes and Carto. Certainly Archimedes, although he did not perfectly square the circle, nevertheless gave the most certain way of squaring it, and taught those things which, once known and understood, necessarily bring it about that the circle itself must be squared: for if he squared the parabola, which is an area intercepted by two lines, one straight, the other curved, why should not the circle itself also, consisting of two parabolas, be able to be squared equally? Then Hippocrates of Chios squared lunules, as is manifest; but if he had squared all those which, in his demonstration in which he asserted the squaring of the circle to be possible, he sets forth, in the middle, then without doubt he would have squared the circle, as even those confess who refute such a demonstration. Why then, if he could square one or another lunule, could he not also have squared the rest, since the reason for all is the same, and the squaring of all would have completed the squaring of the circle? Therefore the squaring of the Circle is not impossible, although perhaps there was no one who actually squared it. And enough, and more than enough, has been said about the Squaring of the Circle: whoever wishes to know more let him consult Simplicius where above, Zimara in the Concordances on the 10th book of the Metaphysics, Alexander of Aphrodisias, on the first book of the Physics, and C e iij

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410 LEXICON Ioannem Bureon, qui peculiari libello omnium demon- strationes in hac re factas accuratè collegit. 10. QVADRIPARTITVM antonomasticè audit insignè opus Claudij Ptolemæi Astrologorum facile Principis, de side- rum Iudiciis edisserens, atque in quatuor partes triburum: in quarum prima agit vniuersaliter de natura, & qualirari- bus siderum, & signorum: in secunda descendit ad effe- ctuum naturalium considerationem, qui à sideribus vniuersaliter producuntur super Regna, & Prouincias; quales sunt pestilentiæ, caritates, diluua, aëris immurationes &c. In tertia progreditur ad particulares effectuum causas, atque ad eam parrem, quam Genethliacam vocant: in qua re modum Antiquorum, præsertim Arabum negligit, ac seponit, & solum rationes vniuersales effectuum ab intima philosophia excerptas, adducit, atque ab experientia rerum magistra confirmat: quod si alij Astrologi nil remerè ansi, & solum Ptolemaeo duce, hanc iudicandi prouinciam inirent, profectò non ità facilè vt accidit sæpissimè salle- rentur, aliosque fallerent, proindeque in hominum deri- sionem, atque indignationem irent: Siquidem, vt benè ad- uertit Titus in breuiariis ad Quadripart. non potest plenè tradi hæc disciplina per aphorismos, qui & omnes recense- ri minimè possunt, & eorum quilibet absolurè procedit, cum ramen innumerabiles exceptiones ex diuersis circumstantiis patiatur. In quarta demum parte agit Ptolemæus de iis, quæ aliunde nato aduentant, & sunt illi veluti exrinseca, vt de Facultaribus, Magisterio, fortuna honoribus, & dignitati- bus &c. Sicque libro finem imponit. Scripsit autem Ptole- mæus græce & obscurè nimis, quapropter variæ circumfe- runtur latinæ operis versiones, quas inter, Gemma Frisio Mathemarico celeberrimo teste, longè præstat translatio facta ab Antonio Gogua Grauiensi, quæ nuper Paravii apud Framborum edita est opera eruditissimi P. D. Placidi de Tisis Monachi O'iuetani in florentissima Ticinensi Aca- demia Mathesis professoris, adiectis ad singula capita bre- vibus noris, quibus speculariones suas iam pridem in Coe- lecti Philosophia Mundo expoliras, omnes ad Ptolomæi mentem excogitatas fuisse demonstrat. 11. QVALITAS ex Arist. 5. Metaph cap. 14. dicitur esse propria cuiusque substantia differemia: est enim, vt explicat D. Th. p. 2. quæst. 49. art. 2. & Suar. in Metaph. disp. 42. sect. 1. Accidens intrinsecum res, quatenus rem in ratione substantia iam constitutam, modificat, ornat, & perficit sum in es- sandum in operando. Huiusmodi sunt, quas meritò pri-

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410 LEXICON Ioannes Bureon, who in a separate pamphlet has carefully collected all the demonstrations made on this matter. 10. QUADRIPARTITUM is an outstanding work, antonomastically so called, of Claudius Ptolemy, the easy Prince of Astrologers, explaining the judgments of the stars, and divided into four parts: in the first, he deals universally with the nature and qualities of the stars and signs; in the second, he descends to the consideration of natural effects that are produced universally by the stars upon kingdoms and provinces, such as pestilences, famines, floods, alterations of the air, etc. In the third, he proceeds to the particular causes of effects, and to that part which they call Genethliac; in this matter he neglects and sets aside the method of the Ancients, especially the Arabs, and brings forward only the universal reasons of effects, drawn from the deepest philosophy, and confirmed by experience, mistress of things: and if other astrologers, with no real attempt, and relying only on Ptolemy as guide, were to enter this province of judging, surely they would not so easily, as happens most often, be deceived themselves and deceive others, and thus incur men’s ridicule and indignation. For, as Titus rightly notes in the abridgments to the Quadripartitum, this discipline cannot be fully conveyed through aphorisms, which cannot all be enumerated, and each of them proceeds absolutely, while nevertheless it suffers innumerable exceptions arising from different circumstances. In the fourth and final part Ptolemy deals with those things that come to a person from elsewhere and are, as it were, extrinsic to him, such as faculties, mastery, fortune, honors, and dignities, etc. And so he brings the book to an end. Ptolemy wrote in Greek, and in a style far too obscure; for this reason various Latin versions of the work are in circulation, among which, according to the testimony of the celebrated mathematician Gemma Frisius, the translation made by Antonio Gogua of Gravia is by far superior; it was recently published at Paris by Frambourg, through the work of the most learned Father Don Placido de Tisis, a Camaldolese monk and professor of mathematics at the flourishing Ticinese Academy, with brief notes appended to each chapter, by which he shows that his own speculations, long since polished in the Coelesti Philosophia Mundo, were all devised in accordance with Ptolemy’s intention. 11. QUALITY, from Aristotle, Metaphysics 5, chap. 14, is said to be the proper difference of each substance: for, as St. Thomas explains, part 2, question 49, article 2, and Suarez, in the Metaphysics, disp. 42, sect. 1, it is an intrinsic accident, insofar as it modifies, adorns, and perfects a thing already constituted in the order of substance, so that it may be in action as in being. Such are those qualities which rightly are first called ...

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MATHEMATICVM. 411 mas qualitates vocant, caliditas, & frigiditas, humiditas & siccitas, quoniam primæ sunt, quæ per omnem substan- tiam materialem transcendunt, in omnibus vniuersaliter reperiuntur, & sunt veluti primi fontes, & radices, vnde cæteræ exsurgant, & quibus mediis operentur. Quando- quidem ex earum contrarietate, qua inuicem se expellunt, combinatione disparatarum, quæ se mutuò fouent, eiusdem quoad certos gradus intensione, ac remissione, mira hæc vniuersarum rerum consurgit varietas, conformitas, & differmitas, passio, & resistentia, mixtio, & alterario, ge- neratio, & corruptio, quæ alternantibus veluti modulis harmoniam quamdam efformantes, mundum istum exor- nant. Ex his, in primis rerum seminibus, hoc est elemen- ris, binæ, exque non contrariæ qualitates insunt, quarum vna actiua est, qua in reliqua possit vnumquodque agere, altera passiua, qua illis agentibus possit cedere, sicque, vt ait Arist. 2. de generat. text. 22. inter elementa sit concordia secundum vnam qualitatem, vt conseruentur, & discordia secundum alteram, vt ex eorum elementorum pugna, & cor- ruptione mixta omnia consurgant: Itaque igni convenit ca- lor, & siccitas, aëti humiditas & calor, Aq[ui]næ frigiditas & humiditas; Tetra siccitas, & frigiditas: itavt ex duabus qualitatibus, quæ in singulis elementis reperiuntur illa di- catur vnicuique magis propria, quæ in eo vincit, & in cer- to illud genere constituit, illa minus propria, quæ priori subseruir, & in suo esse dat conseruari. Sic igni calor est pro- prius, qui illum maximè facit actuum, siccitas autem in suo calore conseruat: Aëri maximè convenit humor, cum sit passibilis, & in aliud facilè transmutabilis, cui præstò est calor, vt possit raresieri: frigiditas propria est aquæ; quæ per humorem sese magis insinuat: Tandem siccitas magis conuenit terræ quæ à frigore habet, quod sit difficile termi- nabilis, quatenus subiectum densat, ac facit difficile termi- nabile. Hinc quia calor & frigus, quatenus habent vim vniendi, & segregandi, seu reddendi subiectum faci è, vel difficile terminabile sunt qualitates actiux, econtra siccitas, & humiditas dicuntur passiux quia ipsis convenit magis pati, quam agere itavt faciant, vt subiectum facile, vel difficile terminetur, cuiusmodi est in lapide cui ob siccitatem diffi- cile est alienam formam recipere, & viceuersa in ceta, quæ ob humorem sit facilis ad quamcumque figuram recipiendam. Cæterum non ideò istæ passiux dicuntur, quia nul- lam habeant activitatem, nam & ipsæ valent eiusdem gene- ris qualitates in aliis subiectis producere, sed ideò dicun- C c iiiij

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MATHEMATICVM. 411 what they call primary qualities, heat, and cold, moisture and dryness, because they are the first, which transcend through every material substance, are found universally in all things, and are as it were the first sources and roots, from which the others arise, and by which they operate as means. For from their contrariety, whereby they mutually repel one another, from the combination of unlike things, which mutually cherish one another, from the same thing according to certain degrees of intensifying and remitting, there arises this wondrous variety, conformity, and difference of all things, passion and resistance, mixture and alteration, generation and corruption, which, alternating as it were in modules, fashion a certain harmony and adorn this world. From these, in the primary seeds of things, that is, in the elements, two qualities, and those not contrary, are present, of which one is active, by which each thing can act upon the other; the other passive, by which, when those things act, it can yield; and so, as Aristotle says, 2 De generatione, text 22, there is among the elements concord according to one quality, so that they may be preserved, and discord according to the other, so that from the conflict and corruption of those elements all mixtures may arise. Thus to fire belong heat and dryness; to air, moisture and heat; to water, coldness and moisture; to earth, dryness and coldness: so that from the two qualities found in each element, that is called more properly its own which prevails in it, and constitutes it in a certain genus; that which is less proper, which serves the former, and causes it to be preserved in its being. Thus heat is proper to fire, which makes it most active; dryness, however, preserves it in its heat: moisture especially suits air, since it is passible and easily changed into another thing, for which heat is at hand, so that it may be rarefied; coldness is proper to water, which through moisture insinuates itself more readily; lastly dryness more suits earth, which by reason of cold has this, that it is difficult to be bounded, inasmuch as it condenses the subject and makes it difficult to be bounded. Hence, because heat and cold, inasmuch as they have the power of uniting and separating, or of making the subject easy or difficult to bound, are active qualities, conversely dryness and moisture are called passive, because it belongs to them rather to suffer than to act, so that they make the subject easy or difficult to be bounded, as is the case in stone, which by reason of its dryness is difficult to receive an alien form, and vice versa in wax, which by reason of its moisture is easy to receive any figure whatsoever. Nevertheless, they are not therefore called passive because they have no activity, for they too are able to produce qualities of the same kind in other subjects, but they are called so because...

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412 LEXICON tur, quia subiectum magis aptum faciunt ad recipiendum, quam ad agendum. Sic ignis magis actiùs est, quam aër, aqua magis, quam tellus; rursus magis passiuus aër, quam aqua, tellus, quam ignis, quia profecto in iis respectu aliorum vincunt qualitates actiuæ. 2. Porrò ex commixtione harum primarum qualitatum, oriuntur in mixtis alia quas secundas vocant, sunt:que præsertim illæ quindecim à Galeno enumeratæ. de vsu partium par. 9. & 1. de fac. natural. cap. 6. & sunt Mollities ac durities, lentor & friabilitas, raritas & densitas, lenitas &c asperitas, leuitas & grauitas, crassitudo & tenuitas, item diuersitates odorum, colorum, & saporum, quorum quilibet, vt notum est, continet varias qualitatum species, & gradus, ex quibus diuersitas illa conturgit: omnes tamen referuntur ad quauor illas primas tanquam ad prima mutationum initia, quæ in hoc mundo Elementari fiunt. 3. An autem qualitates elementares eiusdem rationis sint, ac cælestes, magnum dissidium est inter Philosophos, Astronomosque. Affirmant Conimbricenses 1. de Generat. cap. 3 quæ 4. eo quia experientia ipsa commonstrat eosdem prorsus effectus progigni ab Calore cælesti, elementari, ac vitali. Similiter vbi in planetis colores consimiles his nostis videmus, consimiles etiam effectus eosdem promere experimur. Nogant alij communiter, & admittunt lolum eas habere aliqualem conuenientiam, ac sympathiam. Quinimò & Tius qualitates mixtorum non esse elementares, sed è cælo derivatas affirmat, vt nos fusè diximus in V. Mixta Fernelius, Argenterius, & alij admittunt in mixtis huiusmodi qualitates, quas vocant occultas, quæ quoniam supergrediuntur qualitates elementorum, existimant nullo modo esse ab illis participatas, nec posse ad illas referri, non tamen dicunt à cæcis derivatas, sed esse qualitates totius substantiæ quatenus ipsa per se immediatè & nullo interposito instrumento illam agendi seu operandi potentiam sortiatur, & ideò dicunt occultas, quia nullarum qualitatum auxilio quæ sensibus subiectæ sint manifestari possunt, quippe ea ratione qua substatia ipsa sensibus, & intellectui est occulta, eadem has qualitates occultas, & reconditas dici putar. 14. Et sanè, vt certa ab incertis segregemus, certum est mixta omnia, si puris qualitatibus elementaribus constarent, eas longè remissiores debere esse, quam in ipsis elementis, quippe eas & ab elementis derivatas haberent, & qualitatibus contrariis oppugnatas, vnde & infirmiores, quod non est in elementis puris, qua ratione Arist. de sensu

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412 LEXICON ... are more passive, because they make the subject more fit for receiving than for acting. Thus fire is more active than air, water more than earth; conversely, air is more passive than water, earth than fire, because, certainly, in these, in relation to the others, the active qualities prevail. 2. Moreover, from the mixture of these primary qualities, other qualities arise in mixed bodies, which are called secondary, and these are especially the fifteen enumerated by Galen: in De usu partium, part 9, and in De facult. natural. cap. 6. These are softness and hardness, tenacity and friability, rarity and density, smoothness and roughness, lightness and heaviness, thickness and thinness, likewise the differences of odors, colors, and tastes, each of which, as is known, contains various species and degrees of qualities, from which that diversity arises; yet all are referred to those four primary qualities as to the first beginnings of the changes that take place in this elemental world. 3. Whether, however, the elemental qualities are of the same kind as the celestial ones is a great matter of disagreement among philosophers and astronomers. The Conimbricenses affirm it, in 1 De Generatione, cap. 3, quæ 4, because experience itself shows that the very same effects are produced by celestial, elemental, and vital heat. Likewise, where in the planets we see colors similar to these known ones, we also experience that similar effects are produced by them. Others commonly deny it, and admit only that they have some sort of likeness and sympathy. Indeed, Tius also affirms that the qualities of mixed bodies are not elemental, but derived from the heavens, as we have explained at length in V. Mixta. Fernelius, Argenterius, and others admit in mixed bodies such qualities, which they call occult, and since these surpass the qualities of the elements, they judge that they are in no way participated from them, nor can they be referred to them; nevertheless, they do not say that they are derived from the heavens, but that they are qualities of the whole substance, insofar as it itself directly and immediately, and without any intervening instrument, acquires that power of acting or operating; and for that reason they call them occult, because they can be manifested by no aid of qualities subject to the senses, since in the same way that the substance itself is hidden to the senses and to the intellect, so also these hidden and concealed qualities are thought to be so called. 14. And truly, if we separate the certain from the uncertain, it is certain that all mixed bodies, if they were composed of pure elemental qualities, would have to be far more subdued than in the elements themselves, since they would both have been derived from the elements and be opposed by contrary qualities, and hence weaker; which is not the case in the pure elements, on account of which Aristotle, in De sensu...

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CAP. 4. docuit sola mixta perfecta cedere in viuentium alimentum, neque in hoc negotio quicquam posse pura elementa conferre, quorum qualitates, vipote intensores, non possunt à viuentium qualitatibus alterari, sieque vinci, & transire in substantiam aliti, vt nos etiam alibi adnotamus. Si igitur omnia mixta constarent ex qualitatibus elementorum, vel sanè iis solis, sequeretur, nullum esse mixtum potentius elementis: At enim videmus multa longè potentioribus qualitatibus pollere, multa longè diuersis, quæ non ad illas primas reduci possunt. Sic videmus herculeum lapidem attrahere ferrum, non equidem per vllam calidam; aut frigidam qualitatem, quia nunquam experientia visum fuit calida vel frigida tanta vi ferrum, aut aliud quid adeò ponderosum attrahere; sed nec per qualitates secundas, tum quia istæ ortum habent à primis, tum etiam quia nemo vidit vnquam rarum vel densum, gravè, vel leue, crassum tenue, durum vel molle simile quid præstare. Pari modo electrum allicere paleas, marinum leporem pulmonem, Cantharides vesicam exulcerare, non alias partes, præcipuè verò iccur mollius, & propinquius: Torpedinem manum piscatoris stupore afficere: Echeneidem pisciculum parum magnam nauem turgidis velis volantem firmare, &c. Quis igitur mentis compos existimet admirandas has operationes fieri à caliditate, frigiditate, siccitate, aut humiditate, vel à cæteris consequentibus qualitatibus? Igitur vel ab ipsa rerum substantia, quæ immediat habeat hos miros effectus progi- gnere, vel sanè à superiori, & occulta quadam qualitate, quæ non pateat sensibus prodeant necesse est admirandæ huiusmodi virtutes. Quod autem non ab substantia rerum immediatè prodeant; præter communem ferè omnium Philosophorum, Theologorumque consensum dicentium nullam substantiam immediatè agere, sed mediis suis potentiis tanquam proportionalibus instrumentis; vt præ cæteris euidentissimè probar. D. Thomas 1. part. quæst. 77. art. 1. & in 1. sentent. dist. 3. quæst. 4. art 2 id manifestè suadet ratio & pluribus euincit experientia. Quandoquidem potentiæ operatrices à Philosopho collocantur in prædicamento qualitatis, quod genus differt natura & essentia à substantia: Idque ex eo quod actio ex natura sua petit tum distinctionem agentis à suo termino, tum aliquam dissimilitudinem secundum speciem, inter subiectum & agens, ad hoc vt istud possit suum effectum in illud inducere: nemo enim agit in sibi simile, vt idem Arist, docet 1. Phys. & 1. de Gener. cap. 9. text. 50. &

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CHAP. 4. It taught that only mixed bodies, and perfectly mixed ones, can be changed into the nourishment of living things, and that in this business pure elements can contribute nothing; for their qualities, being more intense, cannot be altered by the qualities of living things, and so be overcome, and pass into the substance of the thing nourished, as we also note elsewhere. If therefore all mixed bodies consisted of the qualities of the elements, or indeed of those qualities alone, it would follow that no mixed body would be more powerful than the elements. Yet we see many things endowed with much more powerful qualities, many with qualities altogether different, which cannot be reduced to those first qualities. Thus we see, by Hercules, the loadstone attract iron, not indeed by any hot or cold quality, because experience has never shown that anything hot or cold attracts iron, or anything else so heavy, with such force; nor yet by secondary qualities, both because these arise from the primary ones, and also because no one has ever seen anything rare or dense, heavy or light, thick or thin, hard or soft, perform anything similar. In the same way amber attracts straw, the sea hare the lung, cantharides cause the bladder to ulcerate, not the other parts, but especially the liver, being softer and nearer; the torpedo fish affects the fisherman’s hand with numbness; the echeneis, a small fish, holds fast a ship flying with swollen sails, and so forth. Who then, if in his right mind, would think that these wondrous operations are caused by heat, cold, dryness, or moisture, or by the other resultant qualities? Therefore such admirable powers must necessarily arise either from the very substance of things, which immediately has these wondrous effects, or else from some higher and hidden quality, which does not lie open to the senses. But that they do not arise immediately from the substance of things; besides the common agreement of nearly all philosophers and theologians, who say that no substance acts immediately, but only through its own powers as proportional instruments; as among others St. Thomas most clearly proves in 1st part, question 77, article 1, and in 1st Sentences, distinction 3, question 4, article 2, reason plainly suggests it and experience confirms it in many ways. For the operative powers are placed by the Philosopher in the category of quality, a genus which differs in nature and essence from substance. And this is so because action by its nature requires both the distinction of the agent from its term, and some dissimilarity in species between the subject and the agent, so that the latter may be able to bring its effect into the former: for no one acts upon what is like himself, as the same Aristotle teaches in Physics 1 and On Generation, book 1, chapter 9, text 50, and

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LEXICON alibi passim. Igitur aliqua contrarietas intercedere debet interagens & passum. Atqui substantiæ nullum est contrarium positiuum, & ipsa alteri non aduersatur, vnde possit ex contrarietate induci ad agendum in aliud. Ergo vt agere possit debet qualitatibus obuiantibus indui; quibus protecto con-gredientibus cum iis, quæ in subiecto reperiuntur, insur-gat pugna, & ex pugna in altero actiuiore præpollentia, & victoria; vnde demum effectus resultet, & introductio nouæ formæ. Porto huic doctrinæ non refragatur experientia: Vbi enim videmus aliquam substantiam, puta fer-rum ignem aut calorem concipere, statim valet eundem in aliud subiectum aptum transfundere; eum alias in suis qualitatibus frigidis manens, frigus etiam in eodem sub- iecto sibi proximo generabit. Neque etiam id clarè vide-re est in dictis qualitatibus, quas vocant occultas, Si enim magnes per suam substantiam ferum traheget, non illi vtique aduersaretur allij succus: Cicuta non magis hominibus esset exitialis, quam sturnis, quos tamen nutrit, & impinguat: Doronici non vtique canes occiderent, homi-nibus aurem potiùs suppetias ferrent, &c. Stat igitur hæc omnia, & similia aliquibus qualitatibus ab rerum substan-tia, atque à primis quatuor distinctis pollere, quæ in diuer-sis subiectis, pro ratione qualitatum quibus constituuntur diuersos etiam sortiuntur effectus. 16. Iam verò, hoc stabilito, clarè, ni fallor, elucet, huius-modi qualitates, aliqua sublimiori causa, nempè à cælorum influentiis ortum ducere, & per virtutes cælitus inditas ope-rari, miroaque hos, quos videmus, effectus progignere. Quæ profectò & multæ sunt, & planè inassequilibes, atque vt vocat Galenus, de locis affectis cap 8. ineffabiles, adeò vt ad Glauconem scribens dixerit, quod si ad vnguem has occultas qualitates nosceret, se proculdubio supparem Æsculapio erederet. De quibus tamen hoc vnum tuto pro-nunciari poterit, eas primas elementorum qualitates, etsi fortè non graduum intensione, nihilominus excellentia agendi & eminentiore virtute longè exuperare, vnde neque in earum ordine poni possunt, neque ad ipsas tan-quam ab ipsis exortas reduci, licet, aliquæ eum iis seruent quandam affinitatem; proindeque habeat ipsis foueri, & ad- iuuari, aliæ nullam, sed longè obscura, sublimiori, ac dissi-ta ratione polleant. 17. QANTITAS est proprium, & latissimum omnium Ma-thematica-um disciplinarum obiectum, non quidem quâ accidens est, materiæ addicta, & sensibilibus qualitatibus

Transcription: Translated (English)

LEXICON likewise everywhere. Therefore some contrariety must intervene between the agent and the patient. But substance has no positive contrary, and it does not oppose another thing, whence it could be led by contrariety to act upon another. Therefore, in order that it may act, it must be endowed with resisting qualities; with which, when they come into conflict with those found in the subject, a struggle arises, and from the struggle, in the more active party, preponderance, and victory; whence at length the effect results, and the introduction of a new form. Moreover, experience does not contradict this doctrine: for where we see some substance, say iron, taking on fire or heat, immediately it is able to impart the same to another suitable subject; otherwise, remaining in its cold qualities, it will also generate cold in the same neighboring subject. Nor is this clearly seen even in those qualities which they call occult. For if the magnet by its substance draws iron, surely the juice of garlic would not oppose it: hemlock would no more be deadly to men than to starlings, which nevertheless it feeds and fattens: aconite would not kill dogs, but rather would bring aid to men, and so forth. Thus stand all these things, and others like them, endowed with some qualities distinct from the substance of things, and from the first four, which in different subjects, according to the measure of the qualities by which they are constituted, also produce different effects. 16. Now then, this having been established, it clearly appears, unless I am mistaken, that qualities of this kind derive their origin from some higher cause, namely from the influences of the heavens, and operate through virtues implanted from above, and wonderfully produce these effects that we see. These indeed are many, and plainly beyond our grasp, and as Galen calls them, in On the Affected Parts, ch. 8, ineffable, so much so that writing to Glaucon he said that if he knew these occult qualities to a hair’s breadth, he would unquestionably consider himself equal to Aesculapius. Concerning them, however, this one thing may safely be declared: that they far surpass the first qualities of the elements, if not in the intensification of degree, yet in excellence of action and more eminent power; whence they can neither be placed in their order, nor reduced to them as though arising from them, although some may preserve with them a certain affinity; and therefore they may be nourished and assisted by them, while others have no such affinity, but possess a far more obscure, higher, and more distant relation. 17. Quantity is the proper, and most extensive, object of all the mathematical disciplines, not indeed insofar as it is an accident, attached to matter, and to sensible qualities

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MATHEMATICVM. 415 implicita, (hoc enim considerare pertinet ad Philoso- phos;) sed provt dicit extensionem partium, & est mensura quædam apta, vt & alia quanta per ipsam metiamur, & vt ipsa vicissim ab aliis menturetur. Et ideò Mathesis pro- priè considerat quantum, hoc est quantitatem non in ab- stracto, sed in concreto, provt in subiecto reperitur: Phi- losophi autem quantitatem abstractam, provt dicit aliquid in corporibus quantis, inhærens substantiæ, ab ipsa eorum substantia, & qualitatibus distinctum, faciensque illam im- penetrabilem: quo pacto definitur ab Aristotele 5. Metaph. c 13. esse id quod est diuisibile in ea qua in sunt: quorum vnumquodque, vnum quid aptum est esse: quibus verbis in- dicare voluit extensionem partium in ordine ad te, itave Quantitas constet ex partibus diuisilibus, & diuisilibus in infinitum, quatum profecto quælibet apta sit esse vnum quid totum respectu aliarum partium, in quas est etiam diuisibilis; itavt nullum sit assignare terminum huius diui- sibilitatis, sed quæuis minima quantitas consideretur, vt semper extensa sit, & sit vltia in alias partes extensas di- uisibilis. Quare Philosophus negat puncta indiuisibilia in- extensa, sed in omni minima quantitate considerat omnem extensionem cogitatione saltem apprehensam, licet fortè Physicam diuisionem non sit capax admittere. Mathemati- cus autem, quoniam rationem Mensuræ solum considerat in quantire, ideò parum illi refert, an Quantitas constet ex partibus diuisilibus in infinitum, vel punctis indiuisibi- libus, sed minimam quantitatem, quæ non sit actu capax trinæ dimensionis vocat punctu indiuisibile, illam quæ vni- eam dimensionem admittit, appellat lineam, primamq[ue] hanc dimensionis rationem, quæ aliam non supponit, longitu- dinem: quæ duplicem habet dimensionem, vocat superficiem, longam quidem, & latam; itavt latitudo secunda dimensionis ratio supponat semper in corpore mensurabili longitudinem: Si verò Quantum omnis dimensionis sit ca- pax, & in longum. & in latum, & in altum dicitur corpus, tertiaque hæc dimensionis species dicitur profunditas, quæ suponit reliquas duas longitudinem, & latitudinem. Hoc autem attenditur solum in quantis continuis, licet in discretis aliqualem earumdem dimensionum similitudinem inueniat Arithmetica, vt nos in loco aduertimus, ac di- ctum est etiam in Verbo Proportionalitas Porrò, ex diuersa quanti provt rationem mensuræ habet, 18. consideratione varia, & diuersa Mathematicarum discipli- narum genera orta sunt. Siquidem vel Quantum considera-

Transcription: Translated (English)

MATHEMATICVM. 415 implicit, (for this belongs to the consideration of the Philosophers;) but as it states the extension of parts, and is a certain fitting measure, so that other quantities may be measured by it, and it in turn may be measured by others. And therefore Mathematics properly considers quantity, that is, quantity not in the abstract, but in the concrete, as it is found in a subject: whereas philosophers consider abstract quantity, insofar as it denotes something inhering in bodies as quantities, distinct from their substance itself and from their qualities, and making them impenetrable. In this way it is defined by Aristotle, Metaph. 5, c. 13, as that which is divisible into the things in which it exists, each of which is adapted to be one thing; by which words he wished to indicate the extension of parts in relation to the whole, so that Quantity consists of divisible parts, and parts divisible to infinity, since every part is apt to be one whole in relation to the other parts into which it is also divisible; so that no limit can be assigned to this divisibility, but whatever the smallest quantity is considered, it is always extended, and is further divisible into other extended parts. Wherefore the Philosopher denies that there are indivisible, unextended points, but in every least quantity he considers all extension, at least as apprehended by thought, although perhaps it is not capable of admitting physical division. The Mathematician, however, since he considers only the ratio of measure in quantity, therefore cares little whether Quantity consists of parts divisible to infinity, or of indivisible points; but the smallest quantity, which is not actually capable of three dimensions, he calls an indivisible point; that which admits one dimension he calls a line; and he calls this first dimension, which supposes no other, length: that which has a double dimension he calls a surface, long and broad; so that breadth is the second dimension, and always presupposes length in a measurable body. But if Quantity is capable of every dimension, and is said to be in length, breadth, and height, it is called a body, and this third species of dimension is called depth, which presupposes the other two, length and breadth. This is considered only in continuous quantities, although in discrete ones Arithmetic finds a certain likeness of the same dimensions, as we have noted in the place, and as was also said in the word Proportionalitas. Moreover, from the different consideration of quantity as it has the ratio of measure, various and diverse kinds of mathematical disciplines have arisen. For either Quantity is considered...

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LEXICON tur vt continuum, (hoc est, provt partes aliqua vnione Phy- sica copulantur, & integrant vnum totum per se) solum sub- ratione mensuræ, proportionisque absque alio respectu; & hoc pettinet ad Geometriam, scientiam vniuersalissimam, Mathesis totius Principem, cui aliæ multæ subalternantur. Et hoc pacto contemplatur quantum Euclides in primis sex Elementorum libris, provt habet duplicem dimensionem, aptumque est in varias figuras abite, necnon à decimo vs- que ad sextum decimum, in quibus transit ad consideranda corpora solidæ omnis dimensionis capacia. Vel Quantum potest considerari discretum in partes, quæ non faciant vnum per se, sed quarum quælibet in se consistat, & dicat indiuisionem in se, & diuisionem à quacumque alia; qua ratione appellat vnitatem, & numeros; & vt tale est ob- iectum Arithmeticæ; de quo agit Euclides lib. 7. 8. & 9. vbi omnem numerorum proportionem acutissimè perscru- tatur. Rursus Quantum continuum contemplari potest, vel vt coarctatum ad amplissimum magnitudinem, nobilis- simamque materiam, qua corpora cælestia potiuntur; & hoc pertinet ad Astronomiam: vel provt est coarctatum ad terrestrem globum, cuius amplitudo, locorum distantiæ, climata, aliaque id genus perquirenda sint, & sic fundat Geographiam, Hydrographiam, Choreographiam, &c. vt suis locis dictum est. Item quantum discretum considerati potest materialiter, & formaliter: materialiter quidem, quando ratio numeri præcisè non attenditur, sed quanti- tas molis, & magnitudinis in aliquo aceruo rerum materia- lium, vt puta in frumento, vino, oleo, lapidibus consti- tuentibus aliquam domum, &c. in quibus consideratur præ- cisè moles, perinde, ac si esset vnum quantum continuum, & inde exhaustur postea artificiosè numerus partium con- stituentium, & hoc est officium Geodæsiæ, cui, & Geome- tria, & Arithmeticæ æquè purtes suas conferunt, atque auxi- liares manus suppeditant. Vel tandem mixtum quid effor- matur ex numeris, & quantitate continua, sed successua, quale est tempus; quâ videlicet fit, vt temporum interualla ad numeros apprimè respondeant, compareturque melos, & harmonia ex sonorum modulis ad tempus corresponden- tibus: & hoc est proprium Musicæ. Et hæ sunt primæ & poriores diuisiones Quanti, quod quemadmodum potest in diuersis subiectis particularibus considerati, ita & peculiares sibi vindicat disciplinas, omnes tamen sub vno Mathesis nomine comprehensas, & vel Geo- metriæ, vel Arithmeticæ duabus præcipuis Mathesis diu-

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LEXICON Either quantity as continuous, that is, insofar as parts are joined together by some physical union and make up one whole in itself, considered solely under the aspect of measure and proportion, without any other respect; and this belongs to Geometry, the most universal science, the prince of all Mathematics, to which many others are subordinated. And in this way it contemplates quantity, as Euclid does in the first six books of the Elements, insofar as it has two dimensions and is fit to be figured in various shapes; likewise in the tenth through the sixteenth, in which he passes on to the consideration of bodies capable of every dimension of solidity. Or quantity may be considered discrete, in parts which do not make one in themselves, but each of which exists in itself and signifies indivision in itself and division from any other; in which way it is called unity and numbers, and as such is the object of Arithmetic; concerning which Euclid treats in books 7, 8, and 9, where he most sharply investigates every proportion of numbers. Again, continuous quantity can be contemplated either as confined to the greatest magnitude and the most noble matter possessed by celestial bodies; and this belongs to Astronomy: or insofar as it is confined to the terrestrial globe, whose size, distances of places, climates, and other things of that kind must be investigated, and thus it founds Geography, Hydrography, Choreography, etc., as has been said in their places. Likewise, discrete quantity can be considered materially and formally: materially, indeed, when the ratio of number is not precisely attended to, but only the quantity of bulk and magnitude in some heap of material things, as for example in grain, wine, oil, stones constituting some house, etc., in which bulk alone is considered, just as if it were one continuous quantity; and then, by art, the number of the parts making it up is afterward drawn out. And this is the office of Geodesy, to which both Geometry and Arithmetic equally contribute their parts and supply auxiliary hands. Or finally a mixed thing is formed from numbers and continuous quantity, but successive, such as time; namely, in such a way that the intervals of times correspond very exactly to numbers, and melody and harmony are compared from the modulations of sounds corresponding to time: and this is proper to Music. And these are the first and principal divisions of Quantity, which, just as it can be considered in various particular subjects, so also claims for itself special disciplines, all nevertheless comprehended under the one name of Mathematics, and either of the two chief divisions of Mathematics, Geometry or Arithmetic,

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MATHEMATICVM. 47 tentiis, subalternas. Ex his manifestè liquet, omne Quantum aliqua figura præditum esse necessario debere: omne enim quodcunque concipiatur sinitum est, & terminis aliquibus clausum; termini autem attenduntur in superficie corporis quanti secundum trinam illam dimensionem, quam supra diximus. Item quantum in ratione quanti non potest suscipere magis, & minus, vt habet Arist. in prædicamentis, bicubitum enim non potest fieri magis, vel minus bicubitum: Quinque non magis quinque quam est. Similiter illi vt quantum est, nil esse contrarium: Quod avtem vnum dicatur densum, aliud rarum; vnum longum aliud breue, vnum graue aliud leue, vnum rectum, aliud curuum, &c. hoc pertinet ad figuram, atque ad qualitatem, quæ intelligiur quanto superuenire, non autem ad quantitatem. Et hæc demùm de Quanto, provt est obiectum nostrarum disciplinarum dixisse sufficiat. QVÆSTIONES ASTROLOGICÆ. Vide in V. In [interrogationes.] QVINTILIS RADIVS, seu [aspectus], est familiaritas [intercedens], inter duo sidera constituta in distania [quintæ] par- tis cæli, iuvt efforment duos angulos æquales, & obtusos in figura pentagona: Et in mundo quidem consideratus sit minor quinta parte quadrati, seu arcus semidiurni, vel seminocturni ipso quadrato; & maior sextili quinta etiam parte ipsius sextilis: in Zodiaco verò, quoniam patibus vtrinque calculus constituitur, in spatio grad. 72. Est radius de sui natura Faustus, & Felix, de nouo à Keplero experientia & ratione repertus, minus tamen effleax quam sextilis, & Trinus. Porrò Quintilis duplicatus efficit radium biquintilem, qui est distania duarum ex dictis quinque parribus figuræ pentagonæ, maior trino quinta parte eiusdem trini, radius, & ipse in genere imperfectæ amicitiæ; de quo fusè suo loco dictum. QVOTIENS apud Arithmeticos dicitur quidquid in certa numero partitione æqualiter facta proflit: seù est numerus partium in quas alius numerùs maior æqualiter diuidendus tribuitur. Talis est quatuor respectu numeri vicenarij, in tot quinarios diuidendi, vel quinque in ordine ad tot quaternarios, in quot idem numerus vicenarius assumitur diuidendus Dicitur autem quotiens, quia indicat quoties numerus diuisor in numero diuidendo contineatur, Diuisor verò is est, qui denominat pattes in quas reducitur numerus maior diuisus: qui in casu nostro est numerus quinarius,

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MATHEMATICVM. 47 ... tensions, the subalterns. From these things it is manifestly clear that every Quantity must necessarily be endowed with some figure: for everything whatsoever that is conceived is finite, and enclosed by certain limits; and limits are observed in the surface of a quantitative body according to that threefold dimension which we mentioned above. Likewise, quantity, in respect of quantity, cannot admit of more and less, as Aristotle has it in the Categories; for a two-cubit measure cannot become more or less two-cubit: five is not more five than it is. In the same way, since quantity as such has nothing contrary to it, what is called dense in one thing, rare in another; long in one, short in another; heavy in one, light in another; straight in one, curved in another, etc., belongs to figure and to quality, which is understood as supervening upon quantity, and not to quantity itself. And let this at last be enough on Quantity, insofar as it is the object of our disciplines. ASTROLOGICAL QUESTIONS. See in V. Under [interrogations.] A QUINTILE RAY, or [aspect], is a familiarity [interceding] between two stars situated at a distance of [one-fifth] part of the heaven, so as to form two equal and obtuse angles in a pentagonal figure. And considered in the world, it is less than a fifth part of the square, or of the semidiurnal or seminocturnal arc, by the square itself; and greater than the sextile by a fifth part also of that sextile. In the Zodiac, however, because the measure is established on both sides, it is in the space of 72 degrees. The quintile ray is by nature auspicious and fortunate, newly discovered by Kepler through experience and reason, though less effective than the sextile and the trine. Moreover, a doubled quintile produces the biquintile ray, which is the distance of two of the said five parts of the pentagonal figure, greater than the trine by a fifth part of the same trine; a ray, and itself among the class of imperfect friendship, concerning which more has been said at length in its place. WHENEVER, among arithmeticians, it is said of whatever results from an equal division in a certain number that it is so, it means the number of parts into which another greater number is equally divided. Such is four in relation to the number twenty, to be divided into so many fives, or five in relation to so many fours, into which the same number twenty is assumed to be divided. It is called quotiens, because it indicates how many times the dividing number is contained in the number being divided. The divisor, however, is that which names the parts into which the greater divided number is reduced: which in our case is the number five,

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LEXICON 418 quem assumo ad diuidendum viginti per quatuor, vel quaternarius, cum eosdem viginti volo distribuerre per tot quinque. Quodsi è contra vice versa numerum quinarium assumam ad multiplicandum quaternarium, &c è contra numerum quaternarium ad multiplicandum quinarium, tunc numerus 10. prosiliens dicitur productus, quia profectò est ductus vnius in alium quoadusque numerus maior confletur, vtrumque in se includens, quod tunc fieri intelligitur, cum alter ipsorum toties augetur, quoties in altero continetur vnitas: vt patet in exemplo allato; vbi quia in numero quaternario quater continetur vnitas, ideò quater adaugeo numerum quinarium, ex quo tandem prouenit numerus vicesimus productus è quaternario in quinarium. Plura de hac re vide in Clauio in Epitome Arithmetica practica cap. 1. RA 1. RABDÆ, vel Rabdi, Græcè sunt de eorum genere ostentorum, quæ in sublimi videntur, ex collisione radiorum Solis in aúqua nube rorida, sed æquabili, quæ proinde ex reflexione ignitum aliquod referunt ad modum Trabis; reuera tamen nullam substantiam habent, sed sunt meræ apparentiæ, & visus deceptiones, non secus ac Iris, Area, Vrgæ, quæ prætet nubem à sole illuminatam, nil amplius sunt. Vide in V. Vi. ga. 2. RADIUS communiter dicitur fulgor ille à sole, vel quocumq[ue] corpore luminoso per rectam lineam immissus ad aliquod aliud corpus seù opaeum, seù similiter luminosum, densum tamen, quod excipiat quidem immissum spiculum, & vlterius progredi non permittat. Ab Opticis verò definitur esse linea recta luminosa, vel illuminatio facta per lineam rectam. 3. Differt à lumine, & à luce, per hoc quod lux est prima passio, & insuper instrumentum corporis luminosi, quo lumen, & radius producuntur; lumen verò sit à luce congrenta per sui diffusionem, qua immisso radio recipitur in corpore diaphano illuminato: At Radius se habet admodum spiculi, (vnde est, quod spiculum etiam appelletur) traiecti à corporeluminoso in corpus illuminandu[m], & interim pari etiam lumen, illudque diffundit per medium diaphanum. Quare latiùs patet lumen, quam Radius, & lux: quandoquidem illud potest esse sine radio, vt in crepusculis, & in domo illuminata aëre ambiente: lux sine radio in corpo-

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LEXICON 418 when I take twenty to divide by four, or the quaternary, when I want to distribute those same twenty among five. But if, on the contrary, I take the quinary in turn to multiply the quaternary, etc., and conversely the quaternary number to multiply the quinary, then the number 10, emerging, is said to be produced, because indeed it is the multiplication of one into the other until the larger number is formed, each including the other within itself, which is then understood to happen when either of them is increased as many times as unity is contained in the other: as is clear from the example given; where because in the quaternary number unity is contained four times, therefore I increase the quinary number four times, from which at last comes the twentieth number produced from the quaternary into the quinary. See more on this matter in Clavius, in the Epitome Arithmetica practica, ch. 1. RA 1. RABDÆ, or Rabdi, in Greek are among those kinds of portents that are seen aloft, from the collision of the sun’s rays in a watery, dewy cloud, but uniform, which therefore from reflection show some fiery appearance in the manner of a beam; yet in reality they have no substance at all, but are mere appearances, and deceptions of sight, no differently from the rainbow, the area, the rods, which, beyond the cloud illuminated by the sun, are nothing more. See in V. Vi. ga. 2. RADIUS is commonly called that brightness from the sun, or from any luminous body, sent in a straight line to some other body, whether opaque, or likewise luminous, yet dense, which indeed receives the impinging point, and does not allow it to go farther. But by the Opticians it is defined as a luminous straight line, or an illumination made by a straight line. 3. It differs from brightness and from light, in that light is the first affection, and moreover the instrument of a luminous body, by which brightness and the ray are produced; brightness, however, is from light through a fitting correspondence by means of its diffusion, whereby, a ray being sent in, it is received in the illuminated diaphanous body: but a ray is related like a point, (which is why it is also called a point) projected from a luminous body into the body to be illuminated, and meanwhile likewise brightness, and it diffuses it through the diaphanous medium. Therefore brightness extends more widely than the ray and light: since indeed that can exist without a ray, as in twilight, and in a house illuminated by the surrounding air: light without a ray in a body-

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MATHEMATHICVM. 419 te luminoso, sed impediro, ne lumen suum diffundat, non autem radius sine luce, à qua est effectiuè, aut sine lumine, quod habet effectiuè, vt instrumentum lucis producendæ. 4. Triplex est radius, rectus modò explicatus; qui à corpore luminoso rectè discedit, & terminatur in aliud: reflexus, qui à corpore illuminato transmittitur, siue in ipsum corpus illuminans, siue in aliud quid sibi aduersum: & refractus, cum à medio minus raro, in rarius dissultat, vel etiam rariore in minus rarum, seù crassum progreditur, vt cum ab aëre in aquam diffonditur. Hæc autem triplex radiorum consideratio fundat triplicem scientiam, Dioptricam, Catoptricam, seù Anacampticam, & Anaclasticam, de qui- quibus. Vide Vitell. lib. 10. Opticæ, & nos suis in locis. Hinc 5. Ratius apud Astronomos audit aspectus, & configu- ratio duorum siderum in certa ab inuicem distan[n]ia è quâ vtrinque sibi immittunt radios, quibus communicata luce se muiuò roborant, aut oppugnant, provt similibus, aut dissimilibus qualitatibus fuerint præditi; vnde etiam est quod influxum erga isthæc inferiora aut augent, aut at- temperant, aut perueriunt. Sunt autem sextilis, Quadra- tus, Trinus, Quintilis, & alij, quos suprà enumerauimus in V. Aspectus. 10: Regiomonranus vult huiusmodi radios immiti per circulos in latum protensos, quorum centrum sit Astrum intuens (excepta tamen oppositione, quæ sit per dia- metrum) finis verò vbi terminatur mensura, & distantia horum radiorum, in quem si inciderit aliud Astrum dicetur accipere, & vicissim immittere talem radium, vnde est, quod quilibet radius sumi debeat in puncto horum circu- lorum, quo intersecant Eclipticam. Blanchinus verò con- tendit esse circulos in longum descriptos, qui transeant per corpora siderum intuentium: sicque radios sumi tamquam puncta super hos circulos in distantiis consuetis, vt pro sex- tili gr. 60. pro quadrato gr. 90. &c. Quapropter prima sen- tentia concludit in directionibus nullam seruandam esse latitudinem occuisantium siderum, sed eius solius, quod recipit radium; quod profectò vbi peruenerit ad circulum radij, siue habeat latitudinem, siue non, recipit immissum radium, atque inde etiam ad inuentem planetam remittit. Secunda verò vult consequenter radios immitti in certa distantia, qua orbitas planetarum intersecet; atque adeò pro sextili, & trino accipiunt dimidium latitudinis planèx intuentis; in quadrato nullam, cum necessariò incidat in

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MATHEMATICVM. 419 the luminous body, but to prevent it from diffusing its own light; not, however, a ray without light, from which it is effectively derived, or without luminosity, which it has effectively as the instrument for producing light. 4. There is a threefold ray: the straight, just now explained, which proceeds directly from a luminous body and ends in another; the reflected, which is transmitted from an illuminated body, whether back to the illuminating body itself or to some other thing opposite to it; and the refracted, when from a less rare medium it passes into a rarer one, or even from a rarer into a less rare, or dense medium, as when it is diffused from air into water. Now this threefold consideration of rays founds a threefold science: Dioptrics, Catoptrics, or Anacamptics, and Anaclastics, about which. See Vitellius, book 10 of Optics, and us in their proper places. Hence 5. A ratio, among astronomers, is called the aspect and configuration of two stars at a certain distance from each other, from which they mutually send rays to one another, by means of which, through the light communicated, they mutually strengthen or oppose one another, according as they have been endowed with similar or dissimilar qualities; whence also it is that they either increase, moderate, or pervert the influx toward these lower things. Now these are the sextile, square, trine, quintile, and others, which we enumerated above in V. Aspects. 10: Regiomontanus wishes such rays to be sent through circles extended broadly, whose center is the observing star (except for opposition, however, which is by diameter), and the end is where the measure and distance of these rays terminate; if another star should fall upon this, it is said to receive, and in turn to send back, such a ray, whence it follows that each ray ought to be taken at the point of these circles where they intersect the ecliptic. Blanchinus, however, contends that they are circles described lengthwise, which pass through the bodies of the observing stars; and thus the rays are to be taken as points upon these circles at the customary distances, as for the sextile 60 degrees, for the square 90 degrees, etc. Wherefore the first opinion concludes that in directions no latitude of the occluding stars is to be observed, but only that of the one which receives the ray; which certainly, when it has reached the circle of the ray, whether it have latitude or not, receives the emitted ray, and from there also sends it back to the discovering planet. But the second opinion holds that rays are accordingly sent at a certain distance, at which the orbits of the planets intersect; and therefore, for the sextile and trine, they take half the latitude of the observing planet; in the square, none, since it necessarily falls in

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420 LEXICON Eclipticam. Hanc controuersiam fusè agitat Titus in Cæleste Philosophia lib. 2. cap. 4 addito etiam demonstrationis schemate. Vide ipsum. Similiter 7. RADIVS apud Geometras appellatur sinus maximus, qui est semidiameter circuli, & semisses chordæ subtensæ integro semicirculo, post quem sequuntur alij sinus semper minores, & minores vsque ad co[m]plementum arcus, cui subtenditur, ex quo per regulam propotionum venamur quantitatem reliquorum sinuum, arcus, cui singuli subtenduntur, nec non lineæ tangentis, atque secantis. 8. RADIVS ASTRONOMI s, seù Geometr. cui est instrumentum Mathematicum factum ad speculanda sidera per radios visuales, eorumque distantiam, diametros, longitudines, aliaque permulta venanda. Eius vsum, atque vtilitates fusè tradit Gemma Fr[anc]sius integro opusculo, Regiomontanus, Tycho, aliique; cui postea non nihil innouato successit. 9. RADIVS LATINVS sic dictus à Latino Vrsino eius inuentore, quem vberrimis Commentariis illustrauit Egnatius Dantes celebris Mathematicus. 10. RADIX communiter dicitur initium reum, sumpra analogia ab radice arboris, quæ est initium plantæ ramusculorum, foliorum, & omnium denique, quæ in radice fundantur. Hinc apud Astronomos frequuensissimè vsurpatur pro fundamento, vnde hauritur ratio cælestis motus instituendi. Sic Natiuitas, seu Thema Genethliacum dicitur Radix in ordine ad revolutiones, directiones, progressiones, aliasque operationes, quæ tum in ex[em]lis ab stellis, tum in terris ab istorum motuum observationibus fiunt, & fundantur in prima cælorum constitutione, vnde homo, aut alia quæcumque res sumpsit initium. Quæ de re vide Auctores in Isagogieis. 11. RAMPHISTES, teste Kitchero, in Oedipo Ægyptiaco, dicitur Pica Brasilica Indorum vocabulo, Toucan, fidus in ex[em]lo ad australem plagam non ita pridem à recensioribus Astronomis detectum, habens stellas 8. infimæ notæ. 12. RAS apud Arabes idem sonat, ac caput. Hinc Ras Aben ab ipsis dicitur stella fixa in capite Draconis consistens: Ras Alangue stella irem in capite Serpentarij. Ras Algesi stella in capite Hereulis: Ras Eleced stella in capite Leonis, &c. de quibus omnibus suis in locis. 13. RATIONALIA SIGNA dicuntur eadem quæ humana, sumpta analogia à definitione hominis, qui dicitur Animal rationale:

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420 LEXICON Eclipticam. Titus discusses this controversy at length in Cæleste Philosophia , book 2, chap. 4, adding also a diagram of the demonstration. See him. Similarly 7. RADIUS is called by geometers the greatest sine, which is the semidiameter of a circle, and half of the chord subtended by the whole semicircle; after which follow other sines, always smaller and smaller, down to the complement of the arc to which it is subtended, from which, by the rule of proportions, we seek the quantity of the remaining sines, the arc to which each is subtended, as well as the tangent and secant line. 8. RADIUS ASTRONOMICUS, or Geometricus, is a mathematical instrument made for observing the stars by visual rays and for seeking their distances, diameters, lengths, and many other things. Gemma Fr[anc]sius gives a full account of its use and advantages in an entire treatise, as do Regiomontanus, Tycho, and others; to whom he was later in some measure succeeded, with certain innovations. 9. RADIVS LATINVS is so called from its inventor, Latinus Ursinus, and was illustrated by very full commentaries by Egnatius Dantes, a celebrated mathematician. 10. RADIX is commonly said to mean a beginning, taken by analogy from the root of a tree, which is the beginning of the plant’s twigs, leaves, and, in short, of everything that is founded in the root. Hence among astronomers it is very frequently used for the foundation from which the method of celestial motion is derived. Thus a nativity, or genethliac theme, is called the radix with reference to revolutions, directions, progressions, and other operations, which are made both in examples from the stars and on earth from observations of those motions, and are founded on the first constitution of the heavens, from which a man, or any other thing whatsoever, took its beginning. On this matter see the authors in the Isagogics. 11. RAMPHISTES, according to Kitcher in the Œdipus Ægyptiacus , is the name given to the Brazilian magpie in the Indian tongue, Toucan, a bird, as an example, toward the southern region, not long ago discovered by more recent astronomers, having 8 stars of the lowest magnitude. 12. RAS among the Arabs means the same as head. Hence Ras Aben is their name for the fixed star situated in the Dragon’s head: Ras Alangue, a star likewise in the head of Serpentarius. Ras Algesi, a star in the head of Hercules: Ras Eleced, a star in the head of the Lion, and so forth, all of which in their proper places. 13. RATIONALIA SIGNA are said to be the same as human signs, taken by analogy from the definition of man, who is called a rational animal:

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MA THEMATICVM. 423 rationale: quæ enim signa humanam figuram præseferunt, nedum æquiuocatione nominis rationalia esse dicuntur, sed etiam per quandam attributionem, ac similitudinem, quoniam ad rationem, atque humanitatem habent influere. Vide quæ diximus in Verbo Humana signa. RATIONA I QUANTITAS, seu etiam irrationalis dici- <141> tur apud Geometras omnis quæcumque proposita quantitas, quæ cum alrera sit commensurabilis, aut incommensurabilis. Qua de re vide Euclid. lid. 10. à defin. 5. & seqq. neconon ea quæ nos tradidimus in V. Apotome, & in V. Proportionalitas. RATIONALIS VIA erigendi cælestem figuram, distribuendique <152> domorum spatia celebris est apud Astronomos, præsertim recensiores, quo nomine Regiom[an]otanus insigniuit methodum ab Abraham Auensra primum inuentam, ab ipso mordicus propugnatam, acque in tabulas redactam constituendi situs moderatorum in cælesti figura, accipiendoque similitudines locorum ad cardines super lineis, & circulis parallelis Verticali magno, qui transit per puncta orius, & occasus æquatoris; ita vt totum fundamentum similitudinum locorum constituatur in huiusmodi circulis parallelis ad verticalem descriptis. Et quia eam facilem, & præ cæteris rationi consonam comprobauit, seu potius suo captui maximè atridentem eam audacter rationalem appellauit; eiusque sectatores rationales dixit; quasi modò cæteræ <153> methodi tum à Ptolema[co], tum ab aliis traditæ irrationales sint, ab ratione abhorrentes, & ex cerebro cuiusque auctoris confictæ. Igitur rationales ducunt duos circulos magnos per communes intersectiones finitoris, & meridiani, qui habeant solum dispescere æquatorem in duodecim partes æquales, nulla habita ratione ad reliquas proportionales distantias à cardinibus sed eoipso, ac sidus aliquod, aut plura coincidunt in vnum huiusmodi hemicyclum dicunt esse in consimili proportionali distantia ad cardines, coquia seruant eandem ad illos figuræ qualitatem, licet non quantitatem. Ad hanc methodum Regiomontanus magno studio, & labore extruxit, vt dixi tabulas ascensionum, ac descensionum obliquarum à primo gradu eleuasionis poli vsque ad 60. quas mirum in modum ampliarunt, Canonibusque & Commentariis illustrarunt Magius, & Argolus. Huic tamen constituendorum situum rationi opposita ex diametro est methodus Ptolemaica, quæ circulos positionis non definit per communes intersectiones Finitoris, & Dd

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MATHEMATICUM. 423 rational: for those signs which exhibit the human figure are not only called rational by an equivocation of the name, but also by a certain attribution and likeness, since they are understood to have influence on reason and humanity. See what we said in the word Humana signs. RATIONAL QUANTITY, or also irrational, is said by the Geometers to be any proposed quantity whatsoever, whether it is commensurable or incommensurable with another. On this matter see Euclid, Book X, from definition 5 and following; and also what we have set down in V. Apotome , and in V. Proportionalitas . THE RATIONAL WAY of erecting the celestial figure, and of distributing the spaces of the houses, is celebrated among Astronomers, especially the more recent ones, by which name Regiomontanus distinguished a method first invented by Abraham Avenezra, vigorously defended by him, and set forth in tables, for determining the positions of the significators in the celestial figure, and for taking the likenesses of places to the angles by means of lines and parallel circles on the great Vertical, which passes through the points of sunrise and sunset of the equator; so that the whole foundation of the likenesses of places is established in circles of this kind, drawn parallel to the vertical. And because he proved it to be easy, and more in agreement with reason than the others, or rather because it was most suited to his own understanding, he boldly called it rational; and he called its followers rational, as though the other methods handed down both by Ptolemy and by others were irrational, repugnant to reason, and fabricated from the brain of each author. Therefore the rationals draw two great circles through the common intersections of the horizon and meridian, which have only to divide the equator into twelve equal parts, no account being taken of the remaining proportional distances from the angles; but then, if a star, or several stars, coincide in one such hemisphere, they say it is at a similar proportional distance from the angles, because it preserves the same quality of figure toward them, though not the quantity. To this method Regiomontanus, with great diligence and labor, constructed, as I said, tables of oblique ascensions and descensions from the first degree of the elevation of the pole up to 60 degrees, which Magius and Argolus enlarged in a remarkable way and illustrated with Canons and Commentaries. Yet opposed directly to this rational way of determining positions is the Ptolemaic method, which does not define the circles of position by the common intersections of the horizon and meridian, Dd

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LEXICON Meridiani, sed per proporciones siderum distantias motu suo horario acquisitas, ac proinde Domorum interualla distribuit per binas temporarias horas. Qua de re egregiè disputat 1. itus in lib. 2. c. 10. cælestis Philosophiæ, ostendens hanc esse veram Ptolemæi mentem, ac veræ, naturalisque similitudinis situum ad cardines rationem. 16. RECEPTIO apud Astronomos est species quædam dignitatis, & fortitudinis accedentis duobus planetis, quando idque præsertim, si amici fuerint permutant inuicem dignitates; itavit alter sit in alterius domicilio, exaltatione, aut Trigono constitutus, & ille vicissim in alterius dignitatibus. Maximè verò si eorum vns applicet alij, qui in eodem loco dignitatem aliquam obtinuetit: Tunc enim naturam commisceent, & dicuntur se mutuò respicere, & recipere. Est autem tanta hæc dignitas, vt merito eenseatur ipsi Domicilij, aut altitudinis prærogariuæ præpollere, aut saltem æquiparari. 17. RECTVM ex Euclide lib. 1. defin. 4. dieitur corpus, aut linea, quæ æqualiter inter sua puncta distenditur, hoc est, in qua nihil flexuosu[m] reperitur: sicut è contrà curuum dicitur quod arcuatim, vel inæqualiter quovis modo porrigitur. 18. RECTANGVLVM, ex eodem, audit figura quævis Geometrica constans angulis rectis, hoc est in quos coëant duæ lineæ rectæ, quarum vna intelligatur perpendiculariter imminere alteri in plano positæ. Sic triangulum rectangulum est quod vnum angulum (neque enim plures habere potest) rectum habet; duosque acutos. Quadrangulum rectangulum, si vnum tandem vt supponitur admittit angulum rectum, iam necessariò omnes quatuor angulos debet habere rectos. Cæteræ autem figuræ rationales rectangulæ esse minime possunt. Vide Euelid. lib 1. defin. 27. & seqq. Meritò igitur Tycho Rectangulum vniuersæ Mathesis Magistrum dixit. Similiter. 19. RECTILINEVM dieitur omne id quod rectis lineis constat, qualia sunt parallelogramma, Rhombi, trianguli rectanguli, &c. Euclid. defin. 9. & defin. 19. 20. RECTITUDO PLANETA, teste Abraham Auenarre, est cum is fuerit in cælesti figura constitutus in angulo, aut succedentibus, quemadmodum obliquatio illi aceidit, cum est in eadencibus. 21. REDIVVS LVMINIS apud Astronomos tunc fieri dicitur inter planetas, cum plures mittunt lumen vni tertio debili, ruta combusto, aut retrogrado, qui ob debilitatem suam illud retinere non valens, remittit iisdem planetis lumen,

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LEXICON Meridiani, but by the proportions of the stars, by the distances acquired in its hourly motion, and therefore it distributes the intervals of the Houses by the two temporal hours. On this matter I. Itus disputes excellently in lib. 2, ch. 10 of Celestial Philosophy, showing this to be the true mind of Ptolemy, and the true, natural relation of positions to the angles. 16. RECEPTION among Astronomers is a certain kind of dignity and strength acceding to two planets, especially when, if they are friends, they exchange dignities; that is, if one is placed in the other’s domicile, exaltation, or Trine, and the latter in turn in the other’s dignities. Most especially if one applies to the other who has obtained some dignity in the same place. Then indeed they mingle their natures, and are said to regard and receive one another mutually. And this dignity is so great that it is rightly judged to excel, or at least to be equal to, the prerogative of domicile or altitude. 17. STRAIGHT, from Euclid, book 1, definition 4, is said of a body or line that is stretched equally between its points, that is, in which nothing bent is found; just as, on the contrary, curved is said of that which extends in an arched, or in any unequal, way. 18. RECTANGLE, from the same author, is the name given to any geometrical figure consisting of right angles, that is, into which two straight lines come together, one of which is understood to lie perpendicularly upon the other in a plane. Thus a right triangle is one which has one angle (for it cannot have more) right; and two acute angles. A right quadrilateral, if it finally admits one right angle as supposed, must of necessity already have all four angles right. Other rational figures cannot be rectangular. See Euclid, book 1, definition 27, and the following. Therefore Tycho rightly called the rectangle the master of all mathematics. Likewise. 19. RECTILINEAR is said of everything that consists of straight lines, such as parallelograms, rhombi, right triangles, etc. Euclid, def. 9 and def. 19. 20. RECTITUDE OF A PLANET, according to Abraham Avenarre, is when it has been placed in a celestial figure in an angle, or in succedent houses, just as obliquity happens to it when it is in cadent houses. 21. RETURNING OF LIGHT among astronomers is said to occur between planets when several send light to one third one, weak, burnt out, or retrograde, who, unable by its weakness to retain it, sends back light to the same planets,

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MATHEMATICVM. 421 quod ab illis accepit: hoc autem fieri potest, & cum pro- ficuo & cum malo: qua de re vide Abraham Ludæum in suo Introductorio pag. 4. REDITVR. Vide Ingressus, aut Revolutio. < 22.> REFLEXIO est reduplicatio actionis, vel qualitatis immis- sæ ab aliquo agente in passum, qua eadem actio, aut qua- litas producta in passo, intenditur, & reproductur, maiori nisi tendens in ipsum agens. Sic lumen à Sole immissum in speculum cum ad ipsum peruenerit intenditur, & revertitur numeris auctum, per idem medium, per quod venerat: quod < 23.> quidem magnum est Naturæ prodigium, vt quod agens na- turale vires suas omnes exerens directè assequi non est potis, hoc in ietu ferè oculi præstet passum de se nihil ad- dens, sed solum resistens productioni agentis, seu receptio- ni effectus in ipsum. Quandoquidem corpus opacum, in quod reflectitur radius corporis luminosi, nil haber lucis, quò possit ipsam intendere in medio interposito; speculum vstorium in se nec formaliter, nec virtualiter ignem conti- net, qui tamen, ex reflexione solarium radiorum, quæ stat in eo, statim prosilit in materia proportionata inter ipsum, & solem constituta: quod ergò radij solis per ipsam tran- seuntes directè præstare non potuerunt, hoc præstant idem, vt reflexi: qua virtute? qua virium adauctione, equidem ignoratur. Videtur tamen causam effectiuam actionis re- flexæ esse ipsummet effectum quatenus ita producitur in ter- mino, vt inde possit alium rursus effectum producere sibi similem; at quorsum nobiliorem? non video. Cæterum ex reflexione solarium radiorum habemus, quod tot luminibus cælum exornetur, quot sunt in eo sidera: ipsa enim in se lucem vllam non habent, sed sunt corpora opaca, in quibus lumen à sole immissum recipitur, & subiectatur, quod po- stea qualitatibus eorum affectum, hanc varietatem effectuum gignit, quam demirantes, stupendaque Naturæ opera col- laudantes, videmus. Sed de hac re, quæ non minus extra aleam nostram est, quam penè suprà captum, satis sint di- cta. Plura de Reflexiæ virtutis prodigiis habet Vitellion lib. 10. & Kircherus in Arte Magna lucis, & Vmbra. < 24.> REFRACTIONIS nomine venit inter Astronomos, & Per- spectiuos diuersitas illa aspectuum, & aberratio visus, quæ accidit in siderum contemplatione, seu etiam quorumcum- que corporum quæ de longè aut instrumentis opticis, aut per aliud interpositum corpus diaphanum speculamur, quan- do per illud transeuntes radij, aut species obiecti visibilis in- fringuntur, & representant illud aliter, ac reuera est. Patet D d ij

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MATHEMATICVM. 421 which it has received from them: but this can happen both for good and for evil: on this matter see Abraham Ludæus in his Introductorio, p. 4. REDITVR. See Ingressus, or Revolutio. < 22.> REFLEXIO is the reduplication of an action, or of a quality sent into a patient by some agent, by which the same action, or quality produced in the patient, is intensified and reproduced, greater unless tending back upon the agent itself. Thus light sent from the Sun into a mirror, when it has reached it, is intensified and returns increased in number through the same medium through which it came: which < 23.> indeed is a great prodigy of Nature, since that which a natural agent, exerting all its powers, is not able to accomplish directly, the patient almost at a glance of the eye performs, adding nothing of itself, but only resisting the production of the agent, or the reception of the effect into itself. For since the opaque body into which the ray of a luminous body is reflected has no light, by which it might intensify it in the intervening medium; and the burning mirror contains fire in itself neither formally nor virtually, yet from the reflection of the solar rays, which lies in it, fire suddenly bursts forth in a proportionate matter placed between it and the sun: what therefore the rays of the sun, passing through it directly, could not accomplish, this they accomplish as reflected: by what virtue? by what increase of powers? indeed, it is unknown. Yet the efficient cause of reflected action seems to be the very effect itself, insofar as it is thus produced in the term, so that from it another similar effect may again be produced; but why a nobler one? I do not see. Moreover, from the reflection of the solar rays we have the fact that the sky is adorned with as many lights as there are stars in it: for these do not have any light in themselves, but are opaque bodies in which the light sent from the sun is received and lodged, which afterward, being affected by their qualities, begets that variety of effects which, marvelling at and praising the wondrous works of Nature, we behold. But on this matter, which is no less beyond our reach than almost beyond our grasp, enough has been said. Vitellio has more on the wonders of reflective power in book 10, and Kircher in the Arte Magna of light and shadow. < 24.> Under the name of REFRACTION among Astronomers and Perspectivists is understood that diversity of appearances, and aberration of vision, which occurs in the contemplation of the stars, or also of whatever bodies we observe from afar, either with optical instruments or through some other intervening transparent body, when the rays or species of the visible object passing through it are broken, and represent it otherwise than it really is. It is evident D d ij

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LEXICON id manifestè, in speculis, aut ocularibus alteratis, quæ pro ratione maioris densitatis, aut raritatis alterant notabiliter species obiecti visibilis; quò fit vt aliter illud nobis obiiciatur, quam sit in re. Id etiam videre est non modo in aqua sed & in p[er]so aëre, ob cuius crassitiam, maximè verò circà horizonem crassioribus vaporibus constiparum alterantur siderum radij ad nos obliquè immissi, proindeque dant illa conspici grandiora, & elaciora, imò & quandoque supra terram, cum tamen ex calculo Astronomico deducatur, id nullatenùs fieri posse, sed ea adhuc sub horizonte persistere. 25. Hinc non mirum, si aliquando in Plenilunio visa sint ambo luminaria supra terram, & Luna in telluris vmbram incidens lumine distituta. Viderius enim hoc ipsum clarissimè in nummo in fundo vasis alicuius alri orificij existente, qui cum directè à latere conspici minimè queat; si nihilominus aqua aut alio crassiori liquore vas repleatur, illius species per medium transeuntes refractè repræsentant obiectum, & præbent illud conspiciendum, cum alias ob vasis impedimentum directè id non potuerint. 26. Porrò refractionum causa est tum visus obliquitas, tum corporis interiecti crassities, quod quò crassius erit & densius eo maiores facit refractiones: quod ideò stellæ in decliviore situ, & circà Finitorem maximè refractionibus sunt obnoxiæ: Eeonìra in Meridie, vtpote in situ eminentiore, ac vaporibus defæcatiore, aur nullas, aut sanè leues patiuntur refractiones. Hinc pro locorum diuersitare diuersæ accidunt siderum apparentiæ, proindeque difficilis admodum est earum obseruario, ni quisque probè callear refractionum materiam, quam primus omnium tradidit Tycho, & redegit in Tabulas refractiones Solis vsque ad altitudinem grad. 45 supra horizontem; & fixarum ad gr. 20. quæ r amen deseruiunt pro locis septentrionalibus, quæ maximè vaporibus scarent: Nam sub æquatore, aliisque regionibus in quibus Polus minus attollitur, illæ tum ratione puritatis aëris, tum ob minorem obliquitatem, incidentiæ radio-rum, longe minores accidunt refractiones Vnde in regione ætheræa, quæ omnino purissima, ac tenuissima est nullæ accidunt. Porrò refractionum doctrina maximè necessaria est in luminarirum Eclipsibus obseruandis, vt verum rempus incidentiæ, magnitudo, duratio ab apparentibus discernatur. Qua de re egregiè scripsit Tycho in suis Progymnasmaris, Keplerus, Maginus, Argolus aliique in tabulis secundorum Mobilium.

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LEXICON it is manifest, in mirrors or altered glasses, which according to the greater density or rarity notably alter the species of the visible object; so that it is presented to us otherwise than it is in reality. This can be seen not only in water but also in thick air, on account of whose thickness, especially around the horizon where it is made denser by thicker vapors, the rays of the stars sent to us obliquely are altered, and therefore cause them to appear larger and brighter, indeed sometimes even above the earth, although from astronomical calculation it is inferred that this cannot in any way happen, but that they still remain below the horizon. 25. Hence it is no wonder if at times, at full moon, both luminaries have been seen above the earth, and the Moon, falling into the earth’s shadow, deprived of light. For one may see this very clearly in a coin existing at the bottom of some vessel’s opening, which cannot at all be seen directly from the side; if nevertheless the vessel is filled with water or some other thicker liquid, its species, passing through the middle, refractingly represent the object and make it visible, whereas otherwise, because of the obstruction of the vessel, it could not be seen directly. 26. Moreover, the cause of refractions is both the obliqueness of the sight and the thickness of the intervening body; and the thicker and denser it is, the greater the refractions it produces. For this reason the stars in a lower position, and especially around the horizon, are subject to refraction; conversely, in the meridian, as being in a more elevated position and in air more purified from vapors, they suffer no refractions, or at least very slight ones. Hence, according to the diversity of places, different appearances of the stars occur, and therefore their observation is very difficult, unless one thoroughly understands the matter of refraction, which Tycho was the first of all to expound and reduced to tables: the refractions of the Sun up to the altitude of 45 degrees above the horizon, and of the fixed stars to 20 degrees, which nevertheless serve for northern places, which are most free from vapors. For under the equator and in other regions in which the Pole is less elevated, refractions occur much smaller, both because of the purity of the air and because of the lesser obliquity of the rays of incidence. Whence in the ethereal region, which is altogether pure and tenuous, none occur. Moreover, the doctrine of refractions is especially necessary in observing eclipses of the luminaries, so that the true time of the incident, the magnitude, and the duration may be distinguished from the apparent. On this matter Tycho wrote excellently in his Progymnasmata, Kepler, Maginus, Argolus, and others in the tables of secondary motions.

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MATHEMATICVM. 425 < 27.> REPRÆNATIO apud Astronomos est genus quoddam deteriorationis planetæ, accidens illi quando motu suo proprio in Zodiaco applicat alteti corpore, aut radio; verum tamen antequam id assequatur sit retrogradus, & vt ita dicam refrænatur, ne talem coniunctionem, aut radium, quem affectare videbatur, obtineat. Coincidit cum frustratione, ac perturbatione. < 28.> REG E STEELÆ apud Astronomos audiunt stellæ quædam insigniores, quæ tum super reliquas tum etiam in influendo regiam potestatem videntur habere, atque in natos inducere. Huiusmodi sunt inter omnes Regulus, cui antonomasticè hoc nomen inhæsit, quasi sit Regulus inter fixas et innumeras prærogatiuas quibus pellet, & nos paulò post explicabimus. Item Palilitium, spica Virginis, Lanx australis, Antares, Hereules, Lyra. In signis etiam seu sideribus quæ vocantur Regia qualia sunt corona Borealis, Capricornus, &c. de quibus vide Argol. in Pandos. sphærico & alibi. < 29.> REGULA instrumentum & notissimum, ac vulgare, quo medianæ lineas rectas describimus, distan[n]ias rectas dimestimur, primaque elementa Geometriæ practicæ compasamus, ea numeris per interualla descripta, ad certamque formam redacta exibet celeberrimum illud instrumentum dictum Magnam Regulam Ptolemæi, cuius vtilitates refert Clauius in Geometria practica. < 30.> REGULA AVREA. V. Aurea Regula. < 31.> REGULA HARMONICA est item instrumentum Musicum, quocum rationis adhibito iudicio consonantiæ, consonantiarumque partes in chorda perquiruntur. Eius ope Keplerus, vt toties monui, adinuenit harmoniam radiorum, atque familiaritatem, quam sidera contrahunt in certa ad inuicem distancia, nouosque aspectus Quintilem, sesquiquadratum, biquintilem hactenus inobseruatos, rationemque qua eorum aliqui hostiles sint, alij fausti, & perfectæ, vt aiunt, vel imperfectæ amicitiæ. Vide quæ diximus in V. Aspe- ctus. < 32.> REGULARES FIGVRÆ ab Geometris appellantur quæ æquilateræ & equiangulæ sunt, quales sunt omnes figuræ Isoperimetræ, licet hæc nomina per se Synonima non sint, nam figuræ Isoperimetræ intelliguntur esse quæ æquales ambitus continent, Regulares, quæ angulos, & lineas, seu superficies. Econtrà irregulares dicuntur, quæ non seruant hanc laterum, angulorumque æqualitatem, vt sunt Prisma- ta, & Trapezia, de quibus suo loco. Porro ad dignoscendum, an aliqua figura sit regularis, vel irregularis descri- D d iij

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MATHEMATICVM. 425 < 27.> REPRÆNATION among Astronomers is a certain kind of deterioration of a planet, occurring to it when, by its own motion in the Zodiac, it applies to another body or ray; yet before it reaches this it is retrograde, and, so to speak, held back, lest it obtain such a conjunction or ray as it seemed to be seeking. It coincides with frustration and disturbance. < 28.> REG E STEELÆ among Astronomers are called certain more distinguished stars, which seem to have royal power both over the rest and also in influencing, and to impart it to those born under them. Of this kind among all are Regulus, to which this name has been given by antonomasia, as if it were a little king among the fixed stars and innumerable prerogatives by which it rules, and we shall explain these a little later. Also Palilitium, the ear of Virgo, the southern Balance, Antares, Hercules, Lyra. Likewise among the signs or constellations called royal are such as the Northern Crown, Capricorn, etc.; see Argol. in Pandos. sphaerico and elsewhere. < 29.> REGULA is a very well-known and common instrument, by which we draw straight median lines, measure straight distances, and compare the first elements of practical Geometry. What is set out with numbers at intervals and reduced to a certain form will yield that very famous instrument called the Great Rule of Ptolemy, whose uses Clavius relates in practical Geometry. < 30.> REGULA AUREA. See Aurea Regula. < 31.> REGULA HARMONICA is likewise a musical instrument, with which, by the application of rational judgment, consonances and the parts of consonances are sought in a string. By its aid Kepler, as I have so often noted, discovered the harmony of rays, and the familiarity which stars contract at certain distances from one another, and the new aspects Quintile, Sesquiquadrate, Biquintile, hitherto unobserved, and the ratio by which some of them are hostile, others propitious, and, as they say, of perfect or imperfect friendship. See what we said under V. Aspectus. < 32.> REGULAR FIGURES are called by geometers those which are equilateral and equiangular, such as all isoperimetric figures, although these names are not synonymous in themselves; for isoperimetric figures are understood to be those that contain equal perimeters, while regular figures are those that have equal angles and lines, or surfaces. On the other hand, irregular figures are those that do not preserve this equality of sides and angles, such as prisms and trapezia, of which in their place. Moreover, in order to recognize whether any figure is regular or irregular, de- D d iij

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LEXICON 426 bendus est circa eam circulus à centro ipsius ad angulos, cu- ius circumferentia, si æquè tangat omnes angulos, figuræ erit regularis, sin minùs, irregularis. 33. REGVLVS, Basiliscus, Cor Leonis Arabicè Alhabor, stella fixa de natura Martis, & Iouis, omnium ferè, quæ sunt in Firmamento potentissima, ac notissima, inter Regias com- purata, existens nunc temporis in gr.25. Leonis, quasi in ipsa Ecliptica, ideoque existimatur maximæ inter reliquas effi- cacæ; quippe quę semper cum Sole congreditur singulis an- nis, & habet cum cæteris etiam planeris aliquando congre- di, quod non aliis datum est. Et quidem ea non multi cor- poris est, vt videre licet ex ipsius diametro, quæ non exce- dit earum magnitudinem, quæ secundi honoris dicuntur, verum ob sui præstantiam, & robur, solet inter primæ ma- gnitudinis numerari. 34. Quinimò aduertit Titus eam solam non modo accipere, sed & remittere radios omnes ad planetas, ac pro eorum qualitate diuersam naturam induere; quod in aliis fixis, siue ob radiorum exilitatem, siue ob aspectus deviationem, qui quoniam extrà Eclipticam numquam assequuntur vt sint partiles, minimè obseruetur. Obseruat etiam campanella lib.2.cap.3. art.2. ex Ptolemæi doctrina, quod, quia Leoni Italia subiecta est, sicut Græcia Virgini, propterea quando stellæ, quæ sunt in Leone transierunt in Virginem, tunc im- perium Italiæ in Græciam transit; at quoniam in eo adhuc perseueravit Regulus, vt dictum est potentior, & in Ecli- ptica; ideò Italia fuit quidem depressa, sed adhuc in ea per- seueravit dominatus, & Imperium saltem Ecclesiasticum: Quando verò etiam Regulus in signum Virginis commi- grabit, quod erit post 600. circiter annos, tunc fortè Ita- liæ virtus, & dominatus desiciet; nisi fortè ex ingressu Ca- niculæ in Leonem accidat conseruari, quod tamen haud sperant cum sit latitudinis multæ. Cæterum Regulum in ho- roscopo, iungi obseruatione compertum est ferè semper tri- buere naturalem quandam animi, morumque grauitatem, prudentiam, atque in rebus bellicis strenuitatem, vt inter alios obseruauit Argolus de diebus erit lib.1.cap.6. Vide etiam in V.V. Basiliscus, & Cor Leonis. 35. REMVNERATTO apud Astrologos, teste Abraham Auenar- te, est cum Planeta, qui cum primum ex puteo, aut alia quauis depressione alterum eripuerit aspiciatur postmodum ab extracto; quo tempore ipse etiam cadat in puteum, aut aliam depressionem ex qua planeta à se primum adhutus, cum vicissim eripiæ: quî sit vt reddat ei quodammodo

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LEXICON 426 is described around it by a circle from its center to the angles, whose circumference, if it equally touch all the angles, the figure will be regular; if not, irregular. 33. REGULUS, Basiliscus, Cor Leonis, in Arabic Alhabor, a fixed star of the nature of Mars and Jupiter, the most powerful and well-known of almost all those that are in the firmament, reckoned among the royal stars, being at present in 25 degrees of Leo, almost on the ecliptic itself, and therefore thought to be the most effective among the rest; for it always joins with the Sun every year, and can also join with the other planets, which is not granted to others. And indeed it is not of a great body, as can be seen from its diameter, which does not exceed the magnitude of those called of second honor; yet because of its excellence and strength, it is usually counted among the first magnitude. 34. Nay, Titus notes that it alone not only receives but also reflects all rays to the planets, and assumes a different nature according to their quality; which in other fixed stars, whether because of the thinness of the rays or because of the deviation of the aspect, since outside the ecliptic they never attain to be partile, is by no means observed. Campanella also observes, book 2, chap. 3, art. 2, from the doctrine of Ptolemy, that because Italy is subject to Leo, just as Greece is to Virgo, therefore when the stars that are in Leo have passed into Virgo, then the rule of Italy passes into Greece; but since Regulus remained in it, as has been said, more powerful, and on the ecliptic, Italy was indeed depressed, but dominion still remained in it, and at least ecclesiastical empire. But when Regulus also shall migrate into the sign of Virgo, which will be after about 600 years, then perhaps the strength and dominion of Italy will fail; unless perhaps, from the entrance of Canicula into Leo, it should happen to be preserved, though they do not hope for this, since it is of great latitude. Besides, it has been found by observation that Regulus in a horoscope almost always imparts a certain natural gravity of mind and morals, prudence, and in military affairs valor, as Argolus observed among others, de Diebus, book 1, chap. 6. See also in V.V. Basiliscus and Cor Leonis. 35. REMUNERATIO among astrologers, according to Abraham Avenarte, is when a planet, which has first drawn another up out of a pit or other depression, is afterward seen by the one extracted; at which time he also falls into a pit or other depression from which the planet first drawn up by him, in turn, may be rescued: so that he in some way returns to it that which

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MATHEMATICVM. 427 beneficium, quod acceperat: Vt proinde iure hæc familiaritas, ac præstiti beneficij species dicta sit Renumeratio. < 36.> RE in Astrolabio dicitur Volu e llum, & tabula perforata in parte extima, seu in facie Astrolabij, te circa limbum voluens ac motum primi mobilis circa tellurem in plano repræsemans. In eo enim descripti sunt omnes circuli sphæræ, stellæ fixæ insigniores, quibusdam veluti denticulis, & suo quæque nomine designatæ, ad earum motus, congressus cum planetis, altitudines, distantias, declinatio[n]es, aliaque pericutanda, ideoque retis nomen iure est illi indicum; nam sicut rete pisces in mari capimus, ita hoc instrumento prudens Astronomus fidera in cælo venetur. < 37.> RE ROGA DVS apud Astronomos appellatur Planeta, qui motu suo proprio in Zodiaco contra successionem signorum incedit, vt si à secundo gradu Arietis abiret in primum; inde ad 1. o. Piscium, posteà ad 19. &c. Est maxima eius deteriora, & imbecilitas, itavt in maleficis ea, (quidquid ali dicant) commodum, & opportunè veniat, & oppido ab Astronomo desideranda sit: sicut è contra directio, & cursus velocitas maxima fortitudo est, atque in infortunis cauenda. < 38.> Retro aurem, cur planeta retrogradus debilis fiat, & viceversa directus, & cursu velox, fortis, & efficax non ita ab omnibus nota est: quare operæ prærium me facturum credo, si hic e in luculenter explicem Ea igitur est, quia qui motu velox est nititur magis contra primi mobilis motum; ac proinde quò est velocior cursus, eò diutiriùs suprà terram consistit, ac tempos habet magis, magisque lucem suam diffundendi, a quo adeò inferiora isthæc suis qualitatibus alterandi: Non si Retrogradus, qui non modò nihil resistit motui primi mobilis verum etiam illo adhuc velocius cadit in inferius hemisphærium, citius perficit suam revolutionem diurnam circa tellurem, minori videlicet temporis spatio, quam 24. horarum, licet id quidem apud nos penè insensibi e sit. Quapropter non tam potens euadit ad hæc inferiora suis qualitatibus afficienda, sed quam imprimis qualitatem citò aliò transfert, sicque debilis fiat. Qua etiam ratione, vt alibi obseruauimus fixæ nedum ob magnam distantiam, sed potissimum quia ferè cum primo mobili integre rapiuntur non eandem activitatem habet quam Erraticæ, quæ dum motu suo peculiari contra motum primi mobilis nituntur, aliquantulum suprà terram consistunt; ac proinde magis quam illa valent, & efficaciùs vires suas exerere, ac terram qualitatibus suis imbuere sicut è contra Lu- D d iiiij

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benefit, which he had received: so that this kind of familiarity, and the sort of service rendered, may rightly be called Recompense. <36.> In the Astrolabe, the Rete is called the revolving wheel, and the perforated plate on the outer part, or on the face of the Astrolabe, which turns around the limb and represents in a plane the motion of the first mobile around the earth. For in it are drawn all the circles of the sphere, the more notable fixed stars, marked as it were with little teeth and each distinguished by its own name, for observing their motions, conjunctions with the planets, altitudes, distances, declinations, and other things; and therefore the name of rete is rightly given to it, for just as with a net we catch fish in the sea, so with this instrument the prudent astronomer hunts the stars in the heavens. <37.> Among astronomers, a planet is called retrograde when, by its own motion in the Zodiac, it proceeds contrary to the succession of the signs, as if from the second degree of Aries it were to go back to the first, then to the 1st of Pisces, afterward to the 19th, and so on. This is a very great weakness and debility of it, so that in the malefics it is a convenience, and opportunely comes, and is greatly to be desired by the astrologer; just as, on the contrary, direct motion and the speed of the course are the greatest strength, and are to be avoided in the infortunes. <38.> The reason why a retrograde planet becomes weak, and conversely a direct one, and a planet swift in motion, strong and effective, is not known by all; wherefore I believe I shall do well to explain it clearly here. It is therefore so because that which is swift in motion strives more against the motion of the first mobile; and accordingly, the swifter the course is, the longer it remains above the earth, and has more and more time to spread abroad its light, by which these lower things are altered by its qualities. Not so the retrograde one, which not only resists not at all the motion of the first mobile, but even falls into the lower hemisphere more swiftly by it, and sooner completes its daily revolution around the earth, namely in less time than 24 hours, though indeed this is almost imperceptible to us. For this reason it does not become so powerful in affecting these lower things with its qualities, but whatever quality it transfers quickly to another, and so becomes weak. For the same reason, as we have observed elsewhere, the fixed stars have not the same activity, not only because of their great distance, but especially because they are carried almost wholly along with the first mobile; unlike the erratic stars, which, while they strive by their own peculiar motion against the motion of the first mobile, remain somewhat above the earth; and therefore they are more powerful than those, and exercise their powers more effectively, and imbue the earth with their qualities, as on the contrary Lu-

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428 LEXICON. na non ob aliud tantam efficaciam habet in hæc sublunaria (quæ proinde vel ob id nomen sumpserunt) nisi quia longè diutius quam reliqua sidera supra terram moratur. < 32.> Portò, exceptis luminaribus, omnes planetæ retrogradi aliquando sunt; non quod verè, & realiter retrogradiantur, sed quia seruntur in suo quisque Epicyclo, qui habet pro centro Solem: ac proinde dum eorum orbis deferentes simul motu primi mobilis rapiuntur, inde fit, vt sub primo mobili respectu nostri ipsa corpora planetaru[m] retrocedere aliquando videantur, stare immobiles, modo citius, modò seriùs progredi, cum tamen in re semper eodem modò, & æqualiter incedant in Epicyclo: ar cum sunt in prima statione descendentes ab Apogæo ad Perigæum nituntur contra successionem signorum, ac proinde apparent rettogradi: sicut in secunda statione ascendentes à Perigæo ad Apogæum semper videntur directi, quia procedunt sinistrorsum in Epicyclo, atque adeò secundum successionem signorum Quæ omnia in schematismo ab omnibus sphære, aut secundorum mobilium authoribus exposito dilucidè videre est. < 40.> REVOLTIO, vt nominis etymon præsefert, apud Astronomos, nil aliud sonat, quam integram circulationem alicuius sphæræ vel sideris donec redeat ad idem punctum, in quo primum erat cum inoueri cæpit. Sie dicimus Saturnum persicere suam revolutionem in Zodiaco spatio triginta ferè annorum: Iouem duodecim: Martem, duorum: Solem vnius anni, Lunam ferè in mense, ac tandem Primum Mobile suam revolutionem diurnam circa tellurem spatio vnius diei naturalis, hoc est viginti quatuor horarum: quo expleto singulæ eius partes redeunt ad eundem suum, eundemque circulum positionis, in quo etant prius. Aliquando pressiùs & antonomasticè accipitur pro annua Circulatione, seu reditu solis ad idem præcisè punctem Zodiaci in quo erat initio alicuius rei: Sic solet erigi figura introjus Solis in quatuor puncta cardinalia. Vnde initium sumunt quatuor anni tempora, ad eorum qualitates dignoscendas: revolutiones cuiusque recurrentis anni tum in genere, tum in specie ab ædificatione vrbis, natiuitate hominis, aut ab inceptione cuiuscumque operis, (quod quomodo fiat, docent passim auctores in libellis isagogicis ad Ephemeridas quæ postea cum radicali conferri solet, & sicut ex hac diuidatur vniuersè de tota vita, ac statu illius rei, sic ex themate revolutionis iudicium fertur de statu illius anni. Cardanus, & alij inutilem indicant hanc figuram revolutionis Solis ad idem punctum Zodiaci, in quo erat Initio alicuius operis,

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428 LEXICON. it has such efficacy upon these sublunary things not for any other reason (which for that cause have therefore taken their name), except because it remains much longer above the earth than the rest of the stars. <32.> Moreover, except for the luminaries, all the planets are at times retrograde; not because they are truly and really retrograding, but because they are carried in their own epicycle, which has the Sun for its center. And thus, while their deferent orbits are at the same time swept along by the motion of the first mover, it comes about that, with respect to the first mover and as compared with us, the very bodies of the planets sometimes seem to move backward, to stand still, and at one time to advance faster, at another more slowly; whereas in reality they always proceed in the same way and evenly in the epicycle. But when they are in the first station, descending from apogee to perigee, they strive against the succession of the signs, and therefore appear retrograde; just as in the second station, ascending from perigee to apogee, they always seem direct, because they move leftward in the epicycle, and thus according to the succession of the signs. All these matters can be seen clearly in the diagrams set out by all authors on the sphere, or on the secondary motions. <40.> REVOLUTION, as the etymology of the word suggests, among astronomers means nothing other than the complete circuit of some sphere or star until it returns to the same point where it was first when it began to move. Thus we say that Saturn completes its revolution through the zodiac in almost thirty years; Jupiter in twelve; Mars in two; the Sun in one year; the Moon in almost a month; and finally the Primum Mobile makes its daily revolution around the earth in the space of one natural day, that is, twenty-four hours. When this is completed, each of its parts returns to the same position in the same circle in which it was before. Sometimes it is taken more strictly and by antonomasia for the annual circulation, or return, of the Sun to the very same precise point of the zodiac in which it was at the beginning of some undertaking: thus the figure for the Sun’s ingress into the four cardinal points is usually drawn up. From this the four seasons of the year take their beginning, so that their qualities may be recognized; the revolutions of each recurring year, both in general and in particular, from the building of a city, the birth of a man, or the beginning of any work (about how this is done, authors everywhere teach in introductory booklets to the Ephemerides, which is afterward compared with the radical figure), and just as from this one judges universally the whole life and condition of that thing, so from the theme of the revolution a judgment is made concerning the state of that year. Cardanus and others indicate that this figure of the Sun’s revolution to the same point of the zodiac in which it was at the beginning of some work is useless,

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MATHEMATICVM. 429 eo quia, inquiunt, materialiter se habet ad radicem, nec vllam similitudinem telinet cum situ radicali reliquorum planetarum, aut cum motu directionum, ex quo totam diuidicandi segiem expiscandum est Et in Aph. 114. segment. 5. de reuolutionibus agens, tripliciter ait eas considerari posse, & in Zodiaco ad idem punctum, vt est reditus Solis initio cuiusque anni ad idem punctum equinoctij, & in Mundo, vt ipse, ait, & est reditus ad eandem fixam; & in Genituris, & est reditus eiusdem Solis ad priorem locum: verum addit, in hac debere addi tantam partem eclipticæ, quantam peragare potest in vna die naturali. Igitur reuolutio annua Natiuitatis, aut inceptionis alicuius rei, non debet attendi solum in reditu Solis ad eundem gradum Zodiaci, sed requirit aliquid amplius, scilicet additionem partis Eclipticæ singulis annis, quantum acquirit Sol singulis diebus successivè à die radicali cæpti operis, quod tamen, qua ratione fiat, & quid connexionis habeat cum themate radicali non explicat. Et sanè, vt benè discurrit accurissimus quidam Astronomus Gallus communis hæc ratio, accipiendæ reuolutionis annuæ ex reditu Solis ad idem punctum Zodiaci, in quo erat in radice operis; atque exinde postea suuros euentus diiudicandi, quàm sit inanis, fallax, erroribusque multis obnoxia, & ratio probat, & euincit experientia. Quid enim, inquit in hoc retum ordine tam firmum, ac stabile dici potest, quod planè in dies singulos ex fortuita rerum emersione notabilem non subear mutationem? Ipsa Genesis & si rerum omnium in vita euenientium prima radix sit, & fundamentum; nihilominus miro ordine & successivo motu transit mox in directiones, in ingressus impingit, & per varios significatorum transitus variatur. Igitur Thema reuolutionis ad summum erit illius tantum differentiæ temporis, in qua erigitur, & non alius mox successuræ: sic nec ipsæ reuolutiones consistunt immobiles, sed perpetua vertigine agitantur, perinde ac ipsa radicalis figura, constituuntque cum ea tam disformem conformitatem, vt inde eiusmodi effectus prodeant, quos nemo vnquam excogirauerit, Porro quisnam sit hic reuolutionis motus, & quomodo cum radice, & cum effectibus inde emanaturis connexionem habeat, operæ pretium est, vt paulò fusiùs explicemus. Igitur erecta, & ritè comprobata cælesti Natiuitatis, seu alterius incipientis rei figura, erigendum est itidem Thema reuolutionis quinti voluentis anni in eodem momento temporis, in quo erectum est thema Natiuitatis, nullo ha-

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MATHEMATICVM. 429 because, they say, it is materially related to the root, and has no likeness to the radical position of the other planets, or to the motion of directions, from which the whole series of dividing must be sought out. And in Aph. 114, section 5, speaking of revolutions, he says that they can be considered in three ways: in the Zodiac to the same point, as is the return of the Sun at the beginning of each year to the same point of the equinox; and in the World, as he says, and as it is, the return to the same fixed star; and in Nativities, and it is the return of the same Sun to its former place: but he adds, in this there must be added as much of the ecliptic as it can traverse in one natural day. Therefore the annual revolution of a Nativity, or the inception of some thing, ought not to be considered only in the return of the Sun to the same degree of the Zodiac, but requires something more, namely the addition of a part of the Ecliptic each year, as much as the Sun gains each day successively from the day of the radical beginning of the work, which, however, in what way it happens, and what connection it has with the radical figure, he does not explain. And certainly, as a certain very accurate French astronomer argues well, this common method of taking the annual revolution from the return of the Sun to the same point of the Zodiac, in which it was at the root of the work; and then afterward judging future events from it, is as empty, deceptive, and subject to many errors as reason proves, and experience demonstrates. For what, he says, in this order of things can be called so firm and stable, that it does not plainly every day undergo a notable change from the fortuitous emergence of events? The very Genesis, though it be the first root and foundation of all things that happen in life, nevertheless, by a wondrous order and successive motion, presently passes into directions, strikes upon ingresses, and is varied through the various passages of the significators. Therefore the Theme of the revolution will at most be only that difference of time in which it is erected, and not the one that will immediately follow; thus neither do the revolutions themselves remain unmoving, but are driven by perpetual whirling, just as the radical figure itself, and together with it they constitute so dissimilar a conformity that from it such effects arise as no one would ever have conceived. Moreover, what this motion of revolution is, and how it has a connection with the root and with the effects emanating from it, it is worth the effort to explain somewhat more fully. Therefore, once the celestial figure of the Nativity, or of some other beginning thing, has been erected and duly verified, the Theme of the revolution of the fifth revolving year must likewise be erected at the same moment of time in which the theme of the Nativity was erected, with no ha-

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430 LEXICON bito respectu ad gradum Solis in Zodiaco, atque earundem tabularum subsidio (vt idem ordo seruetur) quo illud erectum est, quas inter experientia probauit præstare Tychonicas. Huius igitur Ascensio Medij Cæli subtrahenda est ab Ascensione recta, itidem Medij Cæli radicalis figuræ, & prosi- liet numerus graduum, quos supra Naturæ perfecit eorum in his quatuor interiectis annis, qui erunt ferè 348. Hos autem diuide in quatuor partes, & habebis numerum graduum, & minutorum singulis annis competentium, & quos eorum sua circulatione præteriit, qui erunt quasi gr. 87. In super hors gradus singulis annis competentes in duodecim partes æquales dispesce, & habebis numerum singulis mensibus competentem, septem videlicet grad. cum minutis 15. ac tandem si velis id etiam ad dies deducere habebis minuta eorum singulis competentia. Ex his perspicuum fiet, quàm appositè hoc revolutionis nomen iugi cælorum circulationi, quam super res ab earum exordio cælestia corpora faciunt, indirum sit, quia profectò per eam singulis quadrienniis, ad idem ferè punctum reditur. 43. Præterea eum Sol in hisce singulis revolutionum quadriennis quibus ad idem punctum radicale reuertitur augescat duobus ferè minutis, hinc est vt quinquaginta ferè horæ minuta antequam perueniat ad tempus revolutionis, ipse iam tetigerit locum suum radicalem in Zodiaco, quæ minuta in gradus æquatoris conuersa exhibebunt duodecim circiter annos. Nunc defectus horum annorum duodecim gradibus respondentium, signat terminum naturalem, quem Deus constituit vitæ hominum, vt propterea non ab re multi existimaverint, eam naturaliter extendi posse ad centum viginti vsque annos, nec vlteriùs sine miraculo progredi. Siquidem defectus totius circuli spatio quatuor an norum dat 30. quaternas; quæ per quatuor productæ dant 120. Et quidem rationi consonum est, vt cum corpora cælestia, quæ suis motibus quasi quodam vehiculo suas communicant humanis corporibus qualitates; proindeque influendo in illa dant illis esse, & conseruari, quòd à causis secundis prouenit; consequens inquam est, vt dum illa suis in revolutionibus deficiunt, & ista tandem quæ ab illis pendent, deficiant; qui defectus toties reperitus, necesse est, vt extinguat tandem influxum vitalem, qui à sideribus viventi- bus communicatur. 44. Modò vt hæc Theoria reducatur ad praxim, oportet ad gradus æquatoris accipere gradus Zodiaci respondentes, ac distribuere per singulos annos succedentes, & menses; in-

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430 LEXICON with respect to the degree of the Sun in the Zodiac, and by the help of the same tables (so that the same order may be preserved) by which it was erected, which experience has proved to be better than the Tychonic. Therefore this Ascension of the Midheaven is to be subtracted from the right Ascension, likewise from the Midheaven of the radical figure, and there will come out the number of degrees which in these four intervening years it has advanced above Nature, which will be about 348. Divide these, however, into four parts, and you will have the number of degrees and minutes due to each year, and those which it has passed through in its circulation, which will be about 87 degrees. Moreover, divide the degrees due to each year into twelve equal parts, and you will have the number due to each month, namely seven degrees with 15 minutes; and finally, if you wish, reduce this also to days, you will have the minutes due to each of them. From these things it will become clear how aptly this name of revolution has been given to the perpetual circulation of the heavens, by which the heavenly bodies perform their course over things from their beginnings, because indeed by it, every four years, they return to nearly the same point. 43. Moreover, since the Sun in each of these four-year revolutions, by which it returns to the same radical point, increases by about two minutes, it follows that about fifty minutes of an hour before it reaches the time of revolution, it will already have touched its radical place in the Zodiac; and these minutes, converted into degrees of the equator, will amount to about twelve years. Now the deficiency of these twelve years corresponding to the degrees marks the natural limit which God has established for human life, so that for this reason many have not without cause judged that it can naturally be extended up to one hundred and twenty years, and no farther without a miracle. For the deficiency, over the space of a whole circle of four years, gives 30 fourfold measures; and these, multiplied by four, make 120. And indeed it is consonant with reason that, since the heavenly bodies, by their motions as by a kind of vehicle, communicate their qualities to human bodies; and therefore, by influencing them, give them being and preservation, which comes from secondary causes; it follows, I say, that when those bodies fail in their revolutions, these too, which depend upon them, should at length fail; and when this failure is found so often, it must needs at last extinguish the vital influx which is communicated from the stars to living beings. 44. Now, in order that this theory may be reduced to practice, it is necessary to take the degrees of the Zodiac corresponding to the degrees of the equator, and to distribute them through the successive years and months;

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MATHEMATICVM. 43. deque construere tabulas proprias cuiusque labentis anni. Quo præstito ad latus cuiusque anni, & mensis ad rationem culminantis gradus Zodiaci, accipiendus est etiam gradus ascendens in horizonte ad elevationem poli regionis. Ex quibus comparabitur stabile fundamentum veri motus, & ordinis annuarum revulsionum. Simili etiam ratione extrahendæ sunt revolutiones anno- <45.> rum 9. 13. 17. 21. 25. 29 &c. singulorum nempe labentium quadrivenniorum; atque ab vniuscuiusque ascensione recta Medij cæli subtrahenda erit Ascensio competens proximè precedenti quadriennio, numerus quippe graduum prosi- lientium erit quos cælum interim circulauerit: & exinde res vt supra dictum est perficienda. Atque vt accipias tempus præcisum cuiuscumque revolutionis, scias oportet, id du- plici via re assequi posse: Primò subtrahendo Ascensionem rectam Solis ab Ascensione recta Medij Cæli, ac subtractum postea in horas conuertendo. Secundò per tabulas domo- <46.> rum, sumendo horas, & minuta respondentia gradui Me- dij cæli, à quo subtrahendum est tempus respondens gradui Solis: nam id quod profilier erit ipsissimum tempus annuæ revolutionis. Et hæc quidem ex mente huius accutissimi, at- que ingeniosissimi viri. Cæterum Adrianus Negusantius ingenio non minus acer, ac feruidus, aliam adinuenit longè clariorem, naturæque principiis conformiorem instituendæ huius annuæ revolu- tionis rationem quam non tam figuram revolutionis dixerit, quam thema futuræ, vel expletæ directionis. Siquidem est constitutio cælestis ingressus Solis in locum suum radicalem in mundo, hoc est in eundem situm, & circulum positionis, in quo erat in Radice, cum additione partium æquatoris, quibus interm Primum Mobile solem præcessit, quasque Sol singulis recurrentibus annis motu directorio acquirit, vt dictum est in V. Directio: in qua sanè videre est aperri- mè cursum ipsius directionis, deuolutionem promissorum ad loca immobilia significatorum, & habitudinem quam reliqui planetæ ad dicta loca, nec non ad inuicem habent, & hæc est forte quam supra Cardanus terro loco memorauit reuolutionis speciem ingenituris, quam dicit esse reditum Solis ad locum suum radicalem addita tamen parte Ecliptica quantum peragrare potest in una die naturali. quibus mani- festè euincitur, ipsum non de ingressu Solis in locum Zo- diaci radicalem sed ad situm suum in Mundo, in quo cu con- sideretur vt significator, concipitur esse immobilis. Igitur erigenda est figura annuæ revolutionis eadem hora; at non

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MATHEMATICVM. 43. and so to construct proper tables for each passing year. This being done, in the side of each year and month, according to the rate of the culminating degree of the Zodiac, there must also be taken the degree rising in the horizon, according to the elevation of the pole of the region. From these will be compared the stable foundation of the true motion and order of annual revolutions. In a similar way also must be extracted the revolutions of years <45.> 9, 13, 17, 21, 25, 29, etc., namely of each passing four-year period; and from the right ascension of each Medium Coeli the corresponding ascension of the nearest preceding four-year period must be subtracted, for the number of degrees leaping forward will be those which the heaven in the meantime has traversed: and from this the matter is to be completed as above stated. And in order that you may obtain the exact time of any revolution, you must know that it can be reached in a twofold way: first, by subtracting the right ascension of the Sun from the right ascension of the Medium Coeli, and then converting the subtraction into hours. Second, by the house tables <46.> taking the hours and minutes corresponding to the degree of the Medium Coeli, from which must be subtracted the time corresponding to the degree of the Sun: for that which is gained will be the very time of the annual revolution. And these things indeed are according to the mind of this most acute and most ingenious man. Moreover, Adrianus Negusantius, no less keen and fervent in genius, invented another, far clearer and more in accordance with the principles of nature, method for establishing this annual revolution, which he would call not so much the figure of the revolution as the theme of the future, or completed direction. For it is the celestial constitution of the ingress of the Sun into its radical place in the world, that is, into the same position and circle of position in which it was in the radix, with the addition of the parts of the equator, by which meanwhile the Primum Mobile had preceded the Sun, and which the Sun acquires each recurring year by directed motion, as was said in V. Directio: in which truly one can see most clearly the course of the direction itself, the devolution of promises to the immovable places of significators, and the relation which the remaining planets have to the said places, and also to one another; and this is perhaps what Cardanus above, in the third place, mentioned as the species of revolution for nativities, which he says is the return of the Sun to its radical place, with however the addition of a part of the Ecliptic as much as it can traverse in one natural day. By which things it is plainly proved that he is speaking not of the ingress of the Sun into the radical place of the Zodiac but to its position in the world, in which, when considered as significator, it is conceived to be immovable. Therefore the figure of the annual revolution is to be erected at the same hour; but not

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432 LEXICON eadem die radicis, sed tot diebus post, quos anni interfluxerunt eum eo gradu Solis in Zodiaco, quem successiuè acquisiuit in singulos dies à Natiuitate: cuius gradus Ascensio recta quærenda est, eique addenda vel subtrahienda distancia quam habebat in radice à meridiano, proverat vltra vel citrà, nam numerus conflatus, aut reliquus erit Ascensio recta Medij coeli figuræ revolutionis, ad quam postè à more solito erigenda est figura, constituiis planeris in iis Zodiaci gradibus, in quibus reperiuntur ea die sub dera hora radicis. Atque hæc est figura revolutionis respondens eius initio, hoc est radici, vnde expit hic regularis motus institui, quatenus incedit ordine directionis, arque adeo potius dicenda esset revolutio annuæ cuiusque directionis. 47. Parietiam ratione, si inter annum incedat notabilis quædam directio alicuius significatoris, voluerisque cognocere habitudinem planearum ad locum directionis, nec non ad inuicem videndum est, quotus sit arcus directionis, & quot annos, & menses ad amussim appellet iuxta regulam superius traditam rum pro annis tot dies, pro mensibus tot binæ horæ adiiciendæ sunt ad annos qui interim effluxerunt, seu figuræ revolutionis annuæ Solis ad idem puctum Zodiaci, quod in radice tenebat, atque ad eam diem & horam in quam incidit erigenda erit figura more solito, vbi pro miraculo conspicietur Promissor ad locum significatoris quem in radice habebat ad amussim deuolutus: videbitur quomodo se habeant foriunæ ad dictum locum, quomodo infortunæ: atque adeo non temere coniectari poterit de prospero, vel in fausto enentu illius directionis. Sed hæc doctrina melius forte percipietur per reductionem ad praxim, ad quam lectorem remiro. 48. Rhombus græcè significat figuram geometricam quadri-lateram, cuius quidem latera æqualia sint, anguli vero inæquales, quorum duo sibi diametraliter oppositi, acuti sint, duo item obiusi. Talis est forma quam præse fert planus quidam Piscis, ob id Rhombus communiter appellatus. Differt autem à Rhomboide, & perfecto quadrato, quod hoc iam larera, quam angulos habet æquales, & rectos, illa autem etsi cum Rhombo conueniat in hoc quod angulos obliquos habeat, & partim acuros, parrim obtusos; disconuenirtamen in hoc, quod & latera habet inæqualia: vnde medium quid est inter quadratum, & Rhomboidem de vtrisque æquè aliquid participans, atque ab vtrisque in aliquo etiam disconueniens.

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432 LEXICON on the same day of the radix, but after as many days as the years that have elapsed, with that degree of the Sun in the Zodiac which it successively acquired on each day from the Nativity: the right ascension of which degree must be sought, and to it must be added or subtracted the distance which it had in the radix from the meridian, whether beyond or this side of it; for the resulting number, or remainder, will be the right ascension of the Midheaven of the figure of revolution, for which, afterward, in the usual way, the figure is to be erected, with the planets placed in those degrees of the Zodiac in which they are found on that day under the degree of the radix hour. And this is the figure of revolution corresponding to its beginning, that is, to the radix, whence this regular motion ought to be established, insofar as it proceeds in the order of direction, and therefore it would more properly be called the revolution of each annual direction. 47. In the same way, if within the year there occurs some notable direction of any significator, and you wish to know the relation of the planets to the place of the direction, and also to one another, it must be seen what the arc of the direction is, and how many years and months to a nicety it calls for, according to the rule given above, namely: for years, so many days; for months, so many double hours are to be added to the years that have elapsed in the meantime, or to the annual revolution figure of the Sun to the same point of the Zodiac which it held in the radix, and for that day and hour into which it falls, the figure is to be erected in the usual way, where, as if by miracle, the Promissor will be seen devolved exactly to the place of the significator which it had in the radix: it will be seen how the fortunes stand with respect to the said place, how the infortunes; and thus one will be able to conjecture, not rashly, about the prosperous or fortunate outcome of that direction. But this doctrine will perhaps be better understood through reduction to practice, to which I refer the reader. 48. Rhombus in Greek signifies a geometrical figure of four sides, whose sides are equal, but whose angles are unequal, of which two, directly opposite to each other, are acute, and the other two obtuse. Such is the shape presented by a certain flat fish, for which reason it is commonly called a Rhombus. It differs, however, from a rhomboid and from a perfect square, because the latter has both equal sides and equal right angles, whereas the former, although it agrees with the rhombus in this, that it has oblique angles, partly acute, partly obtuse, nevertheless differs in this, that it also has unequal sides: whence it is something midway between a square and a rhomboid, participating equally to some extent in both, and also differing in some respect from both.

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MATHEMATICVM. 433 RHOMBOIDES, vt modò significauimus, est figura quadrilatera habens nedum angulos, sed & latera inæqualia, ita tamen vt duo, iam latera, quam anguli, sibi ex aduerso respondentia æqualia sint, & per consequens constet duo- bus angulis obtusis, ac totidem acutis, vt Rhombus: Itaque Rhomboides est media inter parallelogrammum & Rhombum, quod ab vno habitudinem laterum, ab altero angulorum proportionem sumit: ac si Rhombum in paral- lelogrammum transferas, vel parallelogramum in Rhombum illico Rhomboides efformetur. RIFORITAS DVMVTA græcè audii Genitura duarum foeminarum & vnius masculi, in quam conueniant Venus, Mats, & Luna arab. Dimantarcoris. Ptolem. cap. de Gemell. in vers. arab. RICET arab. Stella fixa primæ magnitudinis de natura Io- uis, & Saturni, clara nimis & fulgens in summitate pedis sinistri Orionis collacata in longitudine sub gr. fere 12. Geminorum cum laritudine australi gr. 31. otitur Rom: cum gr. 13. Cancri, occidit cum 22. Tauti. Ros humor est è cælo serena nocte decidnus, ac parua ve- luti, grataque pluuia, cuius eformationem pulchrè de- scribit Aristoteles 1. Meteor. cap. 11. sic inquiens: Cum Va- por iam modico igne afficiatur, vt non ascendat ad mediam regionem, sed propè terram consistas in imo, accedente no- ctis frigore, expulsoquo igniculo sustentante deorsum relabitur. Ex quibus liquet primò Rorem formari quidem calore solis, sed in insima regione ex vapore sursum elato, qui nocturno frigore concretus in humorem aqueum relabatur. Secundò ad eius formationem requiri moderatum calorem, qui fa- ciat, vt vapor non ascendat nimium, sed circa tetram si- stat, & moderatum frigus, cuius ope fiat vt is in humorem aqueum conuertatur: Nam si immoderatum foret frigus cederet in pruinam. quæ proinde ros congelarus dicitur, & ab eo re ipsa, & productione non differt. Tertiò ipsum non nisi serena nocte destuere; nam si aër foret nubilus, aut plu- uiosus, vel agitatus ventis, vapor ille tenuis facilè dissipa- retur, ac vel coiret in pluuiam, vel aliò dispergeretur. Hinc est, vt aduerit Aphtodiscus, ipsum esse serenitatis indicium. Quamquam autem Ros vegetet plantas, docet tamen Al- bertus Magnus lib. 2. 1. 14. ipsum si diu suprà illas consistat, non paruum nocumentum afferte, quatenus ca- lore solis accedente in æruginem, & in puttedinem verti- tur; similiter herbas adurit, paños lineos cortumpit, &

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MATHEMATICVM. 433 RHOMBOIDES, as we have just now signified, is a quadrilateral figure having not only unequal angles, but also unequal sides; yet in such a way that the two sides, as also the two angles opposite one another, are equal, and consequently it consists of two obtuse angles and as many acute ones, as does the Rhombus. Therefore the Rhomboides is midway between the parallelogram and the Rhombus, taking from the one the relation of the sides, and from the other the proportion of the angles: and if you turn a Rhombus into a parallelogram, or a parallelogram into a Rhombus, a Rhomboides is immediately formed. RIFORITAS DVMVTA, in Greek, the conception of two females and one male, in which Venus, Mars, and the Moon agree; Arab. Dimantarcoris. Ptolem. cap. de Gemell. in vers. arab. RICET, Arab. a fixed star of the first magnitude, of the nature of Jupiter and Saturn, very bright and shining, placed at the summit of the left foot of Orion, in longitude about 12 degrees of Gemini, with southern latitude 31 degrees; it rises at 13 degrees of Cancer, sets at 22 degrees of Taurus. Dew is a moisture falling from the sky on a clear night, as a small and pleasant rain; Aristotle describes its formation beautifully in Metaph. 1, cap. 11, saying thus: when vapor is affected by a moderate heat, so that it does not rise to the middle region, but remains near the earth below, then, when the cold of night comes on and the small sustaining fire is driven out, it falls back. From this it is clear, first, that dew is formed by the heat of the sun, but in the lowest region from vapor raised upward, which, congealed by the cold of night, falls back into watery moisture. Second, that a moderate heat is required for its formation, which causes the vapor not to rise too far, but to remain about the earth, and a moderate cold, by means of which it is turned into watery moisture; for if the cold were excessive, it would pass into hoarfrost, which is therefore called frozen dew, and in fact differs from it neither in substance nor in production. Third, that it occurs only on a clear night; for if the air were cloudy, rainy, or stirred by winds, that thin vapor would easily be dispersed, and either gather into rain or be scattered elsewhere. Hence it is that Aphridiscus notes that it is an indication of fair weather. Although dew does nourish plants, Albertus Magnus teaches nevertheless, in lib. 2, cap. 14, that if it remains on them for a long time it causes no small harm, inasmuch as, when the heat of the sun comes on, it turns into rust and into rot; likewise it scorches herbs, corrupts linen cloths, and

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414 LEXICON pecoribus ventris profluvium excitat, quatenus viscous est, nec facis concoctus, vnde dicitur Ros à todendo, Decidit potissimum, & copiosiùs in Verè, & in Autumno: quia tunc temporis nec nimius calor nec frigus eius efformationi potest obsistere, & cæteris paribus in plenilunio maior est ipsius copia quam quouis alio tempore: Vnde vete à D. Ambrosio in Hexam. libr. 4. caput. 7. Luna larga roris asseritur. < 54.> Rori affine est Manna: liquor, inquam notissimus, suauissimus, in similitudinem gummi concretus, è cælo sereno tempore pluens, atque arborum foliis, lapidibusque adhærens; olim à Deo singulari prouidentia datus Israelytico populo in desetto, dum viam ad Terram promissionis adornabat. Vnde eius leuitatem demirati exclamantes dicebant Manku, scilicet qui est hoc? ex quo postea illi Mannæ nomen adhæsit. Porrò eius productio, vt & istius, quod apud nos est, saltem quoad substantiam, naturalis fuit, eiusdem speciei, licet illud, vt notat Abulensis in cap. 16. Exod. quæst. 8. fuerit longè sublimioribus qualitatibus præditum: quod tum ex formæ similitudine patet, tum ex dulcedine, tum etiam ex formatione: virumque enim noctis tempore cadebat, & cadit, vtrumque eodem nomine insignitur, quod apud Syros nil aliud sonat, quam ros melleus mautinus: Neque enim a iud est, quam ros quidam crassior à sole recipiens dulcedinem, & maturationem, à frigore autem noctis concretionem in morem pruinx. Vnde ait Augustinus Niphus in commentar. de signis sirenitatis cap. 5. Manna ipsum ex rore generari; nam quotiescumque accidit, vt ros decidat in regionem, quæ aliqua ex parte calida est, cum multas partes terreas tenues habeat, quæ calore ambientis aëris coagulantur, resolutis partibus aqueis, manna sit in arborum foliis insidens, à calore inspissatum, atque in formam seminis coriandri coagulatum, ideoque in regionibus calidis maximè reperitur. Quomodo autem, sit erat eiusdem speciei cum nostro; non eosdem effectus habebat, corpus resoluens, dicendum id ex miraculo accidisse, vel ex maiore & firmiore substantia, qua illud erat præditum. Nisi fortè dicere velimus cum nostro Vecchio obseru. medica 148. in sacram scripturam, id etiam manna Israeliticum habuisse, ad quod fortè respiciebat populus cum dicebat: Exod. 16. Anima nostra iam nauseat supercibo isto levissimo. Quandoquidem ex doctrina Hippocratis lib. de alimentis expurgant. constat cibos leues, & qui solidam substantiam corporibus nostris non tribuunt,

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414 LEXICON causes a flux in the belly of animals, insofar as it is viscous, and not fully digested food; hence it is called dew from the downflow. It falls chiefly and more abundantly in spring and in autumn, because then neither excessive heat nor cold can prevent its formation; and, other things being equal, at the full moon its quantity is greater than at any other time. Hence, according to St. Ambrose in the Hexaemeron, book 4, chapter 7, the moon is said to be rich in dew. <54.> Closely akin to dew is manna: that is, a very well-known and sweetest liquid, congealed into the likeness of gum, raining down from a clear sky and adhering to the leaves of trees and to stones. Formerly it was given by God by a singular providence to the Israelite people in the desert, while they were preparing the way to the Promised Land. Hence, astonished at its lightness, they cried out, Manku, that is, what is this? from which afterwards the name manna came to attach itself to it. Moreover, its production, as also that of the manna found among us, at least as regards substance, was natural and of the same species, although that manna, as Abulensis notes in chapter 16 of Exodus, question 8, was endowed with far more sublime qualities: this is evident both from the likeness of shape, from the sweetness, and also from the manner of formation. For both fell, and fall, at night-time, and both are marked by the same name, which among the Syrians means nothing other than honeyed morning dew. For it is nothing other than a certain thicker dew, receiving sweetness and ripening from the sun, but from the cold of night congealing in the manner of hoarfrost. Hence Augustinus Niphus says in his commentary on the signs of serenity, chapter 5, that manna itself is generated from dew; for whenever it happens that dew falls upon a region that is in some part warm, since it contains many fine earthy particles, which are coagulated by the heat of the surrounding air, the watery parts being dissolved, manna lies upon the leaves of trees, thickened by heat and coagulated into the form of coriander seed, and therefore it is found especially in warm regions. But if it was of the same species as ours, it did not have the same effects, dissolving the body; this must be said to have happened by miracle, or because of the greater and firmer substance with which it was endowed. Unless perhaps we wish to say with our Vecchio, Observ. Medica 148, on Sacred Scripture, that the Israelite manna also had this property, to which perhaps the people were referring when they said: Exodus 16, Our soul now loathes this very light food. Since from the teaching of Hippocrates, book On Purgative Foods, it is established that light foods, which do not give solid substance to our bodies,

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MATHEMATICVM. 435 medicamenta etiam esse, & corpus resoluere. Et fieri qui- dem potest, vt cibus iste ab initio eundem illis effectum con- tulerit, & fuerit medicamentum ad deponendam cacochimiam, quam ex vsu cucumerum, cæparum, allitorum & similium ciborum, quibus in Ægypto vescebantur, con- traxerant: postea verò, expurgatis corporibus consuetu- do fecit idoneum, & suauem cibum. Hæc Vecchius. Cæ- terum ipsum optimæ qualitatis, suo tempore abundè colligi fueuisse in Monte Libano, testatur Galenus lib. 3. de alimentis cap 39. addens, eiusdem regionis rusticos expansis hu- mi velleribus solitos fuisse illud excipere. In Calabria item citeriore scimus decidere Manna lectissimum, si non eiusdem prorsus qualitatis ac perfectionis, vt erat Israeliticum, certè non contemnendum: quod per totam Italiam propagatur, & prostat in Pharmacopæis passim ad medicamentorum vsum. Eius casum eleganter describit Iulius Cæsar Recupitus in suo Nuncio de Vesuiano incendio pag. nihi 136. lux: à Al- tomontem, inquit, in Citeriore Calabria, & in Vlceriore, vsque ad antiqua Tuniana vestigia, ros è calo decidinus syl- vestribus prunis exceptus, quà foliis, quà trunco noctis frigo- re consipatur in grana, qua postea in pradulcem aliquata hu- morem, medicamenta suauissima præstant forbinda vel pue- ris; tanta salubritate, vt in eâ caleste munus agnoscas; tanto pretio, vt interdum Neapoli Manna Calabrica vncia septem nummis aureis vanierit: quasi è calo imber aureus co- cidisset. hæc ille. Eius vtilitates, & commoda abundè re- fert Cornelius Celfus, qui eum Rorem Syriacum ap- pellat. Similiter Mel quoad substantiam, & qualitates parum differt à Manna, nisi quod illud tenuissimum sit, & herbis, flotibus, ac terræ solo ita adhærat, vt insensibilis penè sit, & solum apum ministerio colligi possit; hoc autem crassius, & in globulos probè visibiles, manuque contractabiles coëat. Vtrumque autem siderum effectus sunt: constat enim ex aëre decidere certis temporibus sub matutino siderum exortu, præcipuè sub Cane Syrio: Vnde Plin. lib. 11 cap. 14 ait Si- rio exotiente mel optimum comparari: atque si eodem tem- pore accidat Veneris, Iouis, Mercuriique commixtio, nil hominum malis opportunius esse, quam ipsum. Vt meri- tò alij cæli sudorem, alij siderum saliuam, alij purgantis se aëris fructum appellant. Igiur tam Manna, quam Mel ex eodem illo vapore tenui, quo ros producitur, sit; iuxta locorum verò calidorum qualitatem, quia vapor ille habet admixtum aliquid calidæ exhalationis, ideò & inspissatur,

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are also medicines, and they dissolve the body. And indeed it may happen that this food at the beginning produced the same effect in them, and was a remedy for removing the cacochymy, which they had contracted from the use of cucumbers, onions, garlic, and similar foods, with which they were fed in Egypt; but afterward, once the bodies had been purged, habit made it a suitable and pleasant food. Thus Vecchius. Moreover, Galen testifies, in book 3 of On Foods , chapter 39, that the very best quality of it was abundantly gathered in its season on Mount Lebanon, adding that the rustics of that region were accustomed to receive it with fleeces spread on the ground. In Lower Calabria, too, we know that the choicest manna falls, if not altogether of the same quality and perfection as the Israelite, certainly not to be despised; and it is spread throughout all Italy and is commonly sold in apothecaries for medicinal use. Julius Caesar Recupitus elegantly describes its falling in his Nuncio de Vesuviiano incendio , page 136: “At Altomonte,” he says, “in Lower Calabria and in Upper Calabria, as far as the ancient remains of Tuniana, a dew from the sky falls, caught by the wild plum trees, and, both on the leaves and on the trunk, is thickened by the cold of night into grains, which afterward, dissolved into a sweetish moisture, provide very pleasant medicines, even for children; with such wholesomeness that in it you recognize a heavenly gift; with such value that sometimes in Naples Calabrian manna has sold for seven gold coins an ounce, as though a golden rain had fallen from the sky.” Thus far he. Cornelius Celsus abundantly recounts its uses and benefits, calling it the Syrian dew. Similarly, honey, as regards substance and qualities, differs little from manna, except that the latter is very thin and adheres to herbs, flowers, and the surface of the earth in such a way that it is almost imperceptible, and can be gathered only by the agency of bees; whereas the former is thicker and coheres into clearly visible globules that can be handled by hand. Both, however, are effects of the stars: for it is agreed that they fall from the air at certain times under the morning rising of the stars, especially under the Dog Star. Hence Pliny, book 11, chapter 14, says that when Sirius sets, the best honey is obtained; and if at the same time there occurs a conjunction of Venus, Jupiter, and Mercury, nothing is more favorable to human needs than honey itself. Accordingly some call it the sweat of the sky, others the saliva of the stars, others the fruit of cleansing air. Therefore, both manna and honey are from that same subtle vapor from which dew is produced; yet according to the nature of warm places, since that vapor has mixed with it something of a warm exhalation, it is also thickened.

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436 LEXICON & in dulcedinem concoctus transit. Siquidem, vt habet Galenus, 4. de simplicium Medicamentor. facultatibus c. 9. moderatus ealot dulcedinem facit; & omnia dulcia miti calore sunt prædita. 56. RO A. apud Astronomos dicitur genus quoddam Cometæ corpore magni, ac figuræ instar faciei hominis, mixti coloris ex aureo & argenteo. Est de natura Solis, & cum apparuerit portendit mortem Principum, & hominum potentiorum, rerumque mutationem in melius. Vide quæ diximus in V. Pseudostella. 57. ROS H HALLILITH. hebræo nomine, hoc est Caput Misis, dicitur Caput Medusæ, stella fixa perniciosa in Perseo. Hanc autem Musim Hebræorum Thalmudistæ fabulantur fuisse fæminam quandam strigem Adæ coneubinam, postea interfectam atque in Cælum elatam. De qua re vide Kircher. in Oedippo Ægyptiaco. 58. RO RAS equi sidus vide Equiculus. 59. ROTA IXIONIS, sidus in Cælo ad Australem plagam, alio nomine Corona Australis. Vide ibi. 60. RUBAIL arabicè, Latinè Canopus stella fixa primæ magnitudinis in Argonaut, de qua multa diximus in V. Canopus. 61. RVVABAH Ismaelitis audit stella polaris in extremo caudæ vrsæ minoris sita, nomine à toto asterismo desumpto. 62. RYMINANTIA SIGNA, apud Astronomos dicuntur quæ animalium ruminantium speciem præseferunt, qualia sunt Aries, Taurus, & Capricornus. Hæc enim Animalia, sicut & omnia cornigera, quoniam in superiore mandibula dentibus eatent, cibum summatim carpunt, atque in iugulo seruant, quem postea ad o[mn]es iterum reuocantes lente ruminant & comminuunt. In his ergò signis consistens Luna consimilem in nobis effectum progignit, & ideò cautum est ab Astrologis Medieis, ne potiones sumantur Luna signa ista tenente, quæ ideo ruminantia vocauere, atque animantium ruminanium nomine, & figura insigniuere, vt eorum innotescat natura, siquidem, vt iugis semper experientia probauit, potiones eo tempore diu in stomacho retineri non possunt, sed citò euomuntur. Econtrà Vomitoria quamdiu Luna in signis ruminantibus reperitur, appositè exhibentur, vt præ cæteris aduertit Ganiuetus cap.2. differ.3. quia tunc Luna virtutem expultricem toborat. Inter ruminania signa ascribi solet etiam Leo, non quod is vere ex ruminantibus sit, sed quia, vt obseruat Origanus, cum sit Domicilium Solis, præest cordi, ac proinde eundem effe- ctum

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& being cooked in sweetness it passes over. For, as Galen has it, 4. de simplicium Medicamentor. facultatibus c. 9. moderate warmth makes sweetness; and all sweet things are endowed with gentle heat. 56. RO A. among astronomers is said to be a certain kind of comet of great body, and in the shape of a human face, of mixed color from golden and silver. It is of the nature of the Sun, and when it appears it portends the death of princes, and of more powerful men, and a change of affairs for the better. See what we said under V. Pseudostella. 57. ROS H HALLILITH, in the Hebrew name, that is, Caput Misis, is called the Head of Medusa, a harmful fixed star in Perseus. The Talmudists of the Hebrews, however, fabulously relate that this Musim was a certain woman, a witch and concubine of Adam, later killed and carried up into Heaven. On this matter see Kircher, in Oedippo Ægyptiaco. 58. RO RAS, the star of the horse, see Equiculus. 59. ROTA IXIONIS, a star in the heavens on the southern side, otherwise called Corona Australis. See there. 60. RUBAIL, in Arabic, in Latin Canopus, a fixed star of first magnitude in the Argonauts, concerning which we have said much under V. Canopus. 61. RVVABAH, among the Ishmaelites, is the polestar called, situated at the extreme end of the tail of the little Bear, the name being taken from the whole asterism. 62. RYMINANTIA SIGNA, among astronomers, are called those which present the appearance of ruminating animals, such as Aries, Taurus, and Capricornus. For these animals, and likewise all horned animals, because they have no teeth in the upper jaw, take their food only in small portions and keep it in the throat, which later, bringing it up again to the mouth, they slowly ruminate and crush. Therefore when the Moon is in these signs, she produces a similar effect in us; and for this reason medical astrologers warn against taking potions while the Moon occupies these signs, which they therefore called ruminant, and marked with the name and figure of ruminating animals, so that their nature may be made known; for, as constant experience has always proved, potions at that time cannot remain long in the stomach, but are quickly vomited up. On the other hand, vomitives are appropriately administered while the Moon is found in the ruminant signs, as Ganiuetus particularly notes, cap. 2, differ. 3, because then the Moon strengthens the expulsive virtue. Among the ruminant signs, Leo is also usually reckoned, not because it is truly one of the ruminants, but because, as Origanus observes, since it is the dwelling-place of the Sun, it presides over the heart, and therefore the same effe-

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MATHEMATICVM. 437 etum parit, ac ipsa ruminantia signa. RYTHMVS græcè, harmoniam, numerorumque propor- < 63.> tionem sonat. Vnde Logarithmi, Isarythmi, &c. Hinc etiam Scientia quæ de numerorum ordine, qualitate, atque ad inuicem respondentia tractat, Arithmetica dicta est. Vi- de in V. Numerus & in V. Proportionalitas. SA SACLATENI Chaldaicè dicitur prior hædorum, stella fixa 1. Squartæ magnitudinis de natura Martis, & Mercurij, consistens in vola sinistræ manus Aurigæ, de qua vide in V. Hadi. SACRARIVM, Ara, Thuribulum, sidus in Cælo ad Au- < 24> stralem plagam constans stellis septem de natura Veneris & Mercurij, sub signo Libræ. Hoc sidus, tum ratione signi in quo est, tum etiam ob naturam stellarum maximè tempe- stuosum est, ventosque nimios ciere solet. Quod obserua- uit Cicero in Arati Phænom. vbi de eo sic cecinir. Nam cum fulgentem cernes sine nubibus atris Aram sub media celi regione locatam A summa parte obscura caligne tectam Tum validis fugito deuitans viribus Austrum Quem si prospiciens vitaueris omnia cautè Armamenta locans tutò labere per vndas, Sin grauis inciderit vehementi flamine ventus Perfringet celsos defixo robore malos: Vt res nulla feras possit mulcere procellas, Ni parte ex Aquilonis opacam pellere nubem Caperis, & subitis auris diduxerit Ara. Hucusque Tullius. De aliis verò eius significatis abundè < 34> diximus in V.V. Lar, & Ara. SAGEN Lunæ in Sphaera barbarica dicitur secundus decanus 34 Sagittarij manens sub Dominatu Lunæ, proindeque habens significare mæstitiam, ploratum, dolorem, & affectum si- < 41> bi sempertimendi. SAGITTA, Telum, Iaculum, sidus in cælo ad Galaxiam < 41> propè Aquilam, constans stellis quinque de Natura Martis, & Veneris, de qua horoscopante sic venustè cecinit Pontanus in Vrania. Si cælo aspiciens oculo intueare Sagittam, Insignis Iaculo ediceris, celefique sagitta, Contingens possum quocumque in lim. te signum: Sine etiam speculantem alta de turri columbam E c

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MATHEMATICVM. 437 and it produces herds, and the signs themselves are rumination. RHYTHMUS in Greek signifies harmony, and the proportion of numbers. Hence Logarithmi, Isarythmi, etc. From this also the science which treats of the order, quality, and mutual correspondence of numbers is called Arithmetic. See in V. Numerus and in V. Proportionalitas. SA SACLATENI is called in Chaldaic the first of the kids, a fixed star of the first magnitude, of the nature of Mars and Mercury, situated in the left palm of Auriga; see it in V. Hadi. SACRARIVM, Ara, Thuribulum, a constellation in the sky toward the southern region, consisting of seven stars of the nature of Venus and Mercury, under the sign of Libra. This constellation, both because of the sign in which it is, and also because of the nature of the stars, is very stormy, and is wont to stir up violent winds. This was observed by Cicero in Aratus’ Phaenomena, where he sang thus of it. For when you behold the shining Altar without black clouds, set in the middle region of heaven, covered from the upper part with dark gloom, then flee, carefully avoiding the south wind with strong force; if, foreseeing it, you shall have shunned it, placing all things prudently, you will sail safely through the waves. But if a heavy wind shall fall with a violent blast, it will break the lofty masts with their fixed timber; so that no means can soften the raging storms, unless, from the side of the North, you try to drive away the shadowy cloud, and the Altar shall have parted the sudden breezes. Thus far Tully. But we have spoken abundantly of its other significations in V.V. Lar and Ara. SAGEN in the barbaric Sphere is called the second decan of Sagittarius, remaining under the dominion of the Moon, and therefore signifying sadness, weeping, sorrow, and a tendency to fear for oneself always. SAGITTA, a weapon, a dart, a constellation in the sky near the Galaxy, close to Aquila, consisting of five stars of the nature of Mars and Venus; of this Pontanus thus gracefully sang in Urania. If, looking toward the sky, you should behold the Arrow with your eye, you would be proclaimed renowned for the dart, and as a swift arrow, touching whatever sign you may stand in its limit; and even one observing a dove from a high tower E c

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LEXICON Deiicis atherea contorto verbere funda; Squamosumque petis certo sub vulnere piscem. In Occidente verò edicit natum periturum inter cædes & strages viscerum; idque siue bonę siue malæ stellæ astipulauerint. Quod si Saturnus solus aspexerit, damnabitur ad spectacula, aut caucæ includeitur ad mortem: Si verò Mars assistemne Mercurio subdit. Vendetur miser, & fadabit sanguine arenam. Hæc pontanus more poëtico ludens potiùs, quam veri quid auspicarius. 5. SAGITTA etiam dicitur ab aliquibus Sinus versus, hoc est linea recta in area circuli quæ chordæ subtensæ, & sinui recto adiacet, cum eoque angulum rectum efformat, adeo- vt posito quocumque arcu, & chorda illi subtensa; quæ linea in s ar sagitiæ virumque mediat ac diuidit, porrigitur- que à medio chordæ ad arcum, à similitudine teli à chorda per arcum excussi, sinus versus, ac sagitta dicaitur. 6. SAGITTARIVS, Phillèrides, Chiron, Arabicè Elkaùs, vnum è duodecim sig g is Zodiaci, nonum in ordine, Domus Iouis & eiusdem ac Solis Trigonum. Antiqui ponunt in eo exaltari capui draconis, verum id gratis dictum, ac pro- prereà à neotericis non admittitur. Est signum igneum commune, in prima sui medietate humanum, in reliqua ferinum. Eius Asterismus in octaua sphæra incidit in Galaxiam incipiens ab gr. 26. Sagitiarij primi mobilis & exienditur vsque ad gr. 28.1 Capricorni. Habet im[m]ira se stellas 32. secundum Ptolemæum, at iuxta Keplerum 34. quas inter vnam nebulosam in fronte maximè ab Astronomis consideratam. Priores eius partes sunt frigidæ, & humidæ, mediæ ventosæ, posteriores calidæ, & siccæ. Pars borealis ventosa: australis varia, & humida, 7. SALCHADAI idem sonat Ægyptiis ac Dominus anni, testis Aben Ragel de Revolutionibus. Quisnam autem is sit, diximus suo loco. 8. SALTATOR ab aliquibus appellari solet ingeniculus, seu Hercules, Eugonasis, sidus propè Ophiueum, de quo plura sub aliis nominibus dicta sunt. 9. SAMEH arab. alio nomine, Chausine, & Elhaut dicitur signum, & constellatio Piscium, & primus quidem Piscis ac borealis audit Sameh Elschemali, secundus verò, & Australis Sameh Elgenubi. Vide iam dicta in V. Pisces. 10. SARTAI MESARTHIN hebraicè dicitur fixa quartæ magnitudinis, de natura Manis & Saturni, prima in cornu Arieiis stella speciali nota digna, quoniam tempore Ptolemæ

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LEXICON You strike the aerial masses with a whirling sling; And with a sure wound you seek the scaly fish. In the West, however, it proclaims that one born there will perish amid slaughter and destruction of the bowels; and this whether good or evil stars have favored him. But if Saturn alone has looked upon him, he will be condemned to the spectacles, or be shut up in a cage to death; if, however, Mars assists, Mercury subdues him. The wretched man will be sold, and will redden the arena with blood. This Pontanus, playing more in poetic manner than as a true diviner, said. 5. SAGITTA is also called by some Sinus versus, that is, the straight line in the area of a circle which touches the subtended chord, and the right sinus, and forms a right angle with it, so that, with any arc placed there, and the chord subtended to it, that line in s ar sagitiæ virumque mediat ac dividit, extends from the middle of the chord to the arc, from the resemblance of a missile shot from a bow through the arc, it is called sinus versus, and sagitta. 6. SAGITTARIVS, Phyllerides, Chiron, in Arabic Elkaùs, one of the twelve signs of the Zodiac, the ninth in order, the house of Jupiter and the trigon of the same and of the Sun. The ancients place the exaltation of the dragon’s head in it, but this is said without proof, and therefore is not admitted by modern writers. It is a fiery sign, common, in the first half human, in the remaining half bestial. Its asterism in the eighth sphere falls in the Galaxy, beginning from 26 degrees of Sagittarius of the first mobile and extending to 28 degrees 1 of Capricorn. It has in itself 32 stars according to Ptolemy, but according to Kepler 34, among which one nebulous one in the forehead is especially considered by astronomers. Its earlier parts are cold and moist, the middle windy, the later hot and dry. The northern part is windy; the southern variable and moist, 7. SALCHADAI among the Egyptians means the same as Lord of the year, as testified by Aben Ragel on Revolutions. But who this is, we have said in its proper place. 8. SALTATOR is commonly called by some Ingeniculus, or Hercules, Eugonasis, a star near Ophiuchus, of which more has been said under other names. 9. SAMEH, in Arabic, is called by another name Chausine and Elhaut, the sign and constellation of Pisces, and indeed the first Fish and the northern is called Sameh Elschemali, the second, and southern, Sameh Elgenubi. See what has already been said in V. Pisces. 10. SARTAI MESARTHIN in Hebrew is said of a fixed star of the fourth magnitude, of the nature of Mars and Saturn, the first star in the horn of Aries, worthy of special note, since in the time of Ptolemy

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MATHEMATICVM. 439 eiat in sectione verna, atque adeo ab ea computabatur introitus Solis in punctum æquinoctij: nunc autem ob motum octauæ sphæræ elongata est, & præcessit ad grad. 28. min. 47. manens adhuc in Ariete primi mobilis cum latitudine boreali gr. ferè 9. SARTAN siue ELSARTAN arab. Latinè Caneer signum quartum Zodiaci. Chaldaicè verò Sartono. 124 SATELLITIVM Apud Astronomos est eomitatus, & fuleimé- tum, quod Planetæ suo quisque radiorum foenore ad Luminaria faeiunt, eorumque felicitati suis quoque lumini- bus astipulantur: quæ quidem constitutio, vt author est Ptolemæus in Quadrip. lib. 4. cap. 1. felieissima est in natalitio themate, atque huiusmodi natos etsi alioqui ex insima plebè prodierint, ad suprema subsellia euehit, magnosque Reges facit, ac principes. In quo autem consistat huiusmodi Satellitium, non æquè à Professoribus traditur. Nos de hac re non nihil suprà in V. Doriphoria libauimus: hic rem breuiter concludemus. Satellitium igitur in alio non consistit, quam in radiorum concursu ad Luminaria, quibus planetæ dignitatum numeros ipsis cæteroqui fortissimis addunt: itavt ipsis in locis idoneis puta in Angulis existentibus, & in propriis dignitatibus alij planetæ sint ad Solem Orientales, ad Lunam oceidentales, & ipsis aliquo modo configurati siue in Mudo, siue in Zodiaco ne ipsis quidem parallelis exclusis aut radiis alioqui hostilibus, & infaustis, quales sunt sesqui quadratus) qui in hæc re numeros addit) quadratus, & oppositio: qui licet quoad vitam infausti sint, quoad honores verò, ac dignitates semper felicem significatorum positum roborant, eum reuera de genere familiaritatum sint, ac suos radios eiaculentur. Quod etiam habet locum, si in tanta distantia luminarium hinc inde constituantur, vnde ex vicinitate possint eorum lumina absorbere, hoc est intra sphæram lueis illorum in Sole ad gr. 17. in Luna verò ad 12. ante, & retrò. Id etiam de fixis proportionaliter est intelligendum, si & ipsa testimoniis tuis accedant, aut in tanta distantia, vt satellitium ad luminaria facere queant, constituantur. Ergò positis luminaribus, præsertim Sole in angulo Medii Cæli, vel Orientis, aut sanè non valdè à linea orientali distantibus; si omnes planetæ ex angulis, aspectu, parallelo, ac tuis fortitudinum caleulis assentiantur, ea felieissima exlorum constitutio censenda est, atque aptissima ad Principatum decernendum. Quò plures planetæ, iique ex genere fortunarum, atque è potioribus locis respiciant, eo felicio, quò pauciores ac debilio- Ec ij

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MATHEMATICVM. 439 it may be in the vernal section, and so the Sun’s ingress into the equinoctial point was reckoned from it: but now, by reason of the motion of the eighth sphere, it has been carried farther off, and has advanced to 28 degrees 47 minutes, still remaining in Aries of the first moving sphere, with northern latitude of about 9 degrees. SARTAN or ELSARTAN, in Arabic; in Latin, the sign of Cancer, the fourth sign of the Zodiac. In Chaldean, however, Sartono. 124 SATELLITIUM Among astronomers it is an attendance, and support, which the planets each render to the luminaries by the loan of their rays, and by their own lights also give assent to their felicity: and this constitution, as Ptolemy says in Quadrip. lib. 4, cap. 1, is most fortunate in a nativity, and such natives, although otherwise sprung from the lowest common people, it raises to the highest seats, and makes them great kings and princes. But in what this kind of satellite attendance consists is not equally taught by the professors. We have said something above on this matter in V. Doriphoria; here we shall briefly conclude the matter. Satellite attendance therefore consists in nothing else than in a concurrence of rays toward the luminaries, by which the planets add numbers of dignities to the luminaries, even to the strongest of them; so that, being in suitable places, as for instance in the Angles, and in their own dignities, other planets are oriental to the Sun, occidental to the Moon, and in some way configured with them, whether in the Mundo or in the Zodiac, not even their parallels being excluded, nor rays otherwise hostile and inauspicious, such as the sesquiquadrate) which adds numbers in this matter) the square, and the opposition: which, although in regard to life they are inauspicious, yet in regard to honors and dignities they always strengthen a fortunate position of the significators, since they truly belong to the class of familiarities, and send forth their rays to it. The same also holds if the luminaries are placed on this side and that at such a distance that from proximity they can absorb their lights, that is, within their sphere of light, in the Sun up to 17 degrees, in the Moon up to 12 degrees before and behind. This must also be understood proportionally of the fixed stars, if they too come in with your testimonies, or are placed at such a distance that they can make satellite attendance to the luminaries. Therefore, with the luminaries placed, especially the Sun in the angle of the Midheaven or of the Orient, or indeed not very far from the eastern line; if all the planets from the angles, by aspect, parallel, and by your calculations of strength agree, that configuration of the stars is to be judged most fortunate, and most suitable for determining a principality. The more planets there are, and those of the class of fortunes and from the better places, looking toward them, the more fortunate; the fewer and the weaker… Ec ij

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LEXICON 440 ribus radiis conueniant, eò minus apta, & infelix dicenda est Id autem semper intelligendum, quatenus ipsa Luminatia, præcipuè autem Sol cæteros vincat in fortitudine, ac dignitate. Nam cum ipsa sinr naturales honorum significa- tores, iuxta alibi dicta, ad hoc vt ritè eos possint decerne- re, debent eisdem ipsa dignitatum numeris cumulari, atque alios vestigales habere. Quod si alius Planeta fortior fuerit supràque ipsa luminaria eleuatus; iam non ipsa principatum tenebunt, sed potius fortiori subseruient, & sua lumina tribuent. Vt proinde eius qui fortior fuerit, manifesta in genitura impressa vestigia conspiciantur. 3. SATELLITIVM etiam dicitur comitatus, quem non ita pri- dem compertum est facere ad Iouem, & Saturnum, minores vt ita dicam planetas, seu erraticas stellulas, quæ circà ip- sos rotantur ac retinent pro centro eorum corpora, non se- cus ac Venus, & Mercurius solem: Qui proinde vel ob id Iouis, aut Saturni stipatores, & Satellites appellantur. Hi primùm detecti sunt in Ioue quatuor à Galileo, quos stel- las Mediceas nuncupauit, provr in loco diximus. Postmo- dum in Saturno alij duo, qui aliquando cum eo figuram elli- pticam, aliquando vnum corpus omnino sphæricum effor- mant. aliquando etiam ab eo sciuncti apparent. Neque vero credendum est reliquos planetas sine comitatu incede- re, præsertim aurem Martem, nam Venus & Mercurius sunt propriissimi Solis satellites, cum ab ipso non multum elon- gentur, neque omnes aspectuum configurationes ad ipsum possint habere vt reliqui planetæ) sed ob stellarum exilita- tem hoc satellitium non posse oculis discerni Vide quæ ad hanc rem diximus in V. Mars. Hoc etiam modo. 14. SATELLITES dici possunt omnes planetæ ad Solem (excep- ta Luna) max mè in sententia Tychonis, qui in Mundi systemate solem ponit erraticarum omnium centrum, has- que perpetuò circa ipsum roari, provt dicemus suo loco. 15. SATVRNVS græcè Phaton dicitur planera omnium tardissi- mus atque à terra remotissimus, cuius, sphæra est immediatè fixarum orbi subiecta, stella proinde inter erraticas aspectu omnium minima colore plumbeo, albicante, & suboscuro, natura rigens, ac frigida, hominibus vniuersoque animan- tium perfectorum generi inimica. Adeò vt si is ab albo pla- netarum eraderetur, vt etiam eius inimicus Mars, calidæ nimis, & exsiccantis naturæ, homines (inquit Hermes apud Argolum de diebus criticis cap 9) æuiterni forent, & immortales. Sed hoc noluit providentissimus rerum om- nium artis ex constituere; quia hominem, ad cælestem glo-

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LEXICON 440 less fitting to the rays with which they agree, it is to be said to be all the more unfit and unlucky. But this must always be understood, insofar as the Luminaries themselves, especially the Sun, surpass the others in strength and dignity. For since they themselves are natural significators of honors, as has been said elsewhere, in order that they may rightly decide these things, they ought to be endowed with the same numbers of dignities, and to have the others as followers. But if another Planet should be stronger and elevated above the luminaries themselves, then they will no longer hold the principality, but rather will serve the stronger, and will yield their own light. So that the manifest footprints impressed in the nativity by the one who is stronger may be seen. 3. SATELLITIUM is also called the retinue, which it has recently been discovered belongs to Jupiter and Saturn, the lesser, so to speak, planets, or wandering little stars, which revolve around them and hold their bodies as their center, no differently from Venus and Mercury around the Sun. For this reason they are called the attendants and satellites of Jupiter or Saturn. These were first discovered in Jupiter, four by Galileo, whom he named the Medicean stars, as we said in the place mentioned. Afterwards, two others in Saturn, which sometimes with it form an elliptical shape, sometimes one wholly spherical body; at times also they appear detached from it. Nor indeed should it be believed that the remaining planets proceed without a retinue, especially Mars, for Venus and Mercury are the Sun’s most proper satellites, since they do not move far from it, nor can they have all the configurations of aspects toward it as the other planets do; but because of the smallness of the stars this satellite-ship cannot be distinguished by the eyes. See what we said about this matter in V. Mars. In this way also. 14. All the planets, except the Moon, can be called SATELLITES of the Sun, especially in the opinion of Tycho, who in the system of the world places the Sun as the center of all the wandering stars, and has these perpetually moving around it, as we shall say in its place. 15. SATURN is called in Greek Phaton, the slowest of all the planets and the most distant from the earth, whose sphere is immediately beneath the sphere of the fixed stars. It is therefore among the wandering stars the smallest in appearance, with a leaden, whitish, and somewhat dark color, of a rigid and cold nature, hostile to men and to the whole race of perfect animals. So much so that if he were erased from the band of planets, as also his enemy Mars, of a nature too hot and drying, men, says Hermes apud Argolum de diebus criticis cap. 9, would be everlasting and immortal. But the most provident artificer of all things did not wish to establish this; because man, for the celestial glo-

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MATHEMATICVM. 441 iam destinauit, atque adeo hîc in Mundo mortalem voluit, vt suæ desitionis memor in hoc mortali corpore peregrinum agat, atque ad æternam gloriam gressus suos dirigeret, suum vltimum finem. Idecicò inquam voluit Summus Deus inter cælestia corpora, quæ vitam nobis spiritumque suppeditant & Saturnum ponere, qui sua malignitate abseinderet: benè verò quo minus noceret eum longè à nobis dissitum voluit, Iouemque contrariæ prorsus naturæ, hoc est caloris, humidique naturalis fotorem fecit conterminum, qui eius malignitatem contemperaret. Est planetarum omnium maximus excepto lente, & Sole, quippe eius diameter continet tertæ diametrum semel, & nonagies, seu, vt alij volunt nonagies septies. Conficit revolutionem suam in Zodiaco in annis 19. dieb. 157. hor. 22. in Epicyclo verò anno vno & diebus 13. Habet & duas stellas comites, quæ irregulariter circà ipsum rotantur, itaut aliquando sciunctæ, aliquando intrà ipsum, aliquando propè & contiguæ in figuram abcuntes oualem conspiciantur. Habet sub se lapicidas, fossores, senes, auaros Iudæos, inuidos, & huius generis homines. 16. Cædanus contendit naturam eius esse calidam, & humidam, (quoniam omnia Astra his qualitatibus pollent) verum calorem eius non esse tanti vt possit diù hominem conseruare: benè verò conveniens est naturæ plantarum: & ideo cum fuerit benè dispositus iuuat ad sationem, abiaqueationem, insitionemque arborum, &c. quod præstare non posset, si foret natura frigidus, & siccus: ideo, subdit, sub se habet & vitam quâ largitur serpentibus omnibus, exceptis iis qui calidissimi sunt, & quia præest omnibus plantis, eas pro qualitate, & societate aliotum planetarum producit, vt venenosas calidas quales sunt Napellus, & Euphorbium cum Marte: cum Mercurio male disposto intemperate frigidas, vt Cicutam, Aconita, &c. Si Lunæ cominisceatur parit herbas quæ oriuntur in aquis, & graueolentes, parumque salubres: Cum Venere producit Nimpheam, cuius flos maximè lucus benè olet, aduetsatur tamen Veneti. Tandem permixtus Soli, Ioui, aut Mercurio benè disposito, & ipse sit boni status, producit rosas, lilia, spicum, &c. In Genethliacis dominationem genesis nactus facit hominem pallidum, taciturnum, ingenio pollentem, ac tenaci memoria præditum, colore fusco, corpore gracili, ac melancholicum. Dominatur auditui dextro, Vesicæ, spleni, Melancholiiæ, dentibus. Ex morbis causat omnes qui ex frigidis humoribus ortum habent, quales sunt Quartanæ febres, hy- E e iij

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MATHEMATICVM. 441 he has already appointed, and indeed here in the world he wished man to be mortal, so that, mindful of his own ending, he might live as a stranger in this mortal body, and direct his steps toward eternal glory, his ultimate end. Therefore, I say, the Supreme God wished to place among the heavenly bodies, which supply us with life and spirit, Saturn, who by his malignity might cut it off; but in truth, lest he harm us, he wished him to be situated far from us, and made Jupiter, of a wholly contrary nature, that is, of heat, the fosterer of natural moisture, a neighbor, who might temper his malignity. He is the largest of all the planets, except for a little, and the Sun, since his diameter contains the diameter of the third once, and ninety times, or, as others hold, ninety-seven times. He completes his revolution in the Zodiac in 19 years, 157 days, 22 hours; in the epicycle, however, in one year and 13 days. He also has two companion stars, which irregularly revolve around him, so that sometimes separated, sometimes within him, sometimes near and touching, they are seen passing into an oval figure. Under him are masons, diggers, old men, avaricious Jews, envious men, and men of this kind. 16. Caedanus contends that his nature is hot and moist, (for all the stars are endowed with these qualities), but that his heat is not so great that it can preserve a man for long: yet it is well suited to the nature of plants; and therefore, when he is well disposed, he helps with sowing, watering, and grafting of trees, etc., which he could not do if he were by nature cold and dry: therefore, he adds, under him he also has the life which he grants to all serpents, except those which are very hot; and because he presides over all plants, he produces them according to the quality and association of other planets, as poisonous hot ones such as Napellus and Euphorbium with Mars; with Mercury badly disposed, intemperately cold ones, such as Cicuta, Aconita, etc. If he is mixed with the Moon, he produces herbs that grow in waters, foul-smelling ones, and somewhat unhealthy ones. With Venus he produces Nimphea, whose flower is especially luscious and smells well, yet it is opposed to Venus. Finally, mixed with the Sun, Jupiter, or Mercury when well disposed, and when he himself is in a good state, he produces roses, lilies, spica, etc. In genethliac matters, when he has obtained domination of the nativity, he makes a man pale, silent, endowed with a sharp mind, and gifted with a tenacious memory, of swarthy color, slender body, and melancholic. He rules the right ear, the bladder, the spleen, melancholy, and the teeth. Among diseases he causes all those which arise from cold humors, such as quartan fevers, hy- E e iij

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LEXICON 442 dropisis, podagra, obstructiones partium naturalium, hæmorrhoides, herniæ, calculus, leterus niger & similia. Habet duo domicilia opposita domibus Luminarium, Capricornum videlicet, & Aquarium, & exaltatur in Libra. 17. SCALENVM species est trianguli, habentis omnes angulos, & omnia latera inæqualia, per quod opponitur triangulo æquilatero, quos inter mediat triangulum Iosceles, quod duo tantum latera habet æqualia, vt dictum est suo loco. 18. SCHEAT arab. dicitur stella fixa tertiæ magnitudinis de natura Saturni, & Mercurij, in dextrâ tibia Aquarij, apud Astronomos maximè obseruata; quæ tunc temporis est in gr. 4. Piscium cum gr. 8. latitudinis meridianę. Oritur Romæ cum gr. 22 eorumdem Piscium. 19. SCHEDER iuem stella fixa benignissima de natura Louis & Veneris tertij honoris in scapulis Andromedæ constituta, quæ est in longitudine in gr. 17. Arietis cum latitud. ferè 14. boreali. Oritur Romæ cum gr. 20 Aquarij, & occidit cum 27 Arietis. 10. SCHEDIR. Latinè pectus Cassiopeæ stella fixa itidem tertiæ magnitudinis, de natura Veneris, & Saturni, existens nunc temporis in gr. 3. Tauri, cum latitudine boreali ferè gr. 47. proindeque Romæ semper conspicua, nunquam occumbens. Ea in horoscopo, inquit Firmicus, facit aurifices, bracteatores, plasticatores, margaritarios, aut qui gemmis, muroque summoperè delectentur, è quibus etiam maxima vitæ subsidia consequantur. In occasu verò iniquam mortem portendit, aut ex ruina, aut ex dira occisione. 21. SCIOPHIA ex Vitruvio lib. 1. cap. 2. est descriptio frontis, laterumque abscedentium adumbratio, quæ ædificium construendum habiturum est, ex geometrię præceptis exhibita per correspondentiam omnium linearum ad circini centrum: ad cuius ideam postea Architectura opus suum molitur. Differt ab Ichnographia, quæ est eiusdem molitionis descriptio in plano facta, quam nos vulgò plantam vocamus. 22. SCIOTHER, SCIOTHERON, & SCIOTHERIVM latinè horologium vmbratile sonat, quod artificiosè per Gnomonicæ pariter, atque Astronomicę præcepta delineatum per Solis vmbram & radios eius altitudine, declinatione, atque horarum segmenta demonstrat. De eorum constructione multi scripsere: Sed omnibus (pace eorum dixerim) palmam proripuit Marinus Mersennius Religiosus gallus è Minimorum familia, qui etiam noui horologij author fuit, quo per So-

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dropisis, podagra, obstructiones partium naturalium, hæmorrhoids, hernias, calculus, black leterus, and the like. It has two domiciles opposite the houses of the Luminaries, namely Capricorn and Aquarius, and it is exalted in Libra. 17. SCALENUM is a species of triangle, having all its angles and all its sides unequal, by which it is opposed to the equilateral triangle, between which stands the isosceles triangle, which has only two equal sides, as was said in its place. 18. SCHEAT, in Arabic, is said to be a fixed star of the third magnitude, of the nature of Saturn and Mercury, in the right leg of Aquarius, most observed by astronomers; which at this time is at 4 degrees of Pisces with 8 degrees of southern latitude. It rises at Rome with 22 degrees of the same Pisces. 19. SCHEDER, by Jupiter, a very benign fixed star of the nature of Luna and Venus, of the third honor, situated on the shoulders of Andromeda, which is in longitude at 17 degrees of Aries with almost 14 degrees of northern latitude. It rises at Rome with 20 degrees of Aquarius, and sets with 27 degrees of Aries. 20. SCHEDIR. In Latin, the breast of Cassiopeia, likewise a fixed star of the third magnitude, of the nature of Venus and Saturn, now existing at 3 degrees of Taurus, with northern latitude of almost 47 degrees; and therefore always visible at Rome, never setting. In the horoscope, says Firmicus, it makes goldsmiths, leaf-workers, modelers, pearl-dealers, or those who take great delight in gems and in masonry, from whom also they obtain very great means of life. In the setting, however, it portends an unhappy death, either from a fall or from a cruel killing. 21. SCIOPHIA, from Vitruvius, book 1, chapter 2, is the description of the front, and the shading of the receding sides, which the building to be constructed will have, exhibited according to the precepts of geometry through the correspondence of all the lines to the center of the compass: according to which idea Architecture afterward shapes its work. It differs from Ichnographia, which is the description of the same project made on a plane, which we commonly call the plan. 22. SCIOTHER, SCIOTHERON, and SCIOTHERIVM in Latin signify a shadow clock, which, artfully drawn according to the precepts both of Gnomonics and Astronomy, indicates by the shadow of the Sun and its rays the altitude, declination, and the segments of the hours. Many have written on their construction: but from all of them (with their pardon be it said) the palm was seized by Marin Mersennius, a French religious of the Minims, who was also the author of a new clock, by which the So-

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MATHEMATICVM. 443 His radium reflexum intrà cubiculum per foramem traiectum, designantur quotæ horę diei, absque vllô prorsus Gnomone, vt ego vidi Romę in ædibus Eminentissimi Cardinalis Bernardini Spadę ab ipso Auctore delineatum. Sed neque tua laude fraudandum est quod in ædibus Sanctorum Apostolorum Neapoli sua manu descripsit Erudirissimus arque ingeniosissimus Parer D. Ioseph Caracciolus clericus regularis, vir cum in omni literaturâ tum præsertim in mathematicis disciplinis proprio matte comparatis nulli fortè secundus. Hic enim in amplissimo fornice aulæ commodioris diui Cænotij ad meridiem simile Sciorherium delineauit, additis non modò horarum ad singularum nationum morem interstitiis, verum etiam vniuersa penè Geographia ad locorum longitudines, ac latitudines vnico ictu oculi eruandas. SCINTILLATIO est fulgor quidem, ac reuibratio lucis 23. astrorum, qua dum conspiciunrur, veluti subsilire, & scintillas quasdam fundere videntur, quo sic, vt oculorum intuentium acies & præstringarur simul, & oblectetur. Ea propria est fixorum siderum passio; nam planetæ, vt aduertit etiam Philosophus, non scinrillant: & licet cum sunt pro pè horizontem, & ipsi scinuillare videantur id tamen ab intrinseco non prouenit, sed accidit ex refractione visus, siquidem ob terræ vapores species à planeta immissæ per atmosphætam illam transeuntes pertingunt refractæ ad oculos intuentium; quod vel eo pater, quia in medio cæli iam constituti omni lucis mobilitate destituuntur. Causam huius scinrillationis variam afferunt tum Philosophi, tum Astronomi; nec tamen adhuc quisquam eorum, vt reor ad verum collineauit. Aristoteles in fixarum maximam à terra elongarionem refudit: quod assumens Pontanus in Vrania asserit id non ab ipsis sideribus sed à visus debilitate prouenire, sic enim habet lib. 2. Pratereà cur sola acies immota Deorum Cernitur, obtutuque lucet defixa sub ipso Cum tot, illa quidem sidentia signa, micanti scintillent radio, tremulusque internatet ardor. Scilicet alta illis regio, sedesque reposta: Quo postquam aduenit defesso lumine visus Defessus tremit ipse, tamen tremere ipsa videntur. Astra micant radiis, sed lumina nostra tremiscunt. At contrà vicina Deum statio ardua quamquam Prospectu facilis tamen, atque immota tuenti Quò penetrant stant certa loco, insistitque vidende E e iiiij

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MATHEMATICVM. 443 By this reflected ray, passed through a hole into the chamber, the hours of the day are indicated, without any Gnomon at all, as I saw in Rome in the house of the Most Eminent Cardinal Bernardino Spada, drawn by the author himself. But neither should your praise be withheld, since in the house of the Holy Apostles at Naples the most learned and most ingenious Father D. Giuseppe Caracciolo, a regular cleric, a man second to none, perhaps, both in all literature and especially in mathematical disciplines acquired by his own efforts, described it with his own hand. For in the very spacious arch of the more convenient hall of the divine Cenotium, he drew a similar Sciorherium, adding not only the intervals of the hours according to the custom of each nation, but also almost the whole geography for discovering the longitudes and latitudes of places at a single glance of the eye. SCINTILLATION is indeed the brightness and flickering of the light of the stars, 23. by which, while they are seen, they seem as though they leap up and emit certain sparks, so that the sharpness of the eyes of those looking upon them is at once both dazzled and delighted. This is proper to the fixed stars; for the planets, as the Philosopher also notes, do not scintillate: and although when they are near the horizon they themselves seem to scintillate, that nevertheless does not arise from anything intrinsic, but happens from refraction of sight, since because of earthly vapors, the appearances sent from the planet, passing through that atmosphere, reach the eyes of those looking on, refracted; which is evident even from the fact that, when they are now situated in the middle of the sky, they are devoid of all mobility of light. Philosophers and Astronomers alike give various causes of this scintillation; yet, as I believe, none of them has as yet struck the truth. Aristotle attributes it to the great distance of the fixed stars from the earth: adopting this, Pontanus in the Urania asserts that it arises not from the stars themselves but from weakness of sight, for thus he has it in book 2. Moreover, why is only the unmoving aspect of the gods seen, and why does it shine, fixed beneath the gaze itself, when so many, indeed, are the starry signs, that glitter with shining ray and a trembling fire runs through them? Surely the region is lofty for them, and their dwelling set far back: when the wearied sight comes there the wearied eye itself trembles, yet they seem to tremble too. The stars flash with rays, but our eyes tremble. But on the other hand, the neighboring station of the gods, though lofty, is easy to behold, and still to the beholder; to which they penetrate, they stand fixed in place, and the act of seeing continues E e iiiij

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444 LEXICON Nostra acies, fixisque oculis immobilis haret. Hucusque Pontanus: cuius tamen ratio non conuincit; na[ti]o[n]e Mercurius, & Venus nobis viciniores quam Saturnus, & Iupiter scintillant, & Venus quidem in maxima altitudine, vt benè adnotauit Simplicius; cum tamen illi longè remotiores etiam propè horizontem haud scintillent. 14. Deinde alia est scintillatio planetarum circa horizontem, alia fixorum siderum: illa mollis quidem ac tremula, quæ potius visum oblectat, & successiue semper mutatur, ac deperditur, quò magis planetæ ab horizonte elongantur. Hæc semper constans, eiusdem rationis in omnibus, fortis, & aciei oculi præstrictiua. Blancanus in sphæra mundi causam scintillationis siderum attribuit solæ refractioni: ideoque ait plus aliis Sirius, & Proyon scintillant, quia non plusquam gr. 45. supra terram ascendunt: At quonam pacto Iupiter, corpore magnus, lumine clarior, situ etiam humilior non scintillat? quare Arcturus etiam in maxima altitudine non minus quam Syrius rutilat, cum tamen Dexter humerus Orionis, & Regulus, neque propè orientem scintillent? Vt proinde neque consistere possit ratio scintillationis in sideribus fixis, quam affet Cardanus de subtilitate, celeritatem videlicet motus diurni quam præsideribus errantibus habent: nam præterquam differentia ista motus modica est, & planè insensibilis, si id verum esset, dum planetæ retrogradi fiunt, aut stationarij, deberent æquè ac fixæ scintillare, quia æquè imò & reipsa velociore cutu perficiunt iter suum diurnum. Accedit, quod, cum fixæ eodem motu omnes firmamenti concitatissimo moueantut deberent ortnes eodem modo scintillare, & in æquali à terra distantia, cum tamen aliquæ vt Syrius, Proyon, & Arcturus insigniter, & in quacunque cæli parte scintillant, aliquæ mediocriter, vt Rigel, & Spica Virginis, aliquæ nullo modo vt pectus Cassiopeæ, dexter humerus Orionis, & Regulus. <23.> Restat igitur vt scintillationis istius causa in sideribus fixis sit intrinseca, vera & realis proueniens à luce quadam primigenia, & insira haud à Sole mutuata, vt Sol ipse omnis lucis fons & origo, ita rutilat, ac non quidem scintillas, sed validissima lucis spicula mobili quodam semper ardore ciculatur, vt nemo in eum intendere possit aciem. Sic igitur ex fixis, quæ maiore insita luce sunt præditæ, maiorem habent scintillandi materiam, vt fortasse etiam ex planetis Mercurius, & Venus: quæ mediocrem habent, mediocriter etiam scintillant, quæ nullam nullo modo, sed Solis tantum-

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444 LEXICON Our battle line, with eyes fixed, stands motionless. So far Pontanus: whose reasoning, however, does not convince; for by nature Mercury and Venus are closer to us than Saturn and Jupiter, yet they scintillate, and Venus indeed in the greatest altitude, as Simplicius has well noted; whereas the latter, though far more remote, do not scintillate even near the horizon. 14. Next, the scintillation of the planets near the horizon is one thing, the scintillation of the fixed stars another: that of the planets is gentle and trembling, which rather delights the sight, and is always successively changed, and lost, the more the planets are removed from the horizon. This is always constant, of the same kind in all, strong, and striking to the eye. Blancanus, in the sphere of the world, attributes the cause of the scintillation of the stars to refraction alone: and therefore says that Sirius and Procyon scintillate more than the others, because they rise no more than 45 degrees above the earth. But by what means does Jupiter, large in body, brighter in light, and even lower in position, not scintillate? Why does Arcturus also, at the greatest altitude, glow no less than Sirius, while the right shoulder of Orion and Regulus do not scintillate even near the east? Thus neither can the reason for scintillation in the fixed stars stand, which Cardanus derives from subtlety, namely the speed of the daily motion which they have over the wandering stars: for apart from the fact that this difference of motion is slight and quite imperceptible, if that were true, then when the planets become retrograde, or stationary, they ought to scintillate just as much as the fixed stars, because they accomplish their daily journey just as fast, indeed in fact even more swiftly. Moreover, since the fixed stars, all moved by the same swift motion of the firmament, ought all to scintillate in the same way, and at an equal distance from the earth, whereas some, like Sirius, Procyon, and Arcturus, scintillate notably and in whatever part of the sky, some moderately, like Rigel and the Virgin’s Spica, some not at all, like the breast of Cassiopeia, the right shoulder of Orion, and Regulus. <23.> It remains therefore that the cause of this scintillation in the fixed stars be intrinsic, true, and real, arising from a certain primordial and inborn light, not borrowed from the Sun, just as the Sun itself, being the source and origin of all light, shines so that it does not send out scintillas, but very strong darts of light, hurled by a certain ever-moving ardor, so that no one can direct his gaze upon him. Thus then among the fixed stars, which are endowed with a greater inborn light, there is greater material for scintillating; perhaps also among the planets Mercury and Venus: those which have a moderate amount also scintillate moderately; those which have none do not scintillate at all, but only the Sun’s-

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MATHEMATICVM. 44f modò radiis illustratæ mortuo, vt ita dicam modo resplendent. Quæ mihi ratio præ cæteris arridet, ac diu hærenti probabilior tandem, ac verior visa est, quoad vsque alij me- liorem proferant. SCIRON sic dictus est à stupè quadam vnde exsulare potissimum solebat, atque Athenas plurimum infestare Corus ventus occidentalis, lateralis Fauonio, spirans ab occasu æstivali. de quo plura diximus in verbo Caurus. Eo nunc maximè infestatur Iapygia regio in Italiæ vlt. mis finibus constituta, vnde & Iapygis illi nomen adhasit. SCORPI octauum ab Ariete signum aqveum fixum, do- < 26c> micilium Marris & eiusdem Trigonum, vnaque Veneris & Lunæ; sic dictum à mira quam habet cum Scorpionem terre- stri sympathia. Siquidem Luna hoc signum inq[ue] essa scor- piones maximè feri tunc, & infensi; Domusque (quod val- dè mirum est) ædificari ecepta scorpionem in horoscopo ex- sistence, experientia teste scorpionum nidus euadet Est item signum venenosum, turpe, prolificum, mendax: vnde Al- < 27c> mansor in Aphorismis ad regem Saracenorum propos. 106. Auerte, inquit, oculos tuos à figura, in qua fuerit ascen- dens Scorpio. Habet ex membris humanis regere pudenda. Scorpij fidus in octaua sphæra, amplitudine sua duo signa complectitur; Libram videlicet, & scorpium, vnde olim vndecim signa Zodiaci enumerabantur, & stellæ in Libra existentes, etiamnum chelæ seu branchia scorpij ab aliqui- bus appellantur: Sic enim Iudit nobiscum Natura, vt quæ stellæ ob aliquam connexionem occultam ab Scorpionem ter- restri nomen hauserunt, in vnum conglomeratæ efforment fidus omnium maximum, quando is qui nomen indidit, in- ter huius generis animantes inuenitur omnium minimus. Continet sub se stellas Ægino vndeuiiginti. Prolemæo 21. & adhuc tres sporades, Keplero 28. Baiero autem 29. mixtæ naturæ: Nam chelæ sunt de natura Iouis, & Mercurij, & vna potissimum Martis. Similiter tres in fronte sunt Martiæ, & Saturninæ: Antares, seù cot scorpij potissimâ in hoc side- re cum aliis duabus in corpore Martem, & Iouem referunt; Nebulosa est Martia, & Lunaris: reliquæ in flexu caudæ Sa- turninæ sunt, & Venereæ, præter aculeum, qui est de natu- ra Martis, & Mercurij. Vnde nil mirum si ob tantam varie- tatem, & qualitatum mixtionem dicatur signum fallax, ac venenosum mixtio enim qualitatum præsertim contrariarum in cælis corruptionem humorum insert. Primæ eius partes frigidæ sunt, & nives generant; Mediæ temperatæ, vltimæ turbulentæ: Pars borealis calida est; Australis humida. Inci-

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MATHEMATICVM. 44f when illuminated by rays, or rather when dead, so to speak, they now shine back. This seems to me the explanation that pleases me above the rest, and, after long hesitation, has seemed at last the more probable and the truer, until others put forward a better one. SCIRON is so called from a certain stupor from which he was chiefly accustomed to be banished, and to infest Athens greatly: Corus, a western wind, lateral to Favonius, blowing from the summer sunset. We have spoken more at length about this in the word Caurus. The region of Iapygia, situated in the furthest bounds of Italy, is now especially afflicted by it, and hence the name Iapygis has attached itself to it. SCORPIUS, the eighth sign from Aries, a watery fixed sign, the domicile of Mars and his trigon, and also of Venus and the Moon; so called from the marvellous sympathy it has with the earthly scorpion. For the Moon, when in this sign, bites scorpions most sharply and bitterly. And a house, which is very remarkable, if begun to be built with Scorpio in the horoscope, by experience proves to become a nest of scorpions. It is also a poisonous, ugly, prolific, deceitful sign; whence Albumasar in the Aphorisms to the Saracen king, proposition 106, says: “Turn your eyes away from the figure in which Scorpio is ascending.” It has among the parts of the human body rule over the genitals. The fixed Scorpius in the eighth sphere, by its breadth includes two signs, namely Libra and Scorpius; whence in former times the signs of the Zodiac were reckoned as eleven, and the stars existing in Libra are still by some called the claws, or branches, of Scorpius. For thus does Nature deal with us, that the stars which, by some hidden connection, have drawn their name from the earthly scorpion, being gathered together into one, form the largest of all the constellations, when he who gave it the name is found among these creatures of his to be the smallest of all. It contains beneath it twenty-nine stars according to Almagest; according to Ptolemy twenty-one, and still three sporades; according to Kepler twenty-eight; according to Bayer twenty-nine. They are of mixed nature: for the claws are of the nature of Jupiter and Mercury, and one especially of Mars. Likewise the three in the forehead are Martial and Saturnine. Antares, or the heart of Scorpius, together with the two others in the body, chiefly refer to Mars and Jupiter; the nebulous one is Martial and Lunar; the remaining ones in the bend of the tail are Saturnine and Venusian, except the sting, which is of the nature of Mars and Mercury. Hence it is no wonder that, because of so great a variety and mixture of qualities, especially contrary ones, it is called a deceitful and poisonous sign; for the mixture of qualities inserts corruption into the humors, especially when they are contrary. Its first parts are cold and generate snow; the middle are temperate; the last turbulent. The northern part is hot; the southern humid. Inci-

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LEXICON 446 pit à gr. 17. Scorpij primi mobilis, & extenditur vsque ad gr. 26. Sagittarij, non computatis in eo chelis, quæ ita ab æquatore premuntur, vt eum sustinere videantur, ipse autem Scorpio pedibus Ophiuci subditus, extrema cauda circulum Hyemalem contingit. 28. SCOTOMENIA, teste Valla, idem sonat apud Hebræos, ac Lunæ obtenebratio, quando videlicet incidit in radios Solis, vel in penumbram terræ, quò fit vt vel tenebrosa, fusca & sanguinea appareat, aut sanè omninò inuisibilis. 29. SCYPHONES Venti sunt procellosi de Typhonum genere, qui nubibus inclusi procellas generant, & aquas suisum eleuant, & absorbent. 30. SECANS apud Geometras dicitur linea recta ducta à centro circuli ad lineam aliam extra circulum, quæ sit perpendicularis extremo diametri ipsius circuli extra illius ambitum, quæ ideircò dicitur tangens: quia vbi illam tangit facit angulum acutum: ipsa verò è contrà dicitur secans, quia secat arcum circuli, vbi mutuò se sinus tam rectus, quam versus se tangunt. 31. SECTIO EQVI dicitur sidus in cælo mutilatum representas, caput equi truncum propè Pegasus, & æquatorem in parte tamen boreali, quod efformatur à quatuor stellis obscuris, in longitudine circa gr. 18. & 20. Aquarij. Appellatur etiam Equiculus. 32. SECTOR CIRCUL ex Euclide lib. 3. defin. 9 dicitur angulus, qui ad ipsius circuli centrum constituitur, comprehensa nimirum figura, & à rectis lineis angulum continentibus & à peripheria ab illis assumpta. Sicut etiam. 33. SEGMENTVM CIRCUL dicitur figura, quæ sub recta linea, & circuli peripheria comprehenditur: sicuti necessariò segmenti angulus debet esse qui sub recta linea, & circuli peripheria comprehenditur. 34. SECUNDI MOBILES denominantur planetæ, & Orbis fixarum, qui præter primum motum vniuersalem raptus ipsis à primo mobili impressum, habent peculiarem motum cuilibet proprium, ab Occidente in Orientem. Licet reuera non detur iste secundus motus; qua de re vide quæ diximus in V. MOTUS. 35. SEDEVLII, apud Hermetem audit cauda Cygni, stella fixa secundæ magnitudinis de natura Veneris & Mercurij. arab. Deneb. Adigege. Vide ibi. 36. SELAS, teste Apuleio in lib. de Mundo, vocant Græci incensi aëris lucem; Horum, inquit, pleraque iaculari credas

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LEXICON 446 pit at 17 degrees. Scorpio, as the first movable sign, and extends as far as 26 degrees of Sagittarius, not counting in it the claws, which are so pressed by the equator that they seem to support it; but Scorpio itself, subject to the feet of Ophiuchus, with its extreme tail touches the winter circle. 28. SCOTOMENIA, according to Valla, means the same among the Hebrews as an obscuration of the Moon, namely when it falls into the rays of the Sun, or into the penumbra of the earth, so that it appears either dark, dusky, and blood-red, or else altogether invisible. 29. SCYPHONES are stormy winds of the Typhonian kind, which, enclosed in clouds, generate tempests, and lift up and absorb the waters. 30. SECANS, among geometers, is called a straight line drawn from the center of a circle to another line outside the circle, which is perpendicular to the end of the diameter of that circle outside its circumference, and therefore is called a tangent: because where it touches it, it makes an acute angle; but it is called a secant, because it cuts the arc of the circle, where the lines touch one another mutually, both in a straight direction and toward themselves. 31. SECTIO EQVI is said of a constellation in the heavens representing a mutilated figure, the truncated head of a horse, near Pegasus, and the equator in the northern part, however, formed by four faint stars, in longitude around 18 and 20 degrees of Aquarius. It is also called Equiculus. 32. SECTOR CIRCULI, from Euclid, Book 3, definition 9, is said to be the angle formed at the center of the circle itself, namely with the figure enclosed, and by the straight lines containing the angle and by the periphery taken by them. Likewise also. 33. SEGMENTVM CIRCULI is said to be the figure contained beneath a straight line and the circumference of a circle: just as necessarily the angle of a segment must be that which is contained beneath a straight line and the circumference of a circle. 34. SECOND MOVABLES are the planets, and the sphere of the fixed stars, which besides the first universal movement, the motion impressed on them by the prime mover, have a particular movement proper to each, from West to East. Although in truth this second motion does not exist; on this matter see what we said in V. MOTUS. 35. SEDEVLII, among Hermes, means the tail of the Swan, a fixed star of the second magnitude, of the nature of Venus and Mercury. Arabic Deneb Adigege. See there. 36. SELAS, according to Apuleius in his book On the World, the Greeks call the light of incense in the air; The greater part of these, he says, you would believe to be hurled forth

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MATHEMATICVM. 44Z alia labi, stare alia: iaculatio igitur tunc fieri putatur cum meatu aëris, atque impulsu generatus ignis celeritatem sui cursus rapidaque festinationis ostendit Sunt igitur hæc me- dium quid inter cometas & ea ostentorum genera, quæ nul- lam substantiam habent, sed ex collisione visus apparent: quales sunt Virgæ, Iris, & Arcæ, qua de re vide quæ dixi- mus in V. Cometa. SEMICIRCULVS quid sua notione inferat, patet: Dimi- <37.> dium nempe circuli. Vnde in sphæra & in circulis maximis importat congeriem grad. 180. & in Zodiaco sex signa. Qua- re sæpissimè apud scriptores inuenitur semicirculus australis & borealis, Orientalis, & Occidentalis, ascendens & des- cendens, &c. SEMIVLNIVM appellatur tempus illud, in quo Luna est in <38.> quadiato Solis, & apparet dimidiata: quemadmodum No- uilunium, quando est in coniunctione; & Plenilunium, cum est in oppositione luminibus plena. SEMIQUADRATVS est aspectus duorum siderum in distan- <39.> tia grad. 45. vel sane quartæ partis semicirculi in Mundo con- siderati, quem etsi aliqui etiam ex antiquioribus agnoue- rint, tamen nuper ab nouis Astronomis detectum est esse efficaciæ non spernendæ, præsertim in morbis, atque in Aphæiæ consideratione, & motu directionis. Hali Rodoan in Comment. ad Ptolomaum ipsum considerat tantum in <40.> medicinalibus, & in circulo positionis cometarum, & in aliis rebus non item. Titus se tantum obseruasse ait Aphetam in secunda medierate vndecimæ domus constitutum non ita benè aptum euadere ad prorogandæ vitæ rationem incun- dam, quia profectò incidit in semiquadratum ad horoscopum. Alij in omnibus illum aliqua vi præditum de natura ipsius quadrati, se expertos esse testantur. Et sanè in Moisbis nemo ibit inficias, primæ crisis indicationem ab hoc aspe- ctu formari, quod & obseruauit Argolus de diebus critieis, & nos in loco vbi de iisdem sermo incidit, admonuimus. In figura etiam sexdecim laterum, cuius meminit Ptolemaus in centiloquio, ipse etiam suas partes habet. Præterea in lunationibus hie aspectus magnam vim obti- <40> net ad significandas aëris mutationes a tota lunatione ema- naturas, nec quidem absque solido fundamento, quando- quidem Luna in ea distantia à Sole incipit primò se visibi- lem reddere, ac manifestos effectus suæ lucis extensione in sublunaria ista exserere. Vnde Axioma illud rusticum. Qua- <41.> ria, quinta qualis, tota Luna talis. Idipsum Ptolemaus, Plinius, Aratus, aliique experimento probatunt.

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MATHEMATICVM. 44Z one body slipping, another standing still: therefore an ejection is thought to occur when fire, generated by the motion of the air and by impulse, shows the speed of its course and rapid haste. These things are thus something intermediate between comets and those kinds of portents which have no substance at all, but appear from a collision of sight: such are Virgæ, Iris, and Arcæ; on this matter see what we said in V. Cometa. SEMICIRCULUS, what it means by its very notion, is clear: namely, half of a circle. Hence in the sphere and in great circles it denotes a sum of 180 degrees, and in the Zodiac six signs. Therefore one often finds in writers semicirculus australis and borealis, Oriental and Occidental, ascending and descending, etc. SEMIVLNIUM is the time in which the Moon is in the square of the Sun and appears half-illuminated; just as Novilunium is when it is in conjunction; and Plenilunium, when it is in opposition and full of light. SEMIQUADRATVS is the aspect of two stars at a distance of 45 degrees, or indeed the fourth part of a semicircle considered in the world; although some even of the older authors recognized it, nevertheless it has recently been discovered by the new astronomers to be of no slight efficacy, especially in diseases, and in the consideration of the Aphæia, and in the motion of direction. Hali Rodoan, in his Commentary on Ptolemy, considers it only in medical matters, and in the circle of the position of comets, and not in other things. Titus says that he observed only that the Apheta placed in the second half of the eleventh house does not turn out very well for the purpose of prolonging life, because indeed it falls into a semiquadratum with the horoscope. Others testify that in all cases it has been found to possess some force from the nature of the square itself. And certainly in diseases no one will deny that the indication of the first crisis is formed from this aspect, as Argolus observed regarding critical days, and as we also noted in the place where mention of them occurred. In the figure of sixteen sides, which Ptolemy mentions in the Centiloquium, it too has its own parts. Moreover, in lunations this aspect has great force for signifying changes in the air that are to arise from the whole lunation, and not without solid foundation, since at that distance from the Sun the Moon first begins to make itself visible and to produce manifest effects in these sublunary things by the extension of its light. Hence that rustic axiom: Quaria, quinta qualis, tota Luna talis. Ptolemy, Pliny, Aratus, and others have proved the same by experience.

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LEXICON 41. SENACHER SOLI in sphæra barbarica dicitur secundus decanus Arietis, cuius dominum, ac dispositio spectat ad Solem: proindeque est significator nobilitatis, magnanimitatis, altique dominij. Item. 42. SENCINER ibidem audit tertius decanus Scorpij, manens sub dominatu Veneris, habensque significare ebrietates, violentias, scortationes, cum ira, & præualentia. Similiter SECTACER ibidem d eitur primus decanus eiusdem Scorpij, cuius dispositio spectat ad Martem dominum eius signi, 43. qui proinde habet significare rixas, tristitiam, deceptionem, detrectationem, proditionem, insidias. SEPARATIO apud Astronomos est species quædam defluxus planetæ ab alterius coniunctione, quando videlicet planeta leuior post coniunctionem partitem cum ponderoso discedit ab eo, & tantum elongatur, quantum importat agregatum semidiametrorum vtriusque, & ea quidem duplex, simplex vna, quando vterque est directus, sed leuior in pluribus partibus: Altera quæ dicitur mutua, quando nimirum planeta, qui in pluribus partibus est directè graditur; 44. quicque est in paucioribus sit retrogradus. 45. SEPHINA Hebræo nomine dicitur nauis fidus in cælo ad Australem plagam, de qua plura diximus in V. Argonauis, testis est Kircherus in Oedipo Ægyptiaco. 46. SEPTANGVLVS, & Hiperangulus, apud Geometras audit figura septem angulis constans, siue ea plana sit, siue solida: siue regularis, siue irregularis. 47. S PTENTRIONE dicuntur communiter septem stellæ propè polum Arcticum efformantes constellationem, & imaginem Vrslæ minoris: quanquam etiam eo nomine veniunt aliquando, quæ in eadem positione sunt in Vrsla maiore, & constituunt Plaustrum eoquia sunt illis spectabiliores, & quia vtraque figura ad polum Arcticum magis accedit, hinc est, vt polus ipse ab iis denominationem sumperit. Vnde etiam. 48. SEPTENTRIONALE appellari solet omne id quod quodammodò ad dictum polum pertinet, atque ad ipsum refertur. Sic Septentrionalis plaga Mundi dicitur quam nos Europæi citra Æquatorem inhabitamus, Septentrionalis declinatio, latitudo, semicirculus, &c. Similiter. 49. SEPTENTRIO absolutè audit Ventus directè ab ea mundi parte exsufflans, quæ polo Septentrionali substernitur; estque vnus ex quatuor cardinalibus, imo & cardo omnium ventotum, quandoquidem ipse, sicut & eius aduersarius Notus sunt omnium ventorum semina, & radices; capro-

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LEXICON 41. SENACHER SOLI in the barbaric sphere is said to be the second decan of Aries, whose lordship and disposition belong to the Sun; and therefore it is a significator of nobility, magnanimity, and high dominion. Likewise. 42. SENCINER there is called the third decan of Scorpio, remaining under the dominion of Venus, and having to signify drunkenness, violence, fornication, together with anger and predominance. Likewise SECTACER there is called the first decan of the same Scorpio, whose disposition belongs to Mars, the lord of that sign, 43. and which therefore has to signify quarrels, sadness, deception, detraction, betrayal, and ambushes. SEPARATION among astronomers is a certain kind of recession of a planet from the conjunction of another, namely when a lighter planet, after a partile conjunction with a heavier one, departs from it and becomes separated by as much as the sum of the semidiameters of both requires; and this is indeed twofold, one simple, when both are direct, but the lighter is in more degrees; the other, which is called mutual, when, namely, the planet which is in more degrees moves directly; 44. whatever is in fewer degrees is retrograde. 45. SEPHINA is the Hebrew name for the faithful ship in the sky toward the southern region, about which we said more in V. Argonauts; Kircher in the Oedipus Aegyptiacus is witness to this. 46. SEPTANGULUS, and Hyperangulus, among geometers denotes a figure consisting of seven angles, whether it be plane or solid; whether regular or irregular. 47. SEPTENTRION commonly denotes the seven stars near the Arctic pole forming the constellation and image of Ursa Minor; although by that name are sometimes also meant those which are in the same position in Ursa Major and constitute the Wain, because they are more conspicuous than those, and because both figures approach the Arctic pole more closely; hence it is that the pole itself has taken its designation from them. Whence also. 48. SEPTENTRIONAL is usually called everything which in some way belongs to the said pole and is referred to it. Thus the Septentrional region of the world is said to be that which we Europeans inhabit on this side of the Equator; septentrional declination, latitude, semicircle, etc. Likewise. 49. SEPTENTRIO, absolutely speaking, denotes a wind blowing directly from that part of the world which lies beneath the Septentrional pole; and it is one of the four cardinal winds, indeed the cardinal point of all winds, since it, as well as its adversary Notus, are the seed and roots of all winds; capro-

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MATHEMATICVM. 449 pter vt obseruat Arist. lib. 2 Meteor cap. 4. ipsi solum quo- libet anni tempore spirant, quando alij certis tantum tem- poribus. Hunc nos Itali vulgò Tramontanam vocamus Græci Aparctias. Est de natura sua frigidus & siccus, adeo- que salubris omnia à corruptione præseruans, licet ob ni- miam frigiditatem cuadat floribus, & germinanti vineæ per- niciosus. Vide quæ diximus in V. Aparthias. SERPENS Arab. Alangue sidus in cælo ad borealem pla- < 50.> gam propè æquarote constans stellis 18. licet Baierus addens illi quæ propè illum extant informes in sua Vranometria enumeret omninò 37. omnes ferè de natura Veneris, & Sa- turni: vt proptereà contrariis qualitatibus præditæ euadant noxiæ, corruptiæ, ac venenosæ. De hoc sidere horoscopan- te sic cecinit Pontanus in sua Vrania. Exoriens facit Marsos, qui vulnera cantu, Qui sanent morlus, nigro qui sorte veneno Vnguine Poenio, & succis medicentur, & herbis. Si verò fuerit in occasu, sequitur idem Pontanus, ipsum portendere mortem ex morsu Serpentis, aut ex ictu venena- tæ sagittæ, aut sane ex propinatione veneni. SERPENTARIVS aliud sidus representas hominem Marsum, < 51.> siue Æsculapium manu supradictum Serpentem gestantem: Alio nvmine Ophiucus, in quo multa diximus. In hoc si- dere apparuit noua stella anno 1604. & durauit ad multos annos, quæ sui nouitate multam Astronomis fecit materiam speculandi, scribendi, eiusque effectus prognosticandi: quemadmodum aliæ duæ vna in pectore Cygni, altera in fede Cassiopeæ. Sed & de hac, quæ apparuit in genu Ser- pentatij scribit Keplerus, se magnoperè addubitare, num importet Mahometricæ sectæ desitionem, num Indi vniuer- saliter conuertendi essent ad fidem; num monarchia aliqua reliquis omnibus imperatura sit, num Religionis ingens, & vniuersalis mutatio instet, num denique mundi finis. Et aduertit, tres omninò genuinas, veras, & nouas stellas in Firmamento intra paucos annos apparuisse, post maximam superiorum coniunctionem in Piscibus: Et quemadmodum primus Trigonus igneus mundi creatione, quintus Christi domini nou iuitate nobilis extitit; ita hunc postremum haud temerè credendum esse Ecpyrosi, atque incendio Mundi se- cundum Christi aduentum denunciatur præluxisse. Tan- dem pia quadam parenæsi ad lectores facta, concludit. In- terim non sanè peccant si hac stella commonefatti vitam in- siaurent Christianam; itaque se comparent, vt Christum Dominum iam iam excepturi. SERVUM PYPILLÆ sidus. Vide Corona Gnossia < 52.>

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MATHEMATICVM. 449 because, as Aristotle observes, lib. 2 Meteor. cap. 4, they alone breathe at any season of the year, whereas the others do so only at certain times. We Italians commonly call this the Tramontana; the Greeks, Aparctias. By its nature it is cold and dry, and therefore health-giving, preserving all things from corruption, though because of its excessive coldness it harms flowers and the budding vine. See what we said under V. Aparthias. SERPENS. Arab. Alangue, a constellation in the sky toward the northern quarter, near the equator, consisting of 18 stars, though Bayer, adding to it the stars that lie nearby in his Uranometria, counts altogether 37. Almost all are of the nature of Venus and Saturn, so that by their contrary qualities they become noxious, corrupting, and poisonous. Concerning this constellation when rising, Pontanus sang thus in his Urania: Exoriens facit Marsos, qui vulnera cantu, Qui sanent morlus, nigro qui sorte veneno Vnguine Poenio, & succis medicentur, & herbis. But if it is in the setting position, the same Pontanus follows, it foretells death by the bite of a serpent, or by the stroke of a poisoned arrow, or certainly by the drinking of poison. SERPENTARIVS, another constellation representing a Marsian man, or Aesculapius carrying the aforesaid serpent in his hand; also called Ophiuchus, concerning which we have said many things. In this constellation a new star appeared in the year 1604 and lasted for many years; its novelty gave astronomers much material for speculation, writing, and prognosticating its effects, just as did the other two, one in the breast of Cygnus, the other in the chair of Cassiopeia. But about this star, which appeared in the knee of Serpentarius, Kepler writes that he greatly doubts whether it portends the downfall of the Mohammedan sect, whether the Indians are to be universally converted to the faith, whether some monarchy is to rule over all the rest, whether a great and universal change of religion is impending, or finally whether the end of the world is at hand. And he notes that three entirely genuine, true, and new stars appeared in the firmament within a few years after the greatest conjunction of the superior planets in Pisces; and as the first fiery Trigon, at the creation of the world, and the fifth, noble at the coming of Christ the Lord, came to be; so this last, not rashly, must be believed to have heralded the Ecpyrosis and the burning of the world second only to the coming of Christ. At length, after a pious admonition to the readers, he concludes: meanwhile, they certainly do not err if, warned by this star, they renew their Christian life; and so let them prepare themselves as if they were about to receive Christ the Lord now at hand. SERVUM PYPILLÆ, a star. See Corona Gnossia 52.

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450 LEXICON 53. SERVEVTH in sphæra barbarica dicitur primus decanus Libræ manens sub dominatu Lunæ, proindeque habens si- gnificare iustitiam, veritatem, ac genium auertendi fortes ab imbecillis, adiuvandi miseros, & pauperes, &c. 54. SESQVI QVADRATVS RADIVS nouum genus est familiari- tatis à Keplero nuper detectum, atque à Tito aliisque Astronomis experimentis probatum, intercedens inter duo sidera posita in distantia vnius, & insuper medietatis alte- rius sequentis quadrati; hoc est in Zodiaco grad. 135. Est de natura sua infaustus, imperfectæ, vt aiunt, inimicitiæ eiusdem rationis, ac ipse quadratus, licet non tantæ virtu- tis, & efficaciæ. Vide quæ diximus in V. Aspectus. 55. SEXANGVLVS apud Geometras dicitur figura sex angulis constans. 56. SEXAGENARTA DIVISIO celebris est apud omnes Astro- nomos: per eam enim diuiduntur partes signorum, & gra- dus æquatoris in sexagenas minutias, & harum singulæ in alias sexagenas in infinitum. Extat apud Auctores tabula sexagenaria partium proportionalium continens quadrata, & rectangula protracta vsque ad gr.180. ex vno latere 60. per alterum, cuius ope facillimè completur quicumque calcu- lus astronomicus; & levantur tirones à fastidiosa numero- rum multiplicatione, diuisione, & partis proportionalis ex regula aurea inuentione; cum vncio intuitu inueniatur in fronte, vel in area tabulæ numerus multiplicatus, aut ex diuisione quotiens, & pars proportionalis. Nam si quis ve- lit numerum multiplicatum, inueniet ipsum in area com- muni tabulæ, datis duobus per quos facienda est multipli- catio, accipiendis vno ex latere, altero infronte ipsius tabu- læ. Si velit partiri aliquem numerum accipiat diuidendum in area seu corpore tabulæ, & partitorem à latere, & statim habebit numerum diuisum, seu quotiens in fronte ipsius ta- bulæ. Sed enim res meliùs intelligitur per praxim; ac per ea, quæ pænè omnes auctores de eius vsu tradunt, quam per quamcumque nostram descriptionem. Ideò superuaca- neum est in ea re declaranda diutiùs immorari. 57. SEXIANS ASTRONOMICVS, seù Trigonicus est instrumen- tum Mathematicum à Tychone nuper excogitatum, quo stellarum positus, altitudines, remotiones, declinationes, aliaque permulta mira facilitate, ac subtilitate eruuntur. Eius partes, & vsum fusè explicat ipse Tycho to. 2. de noua stella Cassiopææ. 58. SEXILIS RADIVS Græcè Hexagonus est familiaritas à si- detibus contracta per sextam circuli partem, seu in distan-

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450 LEXICON 53. SERVEVTH in the barbaric sphere is said to be the first decan of Libra, remaining under the dominion of the Moon, and therefore signifying justice, truth, and a disposition to turn away the strong from the weak, to help the miserable and the poor, etc. 54. SESQVI QVADRATVS RADIVS is a new kind of aspect, recently discovered by Kepler and confirmed by experiments by Titus and other Astronomers, intervening between two stars placed at a distance of one and a half of the following square; that is, in the Zodiac at 135 degrees. By its nature it is unlucky, of the same kind of imperfect, as they say, enmity as the square itself, though not of so great virtue and efficacy. See what we said in V. Aspectus. 55. SEXANGVLVS among Geometers is said of a figure consisting of six angles. 56. SEXAGENARTA DIVISIO is celebrated among all Astronomers: for by it the parts of the signs and the degrees of the equator are divided into sixtieths of minutes, and each of these again into other sixtieths ad infinitum. There is found among Authors a sexagesimal table of proportional parts containing squares and rectangles extended up to 180 degrees, on one side by 60, on the other, by whose aid any astronomical calculation is most easily completed; and beginners are relieved from the tedious multiplication and division of numbers, and from finding the proportional part by the rule of three; since at a glance one finds in the front, or in the area of the table, the multiplied number, or from division the quotient and the proportional part. For if someone wishes to multiply a number, he will find it in the common area of the table, the two given numbers by which the multiplication is to be made being taken, one from the side, the other from the front of the same table. If he wishes to divide some number, let him take the dividend in the area or body of the table, and the divisor from the side, and straightway he will have the divided number, or quotient, in the front of the same table. But indeed the matter is better understood by practice, and by those things which almost all authors have transmitted concerning its use, than by any description of ours. Therefore it is superfluous to dwell longer on explaining this matter. 57. SEXIANS ASTRONOMICVS, or Trigonicus, is a Mathematical instrument recently devised by Tycho, by which the positions of the stars, heights, distances, declinations, and many other things are drawn out with remarkable ease and precision. Tycho himself explains its parts and use at length in vol. 2, On the new star of Cassiopeia. 58. SEXILIS RADIVS in Greek is Hexagonus; it is an aspect contracted from the sidera through the sixth part of a circle, or at a distance...

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MATHEMATICVM. 451 tia duorum signorum ad inuicem. Eiusdem naturæ est, ac Trinus, licet imperfectior. Stoys propriè exprimit plurium stellarum in certam quan- < 59.> dam formam congeriem, quales sunt omnes 48. imagines octauæ sphæræ; neenon aliæ duodecim in parte australi à nouis Astronomis nuper adiectæ, in quas omnes stellæ si- xæ, quibusdam paucis exceptis, ( quæ propterea informes dict v fuerunt, ) conglomeratæ sunt. Differt autem sidus à signo, eo quod hoc propriè appellet duodecimam quam- que Zodiaci partem in primo mobili consideratam: proin- deque præscindentem à quocumque astro, sed provt habet relationem ad quatuor puncta cardinalia, vnde incipit pro- portionalis influxus astrorum, ( vt mox dicemus) sidus au- tem dicit tantum certum stellarum numerum, siue in Zo- diateo, siue in reliquo stellati orbis expanso consistentium: atque adeo nullatenus consideratur in primo mobili, sed in Firmamento; licet alioqui signa Zodiaci ab ipsis si leribus, quæ tempore Ptolemai erant sub tali positu primi mobilis denominationem sumpserim; cum tamen modò ob motum octauæ sphæræ non parum à loco recesserint: atque adeo constellatio Arietis iam non sit amplius sub eiusdem nomi- nis signo, & circa æquatorem, sed ferè tota transferit in Taurum, sicut & Taurus iam est sub Geminis, &c. Et hæc quidem quoad nominis proprietatem. Cæterum sidus, & si- gnum sæpè confunduntur: Quinimò sidus aliquando ac- < 60.> cipitur non modo pro singulis vnius Asterismi stellis, ve- rum etiam pro ipsis planètis. Vnde Quintilianus: Quid hæc, inquit, fulgentium siderum veneranda facies, quæ quidam veluti infixa, ac cohærentia perpetua semel capta sede collu- cent: alia toto sparsa calo vagos cursus certis emetuntur erroribus. SINERA DISCURRENTIA eriam vocantur species quædam < 61.> accensarum exhalationum in aëre apparentium, quæ in longum eursum protensæ similitudinem exhibent alicuius stellæ per aëra discurrentis, quatenus ex vno loco in alium pergit, siue sursum, si accensa fiat leuior, siue ad latus, si alioqui in altum tendens impediarur à corpore aliquo den- so, & contrariæ qualitatis, vt puta à nube; siue deorsum des- cendat, si videlicet habeat materiam aliquam terream per- mixtam, aut è nube magno impetu foras exiliat ex parte inferiori; vt videmus in ignibus artificiaris. Hæc autem ventos portendere docet Arist. I. Meteor. cap. 7. quia eum tales accensiones eueniunt, necesse est, magnam istiusmo- di exhalationum copiam esse in aëre: Atqui exhalationes

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the relation of two signs to each other. It is of the same nature as Trinus, though more imperfect. Stoys properly expresses a cluster of several stars gathered into a certain form, such as are all the 48 images of the eighth sphere; as well as the other twelve in the southern part lately added by the new Astronomers, into all of which the fixed stars, with a few exceptions, which for that reason were called formless, have been conglomerated. But a constellation differs from a sign, in that the latter properly denotes any twelfth part of the Zodiac considered in the first mobile; and therefore cut off from any star, but as it has relation to the four cardinal points, from which begins the proportional influence of the stars, (as we shall soon say) whereas a constellation denotes only a certain number of stars, whether situated in the Zodiac or in the remaining expanse of the starry sphere: and thus it is by no means considered in the first mobile, but in the Firmament; although otherwise the signs of the Zodiac took their name from the very figures which in the time of Ptolemy were under such a position of the first mobile; since now, however, on account of the motion of the eighth sphere, they have not a little shifted from their place: and thus the constellation of Aries is no longer under the sign of the same name and around the equator, but is almost entirely transferred into Taurus, just as Taurus is now under Gemini, etc. And this indeed concerns the propriety of the name. Otherwise, constellation and sign are often confused: indeed constellation is sometimes taken not only for the individual stars of one asterism, but also for the planets themselves. Hence Quintilian: “What is this,” he says, “the venerable appearance of shining stars, which some, as if fixed and joined together, gleam in a perpetual seat once occupied; others scattered through the whole sky measure their wandering courses with certain movements.” SINERA DISCURRENTIA are also called certain kinds of burning exhalations appearing in the air, which, extended into a long course, present the likeness of some star running through the air, insofar as it passes from one place to another, whether upward, if the kindled matter becomes lighter, or sideways, if, while tending upward, it is hindered by some dense body of contrary quality, such as a cloud; or downward, if it has some earthy matter mixed with it, or if it leaps out of a cloud with great force from the lower part; as we see in fireworks. Aristotle teaches in Meteorology I, chapter 7, that these portend winds, because when such combustions occur, it is necessary that there be a great abundance of exhalations of this kind in the air: but exhalations

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LEXICON 452 commouent ventos, vt suo loco dicemus. < 61.> SIDERATIO aliquando accipitur pro siderum coaptatione in exlesti themeate, aliquando etiam idem sonat, ac sideris percussio, quales sunt certi morbi à determinatis constellationibus, quæ terris proximè iusident, prouenientes, Auctor est Varro. < 62.> SILENS LVNA dicitur in coniunctione cum Sole toto eo tempore, quo non lueettam ante quam post partitem congressum; eo quia iunc temporis nulla, vel saltem exigua virtute pollet; vnde quasi otiosa, & silens esse videtur. Hinc Columella lib. 2. cap. 10, Silente inquit, Luna fabam vellito ante lucem. Durat autem id tempus quorsque à sole liberaratur, exurgitque in cornua; quam Lunæ phasim Græci Menoidem appellant. Toto hoc tempore Formicæ nil operantur. < 63.> SIGNA apud Astronomos, (vt paulò ante explicatum est) sunt notæ quædam in Zodiaco per duodenas æquales partes diuisæ, quarum singuiæ triginta gradibus constant in longum, atque in latum duodecim, atque vt eorum natura dignoscatur, siue ratione stellarum fixarum, quæ in iis sunt, siue ex effectibus, quos parit in hilce inferioribus Sol per illas discutens variis animalium, aliarumque rerum imaginibus insigniæ. Sunt autem Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. Dicuntur autem omnia sidera esse in aliquo signo non modo quæ intra latitudinem Zodiaci consistunt, sed etiam quæ extra vagantur, quatenus si Ecliptica in duodecim partes æquales diuidatur, atque à punctis diuisionum per polos Zodiaci circuli describantur; quidquid inter duos semicirculos includitur, seu in superficie, quam duo semicirculi ab vno in alterum Zodiaci polum claudunt, ad signum illud dicitur attinere, quod in Zodiaco inter duos illos semicirculos intercluditur. < 64.> Porrò hæc distinctio signorum Zodiaci, vt benè aduertit Titus in lib 1. cap. 10. Cælestis Philosophiæ, non est fictitia, nec sine vlla ratione excogitata, sed vera & realis, per realem astrorum influxum à locis vnde incipiunt influere primas qualitates, vel vnde emittunt radios efficaces, quibus intenditur, aut remittitur efficacia talis influxus. Siquidem Planetæ à punctis mobilibus Zodiaci incipiunt influere primas qualitates; atque à punctis proportionalium distantiarum attingunt proportionales gradus talium qualitatum: Quandoquidem initium Tauti est in Trino ad initium Capricorni, & in sextili ad initium Cancri, vnde incipiunt planetæ

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LEXICON 452 commove the winds, as we shall say in its proper place. <61.> SIDERATION is sometimes taken for the arrangement of the stars in the celestial theme, and sometimes it also means the striking of a star, such as certain diseases arising from determinate constellations that are very near the earth. Varro is the author. <62.> SILENT MOON is said to be in conjunction with the Sun during all that time in which it does not shine, neither before nor after the exact conjunction; because at that time it possesses no, or at least only slight, power, and thus seems as it were idle and silent. Hence Columella, book 2, chapter 10: “When the Moon is silent, pull the beans before dawn.” But this time lasts until it is freed from the Sun and rises into the horns; which phase of the Moon the Greeks call Menoides. During this whole time the ants do no work. <63.> SIGNS among astronomers, as was explained a little before, are certain marks in the Zodiac divided into twelve equal parts, each of which consists of thirty degrees in length and twelve in breadth; and in order that their nature may be known, either by reason of the fixed stars that are in them, or from the effects which the Sun produces in these lower regions by passing through them, they are distinguished by various images of animals and other things. These are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. Moreover, all the stars are said to be in some sign, not only those which lie within the latitude of the Zodiac, but also those which wander outside it, insofar as, if the Ecliptic is divided into twelve equal parts and circles are drawn from the points of division through the poles of the Zodiacal circle, whatever is enclosed between the two semicircles, or on the surface which the two semicircles shut off from one pole of the Zodiac to the other, is said to belong to that sign which is enclosed in the Zodiac between those two semicircles. <64.> Moreover, this division of the signs of the Zodiac, as Titus rightly notes in book 1, chapter 10 of Celestial Philosophy, is not fictitious, nor devised without reason, but true and real, through the real influence of the stars from the places where they begin to influence the primary qualities, or from which they emit effective rays, by which the efficacy of such influence is intensified or diminished. For the planets begin to influence the primary qualities from the movable points of the Zodiac; and from points of proportional distances they reach proportional degrees of such qualities: since the beginning of Taurus is in trine to the beginning of Capricorn, and in sextile to the beginning of Cancer, whence the planets

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MATHEMATICVM. 433 planeta influere qualitates passiuas: & initium Geminorum est in Trino ad initium Libræ, & in sexili ad initium Arjctis, vnde incipiunt influere qualitates actiuas: quod idem in aliis signis videre est. Igitur distributio ista signorum realis est, ac nomenclatio non inanis sed iure excogitata ad eorum naturam exprimendam. Similiter non ab re quædam ex ipsis dieuntur masculina, alia fæminina, aliqua humana, aliqua ferina, hæc pulchra, illa deformia, &c. ob diuersos respectus, & effectus, quos habent parere in hisce inferioribus sidera in ipsis constituta. Sie etiam ratione situs dicuntur præsidere super certas regiones & ciuitates, vel quia ipsis sint verticalia, vel quia in earum ædificatione fuerint ascendentia. Ex membris etiam humanis habent singula singulis præesse; item certa certis animantibus, lapidibus, ac plantis: vt in loco sæpius diximus, idque vel ratione, vel sanè ex iugi & nunquam fallente experientia. Quæ autem signa singulis membris præsideant eleganter expressit Manilius in Astronom. lib. 1. his versibus. Namque Aries capiti; Taurus Cervicibas heret; Brachia sub Geminis; consentur pectora Cancro: Te scapula Nemae vocant: teque Ilia Virgo: Libra colit clunes; & Scorpius inquineregnat: Et femur Arcitenens; genua & Capricornus amauit: Cruraque defendit Iuuenis: vestigia Pisces. Horum etiam dominatus est per planetas distributus, itave luminaria, quæ potiora sunt, potiora sibi vendicent, ea videlieet in quibus potentiores fiunt, & manifestos effectus pariunt, & quidem singula suum, & vnicum, Sol nempe Leonem, Luna Cancrum: reliquis planeæ bina singuli obtineant, pro habitudine ad ipsa luminaria, provt provt susè dictum est in V. Domicilium. Hinc etiam. SIGNIFER dicitur circulus obliquus Zodiaci, in quo huiusmodi signa considerantur, & quem motu suo cuique proprio ab Occidene in Orientem Planetæ statis temporibus peragrant, & percurrunt. Qui profectò circulus consideratur in primo mobili latus, vt dictum est sex, aut certè nouem hinc inde gradibus ad omnium planetarum per suam latitudinis orbitam incedentium viam concludendam: itavt extra illum nusquam exorbitent. Nam in Firmamento, scu octaua sphæra intelligitur esse alius Zodiacus huic iam dicto substratus, qui similiter in duodecim signa, seu potiùs Asterismos dispescitur eiusdem nominis, & figuræ, quoniam olim, vt dictum est, erant illis immediate subie- F f

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MATHEMATICVM. 433 planets to influence passive qualities: and the beginning of Gemini is in trine to the beginning of Libra, and in sextile to the beginning of Arctis, from which active qualities begin to influence: the same thing may be seen in the other signs. Therefore this distribution of the signs is real, and the naming not vain but justly devised to express their nature. Likewise it is not without reason that some are called masculine, others feminine, some human, some bestial, these beautiful, those deformed, etc., on account of the diverse respects and effects which the stars placed in them are thought to produce in these lower regions. Thus also, by reason of their position, they are said to preside over certain regions and cities, either because they are vertical to them, or because in their founding they were rising. They also preside over individual human members; likewise certain ones over certain animals, stones, and plants: as we have often said in the proper place, and that either by reason, or certainly from constant and never-failing experience. Which signs preside over the individual members Manilius elegantly expressed in Astronom. lib. 1. in these verses. Namque Aries capiti; Taurus Cervicibus hæret; Brachia sub Geminis; continentur pectora Cancro: Te scapulæ Nemeæ vocant: teque Ilia Virgo: Libra colit clunes; & Scorpius inquinet regnat: Et femur Arcitenens; genua & Capricornus amavit: Cruraque defendit Iuuenis: vestigia Pisces. Their dominion is also distributed through the planets, so that the luminaries, which are the more powerful, may claim the more powerful parts for themselves, namely those in which they become stronger and produce manifest effects, and indeed each its own, and singular one: the Sun namely Leo, the Moon Cancer: the planets shall each hold two of the rest, according to their relation to the luminaries themselves, as was said above in V. Domicilium. Hence also. SIGNIFER is the name given to the oblique circle of the Zodiac, in which signs of this kind are considered, and which by its own movement the planets traverse and pass through at fixed times from West to East. This circle is indeed considered in the first mobile as broad, as has been said, six or certainly nine degrees on either side, to close the path of all the planets moving through their own orbit of latitude: so that they may nowhere stray outside it. For in the Firmament, or eighth sphere, another Zodiac is understood to exist, lying beneath this one just mentioned, which likewise is divided into twelve signs, or rather asterisms, of the same name and shape, because formerly, as has been said, they were immediately under- F f

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454 LEXICON & credebantur esse in primo mobili; Nunc autem experientia compertum est, eos cum sua sphæra esse loco dimotos, & viterius ad 18. ferè gradus processisse. Vnde ista ad eorum differentiam sidera appellantur; quorum natura longè ab illis diuersa, iam non vt olim à proportionalibus distantiis à punctis cardinalibus, sed solum à stellarum ex quibus conglomerantur qualitatibus venanda est, proindeque actiuiora sunt quam illa, quæ ex seipsis nihil habent influere nisi per accidens, quatenus planeæ in ipsis reperiuntur: præcipuè autem Sol, qui ex accessu, & recessu ad hæc & illa loca Zodiaci efficit vicissitudinem temporum, & miram istam effectuum quos in Natura videmus varietatem. Ob idque prouidit sapientissimè terum omnium Artifex, vt circulus ille obliquus esset, secaresurque ab æquinoctiali in duas partes, quarum altera in septentionem vergeret, altera ad Austrum, nam ex accessu Solis ad punctum solstitii maximè ab æquatore distans, hoc est gr. 13. & semis, calot intenditur, quia nos semper directionibus radiis verberat, ex recessu remittitur: Ideoque simicirculus ille ab initio Capricorni per successionem signorum adjunctium Cancri appellatur Ascendens, quia in eo sol semper adverticem capitis nostri ascendit, qui autem ab initio Cancri per Libram ad Capricornum protenditur, vocatur descendens: quia in eo sol semper à vertice capitis nostri descendit. Plura in V. Zodiacus. 67. SIGNIFICATORES apud Astronomos appellantur loca quædam in exlo, quæ se habent tamquam subiectum passibile erga actiones aliorum siderum, in quorum corpora, aut radios directione impingunt, proindeque habent aliquid significare tempore expletæ directionis implendum. Sunt autem quinque ex Prolema Sol, Luna, Linea Orientalis, Culmen, & Pars Fortunæ; ex quorum directionibus accidentia omnia tam prospera, quam aduersa, quæ natis obuenire possunt circa corporis affectiones, animi propensiones, & reliqua tum intrinsecus, tum extrinsecus aduenientia venari posse contendit, 3. Quadrip. cap. 13. qui etiam ab aliis vocantur Prorogatores, moderatores, &c. à moderandarum rerum provincia, quam sortiuntur. Quandoquidem gerunt vicem creditoris recepturi aliquid à promissoribus astris certo, & definito tempore quo ista tandem ad ipsos deuoluantur; itavt ipsi significatores, consideretur immobiles in suis circulis positionum expectare advenrum promissorum, qui motu primi mobilis ad ipsos ferantur; quod quomodo fiat luculenter explicatum est in V. Di-

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454 LEXICON and were believed to be in the primum mobile; but now experience has shown that they with their sphere have been displaced from their place, and have advanced further to nearly 18 degrees. Hence those stars are called in relation to their difference; their nature being far different from those others, is now no longer to be sought, as formerly, from their proportional distances from the cardinal points, but only from the qualities of the stars from which they are compounded; and therefore they are more active than those which of themselves have nothing to influence except accidentally, insofar as the planets are found in them: especially the Sun, which by its approach and retreat to these and those places of the Zodiac produces the succession of the seasons, and that wonderful variety of effects which we see in Nature. And for that reason the wise Artificer of all things most wisely provided that this oblique circle should exist, and that it should be cut from the equinoctial into two parts, of which one would incline toward the north, the other toward the south; for from the Sun’s approach to the solstitial point, which is farthest from the equator, that is, 13 degrees and a half, heat is intensified, because it always strikes us with direct rays; from its recession it is diminished. Therefore this semicircle from the beginning of Capricorn through the succession of the adjacent signs of Cancer is called the Ascending one, because in it the sun always rises to the summit of our head; but that which from the beginning of Cancer through Libra is extended to Capricorn is called the descending one: because in it the sun always descends from the summit of our head. More in V. Zodiacus. 67. SIGNIFIERS, among astronomers, are certain places in the sky, which stand as a kind of passive subject with respect to the actions of other stars, into whose bodies, or rays, they strike by direction, and therefore they are thought to signify something to be fulfilled at the time when the direction is completed. There are five from Ptolemy: the Sun, the Moon, the Eastern Line, the Midheaven, and the Part of Fortune; from whose directions he contends that all events, both favorable and adverse, which can happen to those born, in regard to bodily affections, inclinations of the mind, and the rest, both inwardly and outwardly occurring, can be sought out, 3. Quadrip. cap. 13. Others also call them prorogators, regulators, etc., from the office of regulating things which they undertake. Since they perform the role of a creditor who is to receive something from promising stars at a certain and fixed time, when these things at last are brought down to them; so that the signifiers themselves are regarded as standing immobile in their circles of position, waiting for the advent of the promised things, which by the motion of the primum mobile are brought to them; how this is done has been clearly explained in V. Di-

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MATHEMATICVM. 453 [præ]cio: Addunt Recensiores non modò dicta loca, & lumina naria, sed & reliquos quinque planetas, necnon & cuspides singularum domorum posse obire munus significatorum pro eorum significatis; vt secundam domum pro diuitiis, tertiam pro fratribus, &c. atque adeò habere rationem subiecti passibilis, si considerentur & ipsi immobiles in suis circulis positionum expectare aduentum aliorum siderum, etiam si alias planetæ habeant rationem causæ efficientis respectu aliorum, cum non repugner idem secundum diuersa posse duplici virtute pollere, vt patet in ipsis lumi naribus, quæ inter promissores etiam connumerantur. Nec sanè absque fundamento, cum plurima accidentia, experientia duce, ex eorum directionibus dignoscantur, quorum ne vimbratilis quidem notit a haberi potest ex directione prædictorum quinque significatorum, Proinde rei periculum facere non erit forsan inutile. Vide etiam in V. Moderatores. SIMPHASIS, Græcè dicitur mulrarum stellarum vna emersio, & conspectus: teste Iosepho Laurentio in Amalthia. SENAPHIA dicitur Luna cum alicui stellæ, aur planetæ corpore copulatur. SINVS præcisè indicat amplitudinem quandam intra duos terminos constitutam: Hinc curuitas illa, quæ est intra pectoris, brachiorumque complexum antonomasticè sinus audir. Similiter littora curua, quæ duobus continentis, quasi brachiis in mare longiùs procurrentibus includuntur, & alia his similia per translationem sinus etiam appellantur; vt videre est id Thesauro linguæ Latinæ. Porrò eadem ratione apud Geometras lineæ rectæ quæ alicuius arcus cavitatem, & aream claudunt, sinus vocantur, seu potiùs chordæ, quarum ramen semisses verius dicuntur sinus, & quidem recti, si rectè arcui subtendantur, veri verò si ad modum sagitæ sinubus rectis adiaceant, ita vt cum iis angulum rectum efforment. Omnis igitur sinus cum altero verso modo collatus sinus versus dicitur. Quapropter diameter circuli vocatur vtriusque arcus chorda: semidiameter, seu semisses chordæ sinus tam versus, quam rectus: sinus maximus tota semidiameter, lineæ huic parallelæ reliqui sinus. Plura apud auctores in explicatione Tabulæ sinuum, tangentium, & secanium. SINVS ABRAHÆ, seu, Limbus Sanctorum Patrum, dicitur communiter locus in Inferno, hoc est in telluris meditullio, vbi olim iustorum animæ post mortem loco depositi F f ij

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MATHEMATICVM. 453 [in] price: More recent writers add not only the places mentioned above and the luminaries, but also the other five planets, and likewise the cusps of each of the houses, that they may perform the office of significators in place of their significations; thus the second house for wealth, the third for brothers, etc.; and indeed they have the character of a passive subject, if they are considered as themselves motionless in their circles, awaiting in their positions the coming of the other stars, even though otherwise the planets have the character of an efficient cause with respect to the others, since it is not contrary that the same thing in different respects may possess a twofold power, as is clear in the luminaries themselves, which are also reckoned among the promissors. And certainly not without foundation, since very many events, guided by experience, are recognized from their directions, of which even a shadowy knowledge cannot be had from the direction of the aforesaid five significators. Therefore to make trial of the matter will perhaps not be useless. See also under V. Moderators. SIMPHASIS, in Greek, is called the rising together, and the appearance, of many stars: as Joseph Laurentius testifies in Amalthia. SENAPHIA is said when the Moon is joined to the body of some star or planet. SINVS precisely indicates a certain width established within two limits: hence that curve which is within the embrace of the chest and arms is by antonomasia called a sinus. Likewise curved shores, which are enclosed by the mainland, as it were by two arms extending farther into the sea, and other things like these are also called sinuses by metaphor; as may be seen in the Thesaurus of the Latin language. Moreover, in the same way among geometers the straight lines which enclose the cavity and area of some arc are called sinuses, or rather chords, whose halves are more properly called sines, and indeed straight sines if they are rightly subtended to the arc, but true sines if they lie beside the straight sines in the manner of an arrow, so that with them they form a right angle. Therefore every sine, when compared with another in the opposite manner, is called a versed sine. Wherefore the diameter of a circle is called the chord of both arcs; the semidiameter, or half of the chord, is a sine both versed and straight; the maximum sine is the whole semidiameter, and the other sines are lines parallel to this one. See more in the authors who explain the Table of sines, tangents, and secants. SINVS ABRAHÆ, or the Limbo of the Holy Fathers, is commonly called the place in Hell, that is, in the center of the earth, where formerly the souls of the righteous after death were laid in a place of deposit. F f ij

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456 LEXICON detinebantur, quovsque per Christi mortem redimerentur, atque in cælestem Patriam deportarentur. D. Augustinus pluribus in locis, sed præsertim Epist. 37. ad Dardanum existimat sinuni Abrahæ, de quo sit mentio in Euangelio Luc. 16. vt in cum deportata fuisset ab Angelis Lazari pauperis Anima, non fuisse locum subterraneum, sed vel de paradiso, vel de loco non corporeo dici: quandoquidem in Euangelio magnum chaos constitutum esse dicitur inter sinum Abrahæ, vbi Lazarus solatio fiuebatur, & infernum, vbi diues instormentis ardebat: atqui in loco, quem concipimus, subterraneo quale gaudium esse potest, quæ amænitas, & quodnam chaos inter ipsum, & infernum firm atum, cum sanè non longè ab ipso distans concipi debeat? Nihilominus communis Theologorum sententia docet in inferno ria, seù potiùs quatuor esse receptacula aliquibus claustris, & interstitiis distincta; quorum vnum, & inferius sit obscurissimum, igne repletum, ac recipiendis, torquendisque animabus in lethali culpa decedentibus, destinatum; aliud suprà ipsum, quod dicitur purgatorium, vbi animæ non sacis per poenientiam expiatæ derinentur, atque igne purgantur, quovsque integrè suorum criminum poenam luant: alia duo siue vnum & idem sint, siue etiam repagulis interstincta, pro recipiendis animabus puerorum in peccato originali decedenium, & SS. Patrum, ante completam Christi redemptionem, quæ loca sint aliqua luce perfusa ex terræ hiasibus transpirante, vbi nullus ignis, nullus dolor, sed sola carceris detentio, & poena damni, quæ & pueris nullam de Deo cognitionem habentibus, nullam afflictionem facit, & sanctis Patribus ingens desiderium cælestis patriæ ingerebat, quam spes tuta certæ redemptionis ab omni mæstitia subleuabat. Consonant sacræ paginæ, vbi Christus post mortem in Infernum descendisse fertur vti- que Sanctos Patres redempturus, quod longè antè præuidens Zacharias Propheta pia quadam apostrophe sic ipsum interpellat cap.9. Tu quoque in sanguine testamenti tui emisi- sti vinctos de lacu. quæ verba de infernali loco explicans D. Hieronymus in Commentar. sic ait: In sanguine passionis tua eos, qui vincti in carcere tenebantur, in quo non est vlla misericordia, tua clementia liberasti. Quod autem inter istum locum, & Infernum damnatorum magnum chaos firmatum esse dicatur, vt inde huc transmeari non possit id non officit, cum vel de Purgatorio intelligi possit, vel sanè de firmissimo, atque immutabili Dei decreto, quo veluti interiecto magno quodam impedimento, horum & illorum

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456 LEXICON were detained there until, through Christ’s death, they were redeemed, and carried to the heavenly homeland. St. Augustine, in many places, but especially in Epistle 37 to Dardanus, thinks that the bosom of Abraham, of which mention is made in the Gospel of Luke 16, into which the soul of poor Lazarus was carried by the Angels, was not an underground place, but should be understood either of Paradise or of a non-corporeal place: since in the Gospel it is said that a great gulf was fixed between the bosom of Abraham, where Lazarus was consoled, and hell, where the rich man burned in torments; but in the place that we imagine to be underground, what joy can there be, what pleasantness, and what gulf fixed between it and hell, when indeed it should be conceived as not far distant from hell? Nevertheless the common opinion of the theologians teaches that in hell there are, or rather there are four receptacles, distinct by certain barriers and intervals; one of which, and the lowest, is most dark, filled with fire, and destined for receiving and tormenting souls departing in mortal guilt; another above it, which is called Purgatory, where souls not sufficiently purified by repentance are detained, and are purified by fire until they fully pay the penalty for their crimes; the other two, whether they are one and the same, or even separated by barriers, are for receiving the souls of children dying in original sin, and of the Holy Fathers before the complete redemption of Christ; these places are somewhat filled with light, breathing up from the chasms of the earth, where there is no fire, no pain, but only detention in prison, and the punishment of loss, which both causes no affliction to children who have no knowledge of God, and to the holy Fathers inspired a great longing for the heavenly homeland, which the sure hope of certain redemption from all sadness relieved. The sacred pages agree, where Christ is said to have descended into Hell after death, namely to redeem the Holy Fathers, which long before foreseeing the Prophet Zechariah, in a certain pious apostrophe, thus addresses him in chapter 9: You also, by the blood of your covenant, have sent forth the prisoners from the pit. Explaining these words of the infernal place, St. Jerome in his Commentary says thus: By the blood of your passion you have freed them, who were held bound in a prison, in which there is no mercy, by your clemency. But that between this place and the hell of the damned a great gulf is said to be fixed, so that passage from there to here cannot be made, this does not prevent it, since it may either be understood of Purgatory, or indeed of the most firm and immutable decree of God, by which, as though by a great intervening obstacle, these and those

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MATHEMATICVM. 457 e[m]municatio prohibeatur; cum tamen ambo sub eodem terræ concauitaris ambiru e[m]prehendantr. Cæterum quanta sit loci istius amplirudo certò definiri non potest. Bonardus tamen ex variis congruenriis colligir ipsu[m] distare à superficie terræ milliariis 3748 cum triere, quod quidem cum nuperis recensioru[m] obseruationibus statuenibus telluris semidiame- tru[m] 3035 milliariis cum quinq[ue] vndecimis longâ stare non po- rest. Porrò hic locus modò vacuus est, vel certè à solis infantulis inhabitatur: qui tandem post diem iudicij ruptis repagulis in vnum infernum coibit, quemadmodum & Pur- gatorij locus ad tot corporum multitudinem recipiendam. SIRIUS, non Syrius (vt malè quidam à Syria) sed à Græco verbo , vel à , quod est hiare, dictus est Canis Maior sidereus, Stella fixa primæ magnitudinis, de na- tura Louis, & Martis, eoquod tellius sub hoc sidere præ sic- cirate hiulca reddatur, & arida Et quidem non est in Fir- mamento sidus isto potentius & efficacius: quippe eo exo- riente tota poene Natura turbatur: Canes aguntur in rabiem, fluctuant in doliis vina, febres ardenies grassantur, aliaque mirabilia accidunt quæ referi Plin. lib. 1. cap. 4. sed & con- sideratione dignum est quod scribir lib. 11. cap. 14. de melle sub Sirio elaboraro: ait enim Alterum genus est mellis affi- nti, quod ideò vocatur horæum à tempestate præcipua ipso Si- rio exp[er]iendescente post solstitium diebus triginta fere: namque ab exortu sideris cuiuscumque, sed nobilium maxime, aut celestis arcus, si non sequantur imbes, sed ros tepescat Solis radiis, medicamenta non mella gignuntur, oculis, vlceribus internisque visceribus dona cælestia. Quod si seruetur hoc sirio exoriente, casuque congruat in eum diem, vt sæpè, Ve- neris, aut Louis, Mercuriique ortus, non alia suauitas, vsusque mortalium malis à morte vocandis, quam diuini nectaris fiat. Huevsque Plin. Ergò, vt benè obseruat Ric- ciolus, saliua Canis cælestis, (sic communi hominum vsu mel appellare licer) tunc suauis, & vitalis mortalibus red- ditur, cum canum terrestrium in rabiem abeunrium saliua mortalis euadit ac venefica: idemque fidus vno eodemque influxu, & deleterium exhiber & antidotum. SIRHACER Græco barb. dicitur in sphæra barbarica secun- dus decanus Leonis, cuius dominium est penes Iouem, ha- bens significationem rixarum nesciorum, necessitatis mise- rorum, victoræ vilium per nescios, occasionis enses strin- gendi, præliorum, &c. SOAIL IAMANI in Tabulis Persicis diciur Canopus in Ar- gonaui, Stella fixa fulgentissima primæ magnitudinis, quæ Ff iij

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MATHEMATICVM. 457 emmunicatio be prevented; although both are comprehended under the same circumference of the concavity of the earth. Moreover, how great the extent of this place is cannot certainly be defined. Bonardus however, from various congruities, infers that it is distant from the surface of the earth 3748 miles and three; which indeed, together with the newer observations lately establishing that the semidiameter of the earth is 3035 miles and five elevenths long, cannot stand. Further, this place is now empty, or certainly inhabited only by little infants: who at last, after the day of judgment, the barriers having been broken, shall all be gathered into one hell, just as the place of Purgatory too is for receiving so great a multitude of bodies. SIRIUS, not Syrius (as some wrongly from Syria), but from the Greek word, or from , meaning to gape, is called the Greater Dog star, a fixed star of the first magnitude, of the nature of Jupiter and Mars, because the earth under this star is made open-mouthed by excessive dryness, and arid. And indeed there is no star in the Firmament more powerful and efficacious than this one: for when it rises, almost all Nature is disturbed: dogs are driven into rage, wines ferment in casks, burning fevers spread, and other wonders occur which Pliny relates, book 1, chapter 4. But it is also worth noting what he writes in book 11, chapter 14, about honey made under Sirius: for he says, “There is another kind of honey, which is called attic, because of the special season under Sirius himself, after the solstice, about thirty days after the star’s rising: for from the rising of any star, but especially of the nobler ones, or of the celestial arc, if rains do not follow but the dew grow warm by the sun’s rays, not medicines but honeys are produced, heavenly gifts for the eyes, wounds, and inward viscera. But if this be observed at the rising of Sirius, and by chance it coincide with that day, as often happens, with the rising of Venus, or Jupiter, and Mercury, then no other sweetness, and use to mortals in their evils to be called from death, will be made than that of divine nectar.” Thus far Pliny. Therefore, as Ricciolus rightly observes, the saliva of the heavenly Dog, (thus it is allowed by common usage to call it honey) then becomes sweet and life-giving to mortals, when the saliva of earthly dogs, going into rage, becomes mortal and venomous: and the same star by one and the same influence both exhibits a poison and an antidote. SIRHACER, in barbarous Greek, is called in the barbaric sphere the second decan of Leo, whose rule is with Jupiter, having the signification of quarrels of the ignorant, the necessity of wretched men, the victory of the base over the ignorant, the occasion of drawing swords, battles, etc. SOAIL IAMANI in the Persian Tables is called Canopus in Argonautis, a fixed star of the first magnitude, exceedingly bright, which Ff iij

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458 LEXICON ex Rhodo insula incipit esse visibilis arab. Suhel. < 75.> SOL quasi solus dicitur Planeta omnium nobilissimus, & luce, actiuitate, virtute, corporis magnitudine cæteros omnes præcellens in medio eorum situs, tanquam Vniuersi cor, ac Rex in solio constitutus, atque, vt habet Plinius, Erratum siderum medius Sol fertur amplissima magnitudine & potestate, nec temporum modo, terrarumque, sed & siderum etiam ipsorum calique rector. Hebraicè dicitur Chaminali, & Semes à ministrando, eo quod sit quasi Dei, & Naturæ minister, quo vtatur ad vniuersum fæcundandum, ac viuificandum. Hinc eum Vas admirabile, Opus Excelsi, Mundi Animam, luminis fontem, Coeli oculum, moderator temporum expressam diuinæ bonitatis imaginé, Sacræ Paginæ, Sancti Patres, aliisq[ue] dixerunt. Habet pro cetro tellurem (cum tamen ipse sit omnium planetarum excepta Luna centrum,) circa quam spatio viginti quattuor horarum motu primi mobilis ductus, atque interim motu suo annuo varios parallelos describens efficit diuersitatem illam temporum, ac diei noctisquè vicissitudines, vnde ortus, & interitus rerum, alterationesque omnes, quas in Natura videmus originem ducere testatur Philosophus, & cum eo Areopagita 4 de Diuinis nominibus. < 76.> Cæterum, vt eius claritas, efficientia, calor, fæcunditas omnibus nota est, ita & substantia omnibus obscurissima, Aristoteles aliique Philosophi indignum existimantes Coeli lumina eandem cum sublunaribus hisce participare materiam, quintam quandam conspicati sunt substantiam, quam coelos sideraque obtinere tradunt lib. 2. de coelo cap. 7. atque adeò Sol, inquiunt non re, sed virtute calidus est, eoquod suo lumne calorem, & siccitatem in inferioribus istis producat. Sed enim id coelestibus luminibus indignum non est, eandem cum sublunaribus habere materiam, præsertim cum tot tantique rationes id manifestè suadeant, activitas, effectuum similitudo, rerum proportio, conuenientia qualitatum, connexio, & sympathia, quæ clarè innuunt esse a'iquid coelestibus æquè ac terrenis commune, quo mediante generationes rerum, alterationes, corruptionesque fiant. Neque enim ego vnquam dixerim coelestia corpora participare materiam hanc sublunarem, sed potius inferiora isthæc coelestis substantiæ partem esse, quæ inde hauriant qualitates, mutationumque principia. < 77.> Et sanè igneum solem esse, nec noua, nec adeò absoleta opinio est, vt non quousi tempore suos, eosque magni nominis sectatores habuerit. Eam ex antiquis Anaxagoras,

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458 LEXICON from the island of Rhodes, it begins to be visible, arab. Suhel. < 75.> THE SUN is called, as it were, alone, the most noble of all the Planets, and surpassing all the others in light, activity, virtue, and size of body, placed in their midst, as if the heart of the Universe, and set upon the throne as King; and, as Pliny has it, the Sun is said to be the middle one of the wandering stars, of the greatest magnitude and power, and not only the ruler of times and lands, but even of the stars themselves and of the heaven. In Hebrew it is called Chaminali, and Semes, from ministering, because it is, as it were, the minister of God and of Nature, which He uses for the fecundating and vivifying of the whole. Hence the Holy Page, the Holy Fathers, and others have called it a wondrous Vessel, the Work of the Most High, the Soul of the World, the fountain of light, the eye of Heaven, the governor of times, an expressed image of divine goodness. It has the earth for its sceptre (although it itself is the center of all the planets except the Moon), around which, in the space of twenty-four hours, carried by the motion of the first mobile, and meanwhile by its own annual motion describing various parallels, it brings about that diversity of seasons, and the alternations of day and night, whence the birth and death of things, and all changes, which we see in Nature, are shown by the Philosopher, and with him by the Areopagite, 4 On the Divine Names. < 76.> Moreover, just as its brightness, efficacy, heat, and fecundity are known to all, so also is its substance most obscure to all, since Aristotle and other philosophers judged it unworthy that the lights of heaven should share the same matter with these sublunary things, and therefore they conceived a certain fifth substance, which they say the heavens and the stars possess, as in book 2 of On the Heavens, chap. 7. and thus, they say, the Sun is hot not in reality, but in virtue, because by its light it produces heat and dryness in these lower things. But indeed it is not unworthy of the heavenly lights to have the same matter as the sublunary things, especially since so many and such great reasons clearly persuade this: activity, the likeness of effects, the proportion of things, the agreement of qualities, connection, and sympathy, which clearly indicate that something is common to the heavenly things as well as to the earthly, through which the generations of things, changes, and corruptions are brought about. Nor indeed have I ever said that the heavenly bodies participate in this sublunary matter, but rather that these lower things are a part of the heavenly substance, from which they draw qualities and principles of change. < 77.> And certainly, that the sun is fiery is neither new nor so obsolete an opinion that it has not had, at one time or another, its own, and those of great name, followers. Among the ancients, Anaxagoras,

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MATHEMATICVM. 459 Zeno Citticus, Democritus, Metrodorus, Plato, aliique permulti, quos habet Plutachus lib. 2. de Placitis Philosphorum cap. 26. sequuti sunt. Eam ex recensioribus sustinent Keplerus, Bulliardus, Kircherus, Rheita, Schinerus, & alij, quos refert Ricciolus in Almagesto lib. 3. cap. 1. quibus certè ipsa sacra eloquia non obscurè astipulantur, sæpè Solem igneum appellantes, præsertim Eccli. 43. Fornacem custodiens in operibus ardoris, tripliciter sol exurens montes, radios igneos exsufflans, necnon multi ex SS. Paribus, quos abunde congerit Fornerius, Fauet etiam Ecclesia dum in Hymno Feriæ quartæ sic canit. Quarto die qui flammeam Dum solus accendis rotam. Sed & experientia ipsa & oculorum testimonia id evincunt: Videmus enim ipsum per Telescopia grandiora tanquam ignitam fornacem flammis vndique fluctuantem. Quapropter Resta in lib. de Meteoris, non refugit opinari, corpus ipsum solare aliud planè non esse quam collectionem plurium corpusculorum igniorum lumine insito coruscantium: quod vel ex eo probat, quod Genes. 1. dicitur Deus primo die creasse lucem, & quarto solem constituisse; nec desunt expositores, qui dicant lucem primo die gentam, quarto fuisse in sole repositam, & in eum nihilo secius confluxisse, quàm cum post creationem aquatum, ad Dei nutum facta est separatio aquarum ab aquis, earum inquam, quæ sub firmamento sunt ab his quæ super firmamentum, casque postea coivisse in locum vnum, fuisseque Maria appellata Hinc maculæ illæ sese in orbem mouentes, quas in Mundi oculo oculis plusquam lincæis primus omnium obseruavit præcitatus Scheinerus; sunt etenim partes primigeniæ illius lucis solidiores, quæ in Sole eundem effectum pariunt, eamdemque apparentiam, quam in Saturno stellulæ illæ duæ comites, quæ, vt alibi diximus, circa ipsum sese rotantes aliquando sciunctæ, aliquando intra ipsum perinde ac duæ quædam maculæ videntur. Eius figuram rotundam, ac perfectè sphæricam nemo est, qui non asserat, nihilominus propè horizontem tam in ortu quam in occasu apparet ellipticus, quæ tamen forma paulatim in circularem regreditur, quò nempè Sol magis ab horizonte elongatur: Quæ res multam dedit philosophadi materiam nostris Astronomis recensioribus, præsertim dicto Scheinero, qui peculiarem libellum de hoc argumento edidit inscriptum Sol Ellipticus. Quam visus varietatem in retractiones per vapores horizonti proximos factas re- F f iiiij

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MATHEMATICUM. 459 Zeno Citicus, Democritus, Metrodorus, Plato, and very many others, whom Plutarch has in lib. 2. de Placitis Philosophorum cap. 26, followed this opinion. Among more recent writers it is supported by Kepler, Bulliardus, Kircherus, Rheita, Schinerus, and others, whom Ricciolus cites in the Almagest, lib. 3. cap. 1; to whom certainly the sacred oracles themselves plainly agree, since they often call the sun fiery, especially Eccli. 43: “The furnace guarding in works of heat,” “the sun burning the mountains threefold,” “breathing forth fiery rays,” as well as many of the Holy Fathers, whom Fornerius abundantly collects. The Church also favors this when in the hymn of Wednesday it sings thus: On the fourth day, when thou alone dost set in motion The flaming wheel of the sun. But experience itself and the testimony of the eyes also prove this: for we see it through larger telescopes like a fiery furnace, flames surging on every side. Wherefore Resta, in his book De Meteoris, does not shrink from the opinion that the solar body itself is nothing other than a collection of many fiery corpuscles, sparkling with innate light; which he proves even from the fact that in Genesis 1 it is said that God created light on the first day and established the sun on the fourth; nor are there lacking interpreters who say that the light born on the first day was placed in the sun on the fourth, and nevertheless flowed into it, just as after the creation of the waters, at God’s command there was a separation of waters from waters, namely those under the firmament from those above the firmament, and that afterwards these came together in one place and were called seas. Hence those spots moving themselves about in a circle, which the aforesaid Scheiner first of all observed in the eye of the world with more than lynx-like eyes; for they are the more solid parts of that primitive light, which in the Sun produce the same effect and the same appearance as in Saturn those two companion little stars, which, as we have elsewhere said, sometimes, as they revolve around him, seem separated, and sometimes within him, just like two certain spots. No one denies its round and perfectly spherical shape; nevertheless, near the horizon, both at rising and at setting, it appears elliptical, a form which gradually returns to circular as the Sun is farther removed from the horizon. This matter furnished much material for philosophizing to our more recent astronomers, especially the said Scheiner, who published a special booklet on this subject entitled Sol Ellipticus. This variety of appearance, arising from refractions made through vapors near the horizon, re- F f iiiij

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160 LEXICON fest; idque eò magis quod quantò isti sunt crassiores, eò magis videtur, atque amplior hæc elliptica in sole figura. 30. Magnitudinem eius veram definire impossibile est; appa- rentem, per quam difficile; licer Keplerus asserat, explo- rarum esse Solis diametrum in Apogæo esse minut. 30. in Perigæo 31. quem tamen derider Ricciolus lib. 3. cap. 10. Ratio autem huius difficultratis est tum instrumentorum fal- lacia, tum penumbra interpositio, quæ semper eius appa- rentem figuram variat, & conturbat: vnde & circà horizontem maior apparet, (vt & reliqua sidera) quam circa Meridianum. Communiter tamen visa eius diameter statuitur minutorum 3'. & per consequens magnitudo eius conclu- ditur esse tanta, vt contineat terræ magnitudinem 166 cum duabus tertiis vt testatur Claiius in sphætam. Cæterum sol est Pianeta masculinus calidus, & siccus fortuna per aspe- ctum, infortuna per corpus, habens significare Principes, magnates gloriam, &c. Quade re vide quæ diximus in V. Luminaria. 31. SOLICITIVM LVNA vocat celsus eius cum sole congressum, quo tempore, inquit, ac testatur Argolus de aëbus criticis lib. 1. cap. 16. Cynocephalum animal Ægypro familiare, si id masculum sit nec videre, nec cibum sumere, faminam vero sanguine ex decisione Luna diminui: mox vtique & lumen oculis, & sanguinem reddi visceribus, pro- vt dea in restaurationem sui luminis fraterna chatitate re- dierit. Hæc ille, addens hoc ipsum animal tempore æquinoctij duodecies in die, hoc est singulis horis vrinam mit- tere, ranta illi cum luminaribus conuenientia, & affini- tas. Hinc factum est, vt in posterum dies ac noctes singulæ in duodecim horas dispescerentur, atque ea de causa horologiis incumbentem semihominem istum inculperent. 32. SOLITUDO PLANETÆ ex Abraham Auenarre est cum is se- paratur à suo socio à coniunctione quindecim graduum, vel sex per aspectum, & nulli alij copulatur, donec in illo fuerit signo; aur ipsum non aspiciat planeta donec fuerit propinquis aspectu perfecto, quicumque tandem is fuerit. Vide eius Introductorium cap. 7. SOLIDVM ex Euclide definitur esse Corpus quod longitudinem, latitudinem, & crassitiam habet; per quod differt à linea, atque à superficie; hæc enim admittens longitudinem ac latitudinem, sola crassitudine caret, illa sola longitudine contenta est: solidum autem, & longum, & latum, & profundum requirit esse. Qua propter, vt ritè ipsum con-

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160 LEXICON ... and this the more so because the thicker they are, the more it seems so, and the more the elliptical figure in the sun is enlarged. 30. To define its true magnitude is impossible; its apparent magnitude, difficult beyond measure. Although Kepler asserts that it is plain enough that the Sun’s diameter in apogee is 30 minutes, and in perigee 31, which, however, Ricciolus derides in book 3, chapter 10. The reason for this difficulty is both the deception of the instruments and the interposition of the penumbra, which always varies and disturbs its apparent figure; hence also it appears larger near the horizon (as do the other stars) than near the meridian. Commonly, however, the diameter seen is reckoned at 3 minutes, and consequently its magnitude is concluded to be so great as to contain 166 and two-thirds times the magnitude of the earth, as Clavius testifies in his Sphaera. Moreover, the sun is a masculine planet, hot and dry, fortunate by aspect, unfortunate by body, signifying princes, magnates, glory, etc. On this matter see what we said under V. Luminaria. 31. Solicitium Lunae Celsus calls its conjunction with the sun, at which time, he says, and Argolus in De aëbus criticis, book 1, chapter 16, testifies, the Cynocephalus, an animal familiar to Egypt, if it be male, neither sees nor takes food; but if female, it is diminished in blood by the failure of the Moon. Soon after, both light is restored to the eyes and blood to the entrails, as the goddess, in the restoration of her light, has returned through brotherly charity. He adds that this very animal, at the time of the equinox, urinates twelve times in a day, that is, every hour, so great is its agreement and affinity with the luminaries. From this it came about that thereafter the single days and nights were divided into twelve hours, and for that reason they blamed that half-man who is attached to clocks. 32. Solitudo planetae, according to Abraham Avenarre, is when it is separated from its companion by a conjunction of fifteen degrees, or six by aspect, and is joined to no other until it is in that sign; or the planet does not behold it until it is near by a perfect aspect, whichever it may be. See his Introductorium, chapter 7. Solidum, from Euclid, is defined as a body which has length, breadth, and thickness; by which it differs from a line and from a surface. For the latter, admitting length and breadth, lacks only thickness; the former is content with length alone. But a solid requires to be both long, broad, and deep. Therefore, in order rightly to ...

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MATHEMATICVM. 461 cipiamus, debemus imaginari vel lineam quandam sursum, & in latum moueri, vel sanè superficiem in altum tolli. Porrò corpora quæcumque solida diuiditur in sphærica, aut elliptica, quæ nullum latus propriè dictum, nullumque angulum habent, in Prismata, quæ planis continentur, quorum aduersa duo sunt & æqualia, & similia, & parallela, alia verò parallelogramma, & similiter æquales ex aduerso angulos habent; & in trapezia quæ sunt figuræ irregulares, quæ neque angulos neque latera habent æqualia. Solidus autem angulus dicitur esse qui pluribus, quam duobus planis angulis in eodem non consistentibus plano, sed ad vnum punctum constitutis continentur. Egit de solidorum corporum dimensione Euclides integris sex posterioribus libris; Quamquam non desunt, qui ex iis tres tantum Euclidi tribuant, quartum verò & quinum Hypsieli Alexandrino: Sextus autem seu omnium elementorum geometricorum decimus sextus & vltimus, in quo variæ solidorum regulariu[m] sibi mutuò inscriptorum, & laterum eorum comparationes explicantur, nulli dubium quin Francisci Flussatis Candalla opus sit, quos omnes præclarissimis Commentariis illustrauit Christophorus Clauius. < 83.> Solidus etiam numerus per analogiam dicitur ab Arithmeticis qui ex tribus numeris sese mutuò multiplicandibus efformatus fuerit: in qua re numeri ipsi se inuicem multiplicantes lateræ appellari solent, vt sunt 2. 3. 4. respectu 24. Quemadmodum inter solidos numeros connumerantur etiam suo modo & Quadrati, & Cubi, & alij de quibus fusè agit Euclides lib 7. Est enim Quadratus numerus qui æqualiter æqualis est, vel qui sub duobus æqualibus numeris continentur: Cubus autem, qui sub tribus æqualibus numeris. Sic numerus 27. verbi gratia cubus est, quia ex multiplicatione 9. in 3. si: 27. econtrà numerus 28. dicitur quadratus, quia æqualiter æqualis consurgit ex multiplicatione mutua 5. in 5. < 84.> Solidarium communiter appellatur tempus, quo Sol puncta tropicalia ingressus, maximè ab æquatore deflectit; ac proinde tunc maximè reddit dies noctibus inæquales, quasi modo Sol tropicorum limites assequutus stet, nec ultrà progredi audent, sed mox reuertatur ad æquatorem & declinationem incipiat minuere; siue etiam quia tunc temporis per aliquot dies stare videatur, dum insensibiliter in eodem parallelo mouetur nullis ferè spitis, sed perfectis circulis efformatis. Porrò duo sunt solstitia, Æstiuale, quando initium Cancri ingressus Sol efficit maximum diem artifi-

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MATHEMATICVM. 461 If we are to begin, we must imagine either a certain line moving upward and to the side, or indeed a surface being raised in height. Moreover, whatever solid bodies are divided into spherical or elliptical ones, which have neither a proper side nor any angle, into prisms, which are bounded by planes, of which two opposite ones are equal and similar and parallel; others, however, into parallelograms, which likewise have equal opposite angles; and into trapezia, which are irregular figures, which have neither equal angles nor equal sides. A solid angle, moreover, is said to be that which is contained by more than two plane angles not lying in the same plane, but arranged with one point. Euclid dealt with the measurement of solid bodies in the whole of the six later books; although there are some who assign only three of them to Euclid, but the fourth and fifth to Hypsicles of Alexandria. The sixth, however, or the sixteenth and last of all the geometric elements, in which the various comparisons of regular solids mutually inscribed in one another and of their sides are explained, is doubtless the work of Francesco Flussati Candalla, all of which were illustrated by Christophorus Clavius with the most splendid commentaries. < 83.> A solid number is also called, by analogy, by the arithmeticians one that has been formed from three numbers multiplying one another mutually; in which case the numbers themselves, multiplying one another, are customarily called sides, as are 2, 3, 4 in relation to 24. Just as among solid numbers are also reckoned, in their own way, squares and cubes and others, of which Euclid treats at length in book 7. For a square number is one that is equally equal, or which is contained under two equal numbers. A cube, however, is one which is contained under three equal numbers. Thus the number 27, for example, is a cube, because it arises from the multiplication of 9 by 3; conversely, the number 28 is called a square, because it arises as equally equal from the mutual multiplication of 5 by 5. < 84.> The time is commonly called solstitial when the Sun, having entered the tropical points, departs most from the equator; and therefore then above all it makes the days unequal to the nights, as if the Sun, once it has reached the boundaries of the tropics, were standing still and did not dare to go farther, but soon returns to the equator and begins to lessen its declination; or also because at that time it seems to stand still for a few days, while it moves imperceptibly in the same parallel with almost no spurts, but with perfect circles formed. Moreover, there are two solstices, the summer one, when the Sun, entering the beginning of Cancer, makes the greatest day artifi-

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LEXICON 462 cialem, noctemque breuissimam, quam sit in toto anno; & Hyemalem, quando in primo Capricorni gradu consistens facit diem breuissimum, noctem verò longissimam. Hoc autem accidit solum in nostris Regionibus borealibus, & eò magis, quò maior fuerit elevatio Poli: quandoquidem sub æquatore nulla est varia[ti]o, sed continuum æquinoctium. In regionibus verò Australibus nostris Antæcis contrarium accidit; Nam Solstitium æstiuum, & maximam diem artificialem experiri est, Sole ingresso initium Capricorni, Solstitium verò hyemale, & maximam diem, dum Sol lustrat initium Cancri. 55. Solstitij tempore mutationes maximæ in natura sunt: in hyemali otiganum aliique id genus frutices in domibus aridi asseruati illicò efflorescunt. In æstuiali filix vno die florem profert & fructum. Sed & illud obseruatione dignum, quod hyemale vt plurimum setenum affert, adeoque constans, vt eo tempore Aleyones in littore maris nidificare non dubirent. vnde & dies illi serenitatis, Aleyonij dies audiunt: & æstiuale aquas mirum in modum concitat, & adducit, vnde & pluuiis tempus obnoxium valdè est, & Nilus in Ægypto ex occulta naturæ vi ita exundat, vt campos omnes repleat. Hinc iute Virg. 1. Georg. Humida solstitia, atque hyemes optare serenas Air prouidos Agricolas. An quia Cancri signum in cuius initium incidit solstitium æstiuale aequum est. Capricornus autem terteus: vnde, etsi alioqui temporum conditio aliter petat, nihilominus Sole aequum signum intrante, aquas alliciat, & apportet, terreum verò dum intrat, terreas qualitates adeoque siccitatem, & serenitatem adducat: ita acutè philosophatur amicissimus meus Angelus Durarius, vit ingenij liberalitate ac secretiorum naturæ arcanorum cognitione cum paucis numerandus. 56. SORS accipitur aliquando, sed sæpissimè à veteribus Astronomis pro Fortunæ parte, seu horoscopo Lunari, de quo fusè suolo. 57. Sossos idem sonat ac Dioptra apud, aliquos tamen vsutpatur pro Instrumento geometrico ad mensurandas rerum distancias, magnitudines, ac profunditates ideoneo. 58. SOTHIS in sphæra barbarica dicitur Primus decanus Cancri, cuius dispositio est penes Venerem habens significare alacritatem, amabilitatem, &c. 59. SOTHIN adhuc Ægyptiis dicitur Canis Maior Syrius: Vnde &c 90. SOTNIACA PERIODVS dicebatur Annus Magnus Canicu-

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cial, the shortest night there is in the whole year; and the winter one, when it stands in the first degree of Capricorn, makes the shortest day and the very longest night. This, however, happens only in our northern regions, and the more so the greater the elevation of the Pole; since under the equator there is no variation, but a continuous equinox. In our southern regions, however, the opposite happens among our Antaeci; for the summer solstice, and the experience of the greatest artificial day, occurs when the Sun enters the beginning of Capricorn, while the winter solstice, and the greatest day, when the Sun traverses the beginning of Cancer. 55. At the time of the solstice there are the greatest changes in nature: in the winter, oregano and other shrubs of that kind, preserved dry in houses, immediately blossom. In the summer, a fern in one day brings forth flower and fruit. But this is also worthy of note, that the winter usually brings clear weather, and so constant that at that time the Alcyones would not hesitate to nest on the seashore; whence those days of serenity are called Alcyonian days. And the summer greatly stirs up and brings waters, whence it is very subject to rains, and the Nile in Egypt swells so by the hidden force of nature that it fills all the fields. Hence in Virgil, Georgics 1: Humida solstitia, atque hyemes optare serenas Agricolae. Or is it because the sign of Cancer, in whose beginning the summer solstice falls, is watery, while Capricorn is earthy; whence, even if the condition of the seasons otherwise requires it, nevertheless, when the Sun enters a watery sign, it attracts and brings waters, and when it enters an earthy one, it brings earthy qualities, and thus dryness and serenity: so my dearest friend Angelus Durarius philosophizes most acutely, a man to be counted among the few for his generosity of mind and his knowledge of the more secret mysteries of nature. 56. SORS is sometimes taken, but most often by the ancient astronomers for a part of Fortune, or the lunar horoscope, about which elsewhere at length. 57. Sossos has the same meaning as Dioptra, though some use it for a geometrical instrument suitable for measuring distances, magnitudes, and depths. 58. SOTHIS in the barbarian sphere is called the first decan of Cancer, whose disposition is under Venus, and is said to signify cheerfulness, amiability, etc. 59. SOTHIN is still called by the Egyptians the Great Dog Sirius: whence etc. 90. The SOTNIAC PERIOD was called the Great Year of the Dog-

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MATHEMATICVM. 463 laris, de quo vide in V. Annus. < 91.> SPHÆNISCVS, siue Cuncolus apud Geometras dicitur corpus solidum inæqualem habens longitudini latitudinem, ac longitudini, ac latitudini profunditatem. Sunt qui hanc si- guram vocent Bomiscum. < 92.> SPHERA græcè, larinè Globus definitur ex Euclide, quod sit corpus solidum unica superficie contentum; in cuius medio punctum concipiatur ad quod quacunque linea à superficie ducta inueniantur æquales: seù vt habet Theodosius, est transitus circumferentia dimidij circuli, qua fixa diametro eovsq[ue] circumducatur, quovsq[ue] ad locum suum redeat: itavt totum id quod ab arcu semicirculi circumducto descri- bitur dicatur sphæra. Et per hæc patet in quo sphæra differat à circulo, qui, vt in loco diximus, est figura plana sub vna linea comprehensa: itavt terminus circuli sit linea à centro æqualiter ducta; terminus verò sphæræ sit superficies nullis terminis conclusa. Et hæc quidem de spæra vniuersalissimè ac geometricè sumpta. At verò < 93.> SPHERA ab Astronomis magis pressè accipitur pro tota æleisti machina, seu Ætherea regione, sphæticam figuram habente; maximè vero pro primo mobili omnes orbis, ac ælestitia corpora complectente, quæ spatio vnius diei natu- ralis circà tellurem supra certos quosdam polos sibi oppositos voluitur, & rotatur. Quæ insuper pro diuersa habitudine parium telluris ad polos recta, & obliqua denominatur: Et quidem recta, quando polorum neuter supta terram at- tollitur, sed ambo incidunt in horizontem, in qua æqua- tor rectè semper ascendit, transitque per verticem regionis cuiusmodi experiri est in insula S. Laurétij, Tapobrana, Mal- diuiis, aliisque regionibus sub æquatore degentibus, in qui- bus quouis anni tempore dies noctibus sunt æquales, stellæ omnes sunt visibiles, æqualiter ascendunt, & occidunt, at- que æquales semper arcus tam semidiurnos, quam semino- cturnos efformant. Sphæra obliqua est, cuius alter polorum suprà horizontem attollitur, alter infrà deprimitur; qua- lem experiuntur quotquot extrà æquatorem versantur. Et quò magis polus attollitur, eo spæra nuncupatur obliquior, itavt quæ polum habet verticalem dicatur omnium obli- quissima, quæ etiam dicitur parallela, eoquod æquator di- rectè incidit in horizontem, eique sit parallelus: In quibus profectò locis dies maximus est sex mensium: tanto enim temporis spatio Sol lustrat superius hemisphærium discurrendo per sex signa septentrionalia, aut meridionalia, quæ illic nunquam ascendunt, seu emergunt ex horizonte, aut

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MATHEMATICVM. 463 ...of which see in V. Annus. < 91.> SPHÆNISCVS, or Cuncolus, as the geometers call it, is a solid body having length unequal to breadth, and to length and breadth depth. Some call this figure Bomiscus. < 92.> SPHERA, in Greek, larinè Globus, is defined by Euclid as a solid body contained by a single surface; in the middle of which let a point be conceived, to which all lines drawn from the surface are found equal: or, as Theodosius has it, it is the passage of the circumference of a half-circle, which, with the diameter fixed, is carried around until it returns to its place; so that everything described by the arc of the semicircle as it is revolved is called a sphere. And by this it is clear in what way the sphere differs from the circle, which, as we said in its place, is a plane figure enclosed by one line: so that the boundary of a circle is a line drawn equally from the center; but the boundary of a sphere is a surface enclosed by no boundaries. And this indeed is about the sphere taken in the most universal and geometric sense. But in truth < 93.> SPHERA is taken more strictly by astronomers for the whole celestial machine, or the ethereal region, having a spherical figure; but especially for the first mobile, comprising all the spheres and heavenly bodies, which in the space of one natural day revolves and turns around the earth, above certain opposed poles. Moreover, according to the different relation of the parts of the earth to the poles, it is called right and oblique. And indeed it is called right when neither of the poles is raised above the earth, but both meet the horizon, in which the equator ascends straightly and passes through the zenith of the region, as may be experienced in the island of St. Lawrence, Tapobrana, the Maldives, and other regions living under the equator, in which at any time of the year the days are equal to the nights, all the stars are visible, they ascend and set equally, and always make equal arcs, both semi-diurnal and semi-nocturnal. An oblique sphere is one of which one pole is raised above the horizon and the other depressed below it; such as are experienced by all who dwell outside the equator. And the more the pole is raised, the more oblique the sphere is said to be, so that that which has the pole vertical is called the most oblique of all; it is also called parallel, because the equator falls directly on the horizon and is parallel to it. In such places indeed the longest day is of six months: for so long a time the Sun traverses the upper hemisphere, passing through the six northern or southern signs, which there never rise, or emerge from the horizon, or

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464 LEXICON. occultantur: ac similiter nox est sex mensibus longa, dum scilicet Sol in signis oppositis semper delitescentibus reperi- tur. Hinc etiam in istis locis vnicus dies naturalis comple- tur integro anno. Porrò ex diuisione sphæræ in rectam, & obliquam consurgit etiam diuersitas Ascensionum, graduum scilicet æquatoris, & partium illis respondentium, diuisio- que illarum in rectas, & obliquas: in Recta enim Ascensiones omnes sunt rectæ, in obliqua obliquæ, nec sibi in- uicem respondenres, sed quò magis obliqua fuerit sphæra, eò magis obliquæ erunt arcuum ascensiones, & consequen- ter maior portio graduum æquatoris supra horizontem ascendent. In hac etiam sphæra, ad siderum motus, variasque affe- ctiones declarandas concipiunt Astronomi certos quosdam circulos vt æquatorem, coluros, tropicos, aliosque suo loco descriptos, quos omnes oculis exhibet contem- plandos. 94. SPHERA MATERIALIS Instrumentum videlicet Astrono- micum ad sphæræ cælestis similitudinem efformatum, in quo quidquid in cælo imaginamur, siue circulos, siue polos, si- ue axem mundi, siue situm; id omne per materiales notas, ac circulos, seu sensibiles armillas sibi inuicem coherentes exhibetur ad rerum facilem notitiam comparandam: Ea- que duplex est Arathea, ex globo vndequaque solido in cuius extima superficie ea omnia, ac stellæ fixæ suis quæque locis sunt descriptæ: & Armillaris solidis tantum armillis constans: quæ tamen ad viuum cælorum motus, aliasque siderum affectiones representant, de quibus suo loco dictum. 95. Quoniam autem non ipsum modò Cælum supremum, seu Primum mobile, sed & singuli orbes inferiores suos peculia- res motus, ac periodos habent, ideò ad eorum varietatem facilius indicandam, Astronomi cum Arist. 12. Met. text. 44. modò nouem, modò decem, modò vndecim sphæras in Cæ- lo constituerunt, quarum quæcumq[ue] superior inferiorem sibi contiguam, & concentricam circumferret, idque ad sal- uandas apparentias, atque omnes irregularitates, quas in motibus istis conspicabantur, haud considerantes idem duo- bus motibus contrariis cieri non posse. Itaque Vndecimam Sphæram dicebant esse Primum Mo- bile, quæ vniformi, regulari, concitatissimo motu super mundi polos; vt dictum est, ab oriente in occidentem vo- luitur spatio vnius diei naturalis, secumque omnes infetio- res orbes ac sphæras rapit. Decimam sphæram dicebant, quæ motu librationis à

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are hidden; and likewise the night is six months long, while, that is to say, the Sun is found in opposite signs, always remaining concealed. Hence also in those regions a single natural day is completed in a whole year. Moreover, from the division of the sphere into right and oblique there arises also a diversity of ascensions, namely of the degrees of the equator and of the parts corresponding to them, and a division of those into right and oblique: for in the Right Sphere all ascensions are right, in the oblique, oblique, and not corresponding to one another; but the more oblique the sphere is, the more oblique will be the ascensions of the arcs, and consequently a greater portion of the degrees of the equator will ascend above the horizon. In this sphere also, for the purpose of explaining the motions of the stars and their various affections, astronomers conceive certain circles, such as the equator, colures, tropics, and others described in their proper place, all of which the eye is given to contemplate. 94. MATERIAL SPHERE, namely, an astronomical instrument fashioned after the likeness of the celestial sphere, in which whatever we imagine in the heavens, whether circles, or poles, or the axis of the world, or position, all this is displayed by material marks and circles, or sensible rings cohering with one another, in order to provide an easy knowledge of things: and it is of two kinds, the Arathea, made from a globe solid throughout, on whose outer surface all those things, and the fixed stars, each in their proper places, are described; and the armillary, consisting only of solid rings: which nevertheless represent, as it were alive, the motions of the heavens and the other affections of the stars, about which it has been spoken in its proper place. 95. But since not only the highest Heaven itself, or the Primum Mobile, but also the individual lower spheres have their own particular motions and periods, therefore, in order to indicate their variety more easily, astronomers, with Aristotle 12 Metaphysics, text. 44, have established sometimes nine, sometimes ten, sometimes eleven spheres in the Heaven, any one of which superior sphere would carry around the inferior sphere contiguous and concentric with it, and that for the saving of appearances and all the irregularities which they observed in these motions, not considering that the same thing cannot be set in motion by two contrary motions. Thus they said that the Eleventh Sphere was the Primum Mobile, which with uniform, regular, and most rapid motion revolves above the poles of the world, as has been said, from east to west, in the space of one natural day, and carries along with it all the lower orbs and spheres. They said that the Tenth Sphere was that which, by a motion of libration, from a...

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MATHEMATICVM. 461 septentrione in Austrum, atque ab Austro in septentrionem moueretur sub Coluro solstitiorum primi mobilis per min. 24. vltrò, cirroque remeans, & circulum non perficiens: cuius morus inæqualitas obseruata est in stellis fixis, & maxima Solis declinatione. Censebant autem huius librationis spatium esse annorum 3432. Nona Sphæra erat quæ motu quoque librationis ab ortu ad occasum & iterum ab occasu ad ortum concipiebatur moneueri sub Ecliptica decimæ sphæræ, & super polos eiusdem per minuta 40. spatio annorum 1716. Octaua Sphæra est Firmamentum, & locus fixarum de quo sæpius dictum, quam præter triplicem motum à superioribus sphæris acceptum, dabam moueri super Eclipticæ polis spario annorum 25798. obseruabant enim distârias stellarum fixarum à punctis solstitialibus, & æquinoctialibus non manere semper easdem, sed successiuè crescere, & augeri versus orientales partes. Sequebantur postea planerarum propriæ cuique sphæræ, Saturni, quæ præter quatuor iam dictos morus haberet suum proprium ab occidente in ouienrem annis ferè 36. Iouis, quæ similiter ab occasu in ortum circulationem suam compleret in annis ferè 12. Martis, quæ in duobus, Solis, quæ integro anno, seu diebus 365 & ferè sex horis. Veneris, & Mercurij quæ ferè in vno anno. Tandem Lunæ, quæ circulum suum perageret ferè in mense hoc est diebus 27. & horis ferè 8. Et hæc quidem communis Astronomorum sententia fuit, & etiam nùm apud plurimos viget de pluralitate, ae distinctione coelestium orbium, quoniam, vt dixi cælos constituebant solidos, nec poterant alioqui saluare motuum apparentias. Verum quia modò ex tempore Tychonis iam Cæli fluidi facti sunt, & optimè saluari possunt omnes apparentiæ non modò per vnum coelum, per cuius expansum sidera omnia suo quæque motu discurrant, sed etiam per vnicum motum, ideò nos vnicam tantum sphæram mobilem cum recensiorum peritissimis constituimus, & vnum motum Qua de re vide iam dicta in V. Calum, & in V. Motus. Sphæra etiam dicitur à Philosophis, atque Astronomis sparium quoddam orbiculariter definitum, ad quod se extendit virtus agentis, atque in sideribus exrensio lucis, intrà cuius ambitum dicunrur habere familiaritarem, atque aspectus platicos: ita vt extensio lucis Sarurni sit ad gr. 10. Iouis ad 1. Martis ad 7. cum dimidio. Solis ad 17. veneris ad 8 Mercurij ad 6. Saturni ad 11. cum dimidio. Fixaru[m] primæ magnitu-

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MATHEMATICVM. 461 from north to south, and from south to north it moved beneath the solstitial colure of the first mobile by 24 minutes beyond, and returning with a bend, not completing the circle: the inequality of whose motion was observed in the fixed stars, and in the greatest declination of the Sun. They judged, moreover, the space of this libration to be 3432 years. The ninth sphere was that which, by a motion also of libration, was conceived to be moved from east to west and again from west to east under the Ecliptic of the tenth sphere, and over its poles, by 40 minutes in the space of 1716 years. The eighth sphere is the Firmament, and the place of the fixed stars, of which mention has often been made; and besides the threefold motion received from the higher spheres, it was said to move over the poles of the Ecliptic in the space of 25,798 years. For they observed the distances of the fixed stars from the solstitial and equinoctial points not to remain always the same, but successively to grow and increase toward the eastern parts. After these followed the proper spheres of the planets, each one its own: that of Saturn, which besides the four motions already mentioned had its own proper motion from west to east in about 36 years. That of Jupiter, which similarly completed its circulation from west to east in about 12 years. That of Mars, in two years. That of the Sun, in a full year, or 365 days and about six hours. That of Venus, and Mercury, in about one year. Finally that of the Moon, which would perform its circle in about a month, that is, in 27 days and about 8 hours. And this indeed was the common opinion of the Astronomers, and even now among many it prevails concerning the plurality and distinction of the celestial orbs, because, as I said, they established the heavens as solid, and otherwise could not have saved the appearances of the motions. But because now, since the time of Tycho, the heavens have become fluid, and all appearances can be most excellently accounted for not only by one heaven, through whose expanse all the stars may run each in its own motion, but also by a single motion, therefore we establish only one movable sphere, together with the most skilled of the later writers, and one motion. On this matter, see what has already been said in V. Calum, and in V. Motus. A sphere is also called by Philosophers and Astronomers a certain space defined circularly, to which the force of the agent extends itself, and, in the stars, the extension of light; within whose bounds they are said to have familiarity and a platonic aspect: so that the extension of the light of Saturn is up to 10 degrees; of Jupiter up to 1; of Mars up to 7 and a half. Of the Sun up to 17; of Venus up to 8; of Mercury up to 6; of Saturn up to 11 and a half. The first magnitude of the fixed stars...

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LEXICON 466 dinis ad gr. 7. & semis, secundæ ad 5. min. 30. Tertiæ ad gr. 30. min. 40. Quartæ ad gr 1. min. 30. Quintæ ad mi- nut. 50. &c. 48. SPICA VIRGINIS, arab. Azimech, dicitur stella fixa primæ magnitudinis benignissima, de natura Veneris, & Mercurij, existens in manu Virginis, atque in longitudine gr 19. Li- bræ cum ferè 1. latitudinis meridianæ. Ea hoc peculiare ha- bet præ cæteris stellis, vt diuitiarum, & bonorum tempo- ralium affluentiæ sit naturalis significatrix, itavt in secunda, vel cum Parte fortunæ, aut cum Luminaribus reperta ferè semper immensas afferat diuitias: econtrà cum Saturno mendicitatem. In horoscopo etiam, vt notat Argolus de diebus criticis lib. 1. cap. 6. tribuit morum grauitatem, ac naturaliter ad religionem piumque affectum inclinat. Aliter verò de ea p[er]tonunciat Pontanus in sua Vrania: sic enim canit. Diversos mores, & pectora dura per ortum Spicadabit: frumenta feret, graue figet aratrum; Mella fauis expressa liques, nihil vsque remittens Ad vita varios vsus. Maria alia secabit Piscator, nunc casse cibum: nunc comparat hamo: Dat varios animi fluctus, & pectora turbat. At enim de eadem in occasu reperta cum prauo maleficarum radi o statim subdit. Iratus miseram famen, illauiemque minatur At Mauors furtidamnat, populoque reposcens Annonam dictis, & poena crimen acerbat. Quinpendat sacrum laniato corpore furtum Et populo spectante lacer dat sanguine poenas. Oritur Romæ spica cum gr. 10. libre circa duodecimam diem Octobris, occidit cum gr. 15. eiusdem. Vide quæ diximus in V. Azimech. 49. SPICARVM MANIPULVS dicta est ab aliquibus Coma Bere- nices, fidus ad caudam Leonis, de qua vide suo loco, nec non in V. Triches. 100 SPIRÆ dicuntur circuli non perfecti, seu qui non in seip- sos recurrunt, sed aliqualiter deuiant, quales sunt funium inflexiones, & complicationes serpentium, quo sensu ceci- nit Poëtarum princeps lib. 3. Georg. Squammens in spiram tractu se colligit anguis. Hinc Astronomi siderum diurnas revoluciones, quibus in eundem circulum positionis redeunt, sed non in idem cir- culi punctum, spirales appellant. 101 Ex quibus liques quomodo etsi singulis diebus promissores

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LEXICON 466 of the first magnitude, very benign, of the nature of Venus and Mercury, existing in the hand of Virgo, and in longitude 19 degrees Libra, with almost 1 degree of southern latitude. This has the special property above the other stars, namely that it is a natural significator of wealth and abundance of temporal goods, so that, when found in the second house, or with the Part of Fortune, or with the Luminaries, it almost always brings immense riches; on the contrary, with Saturn, beggary. In a horoscope also, as Argolus notes in De diebus criticis , lib. 1, cap. 6, it grants seriousness of character, and by nature inclines one toward religion and a devout disposition. But Pontanus speaks otherwise of it in his Urania ; for thus he sings: By rising, Spica gives diverse manners and hard hearts; It brings grain, and drives the heavy plough; Honey pressed from the combs it makes to flow, not withholding anything For the varied uses of life. One seaman cuts the seas, Now a catch for food; now he prepares with the hook: It gives various motions of the mind, and disturbs the heart. But of the same star, found in the setting with the evil ray of the malefics, he immediately adds: In anger it threatens wretched hunger and emaciation; But Mars condemns theft, and, demanding from the people Their food by his words, aggravates the crime with punishment. Let him even pay for the sacred theft with his torn body, And, with the people looking on, let him give satisfaction with blood, torn apart. It rises at Rome when Spica is at 10 degrees Libra, about the twelfth day of October; it sets when it is at 15 degrees of the same sign. See what we said under the word Azimech. 49. THE SHEAF OF EARS OF CORN is called by some the Hair of Berenice, a fixed star at the tail of Leo; see about it in its proper place, and also under the word Triches. 100. SPIRALS are called circles that are not perfect, or those which do not return into themselves, but deviate in some measure, such as the bends of ropes and the coils of serpents; in this sense the prince of poets sings in book 3 of the Georgics : The winding serpent gathers itself into a spiral path. Hence astronomers call spirals the daily revolutions of the stars, by which they return to the same circle of position, but not to the same point of the circle. 101 From which you may understand how, although on each day promissors

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MATHEMATICVM. 467 ferantur in circulos positionis significatorum, non tamen inducere effectum directionis; nisi post annum pro singulis gradibus; quia profectò non redeunt ad amussim in eundem situm significatorum, sed ante definitum tempus vel città vel vltrà: definito autem tempore expletis omnibus spirali- bus circulationibus, incidunt immediatè in dicta loca, vnde & effectum statim inducunt. < 102> SPLENDOR est lux à corpore luminoso diffusa, quæ dicitur lux de luce, adeoque est reflexio recepti luminis. Vnde pro- priè loquendo, splendor differt à radio, quod hic est dire- ctus, ille semper reflexus; hic proflit à corpore luminoso, seu prædito ab intrinseco luce, tanquam propria ipsius pas- sio, splendor autem à corpore illuminato, quod in seipso, cum aliàs opacum sit, & ex leuigatione aptu recipere extrin- secus lucem ipsam remittit, quæ proinde aliud non est, quam radius ipsius corporis luminosi, ab eo in corpus illu- minandum immissus, æque ob eius densitatem in seipsum reuersus; vt accidit in speculo, in lapide pretioso, & simi- libus. Hac ratione quoniam Sol vt supra dictum est, est fons totius lucis, sidera autem lucem suam soli acceptam referunt, ideò radius propriè Soli conuenit, splendor au- tem sideribus. < 103> SPORADES apud Astronomos sæpissimè appellantur stellæ quædam informes in Firmamento dispersæ, neque adhuc in certas imagines coarctaræ, quale sunt Arcturus consistens inter crura Bootis, aliquæ supra Lances Libræ, multæ circa Canem maiorem, &c. Dictæ sum autem Sporades, sumpra analogia à Sporadibus Insulis circa Cretam in Mari Carpa- thio consistentibus, quæ à Ptolemæo, non sunt descriptæ, neque in vniuersali Orbis delineatione comprehensæ. < 104> STATIO apud Astronomos audit consistentia illa planetarum in suo Epicyclo, vbi maximè à centro elongantur (in- tellige respectu Zodiaci (æque incipiunt fieri directi, aut retrogradi. Pro cuius rei intelligentia sciendum est, omnes planetas excepta Lunâ moueri in suo orbe parvo, quem di- cimus Epicyclum, circà Solem quem retinent pro centro (vt docet iam plausu omnium recepta Tychonis sententia,) & interim tum ipsos, tum ipsorum maiores orbes deferentes raptari motu primi mobilis, quod quia sui repectatione exæquare non possunt, instituunt alium secundum motum sub Zodiaco secundum successionem signorum, quem nos proprium vocamus ad differentiam motus vniuersalis, provt ex apparentiis obseruamus. Interim corpora Planetarum mouentur, vt dixi regulariter, & continuò in suo Epÿcyclo,

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MATHEMATICVM. 467 are carried into the circles of the significators’ positions, yet they do not produce the effect of direction; unless after a year for each degree; because they do not in fact return exactly to the same position of the significators, but before the fixed time, either sooner or later: but at the fixed time, when all the spiral circulations have been completed, they fall immediately into the said places, and thus produce the effect at once. < 102> SPLENDOR is light diffused from a luminous body, which is called light from light, and therefore is a reflection of received light. Hence, pro- perly speaking, splendor differs from a ray, in that the latter is direct, the former always reflected; the latter proceeds from a luminous body, that is, one endowed intrinsically with light, as its own passion, whereas splendor comes from an illuminated body, which in itself, since it is otherwise opaque, and by polishing is fitted to receive the light from outside and send it back, is therefore nothing else than a ray of the luminous body itself, sent from it into the body to be illuminated, and, owing to its density, returned into itself; as happens in a mirror, in a precious stone, and the like. For this reason, since the Sun, as has been said above, is the source of all light, but the stars refer their own light received from the sun, therefore a ray properly belongs to the Sun, but splendor to the stars. < 103> SPORADES among Astronomers are very often called certain shapeless stars scattered in the Firmament, not yet confined into definite images, such as Arcturus, standing between the legs of Bootes, some above the Scales of Libra, many around Canis Major, etc. They are called Sporades, by analogy with the Sporadic Islands around Crete in the Carpathian Sea, which were not described by Ptolemy, nor included in the universal delineation of the World. < 104> STATIO among Astronomers signifies that state of the planets in their Epicycle, where they are most removed from the center (understand with respect to the Zodiac), and begin equally to become direct or retrograde. For the understanding of this matter it must be known that all the planets except the Moon move in their small orbit, which we call the Epicycle, around the Sun, which they retain as their center (as the now universally accepted opinion of Tycho teaches), and meanwhile both they and their greater deferent orbits are carried along by the motion of the first mobile; which because they cannot balance by their own counter-motion, they institute another secondary motion under the Zodiac according to the succession of the signs, which we call proper, by difference from the universal motion, as we observe from appearances. Meanwhile the bodies of the planets move, as I said, regularly and continuously in their Epicycle,

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LEXICON 468 dumque mouentur, quatuor in eo designant puncta dehorantia varias passiones, quibus afficiuntur eireà motum, & illustrationem à Sole. Primò Apogæum, vbi maximè remouentur à terra, & sunt omnes supra Solem in gradu eclipptico eidem coniuncti, vnde incipiunt fieri Superiores quidem orientales, inferiores occidentales, & augeri lumine. Secundum punctum est Perigæum, vbi sunt infra solem maximè terræ vicini: hiem coniucti eidem Soli in gradu Ecliptico, atque exinde incipiunt esse superiores quidem occidentales, inferiores verò orientales, & lumine minui. Reliqua duo puncta hinc inde ad angulos rectos, in quibus planetæ maximè à Sole elongantur, dicuntur stationes, quia ascendentes ad Apogæum, ac descendentes ab eo ad Perigæum, videntur quodammodò stare, dum non permutant situm in Zodiaco: Et prima quidem statio dicitur, cum à dextris Solis consistunt, & incipiunt rei tocedere in Zodiaco transeundo per Perigæum vsque ad secundam stationem. Hæc verò dicitur secunda statio, quia existentes à sinistris Solis incipiunt fieri directi, & moueri in consequentiam signorum per totam illam medietatem Epicycli vsque ad primam stationem. Hoc totum expressè videtur in Systemate Tychonis, ac præsertim in duobus satellitiis Solis, Venere, & Metcurio. Hinc 105 STATIONAR. vs dicitur planeta existens eireà primam, & secuudam stationem, vt modò explicuimus, ascendens vel descendens in suo Epicyelo ad Apogæum, vel Perigæum; iiavt in Zodiaco vel nullatenus, vel certè insensibiliter moueatur, sed persistat diu in eodem gradu quamdiù ascendit; vel descendit in partibus illis sui orbis, quę directè subsunt vni gradui Zodiaci. 106 STELLA, græcis Astrum est corpus sphæricum lucidum, siue sua, siue aliena luce præfulgens in ætherea regione, ac sua pulehitudine mirè intuentium oculos rapiens, & præst: ingens: ex quo Astri nomen derivatum existimat Plato in Cratilo. Dicitur autem promiscuè tam de erraticis quinque, quarum singulæ suo motu proptio ab aliis diffetente mouentur ab occasu ad ortum, quam de fixis in Firmamento, quæ mouentur omnes simul eum suo orbe motu itidem proprio, ab oceidente in orientem. Et hæ stellarum sibi nomen retinent, (nam illæ proprio nomine Planetæ appellantur) & sunt propemodum infinitæ in expanso Firmamenti dispersæ, atque in varios asterismos, quæ sidera dicta sunt, dispositæ, & ordinatæ. Guius autem substantiæ sint, est prorsus ignotum. Hoc planè certum est, eas neque igneas esse, vt rolebat

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LEXICON 468 and while they are moving, they mark in it four declining points, indicating various passions by which they are affected because of motion and illumination from the Sun. First, the Apogee, where they are most removed from the earth, and are all above the Sun in the ecliptic degree joined to it; from which they begin to become superior eastern, inferior western, and to increase in light. The second point is the Perigee, where they are most near the earth, beneath the Sun; there joined to the same Sun in the ecliptic degree, and from there they begin to become superior western, and inferior eastern, and to diminish in light. The remaining two points on either side at right angles, in which the planets are most removed from the Sun, are called stations, because, ascending toward the Apogee and descending from it to the Perigee, they seem in a certain way to stand still, while they do not change their position in the Zodiac. And the first station is said to be when they are on the right of the Sun, and begin to retrograde in the Zodiac, passing through the Perigee as far as the second station. This is called the second station, because when they are on the left of the Sun they begin to become direct, and to move in the sequence of the signs through that whole half of the epicycle as far as the first station. All this is expressly seen in the system of Tycho, and especially in the two satellites of the Sun, Venus and Mercury. Hence 105 STATIONARY is said of a planet existing between the first and second station, as we have just explained, ascending or descending in its epicycle toward the Apogee or Perigee; so that in the Zodiac it either not at all, or certainly imperceptibly, moves, but remains for a long time in the same degree as long as it ascends or descends in those parts of its orbit which lie directly beneath one degree of the Zodiac. 106 STAR, among the Greeks Astrum, is a spherical luminous body, shining with either its own or another’s light in the ethereal region, and by its beauty wonderfully seizing the eyes of those who behold it, and exceedingly great: from which the name of Astrum is thought by Plato in the Cratylus to have been derived. It is used indifferently both of the five wandering stars, each of which is moved by its own proper motion differing from the others, from west to east, and of the fixed stars in the Firmament, which all move together with their sphere, likewise by their own motion, from west to east. And these retain the name of stars, whereas those are called Planets by their proper name, and they are dispersed almost infinitely throughout the expanse of the Firmament, and arranged and ordered into various asterisms, which are called constellations. But of what substance they are is wholly unknown. This is certainly clear, that they are neither fiery, as

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MATHEMATICVM. 109 Volebat Plotinus neque ex densiori aëre, vt Anaximander, neque adamantinas, vt plures Periparetici, sed ex substan- tia ætheris puriore nobis ignota. An autem eandem eum sublunaribus hisce materiam liabeant valdè inter Philoso- phos controuertitur. Ego sanè non aliunde id affirmarim, nisi ob qualitatum similitudinem, conuenientiam, actiuitatem in ipsa, quæ clarè indieant in vtrisque aliquid esse commu- ne, vt dixi cum de Sole. 107 Cæterum stellarum numerum innumerabilem esse censendum est; licet Ptolemæus & antiquiores 1022. tantum visibili enumerent, quas nec plures, nec pauciores esse conten- dit Clauius, sed etsi aliquando in hyeme plures appareant, ait visum hallucinari. Reeensiores verò ferè omnes longè plures constituunt. Griembergerus 1225. Keplerus 1392. Bayerus 1709. Schickardus, & Schillerus 1692. Sed etsi omnes, quæ nuper Telescopio detectæ sunt numerare velimus, defieiet animus, eum propè infinitæ esse comperiantur. Ior- danus Brunius eas reipsa infinitas esse asserere non dubita- uit lib... de infinito, & mensurabilibus. Equidem Galilæus, vt, testatur in Nuncio sidereo in sola nebulosa Orionis 21. numero stellas conspicatus est, in nebulosa Præsepis 36. in Pleiadibus plusquam 40. atque in Orione intervnius, alte- riusve gradus spatium numerauit plusquam 500. adeo vt de- territus, ac labore fractus manum subtraxerit ab enume- ratione totius Imaginis, quam expingere decreuerat, ac sectoribus exhibere spectandam parauerat in suo Nuncio. In finem non dubitat affirmare quin ex omnes sint numero 10000. & eò amplius. Reita in Orione stellas quasi bis mille se tubo obseruasse testatur. Ex quibus omnibus con- cludit Ricciolus in Almagesto: Itaque si quis stellas ultrà vices centena millia patet, mihi quidem nihil inopinabile sinxerit. De stellarum efficientia diximus in V. Fixa de fein- tillatione, eiusque causa in V. Scintillatio. Denique de singularum præsertim insigniorum qualitatibus, loco, ma- gnitudine, lumine, proprietate, aliisque suis quibusque locis. 108 STEREOMETRIA vna est ex non infimis Mathesis discipli- nis Geometriæ subalterna, quæ agit de solidorum corporum dimensione. 109 STILPON dicitur græcè Mercurij Astrum, hoc est radians; eoquia præ cæteris planetis mirè scintillat, & emissitiam quamdam lucem habet. Hihe etiam STILPONTES apud nonnullos vocantur cætera astra quam- diu in motu sunt, & ex occulta quadam qualitate intensius 110 Gg

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MATHEMATICVM. 109 Plotinus wanted it not from denser air, as Anaximander did, nor from adamantine matter, as most of the Peripatetics did, but from a purer substance of the ether unknown to us. Whether he held that the same matter is present in these sublunar things is very much disputed among philosophers. I certainly would not affirm it on any other grounds than the similarity of qualities, suitability, and activity in it, which clearly indicate that in both there is something common, as I said when speaking of the Sun. 107 Moreover, the number of the stars must be judged innumerable; although Ptolemy and the ancients enumerate only 1022 visible ones, which Clavius maintains are neither more nor fewer, yet even if sometimes in winter more appear, he says the sight is deceived. But nearly all later writers place far more. Griembergerus 1225, Kepler 1392, Bayer 1709, Schickard and Schiller 1692. But even if we wish to count all those that have recently been discovered by telescope, the mind will fail, since they are found to be almost infinite. Jordanus Brunius did not hesitate to assert in his book De infinito et mensurabilibus that they are in fact infinite. For my part, Galileus, as he testifies in the Nuncius sidereus , saw 21 stars in the mere nebula of Orion, 36 in the nebula of Praesepe, more than 40 in the Pleiades, and in Orion between one and another degree of distance he counted more than 500; so that, struck with fear and exhausted by the labor, he withdrew his hand from the enumeration of the whole figure, which he had decided to depict and prepared to display for spectators in his Nuncius . In the end he does not hesitate to affirm that there are 10,000 and more. Reita testifies that he observed as many as two thousand stars in Orion with the tube. From all these things Ricciolus concludes in the Almagest : “Therefore if anyone should prove stars to be beyond twenty hundred thousand, indeed nothing in it would seem improbable to me.” We spoke of the efficacy of the stars in V. Fixa, of scintillation and its cause in V. Scintillatio. Finally, concerning the qualities, position, magnitude, light, property, and other attributes of each one, especially the more notable ones, see their respective places. 108 STEREOMETRIA is one of the not least branches of mathematics, subordinate to geometry, which deals with the measurement of solid bodies. 109 STILPON is called in Greek the Star of Mercury, that is, the radiant one; because among the other planets it sparkles wonderfully, and has a certain emitted light. It is also STILPONTES, among some, called the other stars so long as they are in motion, and from some hidden quality more intensely 110 Gg

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L E X I C O N 470 lumen vibrant, radiosque aliquot extraordinarios eiaculancur. III. STIPATORES propriè audiunt planetæ Solem constipantes, ac circà ipsum veluti in proprium centrum sese voluentes, quales in omnium sententia sunt Venus, & Mercurius, & secundum Tychonem etiam superiores Mars, Iupiter, & Saturnus. Porro hi duo posteriores suos Item habent inferioris notæ stipatores minores stellas, Saturnus quidem duas, Iupiter quatuor, quæ â Galilæo oculatissimo Astronomo non ità pridem detectæ sunt ope sui admirabilis Telescopij: de quibus in Saturno, & Iove, & in V. Medices stella abundantis dictum est. Cæterum stipatorium nomine aliquando veniunt sidera omnia, & planetæ corpore, aut radio Luminaribus assistentes: quæ de re vide in V. Satellitium. <112> STROBLEVE, & Lelaps ex Arist. in lib. de Mundo cap. 3. dicitur ventus de Typhonum genere, qui infernè spirans, fursum versus repente conuoluitur. Huic affinis est Thyella flatus inquam qui repente p[er]tosit, & Cathægis, & Anaphysema de quibus suo loco. <113.> SVBLVNARIA dicuntur omnia corpora infra Lunam consistentia, qualia sunt Elementa, mixta omnia tam perfecta, quam imperfecta; tam inanimata, quam animata irrationabilia, quæ omnia, vt habet Deotus in 2. sentent. aist. 14. subsunt corporum cælestium, præsertim verò Lunæ (vnde iis nomen deriaturum est) impressionibus: habet enim Luna actionem in omnes humores, eos augendo dum lumine crescit, minuendo dum decrescit: habent & omnia sidera in elementa, eadem alterando, corrumpendo, in alia transmutando: habent in mixta imperfecta, cuiusmodi sunt fossilia, lapides pretiosi, meteora, quæ siue in terræ visceribus, siue in aërea regione generantur ex congressu planetarum eum aliquibus sixis, vt experientia ipsa demonstrat: habent super mixta perfecta, vt sunt metalla, quæ in quibusdam regionibus generantur ex constellatione habente respectum ad illas tantum regiones, & non ad alias: habent super vegetabilia, quatenus ex eorum accessu, & recessu ad certas partes Zodiaci germinant, aut languescunt: habent super animantia sensitiva, alterando scilicet eorum corpora ad qualitatem animæ conuenientem, vel disconuenientem, sieque vim habent ad eorum generationem, & corruptionem. Super hominem autem non habent actionem, nisi inquantum sensu, & vegetatione præditus est; non autem inquantum homo hoc est rationalis præditus intellectu, & voluntate, nisi indirectè, & per accidens, per

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L E X I C O N 470 lumen vibrant, and emit several extraordinary rays. III. STIPATORES properly mean planets accompanying the Sun, and revolving around it as though toward their own center, such as, in the opinion of all, are Venus and Mercury, and according to Tycho also the superior planets Mars, Jupiter, and Saturn. Moreover, these two latter likewise have their own smaller attendants of an inferior rank, namely the smaller stars; Saturn indeed two, Jupiter four, which were not long ago discovered by the very sharp-sighted astronomer Galileo with the aid of his marvelous Telescope: of which in Saturn, and Jupiter, and in the star of V. Medices, enough has been said. Besides, under the name of attendants are sometimes included all the stars and planets assisting the Luminaries by body or ray: see on this matter V. Satellitium. <112> STROBLEVE, and Lelaps, from Aristotle in book de Mundo, ch. 3, is said of a wind of the Typhon kind, which, blowing from below, suddenly turns upward. Related to this is Thyella, that is, a gust which suddenly breaks forth, and Cathægis, and Anaphysema, of which in their place. <113.> SVBLVNARIA are called all bodies existing below the Moon, such as the Elements, all mixtures, both perfect and imperfect; both inanimate and irrational animate things, all of which, as Deotus has in 2 Sent. dist. 14, are subject to the impressions of the heavenly bodies, especially indeed of the Moon (from which the name is derived): for the Moon has an action upon all humors, increasing them as her light grows, and diminishing them as it wanes: and all the stars likewise act upon the elements, altering them, corrupting them, and changing them into other things: they act upon imperfect mixtures, such as fossils, precious stones, meteors, which, whether generated in the earth’s bowels or in the air region, arise from the conjunction of planets with certain fixed stars, as experience itself demonstrates: they act upon perfect mixtures, such as metals, which in certain regions are generated from a constellation having reference to those regions alone, and not to others: they act upon plants, insofar as by their approach and recession to certain parts of the Zodiac they sprout or wither: they act upon sentient living creatures, namely by altering their bodies to a quality suitable or unsuitable to the soul, and thus they have power over their generation and corruption. But upon man they do not act, except insofar as he is endowed with sense and vegetation; not however insofar as man is that is, rational, endowed with intellect and will, except indirectly and by accident, by

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MATHEMATICVM. 471 connexionem, ac sympathiam, quæ est inter phantasiam, & rationem; & inter appetitum sensitium & voluntatem. Nam organa sensuum quæ sunt corpora mixta possunt immutari, & alterari ad aliquem gradum illis conuenientem, vt nata sunt esse organa sensuum, & etiam ad disconuenientem sensui, & ita posset organum corrumpi & lædi, & perconsequens etiam intellectio & volitio perturbari; quæ à phantasmatibus pendent, & sunt iis quodam nodo alligatæ. Sic videmus in phrênicis, & Lunaticis, in quibus sunt organa læsa, & per consequens imaginatio confusa, & intellectio perturbata, vt nihil rationabiliter operentur: Sic etiam quando appetitus sensitium est corruptus, & alteratus videmus secum trahere voluntatem ad prosequendum quod efficaciter appetit, & ideo propter istam d[e]cordinationem, habent Planetæ & alia corpora cælestia inclinare voluntatem; non autem vllam actionem directam, quia illa est purè spiritualis, libera, & independens, & potest pro sua libertate inclinationibus sensuum constaire. Hinc quia homo secundum meliorem sui partem non subest impressionibus corporum cælestium, & qua præditus est libertate potest sensibus imperare, stellarum in se activitatem præuertere, ideò absolutè sub vniuersali sublunarium aggregatio ne non ycnit, benè verò: cliqua animantia, & corpora inferiora. Hæc omnia ex Scoto loco citato. SVBSOLANVS, græcè Apeliores Ventus v[er]nus, ex quatuor <114> Cardinalibus spirans ditectè ab ortu æquinoctiali, sic dictus, quod sub Sole nasci videtur, natura sua calidus, & siccus temperatè, ideo salubris, corpora seruans, & contagio putrido obsistens. Spirare soler oriente Sole; & nocte vtpurimum <115> quiescit Dicitur etiam ab aliquibus Eurus; qui tamen verè alius à subsolano est, illi collateralis, & similis in qualitate: ob dexionem autem ad austrum acquirit aliquid humiditatis, & in sive turbat aërem, paritque mutationes repentinas, & tonitrua. Subsolanum mouent præcipuè Pleiades cum Sole exorientes: quò tempore si diutius perfet, catharros, & fluxiones excitat: in æstate verò calorem adauget, bilem mouet, febres acutas ingerit cum siti, & maxima ariditate. SVECEDENS dicitur in cælesti figura Domus quæcumque angulum <115.> sequens, qualis est Vnecima, quæ sequitur Angulum Medij cæli; Secunda, quæ angulum Orientis; Quinta, quæ Imum Coeli; & Octava, quæ cardinem Occidentis. Hæ igitur quarior domus succedentes appellantur, non tam ordine quam conditione ac dignitate: in iis enim reperti Gg ii

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MATHEMATICVM. 471 the connection and sympathy that is between fantasy and reason, and between the sensory appetite and the will. For the organs of the senses, which are mixed bodies, can be altered and changed to some degree suitable to them, since they are by nature organs of the senses; and also to a degree unsuitable to sense, and so the organ could be corrupted and harmed, and consequently also understanding and volition disturbed, which depend on phantasms and are in some manner bound to them. Thus we see it in frenzied and lunatic persons, in whom the organs are injured, and consequently the imagination confused and the understanding disturbed, so that they act rationally in nothing. In the same way, when the sensory appetite is corrupted and altered, we see it draw the will along with it to pursue what it effectively desires; and therefore, because of this disorder, the planets and other celestial bodies are said to incline the will, but not to have any direct action, because that is purely spiritual, free, and independent, and can, by its own liberty, resist the inclinations of the senses. Hence, because man, according to his better part, is not subject to the impressions of the celestial bodies, and because he is endowed with freedom can command the senses and anticipate the activity of the stars in himself, therefore he does not absolutely fall under the universal aggregation of sublunary things; but rather, the other living creatures and inferior bodies do. All these things are from Scotus, in the cited place. SVBSOLANVS, in Greek Apeliores Ventus vernus, one of the four cardinal winds, blowing directly from the equinoctial east, so called because it seems to be born beneath the sun; by nature moderately hot and dry, therefore wholesome, preserving bodies, and resisting putrid contagion. It usually blows at sunrise, and at night for the most part it subsides. It is also called by some Eurus; yet this is truly different from Subsolanus, though collateral to it and similar in quality. But because of its inclination toward the south it acquires some humidity, and in a way disturbs the air, and produces sudden changes and thunder. Subsolanus is moved chiefly by the Pleiades rising with the Sun: at which time, if it continues long, it excites catarrhs and fluxes; but in summer it increases heat, stirs up bile, and brings on acute fevers with thirst and great dryness. SVECEDENS is called, in a celestial figure, any house following an angle, such as the eleventh, which follows the angle of the midheaven; the second, which follows the angle of the east; the fifth, which follows the nadir of heaven; and the eighth, which follows the western angle. These four following houses are therefore called succedent, not so much by order as by condition and dignity; for in them are found Gg ii

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472 LEXICON planetæ existimantur mediocriter fortes, ac vires sumere licet non tantas, ac si forem in Angulis. Econtrà in cadentibus fiunt debiles, & maximè deteriorantur: licet id etiam aliquam exceptionem habeat, vt alibi dictum est. 116 Svevæ latinè audiunt quæ apud Græcos Hyades, stellæ videlicet septem in capite Tauri sideris consistentes, procellosæ nimis, ac pluviosæ, sic dictæ, quod quasi sues luto, & humoribus delectari videantur. De his in horoscopo reperis sic pronunciat Firmicus lib.8 cap.6 Natus, inquit, erit inquietus, turbulentus, populatis, & qui plebem turbulentis semper seditionibus exagiter, eius animos clamosis, ac furiosis contentionibus inflammans; inimicus quietis, & pacis: atque intestina, & domestica bella furiosa mentis cupiditate desiderans. Sed huic varij quæstus ex assidua sollicitudine sæpè nascuntur. Pacit enim hoc sidus bubuleos, opiliones, armentarios, ovinumque pastores. Si verò in occasu fuerint inueniæ, & locum istum maleuolarum radius impugnet, repentinum, & insperatum mortis exitium decernitur. Turbulentis enim seditionibus oppressi, & popularibus passim manibus dissipati penitùs interibunt: itavt mortis eorum auctores nec inueniri possint aliquando, nec dici. Hæc Firmicus. Oriuntur Suciæ Romæ die 27. Maij cum gra.8. Geminorum. Plura in V. Hyades. 117 SVHEL arab. latinè Conopus stella fixa fulgentissima de natura Iouis & Saturni, alio nomine Rubail, in temone Argonautis consistens, nobis Italis inconspicua, de qua vide quæ diximus in V. Canopus. 118. SVPERFICIETE, quasi superna facies apud Geometras dicitur extima pars alicuius corporis, quæ oculis excipitur, aut manu tangitur, & vt definit Enciid. lib.1. def.5. quæ longitudinem quidem & latitudine habet, minimè verò profunditatem. In quo differt à puncto, quod nullam admittit dimensionem: à solido quod omnem / ac tandem à linea quæ sola gaudet longitudine, latitudinis, & profunditatis omninò expers: itavt superficii extrema sint lineæ, quibus ipsa interiacet, superficies autem extremum sic corporis solidi. 119 SVPERFORS antonomasticè ab Astronomis dicuntur tres planetæ Saturnus, Iupiter, & Mars, quorum orbis & situs sunt supra Solem: quemadmodum vice versa Inferiores appellantur reliqui Venus, Mercurius, & Luna, eo quia propiùs terris infra Solem consistunt. 120 SYDVS, SYDERATIO, vide SIDVS. 121 SYMMETRIA græcè, latinè proportio, definitur ex Vi-

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472 LEXICON Planetary powers are thought to be moderately strong, and one may take their strength, though not as great as if they were in the angles. On the contrary, in falling positions they become weak and are greatly worsened, though this too has some exception, as has been said elsewhere. 116 Svevæ are in Latin those which among the Greeks are called the Hyades, namely the seven stars situated in the head of the sign of Taurus, excessively stormy and rainy, so called because they seem almost like sows to delight in mud and moisture. Concerning these, Firmicus speaks thus in the horoscope, lib. 8 cap. 6: “The native, he says, will be restless, turbulent, a disturber of the people, and one who always stirs the populace with turbulent seditions, inflaming their minds with noisy and furious strife; an enemy of quiet and peace, and one who desires with furious passion internal and domestic wars. But from such comes often various gain through constant anxiety.” For this constellation suits cattlemen, shepherds, herdsmen, and shepherds of sheep. But if they are found in the west, and the beam of the malevolent planet strikes this place, a sudden and unexpected end of death is decreed. For those oppressed by turbulent seditions, and scattered everywhere by the hands of the people, will utterly perish, so that neither the authors of their death can ever be found nor named. Thus Firmicus. They rise at Rome on May 27 with the 8th degree of Gemini. More in V. Hyades. 117 SVHEL, in Arabic; in Latin Canopus, a most brilliant fixed star of the nature of Jupiter and Saturn, otherwise called Rubail, situated in the prow of the Argo, invisible to us Italians; see what we have said in V. Canopus. 118. SUPERFICIETE, as it were “upper face,” is the term used by geometers for the outer part of any body, which is apprehended by the eyes or touched by the hand, and, as Enclid. lib. 1 def. 5 defines it, has length and breadth, but by no means depth. In this it differs from a point, which admits no dimension; from a solid, which admits all dimensions; and finally from a line, which enjoys only length, being entirely without breadth and depth: so that the boundaries of a surface are the lines in which it lies between; but a surface is the outer limit of a solid body. 119 SUPERFORS are called by astronomers, by antonomasia, the three planets Saturn, Jupiter, and Mars, whose orbit and position are above the Sun; just as, conversely, the Inferiors are called the remaining Venus, Mercury, and the Moon, because they lie nearer the earth below the Sun. 120 SYDVS, SYDERATIO, see SIDVS. 121 SYMMETRIA, in Greek, in Latin proportion, is defined from the Vi-

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MATHEMATICVM. 475 trupio lib. 1. cap. 2. esse ipsius operis membris conuenientem consensum, ex partibusque separatis ad vniuersæ figuræ speciem ratæ partis responsum, ea est facultas ex geometricis præceptis compara[ti]o[n]e, quæ præstat in Architectura, vt iuxta naturæ ordinem partes alicuius structuræ respondeant ad totum, docetque ex amplitudine domus, quanta debeat esse longitudo, & latitudo, quantæ amplitudinis vestibulum, quanta columnarum moles fenestratum interstitia, &c. vt in statua vt ex pedis, aut manus mensura colligatur quanta debet esse proportio exterorum membrorum: vt verus illud Adagium: Ex vignue leonem. Hinc rata humani corporis dispositio naturæ legibus ad Vniuersi similitudinem præstituta symmetria dicitur, quæ ex eodem Vitruvio lib. 1. cap. 1. ea est, vt os capitis à mento ad frontem, seu ad imas capillorum radices, decima totius corporis pars sit: tantumdem longitudo manus à linea, quam percussuram chiromantes dicunt, ad extremum digitum medium: caput à mento ad summum verticem octaua pars: à summo pectore ad imas radices capillorum, sexta: ad summum verticem quarta: ipsius autem oris tertiam partem longitudinis esse constat ab imo mento ad imas nares: tantundem nasum ab imis naribus ad finem medium superciliorum: tantumdem à superciliis ad radices capillorum, vbi frons prominet: pes item sit sextæ partis longitudinis totius corporis; cubitus quartæ; pectus item quartæ; ac tandem totius corporis habitudo ea esse debet, vt quæ distantia, & longitudo est à planta pedis ad sumnum vericem eadem, ac tanta sit latitudo ab extremis manuum digitis extentis brachiis computanda: quanta est longitudo oris tanta sit latitudo manus, &c. idque per analogiam ad Vniuersum, (cuius, vt alibi diximus, homo imaginem, & compendium præsefert,) in quo videmus tantumdem distare vnum polum ab alio, quantum distat vnum ex duobus punctus æquinoctialibus ab alio: tanta est distantia tropicorum ab æquatore, quanta est polorum Zodiaci à polis Mundi: ignis locus naturaliter in inferno sit, hoc est in Mundicento, vt in homine calor in corde sedem suam obtinet, quod est totius corporis centrum, &c. quæ nobis ad alia properantibus sufficiat tergisse, ac lectoribus consideranda exhibuisse. Porrò, vt ad institutum reuertamur; aliam, ætque aliam symmetriarum rationem quærere locorum, rerumque naturam, in perspecto est: alia enim proximè ad oculos sunt, alia excelsa, & remota; alia obscura & conclusa, alia patentia, & aperta: idcircò ad eam habendam maximè necessaria sunt Geome- G g iii

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MATHEMATICVM. 475 the harmonious agreement of the parts of the work itself, and the response of the separated parts to the form of the whole as a due proportion, is that faculty obtained from geometrical precepts by comparison, which is of advantage in Architecture, so that, according to the order of nature, the parts of some structure correspond to the whole, and it teaches from the size of the house how great its length and breadth ought to be, how large the vestibule, how massive the columns, the intervals of the windows, etc.; as in a statue, from the measure of the foot or hand it may be gathered what proportion the outer limbs ought to have: whence that true saying: From vignue a lion. Hence the ordered disposition of the human body, established by the laws of nature in likeness to the Universe, is called symmetry, which, according to Vitruvius himself, book 1, chapter 1, is such that the length of the head from the chin to the forehead, or to the roots of the hair, is the tenth part of the whole body: the same length of the hand from the line which chiromancers call the wrist-line to the tip of the middle finger: the head from the chin to the top of the crown is the eighth part: from the top of the breast to the roots of the hair, the sixth: to the crown, the fourth: and the face itself is known to be the third part of the length, from the bottom of the chin to the lower nostrils: the nose is likewise the same from the lower nostrils to the middle end of the eyebrows: the same from the eyebrows to the roots of the hair, where the forehead projects: the foot also is the sixth part of the entire length of the body; the cubit the fourth; the breast likewise the fourth; and finally the frame of the whole body ought to be such that the distance and length from the sole of the foot to the top of the crown is the same as, and as great as, the breadth measured from the extremities of the fingers with the arms outstretched: as great as the length of the face, so great is the breadth of the hand, etc. And this by analogy to the Universe (of which, as we have elsewhere said, man bears the image and compendium), in which we see that one pole is as far from the other as one of the two equinoctial points is from the other: so great is the distance of the tropics from the equator as is that of the poles of the Zodiac from the poles of the World: the place of fire is naturally in hell, that is, in the midst of the world, as in man heat has its seat in the heart, which is the center of the whole body, etc.; enough for us to have touched on these matters while hastening to others, and to have set them before readers for consideration. Moreover, to return to our purpose; that one and another arrangement of symmetries is sought by the nature of places and things is evident: for some are near to the eyes, others high and remote; some obscure and enclosed, others open and exposed: therefore, in order to have this, Geome- G g iii

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474. LEXICON triæ præcepta: qua de re vide Vitruu. præsertim libro & cap 1. <111> SYMPATHIA græcè dicitur mira illa rerum in vniuersa Na- turæ consensio, qua duo corpora occulta quædam vi inui- cem afficiuntur, alterantur, ac mirum in modum ad mu- tuum efficientiam exitantur, quantumuis & loco, & tem- pore, & natura dissita, & disiuncta. Et si quidem hæc mu- tua affectio sit in bonum, amicitiamque pariat, aut fouear, Sympathiam; sin autem odium, auectionem, ac pugnam, Antipathiam vocitamus. Nulla in tota Philosophia quæ- stio istâ magis implea; nihil quod magis eaptum hominis fugiat. Vnde enim homini primò in duos colludentes, aut dimicantes occurrenti insitus ille affectus, vt ergà istum na- turaliter sit propensus, ergà illum sentiat se auersum; huic victoriam, illi easum, deterioresque partes precetur? Vnde duarum fidium æquè tensarum interior dispositio, vt si è lupi altera, altera ex agni nerris compacta sit, illis tactis, istæ protinus distumpantur? si verò ex eodem chordarum genere constituantur, inuicem benè respondeant, ac tactâ vna resonet simul & altera? Vnde herculei lapidis ad po- lum conuersio? Vnde ferri ad ipsum attractio? Vnde eam miræ, tamquè diuersæ Malacie affectiones? Quid imagina- tiux vis in membra inferiora? Quid fascinus? aliaque penè innumerabilia Naturæ arcana, quæ quotidie detegimus, oculis tenemus, manibus palpamus, & tamen causam di- gnoscere, ac perscrutati omninò non possumus. Etenim quam vulgò circumferunt sympathiam omnem ex Naturæ similiudine, Antipathiam verò ex dissimilitudine oriri, eo so um capite minùs probare possum. Nam rerum longè dis- similium est compassio, & consensus: econtrà similium plurimorum dissensus, atque antipathia: neque enim ma- gnes magnetem attrahit, sed ferrum; Canis cum Lupo, à quo vix discernitur, magnam habet contrarietatem, at cum oue quantumuis dissimili Sympathiam. Galli gallinacei cum Sole, Lupi cum agno, felis cum mure antipathiam ne dixerim, an sympathiam? cum ni foret illi connaturalis, haud illum tantopere insequeretur, & quocumque cibo suauiorem reperiret. Quidquod videmus quotidie aliquem impensè alium deperire, qui tamen ei naturaliter auersus, tanto respondero, ac despectu, quanto cum ille amore prosequitur. Vidimus Gallos infensos Hispanis, quamuis initimos, atque in eodem ferè elimate constitutos, Hispa- nos Germanis, aliisque septentrionalibus gratos, quamuis, moribus, Religione, elimate toto coelo disjectos. Sed &

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474. LEXICON three precepts: on this matter see Vitruvius, especially book & chapter 1. <111> SYMPATHY, in Greek, is called that wondrous agreement of things throughout universal Nature, by which two bodies are affected by some hidden power, altered, and in a marvelous way stirred up to mutual action, however far apart they may be in place, time, and nature, and however separated. And if this mutual affection is for good and gives rise to, or fosters, friendship, we call it Sympathy; but if it gives rise to hatred, repulsion, and conflict, we call it Antipathy. There is no question in all Philosophy more obscure than this; nothing that more escapes human understanding. For whence, first of all, comes that innate feeling in a man who sees two people wrestling or fighting, by which he is naturally inclined toward one and feels himself turned away from the other; and for the one he wishes victory, for the other defeat and the worse side? Whence comes the inward disposition of two strings equally taut, if one were made from the nerves of a wolf and the other from those of a lamb, so that when those are touched, these immediately snap? But if they are made from the same kind of strings, why do they answer one another well, and when one is touched the other sounds at the same time? Whence comes the turning of the Heraclean stone toward the pole? Whence its attraction to iron? Whence those affections of the plant called Malachia, so strange and so diverse? What of the imaginative power into the lower limbs? What of fascination? And what of the almost countless other secrets of Nature, which we discover daily, behold with our eyes, touch with our hands, and yet are altogether unable to discern or investigate the cause of? For the common explanation that all sympathy arises from likeness in Nature, and antipathy from dissimilarity, I can accept no more than for this one reason. For there is fellowship and agreement among things that are very dissimilar; on the contrary, among many similar things there is disagreement and antipathy: for it is not the magnet that attracts the magnet, but iron; the dog has great hostility toward the wolf, from which it can scarcely be distinguished, but toward the sheep, however unlike it may be, it has sympathy. Shall I call the rooster’s relation to the sun, or the wolf’s to the lamb, or the cat’s to the mouse, antipathy or sympathy? For unless it were natural to it, it would not pursue it so eagerly and would not find more pleasure in any food whatsoever. What of the fact that we daily see someone passionately fall for another, who yet is naturally averse to him, answering him with as much coldness and contempt as the other pursues him with love. We have seen the French hostile to the Spaniards, though they are neighbors and live in nearly the same climate; and the Spaniards friendly to the Germans and other northerners, though in customs, religion, and climate they are separated by the whole sky. But also

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MATHEMATICVM. 475 hanc rerum connexionem, mirumque ordinem in vniuersa penè natura inter dissita quæuis comperimus. Hinc iure meritò eruditissimus Campanella hanc Vniuersi < 123.> faciem demirans, ita philosophatur lib. 2 cap. 5. Nescio inquit, qua sympathia nobis cum tota Natura serie inest: nam cum vna calcatur, solent grassari pralia, & sanguis humanus effundi. Plerumque cum putantur vinea capita truncari humana & suffocatiui catharri grassari sueuerunt. Cum florenti arbores, semina corporis, & ingenij surgent, florentque, & ad quasdam incitantur fructificationes: cum colliguntur sterilescimus: Vnde signum Virginis sterile vocatur. Cum venti plurimi diu flant, colligimur in penetralia domorum, & cuncansilia pessima ineuntur: vnde fæmina solent insidiosa moliminæ prognosticari. Quid cum humano sanguine musti expressio, & non potiùs ouium pecudumque mactatio? Quid capitum detruncatio cum vineæ putatione? Quæ arborum efflorescentiæ cum ingenij seruore connexio? Quæ ventorum vis cum pessima consiliorum molitione? Verum hæc altissima dispositione præordinata sunt, atque vnam superiorem causam appellant, respiciuntque: subdit enim sapientissimus vir. Nec ista ratione vacant: nam etsi respectu causarum secundaru[m] & per accidens fiat, vt hæc herba simul cum illa floreat, inquit S. Thomas super 6. Metaph. ) tamen respectu cali habere causam: similes enim affectus corporeos influunt omnibus sola corporibus, sed modificantur pro genere, & qualitate recipientium Hæc ille. Ergò stellarum induxus vniuersales sunt, æque omnibus < 124> corporibus subiectis communicantur; æquè omnes mundi partes afficiunt, sed non eosdem, pares, aut similes in omnibus subiectis habent effectus producere, quando ista aut genere aut specie diuersificantur, sed pro qualitate recipientium in aliquibus connexos, complexos, consimiles, sibi mutuò correspodentes; in aliis dissitos, alienos, æquiuocos, sibi inuicem aduersantes. Sic vbi Naturæ conformitas, tum mixtorum ad inuicem, tum ad causam superiorem, ibi communicatio, consensus, & amicitia; vbi diffomitas & nullus ordo, contrariæ affectiones, dissidium, atque iniuicitia. Qua de re alibi me dixisse recordor, Luminaria, quæ sunt causæ vniuersales & æquiuocæ omnium producibilium, cum loue, aut Venere Naturæ humanæ conformibus producere mixta hominibus opportuna, cum Saturno verò fossilia, venenata, foetida, vitæ hominum aduersantia. Gg iii

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MATHEMATICVM. 475 this connexion of things, and the wonderful order in the whole of nature, we discover in almost everything however far apart. Hence the most learned Campanella, with good reason admiring this face of the Universe thus philosophizes, lib. 2 cap. 5: “I know not,” he says, “what sympathy there is in us with the whole series of Nature: for when one part is trodden down, battles are wont to rage, and human blood to be shed. Very often, when the tops of vines are thought to be cut off, human catarrhs and suffocating illnesses have been accustomed to spread. When trees are flourishing, the seeds of the body and of genius rise and flourish too, and are stirred to certain acts of fructification; when they are gathered, we grow sterile: whence the sign of Virgo is called sterile. When many winds blow for a long time, we gather into the inner parts of our houses, and the worst councils are entered upon; whence women are wont to prophesy insidious undertakings. What is there in the pressing out of must compared with human blood, and not rather the slaughter of sheep and cattle? What is the cutting off of heads compared with the pruning of a vineyard? What connexion is there between the blossoming of trees and the fervor of genius? What force of winds with the devising of the worst plans? But these things are preordained by the highest disposition, and they look to, and invoke, a single superior cause,” he adds, the most wise man. “Nor are these things without reason: for although, with respect to second and accidental causes, it happens, as St. Thomas says on Metaphysics 6, that this herb flourishes at the same time as that one, yet with respect to the heavens it has a cause: for the stars influence similar bodily conditions upon all bodies alone, but they are modified according to the kind and quality of the receivers.” Thus far he. Therefore the universal influences of the stars are communicated equally to all subjected bodies; they affect all parts of the world equally, but they do not produce the same, equal, or similar effects in all subjects, when these differ either in genus or in species, but according to the quality of the recipients, in some cases connected, complex, and alike, mutually corresponding to one another; in others distant, alien, equivocal, and contrary to one another. Thus where there is conformity of nature, both among mixed things themselves and with the higher cause, there is communication, consent, and friendship; where there is dissimilarity and no order, there are contrary affections, discord, and enmity. On this matter I recall that elsewhere I said that the luminaries, which are the universal and equivocal causes of all things producible, together with Jupiter or Venus, conformable to human nature, produce mixtures suitable for men; but with Saturn they produce fossil, poisonous, foul things, adverse to the life of men. Gg iii

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476 LEXICON <125> Hinc liceat expiscari veram ab'ditissimi huius Naturæ mo- ius originem in partium quamtumuis etherogenearum con- sensu, atque dissensione. Equidem cum omnes Mundi partes sint inuicem colligatæ, omnes in vnum totum con- fluant mira varietate, ac differmi conformitate eonnexum; inde sit vt inter ipsas necessarius intercedat aliquis Ordo, qui miram istam rerum difformitatem faciat, & vbi datur ali- qua seu qualitatum similitudo, seu earundem adinuicem colligantia ex mutua actione, & repassione, ibi necessarius sit consensus, ac sympathia, vbi verò dissimilitudo, diuersitas, nulla agendi, & patiendi necessitudo, ibi dissentio, atque antipathia. <126> Porrò hoc idem per partes explicemus, & vt aliàs con- sueuimus, à Microcosmo ad Macrocosmum transeuntes, philosophemur. Omnem nostri corporis sympathiam Gale- nus Medicorum princeps, tum in propria disputatione ad- uersus Lycum, tum in Lib. de morb. vulg vbi casum Pythonis explanat, in tres differentias commodè diuidit: aliam, quam dicit esse Sympathiam generis; aliam operis familiaritatis; & aliam vicinitatis. Per sympathiam generis intel- ligit consensum illum, qui communicatur alteri parti ob- eiusdem partis viuentis continuitatem; sicut læsa ceruice læditur manus, quoniam neruus vestiens manum è cer- uice dependet, & consensus per eiusdem nerui quamuis in dissitis partibus consistentiam, & continuitatem seruatur, quæ sympathia generis non intercedit inter partes quam- uis viciniores; vtpote inter cor, & ventriculum, atque inter istum, & hepar, aut manum; qua de re 10to ecclo- errasse Lycum aduersit Galenus asseuerantem tremorem ma- nus ab stomacho prodire, cum nullus neruus à ventricu- lo procedat ad brachia vt Anatomes obseruatoribus com- pertum ast. Secunda species sympathiæ est operis fami- liaritatis, quam dicimus intercedere inter mammas, & vuluam, non enim vlla intercedit inter illas connexio, quam quod ad idem opus ambæ à Natura sint destinatæ: hinc ex vteri affectionibus in mammis tuberculi, durities, carcinomata dira suboriunrur, hinc etiam conceptus tem- pore venas vberum oppleti, & turgere conspicimus, ac pro qualitate foetus mammas aut intumescere, aut langue- re, vt docet Galenus in sextum Hippocratis de morbis vulgaribus commentar. 5. & 14. de vsu partium 4. & 8. Andreas Laurent. lib. 7. quest. anatom. 11. Ludouicus Dur- rerus in Coac. in append. de Vulneribus ad commentar. text. 44. & alij. Quin & ipse Hippocrates, loco citato

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476 LEXICON <125> From this it may be permissible to investigate the true origin of this most hidden movement of Nature in the agreement and disagreement of parts, however heterogeneous they may be. Indeed, since all the parts of the world are joined with one another, all flowing together into one whole, linked by a wonderful variety and dissimilar conformity, it follows that among them there must necessarily intervene some order, which makes this wondrous diversity of things; and where there is some similarity of qualities, or a mutual connection of them by reciprocal action and reaction, there necessarily is agreement and sympathy; but where there is dissimilarity, diversity, and no necessity of acting and being acted upon, there is disagreement and antipathy. <126> Furthermore, let us explain the same thing by parts, and, as we have elsewhere been accustomed to do, passing from the Microcosm to the Macrocosm, let us philosophize. Galen, prince of physicians, conveniently divides all the sympathy of our body into three kinds, both in his own disputation against Lycus and in the book De morb. vulg. where he explains the case of the Pythoness: one, which he says is sympathy of kind; another, of familiarity of work; and another, of neighborhood. By sympathy of kind he understands that agreement which is communicated to another part because of the continuity of the same living part; just as when the neck is hurt, the hand is also hurt, because the nerve covering the hand descends from the neck, and the agreement is preserved through the continuity of the same nerve, though it is in distant parts. This sympathy of kind does not exist between parts however near they may be, as between the heart and the stomach, and between the stomach and the liver, or the hand; on which account Galen says Lycus erred against him when he maintained that trembling of the hand comes from the stomach, since no nerve proceeds from the stomach to the arms, as is known to observers of anatomy. The second kind of sympathy is that of familiarity of work, which we say exists between the breasts and the womb; for there is no connection between them except that by Nature both are destined to the same function. Hence, from affections of the uterus, knots, hardness, and dreadful cancers arise in the breasts; hence also, at the time of conception, we observe the veins of the breasts filled and swelling, and according to the condition of the foetus the breasts either swell or slacken, as Galen teaches in the sixth commentary on Hippocrates On Common Diseases, 5 and 14, and in De usu partium 4 and 8; Andreas Laurent. lib. 7. quest. anatom. 11; Ludovicus Durreus in Coac. in append. de Vulneribus ad commentar. text. 44; and others. And indeed Hippocrates himself, in the place cited

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MATHEMATHICVM. 477 sit, si mammarum papilla, & rubrum virido sit, agrotare conceptaculum. Et alia id genus, quæ fusè adducit & explicat Sanctorus Sanctorius de vitandis erroribus in arremedica lib. 2. cap. 4. & seq. Tertia species sympathiæ est quam dicunt vicinitatis, per quam vnum membrum alteri condolet ex vicinia: talis est unus, & vteri, capitiscum ceruice, manus cum brachio, &c. Et hæc, cum manifesta sit, maiore explicatione non indiger. Omnis igitur Sympathiæ affectio in partibus corporis nostri ex aliqua condolentia sit, quæ ex prædictis capitibus originatur. Nam vt benè discurrit Valesius lib. 4. controuers. medie. & philosophic. cap. vlt. Quæ patiuntur, aut ex seipsis patiuntur à suaque natura & na propria illorum passiones sunt, quas proinde Idiopathias possis propriè appellare, aut patiuntur ab aliis, idque vel ratione similitudinis, quæ cum aliis ess intercedit, vel quod contraria sint: tamen contrarij ratio quanto cum maiori similitudine coit, tantò facit maiorem passionem, nimirum quæ sunt omninò similia nullatenus sese immutant. Quæ contraria admodum sunt agrè congrediuntur, tamen cum semel sunt congressa plus mouentur, quia longiùs distant. Da verò quæ contraria sunt, quantum ad agendum est satis, & tamen sunt similia facilius compatiuntur. Ignis oitius mouet aërem, Sed plus mouet aquam. Facilem commutationem, quæ fit gratia similitudinis, potes sympathiam, magnam verò, qua fit gratia contrarij, antipathiam appellare, quamquam est verior altera sympathia species quam in membris humanis Medici considerant, cum scilicet aliquid patitur ab alia, quia simile illi est, & quia illud à quo patitur, patitur ab alia causa prius. Nam natura sit, vt cum res aliqua patitur, eas omnes, quæ idic sunt valdè similes & vicina satis trahat ad contagionem, & post pauca. Membrum quidcumque, inquit, aut patitur per se, aut alteri condolet, vt caput alteri dolet ex intemperie cerebus, alteri ex intemperie ventriculi Quod per se patitur, nec aliunde dependet, hoc ex morbo propriè fieri asserit vocatque Idiopathiam, quod ex alterius membri consensione, hanc sympathiam: Nam omnis morbus, subdit, est affectus, Sympathia autem passio. Aduerit tamen ex Galeno membrum aliquod trahi in alterius sympathiam duobus modis, aut transmisso in illud quod non transmitti oportebat, aut impedito influxu, quo indigebat quæ omnia clarè innuunt, omnia hæc fieri per aliquam alligationem partium inte se cum ex Arist. omne agens semper agat quodam tectu, nec dari possit vlla actio in distans.

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MATHEMATHICVM. 477 if there be, for example, redness on the nipple of the breast, and it be green, the receptacle is diseased. And other things of this kind, which Sanctorus Sanctorius treats of at length and explains in De vitandis erroribus in arte medica , book 2, chapter 4 and following. The third species of sympathy is that which they call of neighborhood, by which one member suffers with another from proximity: such is one of the uterus, the head with the neck, the hand with the arm, etc. And this, since it is manifest, needs no further explanation. Therefore every affection of sympathy in the parts of our body arises from some suffering-with, which has its origin from the heads mentioned above. For as Valesius argues well, book 4 of the medical and philosophical controversies, last chapter: those things which suffer either suffer of themselves, and their sufferings are from their own nature and are proper to them, which therefore you may properly call idiopathies; or they suffer from others, and that either by reason of the similarity which intervenes with the others, or because they are contrary. Yet the relation of contraries, the more it joins with greater similarity, so much the more produces a greater affection; indeed, things that are altogether similar do not change one another at all. Things that are very contrary meet with difficulty; yet when once they have met, they are moved more, because they are farther apart. But given things that are contrary, so far as acting is concerned, this is enough, and yet if they are similar they suffer together more easily. Fire moves air more quickly, but it moves water more strongly. You may call the easy alteration, which comes about by reason of similarity, sympathy; but the great alteration, which comes about by reason of contrariety, antipathy, although the other species of sympathy is more true, which physicians consider in the human members, when namely something suffers from another because it is similar to it, and because that from which it suffers suffers from another cause beforehand. For nature is such that, when some thing suffers, it draws all those things that are very similar to it and nearby enough into contagion, and after a few words. Any member whatsoever, he says, either suffers by itself, or suffers with another, as when the head aches from intemperance of the brain, another from intemperance of the stomach. That which suffers by itself, and does not depend on another cause, he says happens properly from disease and calls it idiopathy; that which comes from the consent of another member, sympathy. For every disease, he adds, is an affection; sympathy, however, is a passion. Nevertheless, according to Galen, a member is drawn into the sympathy of another in two ways: either by what was transmitted into it, which ought not to have been transmitted, or by the influx being impeded, which it needed. All of which clearly indicate that all these things happen through some mutual binding of the parts among themselves, since, according to Aristotle, every agent always acts in some contact, and no action at a distance can be given.

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LEXICON <127> His igitur ita constitutis, iam ad omnem sympathiæ rationem, quæ inter Vniuersi istius partes inuicem colligatas inspicitur explicandam deueniamus. Siquidem ita hominem constituit summus Opifex vt esset veluti Vniuersi ipsius compendium, atque ex eius consideratione vniuersam mundi faciem, inimicamque constitutionem contemplemur. Omnis igitur sympathia reru[m] aut ex naturæ similitudine, viciniâque; aut ex familiaritate operis, actuumque conformitate; aut demum ex genere, quod ex vno eodemque principio promanent, sintque veluti aliquo superiori vinculo colligatæ, originem trahit. Ex naturæ similitudine habetur, quod homo alteri homini condoleat, pecus pecudi, quod vinum in doliis fluctuet, cum vites in vinctis efflorescunt. Ex naturæ similitudine sit, quod in morbis contagiosis alter alterum lædat aspectu, voce, contactu; quod primo sanguine menstruo, aut secundinis in loca exnosa deiectis, foeminae malè habeant, quod cineribus calidis super recens excretas hominis fæces impositis: ille mox dissenteria corripietur, quod mox sistatur lac in vberibus, si foemina eiusdem lactis modicum in prunas emulgeat: & cætera quorum longam seriem affert Kircherus in Artemagnetica, & non quotidie non sine stupenti oculo experimur. Item ex vicinitate accidit, quod vna provincia peste infecta: altera illi propinquior, quamuis non sub eodem cælo eodem morbo afficiatur; quod aër calidus aquam propinquiorem magis quam remotiorem, etsi qualitatibus primis non discrepent, calefaciat, quod magnes, qui polum naturaliter aspicit, ad eam partem, quamuis ab ipso polo remotam feratur, cui, & quantò est ipse vicinior, &c. <128> Secundò ex familiaritate operis, tum etiam ex naturæ similitudine est sympathia illa quam in rebus videmus, cum scilicet, vno aliqvid operante, videmus aliquem ad idem opus quamuis nil tale cogitantem excitari. Vt cum altero oscitante, & ipsi mox oscitamus, altero mingente cietur & nobis lotium, quod ex imagine obscæna, Venus in aspiciente extimuletur. Nec dicas cum Valesio vbi supra hæc, & similia Naturæ arcana ex imaginationis vi, quatenus mens in cerebro residens per facultatem animalem in singula membra influit, atque operari facit, pendere. Nam etsi id vt plurimum verum sit, tamen non semper: quandoquidem videmus sæpè aliquem nil tale cogitantem, vt dixi, quin & ab altero oscitante vultu, aux animo auersum, vel oculis captum, (quò sit, vt nil de oscitatione recogitet) nihilominus oscitare; quod argumento est, ipsam naturam

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LEXICON <127> Having thus settled these things, let us now proceed to explain fully every account of sympathy, which is seen among the mutually connected parts of this Universe. For the supreme Maker so constituted man that he should be, as it were, a compendium of the Universe itself; and from his contemplation let us behold the whole face of the world and its opposed constitution. Every sympathy, therefore, of things either takes its origin from similarity of nature and proximity; or from familiarity of operation and conformity of actions; or finally from kind, because they proceed from one and the same principle, and are as it were bound together by some higher bond. From similarity of nature comes the fact that one human being pities another, one beast another; that wine in barrels is in motion when the vines burst forth in their bindings. From similarity of nature it is that in contagious diseases one harms another by sight, voice, or touch; that women are taken ill from the first menstrual blood or from the afterbirth thrown in foul places; that if hot ashes are placed on fresh human excrement recently voided, the man will soon be attacked by dysentery; that milk is soon stopped in the breasts if a woman milks a small amount of that same milk onto embers; and so on, a long series of which Kircherus gives in the Art Magica, and which we do not every day experience without a wondering eye. Likewise, from proximity it happens that if one province is infected with plague, another nearer to it, although not under the same sky, is afflicted with the same disease; that hot air warms water that is nearer more than that which is farther away, even if they do not differ in primary qualities; that the magnet, which naturally looks toward the pole, is drawn to that part which, though remote from the pole itself, is nevertheless, the nearer it is to it, &c. <128> Secondly, from familiarity of operation, and also from similarity of nature, there is that sympathy which we see in things, when, namely, while one thing is acting, we see someone else excited to the same action, though thinking nothing of the sort. As when one person yawns, we soon yawn too; when another urinates, our own urination is stirred; and from an obscene image Venus is excited in the beholder. Nor should you say, with Valesius in the place cited above, that these and similar secrets of Nature depend on the power of imagination, in so far as the mind, residing in the brain, flows through the animal faculty into

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MATHEMATICVM. 472 ex sola operis familiaritate immediatè, absque vllò supe- rioris facultatis imperio, ad operandum excitari: idipsum planè cuinet duatum chordarum æquè tenarum experien- tia; dum vna pulsata, altera licet sensu, & ratione carens ad eosdem modulos resonet. Tandem longè mirabilior, atque vniuersalior est sympa- < 129> thia generis, quæ per omnes ferè res huius Mundi sublu- naris transcendit, maximè verò eas in quibus, vt suprà di- cebamus, apparet aliqua generis similitudo, aut contratie- tas, quæ eundem penè effectum progignit in iis, quæ agere simul, & pati inuicem nata sunt. Talis est aliquorum ani- mantium, plantarum, hominum mutuus amor, aut dissi- dium: cettarum stirpium qualitas, quæ aliquidibus exitialis est, aliis iucundissimum alimentum. Sic Doronici canes ex eo pastos occidunt, hominibus opitulantur: Cicuta è con- trà his deleteria est, asinis verò ac stutnis commodum pa- bulum. Aconitum venenum est præsentaneum his qui benè habent; at venenatis, & iis, qui quauis ratione venena in cibos sumpserunt, antidotum; Elleborum mente captos in rationem reuocat, sui compones fatuos reddit. Sunt aliqui lapides, (inter quos præstat potissimum Bezoar in visceri- bus cuiusdam animalis repertus) qui omnibus venenis oc- currunt, quamuis contraria qualitate pollentibus; sunt & herbæ, quæ malis ferè omnibus præstò sunt, quæque ob effectus, quos, non in diuersis modò, sed quod mirum est in vno, eodemque subiecto, pro diuersa loci, situs, ac tem- poris ratione pariunt, nescias queisnam qualitatibus po- tiantur. Afari folia si quis decerpendo sursum vellicauerit, purgabunt copus per vomitum, sin verò deorsum carpendo contorqueat, solam alium deijcient: Persicaria, seu Piper aquaticum, Consolida, Brassatella, aliæque plures id genus herbæ id habet peculiare, vt si frigidæ mergantur in aquam, & super vlcus, aut vulnus alicuius ægri intepescant, mox defodiantur cænoso loco; vbi putrete incipiunt, attahunt ex patiente quidquid nocuum est: & alia id genus multa Naturæ arcana, quæ quâuis cognitu difficilia, hoc tamen vnum apud omnes in manifesto est, id non nisi ex quadam mutua rerum alligatione prodite, habereque vnam quandam vni- uersalem causam æquivocam, à qua omnes mihi isti effe- ctus deriuent. Quod & longè antè agnouit Philosophus 8. Physicorum, qui admirans hanc in vniuersa Natura confor- mitatem, omnem in causam vniformem, id est in vnum ac simplicissimum motorem refundit. Quare nullum mihi sumus argumentum ad Mundi for- < 130>

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MATHEMATICVM. 472 from the mere familiarity of the work itself, immediately, without any command of a superior faculty, to be stirred to action: the same thing is plainly shown by the experience of two strings equally tense; for when one is plucked, the other, though lacking sense and reason, sounds in the same notes. Finally, a far more wonderful and more universal sympathy of kind exists, which extends through almost all things of this sublunary world, especially indeed in those in which, as we said above, there appears some likeness or contrariety of kind, which produces nearly the same effect in things that are by nature born to act together and to suffer one upon another. Such is the mutual love or discord of certain animals, plants, and men; such is the quality of certain plants, which is deadly to some, but most pleasant nourishment to others. Thus the dogs of Doronicum, fed on it, kill men, but help humans: cicuta, on the other hand, is deleterious to these, but to asses and stutni a useful fodder. Aconitum is a deadly poison to those in good health; but for the poisoned, and for those who by whatever means have taken poisons in food, it is an antidote; hellebore brings the mind-captive back to reason, and makes fools composed in themselves. There are some stones, among which Bezoar, found in the viscera of a certain animal, is especially esteemed, which meet all poisons, even though endowed with contrary qualities; there are also herbs which are at hand for almost all evils, and which, from the effects they produce, not only in different subjects but, what is remarkable, in one and the same subject, according to the varying condition of place, position, and time, you would not know by what qualities they are endowed. If someone plucks the leaves of an asparagus plant by pulling upward, they will purge the body by vomiting; but if, plucking downward, he twists them, they will merely cleanse it. Persicaria, or water-pepper, consolida, brassatella, and many other herbs of that kind have this special property: if they are dipped in cold water and become warm upon some ulcer or wound of a patient, they are at once to be buried in a dungy place; there they begin to rot and draw out from the sufferer whatever is harmful. And many other secrets of nature of this kind, though difficult to know, have nevertheless this one thing evident to all, that they are brought forth only from some mutual connection of things, and that they have one certain universal, equivocal cause, from which all these effects seem to me to be derived. This, too, long before was recognized by the philosopher in the Eighth of the Physics, who, marveling at this conformity throughout universal nature, referred everything to one uniform cause, that is, to one most simple mover. Therefore there is no argument for me to the formation of the world < 130>

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LEXICON. 480 mam, quam supra probauimus suppetit astruendam, quam minus hic rerum ordo, consensus dissensusve partium, quem non ab alio fonte, quam ab hac Mundi forma perenni motus huius scaturigine, necesse est promanare. Sicut ergo in humano corpore diuersi motus, ac membrorum colligatio, & consensus arguunt vnicam esse animam, quæ omnia regat, & ordinet, vt probè notat Valesius in hæc verba. Igitur hæc mihi significant vnicam esse animam, qua hac omnia fiunt, nutritio, pulsus, & sensus: eam verò vti diuersis potentias. vt ego ipse meas manus moueo, & crura, atque ad alia manu moueo, ad alia crura. Vt ergo ego cum mediocri vehementia solas manus moueo, cum verò maiori vehementia, iam non solas, sed cum eis crura quoque, & nonnumquam membra omnia, quamquam res solis manibus agenda sit, ita anima omnes potentias mouet quasi ad canatus apporendos, cum illarum aliqua mouetur vehementissimè. Hinc, si diuersa anima sorent, non tantum diuersa facultates: non videntur posse fieri, vel saltem non tam concinnè: nam cum unitas membri non sufficiat ad illum consensus, maiori aliqua vnicata est opus: ea non videtur quæ alia sit, quam anima, nam facultatis non est; diuersarum enim actionum diuersas oportet esse facultates: Ad sympathias quasdam; qua ipsis instrumentis contingunt ratione alligationis, sufficit alligatio, sed ad dictos modo consensus non videtur sufficere, si modo à diuersis animis hac agerentur. Hæc ille. Sicut igitur, vti dicebam, hæc omnia in corpore humano vnicam animam probant. Ita hæc eadem in tota mundi conspiratione, atque consensu vnicam formam, eamque vitalem euincunt. 481. Accedit quod, vt paulò antè notauerat idem Valesius, in partibus humani corporis, multæ sunt sympathiæ quæ non videntur ad vllam ex prædictis reduci posse, sed necessariò ad quamdam occulam virtutem & consensionem, quæ prodat ab vno eodemque principio, refundendæ. Quæ enim consensio inter transuersum septum, & cerebrum? aut quis nexus inter os ventriculi & cor? & tamen inflammato septo statim caput delirat, laborante ore ventriculi deficit cor. Nec iuuat dicere, quod ascendunt quidam fumi & halitus ab inflammatione septi transversi ad cerebrum, qui illud perturbant, atque ab ore ventriculi ad cor, qui illud angunt. Nam vt benè idem aduertit, longè vicinius esse cerebro os ventris: ergò maior halituum copia ascendet ex oris ventriculi inflammatione (cum præsertim ibi sit horum alituum officina, & sedes) quam ex septi transversi, & tamen hæc de-

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LEXICON. 480 mam, which, as we have shown above, is needed to be established, and which the order of things here, the agreement or disagreement of the parts, necessarily must flow not from any other source than from this perennial source of movement of the form of the world. Just as, therefore, in the human body the various motions and the joining together of the members, and their agreement, prove that there is one soul which governs and orders all things, as Valesius rightly notes in these words: “Therefore these things signify to me that there is one soul, by which all these things are done, nutrition, pulse, and sensation; but that it uses them as diverse powers. For I myself move my hands and legs, and with my hand I move to one thing, with my legs to another. Therefore, when I move only my hands with moderate force, but with greater force, I no longer move only them, but with them my legs too, and sometimes all my limbs, although the matter to be done is one for the hands alone; so the soul moves all the powers as if to grasp the canatus, whenever one of them is moved most violently. Hence, if there were different souls, there would not only be different faculties: they do not seem able to be produced, or at least not so harmoniously; for since the unity of a member is not sufficient for that agreement, some greater unity is needed: this does not seem to be anything other than the soul, for it is not of a faculty; for different actions must have different faculties. For certain sympathies, which arise in the instruments themselves by reason of their connection, the connection is sufficient; but for the agreements mentioned just now, it does not seem sufficient, if they were carried on by different souls.” This is his view. Therefore, as I was saying, all these things in the human body prove a single soul. Likewise these same things in the whole concord of the world and its harmony demonstrate one form, and a vital one. 481. It is added that, as the same Valesius had noted a little earlier, in the parts of the human body there are many sympathies which do not seem able to be reduced to any of the foregoing, but necessarily must be referred back to some hidden power and agreement, which proceeds from one and the same principle. For what agreement is there between the transverse septum and the brain? or what bond between the mouth of the stomach and the heart? And yet, when the septum is inflamed, the head immediately becomes delirious; when the mouth of the stomach suffers, the heart fails. Nor does it help to say that certain fumes and vapors rise from inflammation of the transverse septum to the brain, disturbing it, and from the mouth of the stomach to the heart, constricting it. For, as he rightly observes, the mouth of the belly is much nearer to the brain; therefore a greater quantity of vapors will ascend from inflammation of the mouth of the stomach (especially since there is the workshop and seat of these vapors) than from that of the transverse septum, and yet these de-

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MATHEMATICVM. 41 firare facit non illa Hac etiam ratione, inquit, cor citius afficeret septum transuersum, quam os ventris; nam viciniam cum corde non habet minorem, & insuper habet motum sed videmus ex affectionibus oris ventriculi promptissimè fieri sincopes, ex affectione septi deliria: ergò non trahunt hac membra alia in sympathiam his rationibus communibus in quibus superantur ab aliis, qua non faciunt perinde, sed intercedit propria aliqua natura, qua hac fiunt inter septum & cerebrum; os vetriculi, & cor, quam nos ignoramus. Hæc igitur in hac mutua facultatum conspiratione consistit, quæ vt dixi, ab vno animæ pendet regimine, atque analogiam non ineptè appellarunt, cum in rebus longè dissimilibus, ac disparatis, quandam nihilominus similitudinem seruet. 132. Simili modo in hac Mundi, & Macrocosmi istius constitutione videre est hanc rerum analogiam, quæ non in sola similitudine, vicinitate, operis familiaritate, aut noto quodam vinculo saluari potest, cum hæc eadem sympathia in rebus longè maiori vinculo nxis minimè videatur, quia tamen eam experimentis sentimus, aliquam longè istis superiorem esse euidenti ratione deducimus, atque adeò in mundi formam, & conuentionem in vnum quoddam vniuersale principium iure merito importamus. Vnde enim uero est, vti dicebam, quod Galli semper, & vbique sunt Hispanis infensi, moribus, colore, genio diuersissimi? illi subiti, isti graues: illi corpore vt plurimum magni, isti breuiusculi; illi colore candidi, & capillitio davi isti nigro? Scoti quamuis eiusdem religionis, eiusdem Insulæ acolæ semper nihilominùs Anglis infensissimi extitere; itavt ne facta quidem regnorum vnione, potuerint vniquam animos temperare, & in mutuæ necessitudinis nexum venire. Itali olim Orbi imperitabant; nunc autem diuersarum gentium imperio, ac ludibrio subsunt, Sed quid est, quod canis vel minimus gallinam fugat, & deuorat; quam tamen postquam pullos exclusit, adeò reformidat, vt eâ visa fugam quantumuis generosus arripiat, hæcque in illum audax prosiliat? hæc enim verò Naturæ ludentis arcana sunt, quæ tamen suam causam, nostro captu superiorem habent. 133. Sed age, eam vteumque explicare conemur. Ptolemæus in Quadrip lib 4. cap. 7. causam omnem amicitiæ, & inimicitiæ naturalis, adeoque consensus, diffensusve rerum, in coelestium corporum constitutionem refundit. Cùm enim eadem seu se solis, seù, cum aliorum adiumento, sint differe-

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MATHEMATICVM. 41 does not make it so. For this reason too, he says, the diaphragm would affect the heart more quickly than the stomach; for it has no less closeness to the heart, and besides it has motion. But we see that from affections of the stomach faintings arise most promptly, and from affection of the diaphragm, deliriums; therefore these parts do not draw the others into sympathy by these common reasons in which they are surpassed by the others, nor do they act in the same way, but some special nature intervenes, by which these things come to pass between the diaphragm and the brain, the stomach and the heart, which we do not know. Thus, then, this consists in the mutual conspiracy of faculties, which, as I said, depends on a single governance of the soul; and they not ineptly called it analogy, since in things very unlike and disparate it nevertheless preserves a certain likeness. 132. In a similar way in this constitution of the World and of that Macrocosm one may see this analogy of things, which cannot be preserved by mere similarity, nearness, familiarity of work, or some known bond, since this same sympathy in things bound by a far greater bond appears by no means so; yet because we feel it by experience, we infer by clear reason that there is something far superior to these, and thus we rightly bring in the form and agreement of the world into one universal principle. For whence indeed is it, as I was saying, that the French are always and everywhere hostile to the Spaniards, so very different in customs, color, and temperament? these quick, those grave; these for the most part large in body, those rather small; these white in color and fair-haired, those black? The Scots, although of the same religion, inhabitants of the same island, have nevertheless always been most hostile to the English; so much so that not even after the union of the kingdoms was effected could they ever temper their spirits and come into the bond of mutual fellowship. The Italians once ruled the world; now, however, they are subject to the dominion and mockery of various nations. But what is it that a dog, even the smallest, frightens and devours a hen, although after she has brought forth her chicks she so shrinks from it that, at the sight of it, however noble it may be, she takes flight, and she boldly rushes upon it? For these are indeed the secrets of playful Nature, which nevertheless have their cause, higher than our grasp. 133. But come, let us try to explain the matter in either case. Ptolemy, in the Quadripartitum, book 4, chapter 7, refers the entire cause of natural friendship and enmity, and therefore of the agreement or disagreement of things, to the constitution of the heavenly bodies. For since the same things, whether by themselves or with the help of others, are differ-

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LEXICON 412 tentium tum genere, tum specie effectuum causæ, exque vniuersalissimæ, & æquiuocæ; cumque etiam inter ipsa intercedat mutua amicitia, aut inim citia, inde est, vt effectus ipsi eandem inter se proportionem, atque analogiam seruent, quam superiùs suæ causæ, & eò maiorem quò maior inter illa intercedit necessitudo. Sic Iupiter exempli gratia habet sub se ex membris humanis pulmonem, coltas, arterias, eartilagines, hepar, &c. I x lapidibus pretiosis Smaragdum, Sapphyrum, Amethystum, Turcoidem; ex animalibus Elephantos, Damas, Ceruos, Tauros, Columbas, Turtures, Corturnices. Mars autem sinistram, fel, renes, adamantem, iaspidem, magnetem, euphorbium, scammonean, &c. Et hæc prima sympathiæ generis radix: quæ enim ab vno eodemque principio originem trahut ea inter se mutua necessitudine vinciuntur. Item Planetæ inter se, idque ratione qualitatum quibus pollent, sunt amore, odio, vel nullo vinculo colligati. Saturnus & Iupiter, Iupiter, & Sol, Mercurius cum Sole, & Saturno sunt adinuicem amici. Iupiter autem amicus Mercurio, at non ipsi vicissim Mercurius, sed neque inimicus: Martis sola Venus amica, cum tamen Veneri non solum Mars, sed & Sol, & Luna, & Iupiter sint amici: Mercurius Veneri neque amicus, neque inimicus; Lunæ solus Sol inimicus, amici Venus & Iupiter, at ipsa non ei vicem rependit, sed neque alteri inimica, aut amica, excepta vt dixi Venere. Hinc, cum semper effectus aliquam similitudinem referre debeat suæ causæ, hanc eandem necessitudinem inter se Planetarum effectus seruare necessum est, quam seruant inuicem suæ causæ. Præterea cum pro diuerso siderum positu tam in Zodiaco, quam in Mundo diuersas contrahant familiaritates, vt suo loco diximus, easdem per quandam analogiam rebus sibi subiectis communicant: quæ verò nulla familiaritate necuntur, vt in signis inconiunctis, ea nullum etiam amicitiæ vinculum in suos effectus derivant, & hic cardo omnis sympathiæ atque antipathiæ. Hinc ire Ptolemæus loco citato præcipit in amicitiis, & inimicitis hominum dignoscendis respicienda esse Ascendentia vtriusque nati, commutationes planetarum, præsertim Luminarium, aspectus, coniunctiones, Antiscia, seu Intuentia, seu Imperantia, atque obedientia, & ex his de hominum amicitia, inimicitiaque iudicium profertendum. Nam si Ascendentia in Genituris consenserint; erit inter natos necessitudo & sympathia; si fuerint inconiuncta erunt naturaliter auersi, si vero fuerint in quadrato, aut opposito erit adhuc inter

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both in kind and in species, of the causes of effects, and from the universal and equivocal; and since there is also mutual friendship or enmity among the causes themselves, it follows that the effects themselves preserve among one another the same proportion and analogy which, as said above, they have to their causes, and in greater degree the greater the connection that exists between them. Thus Jupiter, for example, has under him, from the members of man, the lungs, bowels, arteries, cartilages, liver, etc.; from precious stones, the emerald, sapphire, amethyst, turquoise; from animals, elephants, deer, oxen, doves, turtledoves, quails. Mars, however, has the left side, bile, kidneys, adamant, jasper, magnet, euphorbium, scammony, etc. And this is the first root of sympathy of its kind: for those things which draw their origin from one and the same principle are bound together by mutual necessity. Likewise the planets among themselves, and that by reason of the qualities with which they are endowed, are joined by love, hatred, or no bond at all. Saturn and Jupiter, Jupiter and the Sun, Mercury with the Sun and Saturn are mutual friends. Jupiter is also a friend to Mercury, but Mercury is not in turn to Jupiter, though neither is he an enemy; Mars has Venus alone as a friend, although to Venus not only Mars, but also the Sun, the Moon, and Jupiter are friends; Mercury is neither friend nor enemy to Venus; to the Moon the Sun alone is an enemy, while Venus and Jupiter are friends, but the Moon does not repay the same, nor is she enemy or friend to any other, except Venus, as I said. Hence, since an effect must always bear some likeness to its cause, it is necessary that the effects of the planets preserve among themselves the same relation which their causes preserve among one another. Moreover, since according to the different position of the stars, both in the Zodiac and in the World, they contract different affinities, as we said in its place, they communicate the same by a kind of analogy to the things subject to them. But those things which are joined by no affinity, as in the inconjunct signs, do not derive any bond of friendship even into their effects; and here lies the whole pivot of sympathy and antipathy. Hence Ptolemy, in the place cited, instructs that in discerning the friendships and enmities of men, one must regard the Ascendants of both nativities, the exchanges of the planets, especially the Luminaries, their aspects, conjunctions, antiscia, or intuencies, or imperia and obedientia, and from these a judgment is to be given concerning the friendship or enmity of men. For if the Ascendants in the genitures agree, there will be a bond and sympathy between the persons born; if they are inconjunct, they will be naturally averse; but if they are in square or opposition, there will still be between the

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MATHEMATICVM. 48. illos odium, persecutio, atque antipathia. In locis per mutatis erit similiter, sed longè maior necessitudo: qui Luminaria, Hileg, aut præcipua figuræ loca habebit In alterius antiscio obedienie, illi fatali quadam vi imperitabit. qui verò in imperante eidem subiectus erit. Quæ quidem data proportione in aliis rebus inanimis locum habent. Vnde, vt benè notat Iulius Cæsar Bulengerus de ratione diuinationis lib. 2. cap. 15. triplex rerum ordo consurgit, quarum alia inter se concordant, alia discordant; quadam nihil concordia, aut discordia inter se habent, quæ vtraque simili temperamento sint: & simile à simili non afflicatur Quamquam quod ipse superius dixerat, insimam hanc rerum consensionem, dissensionemque non à cælo, sed à forma petendam esse; aut à primis qualitatibus, in quarum rationibus est innoluta, cum ex iis rerum omnium tempetamenta consurgant; minùs probare possum; quandoquidem suprà tum ratione, tum grauissimorum doctorum auctoritate stabiliuimus mixtorum mirabiles qualitates minimè elementates esse, sed omninò cælitus derivatas. Si enim ipse tantam virutum copiam in Helleboro, quanta à Plinio describitur; cælo acceptam ferte non audet, cum alioqui hoc causa vniuersalis sit eminenter omnes inferiores virtutes continens, qui eamdem vni formæ particulari attribuit, aut primis qualitatibus, ita vt altera alteri non officeret? Restat igitur, vt Soli potius ascribamus corporibusque cælestibus, quorum vniuersalem virtutem, actiuitatem, supereminentiam in isthæc inferiora nemo sanæ mentis derre d ari poterit. Neque enim selenites Lunæ cursum ac motum, phasesque tantopere imitaretur, nisi eidem aliquo superiori vinculo esset asticta. Neque Heliotropium Solem insequeretur; neque canes in tabiem agerentur cane sirio exurgente, neque Luna in Scorpij signo constituta Scorpiones rerrestres tam sæui forent, ni vllam desuper qualitatem referrent, quæ ita eos sideribus illis addiceret. Nunc autem singulorum istiusmodi effectuum origines persecutemur. Magnes ferrum atrahit non alium magnetem, quia iste omninò similis, & in talibus non est passio, ferrum autem, licet in qualitatibus simile, est tamen illi subordinatum, patique magis idoneum. Magnes item ad polum vertitur, quia cum natura sua sit frigidus, & siccus, easque qualitates eminentius quam cætera mixta habeat, eò vertitur vbi siccitas, & frigiditas regnat: quod ideo, vt dixi non ad polum simpliciter, neque ad Arcticum modo, sed ad regionem vtcumque frigidam, & siccam pro situs va-

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MATHEMATICVM. 48. for them, hatred, persecution, and antipathy. In places mutually changed, it will be similar, but with far greater necessity: those who have the Luminaries, Hileg, or the principal places of the figure, in obedience to another’s antiscion, will be ruled by him with a certain fatal force; and, on the other hand, he who is subjected to the ruler will be dependent upon him. These things, in due proportion, have their place also in other inanimate things. Hence, as Julius Caesar Bulengerus notes well in De ratione diuinationis , book 2, chapter 15, a threefold order of things arises: some agree with one another, others disagree; some have neither concord nor discord with each other, being both of a similar temperament; and like is not harmed by like. Although what he had said above—that this deepest agreement and disagreement among things ought to be sought not from the heavens, but from form; or from the primary qualities, in the rationale of which it is involved, since the temperaments of all things arise from them—I cannot approve, seeing that above, both by reasoning and by the authority of the most serious doctors, we established that the wonderful qualities of mixed things are by no means elemental, but altogether derived from heaven. For if he does not dare to attribute to heaven that great abundance of virtues in Hellebore, such as is described by Pliny, since heaven is after all the universal cause, eminently containing all inferior virtues, how does he attribute it to one particular form, or to the primary qualities, so that one should not hinder the other? It remains, therefore, that we ascribe it rather to the Sun and to the heavenly bodies, whose universal virtue, activity, and preeminence over these lower things no one of sound mind will be able to deny. For the selenite would not imitate the course and motion of the Moon, and its phases, so greatly, unless it were bound to it by some higher bond. Nor would heliotrope follow the Sun; nor would dogs be driven into madness when the rising of the Dog Star appears; nor would scorpions on earth be so savage when the Moon is situated in the sign of Scorpio, unless they derived some quality from above that so attached them to those stars. Now, then, let us trace the origins of each such effect. The magnet attracts iron, not another magnet, because the latter is altogether similar, and in such cases there is no passion; but iron, although similar in qualities, is nevertheless subordinate to it, and more fitting to be acted upon. Likewise the magnet turns toward the pole, because since by its nature it is cold and dry, and has those qualities more eminently than the other mixed things, it turns to where dryness and coldness reign: and this, as I said, not simply to the pole, nor only to the Arctic, but to whatever region is cold and dry according to the place.

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LEXICON 484 tiate tendit, adeo vt irans æquatorem se vertat ad Austrum. Similiter succinum, & alia id genus fossilia, non quidem, vi aliqui opinantur, per quodam effluuios spiritus paleas ad se attrahunt (aliasa conficario, quæ in iis ante attractionem requiritur, officeret magis, quam prodesset, sed quia igneis qualitatibus polleni, adeoque aridas stipulas, consimilis naturæ, aptaque ignis pabula sibi copulant, nec nisi confricatione incalescant. Econi[ra] quæ diuersi, aut disparati omninò temperamenti sunt, aut sibi inuicem aduersantur, aut in mutuam consensionem, dissensionemve venire non possunt. Sic allij succus magneti vim adimit, quia cum contrariis qualitatibus inficit: cicuta hominibus exitialis est, quia intempetare frigida, caloris naturalis suffocatiua, at non asino, at non sturnis, quia ratione temperamenti non illa iis incommoda. Aconitum sanos extinguit, venenatos sanirati reddit, quia longè superioribus qualitatibus pollens, in pugna cum iis congrediunt quas ad pugnandum parias, validasque inuenit, easque in pugnando inferiores vincit. Atque ad hæc & similia rerum principia, omnis sympathiæ, atque antipathiæ ratio reducenda est. Quare, vi benè monet doctissimus Maiæuiglia in suo Proteo Ethicopolitico lege 21. Reliqua prorsus admitanda Natura arcana ita rimari debet Natura investigator, vt semper eorum causas, & principia agnoscat in natura, quæ in omnibus, quæ quoquo modo mouentur, aut quiescunt, principium est, vt aiunt Philosophi. SYMPHASIS. Vide Simphasis. SYNECHON, Græcè dicitur Firmamentum fixarum à [mercur]è [satur]i [satur]i [mercur]io quod est continere, quia in suo expanso tot stellarum multitudinem continet. SYNOD[us] Græcè idem sonat ac Latinè convenio, & congiessus. Ideò apud Astronomos accipitur pro duorum vel plurium astrorum conuenientia & concurtu siue in eumdem circulum positionis, siue in eumdem gradum eclipsicum, vbi simulnatutam, atque influxus commisceant. Vide abundantius in V. Corius, & conjunctio. SYRIVS. Vide Sirius. SYROYCVS vulgò dicitur venius spirans à medio loco inter Orientem, & Meridiem, à Syria vnde transiens ad nos venit Græcè nota peliones. Cum perflat visum habeat, capui gravat, humores dissoluit, fluxiones excitat, raucedinem tusses, vertigines, apoplexiam, epilepsiam, surditatem, oculorum lippitudines, mulierum abortiones, aliaque id genus facit, quæ æque Austro ac ventis sibi collateralibus sunt communia. SYSTEMA

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LEXICON 484 …tends, so that it turns itself toward the south when it passes the equator. Likewise amber, and other fossils of that kind, do not attract chaff, as some think, by some effluvia of spirit; for the confectio, which is required in them before attraction, would hinder rather than help, but because, being endowed with fiery qualities, and therefore with dry stalks of a similar nature and fit fuel for fire, they unite to themselves, and are not warmed except by rubbing. Things on the contrary which are of different, or altogether dissimilar temperament, either are opposed to one another, or cannot come into mutual agreement or disagreement. Thus some juice takes away the power of the magnet, because it infects it with contrary qualities: hemlock is fatal to men because, being excessively cold, it suffocates natural heat, but not to the ass, and not to starlings, because by reason of temperament that is not harmful to them. Aconite kills the healthy, restores the poisoned to health, because, being endowed with qualities far superior, it enters into combat with those which it finds fit and strong for fighting, and by fighting conquers them when they are weaker. And to these and similar first principles of things, the whole account of sympathy and antipathy must be reduced. Wherefore, as the most learned Maiæuiglia wisely advises in his Proteo Ethicopolitico, law 21, the investigator of nature ought by no means to omit the rest, but must so explore the hidden things of Nature that he always recognizes their causes and principles in nature, which, as the philosophers say, is the principle in all things that are in any way moved or at rest. SYMPHASIS. See Simphasis. SYNECHON, in Greek, is said of the firmament of the fixed stars, from [mercur]è [satur]i [satur]i [mercur]io, which means to contain, because in its expanse it contains a multitude of stars. SYNOD[us] in Greek has the same meaning as the Latin convenio and congressus. Therefore among astronomers it is taken for the conjunction and concurrence of two or more stars, whether in the same circle of position or in the same ecliptic degree, where they mingle their natures and influences together. See more fully under V. Corius, and conjunction. SYRIVS. See Sirius. SYROYCVS is commonly called the wind blowing from the middle place between the East and the South, from Syria, whence passing it comes to us; in Greek, nota peliones. When it blows strongly it affects the sight, burdens the head, dissolves the humors, excites fluxes, hoarseness, coughs, vertigo, apoplexy, epilepsy, deafness, weakness of the eyes, miscarriages of women, and other things of that kind, which are common both to the south wind and to the winds adjacent to it. SYSTEMA

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MATHEMATICVM. 485 SYSTEMA, Græcè audit Vniuersi proba constitutio, & harmonia cælestium corporum inter se, & ergà tellutem ita dispositorum vt situs, ordo, motus, ac passiones apparentiis, ac demonstrationibus tum philosophicis apprime respondeant. Ricciolus lib. 9. sect. 3. cap. 2. sic illud describit. Systema Mundi nihil aliud est quam coordinatio, seu compositio magnarum munds partium, videlicet elementorum, ac calorum; cuius veluti materia est numerus calorum, atque elementorum tum totalium, tum partialium; forma autem est ordo, ac situs eorum inter se, ac relatiuè ad centrum Vniuersi. Celebertium olim fuit quod co[n]cinnavit Mercurius Trismegistus, admiserunt Timocharis, Epimenides, Hipparchus, Archimedes, ac Ptolemæus in Almagesto insigniter commendauit, probauit, stabiliuitque hoc ordine; vt tetra simul cum aqua vnum globum efficiens foret Vniuersitatis centrum; mox aëre circumquaque ambiretur, quid vt leuius elementum, minus tamen quam ignis secundum locum teneret; inde sphæræ ignis; cuius regionis terminè constituerentur ab vltima superficie supremæ regionis aëris, vsque ad concauum Lunæ: Postea succederet orbis Lunæ, & per ordinem alij superiores Mercurij, Veneris, Solis, Martis, Iouls, & Saturni; eodem ordine & habitudine ad tellurem tamquam ad omnium centrum, post quos sequeretur Firmamentum, seu Orbis fixarum, ac tandem Primum Mobile omnes concentricos habens, & complectens. Inueterata hæc mundi constitutio perdurauit vsque ad Nicolai Copetnici ingeniosissimi alioqui Astronomi tempora; qui ex nouis obsetuationibus videns, non posse subsistere prædictum Systema Ptolemaicum, aliud excogitauit seu potius exsu citauit à paucis olim antiquis Philosophis excogitatum, sed cum ipsis emortuum. In eo constituitur sol immobilis in Vniuersi centro: Post orbis Mercurij, qui diebus 80. suam integram revolutionem perficeret. Secundo loco succederet Venus nouem mensium spatio suum circuitum complectis. Tertio loco terræ globus vna cum Lunâ, quæ itidem continuè ergà teliurem circumagatur. Atque huic triplicem motum assignant; diurnum, quò ex Occidente in Orientem ducitur spatio 24. horarum (quem nos motum raptui p[er]tini mobilis damus:) annuum, quem nos soli: ac tertium, quem vocant libtationis, quo inæqualitas æquinoctiorum ostenditur, atque Eclipticæ obliquatio ab Æquatore. Sequitur postea Mars, revolutionem suam ergà solem in annis duobus perficiens: inde Iupiter in Hh

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MATHEMATICVM. 485 SYSTEM, in Greek, means the sound arrangement and harmony of the heavenly bodies among themselves, and with respect to the earth, so disposed that their position, order, motion, and properties correspond exactly with appearances and with both philosophical and demonstration-based accounts. Ricciolus, book 9, sect. 3, chap. 2, describes it thus: The System of the World is nothing other than the coordination, or composition, of the great parts of the world, namely the elements, and the heavens; of which the number of the heavens and the elements, both total and partial, is as it were the matter; but the form is their order and position among themselves, and relatively to the center of the Universe. The most celebrated of old was that which Mercury Trismegistus contrived; it was admitted by Timocharis, Epimenides, Hipparchus, Archimedes, and Ptolemy in the Almagest, and was notably commended, proved, and established in this order: that the earth together with water, making one globe, would be the center of the Universe; then that it would be surrounded on every side by air, which, as being a lighter element, would nevertheless occupy a place below fire; then the sphere of fire; the boundaries of which region would be fixed from the outer surface of the highest region of air, as far as the concavity of the Moon: after that would follow the orbit of the Moon, and in order the higher orbits of Mercury, Venus, the Sun, Mars, Jupiter, and Saturn; in the same order and relation to the earth as to the center of all things, after which would follow the Firmament, or Sphere of the fixed stars, and finally the Primum Mobile, having and enclosing all the concentric spheres. This ancient constitution of the world endured until the time of Nicolaus Copernicus, otherwise the most ingenious astronomer; who, from new observations seeing that the aforesaid Ptolemaic System could not stand, devised another, or rather revived one previously devised by a few ancient philosophers, but extinct along with them. In this he established the sun as motionless at the center of the Universe: after the orbit of Mercury, which would complete its entire revolution in 80 days. In the second place would come Venus, completing its circuit in the space of nine months. In the third place would be the globe of the earth together with the Moon, which likewise continually revolves around the earth. And to this they assign a threefold motion: daily, by which it is carried from West to East in the space of 24 hours (which we attribute to the motion of the outermost heaven by impelling it); annual, which we attribute to the sun; and a third, which they call the motion of libration, by which the inequality of the equinoxes is shown, and the obliquity of the Ecliptic from the Equator. Then follows Mars, completing its revolution around the sun in two years: then Jupiter in Hh

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486 LEXICON annis 12. Tandem Saturnus in annis 30. Post quos postremam omnium constituunt sphæram fixarum immobilem. <141> Et hæc est constitutio Vniuersi, ex Philolai primum, mox ex Copernici placitis excogitata, in quam mirum est, quam multi ex neotericis conspirantes adhæserint, ac magno plausu receperint. Et sanè si modum spectemus, quo optimè saluantur omnes apparentiæ, ad cuius normam institutæ radices cælestium motuum, isti ad amussim respondent, eâ certè vsque ad Phychonis tempora, nulla visa est concinnior, pulchrior, & vsui accommodatior. Verum hoc systema intolerabilem errorem admittit, terram viique mobilem; quod experientiæ, & (quod magis interest) vni sacræ scripturæ testimonio aduersatur, terram omninò immobilem asserentis. Scio equidem nonnullos esse, qui dicant sacram scripturam vsu humano loqui provt in multis perspicuum est, proindeque ea testimonia huic assertioni minimè refragari. Quin etiam Didacus Astunica ex illo Iobi 9. vbi de Deo dicitur: Qui commouet terram de loco suo, & columna eius concutiuntur; hanc terræ mobilitatem probere nitur, additque nullum esse in tota scriptura locum, qui tam disertè dicat terram non moueri, quam hîc moueri dicit. Sed, vt optimè ostendit Pineda in hunc locum, inde potiùs euinci potest naturalis terræ firmitas, & habitudo, quæ cum ea sit, vt loco minimè dimoueatur, Dei potentia sit, vt contremiscat, atque ad eius nutum concutiatur, quod de terræ motibus, quibus terra à facie Domini trepidare dicitur intelligendum est, vt communiter explicant Patres: eò maxime quod columnæ, (de quibus hic sermo est) quandam stabilitatem magis quam commotionem significant. Quod autem terræ stabilitas à scripturis disertissimè astruatur; patet id apertissimè, & nos in loco adnotabimus: & omnes huiusmodi loquutiones, Sancti Patres communiter ad literam de terræ stabillitate, qua in centro Mundi omninò immobilis constiruta est, explicant, & intelligunt: à quibus profectò recedere temerarium foret. Quare iure meritò hoc systema Copernicum, tamquam falsum, sacræ scripturæ aduersum, atque à veræ Philosophiæ principiis alienum, damnatum fuit à sacra Congregatione Cardinalium peculiari decreto: atque in Galilæum, qui illud nihilominus semel & iterum sustinere ardentius quam Christiano homini par erat, annitebatur, seuerius animaduersum. <142> Tandem Tycho Brahe Danus verus Astronomiæ instaurator, post longam quinquaqinta ampliùs annorum obser-

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486 LEXICON years 12. Finally Saturn in 30 years. After these they place as the last of all the fixed sphere of the immovable stars. <141> And this is the constitution of the Universe, first devised from the views of Philolaus, then of Copernicus, into which it is astonishing how many of the moderns, agreeing together, have attached themselves, and have received it with great applause. And truly, if we look to the method by which all appearances are best saved, according to whose rule the roots of the heavenly motions are established, these correspond exactly; certainly up to the time of Phycho, none has seemed more fitting, more beautiful, or more suited to use. But this system admits an intolerable error: that the earth too is movable; which is contrary to experience, and (what matters more) to the testimony of the one sacred Scripture, which asserts that the earth is altogether immovable. I know indeed that there are some who say that sacred Scripture speaks in human usage, as is evident in many places, and therefore that those testimonies do not at all oppose this assertion. Indeed Didacus Astunica, from that passage of Job 9, where it is said of God, “Who moves the earth from its place, and its pillars are shaken,” strives to prove this mobility of the earth, and adds that there is no place in the whole of Scripture which so plainly says that the earth does not move, as here it says that it moves. But, as Pineda shows very well on this passage, from it rather can be inferred the natural firmness and stability of the earth, which is such that it is not moved from its place, while it is by the power of God that it trembles and is shaken at his nod, which must be understood of the movements of the earth, by which the earth is said to tremble before the face of the Lord, as the Fathers commonly explain; especially since the pillars, of which the present discourse speaks, signify a certain stability rather than a disturbance. But that the stability of the earth is most clearly established by the Scriptures is plain most openly, and we shall note it in its place; and all expressions of this kind the holy Fathers commonly explain and understand literally of the earth’s stability, by which it has been constituted altogether immovable in the center of the world: from which indeed it would be rash to depart. Wherefore this Copernican system was rightly and deservedly condemned by a special decree of the Sacred Congregation of Cardinals, as false, contrary to sacred Scripture, and alien to the principles of true Philosophy: and against Galileo, who nevertheless strove to support it once and again more eagerly than was fitting for a Christian man, more severe notice was taken. <142> Finally Tycho Brahe, the Dane, the true restorer of Astronomy, after a long observation of more than fifty years

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MATHEMATICVM 437 uationem, adiutus à pluribus petitissimis Mathematicis primus omnium cælum liquauit, hæteream omnem regionem fluidam constituens ad morem æris permeabilem, sed longè aere ipso subtiliorem, ac leuiorem: in cuius expanso, & palliue omnia cælestia corpora collocauit, suo quodcumque ordine & loco, motuque proprio præditum, provt ex appareniis cuinci potest. Hinc nouum systema excogitauit sanctæ Rom. Ecclesiæ constitutis inhærens, obseruationibus apprimè respondens, ac sacræ scripturæ oraculis, Patrum dictis, veræque Philosophiæ principiis maximè consonum: in quo terram statuit amborum luminarium, ac Firmamenti, seu Orbis stellati centrum: Solem vetò reliquorum quinque planè arum: qui proinde omnes eccentrici essent ad terram; & per vastissimam illam Ætheris regionem constantissimè, & numquam fallente gradu perpetuo rotarentur ad olem; itavt Mars quando fieret Achronicus in solis oppositione respectu nostri in Zodiaco, fieret etiam ter proximior ipso sole, & consequenter corpore et am grandior videatur uam constitutus in Apogæo, Venerem ipsam magnitudine superet, vmbram faciat, ac trium minutotum paraliasim patiatur, vt ego semel, & iterum obseruaui. Sicque exhibira hæc cæli facies omnes motus, & apparentias saluat, nouis Phænomenis in Æthere visis, haud egrè locum, & materiam tribuit, difficultates omnes soluit, atque humanum captum in rei veritate roborat, & obscurat Alia item Mundi systemata circumferuntur, quæ, quoniam à prædictis parum deuiant, vel non ita communi plausu recepta sunt, ideò breuitati consulentes omisimus. SYRH in sphæra barbarica dicitur secundus decanus Cancri manens sub dispositione Mercurij; iocositatis, confabulationis mulierum, diuitiarum, vbertatis, &c. SYZ apud Gtæcos significant cælestes siderum copulationes; non modò per corporalem coniunctionem, vt aliqui rigorosè nimis intelligunt, sed etiam per aspectum, & quamcumque familiaritatem: quâ videlicet fiat radiorum commixtio, & virtutis in vnum coadunatio. Et ita rem radicitus explicat Valentinus Naiboda in Alchabitium.

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MATHEMATICVM 437 ...revolution, assisted by several most distinguished Mathematicians, first of all imagined the heavens as liquid, constituting the whole ethereal region as fluid and permeable like air, but far subtler and lighter than air itself; in the expanse of which he placed all the celestial bodies, each with its own order and place, and endowed with its own proper motion, as can be judged from the appearances. Hence he devised a new system, adhering to the constitutions of the Holy Roman Church, responding most closely to observations, and most consonant with the oracles of Holy Scripture, the sayings of the Fathers, and the principles of true Philosophy: in which he placed the earth at the center of both luminaries and of the Firmament, or Starry Sphere; but the Sun at the center of the other five planets. Therefore they all would be eccentrics with respect to the earth, and would rotate perpetually through that vast region of Ether with constant and never-failing motion around the Sun; so that Mars, when it is Acronic in opposition to the Sun with respect to us in the Zodiac, would also then be three times nearer the Sun itself, and consequently would appear greater in body and dimension than when it is situated in apogee; Venus itself would surpass it in size, cast a shadow, and undergo a parallax of three minutes, as I myself observed once and again. And so this appearance of the heavens exhibits and preserves all motions and appearances, gives an easy place and material for the new phenomena seen in Ether, resolves all difficulties, and strengthens human understanding in the truth of the matter. Other systems of the world are also circulated, which, since they deviate little from the aforesaid, or have not been received with such common approval, we have omitted in consideration of brevity. SYRH in the barbaric sphere is said to be the second decan of Cancer, remaining under the disposition of Mercury; of playfulness, conversation of women, riches, abundance, etc. SYZ among the Greeks signifies celestial conjunctions of the stars; not only by bodily conjunction, as some too strictly understand it, but also by aspect, and by any kind of familiarity: namely, whereby there takes place a mingling of rays and a union of power into one. And thus Valentinus Naiboda explains the matter from the root in Alchabitium.

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T 1. TABIL apud Ptolemæum in Quadrip. lib. 4. cap. 7. ex versione arabica, idem sonat, ac loca siderum permutata in cælesti figuta: vnde inuestigari posse autumat omnem, quæ inter duos homines intercedit, sympathiæ, antipathiæve rationem, atque originem. Nam si loca luminarium in vtriusque figura perspectâ fuerint inuicem permutata, aut cum horoscopo, vel Parte fortunæ, magna erit, inquit, inter ipsos naturæ conuenientia, atque amoris necessitudo. Econtrà si hæc in locis fuetint inconiunctis, aut oppositis, magnam arguunt naturarum diversitatem, proindeque antipathiæ, & auersionis naturalem fomitem, ac seminarium. Postò hæc permutatio dupliciter fieri potest, & in Zodiaco. si quem gradum eclipticum sol obtinet in alicuius natiuitate, in alterius occupet Luna, & vice versa: Et in Mundi situ, si videlicet permutentur circuli positionum, itavt tantum distet à cu[m]mine, vel ab imo cæli sol in vnius Themate, quantum in alterius Luna: & sic de singulis, de quibus fuse agit Ptolemæus loco citato. TANGENS antonomasticè appellatur à Geometris linea recta perpendicularis extrà circulum cadens ad extremum diametri ipsius circuli; quæ si vltra adhuc protractetur, secaret ipsam lineam trianguli similiter vltrà protractam ad angulos rectos. Hæc, inquam linea ita considerata dicitur Tangens, quia aliam lineam à centro circuli oblique protractam, & ipsum circulum secantem, tandem opus est vt contingat: ex quarum postea habitudine, ac proportione adinuicem arguatur habitudo atcus ad sinus, & complementum sinuum. TAN N siue cum articulo El-tanin hoc est anguis Hebraicè, dicitur Draco sidus ad polum Zodiaci arcticum illud circumquaque ambiens: de quo vide quæ diximus in V. Draco. T RAUP 2 Græco-barb. dicitur in sphæra barbarica Centaurus sidus in cælo, de quo alibi dictum est. TAYR 3 secundum Zodiaci signum, fixum, terreum mutilatum Domicilium Veneris, & Exaltatio Lunæ in quo, vtpote in principe signo sui trigoni, primùm apparet post congressum cum Sole in Ariete ipsius Solis exaltatione: Arabicè Ataur. Præest ex membris humanis collo, cervici, gutturi. Et ideò hoc Tauri nomen est inditum, quia experientia probatum est, homines sub illo nascentes laboriosis quod

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T 1. TABIL apud Ptolemæum in Quadrip. lib. 4. cap. 7. from the Arabic version means the same as the places of the stars transposed in the celestial figure: whence he thinks that one can investigate every reason and origin of sympathy or antipathy that occurs between two men. For if the places of the luminaries in the figure of each have been seen transposed with one another, or with the horoscopus, or the Part of Fortune, there will be, he says, great agreement of nature between them, and a bond of love. On the other hand, if these are found in places not joined, or opposite, they indicate a great diversity of natures, and therefore a natural source and seed of antipathy and aversion. Afterward this transposition can be made in two ways, both in the Zodiac: if the Sun occupies some ecliptic degree in one person's nativity, and the Moon occupies it in another's, and vice versa; and in the situation of the World, namely if the circles of position are exchanged, so that in one person's Themate the Sun is as far from the summit, or from the bottom of the sky, as the Moon is in another's: and so of each individual point, on which Ptolemy treats at length in the cited passage. TANGENS is called by geometers, by antonomasia, a straight line falling perpendicularly outside a circle to the end of the diameter of that circle; and if extended farther, it would cut the line of a triangle likewise extended farther at right angles. This line, I say, thus considered, is called a Tangent, because it must touch another line drawn obliquely from the center of the circle and intersecting the circle itself: and from the relation and proportion of these lines to one another, the relation of the arc to the sine and the complement of sines is afterward inferred. TANN, or with the article El-tanin, that is, “serpent” in Hebrew, denotes the constellation Draco, surrounding on every side the arctic pole of the Zodiac; see what we have said in V. Draco. TRAUP 2, in Greek-barbarous usage, is said in the barbaric sphere to be the constellation Centaurus in the sky, of which something has been said elsewhere. TAYR 3, the second sign of the Zodiac, fixed, earthy, mutilated, the domicile of Venus and the exaltation of the Moon, in which, as in the principal sign of its trigone, it first appears after conjunction with the Sun in Aries, the exaltation of that Sun: in Arabic, Ataur. It presides over the human members, the neck, nape, and throat. And therefore this name Taurus has been given, because experience has proven that those born under it labor in what

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MATHEMATICVM. 48. sed pigri & ingenio rudes, fronte elata, atque vtrinque prominentes, quales sunt boues: sed adhuc alia ratio suppetit, quia hoc signum specialiter eius generis animantes afficit, vt eo malè affecto atque ab infortunis possesso, malè futuram esse pecudibus expectandum sit. Narrant quippe Pontanus ac Niphus in cõment. Apotelesm. Ptolemæi, suo tempore Saturni & Martis coniunctio < 6.> nem in Tauro, horridissima hyemis frigora suscitasse, magnamque bobus calamitatem, perniciemque intulisse: & quanquam oves tolerando frigori sint imbecilliores, nihilominus in boues maximè pestem illam desæuiisse, propter signum coeleste ad quod terrestris bos refertur, vt Arieti bones & armamenta subsun, Caniculę canes terrestres, &c. quapropter si in Ariere ea synodus maleficaru[m] celebrata fuisset vtiq[ue] in oves potiùs ea pestis debachata fuisset. Eins Asterismus in octaua sphæra continet stellas 33. & vndecim in formes: Quamquam Bayerus in eo sidere enumeret stellas 48. & Keplerus 52. inter quas celeberrimæ sunt Pleiades, Hyadesque, hæ in capite, illæ in genibus constitutę: nitium sumit à gr. 17. Tauri primi mobilis, ac protenditur vsque ad gr. 25. Geminorum. Natura eius diuersa est ob diuersitatem stellarum, quę in eo sunt: nam primę eius partes, in quibus sunt Pleyades stellæ procellosę, violentę sunt, & maleficæ: mediæ temperatæ, & aliquantò humidiores: Postremæ calidæ in quibus hyades, fulgura, coruscationes, & similia adducentes. De stellis in eo consistentibus in parti-culari suis quibusque locis differuimus. TE ESCORVM est instrumentum opricum ex tubis, ac < 7.> duplici, vel etiam multiplici vitro, concauo quidem pri-mo, conueris autem, ac lenticularibus aliis, per cuius me-dium in determinata distantia exceptæ obiecti visibilis spe-cies refranguntur, ac mirum in modum dilatentur, referatque obiectum longè potentiæ visuæ approximatum, cu-ius ope factum est, vt corpora cælestia, eorum maculæ for-ma, luminis qualitas, aliæque affectiones probè nostris temporibus internosci potuerint, infinitæ propemodum stellæ in Firmamento obseruaræ, noua Phoenomena circa Iouem & Saturnum item detecta sint, quæ priùs ob sui exilitatem, & loci distantiam oculorum aciem fugiebant. Huius admirabilis instrumenti inuentionem, aut sanè di-lucidarionem debemus Galilæo Galilæi insigni Mathematico, à quo apud nos Italos nomen accepit; licet nostris temporibus ab Fontana, aliisque ingeniosis viris mirum in modum ampliarum sit, vt iam nil amplius in eo gene- Hh iii

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MATHEMATICVM. 48. but sluggish and dull-witted, with a raised brow and prominent on both sides, such as oxen are: but there is still another reason at hand, because this sign especially affects animals of that kind, so that, when it is badly affected and possessed by misfortunes, it is to be expected that cattle will fare badly. For Pontanus and Niphus relate in their commentary on Ptolemy’s Apotelesmata that, in their time, a conjunction of Saturn and Mars in Taurus <6.> stirred up the most grievous cold of winter and brought great calamity and destruction upon oxen: and although sheep are weaker in enduring cold, nevertheless that pestilence raged most strongly among oxen, because of the heavenly sign to which the earthly ox is referred, just as to Aries she-goats and armaments belong, to Canicula earthly dogs, etc. wherefore, if that synod of witches had been held in Aries, that plague would certainly have ravaged sheep rather than oxen. Its asterism in the eighth sphere contains 33 stars, and eleven in figure-form; although Bayer enumerates 48 stars in that constellation, and Kepler 52, among which the most celebrated are the Pleiades and the Hyades, these being situated in the head, those in the knees. It extends from 17 degrees of Taurus of the first mobile, and stretches as far as 25 degrees of Gemini. Its nature is diverse because of the diversity of the stars that are in it: for its first parts, in which are the Pleiades, are stormy, violent, and malefic stars; the middle are temperate and somewhat more humid; the last are hot, in which the Hyades are found, bringing lightning, flashes, and the like. We have spoken in particular, in their proper places, about the stars situated in it. THE ESCORVM is an optical instrument made of tubes, and <7.> of a double or even multiple glass, the first concave and the other convex, along with other lenticular pieces, through whose middle, at a determined distance, the received species of a visible object are refracted and wonderfully enlarged, so that the object appears to be brought close to the power of sight; by its aid it has come about that celestial bodies, their spots, shape, quality of light, and other properties have been well recognized in our times, that an almost infinite number of stars have been observed in the Firmament, and new phenomena around Jupiter and Saturn likewise discovered, which previously, because of their smallness and the remoteness of their place, escaped the sight of the eyes. We owe the invention, or certainly the elucidation, of this admirable instrument to Galileo Galilei, an outstanding mathematician, from whom it received its name among us Italians; although in our times it has been wonderfully enlarged by Fontana and other ingenious men, so that now nothing further in that kind Hh iii

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418 LEXICON re desiderari posse videatur. 1. TELVM, sagitta, iaculum, Demon Meridianus, fidus ad borealem plagam propè Aquilam: de quo satis dictum est sub his dictionibus. 2. TEMPERAMENTVM communiter dicitur proportio, & mixtio quatuor primarum qualitatum, quæ constituunt vniuersa corpora mixta, aique à maiori vel minori vnius super aliam qualitatem prædominio, & excessu, diuerficiatur, vnde & complexio apud nos, & Græcos appellari solet. Eius nouem species ab Hippocrate, Galeano, aliisque Medicis assignari solent: aut enim in corpore mixto istæ qualitates omnes in gradu remissio sunt & æqualis omnium est proportio, & constituit iustum, perfectum que temperamentum, quo melius excogitari nequit, quodque est reliquorum veluti canon, & norma: aut hæc proportio est inæqualis, itavt non sit par intensio qualitatum, & id duobus modis euenire potest, primò vt cæteris tribus moderatè se habentibus vna qualitas superemineat, & sic, vti quatuor qualitates sunt, quatuor etiam differentias temperamenti specificant, atque à seipsis denominant, calidum videlicet, aut frigidum, aut humidum, aut siccum. Secundò, vt duæ reliquis duabus præualeant, quemadmodum in elementis videre est, & sic alias quatuor mixtorum species statuunt ab elementis denominatas, sicqu dicimus illum complexionis esse sanguineæ, quia in eo abundant caliditas, & humiditas; alium esse cholericum, quia in eo flava bilis, & sic calor & siccitas, alium Phlegmaticum, quia flegma, hoc est humor aqueus frigidus, & humidus: alium denique melancholicum, quia præcellit in eomelancholia, & atra bilis cum siccitate & frigiditate. Porrò hæ qualitates, est in pluribus mixtis elementares sint, in cælestibus etiam inueniunrur eminentiori modo, quæ etiam diuersam cælestium corporum constitutionem indicant pro diuersa earum mixtura, quæ ab effectibus innotescit. Vnde & probabile est mixabiles qualitates aliquorum mixtorum quas videmus elementaribus longe præcellere, non ab elementis, sed à cælelestibus ortum ducere, qua de re plura diximus in V. Mixta. TEMPVS quid sit, adeò difficile est explicaru, vt iure divertit Augustinus lib. 1 Confess. cap. 14. Quid est tempus, si nemo ex me quarat scio, si quarenti explicare velim, nescio. Eius quidditatem obscurissimè tradit Philosophus 6. Phjsi cor. text. 10. Tempus est, inquit, numerus motus secundum prius, & posterius: indicat enim rerum fluxibilitatem,

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418 LEXICON it may seem to be desired. 1. TELVM, arrow, dart, Demon Meridianus, faithful to the northern region near Aquila: enough has been said of this under those terms. 2. TEMPERAMENT is commonly called the proportion and mixture of the four primary qualities, which constitute all mixed bodies, and is diversified by the greater or lesser preponderance and excess of one quality over another; whence it is also usually called complexio among us and among the Greeks. Its nine species are usually assigned by Hippocrates, Galen, and other physicians: for either in a mixed body all these qualities are in a moderate degree and the proportion of all is equal, and it constitutes a just, perfect temperament, better than which nothing can be devised, and which is as it were the canon and norm of the rest; or this proportion is unequal, so that the intensities of the qualities are not equal, and this can happen in two ways: first, when the other three are moderately disposed, one quality stands above the rest, and thus, since there are four qualities, there are also four differences of temperament specified, and named from themselves, namely hot, or cold, or moist, or dry. Second, when two prevail over the other two, as may be seen in the elements, and thus they establish four other species of mixtures named from the elements, so we say that one has a sanguine complexion, because heat and moisture abound in it; another to be choleric, because in it yellow bile, and thus heat and dryness; another phlegmatic, because phlegm, that is, watery humor, cold and moist: another finally melancholy, because melancholy prevails in it, and black bile with dryness and coldness. Moreover, although these qualities are in many mixed bodies elemental, they are also found in the heavens in a more eminent way, which also indicate the diverse constitution of heavenly bodies according to the diverse mixture of their parts, which is known from their effects. Whence it is also probable that the mixable qualities of certain mixtures which we see far surpass elemental ones, derive their origin not from the elements, but from the heavenly bodies, concerning which we have said more in V. Mixta. TEMPUS, what it is, is so difficult to explain that Augustine rightly says in book 1 of the Confessions, chapter 14: What is time? If no one asks me, I know; if I want to explain it to one who asks, I do not know. The Philosopher sets forth its quiddity most obscurely in book 6 of the Physics, text 10. Time, he says, is the number of motion according to before and after: for it indicates the fluxibility of things,

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MATHEMATICVM. 491 estque veluti mensura eorum motus, & variationis: Vnde quia cælorum motus est regularissimus, uotissimus, citatissimus, multiplex, ac perpetuus ideò in eo aliqui rationem temporis constituere, indeque dictum autumant, quasi temperatum, ab Solis, Lunæ, aliorumque siderum tenore, & temperato cursu. Sed enim benè insurgit idem Augustinus ? loco cit. cap. 31 Audiui à quodam homine docto, quod solis & Luna, ac siderum motus ipsa sint tempora & anni: cur enim non potius omnium corporum motus sint tempora? An verò, si cessarent cali lumina, & moraresur rota figuli non esset tempus? Iure quidem: quinimò si omnis motus cessaret, omnis fluxibilium duratio deperiret an non esset tempus saltem imaginarium? At enim quia mobilium omnium, vt dictum est constantissimi, ac regularissimi sunt cælestes orbis, ideo non ab re dictum est ab eo viro docto tanquam per antonomasiam ipsos esse tempora & annos, siquidem iure aduertit D. Thomas 1. parte quas. 10, art. 6. tempus esse in primo mobili tamquam in subiecto, ac primo mensurato, correspondet enim quodlibet temporis momentum cælorum conuersioni, & quot in cælo conuersiones, tot etiam tempora distinguuntur; Sed eorum omnium rector est primum mobile, quod spatio 14. horarum sese in gyrum voluens diem constituit naturalem, Lunæ periodus, quatrotum Zodiacum lustrat, mensem; Sol autem sua integra revolutione per Zodiacum efficit annum: sic etiam anni magni, & Epochæ, aliaque temporum differentiæ ex diuersis revolutionibus, aut congressibus cælestium corporum, præsertim vero luminarium vt in locis dictum est, constituuntur. Hinc est quod solis regiam pulchrè describens Ouidius 2. Metamorphos. ei temporum diuersa spatia, & interualla pro satellitio, & comitatu assignet: sic enim canit. In solio Phēbus, claris lucente smaragdis A dextrâ liguâque Dies, & Mensis, & Annus Seculaque, & positæ spatiis equalibus Horæ: Verque nosum stabat cinctum florente corona Stabat nuda Æstas, & spicea sarta gerebat Stabat, & Autumnus calcatis sordidus vuit Et glacialis Hyems canos hirsuta capillos. Sunt autem nouem, præcipuæ temporum differentiæ, seu vt alij volunt, addita etiam hebdomada, decem: Annus, Mensis; dies, quadrans, hora, punctum, momentum, vncia, & atomus. Annus, vt dictum est, desinitur à proprio cursu solis; mensis à Luna, sed rectius ab ipso sole in men- H h iiiij

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MATHEMATICVM. 491 and is as it were the measure of their motion and variation. Hence, because the motion of the heavens is most regular, swiftest, most rapid, manifold, and perpetual, some therefore think that the notion of time is established in it, and that it is so called, as though tempered by the course and measured motion of the sun, moon, and the other stars. But Augustine himself rises up well against this? In the cited place, ch. 31: “I heard from a certain learned man that the motion of the sun and moon and the stars themselves are times and years; why then should not the motion of all bodies rather be times? Or, if the lights of heaven ceased, and the potter’s wheel were to stand still, would there not be time?” Quite rightly, indeed; nay, if every motion ceased, the duration of all things capable of flux would perish; would there not still be time, at least imaginary? But because the motions of all mobile things, as has been said, are most constant and regular in the heavenly spheres, therefore it is not without reason that that learned man said, as it were by antonomasia, that they themselves are times and years; since, as St. Thomas rightly notes, 1st part, q. 10, art. 6, time is in the first movable as in its subject and first measured thing, for every moment of time corresponds to the turning of the heavens, and as many revolutions as there are in the heavens, so many times are distinguished. But their ruler of them all is the first movable, which, revolving in a circuit within the space of 14 hours, constitutes the natural day; the period of the moon, as it traverses the Zodiac four times, a month; but the sun, by its full revolution through the Zodiac, makes the year. Thus also the great years and epochs, and other distinctions of time, are constituted from the various revolutions or conjunctions of heavenly bodies, especially of the luminaries, as has been said in the places cited. Hence it is that Ovid, beautifully describing the royal palace of the sun in Metamorphoses 2, assigns to it the various spans and intervals of time as a retinue and escort: for thus he sings. In the throne of Phoebus, shining with bright emeralds, on the right and left stood Day, and Month, and Year, and Ages, and the Hours placed at equal intervals. Spring stood there too, bound with a blooming crown; Summer stood bare, and bore a wreath of grain; Autumn stood there, grim with treading of the grapes; and icy Winter, rough with white hair. There are, however, nine principal distinctions of time, or, as others hold, ten if the week is added: year, month, day, quarter, hour, point, moment, ounce, and atom. The year, as has been said, is determined by the proper course of the sun; the month by the moon, but more rightly by the sun itself in the mo- H h iiiij

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LEXICON se signum vnum permeante: hebdomada item à Luna, quæ tanto temporis spatio quartam Zodiaci partem per lustrat poniturque in Solis quadrato, inde in opposito, posteà in secundo quadrato, ac demum redit ad nouam coniunctionem. Dies designatur à Solis circulatione diurna motu primi mobilis absoluta, qua totus æquator perfectè in gyrû vettitur, ac singulæ eius partes spatio 24. horarum redeunt ad idem punctum. à quo pridie moueri cæperant: Quadrans est quarta diei pars, sex horis constans, quo tempore Sol & reliqua sidera ab vno ad alium cardinem Mundi ferruntur, ascenduntque æquatoris grad. 90. Hora est duodecima quæque diei noctisque pars, siue ea inæqualis sit, siue æqualis, vt in æquinoctiis, in qua ascendunt quindecim gradus æquatoris supra horizontem, & punctum aliquod transeunt. Hora diuiditur in quatuor puncta, quæ nos horæ quadrantes vocamus, continenique 15. minuta temporis: in quo ascendunt gr. 3. & min. 45. æquatoris. Punctum rursus diuiditur in decem momenta: momentum in duodecim vncias: Vncla in 47. atomos. Atomus autem indiuisilis constituitur, estque instans temporis præsens, qui dicitur nunc, cum aliàs aliæ differentiæ temporis, aut dicantur præteritæ, aut futuræ. 12. Sed hic Philosophi in hac atomi consideratione satiscunt. Quidni enim? Hæc atomus, hoc indiuisibile instans, tempus est, an non tempus? Si tempus; ergò successuum est: ergo habet prius, & posterius: ergò non totum præsens, sed ex partibus constat, quarum vna præteriit, & non est, altera futura est, & adhuc non est: ergò non iam indiuisibile instans. Si non tempus; quonam pacto in huiusmodi atomos diuidi potest tempus? Quomodo cum tempore connexionem habere potest? quomodo præteritum simul, & futurum necti? Et si nectit, quomodò duo quæ reverà non sunt nectit? quonam pacto vnio vlla realis intelligi potest inter duo, quorum vnum iam esse destitit, alterum nondum esse coepit? Rursem si hæc eadem atomus in se fluxibilis est, quomodo successiua? quomodo actu præsens? & qua ratione permanens esse potest, quæ statim corrumpitur, ac desinit esse? Benè August. loco citato: si nihil præteriret, inquit, no[n] esset præteritum tempus; & si nihil adueniret, non esset futurum tempus; & si nihil esset, non esset præsens tempus. Duo ergò illa tempora præteritum, & futurum quomodo sunt, quando & præteritum iam non est, & futurum nondum est? Præsens autem, si semper esset præsens nec in præteritum transiret; iam non esset tempus, sed æternitas: Si ergò præsens,

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As the sign is traversed by one: likewise the week by the Moon, which, in so much space of time, is reckoned as making a circuit through a fourth part of the Zodiac; and it is placed in the square of the Sun, then in the opposite, afterward in the second square, and at last returns to the new conjunction. The day is designated by the daily circulation of the Sun, completed by the motion of the primum mobile, by which the whole equator is perfectly turned in a circle, and its several parts return in the space of 24 hours to the same point from which they had begun to move the day before. A quadrant is a fourth part of the day, consisting of six hours, during which time the Sun and the rest of the stars are carried from one pole of the world to the other, and ascend 90 degrees of the equator. An hour is each twelfth part of the day and night, whether it is unequal or equal, as in the equinoxes, in which fifteen degrees of the equator rise above the horizon, and pass through some point. An hour is divided into four points, which we call the quadrants of the hour, and they contain 15 minutes of time: in which 3 degrees and 45 minutes of the equator rise. A point is again divided into ten moments: a moment into twelve unciae: an uncia into 47 atoms. But the atom is constituted as indivisible, and it is the present instant of time, which is called “now,” while the other differences of time are otherwise called either past or future. 12. But here the philosophers are satisfied in this consideration of the atom. For why not? Is this atom, this indivisible instant, time or not time? If time, then it is of succession: therefore it has a before and an after: therefore it is not wholly present, but consists of parts, one of which has passed and is not, another is future and is not yet: therefore it is no longer an indivisible instant. If it is not time, then how can time be divided into atoms of this sort? How can it have connection with time? How can the past and the future be joined together at once? And if it joins them, how does it join two things that really are not? How can any real union be understood between two things, one of which has already ceased to be, and the other has not yet begun to be? Again, if this same atom is fluxible in itself, how is it successive? how is it actually present? and by what reason can it be permanent, when it is at once destroyed and ceases to be? Well said Augustine in the cited passage: if nothing were passing away, he says, there would be no past time; and if nothing were coming, there would be no future time; and if nothing were, there would be no present time. Those two times, therefore, the past and the future, how are they, when the past is already not, and the future is not yet? But the present, if it were always present and did not pass into the past, would no longer be time, but eternity: if therefore the present,

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MATHEMATICVM. 493 vt tempus sit, ideò fit, quia in præteritum transit, quomodo & hoc esse dicimus, cui causa vt sit illa est, quia non erit, vt scilicet dicamus tempus esse, nisi quia tendit in non esse? Verùm omninò concludendum est, tempus ex atomis indiuisibilibus singulis successiuè præsentibus, atque actu existentibus fieri: si enim ex partibus in infinitum diuisibilibus constaret, vel necessario multæ particulæ temporis adhuc in infinitum diuisibiles simul existerent, vel sanè nunquam præterirent, quia nunquam ad partes vltimas, quæ totæ simul existerent, deueniretur, & si demum deueniretur, ex non essent partes vlterius in prius, & posterius, præteritum, & futurum diuisibiles, sed formalissimæ atomi. Quod autem hæ seorsim tempus non sint, non arguit tempus non ex ipsis constare: Nam Tempus per omnes est numerus, & numetus motus: ergò debet ei conuenite quod numero, & tali numero motus. Numerus autem ex pluribus vnitatibus constiuuitur, quæ quidem singillatim numerus non sunt, sed vnitæ. Ira planè philosophari licet in tempore, quod ex pluribus atomis indiuisibilibus consurgit, quamquam ipsa indiuisibilia seorsim sumpta tempus non sint. Neque enim ex hoc quod omne tempus diuidatur in præsens, præteritum, & futurum, sequitur aut aliquam differentiam temporis totam esse simul, ac proinde non habere successionem: aut quodlibet instans seorsim tempus dicendum esse. Nam quælibet differentia temporis, aut accipitur materialiter aut formaliter: Si materialiter, dicit tot indiuisibilia, quibus constar; si formaliter, dicit totum quid in vnum collectum siue præsens, siue præteritum, siue futurum, quod tamen haber successionem: sicut numerus materialiter sumptus dicit tot, vel tot vnitates in seipsis indiuisibiles, formaliter autem quilibet numerus est totus simul ex pluribus constitutus: quaternarius enim vnus est non quaternus denarius vnus est, contenarius vnus est in plures centenarios indiuisibilis, quamuis horum quilibet materialiter diuidi possit & in plures numeros, vt centum in duos quinquagenarios, decem denarios, viginti quinarios, denarius in duos quinarios, quaternarius in bines binarios, &c. & insuper iam non in numeros, sed in singulas vnitates, quarum singulis non comperit ratio numeri, nisi cum aliis vniatur. Nunc autem quodlibet tempus, quoad vsque ad atomos deducatur vnum est habens prius, & posterius, adeoque rationem successionis, quamuis dicatur formaliter totum præsens, aut præteritum, aut futurum. Sic dicitur præsens (a

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MATHEMATICUM. 493 that time is, it comes to be because it passes into the past, just as we also say of this that it is, for the cause that it is, because it will not be, so that we may say time is only because it tends toward non-being? But it must be concluded absolutely that time is made up of indivisible atoms, each successively present and actually existing; for if it consisted of parts divisible to infinity, either many particles of time, themselves still divisible to infinity, would necessarily exist at once, or certainly they would never pass away, because one would never arrive at ultimate parts, which would all exist together at once; and if one did at last arrive there, there would then no longer be parts further divisible into before and after, past and future, but most formal atoms. Now the fact that these are not time when taken separately does not prove that time does not consist of them: for time is number through and through, and the number of motion; therefore what belongs to number, and to such a number of motion, must belong to it. But number is constituted from many units, which indeed singly are not number, but only united. Thus one may clearly philosophize about time, which rises from many indivisible atoms, although the indivisibles themselves, taken separately, are not time. Nor does it follow from the fact that all time is divided into present, past, and future, either that some difference of time is wholly simultaneous, and therefore has no succession; or that every instant must be called time separately. For every difference of time is taken either materially or formally: if materially, it means so many indivisibles by which it is constituted; if formally, it means a whole gathered into one, whether present, past, or future, and yet having succession: just as number taken materially means so many, or such and such units indivisible in themselves, but formally any number is a whole made up at once of many; for four is one, not four; ten is one, one hundred is one, indivisible into many hundreds, although each of these materially can be divided into many numbers, as a hundred into two fifties, ten tens, twenty fives, ten into two fives, four into two twos, and so on; and moreover now not into numbers, but into individual units, to each of which the character of number does not belong unless it is united with others. Now every time, so far as it is reduced to atoms, is one thing having before and after, and therefore the notion of succession, although it is said formally to be a whole present, or past, or future. Thus the present is said (a

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194 LEXICON culum, quod centum annis constat formaliter totum actu, quia non dum transactum, sed nec futurum: sic præsens annus, præsens mensis, præsens dies, &c. quæ omnia dicuntur in ordine ad præcedentem aut subsequentem diem, mensem, annum, &c. licet & ipsi quoad partes successuii sint, quoadvsque ad ultimos atomos deueniatur: sicut in numeris semper adest diuisibilitas in plures, & plures numeros, quoadvsque tandem deueniatur ad vnitates omninò indiuisibiles. 14. Item tempus, vt dictum est, est numerus motus: ergo id ei competit, quod & motui. Sicut igitur motus est in continua acquisitione, ac deperditione partium; ità & tempus est in continua acquisitione ac deperditione partium, scilicet instantium, quibus constat, licet formaliter in seipso consistat in ratione talis differentiæ temporis indiuisum, atque ab aliis omninò discretum. Quod si cui difficile captu sit, sciat id esse proprium cuiuslibet enis successuii, esse scilicet in continua acquisitione, ac deperditione partium. Nam vt benè Peterius de principiis rerum naturalium lib. 12. cap. 1. Ens successuum dicitur esse, cum habet partes in continua quædam successione; ita vt prior copuletur cum posteriori per nunc præsens; sicut dicitur generatio perpetua, non quod aliquod generatum sit perpetuum, sed quia successio generatorum vnius post alterum sit perpetua, & nunquam interrupta. Id ipsum videre est in quolibet motu, vt in nutritione animalis, itinere, transitu, rota figuli, &c. quæ omnia sunt in continua acquisitione, ac deperditione partium sui esse, quæ inuicem copulantur per nunc præsens, & cum hoc per extrinsecam immediationem, quamuis quæ præterierunt iam destiterint esse, & quæ futura sunt non adhuc sint. Ita profecto & tempus optimè potest intelligi secundum se totum quid reale esse, licet secundum partes semper in motu sit, atque adeò semper in acquisitione, ac deperditione partium sui esse. TEMPORVM DOMINI. Vide Chronocratores. 15. TENACIVM. Cometæ species subcinericio fumoluridi, quem Græci Pitheten appellant: reducitur ad Doliarem. Alij ex forma contendunt dicendum esse Cænaculum. Vide ibi. TENEBROSI GRADVS. Vide in V. Gradus. 16. TEPISATOSOA SOLIS. græcobarb, dicitur in sphæra barbarica tertius Decanus Geminorum manens sub Dominus Solis, dedignationis, iocandi, cauillandi, futilia audiendo, &c.

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194 LEXICON culum, which consists of one hundred years formally as a whole in act, because it is not yet past, but not yet future either: so too the present year, present month, present day, etc., all of which are said to be in relation to the preceding or following day, month, year, etc., although they too, as to their parts, are successive, until one comes down to the ultimate atoms: just as in numbers divisibility is always present into more and more numbers, until at last one arrives at units altogether indivisible. 14. Likewise time, as has been said, is the number of motion: therefore that which belongs to motion belongs also to it. As, then, motion is in a continual acquisition and loss of parts; so too time is in a continual acquisition and loss of parts, namely of instants, of which it consists, although formally in itself it remains in the nature of such a temporal difference undivided, and altogether distinct from others. But if this is difficult for anyone to grasp, let him know that it is proper to every successive being, namely, to be in a continual acquisition and loss of parts. For as Peterius explains well, On the Principles of Natural Things, book 12, chap. 1, a successive being is said to be when it has parts in a certain continual succession; so that the prior is joined to the posterior through the present now; just as perpetual generation is spoken of, not because any generated thing is perpetual, but because the succession of things generated one after another is perpetual, & never interrupted. The same may be seen in every motion, as in the nourishment of an animal, a journey, a passage, the potter’s wheel, etc., all of which are in a continual acquisition and loss of the parts of their being, which are joined to one another through the present now, and with this through extrinsic immediation, although what has passed has already ceased to be, and what is future is not yet. Thus indeed time can very well be understood in itself as something real as a whole, although as to its parts it is always in motion, and therefore always in the acquisition and loss of the parts of its being. TEMPORVM DOMINI. See Chronocratores. 15. TENACIVM. A kind of comet, ash-gray and smoky-yellowish, which the Greeks call Pitheten: it is reduced to Doliare. Others contend from the form that it should be called Cænaculum. See there. TENEBROSI GRADVS. See under V. Gradus. 16. TEPISATOSOA SOLIS. Greek-barbarous term; in the barbaric sphere it is called the third decan of Gemini, remaining under the Lord of the Sun, of disdain, joking, jesting, listening to trifles, etc.

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MATHEMATICVM. 425 TEPISATRAS LVNA. ibidem dicitur tertius Decanus Aquarij, significator detractionum, & deceptionum, sub dis- posirione Lunæ. TEPISEVTH SOLIS. ibidem est secundus Decanus Scorpij, deceptionis, detractionis, nouas inimicitias inter homines lerendi, & veteres confirmandi, cuius dominium spectar ad Solem, TERMINI, seu Fines Planetarum sunt certi quidam, & limitari gradus signorum, in quibus repertos planeras ob- seruauir Antiquitas vires suas augere, ac maximas habere prærogariuas De iis multa diximus in V. Fines. Hic autem nostr curæ erit huiusmodi distributionis congruentem ra- tionem reddere, quam nuper excogitauit Tius in Coelesti, Philosophia: ac non de finibus modò, sed & de iure Domicilij, Altitudinis, ac Trianguli, Sic enim habet lib. 2. cap. 12. Caendum est, quod quinque Planeta Saturnus, Iu- piter, Mars, Venus, & Mercurius ratione suarum proprietatum, & maximè coloris sui lumenis habent inter se deter- minatos quosdam qualitatum gradus similis natura gradibus illis, quos Luminaria producunt omnibus suis lationibus. Di- xi similis natura; intelligo saltem quoad gradus, non quoad naturam qualitatis: Nam Luminaria non efficunt quali- litates, quas Mars, & Saturnus, qua omninò corruptiua sunt, &c. Es censeo, quod Iupiter habeat illos gradus qua- litatis caloris, qui ex radio trino oriuntur; humiditatis verò illos gradus, qui ex radio sextili: & proptereà quod Iupiter sit Fortuna maior, ratione maioris insensionis caloris, &c. Sicut alibi dixi. Venus, quod contineat illos gradus caloris, qui ex radio sextili fiunt, humiditatis vero, qui ex trino: & hinc quod sit fortuna minor ratione maioris qualitatis passi- ua. Saturnus, quod habeat illos gradus frigiditatis, qui ex oppositione fiunt, id est summos, siccitatis verò illos gradus, qui ex quadrato oriuntur, & idcirco quod sit Infortuna Ma- ior, ratione excessus frigiditatis supra siccitatem: Tandem Mars obtineat illos gradus ariditatis, qui ex oppositione emer- gant & caloris destructui illos gradus, qui ex quadrato; & ideò quod sit Infortuna minor. Mercurius, quia inconstantis apparet coloris, inconstantis natura censetur esse, & ex- perimento constat. Cuius rei triplicem rationem assignat: primò quod Luminaria suis lationibus generant quatuor primas qualitates à primo gradu vsque ad octauum, & sum- mum: Secundò quia Luminaria eo quod exhibent omnes colores sua uce, consequenter veniunt exhibere etiam il- los gradus qualitatum, quos singulari planetæ exhibent

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MATHEMATICVM. 425 TEPISATRAS LVNA. there is likewise called the third Decan of Aquarius, significator of detractions and deceptions, under the disposition of the Moon. TEPISEVTH SOLIS. there also is the second Decan of Scorpio, of deception, detraction, and of sowing new enmities among men and confirming old ones, whose dominion pertains to the Sun. TERMINI, or the Bounds of the Planets, are certain fixed and limited degrees of the signs, in which the planets found there were observed by Antiquity to increase their powers and to have the greatest prerogatives. We have said much about these in V. Fines. Here, however, our concern will be to give a fitting account of this kind of distribution, which Tius recently devised in Celestial Philosophy; and not only concerning the bounds, but also concerning the law of Domicile, Altitude, and Triangle. For he thus has it in book 2, chapter 12. It must be noted that the five planets, Saturn, Jupiter, Mars, Venus, and Mercury, by reason of their properties, and especially of their color and light, have among themselves certain determined degrees of qualities, similar in nature to those degrees which the Luminaries produce in all their motions. I said similar in nature; I mean at least as to degrees, not as to the nature of the quality. For the Luminaries do not produce the qualities which Mars and Saturn do, since they are altogether destructive, etc. And I judge that Jupiter has those degrees of the quality of heat which arise from the trine ray; but of humidity those degrees which arise from the sextile ray: and therefore Jupiter is the greater Fortune, by reason of a greater infusion of heat, etc., as I said elsewhere. Venus, that it contains those degrees of heat which are produced by the sextile ray, but of humidity those which are produced by the trine: and hence that it is the lesser Fortune by reason of a greater passive quality. Saturn, that it has those degrees of coldness which are produced by opposition, that is, the highest; but of dryness those degrees which arise from the square, and therefore that it is the greater Infortune, by reason of an excess of coldness over dryness. Finally Mars obtains those degrees of aridity which emerge from opposition, and those degrees of destructive heat which arise from the square; and therefore that it is the lesser Infortune. Mercury, because it appears of inconstant color, is judged to be of an inconstant nature, and experience confirms it. He assigns a threefold reason for this matter: first, that the Luminaries by their motions generate the four primary qualities from the first degree up to the eighth and the highest; second, because the Luminaries, in that they display all colors through their light, consequently also come to display those degrees of qualities which the single planets display

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LEXICON suis coloribus: Tertiò tandem ad proportionem radiorum, ad sonos harmonicos, ac permixtione radio-um ad ipsos. Hinc Luminaria à iure finium excluduntur, & solum quinque erratica assumuntur. (quamquam Campanæ la aliam rationem assignat lib. 1. et 7. art. cur termini luminaribus non assignentur: quia, inqui, terminus specificat effectum: Luminare autem generaliter operatur, sed omnia signa à Leone in Capricornum sunt quasi termini 50 is, vti à Cancro in Aquarium, Lunæ.) Hinc posito hoc stabili fundamento, descendit ad finium rationem reddendam. In exoratio, ait, Arietis sex partes Iouis fines sunt, & sex sequentes Veneris; quia ibi incipit augeri lumen dierum viuificum supra tenebras noctium; ideoque partes il'a benefica sunt: deinde octo partes Mercurij ex radio inde quintili ad Tropicum Cancri: que supersunt fines Martis, & Saturni sunt, qui semper ultimas partes signorum habent eoquod radij antequam attingantur secundum suas proportiones, non adeò felices sunt, quemadmodum consonantia harmonica dissentiunt validissimè ante veram proportionem. In exordio Tauri octo partes, fines Veneris sunt, ratione trini ad tropicum Capricorni, & sextilis ad Cancrum: posteà sex Mercurij ex biquintili ad Libram: quamuis reuerà secundum partes non æquè benè correspandeant: inde octo Saturni ratione sesqui quadrati, qui radius hostilis est, ad initium Capricorni, & Libra; quinque Iouis ratione biquintilis ad tropicum Capricorni: qua remanent Martis sunt. In Geminis sex Mercurij, ratione Domus, & sicut dixi sex Iouis, & sex Veneris ratione quintilis ad initium Arietis: Et ita correspondet hic radius, vt ponatur in medio finium Iouis, & Veneris, ne putes hac esse figmenta; qua potius admiratione sunt digna: reliqua partes infortunis dantur. In Cancro, septem partes sunt Martis ex quadrato ad initium Arietis: sex Veneris, ratione humiditatis tropici: sex Mercurij, & septem Iouis ob quintilem ad initium Libra: quatuor ultima Saturni. In Leone sex Iouis propter trinum ad Arietis initium: quinque Veneris, ob radium biquintilem ad tropicum Capricorni: septem Saturni, quia incidit ibi sesqui quadratus ad initium Capricorni, & Arietis: qua remanent Mercurij, & Martis sunt. In Virgine septem sunt Mercurij ob sextilem ad Cancrum: Decem Veneris, & quatuor Iouis propter quintilem ad tropicum Cancri; reliqua infortunarum. In Libra sex Saturni propter oppositionem ad initium Arietis & quadratum ad Cancrum: octo Mercurij indifferentes: septem Iouis, & septem Veneris, ex quintili ad tropicum Capricorni; adeoq[ue]

Transcription: Translated (English)

with their colors: Thirdly, at last, according to the proportion of the rays, to the harmonic sounds, and by the mixture of the rays with them. Hence the luminaries are excluded from the right of the bounds, and only the five wandering stars are taken up. (Although Campanus assigns another reason, lib. 1 and 7, art., why bounds are not assigned to the luminaries: because, he says, the bound specifies the effect; but the luminary works generally, whereas all the signs from Leo in Capricorn are as it were the bounds of the Sun, just as from Cancer in Aquarius, of the Moon.) Hence, this stable foundation having been laid, he proceeds to give the reason for the bounds. In Aries, he says, the first six degrees are Jupiter’s bounds, and the six following Venus’s; because there the light of the life-giving days begins to increase above the darkness of the nights, and therefore those parts are benefic; then eight degrees of Mercury, from the quintile ray there to the Tropic of Cancer; the remaining degrees are Mars’s and Saturn’s bounds, who always have the last parts of the signs, because the rays, before they are attained, according to their own proportions, are not so fortunate, just as harmonic consonances disagree most strongly before the true proportion. In the beginning of Taurus, eight degrees are Venus’s bounds, by reason of the trine to the Tropic of Capricorn, and the sextile to Cancer; afterward six degrees of Mercury, from the biquintile to Libra: although in truth they correspond not equally well according to the parts; then eight of Saturn, by reason of the sesquiquadrate, which is a hostile ray, to the beginning of Capricorn and Libra; five of Jupiter, by reason of the biquintile to the Tropic of Capricorn; what remains are Mars’s. In Gemini, six are Mercury’s, by reason of the domicile, and, as I said, six Jupiter’s, and six Venus’s, by reason of the quintile to the beginning of Aries: and thus this ray corresponds here, so that it is placed in the middle of the bounds of Jupiter and Venus, lest you think these things are fictions; rather they are worthy of admiration: the remaining parts are given to the infortunes. In Cancer, seven parts are Mars’s from the square to the beginning of Aries; six Venus’s, by reason of the humidity of the tropic; six Mercury’s, and seven Jupiter’s because of the quintile to the beginning of Libra; the last four are Saturn’s. In Leo, six Jupiter’s because of the trine to the beginning of Aries; five Venus’s, on account of the biquintile ray to the Tropic of Capricorn; seven Saturn’s, because there falls there a sesquiquadrate to the beginning of Capricorn and Aries; what remains are Mercury’s and Mars’s. In Virgo, seven are Mercury’s because of the sextile to Cancer; ten Venus’s, and four Jupiter’s because of the quintile to the Tropic of Cancer; the rest are the infortunes. In Libra, six Saturn’s because of the opposition to the beginning of Aries and the square to Cancer; eight Mercury’s, indifferent; seven Jupiter’s, and seven Venus’s, from the quintile to the Tropic of Capricorn; and so on.

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Transcription: ATR-1

MATHEMATICVM. 47 quintilis sit fere in medio finium Iouis, & Veneris: reliqua dua Martis. In Scorpionem septem Martis ex quadrato ad Leo- nem: quatuor Veneris ratione trini ad tropicum Cancri: octo Mercurij, quas censeo maledicas esse ob sesqui quadratum ad initium Cancri, & Arietis: quinque Iouis ex biquintili ad tropicum Cancri: sex Saturni. In Sagittario duodecim sunt Iouis, quinque Veneris propter trinum ad initium Arietis, & quintilem ad initium Libræ, qui inter fines Iouis, & Veneris ad vnquem ponitur: quatuor Mercurij indifferentes: reliqua Saturni & Martis. In Capricorno septem Mercurij, quas potius Veneris putarem cum Chaldais propter initium aug- mentationis dierum: inde septem Mercurij, septem Iouis, sine sine Veneris ob quintilem ad initium Arietis, reliqua infortu- narum. In Aquario septem Mercurij ob sextilem ad Arietem: sex Veneris, septem Iouis: sed ego censeo esso Saturni propter sesquisquadratum ad Cancrum; & ad Libram: & quinque sequentes Iouis, ob radium biquintilem ad Libram: ultima Martis sunt. In Piscibus duodecim sunt Veneris ob trinum ad Cancrum, & sextilem ad Capricornum; qui radium est in medio finium Veneris. & Iouis exquisitè: tres Mercurij in- differentes: reliqua infortunarum. In qua finium vniuersa distributione tantum in medio signi Aquarij videtur aliqua difficultas; in reliquis omnibus correspondent fines miro mo- do, iuxta radios partium signorum ad puncta mobilia, vnde incipiunt Astra influere primas qualitates. Hucusque Titus: cuius ratiocinationem est pro nostro in- stituto longiusculam, volui nihilominus ipsissimis eius ver- bis referre, ne fortè alienis verbis expressa, quicquam suæ maiestatis, atque energiæ deperderet. TERNVELLES in Tabulis Persicis significat Arculem, seu < 20.> Ingeniculum sidus ad borealem plagam coastans stellis 28. secundum Ptolemæum, at iuxta Bayerum 48. de quo satis alibi dictum. TERRA Vniuersi istius Centrum, ac basis, suprà quam < 21.> cætera elementa innixa sunt, & circà quam cælestes orbes rotantur quando ipsa vt ait Poëta. Ponderibus librata suis immoblis haret. Constituit cum elemento Aquæ vnum corpus sphæricum, cuius rotunditati non plus officiunt montium altitudines, valliumque cauitates, quam in aurantij pomo tuberculi prominentes: quod magno Diuinæ prouidentiæ consilio fa- ctum, censendum est; quò homines, & animantia probè ibi possent consistere, & omnem eius regionem inhabitare. Quandoquidem cum primò creata est ea perfectè sphærica

Transcription: Translated (English)

MATHEMATICVM. 47 quintilis is almost in the middle of the bounds of Jupiter and Venus; the remaining two belong to Mars. In Scorpio there are seven of Mars from a square aspect to Leo; four of Venus by reason of the trine to the Tropic of Cancer; eight of Mercury, which I judge to be malicious because of the sesquiquadrate to the beginning of Cancer and Aries; five of Jupiter from a biquintile to the Tropic of Cancer; six of Saturn. In Sagittarius there are twelve of Jupiter, five of Venus because of the trine to the beginning of Aries, and the quintile to the beginning of Libra, which is placed exactly in the bounds of Jupiter and Venus; four indifferent of Mercury; the rest belong to Saturn and Mars. In Capricorn there are seven of Mercury, which I would rather think Venusian with the Chaldeans because of the beginning of the increase of days; then seven of Mercury, seven of Jupiter, without, without Venus because of the quintile to the beginning of Aries, the rest to the infortunes. In Aquarius there are seven of Mercury because of the sextile to Aries; six of Venus, seven of Jupiter: but I judge them to be of Saturn because of the sesquiquadrate to Cancer and to Libra; and the five following belong to Jupiter, because of the biquintile ray to Libra; the last are of Mars. In Pisces there are twelve of Venus because of the trine to Cancer and the sextile to Capricorn, which ray is in the middle of the bounds of Venus and Jupiter exactly. Three indifferent of Mercury; the rest belong to the infortunes. In this whole distribution of the bounds, only in the middle of the sign Aquarius does some difficulty seem to arise; in all the rest the bounds correspond in a marvelous way, according to the rays of the parts of the signs to the movable points, from which the stars begin to influence the primary qualities. Thus far Titus: whose reasoning, though somewhat long for our purpose, I nevertheless wished to set down in his very own words, lest perhaps, expressed in another’s words, it should lose anything of its majesty and energy. TERNVELLES in the Persian Tables signifies Arculae, or the Ingeniculum, a star on the northern side, consisting of 28 stars according to Ptolemy, but according to Bayer 48, of which enough has been said elsewhere. EARTH is the center and base of this whole universe, upon which the other elements are supported, and around which the celestial spheres revolve, when it itself, as the Poet says, Weighed by its own burdens, lies motionless. It forms with the element of Water one spherical body, whose roundness is no more marred by the heights of mountains and the hollows of valleys than in an orange the protruding bumps: which, by a great design of Divine providence, must be thought to have been done so that human beings and living creatures might properly stand there and inhabit every part of it. For when it was first created, it was perfectly spherical

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Transcription: ATR-1

LEXICON fuit, totaque se sola vnum, & eumdem globum forambat, itavit, vndique Mari, quod naturaliter terræ imminere debet, allueretur: At postmodum ad Summi Opificis nutum quo dixit Gen. r. Congregentur aqua in locum vnum, appareat arida; mox plurimæ eius partes in diuersa loca translata sunt, amplissimos sinus, quos aquæ excurrentes implerent, in loco vnde discesserant relinquentes: inde montium sublimitates, & prominentiæ apparuerunt, quos nil aliud esse quam partes terræ, quæ prius maris concauitates implebant, ad Diuinum postea verbum illuc coactas, quò tota terra fieret habitationi satis idonea, grauissimè Expositores testantur: Quam rem vel ex eo probant, quod Nautæ sæpissimè experti sunt, tantam esse alicubi Maris profunditatem, quanta Montium altitudo. Ex quo sequitur, terram in hoc statu consistere quodammodò violenter, ac proinde ad suum statum pristinum naturaliter tendere: idque non leuiter suadent Montium corosiones, locorumque humilium repletiones sensim factæ, quibus manifestè ostenditur terram paulatim complanationem suam affectare. Testantur hoc Romæ ædificiorum fundamenta in summitate Capitolini montis extantia, omni terra nudata, atque in radicibus eius Amphitheatrum, Triumphalis Arcus Septimij, aliaque ædificia iam planè terra è vicino monte declivescente, obruta, ac sepulta. Probat id etiam Maris repletio, præsertim in Adriatico, vbi Aquileia, Adria, Patauium, Rauenna, aliæque vrbes olim ad Mare erant; quæ tamen nunc temporis ob multam terræ aggerationem valdè ab eo distant: eo quia imbrium alluuione fluuiorumque naturali pondere sese in Mare exonerantium magnæ arenæ glareæque vis illuc apportatur, quæ tandem eius alueum paulatim compleat, ac proinde æquæ semper magis ac magis intumescant, ac promineant: vt aliquando futurum sit, terram tandem vsquequeque mari operiendam, atque in pristinum statum redigendam; quemadmodum iam ex parte id plerisque in locis factum videmus, præsertim in littore Balthico, Danico, & Hollandico, vbi non ità pridem integra Prouincia à maris ingluuie absorpta fuit, & ne reliqua tellus inundaretur, indigenæ multis, præaltisque aggeribus occurterunt. Ex quibus omnibus euidenti demonstratione colligitur, Mundum, neque æternum fuisse, nec semper hanc figuram qua nunc præditus est, habuisse, nec in ea perpetuò extiturum, quia profectò veniet tempus, quo terræ globus ad perfectam rotunditatem redibit, atque à mari ita inundabitur, vt iam fiat inhabitabilis, proinde-

Transcription: Translated (English)

...was, and the whole of it alone, and the same globe it washed around, was to be bathed on every side by the Sea, which by nature ought to surround the earth. But afterward, at the command of the Supreme Maker, according to what is said in Gen. r., “Let the waters be gathered together into one place, and let the dry land appear,” many parts of it were straightway transferred to different places, leaving in the place from which they had departed very broad hollows, which the running waters might fill; hence the heights and prominences of mountains appeared, which Expositors most gravely testify to be nothing other than parts of the earth which formerly filled the hollows of the sea, and which were afterward brought together there by the Divine word, so that the whole earth might become fit for habitation. They prove this even from the fact that sailors have very often experienced that the depth of the Sea in some places is equal to the height of Mountains. From this it follows that the earth in this state stands, as it were, by force, and therefore naturally tends toward its former condition; and the corroding of mountains and the gradual filling up of low-lying places strongly suggest this, by which it is clearly shown that the earth is gradually seeking its leveling. This is attested at Rome by the foundations of buildings standing on the summit of the Capitoline Hill, stripped of all earth, and at its base the Amphitheater, the Triumphal Arch of Septimius, and other buildings already plainly buried, as the earth from the neighboring mountain has slipped down. It is also proved by the filling up of the Sea, especially in the Adriatic, where Aquileia, Adria, Patauium, Ravenna, and other cities were once by the Sea; yet now, on account of much accumulation of earth, they are very far from it, because by the flooding of rains and the natural burden of rivers discharging themselves into the Sea, a great quantity of sand and gravel is carried there, which at length gradually fills its bed, and therefore the waters swell and rise more and more: so that it will sometime happen that the earth will at last be covered everywhere by the sea, and reduced to its former state; just as we already see this partly accomplished in many places, especially on the Baltic, Danish, and Hollandish coast, where not long ago an entire Province was swallowed up by the sea’s voracity, and lest the remaining land be flooded, the inhabitants opposed it with many very high embankments. From all these things it is gathered by evident demonstration that the World was neither eternal, nor always possessed that form which it now has, nor will it remain in it forever, because indeed the time will come when the globe of the earth will return to perfect roundness, and will be so flooded by the sea that it will become uninhabitable, therefore-

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Transcription: ATR-1

MATHEMATICVM. 499 que mortalium genus sit necessariò desiturum: quod sanè iam præstitum foret si Mundus ab æterno has rerum vicissitudines passus esset: Est igitur terra, v[er]dictum est, Vniuesi istius centrum, & < iii> quamuis mole tam grandis, vt eius ambitus iuxta Recensiorum obseruationes sir milliar. 1158, 2945. nihilominùs ad eorum, atque ad superiores Vniuersi ipsius partes comparata, est instar puncti planè insensibilis, quod, tum ex siderum præsertim fixorum parallaxi, quæ nulla excipitur à quacumque rerræ parte contemplentur, tum ex aliis experimentis manifestè conuincitur. Vnde pulchrè Seneca in præfatione quæst. Natural. eius considerationem ingerens, dicebat. Hoc est illud punctum, quod inter tot gentes ferro, & igni diuiditur: punctum est illud in quo nauigatis, in quo bellatis in quo regna disponitis. Quare, vt rationi, ac Sacris Paginis repugnans reiicitur Nicetæ Syracusani, aliorumque antiquorum philosophorum opinatio, (quam superiori sæculo excitauit Nicolaus Coppernicus, & Galilæus, ac multi alij, adeò vt oportuerit rem præcepto compescere, eamque opinionem à Sacra Congregatione vri erroneam declarari,) existimantium non terram, sed solem in Mundi centro consistere, ipsamque terram jugiter cum Luna in eius orbe circa solem rotari. Reiicitur inquam hic error, tum quia terra est elementum omnium grauissimum; cui naturaliter debent omnia corpora super esse: est item omnibus mundi partibus, villof debuit ergo nouissimum, atque infimum locum tenere in Mundi ipsius meditullio, vbi tanquam fundamentum omnium staret, & in suo centro quiesceret, vnde Psalm. 130. dicitur. Qui fundasti terram super stabilitatem suam, non inclinabitur in saculum saculi: & apertius Psal. 92. Etenim firmauit orbem terra, qui non commouebitur: vertit Hebr. & Pagnignus, vt non se moueat: item Psalm. 101. Tu in principio Domine terram fundasti. Similiter Eccles. 1. Terra autem in æternum stat: & de Sole Mobili dicitur ibidem. Oritur Sol & occidit, gyrat meridiem, & flectitur ad Aquilonem. Quæ omnia Patres communiter & vnanimi sensu liber aliter intelligunt de terræ stabilitate in centro Mundi, ac de Solis perpetua circumagitatione. Tum etiam quia id clarè euincunt experientiæ: videmus enim grauita omnia in Mundi centrum tendete: perpendicula enim è quocumque loco demittantur in terram, semper & æquabiliter rerræ superficiei insistunt, angulosque æquales cum terræ superficie efformant, quippe vrpote grauia in centrum Mundi naturaliter tendunt: Videmus ex quacumque

Transcription: Translated (English)

MATHEMATICVM. 499 that the race of mortals must necessarily come to an end: which indeed would already have been accomplished if the world had from eternity undergone these vicissitudes of things: Therefore the earth, as has been said, is the center of this universe, and although in mass so great that its circumference, according to the observations of more recent writers, is 1,158,2945 Italian miles, nevertheless, when compared with the other and higher parts of the universe itself, it is like a point, plainly imperceptible; and this is clearly proved both from the parallax of the stars, especially the fixed stars, which is found nowhere, from whatever part of the earth they are observed, and from other experiments. Whence Seneca beautifully, in the preface to his Natural Questions, bringing this consideration forward, said: “This is that point which is divided among so many peoples by iron and fire; it is that point in which you sail, in which you wage war, in which you dispose kingdoms.” Wherefore, as contrary to reason and the Sacred Pages, the opinion of Nicetas of Syracuse and of other ancient philosophers is rejected, an opinion which in the previous century was revived by Nicolaus Copernicus and Galileo and many others, so much so that it was necessary to restrain the matter by decree and for that opinion to be declared erroneous by the Sacred Congregation; these men held that not the earth, but the sun, stands at the center of the world, and that the earth itself, together with the moon, continually revolves in its orbit around the sun. I say this error is rejected, first because the earth is the heaviest of all elements, to which by nature all bodies ought to be beneath; it is likewise among all the parts of the world, and therefore ought to hold the last and lowest place in the very center of the world, where, as the foundation of all, it should stand and rest in its own center, whence in Psalm 130 it is said: “Who hast founded the earth upon its stability, it shall not be moved for ever and ever”; and more clearly Psalm 92: “For he has established the world, which shall not be moved”; the Hebrew and Pagninus render it, “that it may not move itself”; likewise Psalm 101: “In the beginning, O Lord, you founded the earth.” Similarly Ecclesiastes 1: “But the earth stands for ever”; and of the moving sun it is said there: “The sun rises and sets, turns toward the south, and bends toward the north.” All these things the Fathers commonly and with unanimous sense understand more freely of the stability of the earth in the center of the world, and of the sun’s perpetual revolution. Then also because experience clearly proves it: for we see all heavy things tend toward the center of the world; for plumb lines, from whatever place they are let down to the earth, always and evenly rest upon the surface of the earth and form equal angles with the surface of the earth, since heavy things naturally tend toward the center of the world: we see from whatever

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Transcription: ATR-1

L E X I C O N telluris parte cæli medieratem, & easdem stellas in eadem distancia semper esse. Videmus lapides magna vi sursum proiectos in eundem terræ locum, è quo proiiciuntur, recidere, quod non euentiur, si terra circulari moru, eoque velocissimo citeretur: & alta huiusmodi, quæ manifestè probant terræ stabilitatem. Sed adhuc hoc stabiliro, dubium nihilominus integrum manet, An Terra absolutè dicenda sit Mundi Centrum, vel poriùs Sol; quem suprà diximus ex Tychone nobilissimum locum tenere constirurum in medio planetarum, qui omnes excepta Luna circà ipsum rotantur tanquam circa proprium centrum. Et sanè id Vniuersi Centrum dicendum foret, in quod præcipuæ partes concurrant, quod pro centro respiciant, & à quo omnis motus, omnis actio lumar exordium: Atqui in hoc munere Sol longè telluri præualet, quæ potius nouissimo loco posita est Vniuersi pars vilior, ac despectior, nullo prorsus motu (ex quo nobiliras agentis dignoscitur,) nulla actiuitate prædita, est potius subiectum passium operationum cæterorum agentium, proindeque Luminarium, & Orbis stellati Centrum. Verum hac in re distinguendum censerem: Nam vel pro centro sumitur nobilissima pars vnde sit initium omnium operariorum & quodammodo viræ fons vniuersa ordinans, ac viuificans; & hoc sensu dicendus est Sol Vniuersi Centrum. Vel pro centro intelligitur pars despectior, infimo loco posita, proindeque in meditullio, vnde nil habeat ad reliqua operari, sed omnium operationes in se recipiat, sequè passiuè habeat: & tunc dicendum est rellurem esse istiusmodi Centrum, ipsa enim est Vniuersi pars abiectissima, sola immobilis, quæ nil habeat in pulcherrima cæli lumina operari, sed omnium operariones, omnium influxus in se recipiat. Id quod etiam comparatione Microcosmi, qui cum Vniuersum istud mirabilem seruat analogiam, euidenrer probari potest. Nam in homine, si pro Centro nobilissimam parte sumamus quæ sit initium, & regula omnis operationis motus, est Cor: si verò partem abiectissimam, in corporis humani meditullio collocaram, quæ sola omnium operationum sit scopus, is est Vmbilieus & Venrer, solus piger, Solus immobilis, qui nulla operis, nulla rei nobilitate prædirus sit, veluti paruistius Mundi chiloaca, quemadmodum Infernus est Vniuersi: ac proinde secundum diuersas acceptiones diuersum est etiam Mundi Centrum, licer, si pro parte inferiori ac despectiore sumamus, ea sit Tellus. Existimauit

Transcription: Translated (English)

L E X I C O N the middle distance of the heavens from the Earth’s part, and that the same stars are always at the same distance. We see stones, thrown upward with great force, fall back to the same place on the earth from which they are projected, which would not happen if the earth were moved by a circular motion, and that a very rapid one; and such things clearly prove the stability of the earth. But although I affirm this further, nevertheless one doubt remains entire: whether the Earth ought absolutely to be called the center of the world, or rather the Sun; which, as we said above from Tycho, is to hold the most noble place, in the middle of the planets, all of which except the Moon revolve around it as around their own center. And indeed it would have to be called the center of the universe, to which the principal parts converge, which they regard as their center, and from which every motion, every action of light takes its beginning. But in this office the Sun far surpasses the Earth, which rather is placed in the lowest position, a baser and more despised part of the universe, wholly devoid of motion, by which the nobility of an agent is recognized, and of activity, being rather the subject of the passive operations of the other agents, and therefore of the luminaries, and the center of the starry sphere. But in this matter I would think a distinction must be made: for either the noblest part is taken as the center, from which is the beginning of all operations and, in a manner, the fountain of life, ordering and vivifying the whole; and in this sense the Sun should be called the center of the universe. Or the more despised part is understood as the center, placed in the lowest position, and therefore in the midst, from which it has nothing to do with the rest, but receives all operations into itself and is passive toward them: and then the Earth must be said to be such a center, for it is itself the most abject part of the universe, the only immobile one, which has nothing to do in the most beautiful lights of heaven, but receives into itself the operations of all, the influences of all. This can also be clearly proved by comparison with the Microcosm, which preserves a marvelous analogy with this Universe. For in man, if we take as the center the noblest part, which is the beginning and rule of every operation and motion, it is the heart; but if we take the most abject part, placed in the midst of the human body, which alone is the object of all operations, it is the navel and the belly, alone sluggish, alone immobile, endowed with no nobility of work or thing, as it were the sewer of this little world, just as Hell is that of the universe: and therefore, according to different senses, the center of the world is also different, although, if we take the lower and more despised part, that part is the Earth. It was thought

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MATHEMATICVM. 308 Existimauit Origenes, vt videre est in eius Commentar. super Ezechielem, terram esse magnum quoddam Animal sensu, & ratione prædi uni, eoquod ibi cap.1. dicatur coram Deo peccasse: Quæ dicta per prosopopeiam ipse littera- liter intellexit. Sed & Keplerus in Epitome Astronomiæ Coperniceæ terrestrem globum vita præditum, & sua anima non quidem intellectiua, aut sensitiva, sed longe ab his diuersa informarum constantissimè autumat. Cuius rei nul- lum manifestius argumentum proferre se putat, quam Ma- ris fluxum & refluxum, qui magni istius corporis sit velut vita, & respiratio. Cuius ratiocinationes fùsè expendit Ricciolus lib.9. sect.4. cap 4. & fusiùs cap 7 aitque num. 11. in hanc eandem de telluris anima opinionem ex magnetico sibrarum ductu processisse Guillermum Gilbertum lib.5. de Magnetecap.12. vbi vim magneticam ob tam varios, & mi- rabiles motus, aut quamdam animam esse, aut facultatem animæ imitatricem contendit, & lib.6. cap.4 experimentis Terreilæ ostendere conatus erat telluris globum esse ma- gnum magnetem. <24.> Est aurem Terrella nil aliud, quam magnes in globi for- mam contornatus, in quo deprehendere licet id experiri vo- lenti duos polos, ac facies axem ipsius terminantes: & acus magneticæ superimpositæ semper congruunt illius axi secundum sui longitudiuem: sed quoad altitudinem inclinantur magis, minusque versus polos terrellæ p.ovt magis, minus- que distant ab ipsis. Cum ergò similia eueniant in acubus magneticis respectu axis mundi & terræ, hinc sibi satis probabiliter visus est colligete terram esse magnum magne- tem: & sicut terrellæ globus pyxidi lignæ inclusus, vt su- pernatare possit, & aquæ superpositus, itavt eius polus bo- realis in Austrum tendat circulari motu se circà sui centrum conuertit, donec ipsius polus boreus boream respiciat; ita iudicat tellurem revolutioni magneticæ aprum esse, vt posi- tionem suam ad Mundi polos, quam semel habuit conseruet. Quod adhuc verius esset, si, vt affitmat Petrus Peregrinus terrellæ globus super polos suos in meridiano suspensus re- uolueretur in horis 24. Cæterum hanc Kepleri opinationem de terræ anima largo modo sumptâ pro principio intrinseco vitæ, sunt qui existimant non omninò falsam, nec Sæcria Paginis, aut Philosophiæ principiis contrariam, qua de re vide quæ de Mundi forma diximus in V. Mundus. <25.> Credibile est terrestrem globum illuminari à Sole non se- cus ac coelestia corpora, quæ item in ie ipsis opaca sunt, & densa, sed à Solis radiis in eorum superficie plana, ac leui- I i

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MATHEMATICVM. 308 Origen thought, as may be seen in his Commentary on Ezekiel, that the earth is a certain great animal endowed with sense and reason, because in chapter 1 it is said to have sinned before God: which words he understood literally, though they were spoken by way of prosopopoeia. But Kepler also, in the Epitome of Copernican Astronomy, most steadfastly maintains that the terrestrial globe is endowed with life, and with its own soul, not indeed intellectual or sensitive, but something far different from these. For this he thinks he can produce no clearer proof than the ebb and flow of the sea, which is as it were the life and respiration of that great body. Riccioli discusses his reasonings at length, lib. 9, sect. 4, cap. 4, and more fully in cap. 7, and says in no. 11 that William Gilbert proceeded to the same opinion about the soul of the earth from the magnetic movement of bodies, lib. 5 De Magnete, cap. 12, where he argues that magnetic force, because of its so various and wonderful motions, is either a certain soul, or a faculty imitating a soul; and in lib. 6, cap. 4, by experiments with the Terrella he had tried to show that the globe of the earth is a great magnet. <24.> Now the Terrella is nothing other than a magnet fashioned into the form of a globe, in which, to one wishing to test it, two poles and faces terminating its axis may be perceived; and magnetic needles placed upon it always agree with that axis according to their length: but as to inclination, they are bent more or less toward the poles of the terrella, as they are more or less distant from them. Since, therefore, similar things occur in magnetic needles with respect to the axis of the world and of the earth, from this he seemed to himself to infer quite probably that the earth is a great magnet; and just as the globe of the terrella, enclosed in a wooden box so that it may float, and placed upon water, turns around its center by circular motion, so that its northern pole points south, until its northern pole looks toward the north; so he judges the earth to be fitted for magnetic revolution, so as to preserve the position with respect to the poles of the world which it once had. This would be even truer if, as Petrus Peregrinus asserts, the globe of the terrella, suspended over its poles in the meridian, were to revolve in 24 hours. However, some think that Kepler’s opinion about the soul of the earth, taken in a broad sense as an intrinsic principle of life, is not entirely false, nor contrary to Holy Scripture or to the principles of philosophy; on this matter see what we have said about the form of the world in V. Mundus. <25.> It is credible that the terrestrial globe is illuminated by the Sun no differently from the heavenly bodies, which likewise in themselves are opaque and dense, but are made bright on their surface by the sun’s rays, and smooth...

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LEXICON gato terminantibus illuminari. Quamobrem si quis extrà telluris ambitum fieret, atque in Orbe Lunæ constitutus eam de longe contemplari posset, perinde eam videret, ac nos ex ipsius superficie Lunam cum omnibus illis phasibus quas nos in ista videmus, vt præ cæteris aduerit Galilæus verè lyneæus, qui cælestia omnia ita rimatus est, vt iam exinde nil nobis opinabile sit relictum, nihil imperuium. Notauit enim in Nouiluniis Lunare corpus nonnihil lucis habere ea ex parte quæ Soli aduersa ab eo illuminari nullatenùs potest: quæ profectò lux aliud esse non potest quam reflexio lucis terræ à Sole communicatæ, quæ in Lunam incidens eam tali modo illustret: sicque grata vice rependat, quod ab illa noctu accipit, & mutua permutatione Luna, & tellus solis lucem reuerberent, seque inuicem illustrent. Quod confirmari potest ex eo quod propè Nouiluuium id semper, & tantummodo accidit: iunc enim Sol, & Luna sunt in eodem cæli ferè situ; & loco, ad quem directè sit radiorum Solis à terra reflexio: postè à verò recedens Luna à Sole minùs participat de terræ reflexione, quia reflexio de sui natura petit, vt in illud radios dirigat, vnde ij processerunt directè. <26.> TERRAMOTVS est subita atque inopina terræ concussio, ac tremor, ex aëre alicubi incluso, qui siue à subterraneis ignibus, siue calore hyemali tempore per amperistasim concepto incensus, ac rarefactus foras exire contendit, atque ob telluris soliditatem quam sibi opponi sentit, miè eam quatit, & concutit. Accidit autem id, vt habet Philosophus 2. Meteor c. 8. ob exhalationem quandam viscosam, & crassam in cauitaribus terræ conceptam, quæ tandem, vt de ventis etiam suprà terram sit, in aërem resoluitur, ac dilatatur; indeque est, quod ipsum præcedat aliquando sonitus, & mugitus de quo Virgilius: Sub pedibus mugire solum, & iuge alta moueri. Quandoquidem aër collisus in internis illis terræ concuitaribus reboat, & si quidem exhalatio parua sit, habeatque aër spiracula vnde exeat, sit sonitus sine motu; sin minus exitum sibi parat vicumque, sicque terram scindit, atque ædes prosternit. Octo autem horum motuum genera enumerantur à D. Io: Damasceno cap. 16. 1. Physicæ, & Volaterrano in Physiologia. Tromodes, Palmoes, Epiclintæ, Brasæ, Reithen, Mycetias, Palmatiæ, & Mectas. Sed audiamus Apuleium in lib. de Mundo, eleganter eos describentem ac numerantem. Horum, inquit, motuum tam varia nomina, quam diuersi: namque obliquis lateribus proxi-

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illuminated by the terminating horns. Wherefore, if someone were beyond the circumference of the earth, and placed in the sphere of the Moon, could contemplate it from afar, he would see it just as we see from its own surface the Moon with all those phases which we see in it; as Galileo, above all others, rightly observed, who explored all heavenly things so thoroughly that from then on nothing is left for us to conjecture, nothing inaccessible. For he noted that in new moons the lunar body has some light on that side which faces away from the Sun and can in no way be illuminated by it: which light surely can be nothing other than a reflection of the light communicated by the Sun to the earth, which, falling upon the Moon, illuminates it in such a way; and thus in pleasant turn repays what it receives from it by night, and by mutual exchange the Moon and the earth send back the light of the Sun and illuminate one another. This can be confirmed from the fact that near new moon this always, and only, occurs; for then the Sun and Moon are in nearly the same position in the sky, and in a place toward which the reflection of the Sun’s rays from the earth is directed directly; but afterward, as the Moon moves away from the Sun, it participates less in the earth’s reflection, because reflection by its nature seeks to direct rays toward that from which they proceeded directly. <26.> An EARTHQUAKE is a sudden and unexpected shaking and trembling of the earth, caused by air enclosed somewhere underground, which, whether kindled by subterranean fires or by heat conceived in winter through amphe r istasis, strives to break out, and, because it feels the solidity of the earth opposing it, violently shakes and convulses it. This occurs, as the Philosopher says in Meteorology 2, ch. 8, because of a certain viscous and thick exhalation conceived in the cavities of the earth, which at length, as is also the case with winds above the earth, is resolved into air and expanded; and hence it is that sometimes a sound and murmur precede it, about which Virgil says: The ground beneath our feet to groan, and the high peaks to quake continually. For compressed air in those hidden cavities of the earth echoes back, and if the exhalation be small and the air have openings through which it may escape, there is a sound without movement; if not, it makes its own exit and passage, and so splits the earth and throws down buildings. Eight kinds of these movements are enumerated by St. John Damascene in chapter 16 of the first book of Physics, and by Volaterranus in Physiology: Tromodes, Palmoes, Epiclintae, Brasae, Reithen, Mycetias, Palmatiæ, and Mectas. But let us hear Apuleius in his book On the World, elegantly describing and enumerating them. “These,” he says, “have names as various as the movements are diverse; for along oblique sides…”

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MATHEMATICVM. 50) ma quæque inactantes, & acutis angulis mobiles Epiclinta gra- ce appellantur: qui subsiliunt, excutientes onera, & reci- procantes directis angulis Mobiles, Brassa vocantur, illi qui abstrudere videntur, Chasmatiæ dicti: quorum impulsu dissi- lit tellus, Reita sunt nominati: item Osta sunt motus, qui- bus solum quatitur: Palmatiæ verò appellantur quorum pa- uitatione illa qua trepidant sine inclinationis periculo nutant- cum directi tamen rigoris statum retineant Micetias vocantur tetris sudoris inquietudo terrena, &c. aliter autem eo idem des- cribit Ammianus Marcellinus, ac Cælius Rhodiginus 1. b. 16. cap. 64. Vt plurimum generari solent in Vete & in Autumno, arque in regionibus calidis fungosis, & causis, vbi aer in- cludi facile potest; vel huiusmodi exhalationum magna copia gigni Ob idque huic pesti maximè subiectum est Neapolitanum Regnum, vt experientia temporibus nostris audioimus Calabriam bis huiusmodi motibus quassatam, poe- ne totam subuersam. Ipsa quoque Neapolitana Ciuitas fe- re quotannis ob Vesuuij, ac puteolorum vicinitatem his motibus quatitur, licet ob Diui Ianuarij tutelarem opem, si- ue etiam ob multa puteorum aliarumque cauernarum spir- cula à ruina immunis semper existat. Econtra Iberniæ Re- gnum ob Soli duritiem nunquam terremotibus agitatum fe- runt Historicis, ac præsertim Ortellius. Solent autem po- tissimum accidere noctis tempore, etsi de die, ferè semper hora meridiana vt habet Kekermanus, Psellus, & alij. Ratio autem est, quia de nocte ob terræ frigiditatem cum ha- beat poros clausos, euaporatio impeditur, & aliunde diuer- sio, & egressus exhalationum. De die uero in meridie, cum exhalatio inferior continuetur cum exhalatione exteriori, & exterior præ nimio caloris æstu in meridie dissoluatur non continuatur cum inferiore; vnde est, quod inferior intrà terram discutrit, & Terremotus causatur, vel dici potest, quod id in meridie per antiperistasim fiat: vndique enim Solaribus radiis percussa telluris superficies, & calefacta in- tendit interiorum terræ partium frigus; qui sit, vt aer per eiusdem poros exhalare nequeat, sicque foras cum impetu prosilire gestiens terram concuriat. Porrò Terræ motus du- ratio breuis esse solet, eo enim ipso ac terra alicubi scindi- tur, exhalatio prodit, ac terra diu quati sinit. Non nega- uerim r amen aliquando multum etiam temporis durauisse, vt de memorato Calabriæ terræ motu compertum est. Et sa- nè anno Christi 651. Bizantij tempore Theodosi Imperato- ris, quatuor menses durasse scribit Baronius. ac randem pue- ro occlamante; Sanctus Deus, Sanctus fortis, Sanctus, &c I i ij

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MATHEMATICVM. 50) ma Those bodies which, moving on a slope and with sharp angles, are called by the Greeks Epiclinta: those which leap up, shaking off burdens, and return with straight angles are called Mobiles, Brassa; those which seem to be thrust apart are called Chasmatiæ; those by whose impact the earth splits are named Reita; likewise Osta are the motions by which the ground is shaken: Palmatiæ, however, are called those whose trembling makes them nod without danger of inclination, while still retaining the state of straight rigidity; Micetias is the restless quaking of the earth’s gloomy sweat, and so forth. But Ammianus Marcellinus and Cælius Rhodiginus, book 1, ch. 16, 64, describe it otherwise. They are most commonly generated in winter and in autumn, and in hot, fungous, and cavernous regions, where air can easily be confined; or a great quantity of such exhalations may arise. For this reason the Kingdom of Naples is most subject to this plague, as we have learned from experience in our own times: Calabria has been shaken twice by such motions, and almost entirely overturned. The city of Naples itself is shaken by these motions almost every year because of its proximity to Vesuvius and to Puteoli, although, by the protecting aid of St. Januarius, or also because of the many vents of wells and other caverns, it always remains immune from ruin. By contrast, the Kingdom of Ireland, on account of the hardness of the soil, is said by historians, and especially by Ortellius, never to have been disturbed by earthquakes. They usually occur most often at night, although by day, almost always at midday, as Kekermanus, Psellus, and others say. The reason is that at night, because of the coldness of the earth, when its pores are closed, evaporation is hindered, and likewise the diversion and خروج of exhalations. By day, however, at midday, when the lower exhalation continues together with the outer exhalation, and the outer one, because of the excessive heat at midday, is dissolved and does not continue with the lower, it follows that the lower one within the earth is driven about and causes an earthquake; or it may be said that this happens at midday by antiperistasis: for everywhere the surface of the earth, struck by the sun’s rays and heated, intensifies the cold of the inner parts of the earth; so that the air cannot exhale through its pores, and thus, eager to rush out with violence, it collides with the earth. Moreover, the duration of an earthquake is usually brief, for as soon as the earth is split somewhere, the exhalation emerges, and the earth ceases to be shaken for long. I would not deny, however, that sometimes it has lasted for a great length of time, as has been established concerning the mentioned earthquake in Calabria. And indeed Baronius writes that in the year of Christ 651, at Byzantium in the time of the Emperor Theodosius, it lasted four months. And at length, when a child cried out, “Holy God, Holy Mighty, Holy, etc.” I i ij

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504 LEXICON. immortalis miserere nobis, mox diuinitus cessauisse. Sed & Cordubæ terremotum tres annos durasse tradit Auerroes: quo tempore scribit Ioannes Anglicus Hispaniam ab Africa, & Ossam ab Olympo sciunctam tuisse. < 27.> Multa sunt Terræmotus signa, quæ nos, vt contrà ipsum præmuniamus edocent. Imprimis eum naturaliter prænoscunt muta animantia, vt mures, qui è domibus mox casuris ausfugiunt: item Gallinæ, & Pauones hac illac inordinatè discurrentes ac volitantes, atque siue in montes, siue in ædium superiora contendentes: quo signo refert Suessanus in sua Meteorologia præmonitum Anaximenem Philosphum terræmotum mox futurum prædixisse. Cuius rei rationem afferunt tetrum odorem ab ipsis alioqui acutissimi olfactus, è terræ visceribus ob pessimam illam exhalationem prosilientem exceptum, atque adeo ob id animalia loco ausugere. Secundò ipsum terremotum præueniunt leues quædam concussions, mox aliquando, vt supra diximus sonitus, quibus quasi vocibus naturæ Author nos admonet vt fugamus à facie arcus. vt liberentur electi. Tertiò si aqua in puteis ex se fiat turbida, ac tetrum odorem mittat; si ebulliet, & quodammodo subsiliat, & sursum ascendat: etenim hæc omnia effectus sunt exhalationis foras exire contendentis. Item si fiat tranquillitas aëris intempestiua: si interdiu, aut paulò post Solis occasum sereno coelo appareat nubecula quædam tenuis instar lineæ in longum protensæ: si media æstate ingruat insolitum frigus. Si mare absque ventis subito intumescat; & alia huiusmodi, quorum longam seriem affert Arist. loco citato, Seneca in quast. naturali. lib. 6. Plin. lib. 2. cap. 38. Sed omnibus abundantior est Resta de Meteoris lib.... < 28.> Porrò contra terremotus præsidium nullum in Natura extare rectiùs existimauerim. Est enim Dei Vindicis flagellum, quemadmodum & pestilentia, aduersus quam nullum planè datur antidotum. Si vllum esset, id sane foret terram cauernis, & pluribus puteis aperire quò perniciosus illehalitus viam sibi ad exeundum parare possit: vti in vbium obsidionibus per aduersos cuniculos subiecti tormentarij pulueris, atque incensi impetum aliò declinari non sine fructu videmus. Antiqui carbonum, ac lanarum vim in ædium fundamentis iactam unissimum contrà huiusmodi motus præsidium existimabant: vnde & in celebri illo Diana Ephesiæ Fano, vno ex septem Orbis Miraculis idipsum factum legimus, ne terræmotibus quateretur. Alij Domus humiliores habitare consueuerunt, istæ enim difficiliùs

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504 LEXICON. immortalis, have mercy on us,” had soon afterward ceased by divine power. But Averroes says that the earthquake in Corduba lasted three years: at which time John the Englishman writes that Spain was separated from Africa, and Ossa from Olympus. <27.> There are many signs of an earthquake, which teach us to be forewarned against it. First of all, dumb animals naturally foresee it, such as mice, which flee from houses about to fall; also hens and peacocks running and flying about in disorder here and there, and making for the mountains or for the upper parts of houses: by this sign Suessanus relates in his Meteorologia that Anaximenes the philosopher was warned and predicted that an earthquake would soon occur. The reason they give for this is a foul smell perceived by them, who otherwise have the keenest sense of smell, coming forth from the bowels of the earth from that very bad exhalation; and therefore the animals flee from the place. Secondly, the earthquake itself is preceded by certain slight shocks, and sometimes, as we said above, by sounds, by which, as it were by the voices of nature, the Author admonishes us to flee from the face of the bow. so that the elect may be delivered. Thirdly, if the water in wells becomes of itself turbid and gives off a foul smell; if it boils up and in a manner leaps and rises upward: for all these things are effects of an exhalation striving to escape outward. Likewise if there be an untimely calm of the air; if by day, or a little after sunset, in a clear sky there appears a certain thin little cloud in the shape of a line stretched out in length; if in the middle of summer an unusual cold breaks in. If the sea suddenly swells without winds; and other such things, of which Aristotle gives a long list in the place cited, Seneca in the Natural Questions , book 6, Pliny, book 2, chap. 38. But more fully than all these is Resta, De Meteoris , book.... <28.> Moreover, against earthquakes I would judge that no defense exists in nature more rightly than this. For it is the scourge of the avenging God, just as also is pestilence, against which no antidote at all is given. If there were any, it would surely be to open the earth with caverns and many wells, so that that harmful vapor might find a way to escape: as in the sieges of towns, by means of opposite tunnels the force of the buried gunpowder and fire is often seen to be diverted elsewhere, and not without benefit. The ancients thought that the power of coal and wool, cast into the foundations of buildings, was the sole defense against such movements: whence also in that famous Temple of Diana at Ephesus, one of the Seven Wonders of the World, we read that the same thing was done, so that it might not be shaken by earthquakes. Others used to live in lower houses, for these are more difficult

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MATHEMATICVM. 305 runt : vnde & Traianus iussit ne Domus sexaginta pedes excederent. Sue[n]tianus econtrà perpendens periculum hali- tuum pestilentialium è terræ hiatibus erumpentium, putat opporruius esse edita palatiorum inhabitare, hæcque ob validissima & profundissima fundamenta difficilius ruere. Linesius nullum maius effugium fore asserit, quam in mare contendere, atque in Nauibus se recipere. Verum nullum validius antemurale, quam in Deum confugere, & lachrimis, aepiis operibus eius misericordiam implorare. Scribit Nicephorus lib. 17. cap. 3. cum magnus adesset Antiochiae terremotus sub Iustino Imperatore, eas Domos minimè læsas, in quibus præ foribus, aut in angulis hæc breuis oratio scripta esset: Christus nobiscum, state. Potentissimum etiam est quod suprà ex Baronio retulimus Gloriosum Trisagium à puero diuinitùs decantatum, nosque in nuperis Regni nostri motibus mirabilis efficaciæ experti sumus. < 29.> Denique plurima etiam terræ motus effecta connumerantur. Vrbes integræ solo æquatæ; pestilentia mox sequuta: Montium arietatio, & in vnum coëtio, quemadmodum in eremo Sabbæ circà annum Domini 734. Scribit Theophanes Isauricus apud Anastasium Bibliothecarium: & in Agro Mutinensi factum fuisse memoriæ tradit Plin. lib. 2. cap. 38. In agro, inquit, Mutinensi montes duo inter se concurrunt crepitu maximo assultantes recedentesque inter eos, flamma, fumoque in coelum exeunte interdiò, eo concursu villa omnes elise, animalia permulta, qua intra fuerant exanimata sunt; Nouæ aquarum scaturigines, vt scribit idem Plinius: Auuiorum in contrarias partes conuersio: eorumdem exsiccatio: nouarum Insularum, & Montium eruptio, atque ad alia loca translatio; vt de quadam regione refert Sue[n]tianus vi terræ motus fuisse in Mare asportatam, sibique cum permensem stetisset supernatans viuis adhuc hominibus, ob Soli ariditatem, & materiam pumicosam, demum demersa fuit omnibus hominibus illis miserè pereuntibus. Memorabile est etiam quod refert Plato in Timæo in hæc verba. Atlannis Insula vasto gurgete mensa est, quam ob causam in- navigabile pelagus illud propter absorpta Insulua limum reli- tum tunc pelagus illud navigabile erat; Insulam enim hab- bat ante ostium, quod vos columnas Herculis appellatis. Quod tamen fabulosum existimat Ioseph Acosta li. 1. Histor. Indic. Nicephorus quoque testatur foeminas sæpissimè ab- orsum passas: idque facilè credi potest contingere siue ex timore concepto, siue etiam ex noxio halitu quem excipe- rent: sicut etiam quod notat Eurgerius apud Antiochion Ii iij

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MATHEMATICVM. 305 runt : whence Trajan also ordered that houses should not exceed sixty feet. Sue[n]tianus, on the contrary, considering the danger of pestilential vapors bursting forth from the openings of the earth, thinks it more fitting to inhabit elevated palaces, and that these, because of their very strong and very deep foundations, fall with greater difficulty. Linesius declares that there is no greater escape than to make for the sea and take refuge in ships. But there is no stronger bulwark than to flee to God, and with tears and pious works to implore His mercy. Nicephorus writes, book 17, chap. 3, that when a great earthquake occurred at Antioch under Emperor Justin, those houses were least damaged in front of which, or in the corners of which, this brief prayer had been written: “Christ is with us, stand firm.” Most powerful also is that which we related above from Baronius, the glorious Trisagion divinely sung by a child, and which we ourselves have experienced in the recent disturbances of our Kingdom to be of marvelous efficacy. < 29.> Finally, many other effects of earthquakes are also enumerated. Entire cities leveled to the ground; pestilence soon followed: The collision of mountains, and their coming together into one, as happened in the desert of Saba around the year of the Lord 734, as Theophanes the Isaurian writes in Anastasius the Librarian; and Pliny, book 2, chap. 38, records that this also happened in the Modenese countryside. “In the Modenese countryside,” he says, “two mountains rushed against each other with a tremendous crash, advancing and retreating between them, while flame and smoke went up into the sky by day; by that collision all the villas were crushed, and many animals that were inside were killed.” New springs of waters, as the same Pliny writes; the turning of rivers into contrary directions; their drying up; the bursting forth of new islands and mountains, and their transfer to other places; as Su[n]tianus relates of a certain region, it was carried into the sea by force of an earthquake, and after standing there for a month while men were still alive upon it, because of the dryness of the soil and its pumice-like matter, it finally sank, with all those men miserably perishing. It is also noteworthy what Plato relates in the Timaeus in these words: “Atlantis Island was swallowed by a vast whirlpool; for which reason that sea became unnavigable, because the mud left by the submerged island made the sea then navigable. For the island had stood before the opening, which you call the Pillars of Hercules.” However, Joseph Acosta considers this fabulous, book 1 of the History of the Indies. Nicephorus also testifies that women very often suffered miscarriage; and this can easily be believed to happen either from fear conceived, or even from the noxious vapor they received; as also what Eurgerius notes among the Antiochians.

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306 LEXICON homines mente captos remansisse. Hæc & alia plura Terræ motus effecta refert Kekermanus in sua Meteorologia. 30. TERREA SIGNA in Coelestibus sunt quæ participant in qualitatibus terreis, nempè in frigiditate, & siccitate, has- que efficiunt in sublunaribus hisce. Ea autem sunt 1 aurus, Virgo, & Capricornus: signa equidem foeminina, quando- quidem plus abundant in siccitate, adeoque qualitate passiva, quæ vt in loco diximus idcircò foeminea dicitur. At- que ob id Lunæ, ac Veneri, planetis videlicet foemineis iure optimo ascribitur, quorum Lunæ huic triangulo præest de nocte, Venus autem de Die. Obseruat Proleminæus lib. 1. Quam p. cap 16. hunc trigonum esse præcipuè australem ob Veneris Dominatum; quæ proinde ex ea parte eiet ventos calidos, & humidos: sed propter Saturnum, qui est Do- minus Capricorni admittit etiam subsolanum Quæ verò re- giones, & Cinitares huic Triangulo subsint, vide apud eundem Proleminæum lib. 2 cap. 2. TESTVO vide Lyra, Feticula. 31. TETRADRVM apud Geometras audit figura solida sub- quatuor triangulis æqualibus, & æquilateris comprehensa: de quo vide Euclidem lib. 11. defin. 26. 32. TETRAGONIS, siue Tetragonum, græcè significat figuram quatuor angulis constantem. Ab Astronomis verò sæpissimè aceipitur pro radio, & aspectu quadrato. 33. TIV NAZALENE arabicè audit linea meridiana supra terram in planisphætio constitua, atque descripta, cuius opè maiorem siderum altitudinem venari Solemus. 34. THAMYRIS apud quosdam (teste Alchabitio) significat splendidam Coronæ Gnossiæ stellam, secundæ magnitudinis sæpiùs memoratam, quæ etiam apud alios Theseus appellatur. TERRIGOLETEM item hebraicè dicitur Gallina, sidus ad Ga- laxiam, teste Kircheiro in Oedipo Ægyptiaco. 35. TREA græcè dicitur Tertia Domus in figura cælesti ab ho- reseopocadens, eo quod si paruæ Religionis, fratrum, sororum, & itinerum significatrix, adeoque boni ominis: Quæ quidem, etsi eadens est nihilominus fortunata, & habet fortitudinis partem vnam. Simi iter. 36. TURIS dicitur Nona Domus illi directè opposita, eadens ab angulo occidentis: verum si processum planetarum diut- rum consideremus succedens Angulo Medij Coeli: & ideo fortunata habens duos calculos fortitudinis: eo quia inde Planetæ respiciunt trino radio, hoc est perfectę amicitię,

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306 LEXICON humans remaining with their minds deranged. Hæc and many other effects of earthquakes are reported by Kekermanus in his Meteorologia. 30. TERRESTRIAL SIGNS in the Heavens are those which partake of earthly qualities, namely coldness and dryness, and produce these in sublunary things. These are 1 Taurus, Virgo, and Capricorn: indeed feminine signs, since they abound more in dryness, and therefore in a passive quality, which, as in the place we said, is for that reason called feminine. And for this reason they are most rightly ascribed to the Moon and Venus, namely feminine planets, of which the Moon presides over this triangle by night, Venus by day. Ptolemy observes, Proleminæus lib. 1. Quam p. cap. 16., that this trine is especially southern on account of the dominion of Venus; who therefore from that quarter sends out warm and moist winds: but because of Saturn, who is the Lord of Capricorn, it also admits the south-east wind. What regions and cities are subject to this Trine, see the same Ptolemy lib. 2 cap. 2. TESTVO see Lyra, Feticula. 31. TETRADRVM among geometers is the solid figure enclosed by four equal and equilateral triangles: concerning which see Euclid lib. 11. defin. 26. 32. TETRAGONIS, or Tetragonum, in Greek signifies a figure consisting of four angles. But among astronomers it is very often taken for a quadrate ray and aspect. 33. TIV NAZALENE in Arabic denotes the meridian line on a plane sphere set and drawn above the earth, by means of which we are accustomed to seek the greater altitude of the stars. 34. THAMYRIS among some people (as Alchabitius testifies) signifies the bright star of the Gnossian Crown, of the second magnitude, often mentioned, which also by others is called Theseus. TERRIGOLETEM likewise in Hebrew is called the Hen, a star near the Galaxia, as Kircheir testifies in the Œdipus Ægyptiacus. 35. TREA in Greek is called the Third House in the celestial figure, counting from the horoscopos, because it signifies little Religion, brothers, sisters, and journeys, and thus is of good omen: which, although it is cadent, is nevertheless fortunate, and has one part of strength. See also. 36. TURIS is called the Ninth House, directly opposite to it, cadent from the western angle: but if we consider the long course of the planets, it is succedent to the Angle of the Midheaven: and therefore fortunate, having two measures of strength: because from there the planets regard one another with a trine ray, that is, with perfect friendship,

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MATHEMATICVM. 307 horoscopum: linctum ratio, studiorum, ac præsertim me- mori[us] hinc auspiciati solet, nec sanè abque fundamento: hæc enim tempetamentum sequuntur, quod quando est siccum retentiuam adjuuat, quemadmodum humidum de- struit, licet citò capere faciat: Atqui Planetæ ex Nona domo cadentes, ac siccis qualitatibus præditi respicientes de trino horoscopum iisdem qualitatibus nascentis animum im- buunt. Gaudet in hac Domo Iupiter, qui cum naturaliter ad religionem, ac pietatem propellat, nil mirum, si præ- stet vt & ista Domus sit naturalis Religionis significatiux. THEME apud Firmicum aliosque Astrologos passim signi- < 37.> cat delineationem cælestis Signorum, Planetarum, aliorum- que siderum positus in cælesti figura erecta ad aliquod tem- poris momentum, vnde rei alicuius tunc temporis coeptæ af- fectiones expiscari solent. THEMES in sphæra barbarica audit primus Decanus Ca- < 38.> pricorni, manens sub dominatu Iouis, habensque signi- ficata spatiandi, perdendi cum debilitate, & vtilitate gauden- di, &c. Item THESOGR in eadem sphæra dicitur primus, < 39.> decanus Ge- minorum sub dispositione eiusdem Iouis, cuius est indicium tabellionatus, calculi dati, & accepti, petitionum, scien- tiarum inutilium, &c. Item THEOPIAV ibidem dicitur secundus Decanus Piscium quem < 40.> similiter gubernat Iupiter, haberque significare gloriatio- nls genium, animi elati iramiscendis se rebus arduis. Si- militer. THOPITVS in eadem sphæra barbarica audit secundus de- < 41.> canus Virginis sub dominatu Veneris adducens genium quæstus, opum cogendarum, auaritiæ, &c. THRASCIAS alias Circius Ventus vehementissimus, Septen- < 42.> trioni lateralis, mediusque inter ipsum & Borolybicum: de quo alibi fusè diximus. Nomen istud ad Thtacia sortitus est, eo quod ex ufflando per illam prouinciam transeat: qua etiam ratione ab Hispanis ventus gallicus dictus est. Flare solet in Verisinitio, & in fine Autumni, quibus tempori- bus fumina, nimbos, & procellas adducit: nocet musculis, neruis, articulis; adeoque causat pleuritides, lassitudines, arruumque contractiones. TRHONVM, Solium, atque Carpentum, appellant Astro- < 43.> nomi multiplicem, aut saltem duplicatam dignitatem Pla- netę quam tunc is obtinere dicitur, cum repetitur in loco vbi plures dignitates essentiales habet: puta Domicilium, exaltationem, fines: vide in V. Carpentum. Ii iiiij

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horoscope: the temperament, studies, and especially memory are usually judged from this; and not without reason. For these follow the temperament, which when it is dry helps retention, just as humidity destroys it, although it may make one quick to grasp things. But planets falling from the ninth house, and endowed with dry qualities, aspecting the horoscope from a trine, imbue the native’s mind with the same qualities. Jupiter rejoices in this house, and since he naturally impels to religion and piety, it is no wonder if it also serves as a natural significator of religion. THEME, in Firmicus and other astrologers, commonly signifies the configuration of the celestial signs, planets, and other stars in a celestial figure erected for a particular moment in time, from which they are accustomed to divinate the conditions of some matter then begun. < 37.> THEMES in the barbaric sphere is the name of the first decan of Capricorn, remaining under the dominion of Jupiter, and having significations of wandering about, loss with weakness, and enjoying usefulness, etc. Item < 38.> THESOGR in the same sphere is said to be the first decan of Gemini, under the disposition of the same Jupiter, whose indication is notarial work, money given and received, petitions, useless sciences, etc. Item < 39.> THEOPIAV there is said to be the second decan of Pisces, which likewise Jupiter governs, and which is said to signify a glorying nature, and an exalted spirit mixing itself with difficult matters. Likewise. < 40.> THOPITVS in the same barbaric sphere is called the second decan of Virgo, under the dominion of Venus, bringing a nature inclined to gain, to gathering riches, to greed, etc. < 41.> THRASCIAS, otherwise Circius, a very violent wind, lateral to the North and midway between it and the Borolybic wind: of which we have spoken at length elsewhere. This name he derived from Thrace, because it passes over that province when blowing; for which reason it was also called by the Spaniards the French wind. It usually blows at the beginning of spring and at the end of autumn, and at those times it brings smoke, heavy rains, and storms: it harms the muscles, nerves, and joints; and thus causes pleuritis, fatigue, and contractions of the limbs. TRHONVM, throne, and also chariot, astronomers call the multiple, or at least doubled, dignity of a planet, which it is then said to possess when it is repeated in a place where it has several essential dignities: for example, domicile, exaltation, bounds: see under V. Carpentum. < 43.> Ii iiiij

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308 LEXICON 44. THYMIS in sphæra barbarica dicitur tertius decanus Cancri cuius dominatus spectat ad Lunam; proindeque adducit genium venationis, aduerandi, &c. Similiter 45. THYMIS ibidem audit primus decanus Virginis manens sub dominatu Solis, habensque significationem seminandi, arandi, vrbes condendi, opes cogendi, &c. 46. THYRIBULVM sidus. Vide in V[erbi] Lar[um], Sacratium, Aca[dia], &c. 47. THYELLA apud Arist[otele] in lib[ro] de Mundo cap. 3. est ventus de genere procellarum, quas ipse Cetæges appellat, qui flant supernè, & repente prosiliunt. Huic affinis est L[ingua]laps &c strobilus, de quibus suo loco. 48. TONITVM est exhalatio calida, & sicca, intra vapores sursum ascendentes, atque in pluuiam iamiam conuerti incipientes inclusa, quæ exhalatio nubium compressione dum agirarur, calorem concipit, proindeque rarefacta ampliorem locum requirés dum è nubibus erumpit, acrem se indit, & inde sonus varius, pro maiori nubium der sicate & resistentia. Porrò eadem exhalatio & tonitruo, & fuguri & fulmini materiam subministrat, & vt plurimum crania secum affect, licet in re differant, & vtum sine alio gigni possit. Siquidem si exhalatio illa leuis est, & ex calore concepto in nubibus tantum rarefit, nec accenditur, foras crumpens tonitruum parit, si verò accenditur, vertitur adhuc in sulgur: & si sæpissimè sulgura, & coruscationes flant sine sonitu, ac tonitrui strepitu, quia foras exiliunt, nubibus nullatenus obsistentibus, vt præsertim fit in æstate post Solis occasum. At si exhalatio illa habeat admixtas partes vllas terreas, tunc in nubibus inclusa, & calore concepto cogit terreas illas partes in vnum quid Solidissimum, quod foris erupens cum impetu obuia quæque duriora comminuit, interim leuiora imacta relinquens: eoquod dura dum fulminis violentia resistunt, hoc in eorum resistentia superanda moratur, locumque habet in illa suam exerendi activitatem, suasque qualitates imprimendizat per rara quia non resistunt, cito transit; ideò nullam iis iniuriam facit. De his plura apud Arist[otele] 3. Meteor. cap. 1 Restam, & alios. 49. TORQVETVM est instrumentum mathematicum repræsentans motum æquatoris supra horizontem, quem refert basis eius immobilis, supra quam voluitur tabula æquatorem repræsentans, ac proinde ab huius motu, quo veluti in seipsum torquetur, Torqueti mutuauit nomen. Eius fabricam, & vsum docet Abbas Maurolycus, & Io: Paulus Galluccius de Mathematicis Instrumentis lib. 9. cap. 1. 30. TOYCAM Indorum vocabulo dicitur sidus in coelo non ita

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308 LEXICON 44. THYMIS in the barbaric sphere is called the third decan of Cancer, whose dominion pertains to the Moon; and therefore it brings the spirit of hunting, of finding, etc. Likewise 45. THYMIS there is said to be the first decan of Virgo, remaining under the dominion of the Sun, and having the signification of sowing, plowing, founding cities, gathering wealth, etc. 46. THYRIBULVM, a star. See in V[erbi] Lar[um], Sacratium, Aca[dia], etc. 47. THYELLA, in Aristotle in book 3 of On the World, is a wind of the kind of storms, which he himself calls Cetæges, which blow from above and suddenly rush forth. Related to this are L[ingua]laps, etc., strobilus, of which elsewhere in their place. 48. TONITVM is a hot and dry exhalation, enclosed within vapors rising upward and already beginning to turn into rain; this exhalation, while being driven by the compression of the clouds, takes on heat, and therefore, being rarefied and requiring a larger place when it bursts out from the clouds, it becomes sharp, and hence a varied sound, according to the greater dryness and resistance of the clouds. Moreover, the same exhalation supplies material for both thunder and lightning and fulmen, and for the most part affects the head, although in reality they differ, and one may be generated without the others. For if that exhalation is light and, from the heat conceived in the clouds, is only rarefied and not ignited, bursting outward it produces thunder; but if it is ignited, it is still turned into lightning; and if often lightning and flashes occur without sound and without the crash of thunder, it is because they leap out, the clouds in no way resisting, as especially happens in summer after sunset. But if that exhalation has mixed with it any earthy parts, then, enclosed in the clouds and having conceived heat, it compels those earthy parts into one very solid body, which, bursting out with violence, crushes whatever harder things it encounters, while leaving lighter things unharmed: because hard objects, while resisting the violence of the lightning, delay it in overcoming their resistance, and it has there the activity of exerting itself and of imprinting its qualities; but through the rarefied parts, because they do not resist, it passes quickly; therefore it does them no injury. More on these matters in Aristotle, Meteor. 3, chap. 1, and others. 49. TORQVETVM is a mathematical instrument representing the motion of the equator above the horizon, which its immovable base represents, above which is revolved a board representing the equator, and therefore from this motion, by which it is as it were twisted upon itself, it took the name Torquetum. Its construction and use are taught by Abbot Maurolycus and by Io: Paulus Galluccius, On Mathematical Instruments, book 9, chap. 1. 30. TOYCAM, in the Indian language, is said to be a star in the sky not so

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MATHEMATHICVM. 109 pridem detectum, alias Anser Americanus, habens stellas octo infimæ notæ. TRABES, seu lanceæ, & iacula, sunt species quædam ignitarum impressionum, quæ in sublimi generantur ex ac- censis exhalationibus, quæ breui, & æquari crassitie in al- tum porriguntur, & quasi immobiles stare videntur. Sunt medium quid inter cometas, & areas. De quibus vide quæ diximus in V. Apparentiæ, & in V. Cometæ. Eiusmodi fuit Phænomenon in Romano hemisphærio vitum anno 1618. die 18. Nouembris antelucano tempore, cuius meminit Blancarus in sphæra Mundi lib 16. cap.5. & durauit dies vndecim. Quo temporis interua'lo motu proprio processit quasi gr. 24. à loco Crateris ad cor Hydræ, & sui magnitudine oc- cupabat gr. 40. cælestis regionis. Quod ideò multam dedit philosophandi, iimendique materiam. Item, TRAIECTIONES ex eodem genere accessionum sunt, & 52. idem ferè ac cadentia sidera: nisi quod ista decrsum mo- uentur, illæ ad latus non secus ac è pyrio puluere conflata fulgura, & ab igne concepto sursum elata. Sunt enim & ipsæ exhalationes vis siderum sursum elatæ atque accensæ, quæ dum igne impellente motum concipiunt, hac illac dis- currunt, donec penitus absumantur. Differunt autem à Co- metis, quoniam isti maiores sunt, diuturniores, vniuersa- liores, & caudari, vel etiam circu[m]circa crini: illæ vetò bre- uiores sunt, minores effectus habent ac particulares, quos ei tantum loco portendunt in quo apparent, ac ferè sem- per in malum; nisi fortè illi vni, qui seditionem mouet ac vincit. Sunt enim de natura Martis & Mercurii; atque adeò semper adducunt bella, Æstus, iubulentias, & similia: idque siue in deliquiis, siue alio tempore fulsetint. De his intelli- gere voluit Poëta cum dixit Georg. Longosque à tergo flammarum albescere tractus. Et Pontanus in Meteoris. Quin etiam quâ se incandens nocte extulit ignis Ille quidem claro signans liquidum aëra tractu Inde ruit portis quamprimum venus apertis. TRAGOIDIS Græcè dicitur species quædam cometæ, qui 53. Latinè dicitur Hircus: de quo suo loco. TRANSITVS ex Ptolemæo sunt genera familiaritatum inter astra concepta, & acquisita motu vniuersali super loca siderum natalis. Qui si beneficarum fuerint, prosunt; si verò maleficarum, obsunt, pro qualitate radij & modera- torum super quorum loca fiunt huiusmodi transitus. Cum enim loca siderum natalis referant congenitum tempera-

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MATHEMATICUM. 109 long since detected, otherwise called Anser Americanus, having eight stars of the lowest magnitude. TRABES, or spears, and javelins, are certain kinds of fiery apparitions, generated aloft from kindled exhalations, which rise upward with a short and even thickness, and seem to stand almost motionless. They are something intermediate between comets and areas. See what we said in V. Apparentiae, and in V. Cometae. Such a phenomenon was seen in the Roman hemisphere in the year 1618, on the 18th day of November before dawn, of which Blancanus makes mention in Sphaera Mundi, lib. 16, cap. 5, and it lasted eleven days. During that interval it advanced by its own motion about 24 degrees, from the place of Crater to the heart of Hydra, and by its size occupied 40 degrees of the celestial region. This therefore gave much material for philosophizing and marveling. Also, TRAIECTIONES are from the same kind of exhalations, and are almost the same as falling stars, except that these move downward, while those move sideways, like flashes struck from gunpowder and lifted upward by the fire kindled in them. For they too are exhalations of the force of the stars, lifted upward and set alight, which, while they take on motion from the impelling fire, rush hither and thither until they are utterly consumed. But they differ from comets, because these are larger, longer-lasting, more universal, and tailed, or even shaggy all around; whereas those are shorter-lived, have smaller effects and are particular, portending only for that place in which they appear, and almost always for evil; unless perhaps to that one man who stirs up and wins a sedition. For they are of the nature of Mars and Mercury; and therefore they always bring wars, heat, turbulences, and the like: whether they shine in eclipses or at another time. The Poet wished us to understand these when he said, Georg. And long trails of flame whitened behind them. And Pontanus in the Meteora: Nay, indeed, in whatever night the fiery glow arose, That one, indeed, marking the bright air with a clear trail, Then immediately rushes out through the open gates of Venus. TRAGOIDIS in Greek is said of a certain kind of comet, which in Latin is called Hircus: concerning which in its own place. TRANSITVS, according to Ptolemy, are kinds of familiar relations conceived and acquired among the stars by the universal motion over the places of the natal stars. If they are of benefic planets, they do good; if of malefic, they do harm, according to the quality of the ray and of the rulers over whose places such transits are made. For since the places of the natal stars refer the inborn tempera-

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510 LEXICON mentum mixtionis corporis, inde sit, vt transitus astrorum, quia sunt familiaritates ad illa loca, respiciant consequenter congenitum temperamentum mixture corporis, & ipsas potentias, seu principia naturalia omnium motuum vitalium: adeo vt sidera transitibus suis prosint, vel obsint ipsis potentiis, & principiis naturalibus operationum vitalium. 55. Qui profectò (vt de ingressibus dictum est) alij sunt actiui, alij passiui. Actiui sunt à sideribus habentibus in natali rationem causæ efficientis, ad loca prorogatorum natalis, quosque alias in directionibus promissores vocamus. Passiui verò transiùs sunt familiaritates ab ipsis prorogatoribus contractæ, quando transeunt per loca siderum, quæ in natali gerunt vicem promissorum consistentium immobiliter: Itavt per hoc differant transitus ab ingressibus, quod hi respiciunt loca motuum mobilium; transitus verò loca fixa, & immobiliæ natalis. Eos esse aliquando validiores ipsis directionibus, & Progressibus & Cardani authoritate, & sui experientia testatur Campanella: Plus enim, inquit, nocet præsens Musca, quam absens Leo. Quod tamen haud ita facilè admitterem: eo quod directiones, & progressiones sunt non minus reales, & prætentes quam transitus, ac verè per eorundem motum deuoluuntur promissores in loca prorogatorum, qua de re vide quæ diximus in V. Directo. 56. TRANSLATIO LVMINIS, & Naturæ secundùm Astrologos tunc fieri dicitur inter planetas cum tres ex iis inueniuntur, platicè iuncti, aut quouis modo configurati, & medius ipsorum, levissimus separatur à ponderoso, & alteri iungitur: tunc enim dicitur transferre lumen, & naturam anterioris ad posteriorem. 57. TRAPEZIA apud Geometras audiunt figuræ quæuis irregulares, quibus videlicet non æqualiter respondent anguli, & latera: sed extra omnem Geometriæ legem vagantur: & hæ quidem infinitæ excogitari possunt, siue vt omninò irregulares sunt, hoc est, vt nullum latus, ac nullus angulus alteri sit æqualis, siue vt duo vel plures anguli sint æquales, cæteris consistentibus inæqualibus: siue id in planis figuris videre sit, siue in solidis: quæ omnes sub vniuersali Trapeziorum nomine veniunt: & contradistinguntur à figuris Isoperimetris, quæ vndequaque æquales ambitus continent, & per consequens necessariò habent æquales angulos, & æqualia latera. 55. TRAPEZOIDES sunt Trapeziorum species: comprehen-

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510 LEXICON of the mixture of the body, so that the transits of the stars, because they are relations to those places, consequently regard the inborn temperament of the mixture of the body, and the very powers, or natural principles of all vital motions: so that the stars by their transits may benefit or harm those very powers and natural principles of vital operations. 55. Which indeed, as has been said of ingressions, are some active, others passive. Active are those from the stars having in the nativity the role of an efficient cause, toward the places of the prorogated natal, which elsewhere in directions we call promissors. Passive transits, however, are the relations contracted by the prorogators themselves, when they pass through the places of the stars which in the nativity perform the role of promissors standing immovably: so that in this way transits differ from ingressions, in that these regard the places of mobile motions; transits, however, the fixed places and immovable ones of the nativity. That they are sometimes stronger than even directions and progressions is testified by Cardan's authority and by his own experience, Campanella: For, he says, a present fly does more harm than an absent lion. Which nevertheless I would not so easily admit: because directions and progressions are no less real and present than transits, and truly by their own motion the promissors are carried down into the places of the prorogators; for which matter see what we said in V. Directo. 56. TRANSLATION OF LIGHT, and of Nature according to the Astrologers is said to take place then between planets when three of them are found, connected platically, or otherwise configured, and the middle one of them, being the lightest, is separated from the heavier one and joined to the other: then indeed it is said to transfer the light and nature of the former to the latter. 57. TRAPEZIA among geometers are any irregular figures, in which angles and sides correspond not equally: but they wander beyond all law of Geometry: and indeed these may be imagined infinitely, either as they are utterly irregular, that is, so that no side and no angle is equal to another, or so that two or more angles are equal, while the others remain unequal: whether this is seen in plane figures or in solids: all of which come under the general name of Trapezia: and they are contradistinguished from Isoperimetric figures, which in every direction contain equal perimeters, and consequently must necessarily have equal angles and equal sides. 55. TRAPEZOIDES are a species of Trapezia: comprehen-

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MATHEMATICVM. 311 dunt enim figuras omnes solidas irregulares, quæ parallela non habent latera: Et hæ similiter, vel sunt omninò irregulares, vel alicubi quandam æqualitatis regulam seruant, cuiusmodi sunt Parallelopeuræ, Prismata, &c. de quibus omnibus vide Clau. in lib. 1. Euclid. TRIADA sunt species cometarum, de quibus Plin. lib. 2. cap. 23. 59. TRICHES Græcè apud Ptolemæum audiunt tres stellæ fixæ ipsæ quidem informes, ad caudam Leonis positæ verum postea ab aliis in certam formam redactæ, & crines, seù Berenices Coma vocatæ. Proclus, ac Stoephlerinus ponunt in hoc sidere stellas septem: at Keplerus oculatior obseruauit in eo vndecim de natura Veneris, & Lunæ: alio nomine appellatur Plocamos. TRICONVM Græcè idem sonat, ac figura triangularis. 61. Apud Astronomos accipitur pro aggregato trium signorum eiusdem naturæ, & qualitatis, se inuicem de trino, seù per tertiam cæli partem respicientium. Hinc pro diuersa qualitatum comixtione, quatuor constituunt trigonos: Igneum, seu calidum, & siccum complectens signa Arietis, Leonis, & Sagittarij: Terreum, hoc est frigidum & siccum conflatum ex Tauro, Virgine, & Capricorno: Æreum, calidum scilicet, & humidum, constans ex Geminis, Libra, & Aquario: ac tandem Aquæum frigidum nempe & humidum, quod sibi reliqua tria signa vendicat, Cancrum, Scorpionem, & Pisces. Quorum singulis triplicitatibus binos, aut ternos planetas præficiunt iuxta naturarum conformitatem; cuius distributionis rationem affert Ptolemæus in Quadrip. lib. 1. cap. 16. Estque vna ex dignitatibus essentialibus. Dicitur etiam Trigonus radius triangularis, & minus per tertiam cæli partem: qua de re vide paulò inferius in V. Trinus. TRIGONOCRATOR apud Astrologos appellatur Trigoni dispositionem sibi vendicans; Planeta inquam cui, vt modò dictum est ob naturæ vniformiratem, ius hoc trianguli vnà cum alio tributum fuit, vt trianguli ignei, dispositores, ac Trigonocratotes sunt Sol & Iupiter, quia masculi, quia in caliditate vincunt, quia demum ius domicilij obtinent super duo signa Leonem, & Sagittarium. Excluditur autem Mars, etsi alioqui calidus, & siccus, & ius domicilij habens super Arietem, quia vt inquit Ptolemæus adversatur conditioni solis, & sic de reliquis. TRIGONOMETRIA vna est ex Mathematicis disciplinis, quæ agit de analysi triangulorum; docetque modum resol-

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MATHEMATICVM. 311 They indeed define all irregular solid figures, which do not have parallel sides: and these likewise are either altogether irregular, or somewhere observe a certain rule of equality, such as parallelepipeds, prisms, &c. concerning all of which see Clav. in lib. 1. Euclid. TRIADA are species of comets, of which Pliny, lib. 2. cap. 23. 59. TRICHES in Greek, according to Ptolemy, are three fixed stars, themselves indeed shapeless, placed at the tail of Leo; but afterward by others reduced to a certain form, and called hair, or Berenices Coma. Proclus and Stoephlerinus place seven stars in this constellation; but Kepler, with keener observation, noted eleven in it, of the nature of Venus and the Moon: under another name it is called Plocamos. TRICONVM in Greek signifies the same as the triangular figure. 61. Among astronomers it is taken for an aggregate of three signs of the same nature and quality, looking toward one another by a triad, or through a third part of the heaven. Hence, according to the different mixture of qualities, they establish four trines: the Fiery, or hot and dry, comprising the signs of Aries, Leo, and Sagittarius; the Earthy, that is, cold and dry, made up of Taurus, Virgo, and Capricorn; the Airy, namely hot and moist, consisting of Gemini, Libra, and Aquarius; and finally the Watery, namely cold and moist, which claims the remaining three signs for itself, Cancer, Scorpio, and Pisces. To each of these triplicities they assign two or three planets according to the correspondence of natures; for the reason of this distribution Ptolemy gives in Quadrip. lib. 1. cap. 16. And it is one of the essential dignities. It is also called a trigonal ray, and “less by the third part of the heaven”; on this matter see a little below under V. Trinus. TRIGONOCRATOR among astrologers is the planet claiming the disposition of a trine; that is, the planet to which, as was just said, because of the uniformity of nature, this right of the triangle was granted together with another, so that for the fiery trine the disposers, or Trigonocratotes, are the Sun and Jupiter, because they are masculine, because they prevail in heat, and because finally they hold the right of domicile over the two signs Leo and Sagittarius. Mars, however, is excluded, although otherwise hot and dry, and having the right of domicile over Aries, because, as Ptolemy says, he is contrary to the condition of the Sun, and so in the rest. TRIGONOMETRIA is one of the mathematical disciplines, which treats of the analysis of triangles; and it teaches the method of resol-

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L E X I C O N 512 uenti omnia triangula tum plana, tum sphætica: qua videlicet datis tribus lateribus, seu angulis ex sex contentis triangulo reliqua tria ignota innotescunt. Pro quorum solutione vtimur Tabulis sinuum, tangentium, & secantium; quibus ostenditur quantitas semissium chordarum, quæ sub tenduntur partibus circumferentiæ intrà circulum. Extant in numeri penè auctores, qui de ea re luculentissimè tractat. TRILATERVM apud Geometras dicitur corpus; aut figura, < 64.> quæ tribus adminus lateribus constat, hoc est, non minus, quam tribus rectis lineis comprehendatur. Qua de re vide Euclid. lib. 1. à definit. 20. deinceps. TRIMORION Græcè dicitur aggregatum trium signorum < 65.> contiguorum, per quod constituitur aspectus quadratus ad Aphetam vitæ largitorem, qui ad illum directione impingens vitam abscindit. Et hic censetur nunc temporis vltimus vitæ terminus, ad quem potest naturaliter se extendere. Quod misticè docuerunt duo insignes, ac perantiqui Astrologi Arabum Reges Nicepso, & Petolyris (vt testis est Argolus de diebus Criticis lib. 1. c. 9) Dicentes neminem posse transgredi Trimorion, hoc est congeriem trium signorum: quoniam aute ex directionu doctrina tria signa, hoc est arcus 90. graduum potest alicubi ob decluitate eclipsæ dare 120. gradus directionis, ideò non ab te, fortassis Vita hominis post diluuium à Deo dicitur ad hunc terminu coarcta, vt opinatur Iosephus, & multi Hebræorum ex illo Gen. 6. Eruntque dies illius centum viginti annorum: eo quia, vt obseruat Valesius, eo tempore congruebat etiam annus climactericus, & naturale vitæ discrimen, directio inquam Aphetæ ad suum quadratum: Quæ r amen ante diluuium ex Diuina dispositione ob paucitatem hominum vitam non adimebat, sed directio Anæretica protendebatur vsque ad oppositum & vlceriùs, provt Deo Auctori Naturæ placebat. Post diluuium verò vltimus vitæ terminus constitutus est in devolutione Aphetæ ad suum Quadratum, vt dictum est. Nec quia Augustinus, Hieron. & alij Patres arbitrantur, per ea verba, præscriptum esse à Deo terminum poenitentiæ, & conuersionis illorum hominum, tollitur, quin ea etiam ad literam intelligi possint de vitæ termino dicta: Nam, vt benè aduertit etiam Vecchius obseru. medica 40. in sacram Scripturam, id intellexit etiam Moïses cum dixit ad populum Deur. 31. Censum viginti annorum sum hodie, non possum vltrà egredi, & ingredi quia profectò agnoscerebat se ad eum terminum peruenisse, in quo homines post diluuium ex Diuino præscripto vt plurimum moriuntur: Vnde

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LEXICON 512 which indeed includes all triangles, both plane and spherical: namely, when three sides or six angles are given, the other three unknown parts of the triangle become known. For their solution we use tables of sines, tangents, and secants, by which is shown the quantity of half-chords, which are subtended by parts of the circumference within the circle. There are nearly countless authors who have treated of this matter most clearly. TRILATERVM is said among geometers to be a body, or figure, < 64.> which consists of at least three sides, that is, which is enclosed by no fewer than three straight lines. On this matter see Euclid, book 1, from definition 20 onward. TRIMORION in Greek is said to be the aggregation of three contiguous signs, < 65.> by which a square aspect is constituted to the Apheta, giver of life, who, striking it by direction, cuts off life. And this is now regarded as the last limit of life, to which it can naturally extend itself. This was mystically taught by the two distinguished and very ancient astrologers, the Arab kings Nicepso and Petosiris (as Argolus testifies, De diebus Criticis, book 1, ch. 9), saying that no one can pass beyond the Trimorion, that is, the mass of three signs: since, according to the doctrine of directions, three signs, that is, an arc of 90 degrees, can somewhere because of the declivity of an eclipse give 120 degrees of direction; therefore perhaps the life of man after the Flood is said by God to be confined to this limit, as Josephus and many of the Hebrews suppose from Gen. 6: “And the days of him shall be one hundred and twenty years,” because, as Valesius observes, at that time the climacteric year also corresponded, and the natural limit of life, namely, the direction of the Apheta to its square. Yet before the Flood, by divine disposition and because of the small number of men, this did not take away life, but the anaeretic direction was extended even to the opposite and beyond, as it pleased God, Author of Nature. After the Flood, however, the last limit of life was established in the descent of the Apheta to its square, as has been said. Nor, because Augustine, Jerome, and other Fathers think that by those words a term of repentance and conversion was prescribed by God for those men, is it thereby excluded that they may also be understood literally as spoken of the limit of life. For, as Vecchius also rightly notes, Observ. medica 40 in Sacred Scripture, Moses himself understood this when he said to the people, Deut. 31: “I am today a man of twenty years; I can no longer go out and come in,” because he certainly recognized that he had reached that limit at which men after the Flood, by divine ordinance, for the most part die: whence

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MATHEMATICVM. 515 R eo termino expleto mortuus est, vt habetur etiam Deut. 34. Quod autem non statim post diluuium obseruari cæpit sex illa, cum multi fuerint Pattiarchæ, qui immediatè etiam post illius promulgationem terminum illum nihilominus transilierunt, vt præ cætetis obseruauit, & obiecit Abulensis, id non multum videtur officere, quia exceptione aliqua communis regula non infringitur, & alioqui tunc temporis ob paucitatem hominum, ordo uatutæ, & propagatio humani generis postulabat, vt aliqua exceptio fieret, firma tamen lege Trimorionis, qua vita hominis ad 120. annorum terminum protrahi posset, vt plurimum enim homines ab eo tempore intrà præscriptum terminum extin- cti sunt. TRINVS RADIVS est familiaritas intercedens inter duos < 66.> planetas in distantia tertiæ partis cæli, scù grad. centum viginti, (quoniam radij siderum, vt alibi obseruatum est, correspondent musicis consonantiis,) habet ad modos musicos proportionem ad quintam: sicuti chorda diuisa in tres partes æquales, ad alteram consimilem ex toto protensam correspondet quintæ: Et ideo est radius valdè efficax, maximè in signifero, vbi conveniunt planetæ in signis conformis omninò naturæ: estque naturâ sua bonus, maximè < 67.> inter beneficos: cuius bonitatis, & conuenientiæ causam assignat Ptolemaeus similitudinem sexus, eo quia, inquit, omnia sunt masculina, aut fœminiina: sed hæc præcisè videtur valdè debilis ratio: Nam vt benè aduertit Maginus in Primo Mobilis canone 39. Oppositio sit inter duo signa sexu similia, & tamen hostilis est; immo & nequior ipso Tetragono: Quapropter ea conuenientia potius consistit in conformitate naturæ ob similitudinem omnimodam qualitatum, quod in aliis aspectibus videre non est: sed solùm in sextili ob conuenientiam in vna saltem qualitatum, in conditione temporis, & sexu, & ideo dicitur participare de ttino, & vocatur radius imperfectæ amicitiæ. TRIQVETRVM, Triangulum. Apud Astronomos pressùs < 68.> accipitur pro certò sidere octauæ sphæræ in trianguli formam abeunte, non eo quidem, quod citrà æquatorem est in hemisphærio nostro spectabile (illud enim alio nomine Delteton appellatur) sed altero ad polum antarcticum non ita pridem ab Americo Vespucio detecto, atque inter alias duodecim nouas imagines conumerato. Constat autem stellis quinque existentibus in longitudine sub signo Sagittarij.

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MATHEMATICVM. 515 Having completed that term, he died, as is also stated in Deut. 34. But that it did not begin to be observed immediately after the Flood, the six years, although there were many Patriarchs who immediately even after its promulgation nevertheless passed beyond that limit, as, above all, Abulensis observed and objected, does not seem to matter much, because a common rule is not broken by some exception, and otherwise then, because of the scarcity of men, the order of nature and the propagation of the human race required that some exception be made, yet with the firm law of the Trimorion, by which the life of man could be extended to the limit of 120 years; for very many men from that time on were extinguished within the prescribed limit. TRINVS RADIVS is the familiarity existing between two planets at a distance of a third part of the heaven, that is, 120 degrees, (since the rays of the stars, as has been observed elsewhere, correspond to musical consonances,) it has a proportion to musical modes to the fifth: just as a string divided into three equal parts, to another similar one stretched to the full, corresponds to the fifth: and therefore it is a very effective ray, especially in the sign-bearing circle, where the planets meet in signs wholly in accord with nature; and by nature it is good, especially among the benefic. Ptolemy assigns the cause of this goodness and suitability to likeness of sex, because, he says, all things are either masculine or feminine: but this precisely seems to be a very weak reason. For, as Maginus rightly observes in the Canon of the First Mobile, canon 39, opposition exists between two signs similar in sex, and yet it is hostile; indeed even worse than the square aspect itself. Wherefore that suitability rather consists in conformity of nature through the complete similarity of qualities, which is not seen in other aspects: but only in the sextile, by reason of agreement in at least one quality, in condition of time and sex; and therefore it is said to partake of the trine, and is called the ray of imperfect friendship. TRIQVETRVM, Triangle. Among astronomers it is taken strictly for a certain star of the eighth sphere forming a triangle shape, not indeed the one which lies this side of the equator and is visible in our hemisphere (for that is called by another name Delteton), but the other toward the Antarctic pole, not so long ago discovered by Amerigo Vespucci, and counted among the other twelve new figures. It consists of five stars lying in longitude under the sign of Sagittarius.

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114 LEXICON 70. TRIQUETRUM PTOLEMI est instrumentum Mathematicum, perantiqvum cuius authorem faciunt Ptolemæum, aptum ad metiendas rerum distantias, altitudines, longitudines, declinationes. Eius vsum fusè tradit Galluuius de Instrum. Mathemat. 71. TROPÆI Venti sunt Alrani de quibus refert Plin. lib. 2. cap. 43. quod etsi in terra alioqui generentur, tamen semper è maris regione persistant. sunt eiusdem rationis ac Apogæi. Verum illi tunc dicuntur, cum ad mare tendunt; cum verò inde redeunt vocantur Tropæi, ex Græca notione tropos, quæ significat conversionem. Venti sunt nimium violenti, qui maria ex improviso commouent, & pluuias repentinas faciunt; quæ tamen momento siniunt. Familiares sunt in Æstate in toro tractu Italiæ, ac præsertim Neopoli; vbi has repentinas pluuias Tropæas vocant. 72. TROPICI appellantur duo circuli minores in sphæra æqualiter ab æquatore distantes, hoc est per gr. 23. cum dimidio, hinc inde qui sunt limites cursus solis, & deviationis ab æquinoctiali circulo: quos cum attigerit, sistit, & convertit iter ad æquatorem: hinc Tropicorum iis nomen est indium. Quorum alter est, qui declinat ab boream, & dicitur Tropicus Canci, vbi sol efficit maximum diem artificialem, noctemque è contra breuissimam: alter ad Austrum inflectens dictus Tropicus Capricorni, in quo existens sol facit Hyemem, diemque minimum, noctemque longissimam. Quod tamen intelligendum est de nostris regionibus borealibus citra æquatorem Nam in Australibus totum oppositum accidit. 73. TRVTINA HERMETIS apud Astrologos antonomasticè audit artificiosa methodus rectificandi natalitium thema per indagationem diei conceptionis, ab Hermete primum inuenra, ac posteà à Ptolemæo (siue alioquouis Centiloquij Auctore) suo Aphorismo 51. firmata. In quo, inquit, signo Luna est genitura tempore, illud in conceptu fac Ascendens: & in quo signo inuenta fuit in conceptu, illud, aut eius oppositum fac Ascendens in partu. Docet itaque Hermes, magnam intercedere connexionem & rythnum inter diem conceptionis & diem natuitatis, ita vt ordinatissimo semper & constanti motu præcedat Luna à die conceptionis; expletoque dierum numero, quot requiruntur ad maturandum fæcum; tum demùm in lucem edat, quando fuerit in eo signo, quod conceptionis tempore orientalem angulum occupabat. Porrò numerum dierum quibus moratur foetus in vtero, auspicandum præcipit à distantia, quam

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114 LEXICON 70. TRIQUETRUM PTOLEMI is a mathematical instrument, very ancient, whose author is said to be Ptolemy, suitable for measuring the distances, heights, lengths, and declinations of things. Galluuius gives a full account of its use in De Instrumentis Mathematicis . 71. TROPÆI are winds, concerning which Pliny reports in book 2, chapter 43, that although they are otherwise generated on land, they nevertheless always continue from the direction of the sea. They are of the same kind as Apogæi. But those are so called when they tend toward the sea; when, however, they return from there, they are called Tropæi, from the Greek notion tropos , which signifies turning. They are exceedingly violent winds, which suddenly disturb the seas and cause sudden rains; yet these cease in an instant. They are familiar in summer throughout much of Italy, and especially in Naples; where such sudden rains are called Tropæas. 72. TROPICS are the two smaller circles in the sphere equally distant from the equator, that is, by 23 and a half degrees on either side, which are the limits of the sun’s course and of its deviation from the equinoctial circle: when the sun reaches them, it stops and turns its course back toward the equator; hence they are named Tropics from this. One of them declines toward the north and is called the Tropic of Cancer, where the sun produces the longest artificial day and, on the contrary, the shortest night: the other bends toward the south and is called the Tropic of Capricorn, in which, when the sun is there, it makes winter, the shortest day, and the longest night. This, however, must be understood of our northern regions on this side of the equator; for in the southern regions the exact opposite occurs. 73. THE TRUTINA OF HERMES is, among astrologers, by antonomasia, the artful method of rectifying the natal chart by investigating the day of conception, first found by Hermes and later confirmed by Ptolemy (or by whichever author of the Centiloquium) in his Aphorism 51. In that sign, he says, in which the Moon is at the time of the nativity, make that sign the Ascendant at conception; and in the sign in which it was found at conception, make that, or its opposite, the Ascendant at birth. Hermes therefore teaches that there is a great connection and rhythm between the day of conception and the day of birth, so that the Moon always precedes in the most orderly and constant motion from the day of conception; and when the number of days required to ripen the fetus has been completed, then at last it brings it forth into light, when it is in that sign which occupied the eastern angle at the time of conception. Moreover, he instructs that the number of days during which the fetus remains in the womb should be determined from the distance, which

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MATHEMATICVM. 51 habet in figura natiuitatis æstimatitia Luna à linea horizontis, subtrahendo locum Ascendentis à loco Lunæ si ea fuerit sub terra; vel cardinem occidentis à loco Lunæ, sit ea fuerit suprà terram: Ad cuius distantiæ rationem accipiendo di sunt dies moræ foetus in vtero in subiecta tabella à latere dextrorsum respondente: & in prima quidem columna, si in figura æstimatitia Luna fuerit infrà terram, in secunda verò, si suprà: qui postèa dies enumerandi sunt per menses retroactos à die natiuitatis, quousque perueniatur ad vltimum ibi notatum, qui profectò erit dies conceptionis, ad cuius meridiem erigendum est Thema conceptionis. Et si quidem tunc temporis Luna occupet illud ipsum signum, quod in natiuitate reperiebatur in occidente, vel signum eius oppositum; tunc sanè ipsissima erit dies conceptionis ea in quam desinit computatio: sin minus, quod rarissimè accidit, videndum erit, num fortè id contingat duobus retrò, vel antè diebus, & tunc is erit verus dies conceptionis. Ad indagandam verò horam conceptus, obseruabimus in quo signo & gradu reperiatur sol ipso die conceptionis, quod habebimus ex tabula domorum ad eleuationem poli nostræ regionis in columna decimæ domus; & eo reperto accipiemus tempus à meridie à sinistris respondens; quod ex parte ponemus. Deinde sub prima domo inuestigabimus signum, & gradum Lunæ natiuitatis; & ex eo etiam sumemus tempus à Meridie illi respondens: quod postèa conferendo cum tempore à meridiæ prius inuento ad latus loci solis, subtrahendo istud ab illo, remanebit præcisum tempus à meridie, in quo facta fuit conceptio: ad quod posteà more solito erigendum est Thema conceptionis, & locus præcibus Lunæ sumendus est, atque in horoscopo natiuitatis constituendus. Quod gradus Lunæ in figura conceptionis sit idem prorsus, ac gradus horoscopans in natiuitate, hæc erit rata, & firma, nec proptereà immutanda: sin minus notabis, quot horæ, & minuta temporis à meridie correspondeant gradui horoscopanti figuræ æstimatitiæ, ac cipiendo item signum illud ex prima domo; & facta subtractione huius ab illo: differentia, quæ prodibit erit etiam temporis æstimati à vero: atque adeò ad datum tempus, aut addenda, aut minuenda.

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MATHEMATICVM. 51 has in the figure of nativity an estimated Moon from the line of the horizon, subtracting the place of the Ascendant from the place of the Moon if it was below the earth; or the western angle from the place of the Moon, if it was above the earth: from the proportion of this distance taking the days of the fetus’ stay in the womb from the table set below on the right-hand side: and indeed in the first column, if in the estimated figure the Moon was beneath the earth, in the second, however, if above: these days are then to be counted back through the months elapsed from the day of nativity, until one comes to the last number noted there, which will certainly be the day of conception, for whose midday the Theme of conception is to be erected. And if indeed at that time the Moon occupies that very sign, which in nativity was found in the west, or its opposite sign; then surely that will be the very day of conception, the one on which the computation ends: if not, which very rarely happens, it must be seen whether perhaps this occurs two days before or after, and then that will be the true day of conception. To discover the hour of conception, however, we shall observe in what sign and degree the sun is found on the very day of conception, which we shall obtain from the table of houses for the elevation of the pole of our region in the column of the tenth house; and when this is found we shall take the time from midday corresponding on the left; which we shall place aside. Then under the first house we shall investigate the sign and degree of the Moon at nativity; and from this also we shall take the time corresponding to it from midday: which afterward by comparing with the time from midday previously found at the side of the sun’s place, subtracting the latter from the former, there will remain the precise time from midday in which the conception was made: to which afterward, in the usual manner, the Theme of conception is to be erected, and the place of the Moon’s preces is to be taken, and set in the horoscope of nativity. If the degree of the Moon in the figure of conception is exactly the same as the horoscopic degree in the nativity, this will be sound and firm, and therefore not to be changed: if not, you will note how many hours and minutes of time from midday correspond to the horoscopic degree of the estimated figure, and taking likewise that sign from the first house; and after subtracting this from that: the difference that emerges will also be the estimated time from the true one: and therefore, to the given time, it must be either added or subtracted.

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LEXICON Tabula Moræ Fætus in vtero. Signa. Grad. Dios Mora. Dios Mora. 0. 0. 273. 258. 0. 11. 274. 259. 0. 24. 275. 260. 1. 6. 276. 261. 1. 18. 277. 262. 2. 0. 278. 263. 2. 12. 279. 264. 2. 24. 280. 265. 3. 6. 281. 266. 3. 18. 282. 267. 4. 0. 283. 268. 4. 12. 284. 269. 4. 24. 285. 270. 5. 6. 286. 271. 5. 18. 287. 272. 6. 0. 288. 273. Luna sub terra. Luna suprà terram. Atque hæc est via rectificandi natalitium Thema per diem conceptionis ab Hermete Trismegisto inuenta; quæ tamen aliud non est quam rythmus, & numerorum correspondantia ex ordinatissimo Lunæ circuitu circa tellurem: Quî fit,

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LEXICON Table of the Duration of the Fetus in the Womb. Signs. Degrees. Days Delay. Days Delay. 0. 0. 273. 258. 0. 11. 274. 259. 0. 24. 275. 260. 1. 6. 276. 261. 1. 18. 277. 262. 2. 0. 278. 263. 2. 12. 279. 264. 2. 24. 280. 265. 3. 6. 281. 266. 3. 18. 282. 267. 4. 0. 283. 268. 4. 12. 284. 269. 4. 24. 285. 270. 5. 6. 286. 271. 5. 18. 287. 272. 6. 0. 288. 273. Moon below the earth. Moon above the earth. And this is the way of rectifying the nativity chart by the day of conception, discovered by Hermes Trismegistus; which, however, is nothing other than rhythm and the correspondence of numbers from the most orderly circuit of the Moon around the earth: whence it happens ,

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MATHEMATICVM. 317 fit, vt semper in idem recidar, atque adeo variato nimium natalitio themate, variari etiam necessariò debet dies conceptionis. Tum demum quia ob diuersa accidentia, quæ extrinsecùs aduenire possunt facilè etiam, aut immaturè, aut seriùs edi potest foetus, vt patet experientia: in quo casu nims enormiter fallit hæc methodus. Quapropter solidiori fundamento est innitendum. TSAMANGADV GLIESARA, hoc est, via straminis, apud < 75.> Æthyopes & Hebræos dicitur via lactea, teste Kirchero in Oedipo Ægyptiaco: apud Arabes verò Almagires quasi fluxus, seù tractus ex sparsapaleâ. TUBERONI, apud Plinium dicitur stella regia in pectore < 76.> Leonis dicta communiter Regulus, & cor Leonis: sic enim ait, lib 18. cap. 26. Octavo Calendas Februarij stella regia appellata Tuberoni in pectore Leonis occidit matutino. Nescimus qua ratione, & vnde tandem excerpserit. TURBO, apud Geometras dicitur figura solida, quæ ex < 77.> lato in acutum desinit, seù ex parte verticis lata est, atque inferiorem partem acutam habet: ei contrarius est conus, qui pyramidalem formam referens latum habet pro basi, acutum pro vertice. Nomen hausit turbo ab instrumento lusorio, quod à pueris scutica, vel funiculo circumagitur. Hinc etiam Turbineum appellatur quidquid ex lato desinit in acutum. TURBO etiam dicitur Ventus vorticosus, procellæ species, < 78.> obuia quæque impetens, ac deturbans: Gtæcis Typhon; à Plinio, Vibratus venius, ab aliis Vortex; ab Aristotele Ventus indigestus vocatus, hoc est non adhuc perfectè separatus à nube: quippe qui semper affetre secum solet aliquam nubium partem. Differt ab Ecnephia; quod is non rectè ascendit: vt ille, sed potiùs in gyrum voluitur secum eleuans saxa, & alia ingentia corpora; vnde fit postea pluura lapidum, & similium. Plinius aduersus hunc ventum affert pro remedio aceium, quod præcipit debere circum effundi, quia vis, inquit, aceti frigidissima, & subtilissima est; sicque ardorem turbinis extinguit, erassitiemque eludit. Nautæ è contrà bombardarum explosione turbinem disperdunt. TYMPANA appellantur Tabulæ in Planisphærio, seu Astro- < 79.> labio, in quibus ad quascumque poli eleuationes sunt descripti circuli altitudinum, & verticales, vt exiis ortus; & occasus siderum, declinationes, Cæli inedia:ones, aliaque facilè erui possint. Siquidem singula cotum immediatè subjeciuntur reti seu Voluello, quod cæli stellarumque Kk

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MATHEMATICVM. 317 it comes about that I always fall back into the same thing, and thus, with the natal theme excessively altered, the day of conception must also necessarily be altered. Then at last, because of various accidents that can easily happen from outside, the fetus may also be born either too early or too late, as experience shows: in which case this method errs extremely badly. Wherefore a sounder foundation must be relied upon. TSAMANGADV GLIESARA, that is, the way of straw, is called among the Ethiopians and Hebrews the Milky Way, according to Kircher in the Oedipus Aegyptiacus; among the Arabs, however, Almagires, as it were a flow, or a track from scattered chaff. TUBERONI, among Pliny, the royal star is said to be in the breast of Leo, commonly called Regulus and the heart of Leo: thus he says, book 18, chapter 26, “On the eighth day before the Kalends of February, the royal star called Tuberoni in the breast of Leo set in the morning.” We do not know from what source, or from where at last, he extracted it. TURBO, among geometers, is said of a solid figure that ends from broad to sharp, or is broad at the part of the vertex and has the lower part sharp: opposite to it is the cone, which, resembling a pyramidal form, has a broad base and a sharp vertex. The name turbo was taken from the toy with which boys spin something around by means of a whip or cord. Hence also whatever ends from broad to sharp is called turbine-like. TURBO is also said of a whirling wind, a kind of storm, attacking and knocking down whatever lies in its way: among the Greeks, Typhon; by Pliny, a vibrating wind; by others, a vortex; by Aristotle, a wind not yet well-digested, that is, not yet perfectly separated from a cloud: for it is accustomed always to carry some part of the clouds with it. It differs from Ecnephia in that the latter does not rise straight up, as the former does, but rather turns in a circle, lifting with it rocks and other huge bodies; whence afterward comes a shower of stones and the like. Pliny, against this wind, recommends vinegar as a remedy, which, he says, should be poured all around, because the force of vinegar, he says, is very cold and subtle; and thus it extinguishes the heat of the whirlwind and overcomes its thickness. Sailors, on the other hand, disperse a whirlwind by the firing of cannon. TYMPANA are the plates in the planisphere, or astrolabe, in which, for whatever elevations of the pole, circles of altitudes and verticals are drawn, so that from them the rising and setting of the stars, declinations, meridian passages of the sky, and other things may easily be drawn out. For each one is immediately subjected to the rete or wheel, which of the sky and the stars...

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LEXICON diurnam circulationem circa terram repræsentat. Dicta sunt autem Tympana, quia Tympani speciem præseferunt. 80. TYPHON Græcè idem quod Latinè Turbo, de quo paulo ante dictum: licet Plin. lib. 2. cap. 28. Turbinem à Typhone distinguat, dicatque Turbinem fieri, quia spiritus, depresso sinu, arctius rotati nubis cutem infringunt; (si enim latè nubes rumpatur Ecnephias sit,) vocatque turbinem vibratum Ecnephiam; vt nos in loco diximus. Quod si spiritus maiore depressæ nubis eruperit specu, sed minus lato, quam procella, nec sine fragore, Typhonem vocat proxima quæque prosternentem. Et cap. 49. Vorticem, ac turbinem sic distinguit: Vortex remeando distat à turbine, eo modo quo distert stridor à fragore. De eo sequitur. 81. Præcipua nauigantium pessis, non antennes modo; sed ipsa nauigia contorta frangens, repercursus secum in calum refert, sorbetque in excelso. Lius materia est exhalatio calida, & sicea vi siderum elata, atque intrà nubes coacta, quæ solis radiis rarefacta exitum quærens, cum impetu prosilir, atque ab aliis venti partibus directè euniibus repulsus fertur in circulum; indeque est, quod quamdiù à nube perfectè separari non potest; eius partem secum attrahat, & obuiæ quæque abripiens præcipiti iactu ad terram deiiciat: Vnde prodigiosæ illæ saxorum pluuix; de quibus mulia habet Vincentius Belluacensis in speculo historiali lib 25. cap. 87. Aduersit tamen Aristoteles id non contingere, nisi in Vere, & in Autumno: Nam in Hyeme nimia frigiditas extinguit calidam illam, & siccam exhalationem, ex qua typhones formantur. In Æstate verò nimius calor attenuat eam plurimum, dissoluit, & congregari non sinit. Plura apud Senecam in Quæst. Natural. & Plin. loc. cit. V2 1. VACVVS CVRSV dicitur Planeta ab alio separatus, nec proinde alteri applicans corpore, aut radio: Quod debilitatis genus dicitur Feralitas, idque in Luna potissimum obseruatur. 2. VAGIAH Arab. Lyra vide Vvega. 3. VALZAGORA: Chaldaicè Planisphærium. Testis Hermanus contractus. 4. VAPOR est halitus quidam seu aqueus humor è terra calore Solis, & aliorum siderum vi extractus, ac sursum elatus, ibi in media aëris regionis relictus ex varla eorumdem

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LEXICON represents the daily circulation around the earth. But they are called Tympana, because they present the appearance of a tympanum. 80. TYPHON, in Greek, the same as in Latin Turbo, of which mention has already been made above; although Pliny, book 2, chapter 28, distinguishes the Turbin from Typhon, and says that the Turbin arises because the winds, with the hollow cloud depressed, more tightly revolving, break the skin of the cloud; (for if the cloud is torn broadly, it is an Ecnephias,) and he calls the Turbin a roused Ecnephias; as we said in the passage. But if the wind bursts through a larger opening in the depressed cloud, yet one less broad than a storm, and not without a crash, he calls it Typhon, overthrowing whatever lies near. And in chapter 49 he thus distinguishes a vortex and a turbin: A vortex differs from a turbin by turning back, in the same way that a hiss differs from a crash. What follows concerns this. 81. It is the chief thing that harms sailors, not only tearing the sails; but even breaking the ships themselves by twisting them, and carrying the rebound back with it into the sky, and sucking it up aloft. Its matter is a warm and dry exhalation, raised by the power of the stars, and gathered within the clouds, which, being rarefied by the rays of the sun and seeking an outlet, bursts forth with violence, and, driven back by other parts of the wind moving directly toward it, is carried in a circle; and hence it is that, so long as it cannot be completely separated from the cloud, it draws part of it with it, and, seizing whatever lies in its path, casts it down to the earth with a headlong blow: whence those prodigious showers of stones; concerning which Vincentius Belluacensis has much in the Speculum Historiale, book 25, chapter 87. Aristotle, however, objects that this does not occur except in Spring and in Autumn: for in Winter excessive cold extinguishes that warm and dry exhalation, from which typhones are formed. But in Summer excessive heat greatly attenuates it, dissolves it, and does not allow it to gather together. More in Seneca, in the Natural Questions, and in Pliny, the cited passage. V2 1. VACVVS CVRSV is said of a planet separated from another, and therefore not applying to another body or ray: a kind of weakness called Feralitas, and this is observed especially in the Moon. 2. VAGIAH, Arabic. Lyra; see Vvega. 3. VALZAGORA: in Chaldean, a planisphere. Witness Hermanus Contractus. 4. VAPOR is a certain breath or watery moisture drawn from the earth by the heat of the sun and the force of the other stars, and carried upward, there left in the middle region of the air from the various of those same

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MATHEMATICVM. 519 siderum conuentione aut dissolur tur in imbres, aut concrescit in nives, aut in alia meteororum genera commutatur. Vide in V. Meteora. VAZA ZENE TEV Arab dicitur linea meridiana suprà ter- 54 ram descripta in Planisphærio. VAZNEG N VBI Arab. teste Kirchero in Oedipo Ægyptia- 6. co vocatur lanx Austriana sicut & VAZ ESCHEMATI dicitur lanx borealis, stellæ fixæ de qui- 7. bus alibi dictum. VECTOR, Auriga Ericthonius, &c. sidus in cælo ad borea- 8. lem plagam Vide in V. Auriga. VELOX C VRSV: Vide Au[n]ctus numero. 98. VENTER DRACONIS apud Astronomos dicitur maxima 10. planetarum latitudo, & diuiatio ab Ecliptica: Qui duplex est alter Boreus, alter Austrinus: vbi verò orbitæ ipsorum intersecant Eclipticam, vocantur caput, & cauda Draconis, provt in loco diximus: eoquod orbita planetæ vna cum Ecli- ptica efformare videatur duos velui Dracones; qui vt cor- pore magni sunt, & versus caput, & caudam extenuantur; ita latitudinis amplitudo in duabus intersectionibus exte- nuatur, & in d[iffe]rtilum cedit; in medio verò augescit, itavt Draconis ventrem videatur referre. Vocantur etiam limites flexuræ, &c. quemadmodum & intersectiones appellantur nodi, euchens, & attollens vel deprimens, provt ad bo- ream, vel ad Austrum inflectunt. VENTUS ex Alberto Magno in 3. Meteor. tract. 1. cap. 3. est 12 Vapor terreus aeris superiora transcendens, & aerem vehe- menter percutiendo impellens. Consonat Arist. in Meteoris, & schola Periparicorum communiter. Verum hac definitio- ne venit non tam ventus ipse, quam ipsius causa proxi- ma, & effectiua, cum alias Venti nomine, communi omnium acceptione veniat agitatio quidam aeris circà terram; vt obseruauit Speusippus de Platonicis, siuè à Natura occulta vi, siuè à nobis medio aliquo instrumento præstita, cuius effectus sit refrigerare, & exsiccare: quando huius- modi exhalationis effectus foret calefacere, & inflam- mare. Et quidem nulli dubium esse potest, ipsam ventorum materiam aliud planè non esse quam aerem agitatum, itavt ipsa actualis commotio Ventus sit. Audi Augustinum lib. de Quantitate Anima. Nihil aliud, inquit, quam istum aerem commotum & agitatum, ventum esse sentimus, quod in loco tranquillissimo & ab omnibus ventis quietissimo, vel breui istabello approbari potest, quo etiam muscas abigen- tes aerem commouemus, flatumque sentimus. Apuleius de Kk ij

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MATHEMATICVM. 519 by the conjunction of the stars it is dissolved into rains, or solidifies into snow, or is changed into other kinds of meteors. See in V. Meteora. VAZA ZENE TEV, Arab., is said of the meridian line drawn above the earth in the planisphere. 54 VAZNEG N VBI, Arab., according to Kircher in Oedipus Ægyptiacus, is called the southern dish, as also VAZ ESCHEMATI is called the northern dish, the fixed stars of which have been spoken of elsewhere. 7. VECTOR, Auriga Ericthonius, etc., a constellation in the sky toward the northern quarter. See in V. Auriga. VELOX C VRSV: See Au[n]ctus number 98. VENTER DRACONIS, among astronomers, is called the greatest 10 latitude of the planets, and their deviation from the ecliptic. It is twofold: one northern, the other southern. But where their orbits intersect the ecliptic, they are called the head and tail of the Dragon, as we said in that place; because the orbit of a planet together with the ecliptic seems to form, as it were, two Dragons, which, like a body, become thinner toward the head and tail; thus the breadth of latitude is narrowed at the two intersections and yields to a division, while in the middle it increases, so that it seems to represent the belly of a Dragon. They are also called the limits of flexure, etc.; and similarly the intersections are called nodes, euchens, and ascending or descending, according as they bend toward the north or toward the south. VENTUS, from Albertus Magnus in 3 Meteor., treat. 1, chap. 3, is 12 an earthly vapor passing beyond the upper regions of the air and, by violently striking, driving the air onward. Aristotle agrees in the Meteorologica, and the Peripatetic school commonly. But under this definition there is included not so much the wind itself as its proximate and efficient cause, since otherwise, under the name of wind, by the common acceptance of all, there comes a certain agitation of the air around the earth, as Speusippus observed among the Platonists, whether by nature through some hidden force, or by us through some instrument provided as a means, the effect of which is to cool and dry; whereas the effect of such an exhalation would be to heat and inflame. And indeed there can be no doubt that the very matter of the winds is plainly nothing other than agitated air, so that the actual motion itself is the wind. Hear Augustine, book On the Quantity of the Soul: “We perceive,” he says, “that nothing else than this air moved and agitated is wind,” which can even be verified in the quietest place and in one most free from all winds, or by a small fan, by which also, driving away flies, we move the air and feel the blast. Apuleius de Kk ij

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LEXICON 520 Mundo sic ventum describit: Nec enim aliud est, inquit, nisi multum, ac vehementem in unum coacti aëris flamen: hunc spiritum dicemus, &c. 12. Stat igitur ventum in se formaliter aliud non esse, quam impetum aëris in vnam partem violenta coacti. At enim quomodo generentur, & vnde exeat flavius ille ventum impellens, qui processu non modo non deficit, sed validior semper euadit, adeo difficile est explicatu, vt iure dixerit Eueli. esp. 11. Quomodo ignoras, qua sit via spiritus, si opera Dei; & Psal. 134. Psaltes inter potiora Dei magnalia enumerat, quod educit ventos de Thesaurus suis. In quæ verba August. Ab occultis, inquit, causis, vnde nescis: Qua enim pat ventus sentis, qua causa flat, vel de quo thesauro rationis eductus sis nescis. Anaximandër apud Licum existimauit ipsum esse fluxum aëris de subtilissimis, & humidissimis in eo partibus à sole, vel moris, vel liquefactis conflatum: sed enim si hoc esset, quorsum tanta illi violentia inest? Quorsum motus ille obliquus, & non potius sursum; cum alias videamus vapores, hoc est subtiliores aquæ particulas è terra calore solis sursum euehi, & oleuari? Quorsum tandem tanta ventorum diuersitas? 13. Generantur itaque Venti, seù potius excitantur ex variis exhalationibus calidis è terra prosilientibus, quæ ad medium aëris regionem perductæ, ex quidem, siue id â sideribus, siue aliundè fiat, non adeò accenduntur, vt in ignes vertantur, sed calore concepto rarefiunt, ac dilatantur: Quî fit, vt ampliorem locum occupare gestiat exhalatio illa, aëtem contiguum magno nisu impellat, qui successiuè alias partes sibi proximus moueat, ac motu ipso, & calore suppetias afferente, erescat semper impulsus, ac ventus tandem, de quo sermonem agimus suscitetur. Hinc est, vt qua parte ventus spirat, ibi exhalatio multa cogatur, & quæ loca exhalationibus istis plurimum scatent, eadem, seù sibi proxima sint ventis multis obnoxia. Vi plurimum autem venti lateraliter excitantur: quia exhalatio illa dum è media aëris regione deorsum truditur, ipsa sua levitate conatur sursum ascendere, sed interim frigiditate aëris resistente, siue id efficientibus stellis habentibus vim propellendi deorsum materiam eo modo dispositam; cedit tandem ad latera: Pæterquam non omninò incredibile est ea sidera quæ exhalationem istam commouent arque in ventum attenuant, eadem occulta vi adse, vel al partes sibi subiectas illam attrahere, vnde diuersitas illa ventorum. Et quidem Mercurius generalis ventorum motor affecitur. Venus me-

Transcription: Translated (English)

LEXICON 520 Thus Mundo describes the wind: For, he says, it is nothing else than a strong blast of air, driven together into one mass: we shall call this spirit, etc. 12. Therefore it stands that wind in itself is formally nothing other than the violent driving of air into one part. But then how they are generated, and whence that flow comes out driving the wind, which in the process not only does not fail, but always becomes stronger, is so difficult to explain that Eueli. rightly said, esp. 11. “How do you not know what the way of the spirit is, if it is the work of God?” And Psalm 134, the Psalmist counts among the greater wonders of God that he brings forth winds from his treasures. On these words Augustine says: “From hidden causes, whence you do not know. For in whatever way you feel the wind, you do not know by what cause it blows, or from what treasure of reason you have been brought forth.” Anaximander, as cited by Licus, thought that it was itself a flow of air from the subtlest and most humid parts in it, formed by the sun, or by smelting, or by liquefaction: but if this were so, why is there in it so great a violence? Why that oblique motion, and not rather upward; since otherwise we see vapors, that is, the subtler particles of water, raised upward from the earth by the heat of the sun, and carried off? Why finally such great diversity of winds? 13. Therefore winds are generated, or rather stirred up, from various warm exhalations springing forth from the earth, which, brought to the middle region of the air, are indeed, whether this happens from the stars or from elsewhere, not so much kindled that they are turned into fires, but, having received heat, they rarefy and expand: so that that exhalation eagerly seeks to occupy a broader place, and force the contiguous air with great effort, which successively moves the other parts nearest to it; and with motion itself, and heat lending support, the impulse always grows stronger, and the wind at last, of which we are speaking, is stirred up. Hence it is that on the side where the wind blows, there much exhalation is gathered, and the places that abound most in these exhalations, either these or those near them, are exposed to many winds. But winds are very often stirred up laterally: because that exhalation, while it is driven down from the middle region of the air, by its own lightness strives to ascend upward, but in the meantime, the coldness of the air resisting, or the stars causing it, which have the power of driving matter downward in that manner, it finally yields to the sides. Besides, it is not at all incredible that those stars which move this exhalation and thin it into wind, by the same hidden power draw it to themselves, or to the parts subject to them, whence that diversity of winds. And indeed Mercury is affected as the general mover of winds. Venus me-

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MATHEMATICVM. 521 tidionalium, Iupiter borealium; Saturnus Orientalium, Mars Occidentalium. Vbi aduertendum omnes ventos ex sui intrinseca ratione eiusdem esse naturæ, & qualitatis: extrinsecus autem habe- re, quod iste sic calidus, ille frigidus, hic morbosus, ille salubris, hic lenis ille impetuosus, &c. Cum enim ventus formaliter aliud non sit, quam aer commotus, consequenter pro qualitate aeris, & regionis vnde exsufflat, aut pertransit ventus, naturam induit morbificam, aut salubrem, calores facit, aut frigora, exsiccare sit aptus, aut humores adducere. Sic venti Septentrionales, quoniam à frigidis regionibus, atque ab altissimis montium iugis spirantes ad nos aduentant, ideo frigidi, & sicci sunt: Meridionales, quia à Mari proueniunt, ac per Zonam torridam transeunt, ideo calidi, & humidi magis aut minus pro locorum varietate, & qualitate distantiæ. Vnde Syroccus magis humidus est Genuæ, quam Neapoli, coquia ibi amplior est sinus maris maioremque humorum copiam habet asserre. Econtrà in Sicilia calidus & siccus est, quia ad eam insulam non per mare, sed per continentem Africæ tractum permeat; adeoque omnem humorem ex Oceano haustum linquit in Africa, Africanumque aerem calidum siccumque in Insulam illam apportat Quod adeo vetum est, vt in Regno Chile, & in aliis terræ Australis nuper detectæ regionibus accolæ contrarias no, bis experiuntur ventorum naturas, & qualitates: vt testis est Alphonsus de Oualles in descriptione Regni Chile Nam ibi Auster perinde est ac nobis Aquilo, imperiosus, frigidus, & siccus: hic verò è contrà, & ei collaterales venti, qualitates assumunt calidas, & humidas, eo prorsus modo, quo nobis experiri est Syrocum, & Austrum, quia profectò illis à Polo Antartico, & frigida Zona, cuius naturam indunt Auster, & reliqui laterales aduentant, Aquilo verò circius, & Septentrio per Zonam torridam, atque Oceanum transeuntes aerem humoribus repletum, & caloribus feruidum illuc asportant. Quod & nos alibi adnotauimus. Similiter Aquilo in Lusitania, & Neapoli nubes cogit, & pluuius est; in Africa nubes dissipat, ac serenitatem adducit. Septentrio è contrà in Hellesponto, & apud Cyrenen pluuiam creat, in Italia serenus est. Porrò venti cardinales quatuor sunt à totidem mundi partibus flantes. Septentrio, de sub Polo Arctico: Auster à Meridie: Subsolanus, ab exortu æquinoctiali: Fauonius ab occasu item æquinoctiali, quibus totidem intermedios a K k iij

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MATHEMATICVM. 521 of the southern, Jupiter of the northern; Saturn of the eastern, Mars of the western. It is to be noted that all winds, in their intrinsic nature, are of the same kind and quality; but extrinsically they have this or that character, namely, that one is hot, another cold, this one unhealthy, that one wholesome, this one gentle, that one violent, and so forth. For since wind, formally speaking, is nothing other than air in motion, it consequently takes on, according to the quality of the air and of the region from which it blows out, or through which it passes, a nature either morbific or wholesome, producing heat or cold, being suited to dry things, or to bring on humors. Thus the northern winds, because they blow from cold regions and from the highest mountain ranges, and come to us, are therefore cold and dry. The southern winds, because they come from the sea and pass through the torrid zone, are therefore hot and more or less moist according to the variety of places and the character of the distance. Hence the Sirocco is more humid in Genoa than in Naples, because there the gulf of the sea is wider and can bring a greater supply of moisture. On the contrary, in Sicily it is hot and dry, because to that island it passes not by sea, but by the tract of Africa on the mainland; and thus it leaves behind in Africa all the moisture drawn up from the Ocean and brings that African air, hot and dry, to that island. This is so true that in the Kingdom of Chile and in other recently discovered regions of the southern earth the inhabitants experience winds contrary to ours in nature and quality, as Alphonsus de Oualles testifies in the description of the Kingdom of Chile. For there the Auster is just as our Aquilo, impetuous, cold, and dry; here on the contrary, and the winds lateral to it assume hot and moist qualities, in exactly the same manner as we experience the Sirocco and the Auster, because in fact for them the Auster and the other side winds arrive from the Antarctic Pole and the cold Zone, whose nature they imprint, whereas the Aquilo, Circius, and Septentrio, passing through the torrid Zone and the Ocean, carry there air filled with moisture and fervent with heat. This we have also noted elsewhere. Likewise the Aquilo in Lusitania and Naples gathers clouds and is rainy; in Africa it disperses clouds and brings clear weather. The Septentrio, on the contrary, in the Hellespont and near Cyrene produces rain, while in Italy it is clear. Moreover, the four cardinal winds are those blowing from the four parts of the world: Septentrio from beneath the Arctic Pole; Auster from the South; Subsolanus from the rising of the equinox; Fauonius from the equinoctial setting likewise, with the same number of intermediate winds a K k iij

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LEXICON dunt Geographi Bortholybicum, Borthapeliotem, Notape- peliotem, & Notolybicum: Addiderut postea & alios quaruor laterales Subsolano, & Fauonio hinc inde grad 13. & sensis distantantes, hoc est qui spirarent à quatuor punctis ortus & occasus vtriusque Solstitij. Et ab ortu quidem Æsti- uali Cæciam, ab Hyemali Vulturnum, ab occasu Æstiuali Corum, ab Hymeali Africum: Pari etiam ratione deprehenderunt quatuor alios hinc inde laterales septen- trioni, & Austro in eadem distantia ac sunt prædicti à suis cardinibus: Et Circium, & Aquilonem dederunt Septen- trioni, illum ad occasum conterminum Borrolybico, istum ad ortum adiacentem Græco. Phoenicem autem, ac Lyba- notum Austro: hunc ad occasum, illum ad ortum: ac tan- dem singulis lateralibus binos hincinde minores ab iisdem lateralibus denominatos Neotherici appinxerunt, vt Africa verbi gratia Ypafricum & Mefafricum: coro Ypocorum, & Mesocorum, &c. qui tamen venti propriè non sunt ab aliis distincti, sed potius quartæ ventorum. Ergò numerus ven- torum olim erat 10. postea excreuerunt ad 14. inde ad 16. ac tandem adiectis omnibus collateralibus, iam modò sunt omninò 12. Quorum omnium schema passim exhibent scri- ptores tabulæ Geographicæ, & nos singulorum naturam in loco quem sibi quisque vendicat explicamus. Quantiæ autem sint ventorum commoditates eleganter explicat Seneca lib. 5. quæst Natural: cap. 10. Inter cæte- ra, inquit, Prouidentia opera ex una causa ventos aut in- uenit, aut per diuersa dispasuit: sed primùm, vt aëra non sine- rent p[er] grescere, sed assidua vexatione vitalem redderent: de- inde, vt imbrem terris subministrarent, u[m] denique nimios compescerens. Nam modò adducunt nubes, modò deducunt, vt per totum orbem pluuia diuidi possent. In Italiam Auster impellit, Aquilo in Africam reijcit: Etesia non patiuntur apud nos nubes consistere: ijdem totam Indiam & Ætiopiam continuis per id tempus aquis irrigant. cap. 16. Ob idque ali- bi aduerrit, nullam planè regionem esse, quæ non habeat aliquem flatum ex se nascentem, aut circa se cadentem. Tan- ta est numinis prouidentia in orbe isto suauiter per causas secundas administrando. Sed & hic, (quoriam de ventis agitur,) non erit fortè lectoribus iniucundum, nec à nostro instituto abhorrens colæ, seu orbis piscis Mari Ægyptio familiaris miram na- turæ affectionem in medium ferre, & causam inuestigare. Hic enim, & viuus & mortuus se vento semper obuer- tit, ac pyxide quamuis inclusus, domi è filo pendens,

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LEXICON The geographers add Bortholybicum, Borthapeliotem, Notape- peliotem, and Notolybicum. Later they also added four others, lateral to Subsolanus and Favonius, 13 degrees on either side and equidistant, that is, which blow from the four points of the rising and setting of each solstice. From the summer rising, indeed, Caecias; from the winter rising, Vulturnus; from the summer setting, Corus; from the winter setting, Africus. By the same reasoning they likewise found four others lateral on either side to the north and south, at the same distance as the aforesaid from their cardinals: and they assigned Circius and Aquilo to the north, the former bordering on the west with Borr olybicus, the latter adjacent to the east with Graecus. To the south they assigned Phoenices and Libonotus: this one to the west, that one to the east. And finally, to each of the lateral winds on either side they attached two smaller ones derived from the same lateral winds, called Neotherici, as Africa, for example, Ypafricus and Mefafricus; Corus, Ypocorus and Mesocorus, etc., which nevertheless are not properly distinct winds from the others, but rather quarter-winds. Therefore the number of winds was once 10; later they increased to 14; then to 16; and finally, with all the collateral winds added, there are now altogether 12. The diagram of all these is commonly shown by writers on geographical tables, and we explain the nature of each in the place which each claims for himself. How useful the winds are is elegantly explained by Seneca, book 5 of the Natural Questions, chapter 10. “Among other things,” he says, “Providence, from a single cause, either found the winds or distributed them through different regions: first, so that they would not allow the air to grow stagnant, but by constant agitation would make it fit for life; next, so that they might supply rain to the lands; and finally, so that they might check excesses. For sometimes they bring the clouds, sometimes they drive them down, so that rain may be distributed throughout the whole world. Auster drives rain into Italy; Aquilo drives it back into Africa; the Etesian winds do not allow clouds to remain among us; the same winds water the whole of India and Ethiopia with continual rains during that time.” Chapter 16. And for this reason he remarks elsewhere that there is absolutely no region which does not have some wind born from itself, or falling around it. So great is the providence of the deity in administering this world so gently through secondary causes. But here too, since we are speaking of winds, it will perhaps not be unpleasant to readers, nor out of keeping with our purpose, to bring forward and investigate the cause of the colæ, or orb-fish, familiar to the Egyptian Sea, and its wondrous relation to nature. For this creature, both alive and dead, always turns itself to face the wind, and, though enclosed in a box, hanging at home from a thread,

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MATHEMATICVM. 523 clausis adhuc cubiculi foribus, ac fenestris ad eam nihilominus mundi plagam se rictu convertit, vnde ven- tus exsufflat. Hunc ego vidi Veronæ in Musæo Excel- lentissimi Medici ac Philosophi Petri deCastromhi cum primis familiaritate coniuncti, nec sine admiratione rei periculum hisce oculis feci. Athanasius Kircherus in Arte magnetica rem fusè pertractat, aitque id oriri ex Sympathia, ac naturali propensione quam habet piscis ad ventum, quo nimium oblectatur: proindeque ei rictum obuertit, vt eius refrigerantem auram auidè excipiat frui- turus, at enim ego, pace tanti viri, potiùs in Antipathiæ ge- nium huius insitæ conversionis causam refundendam censeo. Quæ enim affectio, quæ conuenientia esse poterit huius piscis ad Ventum, quæ illum naturaliter moueat ad eius affectandam auram, hæcque illi sit oppotura? < 19.> Etsi enim non detrectauerim pisces multos pulmone præ- ditos aëris respiratione gaudere; non tamen id eovsqve con- cesserim, vt admittam etiam ventum præsertim violentissi- mum iis commodùm cedere: idque maxime in pisce isto haud mole magno, quique respirationis beneficio carere, tum ex eo quod pulmone caret, tum quia extra aquam non diù vi- uit, eensendus est. Itaque Antipathiam potiùs dixerim hanc miram piscis affectionem: ad quod asserendum me mouet tum aquaticorum omnium natura, & interior constitutio, qua illis aqua connaturalis, aër exitialis est, tum etiam ipsa particularis piseis exterior forma, quæ vt nomen indicat. Orbicularis est nisi quantum breuis rictus ex parte prominet, atque ex aduerso eauda magis lata, quam oblonga respon- det, quæ eidem per amplissimos maris sinus discurrenti pro temone deseruit. Quia igitur forma orbicularis, vt experien- tia docet, navigatiori non admodum idonea est, etiam huic pisci inopportuna aceidit ad natandum. Atqui Venti, quibus mare percellitur, piscibus omnibus, vel iis etiam, qui respirationis vsu fruuntur, cuiusmodi sunt Delphini, Pho- xæ, &c. sunt incommodi, (quî sit, vt tempestates præ- sentiant, atque ad eas declinandas in penitiora se maris loca recipiant) sed huic maxime pisci, qui à Natura minus omnibus ad se tutandum, & forma ad nandum apta, & au- xiliaribus pinnis fuit instructus, ventus cedit infensus: vnde est quod adversus eum eomodo quo potest se communicat, ac resistat, quod sanè præstat ei rictum obuertendo: tum na- turali omnium animantium impetu, quò se ad ea à quibus ex improuiso impetuntur (conuertunt, tum etiam quia in ea positione magis declinat venti exsufflantis iniuriam: tutatur Kk iiiij

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MATHEMATICVM. 523 with the doors of the chamber still shut, and the windows toward that quarter of the world nevertheless open, it turns its mouth in that direction from which the wind blows. I myself saw this in Verona in the Museum of the most excellent physician and philosopher Pietro de Castromhi, with whom I was especially familiar, and I made trial of the fact with my own eyes, not without admiration. Athanasius Kircher, in his Magnetic Art , treats the matter at length, and says that it arises from sympathy and a natural inclination which the fish has toward the wind, with which it is greatly delighted: and therefore it turns its mouth toward it, that it may eagerly receive and enjoy its cooling breeze. But I, with due respect to so great a man, think rather that the cause of this innate turning is to be sought in antipathy. For what affection, what affinity could there be between this fish and the wind, that would naturally move it to seek that breeze and make it agreeable to it? < 19.> For although I would not deny that many fishes equipped with lungs delight in breathing air, I have not gone so far as to admit that wind, especially the most violent, is also beneficial to them: and this is most especially so in this fish, which is not large in size, and which must be judged incapable of the benefit of respiration, both because it lacks lungs and because it does not live long outside water. Accordingly, I would rather call this strange affection of the fish antipathy. What moves me to assert this is both the nature of all aquatic creatures and their inner constitution, by which water is natural to them and air deadly, and also the fish’s own outward form, which, as the name indicates, is circular, except that a short mouth projects somewhat on one side, and on the opposite side a tail, broader rather than long, answers to it, serving as a rudder to the fish as it courses through the broad channels of the sea. Since, then, a circular form, as experience teaches, is not very suitable for navigation, it is likewise ill adapted in this fish for swimming. But winds, by which the sea is lashed, are harmful to all fishes, even to those that enjoy the use of respiration, such as dolphins, seals, and the like, which is why they perceive storms beforehand and, to avoid them, withdraw into deeper parts of the sea; but especially to this fish, which Nature has equipped less than all others for self-preservation, both in shape for swimming and with auxiliary fins, the wind is hostile. Hence it is that it somehow meets it and resists it as best it can, which it surely does by turning its mouth toward it: both by the natural impulse of all living creatures, whereby they turn toward those things by which they are unexpectedly struck, and also because in that position it more effectively avoids the harm of the wind’s blast, and protects itself. Kk iiiij

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LEXICON enim potissimè caudam, quæ ob sui prominentiam, latitudinem, atque ad formam orbicularem exorbitantiam maximè locum quassationi faceret. Idcircò hic piscis cuique verò naturaliter est aduersus, & ad eam partem vnde spirat, non ex sympathie genio, sed ex insita cuique sese aduersus inimicum tutandi propensione, conuerrit. Et hæc quidem ex occasione Ventorum de hac mira piscis affectione sint dicta. 20. VENUS stellarum omnium tam errantium, quam inerrantium splendidissima, & pulcherrima, quæ sua emissitia lucè mirè intuentium oculos allicit, & oblectat, idque non coquidem, quod sit cæteris omnibus maior, sed quia est terræ (excepto vno Mercurio) vicinior, vt constat ex parallaxi quam patitur ferè minutorum trium: vnde etiam colligitur, ipsam esse minorem tetra, quia, vt notat Clauius in sphæram Io: de Sacro bosco eius diametrum continet septies supra trigesies. Solem semper cum Mercurio comitatur, sese circà ipsum tanquam proprium centrum in suo Epicyclo continenter rotando: vt proinde tam in prima, quam in secunda statione, in quibus ab eo maximè elongatur, non distet plus gr. 48. ibique incipiat fieri directa, aut retrograda, maximèque splendear, & faciat vmbram Ope Telescopi obseruarum est, ipsam subire easdem ferè phases, ac Luua, atque adeò apparere modò plenam, modò semplenam, modo falcatam, modo nullam; quando videlicet sit suprà, vel sub Sole in Apogæo, vel Perigæo sui Epicycli, ipsi in eodem gradu eclepsiico iuncta. Cursum suum in Zodiaco perficit cum Sole spatio ferè vnius anni distat à terra secundum Recensiorum obseruationes milliar. ferè 600165. Cæterum Venus est Planeta foemininus, eo quia abundat humiditate magis, quam caliditate, temperatè tamen, ita vt naturæ viuentium sit accommodata, ob idque dicatur fortuna minor. 21. Præest ex membris humanis vasis seminalibus, ac pudendis, regitque gustum, olfactum, & tactum: vnde est Aphorismus in Ptolemæi Centiloquio n. 17 Venus Nato voluptatem affert in membro, cui signum, in quo ipsa est, dominatur. Quod maximè præstat in propriis domiciliis, quæ sunt Taurus, & Libra, aut in Piscibus, vbi exaltatur. Hinc est, vt benè locata in his signis faciat amabilem, Musicæ, & Choreis addictum, præterim in Ascendente, aut Genituræ Dominium nacta: vbi etiam tribuit colorem album, decoram faciem mixtam cum aliqua rubedine, venustos oculos, vocem gratam, & sonoram, suaritatem morum licet aliquantulum molles, atque effæminatos: quod indicat

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LEXICON especially the tail, which, because of its prominence, breadth, and nearly circular shape, would make the greatest room for shaking. Therefore this fish, which is naturally contrary to everyone, and turns toward that part from which it blows, not from the spirit of sympathy, but from the innate inclination of each creature to defend itself against an enemy, does so. And these things indeed, on the occasion of the Winds, have been said concerning this marvellous affection of the fish. 20. VENUS, the brightest and most beautiful of all the stars, both wandering and fixed, which with her emitted light wonderfully attracts and delights the eyes of beholders; and this not because she is greater than all the others, but because she is nearer to the earth (except for Mercury alone), as is clear from the parallax she undergoes of nearly three minutes; whence it is also inferred that she is smaller than the earth, because, as Clavius notes in the sphere of Ioannes de Sacro Bosco, her diameter contains thirty-seven times seven. She always accompanies the Sun with Mercury, revolving continually around him in her epicycle, as around her own center; so that both in the first and in the second station, in which she is most distant from him, she does not depart more than 48 degrees, and there begins to become direct or retrograde, and shines most brightly. By means of the telescope it has been observed that she undergoes nearly the same phases as the Moon, and accordingly appears now full, now half-full, now crescent-shaped, now none at all; namely when she is above or below the Sun, in the apogee or perigee of her epicycle, joined to it in the same degree of the ecliptic. She completes her course in the Zodiac together with the Sun in the space of nearly one year; she is distant from the earth, according to the observations of more recent writers, about 600165 miles. Moreover, Venus is a feminine planet, because she abounds more in humidity than in heat, though moderately, so that she is suited to living nature; and for this reason she is called the lesser fortune. 21. She has charge among the human members of the seminal vessels and the genitals, and governs taste, smell, and touch; whence there is the aphorism in Ptolemy’s Centiloquium, no. 17: “Venus brings pleasure in the member ruled by the sign in which she is.” This is especially true when she is well placed in her own domiciles, which are Taurus and Libra, or in Pisces, where she is exalted. Hence it is that, if well situated in these signs, she makes one amiable, devoted to music and dancing, especially if she has obtained rulership in the Ascendant or in the nativity; where she also bestows a white complexion, a handsome face mixed with some redness, lovely eyes, a pleasant and sonorous voice, and sweetness of manners, though somewhat soft and effeminate: which indicates

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etiam eius color ac fulgor, mollis & emissitius electro similis. < 22.> Sed & obseruatione dignum est quod ex Platone notat Ficinus in Timæcab. 19. Veneris nempè & Mercurij potentiam contrariam esse Soli; quia, inquit, opposito ad illum motu quandoque mouentur progredientes: Sol occulta prodit, illi econtrà: prætereà Solis potentia cum rebus incomparabilis est, ipsi comparabiles moderantur, comparabilemque efficiunt: Venus conciliationis, & amicitia, Mercurius proportionis, & & commixtionis est author. Hæc Ficinus. < 23.> De Veneris Astro testatur Varro apud D. August. Deciuitate Dei lib. 21. cap. 8 aliquoties mutasse colorem, magnitudinem, figuram, & cursum, quod pro portento habitum fuisse ait: Verum inde iure colligit Augustinus non esse contrà naturam, cum in aliqua re, cuius natura innotuit aliquid ab eo, quod erat notum incipit esse diuersum. Et sanè cum Veneris motus, vti & Martis sit maximè irregularis, adeo vix Tychonis temporibus sit compertus, & quandoque extrà Eclypticam diuagetur ad gr. 9. item Mars in Perigeo sub sole fiat, in eodem ferè situ, vbi semper apparet Venus, maximè terris vicinus, proindeque magnitudine Venerem ipsam exæquet, nil miium si tunc temporis genti sideralis scientiæ minus peritæ, nouis suis irregularitaribus, ac Phoenomenis imposuerit, creditumque fuerit Veneris astrum colorem igneum induisse, locum, motum, ac figuram murasse. Quandoquidem hoc ipsi Tychoni, hoc est homini ad speculanda sidera facto, tantum negotium primò obseruanti facessit, vt diù multumque hæsitauerit, num Martis, aut Veneris Astrum, an potius nouum Phoenomenon coelo pridem natum extiterit. < 24.> VER Anni initium, & apud Astronomos, & apud Orientales dicitur Quarta omnium temperatissima, in qua cuncta florent, omnia exhilarantur, & Mundus ipse exordium sumpsisse creditur: vnde Poëta. Non alios prima nascentis origine Mundi Illuxisse dies, a iumve habuisse tenorem Crediderim: Ver illud erat. Dicitur Ver, vt ait Varro à Virore, quod tum Virgulta omnia virere incipiant: vel vt alij volunt à Vertendo, quod tum vertere se incipiat anni tempus. Diuiditur autem, quemadmodum reliqui Anni quadrantes in tres portiones pro qualitate signorum, quæ tunc temporis perambulat Sol: atque adeo in Ver nouum, hoc est Veris initium, quod computatur toto eo mense quo Sol est in Ariete, qui proinde dicitur

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even its color and brightness, soft and resembling electric amber. < 22.> But it is also worthy of note what Ficino observes from Plato in Timæus, chapter 19: namely, that the power of Venus and Mercury is contrary to that of the Sun; because, he says, in an opposite motion they sometimes move while progressing: the Sun reveals hidden things, but those two do the contrary. Moreover, the power of the Sun is incomparable with things; those that are comparable to it it moderates and makes comparable. Venus is the author of reconciliation and friendship; Mercury of proportion and of mixture. Thus Ficino. < 23.> Varro, cited by St. Augustine in De Civitate Dei , book 21, chapter 8, testifies concerning the star of Venus that it had on several occasions changed color, size, shape, and course, which, he says, was regarded as a portent. But Augustine rightly infers from this that it is not contrary to nature, since in some thing whose nature has become known, something begins to be different from what was known. And indeed, since the motion of Venus, as also that of Mars, is exceedingly irregular, so much so that it was scarcely known in Tycho’s time, and at times it wanders outside the ecliptic by 9 degrees, and likewise Mars, when in perihelion under the sun, is in nearly the same position in which Venus is always seen, being nearest to the earth, and therefore equaling Venus itself in size, it is no wonder if at that time it imposed upon a people little skilled in the science of the stars, with its new irregularities and phenomena, and if the star of Venus was believed to have assumed a fiery color and to have changed its place, motion, and shape. Indeed, this gave Tycho himself, that is, a man made for observing the stars, so much trouble at first in noticing it that for a long time he doubted whether it was the star of Mars or of Venus, or rather some new phenomenon long since born in the sky. < 24.> VER is called the beginning of the year both among astronomers and among the Orientals, the fourth and most temperate of all seasons, in which everything blossoms, everything is made cheerful, and the world itself is believed to have taken its beginning: whence the poet: I would not believe that other days shone at the very birth of the rising world, Nor that it had a different course; that was Spring. It is called Spring, as Varro says, from greenness, because then all the young shoots begin to be green; or, as others will have it, from turning, because then the season of the year begins to turn. It is divided, however, like the other quarters of the year, into three parts according to the quality of the signs which the Sun then traverses: and thus into new spring, that is, the beginning of spring, which is reckoned through that whole month in which the Sun is in Aries, which therefore is called

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516 LEXICON signum Mobile eoquia ex vna quarta, & qualitatum commixtione transitur ad aliam: Ver adultum vocant dum Sol est in Tauro signo fixo, in quo potissimum apparent Veris effectus, tunc enim adoleuit calor & omnia turgent ad fructificationem: & Ver cadens, quòd computatur pro eo tempore, quo Sol est in Geminorum Signo, quod proptere à dicitur Signum commune, eo quia eo tempore Veris temperies præceps ruit, & in Æstatis vredinem commutatur. Correspondet hæc quarta primæ hominis ætati, quæ complexione calida est, & humida, Veris tempus etsi alioqui iucundissimum solet nihilominus sæpissimè pluuiis infestari: vnde imbriferum Ver appellat Virgilius: & Seneca lib. 4. Quæst. natural. cap. 3. Cum Ver coepit, inquit, maior indignatio aëris sequitur, & calidiore cælo maiora fiunt stillicidia: An quia tunc tepefacto aëre maior vaporum exhalationumque copia è terra exilit, quæ materiam multam pluuiis exhibent? Sanè non aliam crediderim causam: ob id nimbi graues magis, quam pertinaces defluunt, cum alias hyems lentas habeat, ac tenuissimas pluuias. 25. VERA, seu potiùs Veru cometæ species criniti, oblongi nimis, ac tenuis, / ad instar ferrei veru, quo carnes asalamus) horribilis quidem visu, coloris plumbei, sed micantis, proindeque naturæ mixtæ ex Mercurio, & Saturno. Solem perpetuò comitatur illum aut præcedens vel sequens, & quando apparet indicat fructuum, & satorum corruptionem, ac mortem principibus viris obnunciat. De eo Plin. lib. 1. cap. 25. 26. VERASVA vocabulum græco barbarum in sphæra barbarica, significans secundum Decanum Geminorum, manentem sub Dominio Martis: vnde excipiuntur significata angustiarum, laboris, inquisitionis rerum, agiliatis, &c. 27. VERGILIA: Pleiades stellæ septem paruæ in vnum compli- catæ de natura Martis, & Lunæ in genu Tauri consistentes; sic dictæ eo quod Veris tempore ex horizonte emergant. Earum naturam fusè tradidimus in Verbo Pleiades. 28. VERTEX dicitur punctum in cælo quod directè imminet vertici capitis cuiuscumque hominis: ac proinde est perpendicularis loco in quo quisque degit: hinc verticalis dicitur stella, quæ in idem punctum cadit, & loco verticaliter im- minet. Similiter verticalis dicitur æquator iis qui conrinuum habent æquinoctium, quia semper, & constantissime per loci verticem transit, & Sol in meridie ita rebus quibusque imminer, vt nullam iis parere sinat vmbram. Hoc punctum Arabes appellare solent Zenith, quemadmodum illi diam-

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516 LEXICON the sign of the Mobile is passed from one quarter and by the mixture of qualities to another: they call it Spring adult when the Sun is in Taurus, a fixed sign, in which the effects of Spring chiefly appear; for then heat has grown and all things swell toward fructification: and Spring falling, because it is reckoned for that time when the Sun is in the sign of Gemini, which for that reason is called a common sign, because at that time the temper of Spring rapidly declines and is changed into the heat of Summer. This fourth corresponds to the first age of man, which is of a hot and humid complexion; the season of Spring, although otherwise most pleasant, is nevertheless very often troubled by rains: whence Virgil calls it rainy Spring: and Seneca, book 4 of Natural Questions, chapter 3: “When Spring has begun,” he says, “a greater disturbance of the air follows, and with a warmer sky the drippings become greater: or is it because then, when the air has been warmed, a greater abundance of vapors and exhalations rises out of the earth, which provides much material for rains?” Certainly I would believe no other cause; for that reason heavy showers flow down more rather than persistent ones, whereas winter has slow and exceedingly thin rains. 25. VERA, or rather VERU, a species of comet, hairy, very oblong and slender, like an iron spit, with which we roast meat), horrible indeed to behold, of leaden color but sparkling, and therefore of a mixed nature, from Mercury and Saturn. It perpetually accompanies the Sun, either preceding or following it, and when it appears it indicates corruption and death of fruits and crops, and it portends death to leading men. Concerning it Pliny, book 1, chapter 25. 26. VERASVA, a Greek-barbarous term in the barbaric sphere, meaning the second decan of Gemini, remaining under the dominion of Mars: hence are excluded the significations of anguish, labor, the seeking of things, agility, etc. 27. VERGILIA: the Pleiades, seven small stars folded together into one, of the nature of Mars and the Moon, situated in the knee of Taurus; so called because in the season of Spring they emerge from the horizon. Their nature we have treated at length under the word Pleiades. 28. VERTEX is called the point in the sky that directly overhangs the vertex of any man’s head: and therefore it is the perpendicular of the place where each person dwells; hence a star is called vertical, when it falls into that same point and vertically overhangs the place. Similarly the equator is called vertical for those who have a continual equinox, because it always and most constantly passes through the vertex of the place, and the Sun at noon thus overhangs all things, so that it does not allow any shadow to fall upon them. This point the Arabs are accustomed to call Zenith, just as they diam-

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MATHEMATICVM. 527 tialiter oppositum subtrus terram, Nadir. VESPERTA olim dicebatur Antiqvis Dea horæ præsidens, < 19.> seu potius Planeta singulis horis inæqualibus ab ortu Solis dominans, vnde horæ planetariæ, de quibus suoloco di- ctum. VESPERTILIO apud Saphoclem dicitur Cor Scorpii, Stella < 30.> fixa secundæ, seu vt alij volunt, primæ magnitudinis de natu- ra Martis, sicut etiam apud alios Veneris Astrum: nescimus qua ratione. VESPERTINVS dicitur Planeta Vespere post Solis occasum < 31.> suprà horizontem conspicuus, & ipse ad occasum vergens; sicut viceuersa Matutinus cum Manè ante Solis exortum ex horizonte emergit. Superiores Saturnus, Iupiter, & Mars Vespertini imbecilliores sunt: econtrà Venus, & Mercurius robustiores, cuius rei rationem naturæ consonam vide in V. Matutinus. VESPERVGO ab aliquibus appellatur Venus occidentalis < 32.> Vespere conspicua post Solis occasum, quæ alio nomine dicitur Hesperus: vnde est Illud Plauti in Amph. Neque Inyula, inquit, neq; Vesperugo neq; Vergilia occidunt. VIA COMBVSTA. Vide in V. Combusta Via. < 33.> VIA LACTEA. Vide. Galaxia. < 34.> VIGILES antonomasticè appellantur ab Astronomis duæ < 35.> stellæ in extremo plaustri minoris, vel Cynosuræ, quas alibi adnotauimus dici etiam Choreutas, & Circitores, eo quia veluti custodes Poli constitutæ sunt, & ipsum circa semper ambiunt, Vigiles nunquam videlicet occi- dentes. VINDEMIATOR, Vindemiatrix audit apud Astronomos < 36.> Ala septentrionalis Virginis, Stella inquam fixa tertiæ ma- gnitudinis, potentissima, de natura Saturni & Mercurij: no- men hausit à Vindemia. quia, vt inquit Plinius lib 3. c. 31. Romæ oriebatur vindemix tempore, hoc est XI. Calend. Septembris: Nunc autem post correctionem Gregorianam < 37.> oritur die 22. eiusdem Mensis cum gr. 29. Virginis: occidit autem die 28. Octobr. cum gr. 9. Scorpii: quo tempore, in- quit Ptolemæus Aquilonem solet mouere. VIOLENTA SIGNA apud Astrologos appellantur in quibus < 37.> Planetæ Malesici humanæque naturæ infensi, Mars videli- cet & Saturnus aliquam insignem prærogatiuam obtinent aut domicilij aut exaltationis, qualia sunt Aries, Libra, Scorpio, Capricornus, & Aquarius, item ea in quibus inci- dunt stellæ fixæ violentæ, præsentim insigniores, suntque in ipsa Zodiaci latitudine, cuiusmodi est Taurus ob pallilitium,

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MATHEMATICVM. 527 tially opposite below the earth, the Nadir. VESPERTA was once called by the Ancients the Goddess presiding over the hour, <19.> or rather the Planet ruling over each unequal hour from sunrise, whence the planetary hours, of which it was said in its place. VESPERTILIO, in Sophocles, is called the Heart of Scorpio, a fixed star <30.> of the second, or, as others think, first magnitude, of the nature of Mars; as also, among others, the star of Venus: we do not know for what reason. VESPERTINVS is called the planet conspicuous in the evening after sunset <31.> above the horizon, and itself inclining toward setting; just as, conversely, Matutinus at morning rises from the horizon before sunrise. The superior planets Saturn, Jupiter, and Mars are weaker in their evening appearance; on the contrary Venus and Mercury are stronger, for the reason of which, consonant with nature, see under V. Matutinus. VESPERVGO is by some called the western Venus <32.> visible in the evening after sunset, which by another name is called Hesperus: whence that line of Plautus in Amph. "Neither the Nile, he says, nor Vesperugo nor the Pleiades set." VIA COMBVSTA. See under V. Combusta Via. <33.> VIA LACTEA. See Galaxia. <34.> VIGILES are antonomastically called by astronomers the two <35.> stars at the end of the Little Wagon, or Cynosura, which we have elsewhere noted are also called Choreutas and Circitores, because they are set, as it were, as guardians of the Pole, and always circle around it, the Watchers, that is, never setting. VINDEMIATOR, or Vindemiatrix, is so called by astronomers <36.> the northern Wing of Virgo, that is, a fixed star of the third magnitude, very powerful, of the nature of Saturn and Mercury; it took its name from the vintage, because, as Pliny says, lib. 3, c. 31, it rose at Rome at vintage time, that is, the 11th day before the Kalends of September: now, however, after the Gregorian correction <37.> it rises on the 22nd day of the same month with 29 degrees of Virgo; but it sets on the 28th of October with 9 degrees of Scorpio: at which time, says Ptolemy, it is wont to stir up the north wind. VIOLENT SIGNS are called by astrologers those in which <37.> malefic planets, hostile to human nature, namely Mars and Saturn, obtain some remarkable prerogative, either of domicile or exaltation, such as Aries, Libra, Scorpio, Capricorn, and Aquarius; likewise those in which violent fixed stars fall, especially the more notable ones, and which are in the very latitude of the Zodiac, such as Taurus because of the Pleiades,

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328 LEXICON stellæ aurem violentæ, vel ob naturam maleficam Saturniam, aut Martiam, vel ex mixtione qualitatum oppositarum, quæque experientia tales compertæ sunt, perhibentur esse Pallilitium, Antares, Regulus, Hereules, seu Caput Pollucis, at omnibus eaput medusæ, stella maximè funerea, & ominosa, de quibus suo loco dictum. 38. VIRGÆ, græcis Rabda , seu Rabdi, sunt apparentiæ in aëre ex collisione radiorum Solis congenitæ, eiusdem rationis, ac Iris, & Area : nisi quod hæc circulares sunt, illæ verò lineæ rectæ ad virgarum speciem è coelo in tetram protensæ: Sunt enim reflexio luminis Solis in nube rorida, sed inæquabili, quæ proinde, vt speculum inæquabile se habet non potens reddere figuram rei, quæ obiicitur. Sunt tamen & ipsæ versicolores, & si vnam formam excipias, in nihilo ab Iride discrepantes: ideoque non apparent, nisi Soie circa occasum, vel ortum existente; rarò autem vel nunquam in Meridie. In hoc quoque differunt ab Iride quod hæc semper ex aduerso Solis appareat, Virgæ autem semper ad latus, aut ex parte boreæ, aut ex parte Austri, cuius rei rationem affert Suessanus in 3. Meteoro. Plures Virgarum species enumerantur, inter quas Irina ab Aristotele dicta quæ semper est aquæ signum, maximè si ab Austro videatur. Plura de his apud Restam de Meteoris... 39. VIRGO sextum Zodiaci signum septentrionale proximum æquinoctio autumnali; adeoque commune: natura sua terreum, frigidum nempè, & siccum; domicilium, & exaltatio Mercurij. Dominatur ex membris humanis Ventri, Diaphragmati, Inrestinis, & Illis. arab. Sombalet, seu Elaadari eius Asterismus in octava sphæra longissimus est: incipit enim nunc temporis à gr. 16. Virginis Primi mobilis, & protenditur vsque in gr. 6. Scorpij. Stellas habet iuxta Polemæum 16. in formam redactas, & sex imformes: At Keplerus in eo enumerat omninò 39. Bayerus 42. diuersæ magnitudinis, & naturæ, inter quas præcipuè spicam in Manu primæ magnitudinis de natura Veneris, & Mercurij arab. Azimech. Item aliam dictam Vindemiatorem tertiæ magnitudinis, nec non alias de quibus suo loco singulatim dictum. Porrò hoc fidus in horoscopo facit hominem amabilem, iucundum, decora facie suauemque moribus, quicque naturaliter in opera pietatis inclinet. Sat sic pro eius integra laude, quod 'eo exoriente, 'Dei Filius in hunc mundum venerit, & Virginis Astrum mysterij causa potiùs quam alia de re suo horoscopo nobilitatum voluerit: quemadmodum testatur Petrus Aliacensis q. 30. in Genesim, & ante

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328 LEXICON stars of a violent nature, either because of their Saturnian or Martian evil influence, or from a mixture of opposing qualities, and which by experience have been found to be such, are said to be Pallilitium, Antares, Regulus, Hercules, or the Head of Pollux; and above all, the Head of Medusa, the most funeral and ominous star, of which something has been said in its proper place. 38. VIRGÆ, in Greek Rabda , or Rabdi, are appearances in the air produced by the collision of solar rays, of the same kind as the Rainbow and the Area: except that these are circular, while those are straight lines stretched from the sky to the earth in the form of rods. For they are a reflection of the sun’s light in a dewy cloud, but an uneven one, which therefore, like an uneven mirror, is unable to reproduce the figure of the object presented to it. Yet they too are variegated in color, and, if you except one form, differ in nothing from the Rainbow; and therefore they do not appear unless the Sun is near setting or rising; rarely, however, or never at midday. In this they also differ from the Rainbow, that the latter always appears opposite the Sun, whereas the Virgae always to the side, either on the north side or on the south side, the reason for which Suessanus gives in Meteor. 3. Several species of Virgae are enumerated, among which is the one Aristotle called Irina, which is always a sign of water, especially if it is seen from the south. More about these in Resta, On Meteors... 39. VIRGO, the sixth sign of the Zodiac, northern, near the autumnal equinox, and therefore common; by its own nature earthy, that is, cold and dry; the domicile and exaltation of Mercury. It rules over the human members of the belly, diaphragm, intestines, and thighs. In Arabic, Sombalet, or Elaadari. Its constellation in the eighth sphere is the longest: for at present it begins at 16 degrees of Virgo on the Primum Mobile, and extends as far as 6 degrees of Scorpio. According to Ptolemy it has 16 stars reduced into shape, and six unformed ones; but Kepler enumerates altogether 39 in it, Bayer 42 of various magnitude and nature, among which especially is the spike in the hand of first magnitude, of the nature of Venus and Mercury, Arabic Azimech; also another called Vindemiator of third magnitude, and likewise others, of which something has been said separately in its proper place. Moreover, this star in a horoscope makes a man lovable, pleasant, with a handsome face and agreeable in manners, and naturally inclined to works of piety. So much, then, for its full praise, that at its rising the Son of God came into this world, and wished the Star of the Virgin to be honored in his horoscope rather for the sake of mystery than for any other matter; as Peter of Ailly attests in Question 30 on Genesis, and before

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MATHEMATICVM. 529 ipsum Albertus cognomento Magnus apud Sixtum Senen- tem in Bibliotheca Sancta tom. 2. lib. 6. annotat. 10. Cæterum primæ huius Asterismi partes calidæ sunt, ac noxię: medię temperatæ: postremæ humidiores. VEROASO LUNÆ in Sphæra barbarica dicitur secundus De- <40.> canus Tauti cuius Dominium, ac dispositio spectat ad Lu- nam, & habet significare potentiam, nobilitatem, Imperium in gentes, &c. Hæc, & his similia, Araóum nugæ sunt, qui eò dementiæ deuenerunt, vt singulis decanis signorum Sin- gulos Genios assignarent, singulos suo nomine insignitos, quos qui animi causa leuandi ab grauioribus cuiis, ac studiis videre voluerit Consular Oedipum Ægyptiacum Athanasij Kircheri, qui ex fide dignissimis exemplaribus, hæc monu- menta excerpsit, & in curiosorum gratiam edidit. VMELI VS ANDROMEDÆ arab. Mirach dicitur ab Astrono- <41.> mis stella fixa valdè insignis, tecundæ magnitudinis, de na- tura Veneris, in cingulo Andromedæ constituta, de qua fusè dictum in V. Mirach. VOCIFERATOR sidus in Vociferantis formam expredit m <42.> alio nomine Bubulcus, Bootes, Plaustri ductor, &c. VOLVELLVM à voluendo dictum est Rete in Astrolabio <43.> motum primi mobilis, ac singulos Solis parallelos, quos in singulos dies describit, necnon fixas insigniores eosque diurnos circulos repræsentans: de quo vide in V. Rete. VORTEX vide Typhon: in idem quippe recidit: & Plinio <44.> auctore, non plus differt à turbinę, quam stridor à fragore: est enim, vt nominis etymon præsefert, ventus vorticinosus omnia in gyrum rapiens, & attolens: dicitur etiam Pinea, verestis est Apuleius in lib. de Mundo; qui eum sic describit. Cum scilicet torquetur humus arida, & ab infimo erigitur ad supremum. VRANISCOS, hoc est calum paruum, teste Kirchero in <45.> Oedipo dicitur græcè apud quosdam Rota Ixionis, seu Co- rona Australis sidus ad austrum, de quo al:bi dictum. VRNA Sidus vide Vas, Crater. VRSA Sidus in coelo duplex ad borealem plagam circa po- <46.> lum arcticum: quorum alterum dicitur Vrsa minor, & Cy- <47.> nosura, quæ polo proximius adhæret, & eum denominat arcticum, constans stellis tantummodò septem; (licet Ke- plerus in eo enumeret omninò 10.) quarum postrema in cauda est polaris, & Nautarum Directrix: Alterum dictum Vrsa maior, Helice, à priore non longè distans, sed contra- rio positu, habens stellas omninò 56. iuxta eiusdem Keple- ri obseruationes, sed septem similiter clariores, omnibusque

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MATHEMATICUM. 529 the same Albertus, surnamed Magnus, notes, according to Sixtus Senensis in the Bibliotheca Sancta, tom. 2, lib. 6, annot. 10. Besides, the first parts of this Asterism are hot and harmful: the middle are temperate: the latter more humid. VEROASO LUNÆ in the barbarian sphere is said to be the second De- <40.> canus of Taut; whose dominion and disposition belong to the Moon, and it is said to signify power, nobility, empire among nations, etc. These and similar things are the trifles of the Arabs, who have fallen into such madness that they assigned to each decan of the signs single Genii, each distinguished by its own name, whom whoever wishes to be relieved in mind from more serious cares and studies may see in the Consular Oedipus Ægyptiacus of Athanasius Kircher, who, from most trustworthy exemplars, gathered these monuments and published them for the benefit of the curious. VMELIUS ANDROMEDÆ, called in Arabic Mirach by the astronomers, is <41.> a very notable fixed star, of the second magnitude, of the nature of Venus, situated in the girdle of Andromeda, concerning which it has been abundantly said under V. Mirach. VOCIFERATOR is a star represented in the form of a Vociferant <42.> otherwise called Bubulcus, Bootes, the driver of the Wain, etc. VOLVELLVM, so called from rolling, is the rete in the astrolabe <43.> representing the motion of the first mobile, and the several parallels of the Sun, which it traces on each day, as well as the more notable fixed stars and those daily circles: of which see under V. Rete. VORTEX, see Typhon: for it comes to the same thing; and according to Pliny <44.> it differs no more from a whirlwind than a hiss from a crash: for it is, as the etymology of the word suggests, a whirling wind that sweeps everything into a circle and lifts it up; it is also called Pinea, and Apuleius uses the term in his book De Mundo; where he describes it thus. Namely, when the dry ground is twisted, and from the lowest part is raised to the highest. VRANISCOS, that is, a little heaven, according to Kircher in the <45.> Oedipus, is called in Greek by some the Wheel of Ixion, or the Southern Crown, a constellation toward the south, concerning which elsewhere it has been said. VRNA, the constellation, see Vas, Crater. VRSA, a constellation in the heavens, double on the northern side around the <46.> arctic pole: of which one is called the Little Bear, and Cy- <47.> nosura, which clings nearest to the pole and gives it the name arctic, consisting of only seven stars; (although Kepler counts ten in it altogether.) of which the last in the tail is the polar star, and the sailors' guide: The other is called the Great Bear, Helice, not far distant from the former, but in a contrary position, having altogether 56 stars, according to the observations of the same Kepler, but likewise seven brighter ones, and all the rest

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330 LEXICON conspicuas in plaustris formam, atque in eadem disposicione ad invicem, quam habent aliæ septem efformantes Vrsam minorem. Ex his quæ in humero vocatur proprio nomine apud Arabes Dubhe: prima caudæ Hlhaoth id est viuificans media Mizar; vltima Alalicth seu Benenatz. Quas ramen Arabes Christiani alio nomine appellant Sorores Lazari, & Plaustrum ipsum Feretrum, suo genili vocabulo Naasch Lazar, provt in loco monuimus. Propè medium caudæ adest stella minima vix quidem visibilis, sed quæ vulgato apud arabes adagio facta est iam celebris nomine Alcor: de quæ scribit Appianus circumferri dictum de homine perscrutare minima, sed seria, & potissima negligente. Vidisti Alcor, sed non Lunam plenam. Alia vii & siderum significata vide in propriis nominibus Helice, Plaustrum, Cynosura, Aictos, &c. 48. VVEGA arabicè dicitur Fidicula, Lyra, Sidus seu stella fixa primæ magnitudinis de natura Veneris, & Mercurij, de qua sepiùs dictum: dicitur etiam Testudo à forma Testudinis quam præsefert; nec non etiam. 49. VVLTVR CADENS, eo quia totum fidus repræsentat vulturem supinum, expensis aliis quasi cadentem, qui supra pectus Lyram, seu Testudinem instrumentum musicum habeat. Sicure contrà. 50. VVLTVR VOLANS dicitur Aquila aliud fidus non adeò longe à prædicto distans, medium inter delphinum, & Cygnum, repræsentans Aquilam volantem sagitta per tranluersum petitam, quæ cominet stellas 9. vel iuxta Keplerum 11. quærum præcipua valdè fulgida secundæ magnitudinis arabice dicitur Alkor. Ioui in colore, & fulgore omninò similis. 51. VVLTVRNVS græcè Eurus dictus est Ventus orientalis spirans ab ortu hyemali, lateralis Subsolano ac directè oppositus Cauro. Vulturni nomen sortitus est coquia, inquir Plin. lib. 2. cap. 47. alsi spirat & quodammodo Vulturis volatum imitari videtur. Natura eius calida est & sicca similis Subsolano; ob deflexionem tamen ad Austrum acquirit nonnihil humidæ, ac tabeficæ qualitatis, & in finem turbat ærem, excitaque subitas mutationes, fulgetra inducens, ac tonirrua. Porrò Euri in anno dominantes (inquit Argolus de diebus criticis lib. 2. cap. 6.) excitant passim vagantes febres ardentes, biliosas, acucas; & in his Exanthemata: pustulas, carbunculos, tumores, efferuescentias, morbillos, variolas, & similia, qua æstate contingunt. De hoc item Vento testatur Aristoteles in Problem. num. 55. quod reddar obiecta visibilia maiora, quam reuera sint. Causa peti potest ex iis, quæ

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330 LEXICON conspicuous in the shape of a wagon, and in the same arrangement toward one another as the other seven stars have in forming the Lesser Bear. Of these, the one on the shoulder is called by the Arabs by its proper name, Dubhe; the first of the tail, Hlhaoth, that is, “life-giving”; the middle, Mizar; the last, Alalicth or Benenatz. Yet the Christian Arabs call them by another name, the Sisters of Lazarus, and the Wagon itself Feretrum, in its native language Naasch Lazar, as we noted in the place concerned. Near the middle of the tail there is a very small star, scarcely visible indeed, but which by a common Arabic proverb has now become famous under the name Alcor; concerning which Appian writes that there is a saying about a man who investigates the smallest things and neglects the serious and most important ones: “You have seen Alcor, but not the full Moon.” See the other meanings of the seven stars in the proper names Helice, Plaustrum, Cynosura, Aictos, etc. 48. VEGA is called in Arabic Fidicula, Lyra, a fixed star of the first magnitude, of the nature of Venus and Mercury, of which it has often been said; it is also called Testudo from the shape of the tortoise it presents; and likewise also. 49. FALLING VULTURE, because the whole constellation represents an upside-down vulture, with the other stars as it were spread out like a falling one, which above the breast has the Lyre, or Testudo, a musical instrument. And conversely. 50. FLYING VULTURE is called Aquila, another constellation not very far from the aforesaid, lying between the Dolphin and the Swan, representing an eagle flying and struck sideways by an arrow, which contains 9 stars, or according to Kepler 11, of which the principal, very bright one of the second magnitude, is called in Arabic Alkor. In color and brilliance it is altogether like Jupiter. 51. VULTURNUS, in Greek called Eurus, is the east wind blowing from the winter sunrise, lateral to the Subsolanus and directly opposite the Caurus. It received the name Vulturnus, as Pliny says, because it blows hot and in some way seems to imitate the flight of a vulture. Its nature is hot and dry, like the Subsolanus; however, by its deflection toward the south it acquires something of a moist and corrupting quality, and in the end it disturbs the air, and brings about sudden changes, causing lightning and thunder. Moreover, the Eurus prevailing in a year, says Argolus in On Critical Days, book 2, ch. 6, commonly excite wandering burning, bilious, acute fevers; and in these eruptions, pustules, carbuncles, swellings, inflammations, measles, smallpox, and the like, which occur in summer. Aristotle also testifies of this wind in Problems, no. 55, that it makes visible objects appear larger than they really are. The cause may be sought from those things which

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MATHEMATICVM. alibi dicit, ipsum nempè esse turbidum, & caligine ple- num: Dum igitur caligo intercipitur inter obiectum visibi- le, & oculum, consequenter species illius per refractionem alterantur, & obiectum amplius repræsentant, quam reue- ra sit. X XIPIHIAS cometæ species colore pallidi in mucronem (à 1. quo illi nomen est inditum) fastigiati, qualem fuisse scribunt qui apparuit anno 1532. De eo mentionem facit Plin lib. 2. cap. 25. Cum apparet portendere solet Infensissi- mos ventos, qui & Domos subuertant, & arbores eradi- cent, ariditatem, maximam frumenti penuriam: ex his fa- mem, & quæ ex famè ac terræ sterilitate oriri possunt, inala. XIPIHIAS item dicitur fidus ad polum Antarcticum, Indo- 2. rum vocabulo dorado, retroacto sæculo ab America Vespuc- cio vna cum aliis vndecim detectum: constat stellis septem in longitudine sub signo Capricorni: quarum tamen dix, spectant potius ad nubeculam illi proximam: quæ verò in ventre est, maximè accedit ad polum Eclipticæ, & nunc temporis vix vno gradu ab eo distat. Y YPAPHRICVS græcolat. ex Yno & Africo vento, cui est 1. collateralis est enim vns est minus principalibus, qui nouissimè ad ventorum seriem adiecti sunt, & vocantur po- tius quartæ ventorum, quam Venti: medius est inter Ze- phirum, & Africum, cui ad dexteram adiacet alius ventus collateralis dictus Masafricus, quarta itidem ipsius Africi ad meridiem tendens, & proxima Vento-Lybico. Sic etiam quotquot sunt venti cardinibus laterales totidem & habent binos ventos minores collaterales sibi hinc inde adiacentes ad dexteram, & sinistram. Vnde Aquiloni adiacet Ypaqui- lo ad Septentrionem, Masaquilo ad Borrhapeliotem, seu Græcum: Coeciæ, Ypocæcias ad Borrhapeliotem, Meso- Coecias ad Orientem. Euro Ypoeurus ad Subsolanum, Me- soeurus ad Notapeliotem, seu Syrocium. Phoenici, Ypo- phoenix ad Notapeliotem, Mesophoenix ad Austrum. Ly- banoto Ypolybanotos ad Notolibycum, Mesolybanotos ad Austrum. Coro, seu Argestæ, Mesocorus ad Fauonium, Ypocorus ad Borrolybicum, tandem Circio Ypocircius ad Borrolibicum, Mesocircius ad Septentrionem. Quorum

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MATHEMATICVM. elsewhere he says it is in truth turbid and full of haze: therefore, when the haze intervenes between the visible object and the eye, consequently its species are altered by refraction, and represent the object more than it really is. X XIPHIAS, a comet’s species of pale color, sharpened into a point (from which it takes its name), such as is said to have appeared in the year 1532. Mention of it is made by Pliny, lib. 2, cap. 25. When it appears it is wont to portend most violent winds, which both overthrow houses and uproot trees, drought, and the greatest shortage of grain: from these, famine, and the evils that can arise from famine and sterility of the earth. XIPHIAS is also said of a fixed star near the Antarctic pole, called by the Indians dorado, discovered in the previous century by Amerigo Vespucci together with eleven others. It consists of seven stars in length under the sign of Capricorn; of these, however, six look rather to the small cloud near it, while the one that is in the belly approaches most nearly the pole of the Ecliptic, and now hardly differs from it by one degree. Y YPAPHRICUS, from the Greek, from the wind Yno and Africus, to which it is collateral; for it is one of the lesser principal winds, which were lately added to the series of winds, and are rather called the quarters of the winds than winds. It lies midway between Zephyrus and Africus, to the right of which there adjoins another collateral wind called Masafricus, likewise the fourth from Africus itself, tending toward the south, and near the Libyan Wind. Thus also, however many are the winds lateral to the cardinal points, so many likewise have two lesser collateral winds adjoining them on this side and that, to the right and left. Hence to Aquilo there adjoin Ypaquilo toward the north, and Masaquilo toward Borrhapeliotes, or the Greek Wind; to Caecias, Ypocaecias toward Borrhapeliotes, and Mesocaecias toward the East. To Euro, Ypoeurus toward Subsolanus, and Mesoeurus toward Notapeliotes, or Syrocius. To Phoenices, Ypophoenix toward Notapeliotes, and Mesophoenix toward the South. To Libanotus, Ypolibanotos toward Notolibycus, and Mesolibanotos toward the South. To Corus, or Argestes, Mesocorus toward Favonius, and Ypocorus toward Borrolybicus; finally to Circius, Ypocircius toward Borrolibicus, and Mesocircius toward the North. Of which

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LEXICON omnium schema atque natura passim exhibetur in tabulis Geographicis, atque etiam ab iis omnibus, qui de ventis Ioquuntur, præsertim Argolo in Astronom. lib 2. cap.6. Cer- te vnsuisque naturam mixtam ex iis, quibus adiacet, prin- cipalibus assumit: Vnde Ypaticus, & Mesocorus sunt de natura Fauonij, licet participent non nihil de Coro, aut de Africa: Ypaquilo, & Mesocircius induunt naturam Septena- trionis: Ypeurus, & Meso Cæcias naturam Subsolani, & sic de reliquis. Z 1. ZAMOCTAR apud Persas idem Sonat ac Arabibus Arg- butar, hoc est nostra lingua Diuisor, & Dominus ter- minorum: cuius inuestigandi methodum vide in V. Di- uisor. 2. ZEDARON hoc est Thorax arab. teste Villetmo Schickar- do, dicitur pectus Cassiopæ, stella fixa, secundæ magnitu- dinis, de natura Veneris, & Saturni alio & visitato nomine Schedir. De qua vide sub hoc Verbo. 3. ZENITH arab. dicitur punctus coeli verticalis, qui directè, perpendiculariter imminet capitibus nostris, nostro com- muni vocabulo Vertex qui necessariò distare debet æqualiter ab horizonte 90. grad. & est velutipolus ipsius horizontis: cui ex aduerso respondet alius locus sub terra, dictus Nader, totidem gradibus ab horizonte distans, semper delitescens, quippe qui concipitur esse immobilis sub pedibus nostris. Porrò stella in Zenit posita, vtpote in loco vnde radios re- tos ad terram demittit plurimum potens euadit, & miræ ef- ficaciæ in imbuendo terram suis qualitatibus, aut bonis, aut malis, quibus pollet: provt nunc malo nostro experimur in Capite Medusæ maleficæ nimis, ac violentæ naturæ quæ iam facta est Regno Neapolis verticalis, ac proinde ea ma- la intulit, quæ iam pridem Argolus in genere pronunciauit in Pandosio Spharico & nos postea experti sumus, ipsumque haud mendacem competimus. 4. ZEPHIRVS græcè, quasi vitam ferens, dicitur Fauonius Ventus vnus ex quatuor Cardinalibus spirans ab occasu æqui- noctiali omnibus lenior, ac iucundior: suo enim: flaru viui- sico plantas germinare facit, & æstate potissimum post Me- ridiem spirare solitus mirè eius calores eleuat & compensat: alij Zephyrum appellant Africum spirantem ab occasu hye- mali, lateralem ipsi Fauonio ob vicinitatem, & naturæ simi- litudinem. Inter

Transcription: Translated (English)

LEXICON The shape and nature of everything is displayed everywhere in geographical charts, and also by all those who speak about the winds, especially Argolus in Astronom. lib. 2, cap. 6. Certainly each one takes on a mixed nature from those principal winds to which it adjoins. Hence Ypaticus and Mesocorus are of the nature of the Favonius, although they partake somewhat of Corus or Africa; Ypaquilo and Mesocircius take on the nature of the Septentrio; Ypeurus and Meso Cæcias the nature of the Subsolanus, and so on for the rest. Z 1. ZAMOCTAR among the Persians means the same as among the Arabs Argbutar, that is, in our language, Divider and Lord of boundaries: see the method of investigating it under V. Divisor. 2. ZEDARON, that is, Thorax in Arabic, according to Villetmo Schickardo, is called the chest of Cassiopeia, a fixed star of the second magnitude, of the nature of Venus and Saturn, under another and more common name Schedir. See about this under that word. 3. ZENITH in Arabic is said of the vertical point of the heavens, which directly and perpendicularly hangs over our heads, in our common speech the Vertex, which must necessarily be equally distant from the horizon by 90 degrees, and is as it were the pole of the horizon itself: opposite to it there corresponds another place under the earth, called Nader, distant from the horizon by the same number of degrees, always hidden, since it is conceived to be immovable beneath our feet. Moreover, a star placed in the Zenit, being in the place from which it sends straight rays to the earth, becomes very powerful and of marvelous efficacy in imbuing the earth with its qualities, whether good or bad, with which it is endowed: just as we now experience to our misfortune in the head of Medusa, of a very wicked and violent nature, which has now become vertical to the Kingdom of Naples, and therefore has brought those evils which Argolus long ago proclaimed in general in the Pandosia Spharica, and which we afterward experienced, and we have found him not to be false. 4. ZEPHIRVS in Greek, as it were bringing life, is called the Favonius, one of the four cardinal winds, blowing from the west of the equinox and gentler and more pleasant than all the others: for with its life-giving breath it causes plants to sprout, and especially in summer, when it is wont to blow after midday, it wonderfully raises and tempers the heat; some call Zephyr the African wind blowing from the western winter point, lateral to Favonius itself because of their closeness and similarity of nature. Inter

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MATHEMATICVM. Inter eius conditiones refert Abrahamus Gorlnitz in 5. compendio Geographico, quod sit venationi contrarius, quia cum sit valde humidus, odor autem sit ex temperie calida, & sicca; Ideò facilè odorem ferarum intercipit in canibus; maximè quia cæteri Venti altiùs spirant iste proximè ad terram. Vide in V. Fauonius. ZIGIATUS dicitur apud Astronomos homo natus sub Libra 6: fidere de quo est Aphorismus in Ptolemæi Centiloquio V.37. quod Mortis sua causa erit. At non video qua id ratione dicatur; eo maximè quia id liberam hominis voluntatem consciscendi sibi mortem appellare videtur, in quam tamen nemo sanæ mentis Astrologus dixerit Astra ullam habere vim. Pontanus in commentatione huius Verbi hæc habet. Qui natus est, inquit, horoscepante Libra, quia Taurus octa- uam locum, qui mortis est occupat, quod utrique etiam si- gno Venus Deminatur, hic sua morti causam afferet: hoc au- tem euenire potest aut propter morbos, quod infania captus ex alto se præcipitet; aut propter desperationem, quod segladio traiciat; aut propter temeritatem, cum facere quippiam pro- hibitus; legi ipsi parum obtemperans, in poenam capitalem, quasi volens incidat s aut cum Pratorem, aut Dominum peruicaciter agendo in se preuocet; aut cum monitus, vt hostem fugiat, facere id recusat; aut cum euitare potest periculum, quod tamen sccurus negligat. Suntem innumerabiles via; rationesque quibus homines, & mortis, & aliorum malorum sibi causa esse possunt. Hæc Pontanus. Verum hæc ratio non euacuat difficultatem; nec pium æquè ac Philosophiæ stu- diosum, arque ex eius principiis omnia metientem animum firmant. Quare ego experientia potius rerum magistra, ac etiam Philosophica ratione ductus Zigiatos dixerim vt plu- rimum cuasuros Poëtas, Musicos, eloquentes, Voluptuarios obsigni æqualitatem existentis sub Dominio Veneris, vel sanè ob benignissimam, & iucundissimam stellam spi- cam Virginis nunc temporis in eo signo consistentem. ZODIACVS græcè dicitur circulus maximus in sphæra latus 7: sex gradus hinc inde, intersecans æquinoctialem illumque secans in duas medietates, quarum altera ad septentrionem vergit, altera ad Austrum: à Latinis signifer appellatus, Cir- culus obliquus, & Via Solis, ac Planetarum, qui per eum constanter discurrunt. Sol quidem per eclipticam in eius me- dio sitam cæteri per suas particulares orbitas intra latitudi- nis eius fines inclusas. Dicitur Zodiacus ανὸ τῶν Σων, quod animal interpretatur, eo quod diuiditur in longum in duodecim signa, vt plurimum animalium nominibus insigni- Ll

Transcription: Translated (English)

MATHEMATICVM. Among its conditions Abraham Gorlnitz reports in the 5th compendium Geographicum that it is contrary to hunting, because, since it is very moist, and odor is from a warm and dry temperament, therefore it easily intercepts the scent of wild beasts in dogs; especially because the other winds blow higher, whereas this one blows nearest to the earth. See under V. Fauonius. ZIGIATUS is said among the astronomers of a man born under Libra, 6: to which there is an aphorism in Ptolemy’s Centiloquium V.37, that it will be the cause of his death. But I do not see on what reasoning this is said; especially because it seems to call that the free will of man to bring death upon himself, in which, however, no astrologer of sound mind would say the stars have any power. Pontanus in his commentary on this word has these remarks. He who is born, he says, with Libra giving the horoscope, because Taurus occupies the eighth place, which is that of death, and because Venus dominates both signs, he will himself bring about the cause of his death: this may happen either because of illness, when, seized by madness, he throws himself from a height; or because of despair, when he drives the sword through himself; or because of rashness, when, being forbidden to do something, and scarcely obeying the law itself, he falls, as it were willingly, into capital punishment; or when, by acting obstinately, he provokes the Praetor or the Lord against himself; or when, warned to flee the enemy, he refuses to do so; or when he can avoid danger, but nevertheless carelessly neglects it. There are countless ways and reasons by which men can be the cause to themselves both of death and of other evils. Thus Pontanus. Yet this reasoning does not remove the difficulty; nor does it reassure a mind equally devoted to piety and to the study of philosophy, and measuring everything from its principles. Wherefore I, guided rather by experience, the teacher of things, and also by philosophical reasoning, would say that Zigiati, for the most part, will be poets, musicians, eloquent men, and pleasure-seekers, by virtue of the equal distribution of the one existing under the dominion of Venus, or indeed because of the most benign and delightful star of the spike of Virgo, now at this time standing in that sign. ZODIACVS is called in Greek the greatest circle in the sphere, 7 six degrees on either side, intersecting the equinoctial and dividing it into two halves, one of which bends toward the north, the other toward the south: by the Latins it is called signifer, the slanting circle, and the road of the Sun and the planets, who constantly travel through it. The Sun indeed is in the ecliptic set in its middle; the others are within the bounds of its width through their own particular orbits. Zodiacus is called from the Greek ἀπὸ τῶν ζῴων, which means “animal,” because it is divided lengthwise into twelve signs, for the most part distinguished by the names of animals.

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334 LEXICON ta, siue potius απὸ τὰς Ζωῶς, quod vitam significat: Sol enim, & extera sidera, vt notauit Philosophus, ex accessu & recessu in hoc circulo est causa ortus & interitus rerum. 7. Duplex est alius imaginatius, alius sensibilis: Primus etsi à secundo olim nomen desumpserit, neque ab illo di- stingeretur, concipitur tamen in primo mobili, cuius nul- lum sensibile argumentum habemus quod verè existat nisi motum aliis orbibus inferioribus impressum, in quo signa diuiduntur in partes æquales sumptis initiis à quatuor cardi- nibus æquinoctialibus, & solstirialibus, constituentibus singulis suas quartas, singulis ex tribus signis, seu 90. gra- dibus constantibus, quæ omnia integrant summam 12. si- gnorum & 360. graduum: & de hoc communiter loquuntur Astronomi cum absolutè de Zodiaco mentionem faciunt. Alter vero dicitur sensibilis ob stellas quibus ornatur, consti- tuitur enim in Octava sphæra in loco olim quidem Zodiaco primi mobilis directè subiecto: verum postea ob motum pe- culiarem octauæ sphæræ sedes suas mutauit, & paulo vlterius ad gr. ferè 28. processur; ita vt stella in cornu Arietis, quæ tempore Ptolemei incidebat in sectionem vernam, nunc ab ea inueniatur distare gr. 26 Hic similiter diuiditur in duo- decim signa, seu potius sidera & Asterismos non tamen æqua- bilitertam in longum, quam in larum, sed pro ratione & numero stellarum, quas intra se singula comprehendunt. Quin immò antiquitus Libra, & Scorpius vnum Sidus erant; propter quod etiam hodiè duæ stellæ Lancis Australis, & Borealis, chelæ Scorpij ab aliquidibus appellantur. 8. Ob id nil mirum, si quæ de signis Zodiaci ex observatio- ne, antiquis scripterunt, iam nunc veritati minus respon- deant: siquidem naturam eorum vt plurimum ab stellarum qualitatibus, quæ in iis incidebant auspicabantur, quæ mo- do vt dixi iam recesserunt. Quare prudens Astronomus debet nunc, ante quam ad quicquam decernendum descen- dat, simul vtriusque Zodiaci & signa & sidera in vnum con- uenientia, simul conferre, & sic postea ex eorum commix- tione iudicium facere. Plurima Zodiaci vtriusque munera, & effectus vide apud Clauium in sphæram Io: de Sacro- bosco 9. ZONÆ apud Geographos, Astronosque dicuntur circuli quidam lati, & Coelum, Terramque velut balthei quidam, ac fasciæ circumplectentes, quas & Maculas & Oras appel- lar Cicero de Rep. & in Tusculan. à quatuor circulis mino- tibus Æquatori parallelis definitæ: quarum duæ à po-

Transcription: Translated (English)

334 LEXICON ta, or rather from τὰς Ζωως, which signifies life: for the Sun, and the other stars, as the Philosopher noted, through their approach and recession in this circle are the cause of the rise and decay of things. 7. There is a twofold zodiac, one imaginative, the other visible: the first, although it once took its name from the second, and was not distinguished from it, is nevertheless conceived in the first mobile heaven, of whose existence we have no sensible proof except the motion impressed on the lower spheres, in which the signs are divided into equal parts, taking their beginnings from the four equinoctial and solstitial points, each constituting its own quarter, each of three signs, or 90 degrees, all together making up the sum of 12 signs and 360 degrees: and it is of this that astronomers commonly speak when they mention the Zodiac absolutely. The other is called visible because of the stars with which it is adorned; for it is established in the eighth sphere, in a place formerly directly beneath the zodiac of the first mobile; but later, because of the peculiar motion of the eighth sphere, it changed its position, and moved a little farther on, to nearly 28 degrees; so that the star in the horn of Aries, which in Ptolemy’s time fell on the vernal point, is now found to be 26 degrees away from it. Here likewise it is divided into twelve signs, or rather stars and asterisms, though not equally in length, but according to the number and arrangement of the stars which each contains within itself. Indeed, in ancient times Libra and Scorpius were one constellation; for which reason even today the two stars of the Southern and Northern Scale are called the claws of Scorpius by some. 8. For this reason it is no wonder if what the ancients wrote about the signs of the Zodiac from observation now corresponds less with the truth: since they for the most part formed their judgments about their nature from the qualities of the stars that fell within them, and these, as I said, have now moved away. Therefore a prudent astronomer ought now, before proceeding to decide anything, to compare together both the signs and the stars of the two zodiacs, where they coincide, and then afterward to make a judgment from their combination. See the many offices and effects of both zodiacs in Clavius on the Sphere of Ioannes de Sacrobosco. 9. ZONES, among geographers and astronomers, are called certain broad circles which, like belts or bands, encircle the sky and the earth; Cicero in On the Republic and in the Tusculan Disputations calls them Belts and Borders; they are defined by four lesser circles parallel to the equator: of which two from the po-

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MATHEMATICVM. 535 sis mundi ad Circulos Arcticum, & Antarcticum p[ro]tensæ frigidæ appellantur, eoquia Sol ab illis maximè elongatur atque ad eas mundi plagas radios maximè obliquos eiaculatur; & ideò nimio frigore algent, habitationique hominum minùs opportunæ existimantur. Aliæ duæ à Circulis Arctico, & Antarcticio ad Tropicos Cancri, & Capricorni productæ constituunt duas temperatas nec multo frigore algentes, nec nimio calore exæluantes, quarum alteram nos Europæi inhabitamus habitationi, vt perspicuum & oppido opportunam. Quinta verò computatur à Tropico Cancriad Tropicum Capricorni, includens ipsum in medio Æquatorem, quæ dicitur Zona torrida, eoquia continua Solis statione torretur, & tellus illi subiecta aliquando ipsum habet verticalem, cum videlicet illam Zodiaci partem lustrat quæ ipsi perpendiculariter imminet. Et hæc quidem ob nimium æstum ab Antiquis reputabatur inhabitabilis; quemadmodum duæ priores ob nimium frigus. Vnde & Virgilius 1. Georg. eccinit. Quinque tenent Cælum Zona, quarum una corusco Semper Sole rubens, & torrida semper ab igne Quam circum extrema dextrâ lauâque trahuntur Cerulea glacis concreta, atque imbribus atris. Has inter, mediamque dua mortalibus ægris Munere concessa diuum, & via secta per ambas Obliquus quà se signorum verteret ordo. Verum experientiâ postmodum compertum est, omnem < 10.> terræ tractum esse habitabilem; & non modo regiones frigidas sub polo arctico, & circum inhabitari, (quod etiam de terra australi nondum detecta pari ratione credendum est,) sed & regiones calidiores sub via Solis obliqua; quales sunt totus ferè Africæ tractus magnaque pars Asiæ, & Americæ, vbi frequentissimi populi sunt, populatissimæ Vrbæ. Quinimò referunt qui eas oras nauigiis per garunt, atque inde postmodum huc appulerunt, adesse ibi temperatissimum æstum, ac potissimum sub æquatore iucundissimam vitam duci. Quamuis enim ex iis quæ diximus debeat ibi esse maximus æstus ex accessu Solis ad Verticem, nihilominus aliundè æstus iste attemperatur, primò ex aquarum inibi consistentium multitudine, aduertunt enim Geographi sub Zona torrida maiorem esse aquarum copiam, quam sub aliis Zonis: quod magna Summi Opificis providentia factum esse docet Cardanus 1. de subtil. ne, inquit, terra nimio eius plagæ calore consumeretur, sed aquæ humoribus, ac naturali frigiditate temperaretur. Secundò ob Ll ij

Transcription: Translated (English)

are called the frigid zones of the world, because the Sun is most distant from them and hurls its rays to those parts of the world most obliquely; and therefore they are chilled by excessive cold and are thought less suitable for human habitation. The other two, extending from the Arctic and Antarctic Circles to the Tropics of Cancer and Capricorn, make up two temperate zones, neither chilled by much cold nor scorched by excessive heat, one of which we Europeans inhabit for dwelling, as is clear and altogether suitable. The fifth is reckoned from the Tropic of Cancer to the Tropic of Capricorn, including in the middle the Equator itself; this is called the Torrid Zone, because it is burned by the constant course of the Sun, and the land subject to it sometimes has the Sun at the zenith, namely when it traverses that part of the Zodiac which hangs perpendicularly over it. And this, indeed, because of excessive heat, was judged by the Ancients to be uninhabitable, just as the first two because of excessive cold. Hence Virgil also in Georgics 1 sang: Five zones hold the heaven, of which one, ever red with flashing Sun, is always torrid with fire; around this, on the far right and left, are drawn icy masses, hardened by blue frost and black rains. Between these and the middle zone is a path assigned to suffering mortals by the gift of the gods, and a way cut through both, where the oblique order of the signs would turn itself. But experience later showed that every region of the earth is habitable; and not only the cold regions under the Arctic Pole and around it are inhabited, (which by the same reasoning must also be believed of the southern land not yet discovered,) but also the hotter regions under the Sun’s oblique path, such as almost the whole tract of Africa, and a large part of Asia and America, where there are very populous peoples and densely inhabited cities. Indeed, those who have sailed along those coasts and afterward landed here report that there is a most temperate warmth there, and especially under the equator a very pleasant life is led. For although, from what we have said, there ought to be the greatest heat there from the Sun’s approach to the zenith, nevertheless this heat is moderated from another source, first by the abundance of waters standing there; for geographers note that under the Torrid Zone there is a greater supply of waters than under the other zones: Cardanus teaches in On Subtlety 1 that this was done by the great providence of the Supreme Creator, lest, he says, the earth be consumed by the excessive heat of that region, but might be tempered by the moisture and natural coldness of the waters. Secondly by

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diei, noctisque minorem inæqualitatem, quam sub aliis Zonis; vnde maior temperies est sub ipso æquatore, quam sub Tropicis: quod & Albertus Magnus, & Auicenna annotarunt dicentes, magis laboriosam habitationem esse sub Tropicis, quam sub Æquinoctiali; & experientia ipsa id manifestum facit. Quando quidem qui sub æquatore degunt albi sunt, aut sanè non nigricum tamen qui sub tropicis nascuntur nigerrimi sint, adusti, deformes, & capillitio crispi. Rationem affert Auicenna, quia, inquit, capitibus habitantium sub æquatore Sol imminet bis in anno, & recessus ab eo est velox ob Zodiaci obliquitatem: capitibus verò habitantium sub tropicis, semel quidem, sed diu consistit in anno ob rectam ascensionem, & Solstitiorum naturam. Accedit quod sub æquatore est perpetuum æquinoctium, vnde sit, vt Sol supra terram tantumdem, quam sub terra, consistens, non possit illam diutius inflammare: immò quantum in die caloris efficit, tantùm remittit in nocte per frigus: quod vt paulatim superet multum temporis insumit, nec prius illud superasse, inueniatur quam ad occasum inflexerit quæ etiam ratio est, cur calidior sit Autumnus quam Ver, etsi alioqui in dies semper humilior fiat Sol, & noctes augescant. Sub tropicis verò & circum ipsos, Sol in æstate diutius supra terram commorarur, & ex vertice intensiores radios eiaculatur: qua propter ex duplici capite intensiores sentiunrur calores. Similiter quoad regiones polis subiectas Plin. lib.4. cap.12. ponit in iis esse summam aëris felicitatem; quod tamen nimis audenter dictum existimauerim, cum Batavi ad eas oras navigantes non nisi ad vsque 75. gradus elevationem peruenire potuerint, & referant mirabilia de eorum locorum frigiditate, qua obstrictum mare iis vlcerius progrediendi potestate non fecerit; Ratione tamen colligi potest, non esse inibi frigus adeo intolerandum, vt non commodè pro inhabitantium mote cum alioqui frigoribus assueti mora iugis sint ita hi possit. Equidem etsi in iis duorum, trium, vel etiam plurium, quò magis ad polum fiat accessus, mensium spatio Sol iugiter delitescat nihilominus viceuersa totidem etiam, & sub polo in æstate sex integrorum mensium spatio nunquam occidit, sed circulariter ferrur, vnde & Periscij accolæ audiunt, eoquod vmbra illis circumferatur, qui sit diurnâ illa Solis consistentiâ in superiori hemisphærio, etsi ex obliquo, nunquam tamen intermitentibus radiis fota tellus, non ita intensum toto anno concipiat frigus, sed in æstate tepescat, & in hyeme ob nimium horizontis obliquitatem,

Transcription: Translated (English)

the lesser inequality of day and night than under other zones; hence there is greater mildness under the equator itself than under the Tropics: which both Albertus Magnus and Avicenna noted, saying that habitation under the Tropics is more troublesome than under the Equinoctial; and experience itself makes this manifest. For those who live under the equator are white, or at least not black; yet those who are born under the tropics are very black, sunburned, misshapen, and curly-haired. Avicenna gives the reason: because, he says, for the heads of those living under the equator the Sun is vertical twice in the year, and its retreat from there is rapid on account of the obliquity of the Zodiac; but for the heads of those living under the tropics, it is indeed vertical once, yet it remains for a long time in the year because of the direct ascension and the nature of the solstices. Added to this is the fact that under the equator there is perpetual equinox, whence it happens that the Sun, remaining just as much above the earth as below it, cannot inflame it for a longer time: indeed, as much heat as it produces by day, so much does it abate at night through cold: and to overcome this gradually takes much time, nor is it found to have overcome it before it has turned toward setting; which is also the reason why Autumn is warmer than Spring, although otherwise the Sun becomes ever lower day by day, and the nights increase. Under the tropics, however, and around them, the Sun in summer stays longer above the earth, and from the zenith shoots forth more intense rays: wherefore greater heat is felt from a double cause. Likewise, as to the regions subject to the poles, Pliny, book 4, chapter 12, states that in them there is the highest felicity of the air; which nevertheless I would judge to have been said too boldly, since the Dutch, sailing to those shores, were able to reach only up to 75 degrees of elevation, and report wonders about the coldness of those places, by which the frozen sea did not allow them the power to proceed further; nevertheless, by reasoning it may be gathered that the cold there is not so unbearable that, with those people being accustomed to cold and their long stay otherwise being suitable to their manner of life, they could not live comfortably there. Indeed, although in them the Sun remains hidden continuously for two, three, or even more months, the further approach is made toward the pole, nevertheless conversely it also remains hidden for the same number, and under the pole in summer it never sets for a space of six full months, but moves in a circle, whence the inhabitants are also called Periscij, because the shadow is carried around them, which comes about through that daily continuance of the Sun in the upper hemisphere, and although the earth, heated by rays never interrupted though oblique, may not throughout the whole year conceive such intense cold, still it grows mild in summer, and in winter, on account of the excessive obliquity of the horizon,

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MATHEMATICVM. 557 solem habeat horizonti proximum semper intra lineam crepusculinam commorantem, atque adeo numquam obscuram noctem, numquam tenebras, numquam etiam intolerabile frigus. < 13.> Vbi quidem magnam connendand Diuinæ sapientiæ argumentum nobis sit considerantibus, quod vbique locorum res ita disposuit, vt æstus immoderantiam æqua diei, noctisque vicissitudo, ac frequentes pluuiæ temperarent; & ex alia parte frigoris intoleranda scuitias, & maximus solis recessus â vertice iugi eiusdem suprà, vel circâ terram consistentiâ compensaretur. < 14.> Sed & illud mirari licet, quod æstas in Zona torrida tepidior est, tolerabiliorque quam Hyems: quamuis enim Sol ibi verticalis existens deberet maximos æstus adducere, tamen hoc regionibus illis prouidens Natura concessit, vt quamdiù Sol vertici appropinquaret nubibus semper obtegeretur, atque assiduis fastidiosisque cadentibus pluuijs subiecta tellus irrigaretur; cum verò à vertice elongatur, cum eo nubes attrahat, quò cursum dirigit, consequenter alias oras inopertas linquit, quas proinde constanti æstu, continuisque radiis percutit. < 15.> Quod mihi plurium annorum experientia edoctus testatus est oculatus testis omni exceptione dignus Antonius Poma Clericus Regularis Apostolicus ad indos Missionarius ad nos redux, vt alios item operarios in Domini vineam conduceret, vir humanissimus, pijssimus, ac rerum vsu longè instructissimus. Ait enim in Golgondæ Regno se id expertum; quin & in Goa ciuitate totius Orientis Principi, ac celebri emporio, mense Maio, quo Sol Tauri signum percurrens sit ei verticalis, continuis integri mensis pluuiis locum repleri, vnde aquarum copia certos quosdam cyniphes producit hominibus nimium infensos: cum tamen in Hyeme magni calores sint, nullæque pluuiæ. Nec id ratione vacat à Natura desumpta: Videmus enim in arte distillatoria, quid non absurile fieri: vbi enim calor ad summum vasis distilatorij contenderit, atque adunatus fuerit, omnes ad se subiecti humoris vapores trahit, atque in odoratam pluuiam vertit. Sic profecto Sol verticalis euadens ad se omnes terræ vapores attrahit, nubibus conuestitur, pluuias creat, atque ad subiectas regiones demittens eas vberrimè lauat, & rigat. Quo sanè remedio Deus ita orbi prouidit, vt nulla esset Prouncia in qua homines æquè bene non possent consistere, suaque munificentia frui. Ll iii

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MATHEMATICVM. 557 the sun should have the horizon nearest, always dwelling within the twilight line, and thus never have a dark night, never darkness, nor even intolerable cold. < 13.> Here indeed we have a great argument for admiring Divine wisdom, when we consider that in every place it has so arranged things that the excess of heat might be moderated by the equal succession of day and night, and by frequent rains; and on the other hand, the intolerable severity of cold, and the greatest retreat of the sun from the summit of that same region above, or around the earth’s surface, might be compensated for. < 14.> But this also may be wondered at, that summer in the Torrid Zone is milder and more tolerable than winter: for although the Sun, being there vertical, ought to bring the greatest heat, nevertheless Nature, providing for those regions, allowed that as long as the Sun approached the zenith it would always be covered with clouds, and that the earth beneath, subject to constant and wearisome falling rains, would be watered; but when it departs from the zenith, it draws the clouds with it, whithersoever it directs its course, and consequently leaves other coasts uncovered, which therefore it strikes with constant heat and continual rays. < 15.> This I have been taught by the experience of many years, as an eyewitness worthy of every exception, testified to me by Antonius Poma, a Regular Cleric, Apostolic missionary to the Indies, returned to us in order to engage other laborers also in the Lord’s vineyard, a most humane man, most pious, and far the most experienced in practical affairs. For he says that he had experienced it in the Kingdom of Golconda; and indeed in the city of Goa, the principal city of the whole East, and a famous emporium, in the month of May, when the Sun, traversing the sign of Taurus, is vertical to it, the place is filled with continuous rains for an entire month, from which abundance of water produces certain gnats exceedingly hostile to men: whereas in winter there are great heats, and no rains. Nor is this without a reason drawn from Nature: for we see in the art of distillation what cannot be said enough, how it comes about. For where heat has pressed to the highest point of the distilling vessel, and has been gathered together, it draws to itself all the vapors of the moisture beneath it, and turns them into fragrant rain. So indeed the Sun, becoming vertical, draws to itself all the vapors of the earth, is covered with clouds, produces rains, and, sending them down to the regions beneath, most abundantly washes and waters them. By this remedy indeed God has so provided for the world that there should be no Province in which men could not dwell equally well and enjoy His bounty. Ll iii

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538 LEXICON 16. ZOODORTS apud Persas idem sonat ac apud Arabes Hileg: significat enim Planetam vel alium locum in cælo vitæ moderandæ dispositionem sortientem, qua de re abunde diximus in V. Apheta. 17. ZOPHOMENTA apud quosdam ex Græco audit Lunæ obscuritas, defectusque lucis, quam patitur in Eclipsi. 18. ZOZAICVS circulus dicitur qui ex linearum quinq[ue] angulis, & adhuc vna linea const. Pap. apud Amaltheum onomasticum. 19. ZVBENESCHEMALI, Arabicè appellatur Lanz australis stella fixa secundæ magnitudinis, de qua alibi fusè diximus, teste Bayero in sua Vranomerria: quam taman melius vocari Vazneganubi, vult Kircherus in Oedipo Ægyptiaco, sicut & Borcalem Vazneschemali. FINIS.

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538 LEXICON 16. ZOODORTS among the Persians means the same as Hileg among the Arabs: for it signifies a Planet or some other place in the sky assuming the disposition of governing life, concerning which we have spoken sufficiently in V. Apheta. 17. ZOPHOMENTA, among some, from the Greek, denotes the obscurity of the Moon, and the loss of light which it suffers in an Eclipse. 18. ZOZAICVS is called a circle which consists of five angles of lines, and still one line more. Pap. apud Amaltheum onomasticum. 19. ZVBENESCHEMALI, in Arabic, is the name of Lanz australis, a fixed star of the second magnitude, of which elsewhere we have spoken at length, as Bayer testifies in his Vranomerria: yet Kircher, in the Oedipus Aegyptiacus, wishes it rather to be called Vazneganubi, as also Borcalem Vazneschemali. FINIS.

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OPERIS CONCLUSIO AD LECTOREM. Atque hic suscepti à me operis finis esto. Quod, si optatam tenuit metam, ac Lectoris vota aqua- uit, in Dei Omnipotentis laudem cedat, bonorum om- nium largitoris: sin minùs, Auctores indiligentiam aliis curis impliciti, excuset quæso Mathesis studiosus: atque inde excidetur ad noua, quæque desiderari pote- runt, suppeditanda, quibus mirificè locupletatus li- ber denuò lucem aspiciat omnibus numeris absolutus. Non enim, ut ille ait, omnia possumus omnes. Consideretque nostram imbecillitatem, & quod teste Moyse solius Dei perfecta sunt opera Cæterum non me latet, ad pleniorem rerum intellegentiam satiùs fuisse Geometricas figuras appingere, atque oculis ex- hibere, sine quibus Mathematicæ facultates agrè per- cipiuntur. Verum quia ea passim apud reliquos Au- ctores obuiæ sunt, & alioqui magnas impensas requi- rebant, quas non ità facilè Typographus suscepisset; eapropter consultius habui has modò omittere, & res sola verborum circumlocutione ita delineare, ut penè earum, ex oculis contemplatio videatur superflua, cum planè quiuis, ni fallor, non rudis Mineruæ facili via mente possit concipere quod stelus in tabulis areis incidisset, nosque studioso verborum circuitu menti ob- ijcere conati sumus. Quodsi id à Lectoribus exoptari

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Conclusion of the Work To the Reader. And here let this be the end of the work I have undertaken. If it has reached the desired goal and satisfied the reader’s wishes, let it redound to the praise of Almighty God, the giver of all good things; but if not, I beg that the studious reader excuse the author’s negligence, as one distracted by other cares. And from this let the work be corrected and expanded with new matter, and whatever else may have been desired supplied, so that the book, wondrously enriched, may again see the light, complete in every respect. For, as the saying goes, we cannot all do everything. And let him consider our weakness, and that, as Moses testifies, only the works of God are perfect. Moreover, it is not hidden from me that, for a fuller understanding of these matters, it would have been better to set out the geometrical figures and display them to the eye, without which mathematical matters are with difficulty perceived. But since these are commonly to be found in other authors, and besides would have required great expense, which the printer would not so readily have undertaken, I therefore judged it wiser to omit them for the present, and to delineate the subject by words alone, in such a way that the contemplation of the things themselves through the eyes may seem almost superfluous; since, I think, anyone not unacquainted with Minerva may easily conceive in the mind what has been cut into bronze tablets, though we have tried to place it before the understanding by a careful circuit of words. But if this should be desired by the readers

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540 nihilominùs intellexero, non grauabor, ac tempus semper aderit, in secunda, si Deus faxit editione præsta- re. Interim pro operis Coronide breuem digressiunculam. De miris vulnerum curationibus per sympathiam quam dudum ab amicis requisitùs conscripseram, ad Li- bri caleem apponere, si que veluti Colophon; atque ap- pendix ad verbum Sympathia; è cuius principiis om- nia sunt deducta. Statueram equidem, has Quæstio- nes, quæ potiùs Theologicæ sunt, unà cum alijs Theo- logicis, ac Moralibus disquisitionibus; (quarum non spernendum sanè volumen longo studio, & labore con- feceram, & iam ultima manu expolitum commodum præstolabar, vt typis darem,) propiore loco tibi lucu- lentiùs exhibere: Verum, quæ est humanarum rerum conditio! Dum Apulia Neapolim cum sarcinulis meis regredior, miserè eas, vel casu deperditas, vel furto sublatas ingenui: quas inter omnes ferè ingenioli mei fætus, omnes integra atatis labores amisi; vt poenè ea- rum iactura Iobi constantiam confregisset, vitæque dis- crimen, præ maroris magnitudine intulisset: nec tantus modò sum, vt prima, ac florentis iuuenta studia, & labores rememorari valeam, ac repetere. Sed pro mi- raculo fuit, vt huius tractationis primam graphidem domi seruarem, cuius subsidio, eam iterum, licet non tam concinnè, delineatam, nunc tibi Lector exhibeo: si quid boni in ea inueneris, fruere; sin minùs, ignosce; Auctorem amice admone, & Vale. DIGRESSIO

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540 Nevertheless, if I shall have understood it, I will not be burdened, and there will always be time, in a second edition, if God grants it, to supply it. Meanwhile, as a brief digression, in the coronis of the work. I had long ago, at the request of friends, composed something about the wonderful cures of wounds by sympathy, to append to the end of the book, as a kind of colophon and appendix to the word Sympathia; from whose principles all has been derived. Indeed, I had intended to present these Questions, which are rather theological, together with other theological and moral inquiries; a volume not to be despised, which I had prepared with long study and labor, and was already waiting, polished with the final hand, to give to the press, and to exhibit to you more clearly in a more suitable place. But such is the condition of human affairs! While returning to Naples from Apulia with my belongings, I miserably lost them, either through accident or by theft; and among them I lost nearly all the offspring of my little mind, all the labors of my entire youth, so that almost the loss of them would have broken Job’s constancy and brought on the danger of life, because of the greatness of my grief. Nor am I so great that I can recall and renew the studies and labors of my first and flourishing youth. But it was a miracle that I preserved at home the first sketch of this treatise, with whose aid I now present it to you, Reader, drawn out again, though not so neatly: if you find anything good in it, enjoy it; if not, forgive; kindly admonish the Author, and farewell. DIGRESSION

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DIGRESSIO PHYSIO-THEOLOGICA AD VERBUM SYMPATHIA. DE MAGNETICA VVLNERVM CVRATIONE. VLT A sunt in Natura, quæ, quoniam humanum captum, adeoque ipsam Naturam transcendere, ac totius Philosophiæ principia euertere videntur, religiosè aliqui tanquam suspecta reiiciunt, improbant, aut saltem extimore, ne Daemonis arte fiant, quò homines in sui societatem alliciat, opere exequi reformidant: cum aliàs, si compertum esset, eorum virtutem naturalem esse, posseque tuta conscientia adhiberi, id in magnum Reipublicæ bonum cederet, abiretque. Horum longam seriem affert Ioannes Baptista Van'. Helmont in suo opere medico peculiars de hac re tractatu, ac Athanasius Kircherus in Arte Magnetica; pars. lib. 2. cap. . Huiusmodi est illud, quod si Mumia, quæ primò hominis tabidi spiritum exsuxerit, protinus bestiæ ad deuorandum obiiciatur; mox illa qualitate morbifica attracta insicitur, & hominem liberum linquit. Item modus curandi morbum regium seu Ictericiam flauam, qui practicatur sæpissimè in Hispania, aliisque regionibus vltrà montes, præsertim septentrionalibus: sumunt enim recens excretam patientis vrinam, atque in ovi putamine inclusam exponunt calidis cineribus lentissimè consumendam: nam ea pe- A

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DIGRESSION PHYSIO-THEOLOGICAL TO THE WORD SYMPATHY. ON THE MAGNETIC CURE OF WOUNDS. There are certain things in Nature which, because they seem to transcend human understanding, and indeed Nature herself, and to overthrow the principles of all Philosophy, are by some religiously rejected as suspicious, disapproved, or at least, through fear that they may be done by the art of the Devil in order to entice men into his society, shrunk from in practice; whereas, if it were once established that their virtue is natural, and that they may be employed with a safe conscience, this would redound to the great good of the Republic and would spread abroad. John Baptist Van Helmont sets forth a long series of such things in his special medical work on this subject, and Athanasius Kircher in the Magnetic Art; part, book 2, chapter . Of this sort is that by which, if Mumia, which first had sucked out the spirit of a man wasting away, is immediately thrown to be devoured by a beast; then, having been struck by that morbific quality, it is infected, and leaves the man free. Likewise the method of curing the king's evil, or yellow jaundice, which is practiced very often in Spain and other regions beyond the mountains, especially in northern ones: for they take the patient's freshly voided urine, and, enclosed in an eggshell, expose it to hot ashes to be consumed very slowly; for it pe- A

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PHYSIO-THEOLOGICA nitus absumpta mox omnis l[et]terus abit. At si forte ex incuria, aut etiam ex malitia res negligentius peragatur, ita vt oui testa minimum quid læsionis aut vredinis contrahat; confestim in ægro l[et]terus flauus in nigrum conuertitur, atque omni spe salutis ablata, mortem certissimam inducit. Quod suo tempore accidisse in quodam sacerdote suæ curæ demandato mihi testatus est Petrus de Castro Medicus doctissimus, atque amicissimus. Sed inter omnia celeberrimus toto orbe est Puluis ille Sympathicus qui vulneratorum sanguini linteaminibus adherenti applicitus; quamuis hæc ab ægro valdè remota sint, mirum in modum curationi confert, & ægro ad paucos dies sanitatem restituit. De hoc magna olim controuersia fuit inter Medicinæ Professores Venetiis primum, tum Romam ad fidei quæsitiores delata, atque acriter inter Theologos agitata tandem sine vlla conclusione dimissa est. De ea ego in facti contingentia interrogatus Patauij, num, stante hac dubietate, licitè, & qua camela adhiberi possit; præsentes quæstiones scripsi: & primò nil de pulueris ipsius virtute, & modo quo agat inquirens, solum Theologicè discutio num possit tuta conscientia adhiberi, & Medicis ac Milibus, (quibus frequens esse solet, ac facilis) liber eius vsus possit permitti. Secundò id etiam quæro de Vnguento Armario, quod licet eadem vi polleat, tamen diuersa ac longe abstrusioni via procedit. Tertiò demum Philosophicè inquiro, quonam pacto Puluis Sympathicus, Vnguentum Armarium, & cætera huiusmodi medicamenta concurrant ad vulnerum aliorumque morborum curationem. Sit igitur -------------------------------------------------------- QVÆSTIO PRIMA. Verum Puluis Sympathicus linteaminibus vulneratorum sanguine infectis applicatus, licitè adhiberi possit in vulnerum curatione. SVMMARIVM. Qvid sit Puluis sympathicus, & quomodo preparatur. num. 1. Ferro non tangendus, dum preparatur, aut in vsum reducitur. n. 2.

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PHYSIO-THEOLOGICA then once the putrefaction is consumed, all the ulcer matter soon departs. But if by negligence, or even by malice, the matter is handled carelessly, so that the sheep’s skin contracts the least injury or heat, then at once in the wound the yellow matter turns black, and all hope of recovery being taken away, most certain death is brought on. That this happened in due time in the case of a certain priest entrusted to his care was attested to me by Peter de Castro, a most learned and very dear physician. But among all things, the most celebrated throughout the whole world is that Powder of Sympathy which, applied to the blood of the wounded adhering to linen cloths, although these may be very far removed from the patient, contributes in a wondrous way to the cure, and restores the patient to health within a few days. About this there was once a great controversy among the Professors of Medicine first at Venice, then brought to Rome to the inquisitors of the faith, and fiercely debated among the Theologians; at last it was dismissed without any conclusion. When I was asked about it at Padua in a case of fact, whether, this doubt still standing, it could lawfully be applied, and in what manner, I wrote the present questions: and first, without inquiring at all into the virtue of the powder itself, and the way in which it acts, I discuss only in a theological way whether it can be used with a safe conscience, and whether its use may be permitted to Physicians and Soldiers, among whom it is usually frequent and easy. Secondly, I also ask this about the Unguent of Armour, which although it possesses the same force, nevertheless proceeds by a different and much more hidden way. Thirdly, I finally inquire philosophically by what means the Powder of Sympathy, the Unguent of Armour, and other medicines of this kind contribute to the cure of wounds and other diseases. Let there be, therefore— -------------------------------------------------------- QUESTION ONE. Whether the Powder of Sympathy, applied to cloths stained with the blood of the wounded, may lawfully be used in the cure of wounds. SUMMARY. What the Powder of Sympathy is, and how it is prepared. no. 1. Not to be touched by iron, while it is being prepared or put into use. n. 2.

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DE SYMPATHIA. 3 In ossium fracturis additur gummi tragacanthi, vel quid hu- iusmodi. n. 3. Vsus ex Papinio. n. 4. In vulneribus interioribus sanguis interior excipiendus. n. 5. Prodest etiam vulneratis per tormenta bellica. n 6. Quomodo panni medicati tractandi, & quo luto reponendia n. 7. In ossium fracturis fragmenta educenda, & locus assulis, ut moris est, fulciendus. n. 8. Aliqui simplex calcanthum nullatemus præparatum adhibent[ur] n. 9. Eius efficaciam, quam probat iugis experientia, nemo non vi- det, & non admittit. n. 10. Dubitatur tamen ab aliquibus an ea sit naturalis, vel super- stitiosa. ibid. Qui superstitiosam asserant, ibid. Qui naturalem contendant. ibid. Vicumque sit, potest tutò, & confidentissimè adhiberi. ibid. Effectus dubias censendus est naturalis. n. 11. Multi similes effectus in natura sunt naturales. n. 12. Qui exponuntur. ibid. Qua in curatione adhibentur, prorsus naturalia sunt. n. 13. Et alioqui eadem virtute pollent, si intimè applicentur. ibid. Quomodo, & quanam agentia naturalia requirant determi- natam distantiam adhoc vt agant. n. 14. Puluis fortius ageret si vulneri applicaretur, sed esset nimius. n. 15. Venenum pulueri admixtum, & sanguini inspersum nocte agro. n. 16. Qua ratione non venenum dumtaxat. ibid. Lac in ignem emulsum mammas steriles reddit. ibid. Secundina canoso loco dejecta ladunt puerperas, secus si in ignem. ibid. Ad urticam siluestrem mingens vrina ardorem contrahit. ibid. Iuglandis umbræ dormientibus obest. ibid. Cicuta hominibus exitialis est, sturnis verò commodum pa- bulum. ibid. Omne agens operatur intrà determinatam spharam attiuita- tis. n. 17. Macula in linteis, ex arborum fructibus contracta ad foliorum decisionem absterguntur. n. 18. Vinum in doliis fluctuat vinea efflorente ibid. Quodnam agens vt operetur requirit determinatam distantiam. ibid. 2 ij

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OF SYMPATHY. 3 In fractures of the bones, gum tragacanth is added, or something of this kind. no. 3. Use from Papinius. no. 4. In internal wounds, the internal blood is to be received. no. 5. It also benefits those wounded by artillery. no. 6. How medicated cloths are to be handled, and in what clay they are to be laid up. no. 7. In fractures of the bones, the fragments are to be drawn out, and the place, as is customary, is to be supported with splints. no. 8. Some use simple chalcanthum, by no means prepared. no. 9. Its efficacy, which continual experience proves, everyone sees and admits. no. 10. Yet some doubt whether it is natural or superstitious. ibid. Those who claim it is superstitious. ibid. Those who contend it is natural. ibid. Whatever it may be, it can be applied safely and with the greatest confidence. ibid. The doubtful effect should be judged natural. no. 11. Many similar effects in nature are natural. no. 12. Which are explained. ibid. In whose cure they are applied, they are altogether natural. no. 13. And otherwise they possess the same power, if they are applied closely. ibid. How, and by what natural agents, a determinate distance is required in order that they may act. no. 14. The powder would act more strongly if applied to the wound, but it would be excessive. no. 15. Poison mixed into the powder, and sprinkled into the blood, is harmful by night. no. 16. For what reason it is not poison only. ibid. Milk drawn out into the fire makes breasts barren. ibid. Afterbirth thrown into a swampy place harms women in childbirth, but otherwise if into the fire. ibid. If one urinates near a wild nettle, the urine acquires a burning sensation. ibid. The shade of a walnut tree is harmful to those sleeping beneath it. ibid. Hemlock is deadly to human beings, but a suitable food for starlings. ibid. Every agent operates within a determinate sphere of activity. no. 17. A stain on linens, contracted from the fruits of trees, is removed when the leaves fall. no. 18. Wine in casks swells when the vineyard is in bloom. ibid. What agent requires a determinate distance in order to act. ibid. 2 ij

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PHYSIO-THEOLOGICA Selenites, & Lunaria Luna mutationes seruant n. 20. In curatione magnetica, & similibus Natura operibus nulla datur actio in distans sed tota fit immediatè à Natura. n. 21. Non est præsumendum curationem ullam magneticam à da- mone esse. n. 22. Curatio magnetica non est suprà Natura vires. n. 23. Cum natura omninò deuicta est, curatio omnis euadit inuti- lis n. 24. Natura arte suffulta breui tempore potest, quòd alias se sola longo temporefacit. ibid In dubiis tutior pars eligenda. n. 25. Quomodo hoc axioma intelligendum. n. 26. Damon affectat maxima quaque natura bona corrumpere, vel suspecta reddere. ibid. Protestatio contraria facto non prodest. n. 27. In quo casu id locum habeat. ibid. Aliquando licitum est factum cæteroqui certò superflitiesum aggredi cum protestatione. n. 28. Aliud est dubium, aliud probabile. n. 29. Male Diana supponit certum esso, puluerem non posse natura- liter operari. ibid. Inter omnia agentia naturalia ignis maximè actium est. n. 30. Vitriolum adhoc vt virtutem suam exerat à nativo passi ca- lore excitari debet. n. 31. Vitriolum non habet sympathiam cum corpore humano, ne- que cum sanguine, neque sanguinis sympathia facit simplici- ter, vt eius mala affectiones in corpus redundent. n. 32. Quadam mixta occulta quadam qualitate operantur, qua longe elementaribus præstat. n. 33. Vitriolum actuatur à sanguine, & agit in sanguinem, natu- ra interim per sympathiam quam habet cum sanguine ad opus se excitante. n 34. Cur id ipsum non accidat in sauguine, qui è vena exsetta ma- nauit, aut cum venefica qualitate inficitur. n. 35. Iaspis ex occulta qualitate habet sanguinem sistere. ibid. Adamantem ledit sanguis non ignis. n 36. Vniones soluit acetum, non aqua fortis. ibid. Cantharides manu pressa ladunt vesicam, non manum. ibid. Vitriolum habet antipathiam cum sanguine, & sanguis sympathiam cum parte affecta, unde manauit. n. 37. Non omnis nobis naturalium verum virtus compensa est, & multa nobis ignota. n. 38.

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PHYSIO-THEOLOGICA Selenites and Lunaria preserve the changes of the moon. n. 20. In magnetic healing, and similar works of Nature, there is no action at a distance, but the whole effect is produced immediately by Nature. n. 21. It is not to be presumed that any magnetic cure is from the devil. n. 22. Magnetic healing is not above the powers of Nature. n. 23. When Nature has been entirely overcome, every cure becomes useless. n. 24. Nature, supported by art, can in a short time do what otherwise it produces by itself only in a long time. ibid. In doubtful cases, the safer part is to be chosen. n. 25. How this axiom is to be understood. n. 26. The devil strives to corrupt, or make suspect, whatever is best in Nature. ibid. A protest contrary to the act does not help. n. 27. In what case this may apply. ibid. Sometimes it is permitted to attack an otherwise certainly superfluous act with a protestation. n. 28. A doubtful thing is one thing, a probable thing another. n. 29. Diana wrongly assumes it is certain that powder cannot act naturally. ibid. Among all natural agents, fire is the most active. n. 30. In order for vitriol to exercise its power, it must be stirred by innate heat. n. 31. Vitriol has no sympathy with the human body, nor with the blood, nor does sympathy with the blood simply cause its harmful affections to pass into the body. n. 32. Certain mixtures act by a hidden quality, which far surpasses the elemental. n. 33. Vitriol is actuated by the blood, and acts on the blood, while Nature in the meantime, through the sympathy it has with the blood, excites itself to the work. n. 34. Why the same does not happen in blood that has flowed from a cut vein, or when it is infected with a poisonous quality. n. 35. Jasper, by an occult quality, has the power to stop blood. ibid. Blood harms the diamond, not fire. n. 36. Vinegar dissolves pearls, not aqua fortis. When pressed by hand, cantharides injure the bladder, not the hand. ibid. Vitriol has an antipathy to the blood, and the blood a sympathy with the affected part from which it flowed. n. 37. Not all the true powers of natural things are known to us, and many are unknown to us. n. 38.

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DE SYMPATHIA. 5 < 11> Anequam ad rei examen deueniamus, præstat primùm explicare quid sit Puluis sympathicus, quibus constet, & qua ratione paretur: hoc enim semel intellecto, facilius nobis erit eius virturem disquirere, & quonam pacto ad vul- nerum curationem, etiam minimè vulneri applicetur, con- ferre possit. Ergò Puluis sympathicus (sic dictus, eo quia cum eius agendi vis clarè non innotescat, creditur ex oc- culta quadam rerum consenstone ac sympathia emanare) sit ex Calchantho, seu, vt vulgò vocant, Vitriolo Romano, quod, postquam pluribus dissolutionibus ex aqua limpida filtrationibus per chartam empareticam, ad ignem euapo- rationibus, ac repetitis coagulationibus, provt ars pyrore- chinea docet, à fæculento magmate fuerit repurgatum, & summam viriditatem adeptum, contunditur crassiusculè, & per quindecim circiter, aut decem et octo dies seruentiori- bus solis radiis mense Iulio, vel Augusto quandiu in Leone fuerit exponitur, donec vi solis calcinatus ad summam pu- ritatem albedinemque deuenerir. Inde ad vsum in loco ido- neo, hoc est siccioris temperiei asseruetur. Quod sibi fortè aut dum paratur aër nubilus, aut pluuius sit, aut dum iam perfectus asseruatur, ex loci humiditate, aut insita, & ex- crementitia natura recruduerit, & aliquid humoris contraxerit, tunc & loco amouendus, & virtutis tactura leui calo- re, vel repetita ad solem expositione reparanda. < 2.> Sunt qui præcipiant, summopere eauendum vello modo dum puluis conficitur, aut dum perfectus fuerit, adhibetur, ferro præsertim æruginoso rangatur, nec id superstitiosum esse crediderim, vt alij arbitrantur: quandoquidem hoc ei insitam facultatem, vt in aliis rebus videre est, adimere potest. Sic Vinum in vase cupreo diu asseruatum veneficam qualitatem induit: sic etiam lac, & alta huiusmodi ex simili con- tagione rabescunt. < 3.> Et hæc est sympathici pulueris præparatio, qui vulneribus quibuscumque quæ nullam ossium fracturam, aut scissuram admiserint est ideoneus: quod si adhuc aliqua ossis fractura, conrusio, aut quæuis læsio intercesserit, tunc addatur ei aliquid sarcocollæ, gummi arabici, aut tragacanthæ vel vt alij malunt symphitti maioris ad vmbram desiccati atque in puluerem redacti: quorum quodlibet ossium consolidationi, se solo, aut cum aliis applicatum, scimus conducere. < 4.> Eius vsus hic est ex Papinio. Vulneribus recentibus, & quibus adhuc emanat cruer immorgitur linteum mundum, id- quo vel ex lino, vel ex cannabe confectum: Cuius loco suffe- A iii

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On Sympathy. 5 <11> Before we come to the examination of the matter, it will be best first to explain what sympathetic powder is, what it is made of, and by what method it is prepared: for once this is understood, it will be easier for us to inquire into its virtue, and in what way, for the cure of wounds, even when applied not immediately to the wound, it may be of service. Therefore sympathetic powder (so called because, since the force by which it acts is not clearly known, it is believed to emanate from some hidden consent and sympathy of things) is made from Calchanthum, or, as it is commonly called, Roman vitriol, which, after by several dissolutions in clear water, filtrations through emporetic paper, evaporations at the fire, and repeated coagulations, as the pyrotechnic art teaches, has been purified from its feculent dregs and attained the deepest greenness, is beaten somewhat coarsely, and for about fifteen, or eighteen days, is exposed while the sun is most intense in the month of July or August, so long as it is in Leo, until, calcined by the power of the sun, it comes to the highest purity and whiteness. Thereafter, for use, it should be kept in a suitable place, that is, of a drier temperature. If by chance, either while it is being prepared the weather be cloudy or rainy, or when it is already finished and is stored, it has grown stale again from the dampness of the place, whether inherent or acquired from outside, and has taken on some moisture, then it must both be removed from that place, and the loss of its virtue restored by gentle heat, or by repeated exposure to the sun. <2.> There are those who prescribe that great care must be taken, either while the powder is being made or when, once finished, it is used, that it not be touched by iron, especially rusty iron; nor would I think this superstitious, as others suppose: since it can take away from it the natural faculty, as is seen in other things. Thus wine long kept in a copper vessel acquires a poisonous quality; thus also milk, and other such things, are made angry by a similar contact. <3.> And this is the preparation of sympathetic powder, which is suitable for any wounds that have admitted no fracture or splitting of the bones; but if some fracture of bone, contusion, or any other injury has occurred, then let there be added to it some sarcocolla, gum arabic, or tragacanth, or, as others prefer, greater comfrey dried in the shade and reduced to powder: any of which, applied by itself or with others, we know to be useful for the consolidation of bones. <4.> Its use here is from Papinius. For recent wounds, and those from which blood is still flowing, a clean linen cloth is soaked, that is, one made either of flax or of hemp: in place of which suffe- A iii

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6 PHYSIO-THEOLOGICA cerit panni quodlibet genus, vel solida ferè qualibet substantia, donec fluente ex parte sanguine intingatur: huic insper- gendus puluis, & alio panno cuncta inuoluta simul asseruen- tur loco temperato, eoque vel vicino, vel quamtumuis remo- to à patiente. Præstat tamen moderata loci intercapedo. Sin vulnus iam inueterauerit, & in vlcus degeneraris, eodem prorsus modo materia ex affecta parte manus, siue pus, siue sanies fuerit, linteo committera, aspergenda puluere, & sedulo asseruanda. Tum vulnus vino tepido priùs ablutum panno minimè sordido obtegendum est, & pannus nouus, ac mundus alternis diebus, vel sapius, provt manantis sordi- tice copia exquirere videbitur, pro inquinato mutandus est. Sordidi autem panni si mul coaceruandi sunt in loco pariter media temperatura. Non est tamen quod puluere inspergan- tur, nec vulnus plusquam semel vine abluere necessum est: quinetiam hoc multi omittunt. 5. Nota autem, quod si vulnus exterius fuerit, sufficiet per- mittere, vt sanguis effluat in pannum: sin interiores etiam partes affecerit, ipsi penitius immittendus est pannus, vt lasam pariter attingat partem. 6. Nota secundò, quod quocunque modo inflictum vulnus fuerit, eadem sit pulueris virtus. Non enim hic locum obtinet, quod Sennertus lib. pract. 1. cap. 10. partis quarta in vnguentum armarum obiicit, quod nullus, qui de eo scripserit, au- sus sit vim eius ad illata à sclopetis vulnera extendere. Quini- mò eiusmodi vulnerum ipsius pulueris ope persanatorum inse- gnia mihi non desunt experimenta, quæ multorum fides con- firmat. 7. Nota, denique, loco mutanda esselintea, illud præsertim sanguine, & puluere aspersum, provt pars intemperie tenta- tur. Sicalida enim intemperies partem innaserit loco frigi- diori, & humidiori asseruari debent, velut sub terra, seu in- clusa pyxide ex electro, aqua aut niue mergantur, donec pars elapsam nacta sit temperaturam: si verò frigida discretia partem occupauerit, locus temperie contrarius pannis asser- uandis deligendus est. Hac de vulnere simplici. 8. Si vulnus ossium fracture complicatum sit, fragmenta fo- ras educenda sunt quæcumque periosteo nudata fuerint. Sin verò fracture aqualis, vt in speciebus qua dicuntur Caule- don, & Praphanodon; vel contrita ossium particula periosteo adhuc cohareant, vulnere priùs sympatheticè curate, pars hypodesmidibus, epidesmidibus, & assulis pro more deligan- da. & fuleienda est, admiscendo videlicet in curando vul- nere puluerem gummi tragacantha, alteriusve eiusdem na-

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6 PHYSIO-THEOLOGICA any kind of cloth, or almost any solid substance, until it is moistened by the flowing blood from the wound: this powder is to be sprinkled on it, and everything wrapped together in another cloth is to be kept in a temperate place, whether near to, or however far from, the patient. Moderate distance, however, is preferable. But if the wound has already become old and has degenerated into an ulcer, the matter from the affected part—whether it be pus or sanies—should in exactly the same way be committed to linen, sprinkled with the powder, and carefully preserved. Then the wound, first washed with lukewarm wine, must be covered with a cloth that is by no means dirty, and the cloth must be changed every other day, or more often, as the amount of flowing discharge seems to require, for a soiled one. Dirty cloths, however, if they are to be stored together, should likewise be kept in a place of moderate temperature. Yet there is no need that they be sprinkled with the powder, nor is it necessary to wash the wound with wine more than once; indeed many omit even this. 5. Note, moreover, that if the wound is external, it will be sufficient to allow the blood to flow out into the cloth; but if the internal parts also have been affected, the cloth must be inserted more deeply, so that it may touch the injured part as well. 6. Note secondly, that in whatever way the wound has been inflicted, the virtue of the powder is the same. For here there is no place for what Sennertus objects in lib. pract. 1, cap. 10, part 4, to the unguentum armorum, namely, that no one who has written about it has dared to extend its power to wounds inflicted by firearms. Indeed, I am not lacking in notable experiments of such wounds healed by means of this powder alone, which the testimony of many confirms. 7. Note, finally, that when the cloth is to be changed, especially the one sprinkled with blood and powder, it should be done according to the temperament by which the part is affected. Thus, if a hot temperament has taken hold of the part, the cloths should be kept in a colder and moister place, as under the earth, or enclosed in a box of electrum, and should be dipped in water or snow, until the part has recovered the temperature it has lost; but if a cold disorder has occupied the part, a place of a temperament contrary to that should be chosen for preserving the cloths. Thus far concerning a simple wound. 8. If the wound is complicated by a fracture of the bones, whatever fragments have been laid bare by the periosteum must be taken out. But if the fracture is level, as in the kinds called Cauleodon and Praphanodon; or if a crushed particle of bone still adheres to the periosteum, then, after the wound has first been treated sympathetically, the part must be bound and supported with hypodesmids, epidesmids, and splints, as is customary, by also mixing into the treatment of the wound the powder of tragacanth gum, or of some other of the same nature...

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DE SYMPATHIA. 7 tura, aqua vel media quantitate, vt superius dictum est. Hæc ille. Et hæc Pulueris sympathici præparatio & vsus, licet mul- < 98> ti ipsum Calchanthum nullo adhibito apparatu, sed quale nobis à Natura suppeditarur, atque in officinis venale pro- stat, prospero eueniu vsurpasse asseuerenti. Quod sanè si ve- rum est, oportet, vt vulnus non ita graue fuerit, vt non potuerit immediatè à natura absque vllo adiumento curari. Sed de hac re nobis non est disceptatio, quærimus enim de illis vulneribus, quæ cum profunda sint, ingenia, atque periculosa, sola natura absque extrinsecis adiumentis ad eorum peruicaciam superandam impotens inuenitur, in quo casu nullius ferè virtutis simplex Vitriolum, sed totam eius virutem à præparatione, astralique vi, per iugem Illam ad solem expositionem communita, pendere credunt omnes, quotquot sunt sympathici pulueris assertores. Et quidem quoad eius efficaciam, & vim planè admirabi- < 103> lem in vulneribus protinus consolidandis nemo est qui ear insicias; id enim iugis probat experientia: At enim nùm id naturali virtute fiat, an potiùs cacodæmonis astu; maximè controuersum est. Detestâtur eum tanquam superstitiosum, infandum, perniciosum ex Medicis ac Philosophis multi, Andreas Libauius, Sennertus, Naudæus, atque eruditissi- ma ad me transmissa lucubraione doctissimus vir Liuius Ignatius de Comitibus; quorum aliqui licet de Vnguenio armario agant, & in ipsum potissimum inuehantur, quia ta- men vniuersim curationem sympathicam omnem euertere satagunt, proinde etiam aut explicitè aur implicitè de pul- uere nostro etiam obloquununt. Ex Theologis verò Mari- nus Deltio disquisition. magic. lib. 3. cap. 5. Ep 6. Athana- sius Kircherus in Arte Magnetica lib. 1. par 7. cap. 2. Bona- cina disp 3. quæst. 5 puncto 4. n. 17. Iann. Roberti in acri dis- ceptatione, quam de hac re suscepit aduersus Crolium, & Goclenium, Hermannus Busembaum in Medulla Theologia moralis lib 3. tr. 1. dub. 4. & alij, quos refert & sequitur An- tonius Diana Clericus Regularis, vir de quo iure nescias an ei magis orbis debeat, quam ipse orbi: part 11. tract. 4. resol. 42. In hanc partem inclinat etiam Tamburinus in De- cal. lib. 7. cap. 6 num. 77. licet paulò ante num. 63. pro na- turali pulueris, & Vnguenti Armarij actiuitare hæc dixisset. Sicut video à magnete ferrum trahi, cognosco virtutem tra- bendi; ita quia video sanitatem fieri à gladio solis naturali- bus medicamentis peruncto, colligo virtutem illis occultam inesse agrum absentem sanandi. E contrà viriliter ipsum pto- a iiiij

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of sympathy. 7 texture, water, or a medium quantity, as was said above. This he said. And this is the preparation and use of the sympathetic powder, although many affirm that they have employed the Calcanthum itself with no apparatus at all, but just as Nature supplies it to us and as it is sold in the shops, with successful outcome. If this is true, then it must be that the wound was not so severe that it could not have been cured immediately by nature, without any help. But on this matter we are not disputing, for we are asking about those wounds which, being deep, dangerous, and perilous, are found to be beyond the power of nature alone to overcome their obstinacy, without external aid; in which case all who defend the sympathetic powder believe that simple vitriol has hardly any virtue of its own, but that its whole power depends on the preparation and astral force conferred by that continual exposure to the sun. And indeed, so far as its efficacy and plainly admirable power in immediately healing wounds are concerned, no one denies it; daily experience proves this. But whether this comes about by a natural power, or rather by the craft of the cacodemon, is most disputed. Many of the physicians and philosophers detest it as superstitious, unspeakable, and harmful: Andreas Libavius, Sennertus, Naudæus, and the very learned Livio Ignazio de Comitibus, whose most learned treatise was sent to me. Some of these, although they speak about the Unguentum Armarium and attack it chiefly, nevertheless since they strive to overthrow all sympathetic healing in general, therefore also speak against our powder, either explicitly or implicitly. Among theologians too, Marinus Deltio, Disquisit. magic. lib. 3, cap. 5, Ep. 6; Athanasius Kircherus, in Arte Magnetica lib. 1, par. 7, cap. 2; Bonacina, disp. 3, quaest. 5, puncto 4, n. 17; Iann. Roberti, in the sharp disputation which he undertook on this matter against Crollius and Goclenius; Hermannus Busembaum, in Medulla Theologiae moralis lib. 3, tr. 1, dub. 4; and others, whom Antonius Diana, a Regular Cleric, cites and follows—a man of whom one can hardly know whether the world owes more to him, or he to the world: part 11, tract. 4, resol. 42. Tamburinus also inclines to this side in Decal. lib. 7, cap. 6, no. 77, although shortly before, at no. 63, he had said this in favor of the natural activity of the powder and of the Unguentum Armarium: “As I see iron drawn by the magnet, I recognize a power of drawing; so because I see health effected by the sword of the sun, when medicinal substances have been anointed with it, I conclude that there is in them a hidden power of healing a distant sick man.” On the other hand, vehemently the same pro- a iiii

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PHYSIO-THEOLOGICA pugnat ex Medicis Carolus Rapinius peculiari libello edita de Puluere sympathico. Ioannes Baptista Helmont. Daniel Becherus, Fabritius Hildan, Basilius Valentinus, Ioannes Vritichius, Ioann. Baptista Sitonus, & alij. Ex Theologis verò admittit Paulus Vecchi in obseruationibus Medicis in sacram script. obseru. 60. pro vtraque parte rationes affert Illuminatus Moronus in respons. moral. resp 95. n. 167. sed præ omnibus defendit Bertrandus Loth. Dominicanus in tesolut. Theolog. tr. 14. quast. 1. art. 3. Ioan. Petrus Crescentius in Prasia. Rom. lib. 3. in num. 113. & Ignatius Lupus in edictum sancta inquisit. pars. 3. lib. 19. quibus etiam tam pro Philo- sophis, quam pro Theologis meritò annumerandus est. P. Nicolaus Cabæus de Meseoris lib. 4. text. 4. quast. 2. qui ex occasione in hanc eurandi vulnera methodum per sym- pathiam in quacumque distantia incidens hæc haber. Sunt aliqui effectus de quibus videtur ab aliquibus dubitatum, vtrum absoluant omninò à medio, vt est illa ratio medenda vulneribus, qua vulnera curantur applicando medicinam crustis sanguino infectis: dicunt enim sic curari vulnera in quacumque distantia equaliter. Nec res omninò superstitioni obnoxia censeri debet: nullus enim intervenit actus religionis, nec vera, nec falsa; nec medicamentum ipsum ullam habet speciem falsi cultus: est enim omninò simplex medicamentum, omninò simplici modo applicatum, neque ex eo quod causam ignores debes statim damoniacum exclamare; quasi verò om- nia noueris naturalia, & sint in te omnis sapientia apices transfusi. Hæc illi: quæ omnia, addiâ tantorum virorum, qui pro naturali pulueris efficientia stant, authoritate, satis sunt, ad aliquam saltem probabilitatem ipsi conciliandam. Ego verò hic non subsisto; sed in primo limine hærens, si- denter me ostensurum spondeo, absolutè liberum cuique esse pulueris sympathici, omnisque magneticæ curationis vsum, in idque vel adversarios ipsos ex suismet principiis debere conuenire. < II.> Moueor quia commune est Theologorum omnium axio- ma. vt quandocumque dubitatur an effectus sit superstitio- sus, an naturalis à causa naturali etsi nobis ignota proue- niens, censendus semper est naturalis, idque ex eo quia no- bis non notæ sunt omnes naturæ vires, omnes lapidum, mi- nervalium, herbarumque virtutes, modusque & celeritas ope- randi: quandoquidem vt author est Plinius Multa sunt Na- tura miracula incomperta adhuc rationis, & in Natura ma- iestate penitus abdita. Ergò fieri potest, vt effectus sit natu- ralis. & nobis in comperta sit eius causa: possessio enim stat

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PHYSIO-THEOLOGICA fought against by the physicians: Carolus Rapinius in a special booklet published On Sympathetic Powder. Ioannes Baptista Helmont. Daniel Becherus, Fabritius Hildanus, Basilius Valentinus, Ioannes Vritichius, Ioann. Baptista Sitonus, and others. Among theologians, however, Paulus Vecchi admits it in Medicae observations on Sacred Scripture, observ. 60. He gives arguments for both sides; Illuminatus Moronus in Respons. moral. resp. 95, n. 167. but above all Bertrandus Loth., Dominican, defends it in Resolut. Theolog. tr. 14, quast. 1, art. 3. Ioan. Petrus Crescentius in Prasia. Rom. lib. 3, no. 113, and Ignatius Lupus in edictum sanctae inquisit. pars 3, lib. 19, among whom he must also with good reason be counted both among philosophers and among theologians. P. Nicolaus Cabæus, de Meseoris lib. 4, text. 4, quast. 2, who on this occasion says the following concerning this method of healing wounds by sym- pathy at whatever distance: “There are some effects about which it seems some have doubted, whether they altogether put superstition out of the way, as is that method of healing wounds, by which wounds are cured by applying medicine to blood-stained crusts; for they say that wounds are thus cured at whatever distance, equally. Nor should the matter be judged altogether subject to superstition: for no act of religion intervenes, neither true nor false; nor does the medicine itself have any appearance of false worship: for it is wholly a simple medicine, applied in a wholly simple manner; and from the fact that you do not know the cause, you should not at once cry out demonic, as though you knew all natural things, and all wisdom had been poured into you. Such are his words: all which, together with the authority of so many men, who stand for the natural efficacy of the powder, are sufficient to secure for it at least some probability. But I do not stop here; rather, lingering at the first threshold, I confidently promise to show that it is absolutely free for anyone to use sympathetic powder and every magnetic cure, and that even the opponents themselves ought to agree to this from their own principles. <II.> I am moved because it is a common axiom of all theologians, that whenever it is doubted whether an effect is superstitious, or natural, arising from a natural cause though unknown to us, it must always be judged natural; and this because all the powers of nature are not known to us, all the virtues of stones, minerals, and herbs, and the manner and speed of their operation: since, as Pliny says, there are many miracles of Nature still unknown to reason, and hidden deep within the majesty of Nature. Therefore it is possible that the effect is natural, and that its cause is unknown to us: for possession stands

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DE SYMPATHIA. 9 pro Natura, cuius intima penetralia explorare licitum est. Secùs autem dicendum, quando constat effectum naturæ vires transcendere; nam tunc præsumendum estesse à Dæmonne, nisi forte talia indicia adsint, vt iure iudicetur esse à Deo, aut à bono Angelo. Ita Lessius, Suar. Sanchez, Del- rius, & alij, quos refert & sequitur idem Bonac. supra n. 9. & Castro Palaus de superstitione disp 1 punto 10. num. 2. Sed an huiusmodi curatio per sympathiam, applicando pul- uerem sympathicum linteis sanguine madefactis sit naturalis neene, maxime controuertitur inter DD. in vtroque ge- nere expertissimos, ita vt multi Philosophi ac Theologi af- firment multi etiam negent. Ergò in maxima dubietate res constituta est, nec eo vsque deuentum, vt iam constet effe- ctum hunc naturæ vires translire, adeoque superstitiosum esse. Si igitur in dubio res posita est, vtique effectus cura- tionis in nostro casu censendus est naturalis, quia in dubio melior est conditio possidentis, & possessio stat pro Natura. Quare appositè ad hanc rem inquit Caramuel lib. 3. Theolog. Moral. num. 1381. Si quid rarum vides, gratias age Natura Conditori. Potentissimus potententissimum condidit: hoc sup- pono. Sub latere aliquod pactum, aut Damonis interuentum quovisque videam euidenter, non credam. Confirmatur, quia multos effectus in Natura huic prorsus consimiles, ex occulta sympathiæ vi productos videmus; quos tamen Dæmoni ascribere ineptum foret, cum nullus finis ad eosdem patrando illum mouere possit: ergò si isti na- turales sunt, quamuis vera causa, & modus operandi sit no- bis ignorus, & ille rationabiliter naturalis censendus est. Antecedens patet inductione. Nam si, vt suprà dictum est, suprà hominis fæces adhuc fumantes cinis calidus insperga- tur, mox alius deieitur & sanguis cum excrementis effertur. Si molæ foeminarum, secundinæ, aut primus sanguis men- struus sordido loco abiiciantur, aut inclementius tractentur, illæ mox gravissima symptomata patiuntur, vt author est, ex aduersariis ipsis, Sennertus. Si mulier ab lactans infantem in prunas ardentes lac emulgeat, statim illi vbera sterilescent: si verò lac in mammis multiplicare velit; à foemina lacte ple- na demorsum quid ipsa manducer, statim occulta naturæ vi, lac, ex illius vberibus ab ipsam transit: Si dum oua, quibus gallina incubat, & iam pulli exclusioni sunt proximi, in eadem domo, vel vicinia ouum aliquod assetur, illicò quæ excubantur, per sympathie vim deperduntur, vt testatur Kircherus in Arte magnetica. Et si demum hæc, est similia imaginationi potius tribuas, quam rerum consensioni, pro-

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OF SYMPATHY. 9 for Nature, whose innermost recesses it is lawful to explore. But the contrary must be said when it is established that the effect transcends the powers of nature; for then it must be presumed to be from the Devil, unless perhaps such signs are present that it may rightly be judged to be from God, or from a good Angel. So Lessius, Suárez, Sanchez, Delrio, and others, whom the same Bonacina cites and follows above, no. 9, and Castro Palaus, On Superstition, disp. 1, point 10, no. 2. But whether this kind of cure by sympathy, by applying sympathetic powder to linen soaked with blood, is natural or not is most disputed among the most expert doctors in both fields, so that many Philosophers and Theologians affirm it, and many also deny it. Therefore the matter is in great doubt, nor has it yet been reached that it is certain this effect goes beyond the powers of nature, and therefore is superstitious. If, therefore, the matter is in doubt, then in any case the effect of the cure in our case must be judged natural, because in doubt the condition of the possessor is better, and possession stands for Nature. For this reason Caramuel aptly says on this matter, lib. 3. Theolog. Moral. no. 1381: If you see anything rare, give thanks to the Creator of Nature. The most powerful one created the most powerful: I grant this. If I see some pact beneath the surface, or the intervention of a Demon, however clearly, I will not believe it. This is confirmed because we see many effects in Nature altogether like this, produced by the hidden power of sympathy; yet it would be foolish to attribute them to the Devil, since no end in bringing about the same could move him: therefore if these are natural, although the true cause and mode of operation are unknown to us, that one too must reasonably be judged natural. The antecedent is clear by induction. For if, as was said above, warm ashes are sprinkled over a person's still-smoking excrement, another person is soon struck down and blood is carried off with the excrement. If a woman's millstones, afterbirth, or first menstrual blood are thrown into a filthy place, or handled harshly, she soon suffers the gravest symptoms, as is stated by Sennertus himself, among the opponents. If a nursing woman, while the infant is being suckled on burning coals, draws milk from her breasts, at once those breasts become dry: but if she wants to increase the milk in her breasts, and what she herself eats is bitten from a woman full of milk, then immediately, by the hidden power of nature, the milk from that woman's breasts passes to her. If, while eggs in which a hen is sitting, and from which the chicks are already close to hatching, are in the same house or neighborhood, some egg is roasted, immediately those under incubation are destroyed by the power of sympathy, as Kircher testifies in the Magnetic Art. And if at last you would attribute these and similar things rather to imagination than to the agreement of things, pro-

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10 PHYSIO. THEOLOGICA bemus id etiam in rebus inanimis. Nam si panibus in elibano existentibus, & semicoctis sumptam inde placentam manibus vel cultro eousque seideris, vt suam formam deperdat, mox alij quantumuis dissiti per sympathiam, & miram naturæ consensionem læduntur, & integra crusta à mica diuellitur; vt author est idem Kircherus, & ego semel, & iterum obseruaui. Cythara æquè cum altera tensa ad eius contactum resonat etsi longiùs constituta, modò tamen sonus ad ipsam perueniat. Maculæ, & sordes in linteis ex pomorum succo eótractę nùquam absterguntur quoadusque ex arboribus, à quibus decerpta sunt folia decidant, & tunc absque vllò prorsus humano artificio. Vinea efflorente, vinum in dolijs fluctuat, &c. quæ abunde congerit Kircherus, & Porta iu sua Magia Naturali. Si ergò in his & similibus nulla Daemonis operatio intercedit, sed omnia a Natura fiunt, neque in vulnerum curatione per sympathiam superstitio intercedet: cum vtrobique eadem difficultates militeut, eadem operatio in distans conspiciatur. 13. Accedit quod quæ in hac mira vulnerum curatione adhibentur, non sunt prorsus inutilia, nec aliàs curationi non conferunt: nam Vitriolum, ex quo puluis sympathieus conficitur, seipso sanguinem sistit, putredini & puris generationi obest; & alia mira præstat, quæ habent eius naturæ scriptores, & passim Medici experiuntur. Non ergo prorsus inane est, si probè compositum, & omni fæce purgatum non vulneri, sed sanguini è vulnere scatenti applicetur, sieque effectum habeat tam mirabilis curationis faciendæ. 14. Dices ex Diana, Bonacina & aliis. Si puluis vlla naturali virtute polleret, vtique proximè vulneri applicatus, eundum effectum pareret: at tantum abest, vt profit ad sanitatem, vt potiusnecem indueat & afferat interitum: tum si naturaliter operaretur, admixto illi veneno malè haberet infirmus, quod est falsum. Ergo signum est, quod si quid agit, agit ope demonis implorata, non quatenus vllam virvirtutem naturalem contineat. Hoc argumentum Bonacina, ex hoc capite præcisè debile videtur quia multa sunt agentia naturalia, quæ non producunt effectum, nisi in determinata distantia, quem non producunt immediatè applicata subiecto, vt patet in sensibili, quod positum supra sensum non facit sensationem: vnde id etiam contingere potest in nostro casu. Verum hæc responsio non infringit obiectionis robur, quia agentia quæ operantur per contactum quencumq[ue] quò fuerint proximiora passo eò validiùs agunt, & fortius per contactum immediatum, quam per mediatum

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10 PHYSIO. THEOLOGICA We observe this also in inanimate things. For if, in the oven, among loaves that are in the process of baking and are half-cooked, you cut with your hands or with a knife a cake taken from them so that it loses its shape, soon the others, however far away, are injured by sympathy and by the wondrous agreement of nature, and the whole crust is torn from the crumb; as the same Kircher relates, and I myself have observed once and again. A cithara, equally with another one stretched, resounds at its contact, though set farther away, provided however that the sound reaches it. Spots and stains on linens produced from apple juice are never wiped away until the leaves have fallen from the trees from which they were plucked, and then without any human artifice at all. When the vine blossoms, the wine in the casks stirs, etc., things which Kircher and Porta in his Magia Naturali abundantly collect. If therefore in these and similar things no operation of a demon intervenes, but all things are done by nature, then in the curing of wounds by sympathy superstition will not intervene either: since in both cases the same difficulties prevail, and the same action at a distance is observed. 13. There is also this addition: the things employed in this marvelous curing of wounds are not altogether useless, nor do they otherwise fail to contribute to healing. For vitriol, from which the sympathetic powder is made, by itself stops blood, is harmful to putrefaction and the generation of pus, and performs other wonderful effects, which writers on its nature record, and physicians everywhere experience. Therefore it is not altogether empty, if, properly compounded and purged of all sediment, it is applied not to the wound, but to the blood flowing from the wound, and thus has the effect of accomplishing so marvelous a cure. 14. You will say from Diana, Bonacina, and others: if any powder possessed a natural virtue, then when applied close to the wound it would surely produce the same effect; but so far from helping health, it rather brings death and destruction. Then if it acted naturally, the poison mixed with it would cause harm to the patient, which is false. Therefore it is a sign that, if it does anything, it acts by the aid of a demon invoked, not insofar as it contains any natural virtue. Bonacina seems to think this argument, from this head precisely, weak, because there are many natural agents which do not produce an effect unless at a determinate distance, and which do not produce it when applied immediately to the subject, as is clear in the sensible object, which, if placed above the sense organ, does not produce sensation: whence this too can happen in our case. But this reply does not break the force of the objection, because agents which operate by contact, however much the nearer they are to the patient, the more powerfully they act, and more strongly by immediate contact than by mediated contact.

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DE SYMPATHIA. 11 & virtualem, vt patet inductione: ea verò, quæ opeatur per immissas species in potentiam requirunt determinatam distantiam, & de his verificatur axioma illud allatum, vt videre est in sensibus auditus, odoratus, & visus. Hîc autem si puluis sympathicus agit per contactum (neque enim aliter intelligitur operari) vtique maiores vires exeret immediatè vulneri applicatus, quam sanguini, per quem concipitur mediatè virtus eius in vulnus transire. <15.> Respondetur igitur meliùs ad argumentum, id verum concludere, quod scilicet puluis fortius agit immediatè vulneri applicarus, quam sanguini, sed ea viiique virtute agir, quæ nimietate sua ægro noxia sit, & maximè violenta, sanguini autem dissito applicatus temperata, lenior, & opportuna. Sic ignis à longè naturam fouet, proximè admotus vrit. Sic Venenum, sic medicamenta nimis violenta præstant. Non igitur mirum, si puluis sympathicus proximè vulneri applicatus, quia nimium violentus, illud exasperet, & grauia inducat symphomaia, qui tamen non vulneri, sed sanguini applicatus prodest; cum tunc non sit ita Naturæ conjunctus. <18.> Ad confirmationem negatur item assumptum, quia vt supra dicebamus, si ferro puluis tractetur inficitur, & curationi euadit incongruus, & fortè etiam perniciosus, quantò magis, si venenum admisceatur? Quod ideò vel ob id à sacra Congregatione, (dum res coram ipsa agitabatur) prouisum reor, vt hæc curatio non nisi à piis ac doctis viris perageretur: Nam catenus, etiam officere potest, quâ prodesse puluis à probo Naturæ inspectore ac sympathiæ, antipathiæque rerum callido speculatore tractatus. Quod autem venenum solum, aut aliud quid sanguini applicarium naturæ non noceat, noceat autem admixtum pulueri, sicut etiam quod solus puluis, aut vnguentum consimile virtutem habeat naturam afficiendi, hoc profectò est quod miramur atque in occultam sympathiæ antipathiæque vim refundimus. Ná similiter peto ego. Curlac cænoso loco emulsum lactenti minimè obest, obest autem si iactetur ad ignem? è contrà secundinæ & primus sanguis menstruus cænoso loco deiectus lædat, minimè verò si in profluentem, aut in ignem deijciatur; Quare cantharides manu detentæ vesicam exulcerant, minimè verò manum, exterasque corporis partes, per quas transeat ad inferiora necesse est vis venefica? Quare ad syluestrem vrticam mingens vrinæ ardorem contrahit, non autem si ad napellum, aconitum, aut pessimam quamuis herbam? & vt ad notiora deueniamus, quate iu-

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and virtual, as is evident by induction: but those things which operate through introduced species in the power require a determinate distance, and of these that axiom which has been brought forward is verified, as may be seen in the senses of hearing, smell, and sight. But here, if the sympathetic powder acts by contact, for otherwise it cannot be understood to operate, certainly it will exert greater force when applied immediately to the wound than to the blood, through which its virtue is understood to pass mediately into the wound. <15.> Therefore the answer is better to the argument, that it concludes what is true, namely, that the powder acts more strongly when immediately applied to the wound than to the blood, but it acts with such force as is harmful to the sick person by its excess and most violent nature; but when applied to the blood at a distance, it is moderate, gentler, and suitable. Thus fire at a distance warms nature, but when brought near it burns. Thus poison does so, thus do medicines that are too violent. It is therefore no wonder if sympathetic powder, when applied near the wound, because it is too violent, aggravates it and produces serious symptoms, though applied to the blood it is beneficial; since then it is not so closely joined to Nature. <18.> In confirmation, the assumption is likewise denied, because, as we said above, if the powder is handled with iron it is infected, and becomes unfit for curing, and perhaps even harmful; how much more so if poison is mixed into it? For this reason, I think, or on account of this, the Sacred Congregation, when the matter was being debated before it, provided that this cure should be performed only by pious and learned men: for even so it can do harm, whereas the powder, handled by a trustworthy observer of Nature and a skilful investigator of the sympathies and antipathies of things, can do good. But that poison alone, or something else applied to the blood, does not harm nature, but does harm when mixed with the powder; just as also the powder alone, or a similar ointment, has the power of affecting nature—this, indeed, is what we wonder at and refer to the hidden force of sympathy and antipathy. For similarly I ask: why does milk drawn into a muddy place do no harm, but does harm if it is thrown into fire? On the other hand, why do the afterbirth and the first menstrual blood, when cast on a muddy place, do harm, but do not harm if they are thrown into a flowing stream or into fire? Why do cantharides, held in the hand, blister the bladder, but not the hand and the other parts of the body, through which the venomous force must pass to reach the lower parts? Why, when one urinates on a wild nettle, does the urine contract a burning, but not if one urinates on monkshood, aconite, or any other bad herb? And, to come to better-known matters, why do we-

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18 PHYSIO. THEOLOGICA, glandis vmbra dormientibus obest, minimè autem cætera- rum arborum, & quidem cætera noxiarum? Quare cicuta hominem interficit nimia frigiditate, non autem potus in summo frigidæ? ver cæteris animantibus nocet, non autem asino aut sturnis? Equidem hæc omnia in rerum naturam sunt refundenda, quæ aliquo sympathiæ, antipathiæque ne- xu sint colligatæ, minimè verò in cæteris. Sic igitur ve- nenum talis naturæ est, vt non nisi proximè applicarum no- cear, minimè verò rebus in natura connexis; at si pulueri admisceatur, quod talem virtutem habet, vtique illum al- terat, arque ab illo repatitur, itavt per illum postea quasi per quoddam vehiculum eius venefica qualitas transmitta- tur in vulnus, adeoque noceat. Sed de hac re fusiùs in ter- tia quæstione. 17. Obijcies vnumquodque agens operatur in determinata sphæra suæ activitatis, itavt extra eam non agat, & ea per obicem interrupta nequeat virtutem suam exerere, vt patet in magnete quod ferrum non attrahit nisi in determinata distantia, & si paries interponatur, non vtique poterit illud attrahere. Ergò si puluis naturaliter operaretur, id habe- ret in determinata distantia, & eò fortius operaretur, quò proximior; & constitutis in medio parietibus impediretur eius actio, quæ vrpote realis exeri debet per quendam con- tactum aut immediarum, aut mediatum: sed puluis eque agit in quacumque distantia, & interjecto quecumque obi- ce: ergo signum est, quod non naturaliter, sed virtute Dæ- monis agat. 18. Respondetur imprimis, hoc argumentum militare etiam contra alia experimenta, in quibus certum est Dæmonem nullatenùs se ingerere. Nam, vt cætera præteream, ad fo- liorum ex arboribus decisionem tam probè exterguntur ma- culæ à linteis longè constiutis, quam propè, tam si quid fue- rit intermedium, quam si non efflorente vinea vinum in do- lijs fluctuar quantumuis dissitum, & multis parietibus in- terjectis, &c. Si igitur in his, & similibus non officit di- stantia atque interjectus obex, nil mirum, si neque in nostri pulueris efficientia. 19. Respondetur secundò: quodlibet agens, quod agit per contactum seu immediatum, seu mediatum, seu etiam per immissionem specierum, alituum, aut corpusculorum, re- quirere determinatam distantiam, & per interiectionem obici sediri; secùs autem ea, quę agunt occultâ qua- dam vi, & planè imperceptibili. Exemplo sint, quę modò adduximus, experimenta: Exemplo sit sol à Bonacina in

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18 PHYSIO. THEOLOGICA, The shade of the acorn tree is harmful to those sleeping beneath it, but not at all that of other trees, and indeed not of other harmful things? Why does hemlock kill a man by excessive coldness, but not a drink at the height of cold? Why does spring harm other living creatures, but not the ass or starlings? Indeed, all these things must be referred to the nature of things, which are joined together by some bond of sympathy and antipathy, and not at all to others. Thus, therefore, poison is of such a nature that it harms only things applied nearby, and not at all things connected in nature; but if it be mixed with dust, which has such a power, it certainly alters it, and is in turn affected by it, so that through it afterward, as through some vehicle, its poisonous quality is transmitted into the wound, and thus does harm. But more about this in the third question. 17. You object: each agent operates within a determinate sphere of its activity, so that outside it it does not act, and if that sphere is interrupted by an obstacle it cannot exert its power, as is clear in the magnet, which does not attract iron except at a determinate distance; and if a wall be placed between, it certainly will not be able to attract it. Therefore, if dust acted naturally, it would have this effect at a determinate distance, and would act all the more strongly the nearer it was; and if walls were placed in the middle, its action would be impeded, since, as a real thing, it ought to operate through some contact, either immediate or mediate: but dust acts equally at whatever distance, and with whatever obstacle interposed: therefore it is a sign that it does not act naturally, but by the power of the Demon. 18. It is answered first that this argument would also apply against other experiments in which it is certain that the Demon does not in any way interfere. For, to pass over the rest, stains are most effectively removed from linens laid far away by the falling leaves of trees, just as when laid near, whether something lies between or not; and wine in casks, not yet fermenting, may be agitated however far away, even with many walls interposed, etc. If therefore in these and similar cases distance and an intervening obstacle are no hindrance, it is no wonder if they do not hinder the efficacy of our powder either. 19. It is answered secondly: every agent that acts by contact, whether immediate or mediate, or even by the emission of species, vapors, or corpuscles, requires a determinate distance and is held back by the interposition of an obstacle; but otherwise are those things which act by some occult and quite imperceptible power. As examples, let the experiments we have just mentioned serve: as an example, let there be the sun, according to Bonacina in

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DE SYMPATHIA. 13 fui sauorem allatus, qui, vt causa æquiuoca, & vniuersalis, plures effectus habet, & multiplicem operandi modum, alium nobis cognitum, alium incognitum. Sic lucem, calorem & his similia sol operatur modo nobis vtiq[ue] cognito, & eo pacto, quo ignis, & cætera luminosa intrà suam amplissimam sphæram, & eò ampliùs quò propius, aut rectius fiat ei passum; & si inter ipsum, & passum ponatur obex, impeditur actio illuminandi, aut calefaciendi: alios effectus habet sol, qui non hac regula mensurantur, & alium operandi modum nobis planè incomprehensibilem; producit enim aurum, & mineralia in visceribus terræ posito quocumque obice: dat animantibus vitam, siue e[ss]e longè sint, siue propè, siue ipse in nostro sit, siue in inferiori hemisphærio delitescat, & equè benè, siue nubibus tectus, siue ijs discussis. An autem & in his casibus operetur perl'contactum, ac transmittendo actiuitatem suam per medium, (quamuis in eo nil simile operetur) dubium est: affirmo ego, sed explicare non audeo. Incomperta adhuc rationis hæc sunt, inquit Plinius, & in Natura maiestate penitùs abdita. Quis non in Lunaria, in selenire l: pide, atque in conchilijs non demiretur lunares motus, & maculas? Lunares vices subeunt, & luna crescente crescunt, ea decrescente decrescunt. quorsum hæc actio? à Luna ne, an potiùs ex insita eorum natura? Si à Luna, quonam pacto hæc in minimis quibusque rebus exquisitissimè operatur, & non in alijs? Quomodò non eius actiuitati obest paries interjectus, quin imò & totus terrarum orbis, quando Luna inferius hemisphærium lustrat? Quomodò eius vim sentit selenites in serinijs, ac domorum penetralibus inclusa? Si immediatè, & ab intrinseca eorum ratione id procedit, quomodò ad operandum ex Lunæ motibus excitantur? Quomodò tam constanter eiusdem affectiones sequuntur? Quod bellè describit Marbodæus Poëta Gallus in selenite, sic inquiens: Lunares motus, & menstrua tempora seruat: Crescit enim Lunâ crescente minorque minutâ Efficitur, tamquam cælestibus anxia damnis. Pari igitur ratione poterit puluis sympathicus vulneribus opitulari, actionemque suam immediatè in sanguinem exerere atque inde in vulnus transmittere. Respondetur tertiò ad argumentum: nullam hîc, & in similibus casibus dari operationem intermediam, sed omnem immediatè fieri à natura rerum, modo quidem ineffabili, sed quem nos in tertia quæstione explicare conabimur. 21.

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I was led to the explanation of sympathy, which, as an equivocal and universal cause, has many effects and a manifold mode of acting, one known to us and another unknown. Thus the sun produces light, heat, and the like in a way certainly known to us, and in that manner in which fire and other luminous bodies act within their most ample sphere, and the more so the nearer or more directly the patient is placed to it; and if an obstacle is placed between it and the patient, the action of illuminating or heating is impeded. The sun has other effects that are not measured by this rule, and another mode of operating altogether incomprehensible to us; for it produces gold and minerals in the bowels of the earth, no matter what obstacle is placed there. It gives life to animals, whether they be far off or near, whether it be itself in our hemisphere or hidden in the lower hemisphere, and equally well whether covered by clouds or with them dispersed. But whether in these cases it acts by contact and by transmitting its activity through the medium, though in it nothing similar is produced, is doubtful: I affirm it, but I do not dare explain it. These things are as yet hidden from reason, says Pliny, and deeply concealed in the majesty of Nature. Who would not marvel, in lunar stones, in selenite, and in shells, at lunar motions and spots? They undergo lunar phases, and as the moon waxes they wax, and as it wanes they wane. Whence comes this action? From the moon, or rather from their inborn nature? If from the moon, by what means does it operate so exquisitely in the smallest things, and not in others? How does a wall placed between not hinder its activity, nay even the whole earth, when the moon illumines the lower hemisphere? How does the selenite feel its power when enclosed in cabinets and in the inner chambers of houses? If immediately, and if this proceeds from their intrinsic nature, how are they stirred to act by the motions of the moon? How do they so constantly follow its affections? This the Gallic poet Marbodus beautifully describes in the selenite, saying thus: It preserves the moon’s motions and monthly periods: For it grows with the waxing moon and becomes smaller at the waning, As though anxious under heavenly losses. In like manner, therefore, sympathetic powder may be able to aid wounds, and exercise its action immediately upon the blood and from there transmit it to the wound. A third reply to the argument is given: that in this case, and in similar cases, there is no intermediate operation, but that everything is done immediately by the nature of things, indeed in an ineffable manner, but one which we shall try to explain in the third question. 21.

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14 PHYSIO-THEOLOGICA < 22.> Probatur secundò nostrum assumptum. Nulla hic actio dæmonis rationabiliter præsupponi debet interuenire: ergò iota in Naturam vniuersale rerum principium refunden- da est Antecedens probatur, quia Dæmon est infensissimus humani generis hostis, qui Naturæ bonis potiùs nos spoliare adnitiùr, quam beneficijs cumulare. Si quos enim suis pollicitis allicit, eos, aut spè sua frustratos, sæpè deludit, aut magno cum fænore animam sibi præmium quærit. Testantur id sæpissimè historiæ, Nicolaus Remigius, ac Delrius in disquisitionibus Magicis. Non est igitur credendum, Dæmonem tantum bonum voluisse hominibus, per hunc puluerem impertiri, itavt vel ipse primitùs eius virtutem alicui sibi deuincto homini explicasset, qui posteà indefinitè esset omnibus hominibus profuturus, vel semper ipse immediatè curaionem perficiat, absque vll fænore graviorum; cum profectò multi sint, qui ignoranter, adeoque innocenter ipsum adhibeant, multi prudenter, examinatâ eius compositione, vsu, curatione, quæ vi vana, futilia & prorsus impertinentia non admittunt, quæque docti homines proband, multi demum in hac rerum dubietate omnem dæmonis opem reijciunt, potestantes explicitè se velle naturæ bonis vti, quatenùs purè naturalia sunt, non quatenùs Dæmon vll pacto se ingerat, &c. Non est ergò verisimile ipsum sine vll emolumento velle tot hominibus opitulari, & vel rejectum, & quando res omni culpa vacat curationem velle gratis impendere: alioquin stultus foret mercator, & sua beneficia osoribus, & ingrasi prodigeret. < 23.> Probatur tertiò: quia Curatio ista non est suprà Naturæ vires, nec talis, vt, quemadmodum à Dæmone intrà naturæ limites fieri posse supponitur, (non enim is quicquam suprà naturæ leges operari potest) ita etiam ab hominibus naturæ subsamulantibus, non æquè fieri vtcumque possit: ergo absolutè censenda est naturalis. Antecedens fusè probabitur in terria quæstione: Pro nunc satis sit à posteriori ex similibus effectibus naturaliter prodeuntibus illud solidissimè confirmasse. Neque nostra curatio maiores difficultates implicat, quam oscitatio ad alterius oris hiatus, macularum abstersio ad foliorum decisionem, oculorum lippitudo ad alterius lippientis aspectum subitò exurgens, chordarum consensus, &c. quæ tamen omnia naturalia sunt, & naturæ limites non transcendunt. Equidem, si das, per Dæmonem posse fieri curaionem hanc; dare etiam debes, posse, & ab ipsa natura; quæ, vt ait Hypocrates, ipsa est

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14 PHYSIO-THEOLOGICA < 22.> Secondly, our assumption is proved. No action of the demon should reasonably be presupposed here as intervening; therefore the whole must be referred to Nature as the universal principle of things. The antecedent is proved, because the Demon is the most hostile enemy of the human race, who strives rather to strip us of the goods of Nature than to enrich us with benefits. For those whom he entices by his promises, he either often deceives, when their hope is frustrated, or he seeks a soul for himself as a reward with great usury. Histories testify to this very often, Nicolaus Remigius and Delrius in their Magical Investigations. It is therefore not to be believed that the Demon would have wished so great a good for men to be imparted through this powder, so that either he himself would first have explained its virtue to some man bound to him, who afterward would have been indefinitely useful to all men, or that he himself would always immediately accomplish the cure, without any usury of heavier kind; since indeed there are many who use it unknowingly, and thus innocently, many who prudently, after examining its composition, use, and healing effect, do not admit vanities, trifles, and things altogether irrelevant, which learned men reject, and many finally, in this uncertainty of things, reject all aid of the demon, explicitly professing that they wish to use the goods of Nature only insofar as they are purely natural, not insofar as the Demon in any way intrudes himself, etc. Therefore it is not probable that he would wish, without any advantage, to help so many men, and, whether rejected, and when the matter is free from all blame, to wish to bestow a cure gratuitously; otherwise he would be a foolish merchant, and would lavish his benefits on haters and the ungrateful. < 23.> Thirdly it is proved: because this cure is not beyond the powers of Nature, nor such that, just as it is supposed possible to be done by a demon within the limits of nature (for he can operate nothing beyond the laws of nature), so also by men assisting nature would not likewise be possible in some way; therefore it must absolutely be judged natural. The antecedent will be fully proved in the third question. For the present it is enough to have confirmed it most solidly a posteriori from similar effects naturally arising. Nor does our cure involve greater difficulties than yawning in response to another’s gaping mouth, the wiping away of spots in comparison with the falling of leaves, the redness of the eyes suddenly arising in comparison with the aspect of another who is bloodshot, the agreement of strings, etc., all of which nevertheless are natural and do not transcend the limits of nature. Indeed, if you grant that this cure can be done by the Demon, you must also grant that it can be done by nature itself; which, as Hippocrates says, is itself the

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DE SYMPATHIA. 15 morborum intima medicatrix; & cui cæteri omnes præsto sunt adiumenta suppeditantes. Quod si Natura nimium deiecta est, itavt nullo prorsus 14. adiumento leuari valeat, tunc profectò cura omnis cuadit inurilis, & si demum perficitur, miraculosa est, non naturalis, nec Sathanica, sed Diuina. Quod autem non quidem subitò (vt falsò quidam prætendunt) sed citius habeatur curatio, & circà vllam molestiam, aut dolorem per hæc sympathica medicamenta, quam per methodica; non eò ipsò arguitur pulueris inefficacia, ac Daemonis assistentia; quandoquidem omne id quod facere potest Daemon per internam, & probam remediorum applicationem potest &c ipsa natura per eadem, vel longè suauiora media hominu[m] arte suffecta: vt videmus in præcoci fructuum productione, in olerum ad semihoram eruptione, & alijs miris, quæ abunde exhiber Porta in sua Magia naturali, & nos quotidie experimur, adeóvt iam nobis vilescant, quæ olim in admiratione erant, & arte Daemonis facta estimabuntur. Quod eruditè expressit Barclaius in Argenide lib. v. introducens perbelle Arsidam apud Mauros hospitanrem, atque in mensa Iubæ poma non ita pridem ex arboribus pendentia, mox subita glacie circumdata demirantem: qui postea rem intelligens ex antiperistasi factam, sale videlicet niui admixro, omnem stuporem abjecit. Sic profectò Natura, arte obstetricante, breui temporis interuallo curationem poterit perficere; via quidem nobis imperscrutabili, sed sibi plana, & facili: Vt proprereà liberum nobis sit, eius semitis inhærendo, eandem viam cæco quamuis ductu fectari. Dices: in dubijs tutior pars est eligenda, ne quis temerè etroris periculo se exponat. Cap. Ad audientiam. & Cap. significasti. 2. de Homicidio. Ergò in dubio num puluis naturaliter agat, an arte Daemonis, eius vsus est omittendus, atque ad noriora, & tutiora remedia confugiendum: aliàs illum, his prætermisssis, adhibens temerè se exponet periculo errandi, & communicandi cum Daemone. Contrà quia id procedit in facto, non autem in iure, 26. vt benè aduertit idem Diana, parte 4. tract. 3. resol. 3. & parte 5. tract. 9. resol. 94. cum aliàs sit regula longè vniuersalior, quod in dubijs benigna fieri debet interpræratio. Cap. Estote 2, de regulis iuris. & quod in dubijs melior est conditio possidentis. req. 61. de regulis iuris in 6. quod etiam notat Bonacina, de Censuris disp. 2. quæst. 2. puncto

Transcription: Translated (English)

DE SYMPATHIA. 15 the inward healer of diseases; and to whom all the rest are at hand, supplying help. But if Nature is too much depressed, so that she can by no means be relieved by any aid whatever, then certainly all cure falls into uselessness; and if it is at last accomplished, it is miraculous, not natural, nor Satanic, but divine. Moreover, that the cure is indeed not brought about suddenly (as some falsely claim), but more quickly, and with no inconvenience or pain, by these sympathetic medicines than by methodical ones, this does not therefore prove the ineffectiveness of the powder, or the assistance of a demon; since whatever the demon can do through the internal and proper application of remedies, nature itself can do by the same, or far more pleasant, means supplied by human art: as we see in the early production of fruits, in the sprouting of vegetables in half an hour, and in other wonders, which Porta abundantly presents in his Natural Magic, and which we experience daily, so that those things now become cheap in our eyes which once were matters of admiration, and will be judged to have been done by the art of a demon. This was elegantly expressed by Barclaius in Argenis, book v., where he very prettily introduces Arsidamus, lodging among the Moors, and marvelling at the table of Juba, at apples that had not long before been hanging from the trees, now suddenly encircled with ice: who afterward, understanding that the matter had been done by antiperistasis, namely by snow mixed with salt, cast off all amazement. Thus indeed Nature, with the midwife-art assisting, will be able in a short interval of time to bring a cure to completion; a path indeed inscrutable to us, but plain and easy to itself. Wherefore it is free for us, by following its tracks, to pursue the same path even with blind guidance. You will say: in doubtful cases the safer part is to be chosen, lest anyone rashly expose himself to the danger of error. Cap. Ad audientiam. And Cap. significasti. 2. de Homicidio. Therefore, in doubt whether the powder acts naturally or by the art of a demon, its use is to be omitted, and recourse is to be had to more certain and safer remedies; otherwise, if one were to apply it while these are neglected, he would rashly expose himself to the danger of error and of communicating with a demon. On the contrary, because this applies in fact, but not in law, 26, as the same Diana well notes, part 4, tract. 3, resol. 3, and part 5, tract. 9, resol. 94; moreover, there is a far more universal rule, that in doubtful matters a benign interpretation should be made. Cap. Estote 2, de regulis iuris. And that in doubtful matters the condition of the possessor is the better. req. 61, de regulis iuris in 6. This also Bonacina notes, de Censuris, disp. 2, quæst. 2, puncto

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16 PHYSIO THEOLOGICA, 6. num. 49. & alij passim. Vnde in casu nostro, vt supra innui, omnes Doctores conueniunt, quod quando dubi- tatur nùm effectus sit superstitiosus, an naturalis, benigna fieri debet interpretatio, & censendus est naturalis; cum possessio stet pro natura; non enim nobis omnes viæ eius compertæ, neque adiùs interclusus ad eas inuestigandas, vt non liberè eius bonis ad nostrum commodum vù possimus. Aliàs si ex formidine incurrendi aliquod implicitum fædus cum Dæmone teneremur tutiora sequi, & bonis dubijs abstinere, magna infensissimo hosti præbere- tur ansa, optima quæque Naturæ bona in dubium reuocandi, corrumpendi, & rebus inutilibus immiscendi, (vt profectò in multis, ac præsertim in his casibus præstat) vt vel ob id nos ab eorum vsu arceat, absterreatque quod nullatenus permittendum. Sat igitur nos in eiusmodi rebus dubijs aduersus omnem Dæmonis fraudem, ac versutiam præmunimus, si omnem eius opem præmissa protestatione reijciamus. Qui Naturæ activitatem sui captus exilitate metitur Deo auctori naturæ injurius est: qui opera sibi incomperta damnat propè blasphæmus: qui alios ab eorum vsu ex vana formi line arceat, inuidus, ac Dæmonis æstro subseruit. 27. At inquies: Protestatio illa non te excusat, cum sit contraria facto, quæ Dæmoni opem nou reijcit, sed facto ipso aduocat & conducit, vt docent Azor. Delrius, Suar. Sanchez, Naldus, & alij communiter: Nam perinde est, inquit Naldus, ac si manum igni admoueamus, nolentes tamen, conburi, aut calefieri. Contrà: quia hæc doctrina tunc locum habet, quando est certitudo de Dæmonis assistentia, & quod opus nullatenus perfici naturaliter possit, secus cum res est dubia, & vbi est opinionum diuersitas; vt monet in specie Delrius, & Sanchez, lib. 2. cap. 40. num. 43. Hic autem omnia absunt, quæ nos certiores reddant occultæ Dæmonis assistentiæ, qualia sunt Verba sacra, characteres, circumstantiæ prorsus inutiles, & alia quæ communiter afferunt D. D. ac præsertim Caietanus, ac Toletus; in Summa lib. 4. cap. 14. num. 6: & licet modus operandi in distans videatur suprà naturalium agentium possibilitatem, tamen is benè saluatur, vt infrà videbimus per indistantiam, & potius vocari debet præter distans, quam in distans. Præterquam non est ita certum in Philosophia, quod agens non possit actionem suam transmittere in distans, vt contrarium sustineri non æquè possit, vt multis probat noster Aretius, de Generat. lib. 1. disp. 5. quæst. 41. sect. 2. Osten- dens

Transcription: Translated (English)

16 PHYSIO THEOLOGICA, 6. num. 49. & others passim. Hence, in our case, as I hinted above, all the Doctors agree that, when it is doubted whether an effect be superstitious or natural, a benign interpretation must be made, and it is to be regarded as natural; since possession stands for nature; for all its ways are not known to us, nor is access to investigating them closed off, so that we should not freely be able to use its good things for our convenience. Otherwise, if from fear of falling into some implicit pact with the Demon we were bound to follow the safer course, and to abstain from good things that are doubtful, great occasion would be given to the most hostile enemy to call into doubt, corrupt, and mix with useless things the very best goods of Nature (as indeed he does in many cases, and especially in these), so that for that very reason he might keep us from their use and frighten us away from it, which must in no way be permitted. It is enough, then, for us in such doubtful matters to guard ourselves against every fraud and cunning of the Demon, if, with a prior protestation, we reject all his help. He who, from his own cramped narrowness, measures the activity of Nature is unjust to God, the author of nature: he who condemns works unknown to him is almost blasphemous: he who keeps others from their use by vain fear serves envy, and the zeal of the Demon. 27. But you will say: That protestation does not excuse you, since it is contrary to the deed, which does not reject the Demon’s help, but by the deed itself calls it in and employs it, as Azor, Delrius, Suar. Sanchez, Naldus, and others commonly teach: for it is all the same, says Naldus, as if we were to put our hand to fire, though unwilling to be burned or warmed. On the contrary: because this doctrine has force only when there is certainty of the Demon’s assistance, and that the work cannot in any way be accomplished naturally; otherwise, when the matter is doubtful and where there is diversity of opinion; as Delrius and Sanchez warn in the case, lib. 2. cap. 40. num. 43. But here all those things are absent which would make us more certain of a hidden Demon’s assistance, such as sacred words, characters, circumstances wholly useless, and other things which the Doctors commonly bring forward, especially Cajetan and Toletus; in the Summa, lib. 4. cap. 14. num. 6: and although the mode of operating at a distance seems beyond the possibility of natural agents, nevertheless it can be well accounted for, as we shall see below, by indistance, and should rather be called beyond-distance than distance-at-a-distance. Moreover, it is not so certain in philosophy that an agent cannot transmit its action at a distance, that the contrary cannot be maintained with equal force, as our Aretius proves at length, de Generat. lib. 1. disp. 5. quæst. 41. sect. 2. Showing

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DE SYMPATHIA. 17 dens nulla censura dignam esse opinionem id asserentium. Addo, quod aliquando lieita est eriam operis aggressio licet alioqui superstitionem apertissimè continentis, præmissa protestatione, quando videlicet id sit ad Dæmonis fraudem detegendam, atque ad fideles erudiendos, vt docet Caiet. in summa Verbo Incantatio & se fecisse testatur in apertissima superstitione, quantò magis eum res est dubia? Namque ad commonstrandum coram multitudine, quod motio annuli super filum ad prolationem neseio cuius versiculi erat arte Dæmonis facta, non naturalis, ipse Caietanus rem facto exequi non dubitauit pronuntians dicta verba, protestans se tamen dicere ea verba, non tanquam à Dæmone instituta ad mouendum annulum, sed simpliciter ad honorandum Deum, qui eorum fuerat auctor: in quo casu annulus non est motus, quia Dæmon reiectus rubore suffusus auffugit, & operi sibi alias non proficuo insistere reusauit. Non est periculum, quod inuidus, ac superbus hostis, vltro se immisceat in iis quæ non vt ab ipso profecta volumus, sed vt dubia, nùm à natura sint, ac proinde, vt liberè id experiamur ac Naturæ bonis vtamur: cum videlicet eius versutiam illudentes omnem eius opem, explicitè reiicimus, ac detestamur. Aecedit, quod, licet nos simus in dubio de veritate operis num sit à Natura nec ne, certi tamen sumus de bonitate, & rectitudine nostri actus in eo opere experiundo, nam vt benè notat Pasqualigius decis. 5. num. 6. operans secundum opinionem probabilem. operatur secundum mensuram conformem rectæ rationi, atque adeò qui prudenter, & probabiliter operatur versatur, nô in dubio, sed in re suo modo certa: certû est enim eum qui prudenter, & rationabiliter operatur nullo modo errare. Atqui pro puluere & curatione magneriea summa adest probabilitas, tum extrinseca, tum intrinseca, quod naturæ viribus fiat: vnde, qui eam experiri vult, & puluere vti, benè ac rationabiliter operatur, cum operetur iuxta opinionem probabilem, atque adeò omni Diabolicæ fraudis periculo se subducit. Vbi aduertè malè Dianam supponere eos qui puluere vtuntur in vulnerum curatione non in casu dubio versari, sed certissimo, quod non sit à natura euratio; sed à Dæmone: Nam peto, quamnam ipse de hæc re certitudinem habeat? Et nùm certissimum dicturus sit, quod à doctissimis viris tam Philosophis, quam Theologis controuertitur? Sat meo iudicio est, ad rem dubiam faciendam, si vns vel alter, in alterutram partem abeat, præsertim, si sit in arte peritus; b

Transcription: Translated (English)

DE SYMPATHIA. 17 there is no censure worthy of the opinion of those asserting it. I add that sometimes the undertaking of a work is also lawful, even though it openly contains superstition, provided a prior protestation is made, namely when it is done to uncover the deceit of the Demon and to instruct the faithful, as Caiet. in summa Verbo Incantatio testifies that he did in the most manifest superstition; how much more so when the matter is doubtful? For to show before a crowd that the movement of a ring on a thread, at the pronouncement of some little verse I know not which, was caused by the art of the Demon and not by nature, Caietanus himself did not hesitate to carry out the experiment in fact, pronouncing the said words, while protesting nevertheless that he spoke those words not as instituted by the Demon for moving the ring, but simply to honor God, who had been their author: in which case the ring did not move, because the Demon, repelled and covered with shame, fled away and refused to insist on a work otherwise unprofitable to him. There is no danger that the envious and proud enemy will of his own accord interfere in matters which we do not want to be understood as proceeding from him, but as doubtful whether they are from nature and therefore to be freely tested by us and the goods of nature used: since, while mocking his cunning, we explicitly reject and detest all his help. Furthermore, although we are in doubt about the truth of the work, whether it be from nature or not, nevertheless we are certain of the goodness and rectitude of our act in testing that work; for, as Pasqualigius rightly notes, decis. 5, no. 6, one who acts according to a probable opinion acts according to the measure conformable to right reason, and thus one who acts prudently and probably is not in doubt, but in something in its own way certain: for it is certain that he who acts prudently and reasonably does not err in any way. But in the matter of powder and the so-called magnetic cure there is the highest probability, both extrinsic and intrinsic, that it takes place by the powers of nature; hence, whoever wishes to test it and use the powder acts well and reasonably, since he acts according to a probable opinion, and thus withdraws himself from every danger of diabolical fraud. Here Diana wrongly supposes that those who use powder in the healing of wounds are not in a doubtful case, but in the most certain one, namely that the cure is not from nature but from the Demon. For I ask, what certainty does he himself have about this matter? And will he say that it is most certain concerning what is disputed by the most learned men, both philosophers and theologians? In my judgment, it is enough to make a matter doubtful if one person or another goes over to either side, especially if he is skilled in the art; b

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16 PHYSIO-THEOLOGICA, 6. num. 49. & alij passim. Vnde in casu nostro, vt suprà innui, omnes Doctores conveniunt, quod quando dubi- tatur nùm effectus sit superstitiosus, an naturalis, benigna fieri debet interpetario, & censendus est naturalis; cum possessio stet pro natura; non enim nobis omnes vix eius compertæ, neque aditus interclusus ad eas inuestigandas, vt non liberè eius bonis ad nostrum commodum vti possimus. Aliàs si ex formidine incurrendi aliquod implicitum fædus cum Dæmone teneremur tutiora sequi, & bonis dubijs abstinere, magna insensissimo hosti præbere- tur ansa, optima quæque Naturæ bona in dubium reuocandi, cogrumpendi, & rebus inutilibus immiscendi, (vt profectò in multis, ac præsertim in his casibus præstat) vt vel ob id nos ab eorum vsu arceat, abstrereatque quod nullatenus permittendum. Sat igitur nos in eiusmodi rebus dubijs aduersus omnem Dæmonis fraudem, ac versutiam præmunimus, si omnem eius opem præmissa protestatione reijciamus. Qui Naturæ actiuitatem sui captus exilitate metitur Deo auctori naturæ injurius est: qui opera sibi incomperta damnat propè blasphæmus: qui alios ab eorum vsu ex vana formidine arcet, inuidus, ac Dæmonis æstro subseruit. 27. At inquies: Protestatio illa non te excusat, cum sit contraria facto, quæ Dæmoni opem nou reijcit, sed facto ipso aduocat & conducit, vt docent Azor. Delrius, Suar. Sanchez, Naldus, & alij communiter: Nam perinde est, inquit Naldus, ac si manum igni admoueamus, nolentes tamen conburi, aut calefieri. Contrà: quia hæc doctrina tunc locum habet, quando est certiudo de Dæmonis assistentia, & quod opus nullatenus perfici naturaliter possit, secus cum res est dubia, & vbi est opinionum diuersitas; vt monet in specie Delrius, & Sanchez, lib. 2. cap. 40. num. 43. Hic autem omnia absunt, quæ nos certiores reddant occultæ Dæmonis assistentiæ, qualia sunt Verba sacra, characteres, circumstantiæ prorsus inutiles, & alia quæ commu- niter afferunt D. D. ac præsertim Caietanus, ac Toletus; in Summa lib. 4. cap. 14. num. 6: & licet modus operandi in distans videatur suprà naturalium agentium possibilitatem, tamen is benè saluatur, vt infrà videbimus per indistantiam, & potius vocari debet præter distans, quam in distans. Præterquam non est ira certum in Philosophia, quod agens non possit actionem suam transmittere in distans, vt contrarium sustineri non æquè possit, vt multis probat noster Aresius, de Generat. lib. 1. disp. 5. quæst. 41. sect. 2. Ostendens

Transcription: Translated (English)

16 PHYSIO-THEOLOGICA, 6. num. 49. & others passim. Hence in our case, as I indicated above, all the Doctors agree that when it is doubtful whether an effect is superstitious or natural, a benign interpretation must be made, and it must be judged natural; since possession stands for nature. For not all of nature’s powers are known to us, nor is access to their investigation barred, so that we may not freely use its good things for our advantage. Otherwise, if through fear of incurring some implicit pact with the Demon we were bound to follow the safer course and refrain from good things that are doubtful, there would be given to the most senseless enemy a great opening for calling into question, corrupting, and mixing with useless things the best gifts of Nature, as indeed in many cases, and especially in these, he prevails, so as by that very fact to keep us from their use and to draw us away from what ought by no means to be forbidden. It is enough, then, that in such doubtful matters we protect ourselves against every deceit and cunning of the Demon if, with prior protestation, we reject all his help. He who measures Nature’s activity by the frailty of his own understanding is unjust to God, the author of nature; he who condemns works unknown to him is almost blasphemous; he who keeps others from their use out of vain fear serves envy and the rage of the Demon. 27. But you will say: that protestation does not excuse you, since it is contrary to the deed, which does not reject the Demon’s help, but in the very act summons and employs it, as Azor, Delrius, Suárez, Sanchez, Naldus, and others commonly teach. For it is the same, says Naldus, as if we were to put our hand to fire while not wanting to be burned or heated. On the contrary: because this doctrine applies only when there is certainty of the Demon’s assistance, and that the work cannot in any way be accomplished naturally; otherwise, when the matter is doubtful and there is diversity of opinion, as Delrius warns in the specific case, and Sanchez, book 2, chap. 40, num. 43. But here all those things are absent which would make us more certain of a hidden assistance of the Demon, such as sacred words, characters, circumstances wholly useless, and other things which the Doctors commonly mention, especially Cajetan and Toletus, in the Summa, book 4, chap. 14, num. 6. And although the manner of acting at a distance seems to exceed the power of natural agents, still it can be well explained, as we shall see below, by non-distance, and it ought rather to be called beyond-distance than at-distance. Besides, it is not certain in philosophy that an agent cannot transmit its action to a distance, since the contrary cannot be sustained with equal force, as our Aresius proves at length, de Generat. book 1, disp. 5, question 41, section 2. Showing

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DE SYMPATHIA. 17 dens nulla censura dignam esse opinionem id asserentium. < 18.> Addo, quod aliquando licita est etiam operis aggressio licet alioqui superstitionem apertissimè continentis, præmissa protestatione, quando videlicet id sit ad Dæmonis fraudem detegendam, arque ad fideles erudiendos, vt docet Caiet. in summa Verbo Incantatio & se fecisse testatur in apertissima superstitione, quantò magis cum res est dubia? Namque ad commonstrandum coram multitudine, quod moto annuli super filum ad prolationem nescio cuius versiculi erat arte Dæmonis facta, non naturalis, ipse Caietanus rem facto exequi non dubitauit pronuntians dicta verba, protestans se tamen dicere ea verba, non tanquam à Dæmone instituta ad mouendum annulum, sed simpliciter ad honorandum Deum, qui eorum fuerat auctor: in quo casu annulus non est motus, quia Dæmon reiectus rubore suffusus auffugit, & operi sibi alias non proficuo insistere recusauit. Non est periculum, quod inuidus, ac superbus hostis, vltrò se immisceat in iis quæ non vt ab ipso profecta volumus, sed vt dubia, nùm à natura sint, ac proinde, vt liberè id experiamur ac Naturæ bonis vtamur: cum videlicet eius versutiam illudentes omnem eius opem, explicitè reiicimus, ac detestamur. < 19.> Accedit, quod, licet nos simus in dubio de veritate operis num sit à Natura nec ne, certi tamen sumus de bonitate, & rectitudine nostri actus in eo opere experiundo, nam vt benè notat Pasqualigius decis. 5. num, 6. operans secundum opinionem probabilem. operatur secundum mensuram conformem rectæ rationi, atque adeò qui prudenter, & probabiliter operatur versatur, nô in dubio, sed in re suo modo certa: certu[m] est enim cum qui prudenter, & rationabiliter operatur nullo modo errare. Atqui pro puluere & curatio ne magnetica summa adest probabilitas, tum extrinseca, tum intrinseca, quod naturæ viribus fiat: vnde, qui eam experiri vult, & puluere vti, benè ac rationabiliter operatur, cum operetur iuxta opinionem probabilem, atque adeò omni Diabolicæ fraudis periculo se subducit. Vbi aduertè malè Dianam supponere eos qui puluere vtuntur in vulnerum curatione non in casu dubio versari, sed certissimo, quod non sit à natura curatio; sed à Dæmone: Nam peto, quamnam ipse de hac re cerritudinem habeat? Et nùm certissimum dicturus sit, quod à doctissimis viris tam Philosophis, quam Theologis controuertitur? Sat meo iudicio est, ad rem dubiam faciendam, si vns vel alter, in alterutram partem abeat, præsertim, si sit in arte peritus;

Transcription: Translated (English)

DE SYMPATHIA. 17 dens states that the opinion of those asserting this is worthy of no censure. < 18.> I add that sometimes the undertaking of an operation is also lawful, even if, in other respects, it openly contains superstition, provided a protestation be made beforehand, namely when this is for the purpose of exposing the fraud of the Demon and instructing the faithful, as Caietan in the Summa, under the word Incantation, teaches and says that he did in the case of the most open superstition; how much more when the matter is doubtful? For in order to show before a crowd that the moving of a ring on a thread at the utterance of some little verse was done by the art of the Demon, and not naturally, Caietan himself did not hesitate to carry out the thing in fact, pronouncing the said words, while nevertheless protesting that he said those words not as instituted by the Demon for moving the ring, but simply to honor God, who had been their author: in which case the ring did not move, because the Demon, rejected and covered with shame, fled away and refused to persist in a work that would otherwise be of no advantage to him. There is no danger that the envious and proud enemy will thrust himself in of his own accord into matters which we do not wish to be regarded as proceeding from him, but as doubtful whether they are from nature; and therefore, so that we may freely test them and make use of the gifts of Nature, while mocking his craftiness we explicitly reject and detest all his help. < 19.> There is also this consideration, that although we may be in doubt concerning the truth of the operation, whether it is from Nature or not, nevertheless we are certain of the goodness and rectitude of our act in testing that operation; for, as Pasqualigius rightly notes, decis. 5, no. 6, one who acts according to a probable opinion acts according to a measure conformable to right reason, and therefore one who acts prudently and probably is not in doubt, but in a matter in its own way certain: for it is certain that one who acts prudently and reasonably does not err in any way. But regarding the powder and the magnetic cure there is the greatest probability, both extrinsic and intrinsic, that it is done by the power of nature; hence whoever wishes to try it and use the powder acts well and reasonably, since he acts according to a probable opinion, and thus withdraws himself from every danger of diabolical fraud. Where note that Dianam wrongly assumes that those who use powder in the treatment of wounds are not dealing with a doubtful case, but with a most certain one, namely that the cure is not from nature but from a Demon. For I ask, what certainty does he himself have about this matter? And will he say it is most certain, when it is disputed by the most learned men, both philosophers and theologians? In my judgment, it is enough to make a matter doubtful if one or another person goes over to either side, especially if he be skilled in the art;

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18 PHYSIO-THEOLOGICA, quanto magis cum res in ancipiti est, & æquè à pluribus affeciiur, ac negatur? < 30.> Sed iam tempus est, vt Liuium de Comitibus audiamus, eiusque ratiocinationes, quibus omnem nostri pulueris actionem cuettere satagit, expendamus. Triplici eum iaculo aggreditur; veriùs tamen ipsa vulneratorum corpora, hoc singulari præsidio, spoliare contendens. Primo ex agentium naturalium activitate; inter quæ agendi vi, inquit præstat omnibus ignis, qui tamen intra suæ sphæræ limites sic concluditur, vt extrà illam, nulla penitùs virtute polleat: Qui igitur modici pulueris energia ad plura milliaria exrendi poterit, vt sanitatem in corpore quantumuis dissito operetur? < 31.> Secundo Vitriolum, subdir, inter ea medicamenta censetur, quæ virtuales, seù mavis dicam, potentiales qualitates habent, quæ, vt agant à nauio animantis calore excitari debent ex Galeno tertiò de temperamentis, & primo de simplicium medicamentorum facultate 11 quem sequuta est, licet diuersimodè vniuersa Medicorum schola, & compiures Philosophi, Scotus, Ruuius, Bagnez, Conimbrienses, & alij. Quinimò siùè actuales sint, siue potentiæ huiusmodi qualitates, omninò tamen debent prius à calore nostro excitari, atque in actum secundum deduci. At experientia compertum est tangentibus nullam harum qualitatum in medicamentis eiusmodi simpliciter propriam apparere. Non poterit ergò à vitrioli potentiali virtute affici corpus dissitum, vtpote adhuc latenii, & inefficaci: neque sanguis, qui extrà venas statini corrumpitur, ac spiritum amittit, vt æquiuocè sanguis sit, ipsius pulueris qualitatem actuare, aut ab ea pati aptus est: quare si quid patitur sanguis à puluere, id ab exigua & refracta qualitate, quæ in eo reperitur, fieri necessum est, sed hæc minima est, nec longè caliditatis activitati, qua pollet ignis æquabilis. < 32.> Tertiò tandem obiicit. Vel ex eo quod Vitriolum sympathiam habet cum corpore humano, habet etiam, quod longè constitutum vulneribus medeatur; vel ex eo quod sanguis solum habet hanc sympathiam; vel ex eo quod ambo simul hanc habeant sympathiam, aut, si mavis dicam, antipathiam; licet nullum eorum per se seorsim id habeant: non enim excogitari potest alia ratio, vel alius modus. Sed nec ex eo quod Vitriolum hanc sympathiam habeat, id euenire potest, quia profectò non esset opus vt sanguini inspurgeretur, sicque etiam intra Pharmacopolarum sciinnia asseuatum eandem virtutem haberet: Nec ex eo quod

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18 PHYSIO-THEOLOGICA, how much more when the matter is uncertain and is affected and denied equally by many? <30.> But now it is time for us to hear from Livius de Comitibus, and to examine his reasonings, by which he strives to overturn every operation of our powder. He attacks it with three javelins; yet rather, while trying to strip the very bodies of the wounded of this singular protection. First, from the activity of natural agents; among these, in active power, he says fire surpasses all others, yet it is so confined within the limits of its own sphere that beyond it it possesses absolutely no power at all: how then could the energy of a small amount of powder extend to several miles, so as to produce health in a body however distant? <31.> Second, he adds, vitriol is reckoned among those medicines which have virtual, or if you prefer, potential qualities, which, in order to act, must be aroused by the native heat of the living being, according to Galen, in the third book On Temperaments and in the first book On the Faculties of Simple Medicines, a view followed, though in different ways, by the whole school of physicians and by many philosophers, Scotus, Ruvius, Bagnez, the Conimbricenses, and others. Indeed, whether such qualities are actual or potential, they must altogether first be aroused by our heat and brought into second act. But experience has made it clear to those who touch them that no quality of this kind appears simply and properly in medicines of this sort. Therefore the distant body cannot be affected by the potential power of vitriol, since it is still hidden and ineffective; nor can the blood, which outside the veins immediately corrupts and loses its spirit, so that it is blood only in an equivocal sense, be able to actualize, or suffer from, the quality of the powder; wherefore if the blood suffers anything from the powder, it must necessarily happen from some slight and broken quality that is found in it; but this is very small, and does not at all match the active heat that belongs to uniform fire. <32.> Thirdly at last he objects: either because vitriol has sympathy with the human body, it also has the power to heal wounds at a great distance; or because only blood has this sympathy; or because both together have this sympathy, or, if you prefer, antipathy; although none of them has it by itself separately: for no other reason, or no other way, can be imagined. But neither can it happen because vitriol has this sympathy, since certainly there would be no need for it to be sprinkled into the blood, and thus even in the storehouses of the apothecaries it would have the same power: nor because

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DE SYMPATHIA. 19 -guis solus habeat hanc sympathiam patitur corpus; quia etiam alias alterationes communicaret corpori provt illis ipse afficeretur, aut vstione, aut putredine, aut frigore, aut quauis maligna alia qualitate, dum tanguini inspergeten- tur venena, & cætera huiusmodi: quod tamen tefragatur experientiæ. Restat igitur, vt simul iuncta id habeant: sed neque hoc dici potest: primò quia sanguis, & vitriolum non miscentur, sed confunduntur extrinsecùs; ergò nulla resultat qualitas, quæ in sepatatis istis non elucesceret. Secundò quia dato etiam quod resultaret aliqua sympathia, non propterea in corpus distas agere posset. Tertiò tandem, quia si vera esset illa sympathia, provt afficeretur illa corpora simul vnit, siue vstione, siue puttedine, siue alio quouis modo, ita etiam eis compateretur corpus ægri, quod non contingit. Hæc sunt quæ acutè obiicit Liuius in puluerem sympathicum, adeoque in omnia sympathica medicamenta: quæ tamen tum ex superioribus, tum ex infrà dicendis facilè diluuntur. Quod ad primum attinet: dico inter elementa, & mixta elementaria excellere quidem activitate ignem, qui, quemadmodum etiam illa per primas qualitates, & per contactum agunt, secus autem cætera mixta, quæ operantur ex occulta qualitate cælitùs derivata, longè superioris otdinis, atque activitatis, vt nos fusè diximus in nostro Lexico V. Mixta, & probat quotidiana experientia. Neque ista opertatio ad normam purè elementarium metienda est, sed altiùs à sideribus, & mira vniuersi conspiratione expiscanda. Quoad secundum. Vitriolum qualitate quidem exsiccante pollet, quæ vtique à spiritibus, & calore innato adhuc in sanguine consistentibus actuatur atque ad agendum in ipsum sanguinem excitatur. Quamquam enim sanguis extrà Venas positus cortumpitur, inspissatur, dur scit, & non nihil spirituum, & caloris amittit, retinet nihilominus semper eandem cum corpore, aut membro, vnde excisus est, vniorem, ac sympathiam, vt videre est in sanguinem menstruo, qui licet ciectitius, malè tamen habitus affligit corpus vnde excussus est: & quod est mirabilius, passim experimur in salibus ex vrina, sanguine, ossibus, atque aliis ex humano corpore comparatis medicamentis, ac præsertim in Mumia, quæ ob spiritus, & naturæ conformitatem (balsamum alij dicunt) maximam retinent cum vniuerso hominum, quin & animantium genere sympathiam: vnde inter reliqua medicamenta summam obtinent vim, & cæteris omnibus præstant. Quod etiam locum habet, & suo b ij

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On Sympathy. 19 —can have this sympathy alone, the body suffers; because it would also communicate other alterations to the body, as it itself were affected by them, whether by burning, or putrefaction, or cold, or any other malignant quality, when poisons and other such things are sprinkled into the blood; which, however, is refuted by experience. It remains, therefore, that they have it when joined together: but neither can this be said; first, because blood and vitriol are not mixed, but are confused externally; therefore no quality results, which would not shine forth in those things when separated. Secondly, because even if some sympathy did result, it would not on that account be able to act in a distant body. Thirdly, lastly, because if that sympathy were true, as the body, when it is affected, unites them together, whether by burning, or putrefaction, or by any other means, so also the body of the sick person would sympathize with them, which does not happen. These are the things which Livius sharply objects against sympathetic powder, and indeed against all sympathetic medicines: yet these objections are easily dissolved, both from what has gone before and from what will be said below. As to the first point: I say that among the elements, and among mixed things, fire does indeed excel in activity; it acts, as the others also do, through the primary qualities and through contact, whereas the other mixed bodies operate from an occult quality derived from the heavens, of a far higher order and activity, as we have explained at length in our Lexicon V. Mixta, and daily experience proves. Nor should this operation be measured by the standard of pure elements, but rather sought more deeply from the stars and the marvelous conspiracy of the universe. As to the second. Vitriol indeed possesses a drying quality, which is certainly actualized by the spirits and innate heat still remaining in the blood, and is stirred up to act upon the blood itself. For although blood placed outside the veins becomes corrupted, thickened, hardened, and loses no small part of its spirits and heat, nevertheless it always retains the same sympathy and union with the body or limb from which it was cut, as can be seen in menstrual blood, which, although quickly expelled, nonetheless afflicts the body from which it was thrown off when in poor condition; and what is more remarkable, we often experience it in medicines made from salts obtained from urine, blood, bones, and other parts of the human body, and especially in Mumia, which on account of the conformity of its spirits and nature (some call it balsam) retains the greatest sympathy with the whole human race, indeed with the whole race of living creatures; whence among other medicines it possesses the greatest power and surpasses all the rest. This also applies, and in its own

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20 PHYSIO-THEOLOGIA, modo, videre est in ipsis brutis animantibus, ac plantis, atque ex eorum partibus conflatis medicaminibus, quò magis externa similitudine, aut interna constitutione ad alterius naturam accedunt. Sic equidem in casu nostro sit, vt sanguine è vulnere exciso, inspers vi puluetis alterato, alteretur & corpus per sympathiam quam cum sanguine obtinet, eiusque motum persentiscens Natura intime excitatur ad curationem perficiendam, vt eadem sympathiæ vi excitatur Cithara ad resonandum alteri tactæ atque ad eosdem <35.> modulos tensæ. Quod autem idipsum non accidat in sanguine, qui è vena exsecta manarit, aut cum idem amburitur, inciditur, elixatur, aut alia quauis praua qualitate inficitur, id oritur, vel qu a homo, cui vena scinditur, alioqui vegetus, ac robustus tesistit levissimo illi naturæ motui, quæ proinde valens est non insiruia, & nil reparitur ad alterius passionem, vt videre est in multis fæminis validi roboris, & optimæ sanitatis, quæ nil mali persentiant per inclementem secundinarum, & primi sanguinis menstruita- ctationem, cum aliàs debiles, & infirmæ in eo casu diuis symptomatis corripiantur: vel quia sanguis è vena excisus non tantam habet cum vulnere sympathiam, ac is qui immediatè ab illo profluxit. Est quippe inter sanguinem aliqualis diuersitas, & vnsquisque ad partem vnde profluit dicit ordinem: vel denique quia sanguis quicumque non ita patitur atque alteratur per qualitates elementares puta vstionem, frigus, putredinem, &c. aut per alias occultas, non tamen alretando sanguini aptas, quales sunt quæ in vitriolo, ob occultam cum sanguine antipathiam reperiuntur: Sic etiam Iaspis per simplicem contactum habet sanguinem sistere, quod non habet venenum. aut aliud quoduis actiuius & cæteroqui violentissimum mixtum: quod sanè retum naturis conformibus, differmibus, aut nullo ordine inter se connexis acceptum ferendum est. Neque hoc voluntariè, & irrationabiliter dictum proclames: quandoquidem id in vniuersa penè Natura irrefragabilis probat, & euincit experientia. <36.> Nam dic mihi, quæso, cur adamantem non lædit actiuiissimus ignis, cæteroqui omnia comminuens, ac deuastans, lædit autem modicus sanguis, isque non hominis, non Leonis, non equi, non rabidissimi canis, sed mitissimi pecudis? cur vniones non soluit ardentissima aqua, cui nec silices, nec ferrum obsistere possunt, soluit autem acetum? Cur Cantharides manu pessæ, manu illæsâ vesicam exulcerant, lotiumque reddunt sanguinolentum? Equidem hæc totum natuta est non à primarum qualitatum gradu, agen-

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20 PHYSIO-THEOLOGIA, in this way, it is seen in brute animals themselves, and in plants, and in medicines compounded from their parts, the more they approach another nature by external likeness or internal constitution. Thus, indeed, it is so in our case, that blood taken from a wound, if sprinkled with altered powder, is altered, and the body too is altered through the sympathy which it has with the blood, and, sensing its motion, Nature is inwardly stirred to complete the cure; just as by the same force of sympathy a cithara is stirred to resound when another is touched and tuned to the same <35.> notes. But that the very same thing does not happen in blood which has run from a severed vein, or when it is burned, cut, boiled, or infected by any other evil quality, arises either because the man whose vein is cut, if otherwise vigorous and strong, resists that least motion of nature, which therefore, being sound, is not stirred, and nothing is restored toward another’s passion; as may be seen in many women of strong strength and excellent health, who feel nothing bad through the rough handling of the afterbirth and of the first blood of menstruation, while otherwise weak and infirm women in that case are seized by various symptoms: or because blood drawn from a vein does not have as much sympathy with the wound as that which flowed immediately from it. For there is some diversity between bloods, and each one follows the order of the part from which it flows: or finally because any blood whatsoever does not suffer or alter itself so much through elemental qualities, such as burning, cold, putrefaction, and the like, or through other occult qualities not, however, suited to alter blood, such as those found in vitriol, on account of its hidden antipathy with blood. Thus also jasper, by simple contact, has the power to stop blood, which poison does not have, or any other more active and otherwise most violent mixture: which surely must be accepted in things conformable in nature, different, or connected with one another by no order. Nor should you declare this to be said voluntarily and irrationally: since experience proves and establishes it in nearly all of Nature beyond contradiction. <36.> For tell me, I ask you, why does the most active fire, which otherwise crushes and devastates all things, not injure the diamond, but rather a small amount of blood does, and not human blood, nor that of a lion, nor of a horse, nor of a rabid dog, but of the gentlest sheep? Why does ardent water not dissolve pearls, against which neither flint nor iron can resist, but vinegar does? Why do cantharides, crushed in the hand, wound the bladder with the hand uninjured, and make the urine bloody? Indeed, this whole nature is not from the degree of primary qualities, agen-

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DE SYMPATHIA. 27 tium actiuitate, constitutione, approximatione, similitudine, sed a tius eiuenda. Si namque, vt supra dixi, foeminis non efficit, si sanguis menstruus in ignem, aut in profluentem deciciatur, plurimum autem, si in locum sordidum, ac cænosum: econià ignis excrementia torrens, alium sese exonerantis torminibus torquet, minimè verò venenum, aut aliud quid super illa proiectum: cuius rei rationem vicumque reddere conari sumus in nostro Lexico v. sympathia. Fortassis etiam alia mineralia, vegetabilia, &c. Sanguini applicata eundem, aut longè mirabiliorem effectum patiunt. sed is hactenus nobis incomperius. Non igitur mitum, si puluis sanguini impertus id præstat, quod non venenum, quod non ignis, quod non alia quauis qualitate præditum mixtum: si demum id ipsum in alio sanguine non sit videre, sed in eo solum, qui è parte affecta de sumptus est. <37.> Denique quoad tertium dico breuiter, id accidere partim ex sympathyia quam habet sanguis cum suo principio, præsertim cum parte affecta, vnde proximè excisus est, partim ex antipathia vitrioli cum sanguine: quippe videmus hoc semper sanguinis profluvio aduersari; ita vt etiamsi super sanguinem e vena aut naribus profluentem modicum quid pulueris inspergatur, mox in vena, aut naribus sanguinem sisti, idque ex mira hac cum sanguine contrarietate atque dissidio. Neque enim ex vitrioli & sanguinis permixtione tertia quædam exturgit qualitas, quæ in ægrum transmittitur, sed Vitriolum in sanguinem ex antipathia agit, Natura verò ex occulta sympathiæ vi sanguini condolet, atque alteratur in quacumque distantia, quæ planè impertinens est ad huius generis actionem. Sed de hac refusiùs, & ex professo in tertia quæstione. <38.> Concludendum est igitur non levia argumenta suppetere ad magneticæ curationis opus solius Naturæ opera. factum probabiliter astruendum: atque ex his evidenter deduci. tuto ac libere posse ab omnibus practicari, absque vlla violatæ religionis formidine, etiamsi operandi modus non sit co[m]pertus, modo tamen apertè Sathanicus non appareat, quod in puluere nostro minime est, quippe nullam admittit circumstantiam vanam, nulla verba, characteres nullos, quibus rationabiliter tumeri possit Dæmonis opem in adiutorium inuocari. Non enim nobis omnis agentium naturalium virtus comperta est, & ea est nostræ humanitati, conditio, vt in peccati poenam plurimarum, earumque præstantissimarum rerum notitia (quam primus parens habebat) iii

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of sympathy. 27 of activity, constitution, approximation, similarity, but to be avoided further. For if, as I said above, in women it does not take effect if menstrual blood is dropped into fire or into a running stream, but most of all if into a dirty and filthy place, since fire, consuming its refuse, torments itself with the pains of that which is being discharged; yet not at all poison, or anything else thrown upon it: the reason for this I have tried to explain at length in our Lexicon under sympathia . Perhaps also other minerals, vegetables, &c., applied to blood undergo the same, or a far more wonderful effect. But as yet this is unknown to us. It is therefore not surprising if a powder applied to blood produces what neither poison, nor fire, nor any other mixture endowed with any quality produces: provided that this same thing is not seen in other blood, but only in that which has been taken from the affected part. <37.> Finally, as to the third point, I say briefly that this happens partly from the sympathy which blood has with its principle, especially with the affected part from which it has been recently cut off, partly from the antipathy of vitriol with blood: for we see that this always opposes the flowing of blood; so that even if a little of the powder is sprinkled over blood flowing from a vein or the nostrils, the blood is immediately stopped in the vein or nostrils, and this from that marvelous contrariety and dissension with blood. Nor indeed does some third quality arise from the mixture of vitriol and blood, which is then transmitted into the sick person; but vitriol acts upon the blood from antipathy, while Nature, by the hidden power of sympathy, is affected by the blood and altered at whatever distance, which is plainly irrelevant to action of this kind. But of this more fully and expressly in the third question. <38.> It must therefore be concluded that there are not lacking strong arguments for establishing the work of magnetic healing as a deed probably done by the operation of Nature alone; and from these it can clearly be inferred that it may safely and freely be practiced by all, without any fear of violated religion, even if the manner of operating is not known, provided however that it does not plainly appear Satanic, which in our powder is by no means the case, since it admits no vain circumstance, no words, no characters, by which one could reasonably think that the help of a demon is being invoked as an aid. For the power of all natural agents is not known to us, and such is the condition of our humanity, that as punishment for sin we have not the knowledge of many, and those most excellent things (which our first parent possessed)

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22 PHYSIO-THEOLOGICA, priuati simus: sed non proptereà nobis vetitum, eam è na- turæ arcanis eruere, atque ex effectibus comparare. -------------------------------------------------------- QVÆSTIO II. An pari ratione Vnguenti Armarij vsus in Vulnerum curatione sit licitus? SUMMARIVM. Eadem est sympathici pulueris, & Vnguenti Armarij in me- dicandis vulneribus vis, & conditio. n. 1. Maior tamen difficultas videtur esse in Vnguento Armario. num. 2. Qui eius naturalem virtutem astringant. ibid. Vnguenti armarij compositio. n. 3. Eius inuentor Paracelsus. Apud antiquos aliqua fuit Vnguenti praxis & cognitio. ibid. Sed non sine superstitione admixta. ibid. Modus illud parandi. n. 4. Vsus. n 5. Effecta. n. 6. Qua potissimum veniant examinanda. n. 7. Auctores qui contra Vnguentum scripsere. ibid. Diuersitas compositionis non arguit, vnguenti suspicionem, aut inefficaciam. n. 8. Nullum est nobile medicamentum, quod eodem modo ab au- ctoribus tradatur. ibid. Mirabilius est vnum medicamentum simplex pluribus malis occurrere, quam plura composita contrà eumdem morbum valere ibid. Quam multiplices, ac diuersos effectus præstet elixir vita. n. 9. Idipsum præstare poterit Vnguentum, quod p'uribus constat, quorum singula suos effectus habent. ibid. Diuersa Vnguenti compositio diuersis naturis, & vulnerum qualitatibus confert. n. 10. Etiam si vnguentum mumiem non admittat, adhuc tamen efficax est ad vulnera curanda. ibid. Multa circumstantia à plerisque adhibita superstitionis suspe- etc, non tamen absolutè damnanda. n. 11. Et adhiberi possunt cum protestatione. n. 12.

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22 PHYSIO-THEOLOGICA, we are private persons: but for that reason we are not forbidden to draw it forth from the hidden recesses of nature, and to compare it from its effects. -------------------------------------------------------- QUESTION II. Whether the use of Armary Unguent in the healing of wounds is likewise lawful? SUMMARY. The force and condition of sympathetic powder and of Armary Unguent in healing wounds is the same. no. 1. Yet there seems to be greater difficulty in Armary Unguent. no. 2. Those who defend its natural virtue. ibid. The composition of Armary Unguent. no. 3. Its inventor, Paracelsus. Among the ancients there was some practice and knowledge of the Unguent. ibid. But not without superstition mixed in. ibid. The manner of preparing it. no. 4. Its use. no. 5. Its effects. no. 6. By what matters they should chiefly be examined. no. 7. Authors who wrote against the Unguent. ibid. A diversity of composition does not argue suspicion or inefficacy in the unguent. no. 8. There is no noble medicine which is handed down by authors in the same way. ibid. It is more remarkable that one simple medicine should meet several ailments than that many compound ones should be effective against the same disease. ibid. How many and how varied effects the elixir vitae produces. no. 9. The same can be produced by the Unguent, which consists of several ingredients, each of which has its own effects. ibid. A different composition of the Unguent suits different natures and qualities of wounds. no. 10. Even if the unguent does not admit mummy, it is still effective for healing wounds. ibid. Many circumstances employed by most people, etc., though suspicious of superstition, are not however to be absolutely condemned. no. 11. And they may be used with a protestation. no. 12.

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DE SYMPATHIA. 24 Probatur fatto piorum ac doctorum hominum. ibid. Non est periculum, quod Damon resectus præstò sit ad sanitatem donandam n. 13. Neque id permitteret Deus. ibid. Alia circumstantia quamuis occulta, non sunt tamen euani- da. n. 14. Inferiora isthac à superioribus reguntur. ibid. Sidera calestia pro qualitatum, & effectuum diuersitate diuersis nominibus insignita. n. 15. Dicuntur calida, humida, &c. non quod talia sint, sed quia has qualitates in inferioribus causant. n. 16. Quod Antiqui, vt posteritas doctiorum exisceret, hieroglyphicis expresserunt. ibid Signa ruminantia ex effectibus dicta sunt. ibid. Vnquentum horabene constituta parare, superstitiosum non est. n. 17. Superstitiosa tamen sunt circumstantia à Crolio, & aliis præcepto. n 18. Ex his potius Vnguenti efficacia demonstratur. ibid. Non est absolutè relinquendum medicamentum, eo quod habeat circumstantiam superstitiosam admixtam. n. 19 Optima quæque sunt magis corruptioni, & inuidorum malignitati exposita. ibid. Conditio quod Vsnea sit è capite strangulati hominis superstitiosa non est. n. 20. Tota Vnguenti contradictie in hoc sita est, quod producat effectum in distans. n. 21. Eius operandi modus diuersimodè ab auctoribus traditus. n. 22. Omnes explicatienes, quacunque sint recidunt in formam mundi omnia connectentem. n. 23. Adhuc à nullo res verius explicata. n 24. Efficacia Vnguenti à posteriori arguitur, licet causam ignoremus. n. 25. Natura arcana nobis admirari potius datum est, quam nouisse. ibid. Neque maior difficultas est in Vnguento, quam in reliquis natura arcanis. n. 26. Quando manifesta implicantia non apparet, effectus sequutus censendus est naturalis. ibid. Paracelsi malum nomen non officit Vnguento ab ipso primùm detecto. n 27. Licitus est scientia vsus, quaprius ope Damonis fuerit acqui- sita. n. 28. b iiiij

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OF SYMPATHY. 24 It is proved by the fact of pious and learned men. ibid. There is no danger that Damon, once removed, should be ready for the restoring of health. n. 13. Nor would God permit it. ibid. Another circumstance, though hidden, is not therefore to be disregarded. n. 14. These inferior things are governed by those above. ibid. The celestial stars are marked with different names according to the diversity of qualities and effects. n. 15. They are said to be hot, moist, etc., not because they are such in themselves, but because they cause those qualities in inferior things. n. 16. What the Ancients expressed by hieroglyphs, so that posterity might be wiser. ibid. Ruminating signs are named from their effects. ibid. To prepare the ointment at the hour duly appointed is not superstitious. n. 17. Yet the circumstances prescribed by Crollius and others are superstitious. n. 18. From these rather the efficacy of the Ointment is demonstrated. ibid. A medicine is not absolutely to be abandoned because it has some superstitious circumstance mixed with it. n. 19. Whatever is best is most exposed to corruption and to the malice of the envious. ibid. The condition that the Usnea should be taken from the head of a strangled man is not superstitious. n. 20. The whole contradiction concerning the Ointment lies in this, that it produces its effect at a distance. n. 21. The manner of its working has been variously handed down by authors. n. 22. All explanations, whatever they may be, fall back upon the form of the world, which connects all things. n. 23. It has as yet been more truly explained by no one. n. 24. The efficacy of the Ointment is argued from the effect, though we are ignorant of the cause. n. 25. It is given us to admire, rather than to know, the hidden works of nature. ibid. Nor is there greater difficulty in the Ointment than in the other hidden works of nature. n. 26. When no manifest contradiction appears, the effect that follows is to be deemed natural. ibid. The bad name of Paracelsus does not discredit the Ointment, first discovered by him. n. 27. The use of knowledge is lawful, even though it was first acquired by the help of Damon. n. 28. b iiiij

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PHYSIOTHEOLOGIA, Nos eadem quæ Demon operatur, operari possemus, si eandem, quam ipse habet rerum naturalium notitiam habemus. n. 29. Paracelsus ab omnibus maledictis vindicatus. n. 30. 1. Nec maiorismiki negotij erit Vnguenti Armarij vsum, atque efficaciam in curandis vulneribus propugnare: quippe quod etsi non parum à memorato puluere discrepet (componitur enim ex diuersis simplicibus aliisque ex humano corpore comparatis, vt videre est apud Auctores, qui de eo ex professo scripserunt, quorum adhuc singuli non eandem componendi methodum tradunt, sed pro suo quisque genio quod lubet, aut magis ad rem facere videtur, Vnguento studet ingerere quia tamen non eo vulnus, sed telum vulneris inflictium inungitur, aut etiam pannus, quo cruor è vulnere manans excipitur; ideo sympathico pulueri valde affinis est, & eandem cum eo difficultatem inuoluit propter miram illam curationem in distans factam; quo virtus vnguenti ferro, aut linteis applicata transfertur, magneticè in ipsum vulnus, illudque etsi distans consolidat. Qua propter eadem ferè argumenta, quibus in asserenda probabilitate lieitoque vsu pulueris sympathici vsi sumus, militant etiam pro vnguento armario, quod eadem sane virtute agit, habetque plurimos ex Medicis, ac Philosophis qui pro eo scribunt, ac naturali virtute illud operari demonstrant. Interquos Petrus Seruius in Romana Sapientiæ Academia Professor primarius peculiari libello de Vnguento Armario Rodulphus Goclenius senior, atque etiam Iunior in Synarchrosi Magnetica, Osuualdus Gabelchone- rus in Practica Germanica, Cæsar Nagatus de rara vulnerum curatione. Burggrauius in Biolychnio, Psellus, Colerus, Schenchius, Patrisius, Basilius Valentinus, & alij multi. 2. Verumtamen, quia, vt dixi, non æquè ab omnibus traditur; non idem cum puluere parandi modus, ac tempus: multas habet circumstantias, quæ videntur planè inutiles, ac manifestè superstitiosæ, quas non puluis sympathicus: ac tandem, quia in illum longè maiore nisu scriptores multi iique piissimi, ac scientissimi conspirarunt: idcircò operæ pretium erit de eo peculiarem quæstionem instituere, atque eius partes, vsum, curandi vim distinctiùs examinare. 3. Est igitur Vnguentum Armarium conflatum ex diuersis ingredientibus; præcipuè verò pinguedine humana sangui-

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PHYSIOTHEOLOGIA, We could perform the same things that a demon works, if we had the same knowledge of natural things that he has. n. 29. Paracelsus vindicated from all curses. n. 30. 1. Nor will it be a greater business to defend the use and effectiveness of the Weapon Ointment in curing wounds: for although it differs not a little from the aforesaid powder (for it is composed of various simples and of other things prepared from the human body, as may be seen in the authors who have written on it professedly, each of whom still does not teach the same method of composition, but according to his own bent mixes into the ointment whatever he likes, or whatever seems more to the point), yet because it is not the wound itself that is smeared with it, but the weapon that inflicted the wound, or even the cloth in which the blood flowing from the wound is received; for that reason it is very closely akin to the sympathetic powder, and involves the same difficulty as it, on account of that wondrous healing at a distance; by which the virtue of the ointment, applied to the iron or to the linen, is transferred magnetically to the wound itself, and though distant, it heals and consolidates it. For this reason, the same arguments, or nearly the same, which we employed in asserting the probability and lawful use of the sympathetic powder, also apply in support of the weapon ointment, which surely acts by the same power, and has very many physicians and philosophers who write in its favor and demonstrate that it operates by natural virtue. Among them are Petrus Servius, chief professor in the Roman Academy of Wisdom, in a special treatise on the Weapon Ointment; Rodolphus Goclenius the elder, and also the younger, in Synarchrosis Magnetica; Oswaldus Gabelchonerus in the German Practice; Caesar Nagatus on the rare curing of wounds; Burggrauius in Biolychnion; Psellus, Colerus, Schenchius, Patrisius, Basilius Valentinus, and many others. 2. Nevertheless, because, as I said, it is not handed down by all in the same way, the mode of preparing it, and the time, are not the same as with the powder: it has many circumstances which seem entirely useless, and plainly superstitious, unlike the sympathetic powder; and finally, because many writers, and those most pious and most learned, have conspired in its favor with far greater effort: therefore it will be worth the trouble to institute a special inquiry into it, and to examine more distinctly its parts, use, and healing power. 3. Therefore the Weapon Ointment is composed of various ingredients; but especially of human fat and blood-

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DE SYMPATHIA. 25 ne, mumia, Vsnea, seù musco in etanio suspensi hominis nato, aliisque simplicibus medicamentis: ex quibus alij plura, alij pauciora vsurpant; vt videre est apud Sennertum lib. 5. quarta parte cap. 10 suæ Practicæ Medicinæ, vbi ex professo de Vnguentor armario agit, ac singulas singulorum descriptiones adducit. Potissima verò, & magis recepta est descriptio Paracelsi, qui primus omnium huius Vnguenti inuentor perhibetur, eoque veluti insigni munere Maximilianum Cæsarem' donasse fertur. Quamquam apud Antiquiores etiam aliqua huius vnguenti adumbratio reperitur, vt præ aliis notat eruditissimus Leo Allarius, qui ex Iulio Africano sexto de cætis eius formam desumpsit, atque in hæc verba ex Græco in Latinum transtulit. Vulnerato à ferro illud doloris remedium erit; ferrum quod vulnus inflixit inungere opus est, deinceps illud quasi percutientes, in vulnus adigere. Licet & hoc non sine aperta superstitionis nota vsurparetur, vt ex sequentibus constat. Cæterum Paracelso subscribit etiam Ioannes Baptista Porta in sua Magia natusrali lib. 8. cap. 12. addita solum Terebinthinæ vnciâ. <4.> Modus autem illud parandi, atque opportunum tempus Paracelso, & aliis indefiuitum. Crolius id restringit ad tempus, cùm sol est in Libra: Alij magis coarctant ad diem decimam, & vndecimam Septembris, stilo veteri. Alij obseruant tempus, in quo luna lumine augeatur, sitque in bonadomo, & in signo humanæ figuræ. Alij demum quouis tempore parant: Quinimó Gabelchouerus solum ex humano corpore museum adhibet, quem etiam panem referre ait, siù adhibeatur, siue non. Ioannes Vvitchius, & Sennertus testantur, se nouisse hominem, qui absque tot circunstantiis, ac speciebus, solum poti domestici adipem in vsum adhibebat. <5.> Vsus verò hic est ab omnibus fere eadem methodo traditus; licet Crolius alias etiam circumstantias adhibendas præcipiat (quas tamen nos ex nunc prorsus reiicimus vti superstias, ac planè superstitiosas.) Habitum telum, quo quis vulneratus fuit, immergatur in pyxidem vnguento plenam, vel eo inungarur alternis diebus: quod si necessitas vrgeat, & vulnus sit ingens, id singulis diebus fiat: deinde inuolutum panno mundo seruetur in loco temperato non multum calido, aut frigido, nec vbi ventus afflat, sed vel in arcula, vel alio quouis repositorio magis proportio- nato. Si verò telum haberi nequit satis erit lignum saliceum, aut etiam pannus, qui in vulneris cauitatem immer-

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DE SYMPATHIA. 25 also, mumia, Vsnea, or moss hanging in the smoke of a hanged man, and other simple medicines: of which some use more, others fewer; as may be seen in Sennertus, book 5, fourth part, chapter 10 of his Practica Medicina, where he treats expressly of the Vnguentor armario , and gives the descriptions of each. But the chief, and more commonly received, is the description of Paracelsus, who is said to have been the first inventor of this Unguent, and to have bestowed it on Emperor Maximilian as a singular gift. Although among the ancients also some outline of this ointment is found, as learned Leo Allatius notes especially; who from Julius Africanus, sixth of the cætis , took its form, and translated it out of Greek into Latin in these words. For one wounded by iron, this remedy for pain will be: it is necessary to anoint the iron that inflicted the wound, then, as if striking it, drive it into the wound. Yet even this was used not without an open mark of superstition, as is clear from what follows. Moreover, Johannes Baptista Porta also subscribes to Paracelsus in his Magia naturalis , book 8, chapter 12, adding only an ounce of terebinth. <4.> Now the manner of preparing it, and the proper time, are left indefinite by Paracelsus and others. Crolius restricts it to the time when the sun is in Libra: others confine it more closely to the tenth and eleventh day of September, old style. Others observe the time when the moon is increasing in light, and is in a good domicile, and in the sign of the human figure. Others, finally, prepare it at any time: indeed, Gabelchouerus uses only moss from the human body, which he says may also be applied to bread, whether it is applied or not. Ioannes Vvitchius and Sennertus testify that they knew a man who, without so many circumstances and ingredients, used only the grease of domestic fat for his purpose. <5.> The use, however, has been handed down by almost all in the same method; although Crolius also prescribes other circumstances to be observed (which nevertheless we now entirely reject as superstitious, and plainly superstitious.) Let the weapon with which one was wounded be immersed in a box full of ointment, or let it be anointed with it on alternate days: but if necessity presses, and the wound is large, let this be done every day. Then, wrapped in a clean cloth, let it be kept in a temperate place, not too hot or cold, nor where the wind blows, but either in a small chest or in some other more suitable repository. But if the weapon cannot be had, it will suffice to take a willow stick, or even a cloth, which is immersed in the cavity of the wound

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26 PHYSIO-THEOLOGICA gatur, sanguinemque fluentem excipiat; cui ex se exsiccato inspergatur supradicto modo vnguentum, vel in pyxidem vnguento plenam deiiciatur, intus linguendo. 6. Porro effectus est, vt si naturali via curatio haberi poterit, ea protinus sequatur, nulla prorsus alia cura vulneri præstita, nisi quantum naturæ subseruiatur, illud leniter à sordibus, quæ forte contraxerit expurgando, singulisque d[e]lebus nouo ac mundo linteolo sola patientis vrina prius ma[n] defacto circum ligando. 7. Nunc igitur hæc tria potissimum veniunt à nobis examinanda. Primò tam diuersa, totque modis exhibita Vnguenti huius paratio: quæ nihilominus potis sit eadem felicitate eundem prorsus effectum curationis, ac sanitatis inducere; quod naturali via præstare videri poterit alicui impossibile. Secundò modus, ac tempus illud parandi, quæ omnia ad curationem perficiendam videntur impertinentia, nec vllor modo conducere, sicut & aliæ circumstantiæ, quas passim auctores præcipiunt admittendas. Tertiò tandem ipse effectus curationis per medicamentum quantumuis ab ægro remorum expectandus, cum aliàs ex Philosopho quoduis agens ad hoc, vt agat requirat approximationem, & contactum ad passum. Quamobrem vel ob id Sennertus loco suprà citato, Naudæus in Syntagmate de studio Militari lib. 1. cap. 33. num. 4. Kircherus de Arte Magnetica lib. 3. part. 7. cap. 2. Ioannes Roberti speciali animaduersione aduersus Grolium, & Goclenium suscepta, ipsum vnguentum vti superstitiosum, Sathanicumque inuentum de prædicant, ac totis viribus aggrediuntur. 8. Et quidem quod ad diuersam Vnguenti præparationem attinet, miror, viros tam doctos, tamque eximios, ob id solum illud vanitatis, ac superstitionis arguere, quod non idem semper, ac constans apud Auctores sit componendi modus. Equidem, (vt benè Seruius de Vnguento Armario pag. 111.) nullum ferè est generosum, ac nobile medicamentum, cuius apud omnes vna sit compositio. Videmus id in Teriaca, Mithridaticæ, Elixire, vt vocant Vitæ, aliisque aduersus vertena antidotis, quæ cum vnum ferè habeant scopum, diuersa tamen incedunt via, diuersissimè à diuersis parantur. Neque enim tam arcta est Naturæ pharmacopæa, quin possit plura medicamenta suppeditare in idem genus morbi conuenientia; nec ars tam rudis, quæ pluribus experimentis edocta per diuersi generis compositiones eidem malo præstò esse non valeat: cum proinde longe maiora videamus, posse inquam vno eodemque Pharmaco, herba,

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26 PHYSIO-THEOLOGICA so that it may receive the flowing blood; when this has dried on its own, let the aforesaid ointment be sprinkled on it in the above-mentioned manner, or let it be thrown into a box full of ointment, licking it within. 6. Moreover, the effect is that, if a cure can be obtained by the natural route, it should immediately follow, with absolutely no other treatment applied to the wound, except insofar as nature is assisted, namely by gently cleansing it of any dirt it may have contracted, and each day binding it up with a new and clean linen cloth, first moistened with the patient’s own urine. 7. Now then, three things especially come before us for examination. First, the preparation of this Ointment, so varied and presented in so many ways, which nevertheless may be able, with equal success, to produce exactly the same effect of cure and health; something which by the natural route would seem impossible for anyone to accomplish. Second, the manner and time of preparing it, all of which seem irrelevant to bringing about the cure, and in no way helpful, as also are the other circumstances which authors everywhere prescribe to be admitted. Third, finally, the very effect of the cure to be expected from the medicine by the sick person, however helpless, since otherwise, according to the Philosopher, whatever acts for this end requires approximation and contact with the thing acted upon. For this reason, or for that one alone, Sennertus in the passage cited above, Naudæus in the Syntagma de studio Militari, book 1, chapter 33, number 4, Kircher in De Arte Magnetica, book 3, part 7, chapter 2, and Ioannes Roberti, in a special warning undertaken against Grolius and Goclenius, denounce the ointment itself as a superstitious and satanic invention, and attack it with all their might. 8. And indeed, as far as the different preparation of the Ointment is concerned, I am amazed that men so learned and so outstanding should for that very reason accuse it of vanity and superstition, merely because the method of composition is not always the same and constant among the authors. Truly, as Servius says well concerning the Armarium Ointment, page 111, there is scarcely any noble and choice medicine whose composition is the same among all. We see this in Theriaca, Mithridatic, the Elixir of Life, as they call it, and other antidotes against the plague, which, though they have almost one and the same aim, yet proceed by different paths and are prepared in very different ways by different people. For nature’s pharmacy is not so narrowly confined that it cannot supply several medicines suitable for the same kind of disease; nor is the art so crude that, taught by many experiments, it cannot be at hand for the same ailment through compositions of different kinds: since therefore we see much greater things, I say, can be done in one and the same drug, herb,

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DE SYMPATHIA. 37 aut lapide, deleteriis ferè omnibus, quamuis contraria qualitate pollentibus obuiari: vno Elixir vitæ, vno Azoth mirabili Paracelsi, vno illo viuifico lapide Seuerini omnes morbosos affectus licet à contrariis causis exortos depelli. Non ergò mirum, si quod diuersa à prædictis Auctoribus compositio excogitata in omnium morborum affectionibus præstat, id ipsum præstet diuersa huius vnguenti præparatio in vno vulnere consolidando: Faciliùs enim possunt diuersæ æqualis, parisque virtutis causæ eundem effectum producere, quam vnicum remedium, idemque simplex in diuersos, contrariosque fines contendere, atque omnes ad eundem scopum reddendæ salutis per diuersas semitas ordinaré. Et ex his etiam diluitur, quod obiectat Sennertus, non posse videlicet idem vnguentum omnes effectus, eosque inter se diuersos, qui in vulnerum curatione habentur, præstare; cuiusmodi est, fuentem sanguinem sistere, imminentem inflammationem cauere, suppurare contusam carnem, nouam sufficere, agglutinare, &c. Namque si potest Elixir vitæ, & naturalem calorem fouere, & radicale humidum sustentare, & noxia euncta depellere, atque vt vno verbo dieam, tam miros effectus in vno, eodemque corpore parere, sicque eodem tempore, & crassa ineidere, & subtilia condensare, & molificare dura, & macilenta pingue facere, & pingua extenuare, vt eruditè demonstrat ex Aduersariis ipsis Kircherus parte 7. cap. 3. eoquia ex innu- meris speciebus constatum id præstat se solo, quod singulæ singillatim; cur non longè pauciores effectus poterit vnguentum hoc gignere, quod ex pluribus speciebus constat, quæ seorsim singuæ valent? Siquidem, vt testes sunt peritissimi Medieorum, & probat quotidie experientia Bolus Armenus, (qui ab omnibus ferè in huius vnguenti præparatione abhibetur) duo potissimum præstat, & sanguinem sistit, & glutinationem coadiuuat: terebinthina abstersioni, expulsioni putis, nouæ carnis inductioni; adeps quicumque contusæ carnis suppurationi, alia demum spiritibus vitalibus generandis, conseruandis, roborandis, calorique naturali fouendo conferunt, confluuntque. Vnde iam patet, vnguentum ipsum ex se ex modo diuersimodè illud parandi, non esse vulneribus curandis ineptum; quippe quod ingredientibus constat singulis per partes in in eundem finem collineantibus, ac vices suas implentibus. Qua autem ratione non vulneri, sed sanguini iam exereto applicatus hos omnes simul effectus parere valeat,

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On sympathy. 37 either by stone, by almost all destructive things, however they may be endowed with contrary qualities, one may be opposed: by one Elixir of life, by one marvelous Azoth of Paracelsus, by that one vivifying stone of Severinus, all morbid affections may be driven away, even though they arise from contrary causes. It is therefore no wonder that what a composition devised by the aforesaid Authors accomplishes in the affections of all diseases, the same should be accomplished by the different preparation of this ointment in consolidating a single wound: for it is easier for diverse causes of equal and like virtue to produce the same effect than for one and the same simple remedy to strive toward diverse and contrary ends, and to direct all by different paths to the same goal of restoring health. And from this also there is answered what Sennertus objects, namely, that the same ointment cannot produce all those effects, and those diverse among themselves, which are found in the treatment of wounds; such as stopping flowing blood, preventing imminent inflammation, suppurating contused flesh, replacing new flesh, agglutinating, and so forth. For if the Elixir of life is able both to nourish natural heat and to sustain radical moisture and to drive away all harmful things, and, to put it in a word, to produce such marvelous effects in one and the same body, and thus at the same time both to cut gross things and to condense subtle things, and to soften hard things and make lean things fat and to make fat things thin, as Kircher learnedly demonstrates from the very Adversaria, part 7, chap. 3, because it performs by itself, though made up of innumerable species, what each species does separately; why then should not this ointment, which consists of far fewer effects, be able to generate effects, when it is composed of several species, each of which is effective on its own? Since, as the most skilled physicians testify, and experience proves daily, Armenian bolus— which is used by almost everyone in the preparation of this ointment— accomplishes chiefly two things, namely, it stops blood and assists agglutination; turpentine contributes to cleansing, expelling pus, and inducing new flesh; any fat whatever contributes to the suppuration of contused flesh, while other ingredients contribute at last to generating, preserving, strengthening the vital spirits, and nourishing natural heat. Hence it is now clear that the ointment itself, by virtue of the different ways of preparing it, is not unfit for healing wounds; for it is made up of individual ingredients, each of which separately tends toward the same end and performs its own office. But in what way it may be able, when applied not to the wound itself but to blood already drawn forth, to produce all these effects at once,

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18 PHYSIO-THEOLOGIA, ad tertium quæstionis eaput attinet id discutere. Pro nunc sufficiat demonstrasse multiplicem vnguenti præparationem non arguere eius inefficaciam. <10.> Deinde, cum prædicti Auctores pluribus experimentis suam quisque compositionem probaucerint, & ipsa vulnera non omnia eiusdem rationis, sed alia leuia, alia grauiora esse necessum sit: Item & hominum naturæ, (quæ vt ait Hippocrates sunt morborum medicatrices, quasque ego in hoc negotio potissunam partem habere, vnguentum autem leuissimo solum præsidio naturas ipsas subleuare, peculiari quæstione ostendam.) Cum inquam naturæ hominum non sint æquales, sed aliæ robustiores, aliæ nimis deiectæ: mirum non est, si quod hi præcipuam vnguenti materiam dixere, hoc alij suis experimentis edocti in fortis naturæ hominibus, vulneribusque non tam profundis, quæ forte natura se sola potuisset agglutinare, superuacaneum prædicarint, at longe leuiere vnguenti præparatione vsi, eundem planè effectum adepti sunt. Non igitur ex eo quod Natura huius se sola curationem feliciter aggressa est, vnguentum quamvis leuissimum inefficax dicendum erit; si cut non per hoc cætera vulneraria medicamenta prorsus inefficacia exclamarem Philippus Palatius, Petrus Parisius, aliique, eoquod ipsi solo balsamo communi ex oleo, & vinò, aut etiam aqua simplici, & turundis ex cannabe, aut ex lino confectis, etiam deploratæ spei vulnera se curasse testentur. Nam in aliis fortè deiectæ, atque imbecillis naturæ hominibus id ipsum non assequuti fuissent. Quare in hoc etiam à Petro Seruio acerrimo. Vnguenti huius propugnatore dissentio, qui vnguentum à Ioanne Vitiehio excogitatum, eo quod Mumiam, cæteraque ex humano corpore fulcimenta prætereat, tanquam inefficax & nullius roboris reijcit asserens nullam tunc ipsi cum ægro intercedere Sympathiam; sed si fortè æger salutem consequatur, eam soli Naturæ acceptam ferendam esse. Non inquam, id piacet; nam fieri potest, vt licet Natura multoties se sola salutem asserre sit apta, quandoque tamen ita debilis reperiatur, vt se sola non satis sit, at vel leui præsidio fulta, vires suas exserat atque opus perficiat. Sed de his fusius sequenti quæstione. <11.> Quoad secundum eaput, de modo, ac tempore vnguentum parandi, etsi reuerâ tot, tantasque circumstantias superuacaneas dixerim, atque earum plurimas à Goclenio, Crolio, Gabelhouero, nescio, nùm animosè magis an scrupulosè præceptas, omninò vitandas suadeam, eo ma-

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18 PHYSIO-THEOLOGIA, with regard to the third chapter of the question, to discuss this. For the present it is enough to have shown that the manifold preparation of the ointment does not argue its ineffectiveness. <10.> Then, since the aforesaid authors by many experiments each proved his own composition, and since the wounds themselves are not all of the same kind, but some slight, others more serious, it is necessary also that human natures, (which, as Hippocrates says, are the healers of diseases, and which I shall show in this matter to have the chief part, while the ointment with only the slightest aid merely supports nature itself, in a special question.) Since, I say, human natures are not equal, but some stronger, others too much weakened: it is not surprising if what these men said to be the chief material of the ointment, others, taught by their own experiments, in men of strong nature and in wounds not so deep, which perhaps nature alone could have healed together, proclaimed to be superfluous, yet having used a much more slight preparation of the ointment, they obtained the very same effect. Therefore, from the fact that Nature has happily undertaken the cure of this wound by itself, the ointment, however slight, must not be called ineffective; just as I would not therefore cry out that the other wound medicines are utterly ineffective, as Philippus Palatius, Petrus Parisius, and others did, because they themselves testify that with only the common balsam made from oil and wine, or even with simple water, and with pledgets made from hemp, or from linen, they cured wounds even of desperate hope. For in others, perhaps of weakened and feeble nature, they would not have achieved the same thing. Wherefore in this also I disagree with Petrus Servius, the most ardent champion of this ointment, who rejects the ointment invented by Ioannes Vitiehius, because it omits Mumia and the other supports from the human body, as ineffective and of no force at all, asserting that then there is no Sympathy between it and the sick person; but if the patient should perhaps recover health, that must be attributed to Nature alone. This, I say, does not please me; for it can happen that although Nature many times is able to bring about health by itself, at times nevertheless it is found so weak that it is not sufficient by itself, but supported even by a slight aid, it exerts its strength and brings the work to completion. But of these matters more fully in the following question. <11.> As for the second chapter, concerning the manner and time of preparing the ointment, although in truth I have said that so many, so great circumstances are superfluous, and I advise that very many of them, prescribed by Goclenius, Crolius, and Gabelhouerus, I know not whether more vehemently than scrupulously, should by all means be avoided, to that ex-

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DE SYMPATHIA. 19 ximè quod cæteri non obseruent, & vnguentum nihilo secius proficuum inueniatur; eas tamen vniuersè damnare non audeo, præsertim si nullam apertè superstitionem oleant, atque omnis Daemonum assistentia explicitè reijciatur: quippe ex occulto forsan hominibus modo possunt naturam, naturalemque vnguenti efficientiam coadiuuare. < 12.> Moueor, quia id licitum esse vel in manifestis superstitionibus (ex causa tamen, & præmissa priùs debita protestatione) ex multis D. D. iam suprà dictum est: quantò magis cum res est dubia, ac de hominis agitur sanitate? Fecit id Caietanus, vt de se testatur in summa V. superstitione in apertissima superstitione, quæ ex sacra Scriptura verba vsurpabat, præmissa protestatione, & verbis Psalmi prolatis, nec tamen effectus sequutus est, quia Daemon reiectus non aduit. Fecit Athanasius Kircherus vir pijstlinus æquè, ac doctissimus ex Societate I E S V, ad explorandum num naturali virtute possit iaspis ictu horas ostendere, vnde ipse præmissa protestatione, non dubitatit rei periculum facere, irrito tamen, vt ipse fatetur euentu. Fecit & Cardinalis de Lugo, (testatur id Tambur. in Decalog. lib. 2 cap. 6. 6. 1.) qui Romæ tandem degens ex diuersitate ictuum sese ad Italicum horologium conformantium agnouit tandem hanc Daemonis imposturam; quandoquidem, vt ipse ait, & notat etiam Kircherus par. 5. cap. 3. horarum distributio, & pro locorum varietate diuersitas non à natura, sed hominum placito sit inuenta: cur non etiam licitum erit in ijs, quæ minimè ab hominum voluntate, sed, ab occultissimis causis, à cælorum influentiis, à naturæ affectæ qualitate, aliisque conditionibus pendet, quæ purè naturalia sunt explorare, simili protestatione præmissâ; quamuis ad rem videantur impertinentia? Sed & in casu nostro, doctus quidam, ac pius Theologus apud Helmontium, in Blacharo pag. mihi 589. cum non assequi posset, subesse in Chalcantho vim naturalem sanandi vulnus absens si linteo cruento adspergeretur, ideoque reuptaret opera diaboli sanationem istam contingere ex altera autem parte cum videret multas experientias à viris probis factas, elegit rei periculum salua conscientia facere. Insperit itaque puluerem optimi chalcanthi linteo cruento cum protestatione, se nolle quicquam experiri, aut sanatum iri, si vel minima esset pacti, vel cacodæmonis operatio at verò ait se vidisse nihilominus vulnus soliio citius sanatum, cruorem quoque statim sedatum; quod argumenta

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ON SYMPATHY. 19 seems because others do not observe it, and the ointment is nevertheless found to be no less effective; yet I do not dare condemn them universally, especially if they plainly smell of no superstition, and if all assistance of demons is explicitly rejected: for perhaps in some hidden way they may be able to aid nature and the natural efficacy of the ointment. <12.> I am moved by this, because it has already been said by many learned doctors above that it is lawful even in manifest superstitions (for a cause, however, and after a prior due protestation); how much more so when the matter is doubtful, and a person’s health is at stake? Cajetan did this, as he testifies of himself, in the case of a very superstitious practice, in a most obvious superstition that made use of words from Sacred Scripture; after making a protestation and reciting the words of a Psalm, yet no effect followed, because the demon had not been excluded. Athanasius Kircher, a most pious and equally learned man of the Society of Jesus, did likewise, to test whether a jasper by its natural power might indicate the hours by a blow; whereupon he, after making a protestation, did not hesitate to make the experiment, though with a fruitless result, as he himself admits. Cardinal de Lugo also did this (Tamburini testifies to it in the Decalogue, book 2, chapter 6, § 1), who, dwelling at Rome, finally recognized this deception of the demon from the variety of the blows conforming to the Italian clock; for, as he says, and Kircher likewise notes in part 5, chapter 3, the division of the hours, and their diversity according to the variety of places, was invented not by nature but by human choice: why then should it not also be lawful to investigate, with a similar protestation previously made, those things which depend least of all on human will, but rather on most hidden causes, on celestial influences, on the quality of the affected nature, and on other conditions, which are purely natural; even though these things may seem irrelevant to the matter? And in our case too, a certain learned and pious theologian, with Helmont, in Blacharo, page, as I have it, 589, when he could not understand that in chalcanthum there lay a natural power of healing a wound absent when the cloth was sprinkled with blood, and therefore judged that this healing occurred by the work of the devil, on the other hand, seeing many experiments made by honest men, chose to test the matter with a clear conscience. So he sprinkled the powder of the best chalcanthum on a bloodstained cloth, with the protestation that he did not wish to try anything, nor that it should be healed if there were even the least pact or operation of an evil spirit; yet, he says, he nevertheless saw the wound healed sooner than expected, and the blood at once checked; which are arguments

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30 PHYSIO-THEOLOGICA, to est, vt ipse postea indubitato credidit, opus natura duce perfici, quamuis via nobis ignota. Neque verò periculum est, in tali casu circumstantiam fortassis inutilem, quæ adhibetur, Dæmonem in tædus aduocaturam, cumque præsto ad sanitatem donandam affuturum: Nam vt sæpè dixi, Dæmon non est tàm bonus, tamue munificus, vt vel rejectus velit assistere, atque hominem sibi inimicum præsertim cum res culpa vacat, & eius ope rejecta suo vtentem iure velit beneficiis promereri. Patet id satis in memoratis modo experimentis à prædictis Theologis factis: patet id etiam ex implacabili odio, atque inuidia, qua totum hominum genus prosequitur. Nec clementissimus Deus id vnquam permitteret, vt nobis veritates causarum naturalium inuestigantibus, adeoque Deum ipsum, vt Auctorem Naturæ aduocantibus, callidus hostis suis præstigiis in præiudicium veritatis imponeret, falsamque protruderet sed nec permittere potest, vt Theologi omnes consentiunt. 13. Moueor secundò quia huiusmodi circumstantiæ, qualis forte erit vnguentum istud parandum esse Lunâ crescente, in bonadomo constituta, & in signo humanæ figuræ, Sole etiam libræ signum, vel certos quosdam eiusdem signi gradus permeante, non sunt prorsùs euanidæ, ac proinde vti suspectæ reijciendæ. Quandoquidem negare non possumus in vniuersum inferiora isthæc occulta quadam vi à superioribus regi, vt patet præsertim in aliorum medicamentorum præparatione, ægrorum decubitu, pharmacorum sumptione venæ sectione, plantarum insitione, alij quæ rerum electionibus, in quibus à peritis, & quidem legumè, vt in loco diximus, plurimum obserua ut situs cælestium corporum ac præcipuè luminarium, à quorum bona vel mala constitutione, configuratione, ac positu pendet bonus, vel malus euentus rerum, provt fusè probat Galenus de diebus Dectetorijs, atque erudiè prosequitur Maginus in lib. de legitimo Astrologia in medicina vsu. Non ergò ob id quod vnguentum in certa syderum constitutione fieri præcipiatur, vanitatis proinde, ac superstitionis erit damnandum. 14. At, inquies. Quid sibi vult humanæ figuræ signum in quo constituta Lunâ præcipitur vnguenti præparatio? Quid Sol in Libra, adhoc vt felix, & auspicata prodeat compositio? Ex signis quidem cælestibus, vt & planetis, alia esse humanæ naturæ amica, alia inimica, alia ignea, alia terrea, alia aliis qualitatibus prædita, verum est, ac quod

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30 PHYSIO-THEOLOGICA, that is, as he himself later believed without doubt, that the work is accomplished by the guidance of nature, though the way is unknown to us. Nor indeed is there danger that, in such a case, a circumstance perhaps useless, which is employed, should summon the Demon to the torch, and that he, being at hand, would come to grant health: for, as I have often said, the Demon is not so good, nor so generous, that even if rejected he would wish to assist, and especially a man hostile to him, when the matter is free from fault, and when he is rejected, by his aid, would wish to earn benefits by right of his own. This is sufficiently clear from the experiments just mentioned, made by the aforesaid Theologians: it is also clear from the implacable hatred, and envy, with which he pursues the whole human race. Nor would the most clement God ever permit this, that when we are investigating the truths of natural causes, and thus invoking God Himself as the Author of Nature, a cunning enemy should by his tricks impose upon us to the prejudice of truth, and put forward falsehood; nor indeed can He permit it, as all Theologians agree. 13. I am moved secondly because circumstances of this kind, such as perhaps will be that this ointment ought to be prepared while the Moon is waxing, with it placed in a good house, and in the sign of the human figure, with the Sun also passing through the sign of Libra, or certain degrees of the same sign, are not altogether void, and therefore should not be rejected as suspect. Since we cannot deny in general that these lower things are governed by some hidden power from the higher, as appears especially in the preparation of other remedies, the lying down of the sick, the taking of medicines, bloodletting, the grafting of plants, and other choices of things, in which, as in the place we have said, the positions of the celestial bodies, and especially of the luminaries, are greatly observed by experts, and indeed lawfully; for the good or bad outcome of things depends on the good or bad constitution, configuration, and position of them, as Galen proves at length in De Diebus Decretoriis, and Maginus expounds learnedly in the book De legitimo Astrologia in medicina vsu. Therefore, because an ointment is ordered to be made in a certain constitution of the stars, it is not for that reason to be condemned as vanity and superstition. 14. But, you will say, what is meant by the sign of the human figure, in which the preparation of the ointment is ordered to be made while the Moon is in it? What is the Sun in Libra, so that the composition may come forth fortunate and auspicious? From the heavenly signs, as also from the planets, some are friendly to human nature, others hostile, some fiery, others earthy, others endowed with other qualities; this is true, and what

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DE SYMPATHIA. 51 hoc hominis figuram, illud Arietis, aliud Leonis referat, &c. Hoc planè fictitium est, hominum placitum, ac nugæ vt plurimum à Poëtis excerptæ: idque factum est vel quia stellæ in tali astrismo positæ talem figuram quodammodo referebam, vel potiùs, quia Poëtæ, ne sua figmenta ab hominum memoria exciderent, sideribus appinxerunt, quò in cælestibus perennarent. Cæterum tam nocet homini canis sidereus quod in eum sirij Fabula translata est, quam canis pietus aut marmore exsculptus: si quid autem nocet, id potius habet à qualitatibus intempetatè calidis, quam à cognomento, aut similitudine canis, quam præ se fert, non quod aliquid commune cum eo habeat. Verum, vt his satisfaciam, notandum est, ex iis, quæ in nostro Lexico diximus, huiusmodi fictiones, ea nomina, non temerè à priscis illis Astronomis esse excogitata, ac sideribus attributa, sed vt aliquid sub fabulæ cortice nobis degustandum præberent, eorumque prauas; aut benè has qualitates notas facerent. Nam neque Astra calida sunt, aut frigida, humida, aut sicca, provt communiter dicuntur esse, cum hæ qualitates propriæ elementorum sint, ac solum in sublunaribus hisce, à quibus cælestia longe discrepant, reperiantur. Sed quia nostri antiqui experimentis multis edocti agnouerunt has primas qualitates à certis planetis, ac sideribus gigni, destui, conseruari, &c. Ideò non ineptè eas dictis planetis & sideribus attribuerunt. Sic quia viderunt aliqua signa suis benignis influxibus humanum potissimum genus afficere, vt id nobis significarent, placuit eis in humanam figuram redigere, & his veluti hieroglyphicis eorum naturam explicare: quia viderunt maleficis in primo Zodiaci signo constitutis, aut luminatium defectionibus in eodem signo incidentibus, arietes malo aliquo laborare, cane sidereo exoriente, canes nostros in rabiem agi, &c. Quamuis nil habeant cum Ariete, aut cane commune præter nomen æquiuocum, & aliqualem effectuum similitudinem, eadem talibus nominibus indigitarunt. Et hinc prodiit tanta signotum nomenclatura, atque distinctio in humana, ferina, deformia, pulchra, mutilata, ruminantia, muta, vocem habentia, &c quæ passim memorant Astronomi. & obseruant in curationibus Medicis. Hinc singulis membris humanis singula Zodiaci signa præfecerunt; obseruationibus quippe cautum est, ea ta ibus membris, nescio qua virtute præesse, itavt nefas sit illud tangere ferro, cum Luna permeat signum quod tali membro

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of this man’s figure, that of Aries, another of Leo, and so on. This is plainly fiction, a human device, and mostly trifles taken from the poets; and this was done either because the stars placed in such a constellation in some way resembled such a figure, or rather because the poets, lest their inventions should slip from men’s memory, fastened them upon the stars, so that they might remain perpetually among the heavens. Moreover, just as a starry dog does no harm to a man because the fable of Sirius has been transferred to it, any more than a painted dog or one carved in marble; if it does, however, do any harm, that comes rather from qualities excessively hot, than from the name or likeness of a dog which it bears, not because it has anything in common with it. But, in order to satisfy these points, it must be noted, from what we have said in our Lexicon, that such fictions, those names, were not rashly invented by those ancient Astronomers and attributed to the stars, but so that they might offer us something to taste under the bark of the fable, and make known their evil or good qualities. For neither are the stars hot, or cold, moist, or dry, as they are commonly said to be, since these qualities belong properly to the elements, and are found only in these sublunar things, from which the heavenly bodies differ greatly. But because our ancients, taught by many experiments, recognized that these primary qualities are generated, destroyed, preserved, and so forth by certain planets and stars, therefore they not inappropriately attributed them to the said planets and stars. Thus, because they saw that certain signs, by their kindly influences, especially affect the human race, in order to signify this to us, it pleased them to represent them in human form, and by means of these hieroglyphs to explain their nature: because they saw that with the malignant ones placed in the first sign of the Zodiac, or with the luminaries eclipsed when they fall in the same sign, rams suffer some misfortune; when the starry dog rises, our dogs are driven into madness, and so forth. Although they have nothing in common with Aries or with the dog except an equivocal name and a certain likeness of effects, they indicated them by such names. And from this there arose so great a nomenclature of the signs, and distinction into human, wild, deformed, beautiful, mutilated, ruminant, mute, vocal, and so on, which Astronomers everywhere mention and observe in medical treatments. Hence they assigned individual signs of the Zodiac to the individual human limbs; for by observation it has been established that they somehow preside over such limbs by a certain virtue, so that it is unlawful to touch that member with iron when the Moon passes through the sign which

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32 PHYSIO-THEOLOGIA, præficitur. Sic etiam abstinendum à potionibus medica- mentorum per aluum euacuantium Lunâ versante in siguis animalium ruminantium, nam tunc vomitus excitatur, vt experientia docuit, & ipsemet semel, & iterum obseruaui. Non quod ruminatio illa, quæ eius nominis animalibus competit sit cælestibus signis aliquo pacto communis, sed quia obseruario vomitus semper occurrentis cum Luna permeat dicta signa, causa fuit, vt eadem signa, vt nota fierent, ruminantia dicerentur. Notum etiam est, Luna in Scorpionis signo versante scorpionibus nostris vires augeri, ac tunc temporis infensissimos esse, vt suo malo probauit amicissimus Petrus de Castro Medicus eruditissimus, de quo sæpè in nostro libro meminimus: exorientibus stellis in Delphino positis, in Arginaui, in ceto, & cæteris eiusdem generis, tempestates in Mari excitari. Numquid ne id aceidit, quia Delphini in mati exultantes tempestates præsignant, ideò & stellæ tali nomine insignitæ ex hor capite etiam tempestates decernent? non equidem, sed ideo hoc illis nomen inditum, quia talis naturæ sunt, qua tempestates cum Luna exorientes faciunt, quas Delphini pisces exultatione præsagiunt; vnde æquum fuit, vt eo nomine appellarentur, &c. Neque istæ aniles fabulæ sunt, vt benè aduertit Argotus in Astronomicis lib. 2. cap. 14. Sed obseruationes propè infallibiles longissimi temporis vsu comprobatæ, quæ quidem licitæ sunt, & verissimæ. Nam quamuis Ecclesia damnarit Astrologiam iudicariam, quæ de hominis vita, & iis quæ à libera voluntate dependent, temerè quicquam pronunciat, (quandoquidem ea impia est, ac planè superstitiosa) tamen quatenus tradit præcepta in Medicina obseruanda, quemadmodum etiam circà Artem navigatorium, & agticulturam, permisit, & sua permissione probauit. <17.> Nunc igitur non mirum cuiuis esse debeat, si vnguentum nostrum præcipiaur fieri crescente Luna, in bono signo humanam figuram præseferente, & in bona domo constituta. Nam licet id fortè nimis scrupulosum sit, & quandoque superfluum, non est tamen superstitiosum, aut à legitimis Astronomorum præceptis alienum: quando certum est ideo hæc signa talibus figuris, ac nominibus insigniri, quia cum rebus, quæ talem figuram præseferunt, aut nomen obtinuerunt, aliquam seruant analogiam. <18.> Potiùs superstitiosæ dicendæ erunt reliquæ circumstantiæ à Crolio præceptæ: vt scilicet ferrum potius inungatur, quam

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32 PHYSIO-THEOLOGIA, is placed over it. In like manner one must also abstain from medicinal potions that purge the bowels when the Moon is passing through the signs of the ruminant animals, for then vomiting is excited, as experience has taught, and I myself have observed it once and again. Not that that rumination, which belongs to animals of that name, is in any way common to the heavenly signs; but because the observation of vomiting, which always occurs when the Moon passes through those signs, was the reason that those same signs, so that they might be recognized, were called ruminant. It is also well known that when the Moon is in the sign of Scorpio, our scorpions are strengthened and are then most hostile, as my very dear friend Peter de Castro, a most learned physician, discovered to his own hurt, of whom we have often made mention in our book: and that when the stars are rising in the Dolphin, in Argo Navis, in the Whale, and in others of the same kind, storms are stirred up in the sea. Has this perhaps happened because dolphins, leaping in the sea, foretell storms, and therefore the stars distinguished by such a name likewise from that same source predict storms? Not at all; rather, this name was given to them because they are of such a nature that, when rising with the Moon, they produce storms, which the dolphins, fish, foretell by their leaping; whence it was fitting that they should be called by that name, etc. Nor are these old wives’ tales, as Argotus rightly notes in Astronomical Matters, book 2, chapter 14. Rather, they are observations of nearly infallible reliability, confirmed by very long use, which are indeed permissible and most true. For although the Church has condemned judicial astrology, which rashly pronounces on a man’s life and on those things that depend on free will, (since it is impious and plainly superstitious,) yet in so far as it sets forth precepts to be observed in medicine, just as also in navigation and agriculture, it has permitted it and approved it by its permission. <17.> Therefore now no one should wonder if our ointment is ordered to be made while the Moon is waxing, in a good sign bearing the human figure, and established in a good house. For although this may perhaps be too scrupulous, and at times superfluous, it is nevertheless not superstitious, nor alien to the lawful precepts of the astronomers: since it is certain that these signs are marked with such figures and names because they preserve some analogy with the things that bear such a figure, or have obtained such a name. <18.> The remaining circumstances prescribed by Crolius will rather have to be called superstitious: namely, that the iron should rather be anointed, than

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DE SYMPATHIA. 55 quam pannus sanguine patientis infectus: vt, si vulnus punctim inflictum sit, tertium à cuspide ad capulum illinia- tur, secus, si cæstum, nam tunc debet fieri inunctio ab acie versus tergum: quod qui telum inungit deber eo die à Venere abstinere, & cætera huiusmodi, quæ neque boni auctores admittunt, neque prætermittere tantillum variat curationem, cum semper æquè benè habeatur curatio siue ijs adhibitis siue non. Quare ex his ego argumentum po- rius sumo conijciendi vnguenti huius vtilitatem, æque à Natura perfici immediatè curationem: tum quia Dæmon ex inuidia tanti boni, studet illud suis tricis implicare, vt vel ab eo ex timore culpæ abstineamus, vel admissa ali- qua circumstantia, quæ eius opem imploret, adhibeamus. Tum quia si à Dæmone perficeretur immediatè curatio ex federe implicito circumstantijs istis annexo, si vna vel al- tera, casu, aut datâ operâ præteriretur, effectus nullus prodiret, vt in alijs superstitiosis factis perspicuum est: si- quidem cum is Dei simiam in suis præstigijs se exhibeat, in ijs certâ formâ, materia, & conditionibus vtilitur ad si- militudinem Sacramentorum, itavt minimum his variatis non sequatur effectus, vt ex nostris aduertit doctissimus Ver- celli, tract. 8. Miscellan. quast. 12 num. 8. Dum ergò sem- per aliquis in opere effectus prodit, siue Vnguentum hoc adhibeatur, siue aliud simile, siue hæ circumstantiæ acce- dant, siue prætermittantur; signum euidens est, in eius efficaciam vim omnem habere Narutam, quam semper aut totam, aut ex parte exserit ad rationem factæ com- positionis, vsus aut naturæ affectæ condiione. Quod si quando nil operetur, signum est, quod, aut quid valdè necessarium fuerit prætermisium, aut natura ita deiecta sit, vt quibusuis fulcimentis adiuta, excitari mi- nimè possit ad curarionem perficiendam. Nec valdè curan- dum, si fortè superstitiosa aliqua circumstantia Dæmonis arte admisceatur, nam, vt dixi, hoc eius studium est, vt optima quæque & sanctiora corrumpat: vt habetur Mat- thai 13. vbi inimicus homo in bono agro in quo semina- tum fuerat bonum semen superseminauit zizania. At non per hoc statim eradicanda præcipiuntur, ne simul eradice- tur & tricium, sed permissum est vtraque crescere, & tum demum ea in fasciculos colligata ad comburendum mitti, triticum auem ab iis segregatum seruari. Ita planè irritus erit omnis Dæmonis astus, si vnguentum stutò adhibeatur, omni quacumque Pænonis ope reiecta, & ita hæ circum- stantiæ admittantur, vt si aliquo pacto curationem iuuare 6

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Of sympathy. 55 as a cloth stained with the patient’s blood: thus, if the wound has been inflicted by a puncture, the third part from the point to the hilt should be anointed; otherwise, if by a blow, for then the unction should be made from the edge toward the back; and whoever anoints the weapon ought on that day to abstain from Venus, and other such things, which neither good authors admit, nor does leaving them out in the least alter the cure, since the cure is always equally well effected whether these things are used or not. Wherefore from these I rather draw an argument for conjecturing the usefulness of this ointment, that the cure is immediately brought about by Nature: first, because the Demon, out of envy of so great a good, strives to entangle it with his tricks, so that either through fear of guilt we refrain from it, or, once some circumstance has been admitted that invokes his help, we use it. Then because if the cure were effected immediately by the Demon, under an implicit pact joined to those circumstances, if one or the other, by chance or intentionally, were omitted, no effect would arise, as is evident in other superstitious acts: since, as he displays himself as God’s ape in his deceits, in them he uses a fixed form, matter, and conditions in likeness to the Sacraments, so that with even the slightest change in these no effect follows, as among our own writers the most learned Vercelli notes, tract. 8. Miscellan. quast. 12 num. 8. Therefore, so long as an effect always arises in the work, whether this ointment is applied, or another similar one, whether these circumstances are added or omitted; it is an evident sign that all the power in its efficacy lies in Nature, which always exerts herself either wholly or in part according to the nature of the composition made, the use, or the condition of the affected nature. But if at any time it does nothing, it is a sign that either something very necessary has been omitted, or that nature is so debased that, even aided by any supports whatever, it can scarcely be roused to bring the cure to completion. Nor need one greatly concern oneself if by chance some superstitious circumstance is mixed in through the Demon’s art, for, as I said, this is his aim: to corrupt the best and holiest things: as is found in Matthew 13, where the enemy of man in the good field in which good seed had been sown oversowed weeds. But for this reason they are not at once commanded to be uprooted, lest the weeds be uprooted together, but both are allowed to grow, and only then, when gathered into bundles, are they sent to be burned, while the wheat separated from them is preserved. So indeed every craft of the Demon will be vain, if the ointment is applied prudently, all aid of the Devil being rejected, and if these circumstances are admitted in such a way that they may in some manner aid the cure 6

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34 PHYSIO-THEOLOGIA, possint, sint volita, sin secus despiciantur. 20. Quapropter ad tertium caput transibo, si in hac re vnum tantum monuero, conditionem videlicet Vnæ in vnguento adhibendæ, quæ sit è cranio strangulati hominis excerpta, superstitiosam non esse: nam vt benè aduertit seruius pag 28 homo hic mortuus abundantioribus viuidioribusque spiritibus scater, qui interclusis faucibus, ad caput confluunt, ibique sistunt: quod nimius calor, faciei rubor, ac plumbeus color, qui statim inducitur manifestum facit: Vnde istius cranium ad medicas functiones euadit aptius, quam quoduis aliud hominis, vel exsecti, in quo spiritus qui subtilissimi sunt, subitò euanescunt: vel morbo aliquo laborantis, in quo & ipsi laborant, deficiunt, & flaccescunt. Non negauerim tamen musem ex aliis cadaueribus comparatum idoneum quoque fore, sed quem diximus è crario suspensi hominis eligendum aptiorem nouit experientia, quippe habet spiritus longè viuidiores. 21. Iam verò ad tertium caput in quo tota fere vnguenti contradictio sita est, aditum faciamus. Qui fieri potest, vt medicamentum hoc non vulneri applicatum sed sanguini iam exciso, iam corrupto, iam exsiccato, & quod mirabilius est multis ab ægro milliariis dissito, vulneri nihilominus medeatur, eiusque vim sentiat æger in quacumque distantia? Nos hîc aliotum rationes examinabimus vna cum aduersariorum obiectis, nostram delinc sententiam in aliam ac distinctam quæstionem rejicientes. De efficacia vnguenti, & modo quo operatur, hæc habet Crolius. Perficitur, ait, hæc cura per medicamenti huius vim magneticam attractiuam à sideribus causatam, qua mediante aëre vulneri adducitur, & coniungitur, vt spiritualis actio in effectum deducatur, fit, inquam, per coniunctionem astralem. & elementarem. Itaque ex eius sententia tria concurrunt ad tam mirum effectum causandum: Sympathia, & naturæ conformitas, quæ est inter vnguentum, & corpus vulneratum; influxus cælorum coniunctus cum vnguenti elementari virtute, qui illud eleuant ad curationem perficiendam; & Balsamum, quod sanandi virtute præditum cuilibet homini inditum est. A Crolio cæteri auctores, parum discordant. 22. Cæterum hanc coniunctionem astralem cum vnguenti elementari virtute, & vim in balsamo transferendi virtutem vnguenti ad vulnera non satis apertè explicant, Papin. de Puln. sympat. pag. mihi 33. neque omnes eodem modo-

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34 PHYSIO-THEOLOGY, whether they can, they are to be desired; if not, they are to be despised. 20. Wherefore I shall pass on to the third chapter, if in this matter I first note only one thing: namely, that the condition of the unguent to be applied, namely that which is taken from the skull of a strangled man, is not superstitious. For, as Servius rightly observes, page 28, this dead man abounds in more abundant and more lively spirits, which, the passages of the throat being closed, flow up to the head and there settle; this is made manifest by the excessive heat, redness of the face, and livid color, which is immediately produced. Hence that skull is more suitable for medical uses than any other human skull, whether of one who has been cut open, in whom the spirits, which are most subtle, suddenly vanish; or of one laboring under some disease, in whom they too suffer, fail, and wither. I would not deny, however, that the moss obtained from other corpses would also be suitable; but experience knows that the one we mentioned, chosen from the skull of a hanged man, is more fitting, since it has far more lively spirits. 21. Now indeed let us approach the third chapter, in which almost the whole contradiction concerning the unguent lies. How can it happen that this remedy, not applied to the wound but to the blood already drawn out, already corrupted, already dried up, and, what is more marvelous, many miles distant from the patient, nevertheless heals the wound, and that the patient feels its power at whatever distance? Here we shall examine other men’s reasons together with the objections of our opponents, setting aside our own opinion for a separate and distinct question. Concerning the efficacy of the unguent, and the manner in which it operates, Crollius says this: this cure is accomplished, he says, through the magnetic attractive power of this medicine, caused by the stars, by means of which it is brought through the air to the wound and joined to it, so that a spiritual action may be brought into effect; it is done, I say, through an astral and elemental conjunction. Therefore, according to his opinion, three things concur in producing so wondrous an effect: sympathy and conformity of nature, which exists between the unguent and the wounded body; the influence of the heavens, joined with the elemental power of the unguent, which elevates it to complete the cure; and the Balsam, which is endowed with healing power and implanted in every man. The other authors differ little from Crollius. 22. Moreover, they do not explain sufficiently clearly this astral conjunction with the elemental power of the unguent, and the power of transferring the virtue of the unguent to wounds through the balsam, Papin. de Puln. sympat. p. 33, nor do all of them in the same way-

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DE SYMPATHIA. 31 Alij enim id fieri autumant per igniculos quosdam cælestes, seu portiunculam substantiæ illius lucidæ simplicis, & homogeneæ quæ in prima rerum sublunarium formatione sit illis congenita, & admixta, cuius solius ope cælestes influxus participent; vnde etiam sit omnis sympathiæ vis, & cælestium corporum cum terrenis consensio. Alij per effluuium corpusculorum è sanguine medicato ad partera læsam sibi affinem rectà, & naturali impetu commeantium. Alij præsupponunt dari quemdam spiritum Mundi per totum orbem diffusum, qui sit vector occultarum potentiarum, & operationum, quique omnes mundi partes connectat, ac mirum illum consensum, quem nos sympathiam vocamus, pariat, exciterque. Atque per has, & consumiles hypothesium fictiones, rum vnguenti miram virtutem, rum reliqua naturæ arcana, quæ hominum captum fugiunt, explicare contendunt Verum etsi hæc in aliquibus locum habeant, atque ad scopum aliquo pacto colliment, tamen in vnguento armario, & in aliis plerisque nemo ex mea sententia illum tenere potuit. Nam primò, quoad spiritum Mundi vectorem huiusmodi qualitatum, si hunc velimus cum Gotlenio, Auctore Mosaicæ Philosophiæ, & aliis quibusdam, Centralissimum illum Diuinitatis spiritum dicere, qui ab initio vt habetur, Gen. 1. ferebatur super ignas, hoc profectò vel inde impietatem redolet, quod videtur maximè pium. Nam, vt benè Kircherus arguit, iam correret vniuersa Philosophia; iam nulla in causis secundis foret actiuitas, nulla virtus, nulla in rebus proprietas, nulla actiuitatis sphæra, nulla denique in Natura ipsa, hoc est ordinata illa causarum congerie operositas, & causalitatis ratio, proindeque omnia refunderentur in Deum, vt causam immediatam & (quod blasphænum est) etiam peccata; cum rum potentiæ perinde se haberent, vt mera organa; & instrumenta Deo omnia in omnibus operanti inseruientia. Si verò hunc spiritum mundi latiùs sumptura connexionem illam dicamus, qua in vniuersa natura res cognatæ inter se mirum in modum afficiuntur, contrariæ sibi inuicem aduersantur, vna alteri condolet, hæc illi fatali genio, subest, altera prædominatur, ita vt in hoc verè saluetur mira illa sympathiæ, antipathiæque vis, ac dissitarum quantumuis rerum nexus, & colligatio, tunc profectò à voto non aberramus vt nos fusè tradidimus, in V. Sympathia, & in V. Mundus, eum de eius forma ageremus, & alibi sæpè: neque à nobis dissentit præcipua Philosophorum schola, neque ipse Kircherus, qui par. 9. cap. c ij

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ON SYMPATHY. 31 Some, indeed, think this happens through certain heavenly sparks, or a little portion of that bright, simple, and homogeneous substance which, in the first formation of sublunary things, is naturally inherent in them and mixed with them, by the aid of which alone they partake of celestial influences; whence also comes all the force of sympathy and the agreement of celestial bodies with earthly ones. Others explain it by the efflux of little corpuscles from medicated blood, rushing straightway and by a natural impulse to the wounded part akin to them. Others suppose that there exists a certain Spirit of the World, diffused through the whole orb, which is the bearer of hidden powers and operations, and which connects all parts of the world, and produces and awakens that marvelous concord which we call sympathy. And through these and similar fictional hypotheses they strive to explain both the wonderful virtue of the unguent and the other secrets of nature that elude human understanding. Yet although these theories may have some application in certain cases, and may in some measure hit the mark, nevertheless, in the case of the weapon-salve and in most other matters, no one, in my opinion, has been able to grasp the truth. For first, as regards the Spirit of the World as the bearer of such qualities, if we choose, with Gotlenius, author of Mosaic Philosophy, and certain others, to call it that most central spirit of divinity which from the beginning, as it is said in Gen. 1, moved upon the waters, this surely smells of impiety, even from the very fact that it seems most pious. For, as Kircher rightly argues, then all philosophy would already collapse; there would then be no activity in second causes, no force, no property in things, no sphere of activity, and finally no operation in nature itself, that is, no labor of that ordered heap of causes, no principle of causality; and thus everything would be transferred back to God as the immediate cause and, which is blasphemous, even sins as well; since the powers would stand in the same relation as mere organs and instruments serving God, who is operating all things in all things. But if we take this Spirit of the World more broadly, meaning that connection by which, throughout universal nature, related things affect one another in a marvelous way, opposites are hostile to one another, one thing pities another, this one lies under that fatal genius, another prevails, so that in this way the wondrous force of sympathy and antipathy, and the bond and connection of things however distant, is truly preserved, then indeed we do not go astray from the aim, as we have explained at length in V. Sympathia and in V. Mundus, where we treated its form, and elsewhere often; nor does the chief school of philosophers disagree with us, nor does Kircher himself, who in part 9, chapter c ij

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PHYSIOTHEOLOGIA 1. de Magnetismo Amoris, vniuersi istius partes, tamquam magni cuinsdam Animalis membra, hac veluti anima informari non diffiterut. Quod & longè antè dixerat Plato in Timaeo, & Virgilius Æneid. lib. 6. vt nos in loco monuimus. 23. Et huc tandè recidunt omnes p[er]tæsatæ explicationes dum hâc retum consensione diffensionemve, modò per effluuium corpusculotum, (quod videre licet in Plantis, pomis, humoribus, &c. quæ intrà determinatam sphæram certos quosdam vapores emittunt vni quidem corpori gratos, vnde illi profectus, alteri ingraios, & noxios, vnde molestia, & interitus) modò per congenitos ignes è cælesti substantia atque in sublunaribus interclusos, qui per astrorum occultos quosdam radios excitantur ad morum; modò per cælestem quandam substantiam immediatè per vniuersum o[mn]ibem diffusam totum causari contendunt. 24. Verum adhuc in limine hæremus, cum sanè eosdem effectus non in omnibus dispiciamus, in quibus tamen eandem cælestem substantiam reperiri, eosdem igniculos, eademque, vt ita dicam, anima omnia informari necessum sit: & tamen non in omnibus eadem sympathia, non omnia eodem modo promiscuè afficiuntur: cur igitur, aliqua consentiunt, alia non? in aliquibus activitatis sphæra p[er]tæscribitur, in aliis non item? cur hæc eadem connexionis vis, & æthereæ substantiæ mira diffusio non officit Antipathiæ retum, quam dihilominus in multis videmus? cur demum quæ in determinata distantia operantur, proximè ad nota omne robur, omnem activitatem deperdunt? 25. Sed enim antequam huic implexissimæ difficultati manum admoueamus, quæ pro sui dignitate specialem quæstionem sibi vendicat, operæ pretium est ad superiora regredi, ac præsenti quæstioni finem imponere. Efficacia igitur huius vnguenti eadem ac tanta est, quæ aliorum medicamentorum, quæ immediatè vulneri applicantur; operatio eiusdem prorsùs generis, ac cæterorum agentium, quæ pari modo in distans videntur agere, & tamen nemo dixerit superstitiosa, de quibus fusè egimus in prima quæstione. Quomodo autem agant, pluribus plutimi iuquisiuere: an, & quinam eorum ad setpum collimarint, id nos ignotamus. In his enim certò effectum habemus, veram causam & modum quo opetetur inquirimus, & pro sua quisque vitili parte è Naturæ latebtis eruerè conatur. Siquidem vt ait Seneca lib. 7. quast. natural. cap. 37. Illa arcana non promiscuò, nos omnibus patens,

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PHYSIOTHEOLOGY 1. Concerning the Magnetism of Love, they do not deny that the parts of this universe, as though the limbs of some great Animal, are informed by this as by a soul. And Plato had said this long before in the Timaeus, and Virgil in Æneid, book 6, as we have noted in the place. 23. And hither at last all those tiresome explanations come down, while by this agreement or divergence of things, now by the effluence of corpuscles, (which may be seen in plants, fruits, humours, etc., which within a determined sphere emit certain vapours, some indeed pleasant to one body, whence benefit comes to it, but unpleasant and harmful to another, whence trouble and destruction) now by inborn fires from celestial substance and enclosed in sublunary things, which are stirred into motion by certain hidden rays of the stars; now by a certain celestial substance immediately diffused through the whole universe, they maintain that the whole is caused. 24. But still we are lingering on the threshold, since we certainly do not observe the same effects in all things, though in them the same celestial substance must be found, the same little sparks, and, so to speak, all things informed by the same soul: and yet not in all things is there the same sympathy, nor are all things affected promiscuously in the same way: why then do some agree and others not? in some the sphere of activity is circumscribed, in others not so? why does this same force of connection, and the wondrous diffusion of the ethereal substance, not hinder the antipathy of things, which nevertheless we see in many? why finally do those things which operate at a determined distance, lose all strength, all activity, when brought near the mark? 25. But indeed, before we put our hand to this most intricate difficulty, which by its dignity claims a special question for itself, it is worth while to return to what was said above, and to bring the present question to an end. The efficacy, then, of this ointment is the same and as great as that of other medicines which are applied directly to a wound; its operation is altogether of the same kind as that of other agents, which in like manner seem to act at a distance, and yet no one would call them superstitious, about which we have discoursed at length in the first question. But how they act, many have inquired into; whether, and which of them have aimed at the mark, that we do not know. For in these things we certainly have the effect; we inquire into the true cause and the manner in which it operates, and each man seeks, according to his own poor ability, to draw it forth from Nature’s hidden recesses. For, as Seneca says, book 7 of the Natural Questions, chapter 37. Those secrets, not indiscriminately, are open to us all.

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DE SYMPATHIA. 37 reducta, & inferiore sacrario clausa. Ex quibus aliud hac atas, aliud, qua post subibit accipies. Omnes ad verum collineamus: qui propiùs accedit, gaudeat se in Naturæ penetralia introductum assequi quod cæteris negatum est; qui aberrat, reique veritatem tenere non valer, neque animum suum firmant quæ ab aliis proficiscuntur, fateatur cum Seruio hæc sibi abmirari potiùs datum esse quam nosse: nec proinde ignorantiæ suæ tenebras in potestatem tenebrarum refundar, inde causam tantæ operationis exquirens, quod Philosopho æquè indignum est, ac in primam omnium causam tanquam ad sacram anchoram aduolare. Neque verò mihi vsquequaque probandum est (vt contendit sennertus) dari in vnguento talem vim, quæ vt < 26.> agat non requirit corporum contingentiam, quando id à posteriori per effectus videmus; atque in aliis rebus ipsemet sennertus non diffutetur. Neque enim, air, sequitur, dantur aliarum rerum tales actiones mirabiles; ergò & vnguentum talem vim habet: sed adhuc id probandum. Nam peto ab ipso: Vnde habes mi homo, dari in rerum natura huiusmodi actiones mirabiles, quas non à Dæmone; sed ab ipsa maiestate Naturæ esse intelligas, & vnde demum id homini protritæ frontis probares? Certè, inquiet, ab experientia, & quia sæpius mirabiles huiusmodi effectus emanare vider. Quod si quis adhuc obstinatior effectus quidem admitteret, de causa verò dubitaret, atque à Dæmone esse contenderet, vel sanè à Deo miraeulosè suprà naturæ vires; vtique ipse statim subiungeret, non esse recurrendum ad causam primam aut ad Dæmonem, quando effectus videtur, nec implicat à Naturæ viribus proficisci, nam tunc censendus est naturalis. Pari igitur ratione effectum eurationis per vnguentum armarium, & alia id genus medicamenta præstitum, naturalem debemus supponere, quando illum sæpè videmus, & veram causam omninò ignoramus. Illi potiùs probandum venit, curationem naturalem non esse, neque naturali via posse haberi, cui inest genius impugnandi, elucetque disparitatis ratio inter hæc & alia naturæ areana: Quod neque à Sennerto, neque ab alio, quod sciam, hactenus factum est. Cum aliàs possessio stet pro Natura; ac tum ratio, tum sexcenta in eodem genere experimenta suppetant, quæ naturalem vnguenti virtutem probant, nec minus pro eo, quam pro aliis Naturæ miraculis militent, vt discurrenti pater. Verum adhuc scrupulus est; Vnguentum istud Paracelsus c iii

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DE SYMPATHIA. 37 reduced, and enclosed in the lower shrine. Of these, you will receive one here, another where it will next come to pass. Let us all aim at the truth: he who comes nearer, let him rejoice that he has been brought into the inward places of Nature and has attained what has been denied to others; he who strays, and cannot hold fast to the truth of the matter, nor strengthen his mind with what proceeds from others, let him confess, with Servius, that it has been granted him to admire these things rather than to know them. And so let him not, in the darkness of his own ignorance, cast himself into the power of darkness, seeking from that the cause of so great an operation, which is as unworthy of a Philosopher as to fly to the first cause of all things as to a sacred anchor. Nor indeed is it altogether to my liking, as Sennertus argues, that in an unguent there is such a power that, to act, it does not require the contact of bodies, since we see this from the effects a posteriori; and in other matters Sennertus himself does not deny it. For, says he, it does not follow that there are such marvelous actions of other things; therefore the unguent too has such a power: but this still has to be proved. For I ask him: Whence do you have it, my good man, that in the nature of things there are such marvelous actions, which you understand to be not from a Daemon, but from the very majesty of Nature itself; and whence at last would you prove this to a man of brazen forehead? Certainly, he will say, from experience, and because I have often seen marvelous effects of this kind arise. But if someone more stubborn should still admit the effect indeed, yet doubt the cause, and maintain that it is from a Daemon, or truly from God miraculously beyond the powers of nature, he would surely immediately add that one must not have recourse to the first cause or to a Daemon when the effect appears and it does not involve anything impossible for the powers of Nature to produce; for then it must be judged natural. By the same reasoning, therefore, we ought to assume as natural the healing effect produced by the armory unguent, and other medicines of that kind, when we often see it, and are altogether ignorant of the true cause. Rather, it is for him to prove that the cure is not natural, and cannot be obtained by a natural way, in which there is a spirit of attack; and the reason for the disparity between these and other secrets of Nature is evident. This has not yet been done by Sennertus, nor by anyone else, so far as I know. Otherwise, possession stands for Nature; and both reason and six hundred experiments of the same kind are at hand, which prove the natural virtue of the unguent, and no less serve for it than for the other miracles of Nature, as will be clear to the reader. But there is still a difficulty; this unguent Paracelsus c iii

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38 PHYSIO-THEOLOGIA, primus in orbem inuexit, hoc est homo supectæ fidei, auctor damnatus, & cui Dæmonem familiarem suisse scribunt, à quo tandem, pacto tempore, strangularus, non leue dedit ind cium, se quidquid sciret, quidquid operaretur arcani, à diabolo accepisse. Sed enim ego rem ipsam considero, non vnde sit: parum de soli bonitate curo, dummodò bonam mihi segetem proferat: Naturæ opus agnosco, eam veneror, ipsius munera insequor, auctorem detestor, modum quo arcanum hoc comparauit abominor: ast ipsum aranum tamquam Dei donum in Natura prouisum ad humani generis tutamentum complector. Do vti que Paracelsum suspectæ fidei auctorem suisse; do fædus cum Dæmone iniisse; do etiam huius secreti notitiam auctore diabolo comparasse: ac quid inde? num mihi idcircò eius vsus prohibitus, quando solis naturæ viribus factum agnosco? non equidem: astipulantur mihi omnes Theologi vno ore docentes, licitum mihi esse vti scientia, seu rerum < 38.> naturalium notitia semel à me, siue ab alio ope Dæmonis acquisita, dummodo tamen vsus à Dæmonis auxilio non dependeat; quia rerum naturalium cognitio per sebona est, & peccatum quo parta fuit, pertransit. Ita in specie Suar. de superstit. lib 2. cap 17. Sanchez, in opere moralib lib 1. cap. 41 Valentia, 1. 2. disputat. 6. quest. 13. puncto. Bonac. hic disput. 2. quest. 5. puncto 4. num 6. & alij. Sat mihi ad omnem culpam euadendam, si Dæmonis operibus non assentior, si eius opem reiicio, & quod ipse ex mirabili rerum qua præditus est cognitione assequitur, id ego parta vt cumque viarum suarum notitia tentare adnitor: < 39.> Neque enim operatio Dæmonum sua est sed naturæ, & ideò, (vt benè aduertit Abulensis, in cap. 7. Exodi quest. 10. in fine.) non est valde miranda, benè autem scientia, qua aliquid faciunt, nam & nos eadem quæ ipsi faciunt, faceremus, si tantam rerum notitiam haberemus: non enim aliud faciunt quam applicare actiua passiuis, sicut faciunt medici, probè colentes rerum naturam consensum, atque dissensum, quid agere possit, & quid & à quo pati, & vbi hoc fieri debeat, & quo tempore; atque adeò hæc illis debito ordine applicantes, quod vti que & nos facere, aut imitari possumus per eam quam vt cumque adepti sumus notitiam: quem etiam longo vsu, experientia, & ingenij < 30.> acumine fortè adeptus est Paracelsus in hac mira vnguenti huius inuentione, quem profectò ab omni inuidiæ nota vindicat egregiè Helmontius afferens luculentissimum de eo testimonium Archiepiscopi Salisburgenus in

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38 PHYSIO-THEOLOGIA, first introduced into the world, that is, a man of suspected faith, an author condemned, and of whom they write that he had a familiar demon, by whom at last, in due time, being strangled, he gave no slight indication that whatever he knew, whatever secret things he did, he had received from the devil. But I consider the thing itself, not whence it comes: I care little for the soil’s goodness, provided it produces for me a good harvest: I acknowledge it as a work of nature, I revere it, I seek after its gifts, I detest the author, I abhor the manner by which he procured this secret: but the secret itself, as a gift of God provided in Nature for the safeguard of the human race, I embrace. Indeed I grant that Paracelsus was an author of suspected faith; I grant that he entered into a pact with the Demon; I grant also that he obtained knowledge of this secret from the devil as author: and what of that? is its use therefore forbidden to me, when I acknowledge that it was accomplished by the forces of nature alone? Certainly not: all the Theologians agree with me, teaching with one voice that it is lawful for me to use the science, or knowledge of natural things, once acquired by me, whether by myself or by another with the help of a Demon, provided, however, that the use does not depend on the Demon’s assistance; because the knowledge of natural things is in itself good, and the sin by which it was obtained passes away. Thus in particular Suar. de superstit. lib 2. cap 17. Sanchez, in opere moralib lib 1. cap. 41 Valentia, 1. 2. disputat. 6. quest. 13. puncto. Bonac. hic disput. 2. quest. 5. puncto 4. num 6. and others. It is enough for me to escape all blame if I do not agree to the works of the Demon, if I reject his aid, and if that which he himself achieves through a marvelous knowledge of things, I strive to attempt by whatever acquaintance I have gained with his ways. For the operation of Demons is not theirs but nature’s, and therefore, as Abulensis rightly observes, in cap. 7. Exodi quest. 10. in fine, it is not very wonderful; but the knowledge by which they do something is wonderful, for we too would do the same things that they do, if we had so great a knowledge of things: for they do nothing other than apply active things to passive ones, just as physicians do, well observing the consent and disagreement of things, what it can do, and what and from what it can suffer, and where this must be done, and at what time; and thus, applying these to them in the proper order, which indeed we also can do, or imitate, through the knowledge we have somehow acquired: which perhaps Paracelsus also acquired through long use, experience, and the acuteness of his intellect in this marvelous invention of this ointment, whom indeed Helmontius splendidly vindicates from every stain of envy by producing a most clear testimony about him from the Archbishop of Salzburg in

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DE SYMPATHIA. 39 eius funete lapidi insculptum, qui etiam nunc Salisburgi extat ad templi murum in Nosocomio S. Sebastiani in hæc verba Conditur hic Philippus Theophrastus insignis Medicinæ Doctor, qui dira illa vulnera, lepram, podagræm, hydropisim, aliaque insanabilia corporis contagia, mirifica arte sustulit, ac bona sua in pauperes distribuenda, collocanda- que honorauit. Anno 1541. 24. Septemb. vitam cum morte commutavit. -------------------------------------------------------- QVÆSTIO III. Quonam pacto puiuis sympathicus, Vnguentum Armarium, & cætera huiusmodi medicamenta conferant ad Vulnerum, aliorumque morborum curationem. SYMMARIUM. Dantur in Natura diuersi diuersi generis sympathia, quas ne- gare non possumus. n. 1. Etiam in multis longe naturâ diuersis, & dissimilibus, vt inter materiale, & spirituale. n. 2. Imaginatiua vis in rebus timorem in cutientibus in alieno cor- pore n 3. Exemplis res comprobatur. ibid. Celestium cum terrestribus dissimilitudo, & tamen sympa- thia. n. 4. Sympathia in rebus tempore dissitis. n. 5 Phalangj miraculum omnia in se uno complectitur. n. 6. Plurima in eo notanda. ibid. Tarantula vitreo loculo inclusa ad certos sonos subsilire visa. ibid. Forma mundi astringitur. n. 7. Triplex sympathia differentia in humano corpore, & in Mundo. ibid. Adhuc vitrobique certa inspicitur sympathia, quæ ad vnum ex his tribus capitibus referri non potest. n. 8. Omnes isti effectus naturales sunt, quia multi neque mira- culo, neque Damone asscribi possunt. n. 9. Vitis efflorescentis tempore fluctuat in deliis vinum. ibid. c iiiij

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OF SYMPATHY. 39 its coffin stone, which even now exists in Salzburg on the wall of the temple in the Hospital of St. Sebastian, with these words: Here lies Philip Theophrastus, distinguished Doctor of Medicine, who by wondrous art cured those dreadful wounds, leprosy, gout, dropsy, and other incurable contagions of the body, and who honored his possessions by distributing and bestowing them among the poor. In the year 1541, on the 24th of September, he exchanged life for death. -------------------------------------------------------- QUESTION III. By what means does sympathetic powder, the Unguentum Armarium, and other medicines of this kind contribute to the cure of wounds and other diseases. SUMMARY. There are in nature diverse sympathies of different kinds, which we cannot deny. n. 1. Even among many things widely unlike and dissimilar in nature, as between the material and the spiritual. n. 2. The imaginative power causes fear in things affecting the body in another body. n. 3. The matter is confirmed by examples. ibid. The dissimilarity of the heavenly and the earthly, and yet sympathy between them. n. 4. Sympathy in things separated by time. n. 5 The miracle of the Phalangium embraces everything in itself. n. 6. Many things are to be noted in it. ibid. A tarantula enclosed in a glass vessel was seen to leap at certain sounds. ibid. The form of the world is constrained. n. 7. A threefold difference of sympathy in the human body, and in the world. ibid. Yet in both a certain sympathy is perceived, which cannot be referred to one of these three heads. n. 8. All these effects are natural, because many cannot be ascribed either to miracle or to demon. n. 9. At the time when the vine is in bloom, the wine in the vessels is agitated. ibid. c iiiij

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40 PHYSIO-THEOLOGIA Et non quando genuina, sed loci propria, aut vicinior. ibid. Natura est morborum immediata expultrix, & Medica- num. 10. Medicus tantum natura subfamulatur. ibid. Vulgaria medicamenta sunt vt lixiuium, purgantiæ qui- dem, sed naturam concutientia. ibid. Demon optimè naturæ opitulari calles absque virium iactura. ibid. Magnetica cura sit à natura immediatè, extrinsecè excita- tur ad mosum sanguinis. n. 11. Experimentis res comprobatur, & vna est omnium arcanorum ratio. ibid. In hoc opere nulla datur actio in distans, sed est omnis imme- diata. ibid. Elitropium ad solis motum intrinsecè à sua natura ad similem motum excitatur. n. 12. Multa planta ad viciniam amicarum sympathicè excitantur ad ojus, multa etiam ad intimicarum præsentiam exsic- cansur. n. 13. Rosa cur allio complantata odoratior. ibid. Non potest dico cum Aresio excitari in nobis appetitum rerum obiectarum. ibid. Ratio est dissonantia, & antipathia rerum, qua facit vt natura sua sponte sese dociciat. n. 14. A Phalangio ictorum symptomata vnde. n. 15. Historiado naso adjunctio. n. 16. Experientia de felis abortu, ibid. n. 17. In uno Phalagio vniuersa Natura sympathia, antipathiaque arcana continentur. n 18. Modicus pulu[s]s curationi sufficit. n. 19. Pulu[s]s non agit in vulnus. ibid. Natura ipsa ad sanguinis curationem, quasi amica voce cri- gitur ad curationem faciendam. ibid. In vulnusibus à sclopetis factis non eadem ratio est, qua in iis qua per gladium fiunt. n. 20. Historia mulieris solo attactu podagram concipientis. n. 21. Sanguis solo aspectu rerum rubrarum accenditur. ibid. n. 22. In sanguine quamuis exciso aliquo semper remanes primitua substantia. n. 23. Intresolutione compositi non solum remane[n]t multa accidentia, sed & multa forma substantiales ibid. Id maximè ouincit experientia. n. 24. Hinc ob substantia similitudinem mutua congruentia ac re- mediorum ?nuentio. ibid.

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40 PHYSIO-THEOLOGIA And not when genuine, but proper to the place, or nearer to it. ibid. Nature is the immediate expeller of diseases, and the medicine. 10. The physician only serves nature as an assistant. ibid. Common medicines are like lye, indeed purgative, but shaking nature. ibid. You know best how to help nature without loss of strength. ibid. Magnetic cure is from nature immediately, externally stirred up to the motion of the blood. n. 11. The matter is confirmed by experiments, and there is one reason for all the secrets. ibid. In this work no action at a distance is given, but all is immediate. ibid. Heliotrope is stirred by the motion of the sun, inwardly by its own nature, to a similar motion. n. 12. Many plants are sympathetically excited by the neighborhood of friendly ones to their growth, many also dry out at the presence of intimate ones. n. 13. Why a rose planted with garlic is more fragrant. ibid. I cannot say with Aresius that in us an appetite for objects can be excited. ibid. The reason is the dissonance and antipathy of things, by which nature of its own accord teaches itself. n. 14. The symptoms of blows from a Phalangium, from where. n. 15. A joining of histories to the nose. n. 16. Experience of the miscarriage of a cat, ibid. n. 17. In one Phalangium the whole arcana of Nature’s sympathy and antipathy are contained. n. 18. A moderate pulse suffices for healing. n. 19. The pulse does not act on the wound. ibid. Nature itself, as though by a friendly voice, is stirred up for the curing of blood, to make a cure. ibid. In wounds made by guns, the same reason does not hold as in those made by a sword. n. 20. History of a woman who, by a mere touch, contracted gout. n. 21. Blood is kindled by the mere sight of red things. ibid. n. 22. In blood, even when some part has been cut away, there always remains the primary substance. n. 23. By the separation of a composite, not only many accidents remain, but also many substantial forms. ibid. This is confirmed especially by experience. n. 24. Hence, because of similarity of substance, mutual agreement and the invention of remedies. ibid.

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DE SYMPATHIA. 41 Hinc multa remedia ex humano corpore comparata. n. 25. Quidam Medicus solo paluere omnibus morbis occurrebas. n. 26. Tota curatio magnetica à natura sola fit æqri, modo aliquam cum re medicata retineat sympathiam. n. 27. Magnetica curationis excellentia. n. 28. Probantur alia curationes magnetica, & alia experimenta. n. 29. Diuersa, ac mira curationes per sympathiam. ibid. Virtus ungula Alcis contrà morbum comitialem. ibid. Sapphirus contra pestem n 30. Omnes isti effectus ab eodem genere causa promanant. n 31. Qua ratione sanguis è venis occisi ad præsentiam occisoris emaret. n. 32. Non potest id arte Damonis fieri n. 33. Conteà taliter iudicantem non potest iudicialiter procedi. ibid. Id accidit ex sympathia oteris familiaritatis. n. 34. Sape etiam effunditur ad præsentiam gentilium, & amicorum. n 35. Ratio ex superioribus congruenter deducta. n. 36. Experimentis ex animalium exclusis confirmatur. n. 37. Quo consilio Zischas hæreticus tympanum ex sui pelle post mortem confici iusserit. n. 38. Cur sanguis non effluat à cadauere eius, qui dormiens fuerit occisus, aut quomodocumque occisoris notitiam non habuerit. n. 39. Cur non etiam ad illius præsentiam, qui mortem alteri mandauit in sui absent. a exequendam. n. 40. Epilogus. ibid. Hoc equidem dilucidare non erit forsan Lectoribus in- iucundum: & quamquam de hoc argumento non nihil etiam in præcedentibus excidit; præstat tamen hic rem exa- cle discutere, & quæstionem philosophicè magis, quam Theologicò pertractare. Principiò verò id statuendum, dari vniuersè in hac rerum Natura diuersi generis sympathias, consensus, affectus, amicitias, atque inimicitias quibus res quantumuis dissiræ aut natura, aut loco, aut tempore, inuicem exardescunt, afficiuntur, condolent, atque in mutuum amorem vel odium affectus huius indicium excitantur. Id quod, & suo loco luculenter probauimus, & per singula discurrendo, euincit nulquam fallax experientia. Videmus enim, vt di-

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ON SYMPATHY. 41 From this many remedies are derived from the human body. n. 25. A certain physician alone was superior to all diseases. n. 26. The whole magnetic cure is effected by nature alone in the sick person, so long as it retains some sympathy with the medicated thing. n. 27. The excellence of magnetic healing. n. 28. Other magnetic cures and other experiments are proved. n. 29. Various and marvelous cures through sympathy. ibid. The power of the hoof of the elk against epilepsy. ibid. The sapphire against the plague. n. 30. All these effects proceed from the same kind of cause. n. 31. By what reasoning blood from the veins of the slain would flow at the presence of the slayer. n. 32. This cannot be done by the art of Damon. n. 33. Against one judging in such a way, judicial proceedings cannot be taken. ibid. This happens from sympathy or familiar affinity. n. 34. It is also often shed at the presence of relatives and friends. n. 35. The reason rightly inferred from the foregoing. n. 36. It is confirmed by experiments drawn from animals. n. 37. For what purpose the heretic Zischas ordered a drum to be made from his own skin after his death. n. 38. Why blood does not flow from the corpse of one who was killed while asleep, or in whatever way had no knowledge of the killer. n. 39. Why also not at the presence of the one who ordered another’s death to be carried out in his absence. n. 40. Epilogue. ibid. Indeed, it will perhaps not be unpleasant to readers to clarify this; and although something on this subject has also slipped into what precedes, nevertheless it is better here to examine the matter carefully, and to treat the question more philosophically than theologically. First, then, this must be established: that in this whole nature of things there are universally sympathies of different kinds, concords, affections, friendships, and enmities, by which things however disparate, whether by nature, place, or time, are mutually stirred, affected, suffer together, and are moved into mutual love or hatred; and the sign of this affection is aroused. This we have both clearly proved in its proper place and, by going through each point, unerring experience confirms. For we see that di-

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42 PHYSIO-THEOLOGIA, xi, res longè natura diuetsas, loco separatas, tempore diffitas, inuicem colligatas & mutuo amore connexas, è contra alias specie, forma, natura, qualitatibus similes dissidere, vnam ad alterius præsentiam pati, approximatam, interna vi, quamuis sensus expertem diuelli, deficere alteram, alteram ad inimici præsentiam alterari, atque ad illius 2. exitium toris viribus niti. Enimuerò quid natura magis dissonum, quam materiale, ac spirituale? Et r amen quæ major connexio, quæ sympathia potior, quam corporis, & animæ? quam mentis, & phantasiæ? quam voluntatis, & voluptatis? appetitus videlicet sensitiui, qui liberam voluntatem, cui aliàs parêre natus est, ad sibi placita trahit, præuenit, obtenebrat, fascinatque vt de se lugens testatur Apostolus ad Romanos scribens, ac paucis expessit Poëta cum cecinit Buchol. 2 Trahit sua quemque volupias? Quæ imaginatiuæ proportio cum membris inferioribus, quæ colligatio inter fæcum & visam à Matre rem seu concupitam, seu exosam, quæ mox ex oceulta sympathiæ, antipathiæue vi transeat in affectum, & quod mitabilius, non in concipiente faciat casum, sed in conceptu, statim que appareant vestigia rei quantumuis absonæ in corpusculi membris impressa? Mitto Malacæ affectiones ex immoderato desiderio exortas, vtpotè frequentes, & cuilibet noras; afteram auer- sioni exempla, quæ nihilominus eosdem in concepto fætu effectus dederunt, & ne fides authorem deserat, desumam 3. ex Helmontio cap de iniectis materialibus ipsissimis verbis, quæ propriis ipse oculis hausit. Sartoris vxor, inquit, Mechlinia, præ foribus vidit in conflictu, manum amittere: statim perculsa horrore poperis filiam vna manu, altero autem cruentoque brachio extinctam quod manus eius non reperiretur, & hamorrhagia infantem interimeret. Vxor Marci de Vogeler Mercatoris Antuerpiensis anno 1692. videns militem mendicantem cuipila ferrea in obsidione Ostendana dexterum brachium abstulerat, illudque adhuc cruentum circumferebat: mox abinde filiam peperit orbam brachio, & quidem dextero, cuius cruentur adhuc humerus per chirurgum solidam debuit. Nupit Mercatori Amstelodami, cui nomen Hoochcamer, illa adhuc anno 1638. superes. Caterum nuspiam reperibile fust brachium dexterum, nec offa, nec vlla apparuit putre: ago, in quam brachium contabuisset parua horula. Attamen nondum conspecto milite fæcus bina habebat brachia: nec potuit brachium auulsum annihilari. Ergo clauso vtero ablatum est brachium. Quis autem auulserit naturaliter, & quorsum ablatum sit, certè non quadrans

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42 PHYSIO-THEOLOGIA, things very different in nature, separated in place, distinct in time, bound together with one another and joined by mutual love, while on the other hand others, similar in kind, form, nature, and qualities, are at variance; one, at the presence of the other, suffers, being brought near, by an inward force, though beyond the reach of sense, to be torn away; one fails, another is altered at the presence of an enemy, and with all its strength strives for that enemy’s destruction. Indeed, what in nature is more discordant than material and spiritual? And yet what greater connection, what stronger sympathy, than between body and soul? than between mind and imagination? than between will and pleasure? namely, the sensitive appetite, which draws the free will, to which it is otherwise born to submit, toward what pleases it, anticipates it, darkens it, and bewilders it; as the Apostle sadly testifies of himself when writing to the Romans, and the Poet briefly expressed when he sang in Bucol. 2: “Trahit sua quemque voluptas.” What proportion is there between the imagination and the lower members? What bond between the fetus and the image seen by the mother, whether of something desired or something hated, which then, by the hidden force of sympathy or antipathy, passes into an affection? And what is more remarkable, not in the one conceiving does the effect occur, but in the conceived, and at once there appear traces of a thing, however discordant, impressed upon the limbs of the little body? I pass over the affections of the womb arising from immoderate desire, as being frequent and known to everyone; I shall mention examples of aversion, which nevertheless produced the same effects in the conceived fetus, and lest faith abandon the author, I shall take from Helmontius, in the chapter on injected material things, his very own words, which he drew from his own eyes. “The wife of the tailor, says he, in Mechlin, saw before the door, in a struggle, a hand being lost: straightway, struck with horror, she brought forth a daughter with one hand, and with the other arm bloody and extinguished, because her hand could not be found, and the hemorrhage had killed the infant. The wife of Marcus de Vogeler, merchant of Antwerp, in the year 1692, seeing a soldier begging, to whom an iron bullet in the siege of Ostend had taken off his right arm, and who was carrying it about still bloody, soon after gave birth to a daughter lacking an arm, indeed the right one, whose bloody shoulder the surgeon had to bind up. She married a merchant in Amsterdam, whose name was Hoochcamer; she was still alive in the year 1638. Moreover, the right arm was nowhere to be found, nor any bone appeared, nor any putrid matter: so that the arm would have wasted away in a short hour. Yet the fetus, before the soldier was seen, had both arms: nor could the severed arm be annihilated. Therefore the arm was taken away when the womb was closed. But who naturally tore it away, and for what purpose it was taken away, certainly does not fit in the least.”

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DE SYMPATHIA. 43 triuiales rationes in tanto portento, aut paradoxo. Non sum qui hac dicam: Hæc dicam saltem non fuisse brachium ablatum, vt neque auulsum à Satana. Deinde minoris opera esse deferri aliò brachium auulsum, quam fuit brachium à toto auulsisse absque nece. Vxor mercatoris cognita robis, vt audiunt, quod uno mane decapitarentur tredecim (tempore ducis Albani contigis Antuerpiæ) ducunturque inordinatis appetitibus pragnantes, statuit spectare descruncationes. Ascendit ergo cubiculum familiaris sibi vidua in foro morantis; visoque spectaculo, statim illam adorsus est dolor parturientis, peperitque maturum infantem cruento collo, cuius caput nusquam apparuit. Hæc ille: quæ vti que neque contactui seu Physico, seu Mathematico neque effluuiis, neque similitudini, aut connexioni naturæ accepta referri possunt. Sed tantummodò abditissimo ipsius naturæ mysterio. Item quanta sit cælestium cum terrestribus loci distantia, < 4.> dissimilitudo, & formaru disparitas nemo est qui non videat. Concinunt omnes penè Philosophi nedum formas, sed & materiam corporum cælestium longè esse à sublunaribus diuersam: At enim, hoc non obstante, magna est inter hæc & illa consentio: cursum solis sequitur helitropium, illum, emenso mediæ noctis curriculo, ad nostrum hemisphærium properantem occinens, & exsiliens intelligit Gallus gallinaceus: Lunaria, & selenites Lunæ affectiones persentiunt, easdem prorsus phases, & maculas, provt illa subit, in facie ostendentes: Lunæ cum sole compressum sentit oleæ cinis in fundo argentei vasis aqua pleni consistens, dum mox turbatur, & eovsqque in gyrum vertitur, quoad illa à solis complexu se extricauerit: Martis sidere in cælestibus infirmato, aut ab inimicis obesso hebetatur apud nos ferrum, lentescit spiralis throcea in horologiis, & segnius signat horam: econtrà eo benè posito, hoc rigescit, & vires suas duplo auctas resumit. Solè Leonis signum permeante leones febre corripiuntur: Luna in scorpio existente, scorpius noster fuit: Cane sidereo ex oriente canes aguntur in tabiem, & alia penè innumera, quæ sparsim habet Plinius, & nos alibi ex occasione retulimus. Sed & temporum vices fato quodam recutrente recurrunt, vnde, vide in Lexico nostro V. Annus Periodicus. & Imperia suas mutationes subeunt, sata quæque ac plantæ statis temporibus germinant, efflorescunt, fructus parturiunt, vt præ cæteris Iuniperus, Aloës, Palma, & tunc miri etiam motus in vniversa Natura insurgunt; ac profectò mirum est, & multorum obseruatione literis consignatum, Neapolita-

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ON SYMPATHY. 43 trivial reasons in so great a prodigy, or paradox. I do not mean to say this: I shall at least say that it was not the arm that was taken away, nor yet torn off by Satan. Next, it is a lesser feat to carry off an arm once torn away than it was to tear the arm from the whole body without death. The merchant’s wife, having learned, as they say, that on one morning thirteen were to be beheaded (at the time of the Duke of Alba’s rule it happened at Antwerp), and being pregnant with disordered appetites, determined to go and watch the decapitations. She therefore ascended to the chamber of a widow known to her, living in the marketplace; and when she had seen the spectacle, at once the pain of childbirth seized her, and she brought forth a full-grown infant with a bloody neck, whose head nowhere appeared. Thus he says: which indeed cannot be referred either to contact, whether Physical or Mathematical, nor to effluvia, nor to likeness, nor to any natural connection. But only to the most hidden mystery of nature itself. Likewise, how great is the distance of the heavenly bodies from earthly things, their dissimilarity, and the disparity of their forms, there is no one who does not see it. Almost all philosophers agree that not only the forms, but also the matter of the heavenly bodies is far different from that of sublunary things: yet, despite this, there is a great harmony between these and those: heliotropium follows the course of the sun; the cock, when the sun, after completing the course of the middle of the night, is hastening toward our hemisphere, perceives it by its crowing and its leap; lunar stones and selenites feel the affections of the moon, displaying on their face the very same phases and spots as it undergoes: ashes of olive, lying in the bottom of a silver vessel filled with water, feel the compression of the moon along with the sun, and are stirred as soon as it becomes troubled, and whirl in a circle until it has freed itself from the embrace of the sun: when the star of Mars is weakened in the heavens, or besieged by enemies, iron becomes dull among us, the spiral string in clocks grows sluggish, and marks the hour more slowly: on the contrary, when that star is well placed, it stiffens, and recovers its powers doubled. When the sun passes through the sign of Leo, lions are seized with fever: when the moon is in Scorpio, our scorpion was there: when the star of the Dog rises in the east, dogs are driven into wasting disease, and there are almost countless other things, which Pliny has scattered here and there, and which we have elsewhere recounted on occasion. But also the changes of times, by some recurring fate, return again; whence, see in our Lexicon, s.v. Periodic Year. And empires undergo their changes, and all seeds and plants germinate at fixed times, blossom, bear fruit, as especially Juniper, Aloes, Palm, and then wondrous motions also arise in the whole of Nature; and indeed it is astonishing, and recorded in writing by the observation of many, Neapolitan-

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44 PHYSIO-THEOLOGIA, nam defectionem anno huius sæculi quadragesimo septimo factam alteri præcedentis sæculi ab eiusdem nominis homuncione eodem anno motæ optimè respondisse. Vt iam nullus dubitandi locus reliclus sit, hæc omnia sibi inuicem cohærere, & quantumuis natura, conditione, tempore, aut loco dissita mutuo quodam sympathiæ, antipathiæve vinculo complicari. 6. Verum vt quid Phalangij miras conditiones, & effecta prætereo, quod in se vno omnes prædictos effectus, naturæque motus continet, superatque? Est id ex Araneorum genere in Apulia frequens, nigri coloris, & morsu perniciotissimum: Namque vbi aliquem pupugerit, mox illum, nec nisi elapso anno, diræ affectiones corripiunt: dolet, gaudet, tristatur, exultat, atque ad certos sonorum modulos saltat appositè & in numerum, quamquam priùs omnem saltationis ordinem ignorasset; illum speculum, illum certi coloris vittæ, illum nudatus ensis oblectant, nec finem saltationi sacit, quousque effecto corpore virus omne in sudorem dehiscit: quo postea ad duos, aut tres dies saltationis absumpto, levatur æger, & dira ila symptomata cessant. Verum reuertente anno eadem prorsus methodo reuertuntur, nec omninò abscedit anniversarius morbus donec extincta bestiola, per sympathiam & ipsa venefica qualitas per ipsam ictu transmissa in humano corpore extinguatur, ni fortè alicui incredibile videatur, quod præ cæteris notat Kircherus in Arte Magnetica ad triginta ampliùs annos vixisse tarantulam, quæ olim nescio quem toto hoc temporis spatio morbo huiuscemodi laborantè momorderat. Circà quam rem adnotare licet plurimas huius morbi affectiones planè mirabiles, omnemque humani capius aciem fugientes. Primò Veneni inauditam vsque adeò naturam & qualitatem ad factus, & alia huiusmodi incitantem. Secundò non omnem sonum cuiuis à Phalangio icto conducere sed eum tantum, qui bestiolam serientem oblectet, eiusque peruerso genio sic artidens: vbi lepidum est quod narrat idem Kircherus, seruatam apud Andriensem Ducissam huiusmodi bestiolam christallino vase inclusam, cum priùs od diuersos sonorum modos immota pestiterit, mox nescio quo instrumento pulsato, atque ad certam harmoniæ speciem tenso, illam subsiluisse, ac motis ad numeros chelulis apprimè tripudiasse. Tertiò locorum quamuis distantiam, aut propinquitatem huic motui non officere, nec prodesse; etsi enim phalangio ictus procul abscedat, atque in regiones toto exlo, ac uari dissitas abeat, petinde eisdem affectibus qua-

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44 PHYSIO-THEOLOGIA, for the collapse that took place in the forty-seventh year of this century answered very well to that of the preceding century, stirred up in the same year by a creature of the same name. So that now no room for doubt is left, that all these things cohere with one another, and that, however far apart in nature, condition, time, or place, they are mutually bound together by some bond of sympathy or antipathy. 6. But why do I pass over the wondrous conditions and effects of the Phalangium, which in itself contains and surpasses all the aforesaid effects and motions of nature? It is a kind of spider common in Apulia, black in color, and most deadly in its bite: for when it has stung someone, straightway that person is seized by dreadful afflictions, and not until a year has elapsed. He feels pain, rejoices, grows sad, exults, and dances fittingly and in time to certain patterns of sound, although he had previously been ignorant of all the rules of dancing; a mirror delights him, as do ribbons of a certain color, as does a naked sword, and he does not cease dancing until, the body being worn out, all the poison bursts forth in sweat: after this, the sweat having carried off the dancing for two or three days, the sick person is relieved, and the dire symptoms cease. But when the year returns, they return by the same exact method, and the annual illness does not depart entirely until the little creature is killed, and even the witchlike quality itself, transmitted by the bite into the human body, is extinguished through sympathy—unless perhaps it should seem incredible to someone what Kircher notes above all in his Magnetic Art, namely that a tarantula had lived for more than thirty years, which long ago had bitten, I know not whom, who was suffering from such an illness throughout that whole span of time. On this matter it may be noted that there are many utterly remarkable features of this disease, escaping altogether the reach of human understanding. First, the unheard-of nature and quality of the poison, which prompts these effects and others of this kind. Second, not every sound is beneficial to one struck by a Phalangium, but only that which delights the little beast and, so to speak, charms its perverse nature: as Kircher relates a pleasant story, a creature of this kind was kept by the Duchess of Andria enclosed in a crystal vessel; after it had previously remained motionless through various sounds, then, when some instrument was struck and tuned to a certain kind of harmony, it sprang up and danced most excellently to the rhythm. Third, the distance or nearness of places does not hinder this motion, nor help it; for even if the one struck by the Phalangium withdraws far away and goes off into regions wholly distant, even so he is affected by the same ...

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DE SYMPATHIA. 45 titur, ac si in Apulia propè inimicum consisteret. Quartò demum temporis respondentia, quo sit mali recursus nunquam intermittentis, nisi aut alteruter moriatur, aut omne virus penitus extinguatur. Hæc omnia, quæ neque in naturæ similitudinem, aut 7. dissimilitudinem præcise, neque in effluuios spiritus, neque in occultam qualitatem immissam refundi possunt; certò mihi persuadent, atque in mea opinione confirmant, quam alias docui in Lexico V. Mundus, dari aliquam communem formam, quæ Vniuersi istius partes inuicem nectat, atque ad constituendum vnum per se habilitet, tribuatque vnam alteri condolere, aliam ab alia pati, ac diuersis motibus intrinsecus affici, respondere, in totius conseruationem, & ordinem à Natura constitutum viritim conspirare: si enim vniuersum hoc vnum compositum per accidens diceretur, vt quid lapis contrà suam naturam sursum ad repleendum vacuum impelleretur, vt quid selenites Lunam, tota substantia, toto cælo diuersam motibus suis imitatetur? Vtque iu humano corpore cum Galeano plures sympathiæ species conspirati sumus, aliam, quæ dicitur operis familiaritatis, aliam generis, & aliam vicinitatis; ex quibus veluti fontibus, omnes internæ membrorum affectiones deriuant; ita, & in magno isto corpore Mundi omnes internæ partium affectiones, condolentiæ, dissensiones, mutuæ earum colligationi in vna vniuersali forma acceptæ referri debent, atque ad vnam ex dictis tribus sympathiæ speciebus reduci. Sic aëris contagiones, atque adeo hominum, & iumentorum, vicinitati; sic magneticæ attractiones, & forte fascinus, quæ per medium obicem impediuntur: per effluuios, (vt cerebri affectiones ab stomachi vaporibus sursum elatis) sic etiam ex familiaritate operis, vti in corpore humano mammæ vtero præsertim conceptus tempore sunt colligatæ, ita in Vniuerso, Vêre omnia efflorescunt, nedum plantæ, sed & corpora, & ingenia turgent, atque ad quasdam fructificationes mutuò incitantur. Verum vti eodem loco Verbo S. Sympathia num. 1. 8. diximus, sunt aliquæ partium affectiones, & condolentiæ in humano corpore, quæ ad hæc capita omninò reduci non possunt, sed ad aliam occultam virtutem, quæ his tandem accedat, vt pater in delitio mentis, quod ex inflammatione septi transuersi solum oritur, non autem ex obstructione ventriculi, quæ tantum caput dolere facit, ita in hac Vniuersi constitutione plures rerum affectiones sunt, quæ ægè

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DE SYMPATHIA. 45 is stirred, as if in Apulia it were standing near an enemy. Fourthly, finally, by corresponding periods of time, in which there is a recurrence of the evil, never intermitted, unless either one or the other dies, or the whole virus is utterly extinguished. All these things, which can neither be referred precisely to a likeness or unlikeness of nature, nor to effluent spirits, nor to an infused hidden quality, certainly persuade me, and confirm me in my opinion, which I have elsewhere taught in the Lexicon V. Mundus, that there is some common form, which links together the parts of this Universe with one another, and qualifies them to constitute one thing in itself, and grants that one should sympathize with another, one suffer from another, and be affected by diverse movements inwardly; they respond, in the preservation of the whole, and to the order established by Nature, each one conspiring: for if this universe were said to be one composite thing by chance, why should a stone, contrary to its nature, be driven upward to fill the void, why should selenite imitate the Moon, though its whole substance and whole heaven differ from it in its motions? And just as in the human body with Galen we are agreed that there are several kinds of sympathy, one which is called that of familiar operation, another of kind, and another of vicinity; from which, as from sources, all the internal affections of the members derive; so too, in that great body of the World, all the internal affections of the parts, their mutual suffering, their concords and discords, as accepted in one universal form through their mutual linkage, must be referred, and reduced to one of the said three kinds of sympathy. Thus the contagions of the air, and indeed of men and beasts, to vicinity; thus magnetic attractions, and perhaps fascination, which are impeded by an intervening obstacle: through effluvia, (as affections of the brain from vapors of the stomach borne upward) thus also from familiar operation, as in the human body the breasts are especially linked to the womb at the time of conception, so in the Universe, in Spring, all things blossom forth; not only plants, but bodies and minds also swell, and are mutually incited to certain kinds of fruitfulness. But as in the same place, in the word S. Sympathia no. 1, we said, there are certain affections and sympathies of the parts in the human body which cannot at all be reduced to these heads, but to another hidden virtue, which at last may be added to them, as a father in the delight of the mind, which arises only from inflammation of the transverse septum, but not from obstruction of the ventricle, which merely makes the head ache, so in this constitution of the Universe there are many affections of things, which with difficulty

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46 PHYSIO-THEOLOGIA, ad supradicta capita reduci possunt, sed necessariò occultæ cuidam qualitati sunt tribuendæ, quæ quidem sideribus, (vti etiam ibi docui vni, & eidem rei prædominantibus, aut p[er]iurium colligationi, quæ ad inuicem aut amica, aut inimica sunt, aut demum nullo ordine colligata, provt diuersis specie, aut genere rebus præsident, eademque qualitate afficiant est imputanda. Et ad huius generis sympathiæ, antipathiæve normam omnes supradictæ rerum affectiones, morus, condolentiæ consensiones, dissensionesvé in partibus quamtumuis loco tempore, aut natura dissitis, quæ vtpote frequentes, continuæ, & vt plurimum in rebus sensu, rationeque carentibus conspicuæ minimè miraculo, aut cacodæmonis operæ ascribi possunt, sunt metiendæ. Iam verò his constitutis singula examinemus, & causam huius abditissimi arcani, quo vulnera magneticè consolidantur, pro nostra virili parte reddamus. Et primò. 9. Supponendum est ex iis quæ modò, & In superioribus diximus, effectum hunc naturalem esse, si non aliunde certe ex paritate aliorum, quæ eandem prorsus difficultatem patiuntur, & neque ad miraculum, neque ad cacodæmonis operam reduci possunt: cuiusmodi sunt ad Lunæ incrementum, aut decrementum selenitis lapidis mutationes, ac maculæ: vini in doliis fluctuatio ad vitis efflorescentiam, idque vt notat Helmontius in vi magneticæ non constituto tempore, sed tunc potissimum, quando pro locorum diversitare aut serius, aut tempestivius vitis floret, quamuis multis milliariis dissita, quamuis enim vinum extrà provincias conterminas natum, aliò asportetur, vbi pro soli qualitate vitis provincialis, aut Aprili mense, vt apud nos, aut Octobri, vt in Chile Regno floret, attamen vinum non turbatur quando vitis genuina floret, sed quando vitis provincialis, nec cessat huiusmodi confusio, quamdiù flos viti non decidit: macularum in linteis ex fructibus contra- clarum abstersiones, quando arbores eosdem fructus producentes foliis spoliantur, &c quæ omnia, vt dixi, nulla locorum distantia, (aut easanè, quæ nostram difficultatem non releuat) iuuare cernitur, aut vllarenus impedire: neque etiam miraculo, aut Dæmonis operæ ascribi possunt, sed verissimæ, & immediatæ Naturæ activitati non tam occultè, quum ordinatè singula operantis sunt citrà dubium relinquenda. 10. Supponendum secundò ex Hippocrate 6. Epidem. textu 1. Naturam esse morborum medicatricem. hoc est (vt inquit

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46 PHYSIO-THEOLOGIA, may be reduced to the aforesaid heads; but they must necessarily be attributed to some hidden quality, which, as I likewise taught there, is to be assigned either to the stars predominating over one and the same thing, or to the concatenation of things, which are either friendly or hostile to one another, or finally linked without any order, insofar as they preside over diverse things of different species or genus, and affect them with the same quality. And according to the rule of this kind of sympathy or antipathy, all the aforesaid affections of things, such as habits, compassionate consensuses, dissensions, whether in parts however far removed in place, time, or nature, which, since they are frequent, continuous, and for the most part conspicuous in things lacking sense and reason, cannot be ascribed to a miracle or to the work of a cacodaemon, are to be measured. Now, these things being established, let us examine each point, and let us give, according to our ability, the cause of this most hidden secret, by which wounds are magnetically consolidated. And first. 9. It must be supposed, from what we have now said and in the foregoing, that this effect is natural, if not from elsewhere then certainly from the parity of other things which suffer the same difficulty in precisely the same way, and can be reduced neither to a miracle nor to the work of a cacodaemon: such as the changes and spots of the selenite stone corresponding to the increase or decrease of the moon; the fluctuation of wine in casks corresponding to the flowering of the vine, and that, as Helmont notes, not at a fixed time in the magnetic force, but then especially when, according to the diversity of places, the vine blossoms later or earlier, although many miles distant; for although wine, born outside neighboring provinces, is carried elsewhere, where, according to the quality of the soil, the provincial vine blooms either in April, as אצל us, or in October, as in the Kingdom of Chile, nevertheless the wine is not disturbed when the genuine vine blossoms, but when the provincial vine does, nor does this sort of confusion cease as long as the flower of the vine does not fall: the clearing of stains in linens from fruits, when the trees producing the same fruits are stripped of their leaves, and so forth; all of which, as I said, are seen to be aided by no distance of places whatsoever, or by anything that does not relieve our difficulty, nor can they be hindered in any way; nor can they be ascribed to a miracle or to the work of the Devil, but must without doubt be left to the most true and immediate activity of Nature, not so much hidden as orderly operating each thing. 10. It must be supposed secondly, from Hippocrates, Epidemics 6, text 1, that Nature is the healer of diseases. that is to say (as he says

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DE SYMPATHIA. 47 Rapinius) instrumentaria illa causa, qua immediatè vticur anima ad præcipuas facultates in corpore exercendas, tum in vitali, tum in naturali genere: idque vel instaurandi, vel conseruandi causa quæ consistit non modo in elementari partium commixtione primarumve qualitatum crasi, verum etiam in substantia illa potissimum ex humido radicali, calido iunato, primigenioque spiritu coalita. Huic profectò Medicus sedulò inferuit (est enim vt addit idem Hippocrates, Naturæ famulus) opportunè singula suppeditando, sollicitus nempe de ipsius integritate custodienda; in id semper incumbens, vt tria illa, quæ eam omnibus numeris absolutam in sua bonitate constituunt, humidum videlicet radicale, spiritus primigenius, & calor innatus conuenienti nexu & proportione cohæreant, ne calori humidum radicale sustentans vquam deficiat, neve calor humidum omninò absumat, spiritumque deuastet. Quod cum obtinuerit, eunctis ad talem moderationem redactis, Natura ipsa propria indole in sui conseruarionem conspirans, ad perfectam integritatem corpus nostrum reducit, opusque suum perficit. Et quidem quò id, absque vlla ipsius naturæ iactura fit, eò fortiùs ipsa vires suas exerit, citiusque sanitatem adducit; sæpè enim vulgaria medicamenta, suam nimia activitate naturam premunt, aut non ira adiuvant, vt non etiam defatigent, & aliquo pacto deiiciant; verissimum damque est quod vulgò circumfertur, ea esse instar lixiuij, quod vestimenta quidem è soddibus purgat, abstergit, emundat, verum etiam sensim quatit, conterit, adurit, ac tandem penitùs dissipat: at cum non habet Natura vnde extrinsecus repatiatur, & cum pluribus confictando vires suas dispertiat, ac dispersat, validiùs opus suum exequitur, ac citò perfectam sanitatem, quæ in partium cohærentia & harmonico nexu consistit, adducit. Si igitur Medicus ità naturæ opitulatur, vt eins inopiam dilet, deiectionem releuet, robur confirmet, ac vires nullo modo prosternat. Hoc equidem optimè callet, & prouidere vti que potis est Naturæ cæteroqui infensissimus hostis Diabolus, & quandoque fideliter præstat à suis asseclis inuocatus: sed id horreat Christianus Medicus ope Daemonis assequi cum animæ suæ, proximique dispendio: gaudeat se posse suo acumini, ac naturæ viribus sisum eadem imitari, feliciter obtinere: sicque vt ex aliis Naturæ operibus medendi peritiam comparauit, ita hoc mirabili magnetismo quem in omni penè Natura videt, edoctus, discat quid valeat in Natura alioqui infirma diuino planè fulcimine operari, ipseque vicissim,

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Of Sympathy. 47 …instrumental cause, by which the soul immediately makes use of it for exercising the chief faculties in the body, both in the vital and in the natural kind: and this for the sake either of restoring or preserving, which consists not only in the elemental mixture of the parts, or in the temperament of the primary qualities, but also chiefly in that substance compounded of radical moisture, innate heat, and the primordial spirit. To this, indeed, the Physician diligently lends his aid (for he is, as Hippocrates adds, Nature’s servant), suitably supplying each thing in turn, careful, namely, to guard its integrity; always striving that those three things which constitute it complete in every respect in its goodness—namely radical moisture, the primordial spirit, and innate heat—may remain joined together in a fitting bond and proportion, lest the radical moisture that sustains the heat ever fail, or lest the heat entirely consume the radical moisture and ravage the spirit. When he has achieved this, all things having been reduced to such moderation, Nature itself, with its own disposition conspiring toward its preservation, brings our body back to perfect integrity and completes its work. And indeed, the more this is done without any loss to nature itself, the more strongly does it exert its powers and the more quickly does it restore health; for often ordinary medicines, by their excessive activity, oppress nature, or do not merely assist it, but also weary it and in some degree cast it down; and it is most true what is commonly said, that they are like lye, which indeed cleanses, wipes away, and purifies garments from dirt, but also little by little shakes, wears away, scorches, and finally utterly destroys them. But when Nature has no means of recovering from outside, and when, by struggling against many things, it disperses and scatters its powers, it carries out its work more vigorously and quickly brings about perfect health, which consists in the coherence of the parts and their harmonious union. If therefore the Physician helps Nature in such a way that he lessens its lack, relieves its dejection, strengthens its power, and in no way prostrates its forces, he understands this very well; and what is more, the Devil, otherwise most hostile to Nature, is able to foresee it and sometimes even faithfully supplies it when invoked by his followers. But the Christian Physician should shrink from attaining this by the aid of a Demon, to the harm of his own soul and that of his neighbor; let him rejoice that he can, by his own skill and by the powers of nature, happily imitate and achieve the same thing. And thus, just as he has acquired the art of healing from the other works of Nature, so, instructed by that marvelous magnetism which he sees in almost all Nature, let him learn what he can do in Nature, otherwise weak, supported by a truly divine sustenance, and he himself in turn,

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48 PHYSIO THEOLOGIA, qua via possit suas partes exequi, ac Naturæ optimè inferuire. Ergò Magnetica curatio vulnerum Naturæ opus est: ipsa eam immediatè aggreditur, perficit, obtinet; Medico tantum Naturæ opus, ac Magnetismum coadiuuante. Et hic demum est abditissimi huius arcani aditus, ac verissima causa, quam Goelenius, Papinius, Helmontius, aliaque detegere satagentes, maximopere se implicarunt. 11. Dico igitur Magneticam curationem fieri à Natura immediatè & intrinsecus operante, excitata tamen extrinsecus à motu sanguinis medicati, & à vitriolo, siue ab alio quo- uis id genus medicamento alterati, ob sympathiam, & connexionem, quam habet cum ipso sanguine, qui pars eiusdem corporis est, quamuis abscissa, proindeque eiusdem naturæ, ac substantiæ, quam nihilominus seruat, atque in Vniuersitistius communi forma, vel (quam nemo negare poterit) partium cohærentia, necitur, vniturque. Patet id apertissimè tum ex his quæ hîc, & alibi diximus; tum ex plurimis experimentis eiusdem rationis, quæ plane hanc veritatem cuincunt, tam in ipso homine, quam in cæteris animantibus, ac sanè in reliquis rerum ordinibus, quæ aliquo sympathiæ vinculo inuicem colligantur: vt proinde in hoc tam arduo negotio veluti in gordiano nodo suo primo vniuersali principio iam detecto omnia naturæ arcanæ, omnes sympathiæ affectiones tanquam in vno glo- mere complicatæ facilè exsoluantur. Sic vrina, sic sanguis, sic cæteræ pattes corporis iam excretæ, suam seruant cum corpore sympathiam, vnde mirum non est, si vno male affecto, & alterato, condoleat, & intrinsecus alteretur alterum: si diciduis foliis ex arboribus, tanquam natura effæta, & succus pannis illius vires suas deperdat, & contractæ ex eo maculæ abigantur, si vinea efflorente vinum intrinsecus fluctuat; excitatur quippè istius natura ad sui affinis commotionem ad similem motum promendum, & intrinsecam condolentiam: ac sic per singula discurrendo, cæterarum in vniuersa Natura affectionum, facile est originem inuenire. Vnde est profectò, quod nulla actio datur in distans, sed vnumquodque immediatè agit in passum sibi contignum, atque approximatum, altero interim affine intrinsecùs à Natura ad similem motum excitata, repatiente. 11. Ergò in Helitropio sese ad motum solis vertente, motus ab intrinseco est, excitato tamen à solis motu, cui est natura affinis, & quodammodo subordinatus; vt externa eriam facies monstrat, simili à Natura characterismo si- gnatum

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48 PHYSIO THEOLOGIA, through which it may carry out its parts and best serve Nature. Therefore magnetic curing of wounds is a work of Nature: itself it undertakes, accomplishes, and effects it immediately; the physician only cooperates with Nature’s work, with Magnetism assisting. And here at last is the entrance to the hidden secret, and the truest cause, which Goelenius, Papinius, Helmontius, and others who have striven to uncover it, have most entangled themselves in. 11. I therefore say that magnetic healing is done by Nature immediately and internally acting, though stirred up externally by the motion of medicated blood, and by vitriol, or by some other such altered medicine of that kind, because of the sympathy and connection which it has with the blood itself, which is a part of the same body, though severed, and therefore of the same nature and substance, which nevertheless it preserves, and in the universal common form of that body, or (as no one can deny) the coherence of the parts, is bound and joined. This is most clearly evident both from the things we have said here and elsewhere; and also from many experiments of the same kind, which plainly prove this truth, both in man himself and in other living creatures, and indeed in the remaining orders of things, which are connected with one another by some bond of sympathy: so that therefore in this very difficult matter, as in a Gordian knot, with its first universal principle now discovered, all the hidden secrets of Nature, all the affections of sympathy, as though tangled together in one ball, may easily be untied. Thus urine, thus blood, thus the other parts of the body already excreted, preserve their sympathy with the body, whence it is no wonder if, when one is badly affected and altered, the other is harmed and inwardly altered: if fallen leaves from trees, as though nature were exhausted, and the sap of their stalks loses its strength, and the stains contracted from it are driven off; if wine in a flowering vineyard swirls within; for the nature of that thing is stirred toward the movement of its like, to produce a similar motion, and an inward suffering together: and thus, running through each case, it is easy to find the origin of the affections in the whole of Nature. Hence it is indeed that no action is given at a distance, but each thing acts immediately upon the patient contiguous and near to it, while meanwhile another thing akin to it is inwardly stirred by Nature to a similar motion, and responds. 11. Therefore in the Helitropium turning itself toward the motion of the sun, the motion is from within, though stirred up by the motion of the sun, to which it is by nature akin and in some way subordinate; as the external appearance also shows, marked by a similar character of Nature.

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DE SYMPATHIA. 49 gnatum: quod etiam, quamuis obscurè agnouit Hieronymus Dandinus, Digress. 6. in libros de Anima. afferens florem hunc à principio intrinseco moueri, ad motum solis, sicut lapis ad centrum: quod etiam affirmat de Lunaria sese ad motum Lunæ confoimanre, quam ideò Lunitropium vocat. Similiter in Selenite lapide mira illa mutario macularum ad Phasium Lunarium normam, (cum in solido lapide fiat, nec in externa facie modò sed & in toto corpore, vt eo dissecto videre est,) non nisi ab intrinseco esse potest: mutatur autem per insitam ei cum Luna similitudinem, ac sympathiam quâ, eâ motâ ad similem motum & passionem intrinsecus excitatur. Sic chordæ similes ad alterius contactum resonant non ab aëre moto, vt vult Fracastorius lib. de Sympathia cap. 11. & Aresius de Generat. disp. 1. quast. 41, sect. 7. quandoquidem in alia cythara viciniori, sed non vnisona, & in longe maiori impulsu aëris ad cytharam vsque peruëniente non eumdem effectum parit, sed à verissima sympathia intrinsecus chordas vnisonas ad vniformem sonum excitante: neque enim maior dispositio, quam dicunt in istis esse ad recipiendum motum, & edendum sonum, quam in aliis non æquè tensis explicari potest per aliud, quam per istam Naturæ consensione: sed & id contrariâ ratione, Antipathiæ videlicet, euincit alia experientia chordarum ex agni neruis formatarum, quæ ad cytharæ è lupi chordis compactæ pulsationem statim intrinseca vi dirumpuntur; earum quippe naturâ ad contrarij motum, quod ferre non potest, sese deuïciente. Hinc etiam in plantis idipsum videre est, quæ aliis sibi mutuo amoris nexu deuinctis complantaræ feræiores ac viuidiores redduntur, provt de malo punico, & Myrto testantur Democritus, & Mizaldus lib. 1. arcanorum, ac de Ruta sub ficu crescente Plinius lib 19. c.8. ac Dioscorid. lib. 1. cap. 31. Aliarum autem naturâ dissitarum propinquitate læduntur, & sterilescunt, vt præsertim vitis à brassica. Econtrà multæ sunt, quæ ob inimici fruticis, aut oleris viciniam roborantur, & vires conduplicant; vt rosa allio complanta ta odoratior sit, non quod allium, quod alioqui graueolentissimum est, quicquam boni in illam transmittat, eiusque fragrantiam augeat, sed qvia ad inimici præsentiam excitata intime natura rosæ ad pugnandum accingitur, viresque suas omnes exerit. Et sic discurre per singula, in oscitatione, oculorum lippitudine ad caligantis oculi visum dentium stupore ad acidarum rerum aspectum, aut considerationem, atque aliis corporis affectionibus, ac deliquiis, quæ

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On Sympathy. 49 generated: which Jerome Dandinus also, though obscurely, recognized, Digress. 6 on the books De Anima , where he maintains that this flower is moved from an intrinsic principle toward the motion of the sun, like a stone toward the center; and he likewise affirms of the Lunaria that it conforms itself to the motion of the moon, which is why he calls it Lunitropium . Similarly, in the Selenite stone, that wonderful change of the spots according to the phases of the moon, (since it takes place in a solid stone, and not only on the outer surface but throughout the whole body, as may be seen when it is cut open,) can arise only from something intrinsic: moreover it is changed by the likeness and sympathy implanted in it with the moon, by which, when the moon is moved, it is inwardly stirred to a similar motion and passion. Thus similar strings sound together when one is touched, not from the air being moved, as Fracastorius would have it, book De Sympathia , ch. 11, and Aresius, De Generatione , disp. 1, question 41, sect. 7; for in another, nearer cithara, but not in unison, and with a much greater impulse of air reaching the cithara, it does not produce the same effect, but from a most true sympathy, which inwardly excites unison strings to a uniform sound. For the greater disposition, which they say exists in these things for receiving motion and producing sound, than in others not equally strained, cannot be explained by anything else than by this agreement of Nature: and likewise, by the contrary reasoning, namely antipathy, another experiment proves it: strings made from lambs’ nerves, when struck by the cithara made of wolf’s strings, are immediately torn apart by an intrinsic force; for their nature yields to the motion of what is contrary, which it cannot bear. Hence also the same thing is seen in plants, which, when joined to others bound to them mutually by the bond of love, are made more fertile and more vigorous; as Democritus and Mizaldus testify concerning the pomegranate and myrtle, book 1 of Arcana , and concerning rue growing under a fig-tree, Pliny book 19, ch. 8, and Dioscorides book 1, ch. 31. But others, by contrast, of a different nature, are harmed by proximity, and become sterile, especially the vine by cabbage. On the other hand, there are many which, because of the neighborhood of a hostile shrub or herb, are strengthened and double their power; as the rose, planted with garlic, is more fragrant, not because garlic, which is otherwise most foul-smelling, transmits anything good to it or increases its fragrance, but because, stirred by the presence of an enemy, the inner nature of the rose is aroused to battle and exerts all its strength. And so go through the individual cases: in yawning, in bloodshot eyes at the sight of a dim eye, in the numbness of the teeth at the sight or consideration of sour things, and in other affections of the body, and faintings, which

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30 PHYSIO-THEOLOGIA, mox, insurgunt ad ingratæ rei aspectum, imaginationem, sonum, & similia: nec dici potest cum Aresio, ad hæc excitari in nobis appetitum illius rei eo ipso ac phantasix proponitur tale obiectum, tum quia hæc vt plurimum sunt naturæ contraria, ad quæ non datur appetitus sed potius aueisio; natura enim naturaliter ad sui bonum tendit, non ad malum; tum etiam quia hoc ipsum est quod difficultatem facessit, quomodo inquam Phantasia tam subitò casum faciat, & per physicam actionem naturam protinus deiiciat: 14. Est igitur ratio obiectorum dissonantia, quæ phantasix obiecta per huius cum certis corporis partibus sympathiam natura concutitur, ac deiicitur: vnde monstra illa, & affectiones sequuntur. Sic vidimus aliquos ad frigidæ guttam eadentem, quam bipennem apprehendebant, extinctos: sic malacix effectus quotidie videmus, siue ex appetitu, siue ex horrore obieclarum rerum progenitos, quos etiam aduentante tempore illarum rerum, turgere, maturescete, exsiccari, provt illæ efflorescunt, turgent, maturescunt, vel flaccescunt, conspicimus, natura siquidem ob cogenitam cum illis rebus sympathiam fese ad similes motus inirinsecus excitante. Ego sanè in meipso experior, quoties aut ingens vleus, aut sanguinis magnum aliquod profuuium, spectare, aut mente concipere contingit, statim in animi deliquium, nec sine periculo deuenire, natura equidem horrore concepto se propria indole prosternente, ac vitæ officia relinquente. Quid igitur mirum si & in foetibus, vt supra ex Helmontio adnotauimus eadem, & maiora naturæ portenta suboriantur, quæ à Matre ex obiectis visis, imaginatione, ac terrore perculsa, statim ex occulta sympathiæ vi ad tenellum infantis corpusculum transmittuntur, eaque monstra ex naturæ deiectione prosiliant? 15. Sanè Phalangij naturam explicare, eiusque ictus tam multiplices affectiones, easdemque tam varias pugnantesque inuicem inducentis, rationem reddere difficilius est, quippe arcanum est longè in natura nouum, & cui simile non sit inuenire: quis enim ordo, quæ connexio animalis cum sonis, & huius cum hoc præcisè non alio genere harmoniæ? Quæ temporum respondentia? Qualis Veneni qualitas? Et num naturæ humanæ amica, vel inimica? Si amica, quomodo dira illa symptomata inducit? Si inimica, cur ad destructionem non tendit? Cur ea ad sonorum modulos non magis intenditur, (quippe eam cum sonis sympathiam aliquam habere necesse est) & si intenditur, cur non potius hominem releuat, quam maioribus cruciaribus vexar? Cur

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30 PHYSIO-THEOLOGIA, then they rise up at the sight of an unwelcome thing, at the imagination, at the sound, and the like; nor can it be said with Aresius, that in this way the appetite for that thing is aroused in us as soon as such an object is presented to the phantasia, both because these things are for the most part contrary to nature, toward which there is no appetite but rather aversion; for nature naturally tends toward its own good, not toward evil; and also because this is precisely what creates the difficulty, how, I say, the Phantasia can so suddenly produce a collapse, and by physical action at once cast nature down: 14. Therefore the cause is the dissonance of the objects, which, through their sympathy with certain parts of the body, strikes the objects presented to the phantasia and casts it down: whence those monsters and affections follow. Thus we have seen some, from the falling of a drop of cold water, which they grasped with a hatchet, to have been extinguished; thus we daily see the effects of bad air, whether produced by appetite or by horror of outward things, which even at the coming of the time of those things we observe to swell, to ripen, to dry up, just as those things themselves blossom, swell, ripen, or wither, nature indeed, because of its inborn sympathy with those things, stirring itself to similar motions inwardly. I myself surely experience in myself that whenever it happens either to see a huge ulcer, or some great effusion of blood, or to conceive it in my mind, I immediately come into a fainting of the spirit, and not without danger; nature, indeed, horror having been conceived, prostrating itself according to its own disposition, and abandoning the offices of life. What wonder, then, if in foetuses also, as we noted above from Helmontius, the same and greater prodigies of nature arise, which from the Mother, struck by the objects seen, by imagination and terror, are at once transmitted through the hidden force of sympathy to the tender little body of the infant, and those monsters spring forth from the downfall of nature? 15. Truly to explain the nature of the Phalangium, and to give an account of its stroke, which induces so many affections, and those too so various and contrary to one another, is more difficult, since it is an arcanum long new in nature, and one like which there is nothing to be found: for what order, what connection is there between an animal and sounds, and between this and this specifically, not by any other kind of harmony? What correspondence of times? What sort of quality of poison? And is it friendly to human nature, or inimical? If friendly, how does it induce those dire symptoms? If inimical, why does it not tend toward destruction? Why is it not more directed toward the measures of sounds, (since it must have some sympathy with sounds) and if it is directed, why rather does it not relieve a man than afflict him with greater tortures? Why

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DE SYMPATHIA. 11 demum mortuo phalangio ea prorsùs extinguitur, & extera quæ non facilè quis poterit explicare. Neque enim placet quod ait Aresius loco citato num. 12. quod si de morte natu- rali huius bestiolæ agatur, rem verisimilitudine non carere, quia fieri potest, inquit, vt quò longius à morte hoc animal di- stat, eò vim habeas acriorem, ad venenum infundendum: si verò de morte violenta non videtur verum, quia nulla apparet probabilis causa vt hoc contingere possit. Non inquam placet, quia huic postremo dicto refragatur experienria, & fides rot hominum id indubitatò dicentium, ex quo tandem ortum prouerbium apud nos Italos: Morta la bestia, morto il ve- leno. Et si demùm id aliquando casu contigisse dicatur, affero < 16.> duo experimenta, vnum quod affert Taliacotius in sua Chi- rurgia, de quodam, qui amissum in prælio nasum, vt sibi reficeretur, Bononiam ad ipsum Taliacorum concessit, ve- rum cum præceptam incisionem brachij sui timeret, vt de eo nasus sibi efformaretur, seruum conduxit, è cuius brachio nasum sibi dato pretio eruit, atque eo ad tredecim circiter menses ad decorem in patriam reuersus vsus est: quando ec- ce tibi repente nasus ascititus friguit, mox post aliquot dies putrefactus cecidit. Rei inopinam causam merantibus, & inquirentibus cunctis, inuenrum est, eodem fere mo- mento, quò nasus friguit, expirasse Bononiæ illum, qui venale eorum exposuerat. Alterum exemplum sit, de quo quiuis periculum facere porerit. Si felem masculum, post- quam foeminæ superincubauit, eaque prægens eatulos non- dum edidit, quis occidar, mox illa aborum patitur, & ca- tuli mortui eduntur, eorum natura sui genitoris casum ex occulta sympathiæ vi, minimè sustinente: Sic igitur veneni virtus in hominibus à phalangio ictis extingui poterit eo vt- cumq[ue] mortuo; per sympathiam veneficæ qualitatis cum suo principio à quo transmissa fuit, licet etiam aliunde extingui possit, vel per alia anidora, quorum longam seriem affert Plinius in sua Historia, vel per ipsius qualitatis desitionem, provt validior aut segnior fuerit in ea superanda percussi na- tura, ictusque aut Lenior aut profundior. < 17.> Restar igitur, vt dicamus in hoc vno Naturæ ateano reli- qua omnia quæ sparsim in aliis eius operibus conspicimus, comprehendi, vtque hoc totum Naturæ opus absolutissimum est; cuius tamen causam ignoramus; ita magnetica omnis curatio naturæ viribus facta præsumi debet, quamquam non plenè ratio innotescit. < 18.> Postumustamen in phalangij casu dicere intercedere par- d ij

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DE SYMPATHIA. 11 then after the phalangium has died it is wholly extinguished, and the rest which one can scarcely explain. Nor indeed does what Aresius says in the cited place, no. 12, please me: that if the natural death of this little beast be in question, the matter is not without likelihood, because, he says, it is possible that the farther this animal is from death, the sharper may be the power you have for infusing the poison; but if it be by violent death, it does not seem true, because no probable cause appears why this could happen. I say it does not please me, because experience and the testimony of many men who declare this without doubt contradict this last statement; from which at last arose among us Italians the proverb: Morta la bestia, morto il veleno. And if finally it be said that this has sometimes happened by chance, I bring forward < 16.> two experiments: one, which Taliacotius reports in his Chirurgia, about a certain man who, having lost his nose in battle, came to Bologna to Taliacotius himself so that it might be restored to him; but since he feared the prescribed incision of his arm, from which a nose was to be fashioned for him, he hired a servant, from whose arm he had a nose cut out for a price, and with it, after about thirteen months, he returned to his homeland and used it for adornment: when behold, suddenly the grafted nose grew cold, and after a few days it became putrid and fell off. When everyone marveled at and inquired into the unexpected cause of the event, it was found that at the very same moment when the nose grew cold, the man in Bologna who had supplied it for sale had died. Let the other example be one that anyone can test for himself. If a male cat, after it has lain upon the female, and she, being pregnant, has not yet brought forth the kittens, is killed, then soon afterwards she suffers a miscarriage, and dead kittens are born; their nature not bearing, through the hidden force of sympathy, the death of their own sire. Thus, therefore, the power of the poison in men struck by the phalangium may be extinguished by its death in any way whatever; by sympathy of the venomous quality with its own principle from which it was transmitted, although it may also be extinguished from elsewhere, either by other antidotes, whose long series Pliny gives in his History, or by the cessation of the quality itself, according as the nature of the person struck is stronger or weaker in overcoming it, and the sting either milder or deeper. < 17.> It remains therefore that we say that in this one mystery of Nature the rest of all those things which we see scattered in her other works are contained, and that this whole work of Nature is most complete; yet we do not know its cause. Thus every magnetic cure made by the powers of nature ought to be presumed, although the reason is not fully known. < 18.> However, in the case of the phalangium it must be said that there intervenes a

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51 PHYSIO-THEOLOGIA, tim sympathiam, partim antipathiam: sympathiam inter phalangium, & certam speciem harmoniæ, colores, arma, &c. atque eriam in percussio id euenire ob qualitatem immissam, quæ proinde totam naturam insicit, antipathiam inter ipsam veneficam qualitatem, & hominem, talem tamen quæ facilè in ipsam naturam redundet, præsertim cum ex Arist. septim Metaph. cap. 6. contrariorum eadem forma sit, atque adeo intercedat necesse est aliqua similitudo, & connexio. <10.> Hinc ad obiecta in naturalem pulueris sympathici activitatem, cæterotum eiusdem generis medicamentorum, facilis est responsio: quomodo enim, inquiunt, tam modicus puluis sanguini iam emortuo applicarus, magnum alioqui vulnus, idque dissium sanare potest? quomodo vnguendum ferro illium, in quo vix sanguinis vestigia extant, eadem virtute pollet? Quomodò in vulneribus à sclopetis factis eadem miracula non experimur? Verum, vti dicebam, curatio immediatè à natura sit, extrinsecis hisce fulcris effectiuè in vulnus ne minimum quid operandibus, sed solum in ea quibus immediatè applicantur, puta sanguinem, pus, & similia, ad quorum tamen alterationem natura, ob substantiæ similitudinem, & conformitatem alteratur, intrinsecùs excitatur & maiori nisu curationem perficit; eo prorsus pacto, quo per morbum deiecta solo suffluu, aromatum, vini, aliorumque id genus extractorum, quæ spirituales magisque æthereas rerum portiones seriant, natura erigitur, spiritusque nostri corporis aliàs torpentes momento temporis excitantur, & pro naturæ affinitate proficiunt, & instaurantur. Sic profectò Natura per eius partis, quæ quatuus excisa, retinet nihilominus aliquid primigeniæ substantiæ, veluti somno expergefacta, & amica voce erecta accingitur ad curationem perficiendam morbumque superandum, eò faciliùs, quo ad id aliàs prona est, vt vel levissimo adiumento, (eo maximè quod non, vt cætera medicamenta immediate applicata naturam premit) suffulta alacrior exit ad opus perficiendum. <21.> At cum vulnus igneo globulo lavata rota à sclopetis indigitur, instrumentum, quod ad explosendum dumcaras globum inferuit, nullam contrahit cum vulnere sympathiam, cum non corpus attingat, non vulnus per seipsum faciat sed per immisum plumbum; ac proinde nil mirum, si ineprum prorsus euadat ad curationem magneticè perficiendam, benè autem opus feliciter fortè prodiret, si globus extrahi pollet, atque in vnguentum immitti; militat enim pro eo

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51 PHYSIO-THEOLOGIA, partly sympathy, partly antipathy: sympathy between the phalangium and a certain kind of harmony, colors, weapons, &c., and also that the same occurs in the case of the wound on account of an infused quality, which therefore affects the whole nature; antipathy between the poisonous quality itself and man, yet such that it can easily redound upon nature itself, especially since, from Aristotle, Metaphysics 7, ch. 6, contraries have the same form, and therefore some similarity and connection must necessarily intervene. <10.> Hence the reply to the objections against the natural activity of the sympathetic powder and other remedies of the same kind is easy: how, they ask, can so small a powder, applied to blood already dead, heal a great wound, and that at a distance? How can the salve on the iron have the same power, in which scarcely any traces of blood remain? Why do we not experience the same miracles in wounds made by gunshots? But, as I said, the cure is immediately from nature; these external supports contribute nothing effectively to the wound, but only to those things to which they are immediately applied, such as blood, pus, and the like, and yet because of the similarity and conformity of the substance, nature is altered, inwardly excited, and accomplishes the cure with greater effort; exactly in the same way that, when a person is laid low by illness, he is raised up by the effusion of perfumes, wine, and other extracts of this kind, which seize upon the spiritual and more ethereal parts of things: nature is lifted up, and the spirits of our body, otherwise sluggish, are stirred in an instant, and, according to their affinity with nature, are improved and restored. Thus indeed Nature, through that part which, though cut off, nevertheless retains something of its original substance, as though awakened from sleep and raised by a friendly voice, girds herself to complete the cure and overcome the disease, and the more easily the more she is otherwise inclined to it, so that even with the slightest aid (especially since it does not, like other medicines applied immediately, oppress nature), being supported, she goes forth the more eagerly to accomplish the work. <21.> But when a wound caused by a fiery bullet from a gun is treated with the wash of the wheel, the instrument which was brought in to discharge the explosive bullet has no sympathy with the wound, since it does not touch the body, does not itself make the wound, but only by the introduced lead; and therefore it is no wonder if it proves altogether unsuitable for carrying out the magnetic cure. Yet the work might perhaps be successfully accomplished if the bullet could be extracted and put into the ointment; for that militates in its favor

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DE SYMPHÆTHIA. 13 eadem ratio, ac in gladio, qui partem affectam immediatè appetiit, & sanguine fuit infectus, cuius ad minus aliquam maculam seruat; quæ satis est in hoc leuissimo adiumento ad sympathiam cum corpore retinendam, atque adeò naturam. vt dictum est, excitandam ad opus intrinsecè perficiendum, Nec id mirum alicui videri debeat, cum longè maiora miracula videamus per sympathiam Solo tactu contractam: Narrat quippè Helmontius de quadam muliere, quæ Solo attactu sellæ, podagrá, quâ aliàs laborabat, mox solito suius corrupiebatur: sic enim ait de magnes vulner. curat. num. 33. Matronam nobilem mihi notam abennse podagra paroxysmo uno, nouus subinde alius excepit, ac per multas menses podagra sine remissione insolito infestauit recursu. Nesciens verò, vnde tanta sibi, inauspicataque morbi residua, quæ tandem quovies remisso accessus feruore è cubili iam surgens sederet sede, quæ frater eius olim, & in alia urbe podagricus sedere solitus erat, ex templo nimirum abinde morbum repullulaye reperit. Effectus vtique nullatenus imaginationi, aut scrupulo adscribendus: ut posse que duo effectu longè fuerunt posteriora. Qua autem sede si contingeret alium sedisse podagricum, nulla ei accidit morbi reinecrudatio. Itaque iam fratris mortui mumia sedem consagio suspedam meritò reddidit, qua sorori, & non alteri podagrico fluxus illos secùs quicuor moueret, trans omnes vestes penetrans. Magnetismus fuit ad uterinam scilicet sororis mumiam idque longo post funera lustro. Tantum equidem potest vel leuissimus tactus, vbi mumialis dumcaxat interuenit sympathia: Sed quid dico: tactus 1 Solus aspectus, Sola præsentia rei sibi conformis, aut difformis, quamuis ea conformiras aut difformitas puro accidente consistat satis est ad hanc motionem in Natura, siue ad amorem, siue ad odium excitandum. Quid enim maiorem sympathiam cum sanguine in venis contento retinet, sanguine ex iisdem venis excisus, an color rubrus? An non ad rubei coloris præsentiam, sanguis iuuenis ebullit, excitatur, accenditur, & foras exire contendit, aut cor obsidens adriam extimulat: Frequens est huius rei experientia non in nobis modo, sed & in bubalis, in Elephantis aliisque animantibus, quæ ad rubei coloris aspectum commouentur ad iram, & furunt vnde 1. Machab. 6. legitur quod Elephantis ostenderunt sanguinem una ad acuendos eos impralium. non quidem ab imaginatione vt benè ex Valesio lib. de sacra Philosophia notat Vecchius obseruat. medic. 15. in sacram scripturam, sed à propria sanguinis natura, quæ ad d iij

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ON SYMPATHY. 13 the same reason, as in the case of a sword which immediately attacked the affected part, and was infected with blood, of which it retains at least some stain; and that is enough in this very slight aid to preserve sympathy with the body, and therefore, as has been said, to arouse nature to complete the work inwardly. Nor should this seem surprising to anyone, since we see far greater wonders brought about by sympathy contracted by a mere touch: For Helmont relates of a certain woman, who, by the mere touch of a chair, was immediately troubled by the gout, with which she otherwise suffered; for thus he says in De magnet. vulner. curat. num. 33. A noble matron known to me, after one paroxysm of gout, was soon followed by another, and for many months the gout afflicted her with an unusual recurrence, without remission. But not knowing whence such troublesome and ill-omened remnants of the disease came to her, which at last, whenever the heat of the attack had abated, as she rose from her bed, she sat on a seat where her brother had once been accustomed to sit, in another city, when he too was gouty, and she immediately discovered that the disease sprang up again from that very place. The effect certainly is by no means to be attributed to imagination or to superstition, as those two are far later in effect. But if someone else happened to have sat in that seat, no recurrence of the disease occurred to her. So the mummy of her dead brother made the seat rightly suspected, through which those fluxes were stirred up for the sister and not for another gouty person, penetrating through all the clothes. It was a kind of magnetism, namely toward the uterine mummy of the sister, and that long after the funerals had passed. So much, indeed, can even the slightest touch achieve, when only mummial sympathy intervenes: But why do I say touch? 1. The mere sight, the mere presence of a thing like or unlike itself, even if that likeness or unlikeness consists in a mere accident, is enough to excite this motion in nature, whether to love or to hate. For what retains a greater sympathy with the blood contained in the veins than blood drawn from those same veins, or a red color? Does not, at the presence of a red color, the blood of youth boil up, is aroused, kindled, and strives to go forth, or, besieging the heart, spur it on? Frequent is the experience of this thing not only among us, but also in buffaloes, elephants, and other animals, which are stirred to anger at the sight of red color and rage; whence in 1 Maccabees 6 it is read that they showed the elephants blood, to sharpen them at once for battle. This was not indeed from imagination, as Vecchius rightly notes from Valesius in his observations on Scripture, lib. de sacra Philosophia, but from the proper nature of blood, which tends to

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34 PHYSIO-THEOLOGIA, præsentiam rei vt cumque similis commouetur, & feruet, quæ est causa iracundiæ commouendæ: siquidem hæc aliud non est quam accensio sanguinis circa cor. Qua etiam ratione Galenus lib. de suppurat. empyrica vetat Spuenti sanguinem aut hæmorrhagiam patienti aspectum ipsius sanguinis aut alterius rei rubræ, & ad cærulea & nigra rubet oculos conuertere: præcipit contra exanthematis iuxta cætem laborantibus rubris vestimentis operiri Non quod hæc quidqua[m] conferant aut immittant intus in sanguinem aut contraponant, sed ipsum fiat quia, spiritus in sanguine consistentes ob sympathiam alliciuntur splendore illo sanguini prorsus consimili, ac sanguinem ipsum commouent, vnde est quod sic agitatus, aut circa cor adunatur, aut alias cum exiium sic foras erumpit. Id quod etiam eo modo in rebus inanimis videmus vt in purpura, in corallio quæ cum aliis eiusdem coloris, aut naturæ seruantur in naviuo splendore persistunt, atque perficiuntur. Mitto alia experimenta passim obvia, sed non minus admiratione digna. 13. Cogeris itaque iam, vel reluctans frequenti demonstrationi assentiri, quod sanguini, & pari excisæ quamuis emortuæ aliquid remanet primitiuæ substantiæ, quo himirum seruatur huiusmodi proportio & consensus cum reliquo corpore, cuius virtute magneticæ istæ operationes in Natura intrinsecus excitentur. Ex quo, vt id obiter dicam, non modò planè euincitur contra Thomistas in corruptione compositi non dari resolutionem vsque ad materiam primam, sed adhuc in corupto perseverare plures formas substantiales, quas vocant partiales partium similarium distinctas, vt puta, carnis, ossis, nerui, &c. vt volebat Scotus in 4. distinct. 11. quæst. 3. quem sequuntur Maiorius in 2. distinct. 16. & 15. Niphus primo de Generat. comment. 78. Piccolominus lib. de multitudine formarum cap. 2. Hieron. Dandinus digress. 8. par. 3. 2. de anima Antonius Trombeteta 8. Metaph. 9. & passim recentiores, quam sententiam acriter, & egregiè propugnat ex nostris Aresius in lib. 1. Generat disp. 2. quæst. 10. sect. 3 asserens hanc fuisse mentem Aristotelis pluribus in locis præsertim primo de Anima textu 58. ac plurium veterum Peripateicorum Alexandri, Simplicij, Auerrois quibus Picolomineus addit Galenum, & Platonicos. 14. Et quidem si non alia argumenta suppeterent, certè ipsa torius substantiæ similitudo euinceret, in plantis, lignis, animantibus, aliisque iam corruptis, & exsiccatis aliquam radicalem, maximeque vitalem substantiam reperiri; quæ

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34 PHYSIO-THEOLOGIA, is stirred and heated by the presence of some similar thing, which is the cause of arousing anger: for this is nothing else than an inflaming of the blood around the heart. For the same reason Galen, in the book De suppurat. empyrica, forbids a patient suffering from spitting of blood or hemorrhage to look at blood itself or any other red thing, and to turn his eyes toward blue and black things; on the contrary, he orders those suffering from eruptions, and the like, to be covered with red garments. Not because these contribute anything or send anything into the blood or oppose it, but because the spirits residing in the blood, by sympathy, are attracted by that brightness wholly similar to blood, and they move the blood itself; whence it is that, thus agitated, it either gathers around the heart, or otherwise, with a rush, bursts forth outward. We see the same thing also in inanimate objects, as in purple and coral, which, when kept with others of the same color or nature, retain their vivid luster and are perfected. I omit other experiments commonly encountered, but no less worthy of admiration. 13. Thus you are now compelled, even if reluctantly, to assent to the frequent demonstration that in blood, and in a severed part though dead, something of the original substance remains, whereby, it is clear, such proportion and agreement with the rest of the body is preserved; by virtue of this, these magnetic operations are excited within Nature. From which, as I may note in passing, it is not only plainly proven against the Thomists that in the corruption of a composite there is not a resolution all the way down to primary matter, but also that in the corruptible there persist several substantial forms, which they call partial and distinct forms of similar parts, such as, for example, of flesh, bone, nerve, and so forth; as Scotus maintained in the 4th distinction, question 3, whom Maior follows in 2nd distinction 16 and 15, Niphus in the first De Generatione, comment. 78, Piccolomini in the book De multitudine formarum chap. 2, Hieron. Dandinus, Digress. 8, part 3, 2 De anima, Antonius Trombeteta 8 Metaph. 9, and recent writers everywhere; this opinion is vigorously and excellently defended by our Aresius in book 1 De Generatione, disp. 2, question 10, section 3, asserting that this was Aristotle’s meaning in many places, especially in the first book De Anima, text 58, and of several ancient Peripatetics, Alexander, Simplicius, Averroes, to whom Piccolomini adds Galen and the Platonists. 14. And indeed, if no other arguments were available, surely the very similarity of the whole substance would prove that in plants, woods, animals, and other things already corrupted and dried up, there is found some radical, and especially vital, substance; which

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DE SYMPATHIA. 33 posteà similium conseruarioni plurimum conferant. Hinc congruus animantium cibis, animantia, & quæ magis ad huius similitudinis rationem accedunt. Hinc aues auibus; pisces piscibus, feræ feris commodum nutriuntur: Hinc ad singulas partes corporis descendentes, plura simplicia detecta sunt, quæ quia capisi humano; cordi, stomacho, aliisque membris conferunt, & naturæ characterismo assimilantur, cephalica, cardiaca, stomachica, &c. Dicta sunt, quoniam iorius substantiæ similiudine parrium, quibuscum consensum habent, narium humiditatem, calorem, temperamentum augent, & inculpata seruant; quorum longam seriem affert Crolius in Basilica chimica, tractatu de signaturis internis rerum. < 25.> Porrò hæc remedia, quæ ex inanimitatis, vegetabilibus, & nonnullis animaniibus deprompta, substantiæ similiudine corporis nostri partes afficiunt, quò maiorem affinitarem possident cum partibus, quibus addicta sunt, eò potentius ipsas roborari, & nativæ substantiæ opitulanur. Ex quo demum colligirur, quod, si ex emortuo corpore eiusdem speciei possit residuum congeniri humoris arse quadam educi, multò magis id alteri viuenti corpori suurum sit apuissima medicina. Hinc tot pulueres, sales, tincturæ, magisteria, elixiria, ex humano corpore parata hodiè prostant apud auctores. Si vero ex toto corpore adeo efficax singulis partibus medicina paratur, quanto plus auxilij è partibus eiusdem naturæ, conformationis, & figuræ sperandum est? Hinc non immeritò cranij humani puluis, sal, cæteræque præparationes affectus capitis peruicacissimos soluunr. < 26.> Ob id per toram ferè Italiam celeberrimum fuit nomen eiusdam Medici, qui solo puluere ex singulis corporis partibus propria arte constato, omnes affectus contrà naturam radicitus euellebat: vt si afficeretur caput, puluis è solis capitibus pereretur, si cor è cordibus, & sic de cæteris. Quanto magis igitur id præstaretur, si ex eodem corpore, eademque parre sublata ipsi rursus affatim applicaretur, aut secundum rotam substantiam, aut secundum partem potentiorem, quanto diuinius, si absque corporis afflictatione, sed solo naturæ consensu, per sympathiam intrinsecus operante? < 27.> Constat igitur tum ratione, tum plurimis experimentis, magnicam curationem posse naturaliter perfici, per solam medicamenti applicationem pari corporis, quantumuis dissitæ, modò aliquam retineat cum patie affecta similitudinij

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DE SYMPATHIA. 33 afterwards they contribute greatly to the preservation of things similar to themselves. Hence animals are suitably nourished by animals, and by those things which more nearly approach the nature of this similarity. Hence birds by birds; fishes by fishes; beasts are profitably nourished by beasts: hence, descending to the individual parts of the body, many simple things have been discovered, which, because they belong to the human body; to the heart, stomach, and other members, and are assimilated to the character of nature, are called cephalics, cardiacs, stomachics, and the like. They are so called because, by the likeness of substance and of the parts with which they have agreement, they increase the moisture, heat, and temperament of the nose, and preserve them unharmed; Crolius gives a long series of these in the Basilica Chymica, in the treatise on the internal signatures of things. <25.> Moreover, these remedies, drawn from inanimates, vegetables, and certain animals, affect the parts of our body by the likeness of substance; and the greater affinity they possess with the parts to which they are applied, the more powerfully do they strengthen them and assist their native substance. From this, finally, it is gathered that if from a dead body of the same species the remaining humor can be drawn out by some art, much more may it be a most fitting medicine for another living body. Hence so many powders, salts, tinctures, magisteries, elixirs, prepared from the human body, are today found among authors. But if from the whole body a medicine so efficacious is prepared for individual parts, how much more help is to be hoped for from parts of the same nature, formation, and shape? Hence, not undeservedly, the powder of the human skull, salt, and other preparations cure the most stubborn diseases of the head. <26.> For this reason, throughout almost all Italy the name of a certain physician was celebrated, who, by a powder made solely from the individual parts of the body, fashioned by his own art, completely uprooted all diseases contrary to nature: thus, if the head were affected, powder from heads alone was used; if the heart, from hearts; and so of the rest. How much more, then, would this be achieved if, from the same body, and even from the same part removed, it were again applied to it in abundance, either according to the whole substance or according to the more powerful part; how much more divine, if without afflicting the body, but by the mere consent of nature, operating inwardly through sympathy? <27.> It is therefore established both by reason and by many experiments that a great cure can be effected naturally by the mere application of a medicine to a like part of the body, however distant it may be, provided that it retains some similarity with the affected part.

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16 PHYSIO THEOLOGIA, nem, & sympathiam: Natura quippe ad rei sibi similis affectionem intrinsecè, & ipsa afficitur, excitatur, & opus suum ad quod alias procliuis est, promptissimè exequitur: nihil enim magis auet Natura, quam totius integritatem suique conseruationem, vt docet Philosophus pluribus in locis, presertim verò lib. 1. de paribus animalium cap. 5 & 1. Phisic. cap. 5. ac proinde vel leuissimo adiumento suffulta opus aggreditur, ac felicissimè perficit. < 18.> In quo sanè negotio longè aliis præstant quæ per sympathiam, & vniversalem rerum connexionem operantur; quippe quæ, cum non immediatè parti affectæ applicentur, non habent ipsam premere sua actiuitate, & vt ita dicam, naturæ vires suffocare, sed solum reficere, & auge- re, eo prorsus pacto, quo in ciborum delectu, ij sunt optimi, qui & leuissimi, & calidi & moderatè humidi, & insito temperamento naturæ viuentis maximè approximantur, & ita illam sustentant, vt natius calor ab adscititio alimenti calore foueatur, & humidum radicale ab vtroque non deuastetur, sed eius loco inueniat in tibo calor naturalis commodum suæ actiuitatis pabulum, atque ita virumque minimè difflatis viribus in suo ordine conseruetur. < 19.> Hinc eadem ratione admitti etiam poterunt aliæ cura- tiones simili modo præstitæ; in quibus hæc sympathiæ ratio intercedit, aut certè arte quadam inducitur: Vt, quæ suprà enumerauimus, curatio Icteri, per consumptionem vrinæ patientis oui putamine inclusæ, quæ mumialem spiritum tabidi hominis in se habeat, ad lentum ignem: lactis exsiccatio in maminis ad eiusdem emulsionem ad ignem: eiusdem multiplicatio per attractionem mummialis spiritus alterius foeminæ, vel vacæ lacte plenæ, in cibo ab ea priùs degustato relicti: similis translario morbi in bestiam, quæ deuoret carnem, spiritu morbidi hominis per eius vrinam, aut sanguinem fermentatam: Lienis tumor inhibitus, ac propulsus, per suspensionem lienis alterius animalis ad fumi in camino, quò paulatim flaccescat, & exsiccaturæ hæmorrhoridarum depressio per applicationem radicis Chondrillæ, seu scrophulariæ herbæ vulgaris (quæ illarum formam præstet) ad latus patientis; nam vbi hæc exsiccati cæperit, sensum exsiccantur & illæ: curatio vulneris cancerosi si alterius, qui eodem morbo prius affectus, & postmodum curatus est sanguine illinistrur pars affecta; quo modo modo testatur Kircherus solitos esse cantabros morbus sacrum pellere, nosque videmus in Alcis vngula, qua hoc animal morbo comitiali correptus aurem sinistram vellicans libe-

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16 PHYSIO THEOLOGIA, namely, and sympathy: for Nature itself is inwardly affected by an affection of a thing similar to itself, is stirred up, and most readily performs the work to which otherwise it is inclined; for Nature desires nothing more than the integrity of the whole and its own preservation, as the Philosopher teaches in many places, especially in Book 1 of On the Parts of Animals, chap. 5, and in Physics, book 1, chap. 5; and therefore, supported even by the slightest aid, it undertakes the work, and brings it to a most successful completion. <18.> In this matter, indeed, those things excel others far more which operate by sympathy and the universal connexion of things; for since they are not applied immediately to the affected part, they do not have the power to press upon it with their activity and, so to speak, suffocate the forces of nature, but only to refresh and increase them, and that entirely in the same way that, in the choice of foods, those are the best which are both light, and warm, and moderately moist, and most nearly approach the inborn temperament of living nature, and thus support it, so that the natural heat is fostered by the adventitious heat of the nourishment, and the radical moisture is not wasted by either, but in its place natural heat finds in the food a suitable nourishment for its activity, and thus both are preserved in their own order with their forces least dissipated. <19.> Hence, by the same reasoning, other cures performed in a similar manner may also be admitted, in which this relation of sympathy intervenes, or is certainly introduced by some artifice: such as the cures we listed above, the cure of jaundice by the consumption of the patient’s urine enclosed in an eggshell, which has in itself the mummy-spirit of a wasting man, over a gentle fire; the drying up of milk in the breasts by its emulsion over fire; the increase of the same by the attraction of the mummy-spirit of another woman, or of a cow full of milk, left in food previously tasted by her; a similar transfer of disease to a beast that devours flesh, by the spirit of the sick man through his urine, or fermented blood; the swelling of the spleen checked and driven away by hanging the spleen of another animal in the smoke of a chimney, so that it gradually withers and dries; the reduction of haemorrhoids by the application of the root of Chondrilla, or of the common herb scrophularia (which bears their form) to the side of the patient; for where this has begun to dry up, they too are believed to dry up by sympathy: the cure of a cancerous wound, if the affected part is smeared with the blood of another who had previously been afflicted by the same disease and afterward cured; in this manner Kircher says that the Cantabri were wont to drive away holy disease, and we see in the hoof of an elk, by which this animal, when seized by epilepsy, rubbing its left ear, liber-

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DE SYMPATHIA. 31. tatur, ea enim nec alia, quantumuis ciufdem Aleis, virtutem induit efficacissimam contrà eundem morbum; quo etiam modo Saphirus si semel anthracem quo pestis se prodit, attigerit, & aliquandù affrictus fuerit, mox cui- cumque peste laboranti singulare præsidium est; virus namque totum è contaminato magneticè attrahit, si buboni similiter affricetur, atque eo circulus describatur, quo virus omne intrà eius fines se continens latius non exspatieret, sicque alias parres inficiat; in cuius rei testimonium olim ab Ecclesiæ proceribus introductum reor, quod annulos hac potissimum gemma co[n]spicuos gestare soliti sunt, iiq[ue] omnes, quibus ex officio incumbit peste infectis assistere, &c. Hæc, inquam, omnia eidem principio innixa sunt, sympathiæ, videlicet, antipathiæve rerum, quâ mira hæc ope- rentur, & natura propria indole mumialem spiritum hauriat, atque exinde ad sui contrarij, vel affinis præsentiam, passionem, motum ad similes, vel dissimiles affectiones sese intrinsicus excitet. Hinc non absimili ratione, si fascino, philtris, aliisque id genus operibus fides præbenda est, de eorum miris effectibus discurrendum. Ex his apertè colligitur quænam sic ratio, cur ad occisoris præsentiam sanguis in occisi cadauere alias congelatus < 32.> ebulliat, & foras prosiliar: In qua sanè inuestiganda atque reddenda Philosophi omnes, vsque ad sanguinem decerta- runt, atque in varias sententias planè ridiculas abierunt: quas omnes egregiè confurat noster Verricelli in Quæstionibus moralib[us] & legalibus tract. 1. quæst. 22. sect. 2. Sed tamen quam ipse adducit non minus improbabilis est, & Philosopho prorsùs indigna. < 33.> Ait enim id fieri à Dæmone intrinsecus sanguinem commouente ex odio in humanum genus ad finem acuendi iudices & inspectores ad odium aduersus homicidam illum, proindeque morti adiudicandum. Id quod nullo pacto potest subsistere. Primo, quia, vt alias diximus, quæ frequenter accidunt suprà vel præter naturam esse minimè censenda sunt, sed omninò naturalia, quamuis vera eorum causa sit nobis ignota: secundò minimè præsumendum, velle Deum id permittere Dæmoni præter naturæ ordinem, præsertim cum aliàs occisor, est facti poenitens, aut iustam occiden- di causam habuerit, puta in justo bello, aut fuerit ipse pro- uocarus, & alium occiderit cum moderamine inculpatæ tu- telæ. Nam si id semel admittamus, cur non etiam dici poterit Dæmoni alia etiam in hominum perniciem eaque mi- nora, & seruato naturæ ordine à Deo permitti? cur non id-

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DE SYMPATHY. 31. is applied; for that indeed, and no other, so far as it is of the same kind, assumes the most effective power against the same disease; in this way too, if Sapphire has once touched the anthrax by which the plague shows itself, and has been rubbed on it for a time, it is immediately a singular protection to anyone suffering from the plague; for it magnetically draws away all the poison from the infected part, if it is likewise rubbed on the bubo, and a circle is drawn around it, within whose bounds all the poison remains confined and does not spread farther, and so infect other parts; in testimony of which thing I think that it was formerly introduced by the leading men of the Church that rings conspicuous with this gem especially were customarily worn, and all those upon whom it is incumbent by office to assist the infected with plague, etc. These things, I say, are all founded on the same principle, namely, sympathy or antipathy of things, by which these wonders are wrought, and by its own natural bent the spirit draws in a kind of “mumia,” and then, in the presence of what is contrary to it or akin to it, inwardly excites in itself a passion and motion toward similar or dissimilar affections. Hence, by no dissimilar reasoning, if credence is to be given to charms, philtres, and works of that sort, one must discourse on their marvelous effects. From these things it is clearly gathered what the reason is, why at the presence of the murderer blood in the dead body of the slain, which had otherwise congealed boils up and leaps forth; in investigating and explaining this surely all the philosophers fought tooth and nail, and went off into various and downright ridiculous opinions: all of which our Verricelli excellently confutes in the Moral and Legal Questions, tract. 1, qu. 22, sect. 2. Yet the explanation he offers is no less implausible, and altogether unworthy of a philosopher. For he says that this happens because a demon inwardly moves the blood from hatred of the human race, in order to incite judges and examiners to hatred against that murderer, and consequently to have him sentenced to death. But this can in no way stand. First, because, as we said elsewhere, things that happen frequently are by no means to be thought to be above or contrary to nature, but altogether natural, even though their true cause is unknown to us. Second, it must by no means be presumed that God would permit this to the demon, contrary to the order of nature, especially when otherwise the slayer is penitent for the deed, or had just cause for killing, as in a just war, or had himself been provoked and killed another with moderation of blameless self-defense. For if we once admit this, why could it not also be said that other things harmful to men, even lesser ones, and with the order of nature preserved, are permitted by God to the demon? why not this-

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PHYSIO THEOLOGIA, ipsum potius accidit, non in aggressoris, sed in mandantis occisionem præsentiam? cur inquam in aggressoris duntaxat præsentia, & eius solum qui vulnera infixit, non qui venenum propinando, aut aliàs vitam ademir? Tertiò quia saltem id non nisi post longum temporis spatium vsu, & frequentia compertum est, vnde quoad vsque id plenius innotuerit Dænon suo fine frustratus rem prorsus inutilem ex Dei permissione prosequutus est: cur igitur hoc porius in sanguinis effusione manifestare elegit, eique permissum est, & non in alio potiori argumento, quod rem cuinceret? Quartò demum, quia id nihilominus, quamuis frequens, non est certum indicium rei, cum non constet adhuc qua ratione fiat; & ideò ex hoc præcisè non posset simpliciter animaduerti in huiusmodi indiciatum, nec etiam modò non alia indicia concurrerent ad criminalem inquisitionem procedi, vt multis probant Hippolytus de Mars. in praxi crimin. 6. diligenter. Paris de Puteo, in sindicatu Verbo Tortura, & alij iuristæ apud Maiolum in duabus canicular. colloqu 1. Phys. eò maximè quia aliquando etiam huiusmodi sanguinis effusio subsequua est ad præsentiam amicorum, aut sanguine coniunctorum, vt notat idem Maiolus, de quibus tamen eoquia homicidium publicè fuerat, ab alio factum nulla suspicio inesse poterat, quod ab iis homicidium fuerit perpetratum: Vnde à primo ad vltimum, nulla est ratio credendi hanc sanguinis effusionem in occisi caduere prætet naturam à Dæmone fieri, ad occisorem manifestandum. 34. Dico igitur consequenter ad superius dicta, id fieri naturaliter ex sympathia operis familiaritatis, non ab vlla antipathia, aut immissione vel regressione spirituum, ex occisi corpore ad occisorem, aut è contrà. Equidem in diversitate casuum, qui referuntur: suppono occisionem fuisse semper factam in aperto conflictu, & sciente, atque adniente contra aggressorem occiso: quo posito, credendum est hunc ira in aggressorem incaluisse; ac demum viribus imparem occubuisse. Cum igitur ira fit accensio sanguinis, circà cor, qui posteà succumbente natura per inflicta vulnera foras prosiliit; & sanguis ira infectus quandam antipathiam cum aggressore contraxit; inde fit, vt eodem præsente sanguis ex familiaritate operis iterum accendatur, ebulliat, ac per eandem vulnerum viam exitum sibi paret, & vtcumque natura duce, in aduersarium admittatur. 35. Ex quo etiam deduco id ipsum quandoque accidere ad præsentiam amicorum, fratrum, &c. Quia profectò con-

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PHYSIO THEOLOGIA, does the same thing rather occur, not in the presence of the aggressor, but of the one who commands the killing? Why, I say, only in the presence of the aggressor, and of the one only who inflicted the wounds, and not of the one who, by giving poison or otherwise, took away life? Thirdly, because at least this is not known except after a long space of time by use and frequent experience, whence, until it should be more fully made known, the devil, frustrated of his end, pursued a thing altogether useless by God’s permission: why therefore did he choose rather to manifest this in the shedding of blood, and was it permitted to him, and not in some other stronger argument that would prove the matter? Fourthly at last, because nevertheless, although frequent, it is not a certain sign of the thing, since it is not yet established by what reason it happens; and therefore from this precisely one could not simply infer such an indication, nor even now could criminal inquiry proceed unless other indications were also present, as Hippolytus de Mars. in praxi crimin. 6. diligently proves; Paris de Puteo, in sindicatu, under the word Tortura; and other jurists cited by Maiolus in the two canicular colloquies, colloq. 1. Phys., especially because sometimes also such effusion of blood follows upon the presence of friends or blood-relatives, as the same Maiolus notes; yet since the homicide had been committed publicly, there could be no suspicion that it was done by another, that the homicide had been perpetrated by them. Whence, from first to last, there is no reason to believe that this effusion of blood in the body of the slain man, beyond nature, is done by a demon in order to reveal the killer. 34. I therefore say, consequently to what has been said above, that it happens naturally from the sympathy of a familiar operation, not from any antipathy, or from the sending in or return of spirits, from the body of the slain man to the killer, or vice versa. Indeed, in the diversity of the cases that are reported, I suppose the killing was always done in open conflict and with the knowledge and consent of the slain man against the aggressor; granted this, it must be believed that he was inflamed with anger against the aggressor, and at last fell overcome by unequal strength. Since therefore anger is an accension of the blood around the heart, which afterward, nature giving way, bursts forth through the wounds inflicted; and the blood, infected by anger, contracted a kind of antipathy toward the aggressor; hence it happens that, when the same person is present, the blood is again kindled by the familiarity of the act, boils up, and makes for itself an exit through the same path of the wounds, and, as it were, under the guidance of nature, is admitted against the adversary. 35. From which I also infer that the same thing sometimes happens at the presence of friends, brothers, etc. Because indeed...

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DE SYMPATHIA. 55 iunctio sanguinis, aut amoris necessitudo, vt sæpè in nobis experimur ad amatæ rei conspectum facit, vt sanguis in venis ebulliat, alteretur; atque in arteria pulsus inæqualitatem exhibeat: Vnde ex hoc Erasistratus apud Galenum, quandam mulierem agnouit ex nimio amore ergà priuignu[m] decumbere, prolato enim vix Pyladis nomine, statim Nouerca expalluit; vnde ipse apposita ad carpum manu, inuenit pulsum maxima inæqualitate fluctuare, quod erat indicio, cor etiam interiùs, sanguinem, & spiritus fluctuasse ex amoris affectu. Ex quo fieri potest, vt amante iam mortuo, sanguis, & spiritus vitales, qui reliqui sunt in cadauete ob sympathiam operis, atque eiusdem substantiæ vnitatem, ad solam obiecti amati, vel odio habiti præsentiam excitentur ad similem, & aliàs sibi familiarem motum; vnde posteà ex vulneribus, in quibus habet apertum ad exitum viam, vbertim profluat & exsiliant. Quod etia[m] videre est suo modo in exteriori animantium exuuiis, quos enim affectus inter se viuentes habuerunt, hos etiam seruant in motte, horum vmbram videmus adhuc in extis, sanguine, sibris, corio & similibus. Sic quia ad lupi præsentiam agnus viuus timore interiùs concutiebatur, posteà iisdem mortuis, idem affectus, & contrarietas, in teliquiis cernitur; vnde Lyta, aut tympanum ex ouina pelle, aut intestinis compactum, tacta Lyra, aut tympano è lupi corio, aut neruis constante, dirumpitur. Similiter sonitus lyræ ex vulpeculæ extis, gallinas tertitat, & in fugam vertit, ex serpentium neruis, hominibus, ac præsertim foeminis ob insitam contrarietatem, & inimicitiam, retrorem incuit. Qua ratione Zischas hæreticus infensissimus Catholicorum hostis, cum in pugna oculos amisisset, iterum pugnaturus præcepit suis, vt, si fottè ei occumbere contigisset, detracto sibi corio, tympanum conficeretur, quo bellum inauguratum, hostes, quibus viuens terroli fuit, eodem timore perculsi in fugam conuertetentur. Sic igitur in casu nostro contrario affectu, tum odij, tum amoris, fieri potest, vt cuius præsentia viuenti animi motus, & sanguinis fluctuationem circà cor, siue ex amore, siue ex odio suscitabat, in iam mortuo eorumdem effectuum causa sit, sicque sanguis è vulneribus profluat naturaliter tam ad inimici, quam ad amici præsentiam. E contrà in eo, qui aut dormiens, aut quouismodo ignorans occisus est, quia nulla inerat dum adhuc vinebat in aggressorem ita, & odij exardescenda, nulla etiam esse poterit in iam de mortui sanguine operis sympathia; vnde nil mirum, si nulla in eo fiat sanguinis ebullitio, & effusio ad ini-

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DE SYMPATHIA. 55 the union of blood, or the bond of love, as we often experience in ourselves, at the sight of the loved object causes the blood to seethe in the veins and be altered; and also for the pulse in the artery to show irregularity: whence from this Erasistratus, as reported by Galen, recognized that a certain woman was lying down from excessive love toward her stepson; for when the name of Pylades was scarcely uttered, the stepmother at once turned pale; whereupon, placing his hand upon her wrist, he found the pulse wavering with the greatest irregularity, which was an indication that the heart also inwardly, the blood, and the spirits had fluctuated from the passion of love. From which it can happen that, the lover now dead, the blood and vital spirits, which remain in the corpse by sympathy of function and the unity of the same substance, may be stirred at the mere presence of the beloved object, or of the hated one, to a similar, and otherwise familiar, motion; whence afterwards from wounds, in which there is an open path for exit, they flow abundantly and gush out. And this may also be seen in its own way in the outer skins of animals; for the passions which the living had among themselves, these they also retain in death; we still see their shadow in the entrails, blood, fibers, hide, and the like. Thus, because in the presence of the wolf the living lamb was inwardly shaken with fear, afterwards, once both were dead, the same affection and contrariety are seen in the remains; whence the lyre, or drum, made from sheep’s skin, or from intestines, is torn apart when touched by a lyre or drum made of wolf’s hide or consisting of sinews. Similarly, the sound of a lyre made from fox entrails terrifies hens and turns them to flight; from the sinews of serpents, it strikes men, and especially women, backward, because of the inborn contrariety and enmity. For this reason Zischas, a most hostile heretic, enemy of the Catholics, when he had lost his eyes in battle, intending to fight again, ordered his men that, if perhaps it should happen that he fell, his skin should be stripped off and a drum made from it, by which the war begun would so fill the enemies, whom while alive he had terrified, with the same fear that they would be driven into flight. So therefore in our case, by contrary affection, both of hatred and of love, it can happen that the same person’s presence, which while he was alive stirred motions of the mind and fluctuation of the blood around the heart, whether from love or from hatred, when now dead may be the cause of those same effects, and so the blood may flow naturally from wounds at the presence both of an enemy and of a friend. And contrariwise, in the case of one who was killed either while asleep, or in any way unaware, because while he was still living there was in him no such rising up of rage against the attacker, nor of hatred, there can also be none in the blood of the now dead any sympathy of that operation; whence it is no wonder, if in him there is no seething and effusion of blood to ini-

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PHYSIO-THEOLOGIA, DE SYMPATHIA. mici aggressoris præsentiam. Similiter in occiso per venenum, suffocationem, &c quamuis enim fieri possit, vt suffocati corpus eosdem motus intorius habeat ad inimici præsentiam, si alias in morte aduersus illum ita excanduit, tamen quia sanguis promptum non habet ad exitum viam, si cur habet in vulnerato, ideò foras non exit; nisi fortè è naribus, præsertim quando mox post præfocationem sanguis adhuc calens, è naribus fluxit: tunc enim eadem intercedit fluxionis causa, & operis sympathia. Denique eadem ratione crediderim hanc sanguinis effusionem in occisi caduere non fieri ad præsentiam inimici, quem nusquam agnouit, aut si agnouit, mortem, non per se ipsum, nec se præsente, sed per mandatarium immediatè, & facie ad faciem aggredientem, in sui absentia exequutus est: tunc enim vel nulla in occiso ergà illum sanguinis effervescentia, dum viueret præsupponi potest, vel si quæerat, tota demum in morte in actualiter aggressorem conuersa est, atque adeò erga istum duntaxat odium seruat & operis sympathiam, vi cuius ad illius præsentiam sanguis iterum accendatur, atque à vulneribus affueta sibi ad exitum via foras, naturali quodam impetu profluat. Atque hæc de arcanis hisce naturæ motibus, ac de magnetica vulnerum curatione dicta sint, cuius sanè effectus consimiles, dissimiles, disparatos, complexos, ac longè superiores in Natura videmus, quos vii dicebâ, miraculo, aut Daemonis operæ ascribere, ineptum est, quando ij frequenies sunt, casu, aut naturali rerum notitia comparati, ijdemque deinceps perpetui, aliàs omnia, quorum causam ignoramus, supra aut præter naturam dicere protritâ fronte quis posset. Hanc nos in præsenti aliarum rerum inductione, è latebris eruere, ipsa Natura duce, conati sumus: si veram tenuimus, & Lectori tandem arriserit, Naturæ ipsius munus, proindeque Dei, auctoris Naturæ, beneficium agnoscamus: sin minus, non idcircò singulare hoc Naturæ præsidium sathanicum proclamandum, sed cuique pro viribus satagendum, viam eius, & causam dignoscere, discutere, speculari, ac demum agnitam ad commune bonum in medium ferre, tanquam bono Naturæ administro, cui nefas sit, quæ liberaliter illa suæ curæ credidit, inuidè occultare. FINIS.

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PHYSIO-THEOLOGY, ON SYMPATHY. the presence of the aggressor. Similarly in one killed by poison, suffocation, etc. For although it may happen that the suffocated body has the same inward motions at the presence of the enemy, if otherwise in death it had thus burned against him, nevertheless because the blood has no ready way of exit, as it does in the wounded man, it therefore does not flow out; unless perhaps from the nostrils, especially when, soon after suffocation, the blood, still warm, flowed from the nostrils: then indeed the same cause of the flow intervenes, and the sympathy of the act. Finally, for the same reason I would believe that this effusion of blood in the corpse of the slain does not occur at the presence of the enemy, whom he never recognized, or if he did recognize him, death, not by his own hand, nor in his presence, but immediately through an agent, and attacking face to face, he executed in his absence: then indeed either no effervescence of blood in the slain man against him, while he lived, can be presupposed, or if there was any, in death at last it has turned against the actual aggressor, and therefore retains hatred and the sympathy of the act toward that one only, by virtue of which, at his presence, the blood is again kindled, and, from the wounds, through the accustomed way out to the exit, flows forth by a certain natural impulse. And so let these things be said concerning these hidden motions of nature, and concerning the magnetic healing of wounds, the effects of which, indeed, we see in Nature to be similar, dissimilar, disparate, combined, and far superior; to attribute them to miracle, or to the work of the Demon, is foolish, when they are frequent, produced by chance or by natural knowledge, and thereafter perpetual; otherwise anyone could say with brazen face that everything of which we are ignorant of the cause is above or beyond nature. We have in the present work tried, with Nature herself as our guide, to draw this forth from its hiding places: if we have grasped the truth, and if at last it has pleased the Reader, let us acknowledge the gift of Nature itself, and therefore the benefit of God, the author of Nature; but if not, for that reason this singular protection of Nature must not be proclaimed satanic, but each person ought, according to his powers, to strive to discern, examine, observe, and at last bring to light for the common good its way and cause, once recognized, as a good servant of Nature, for whom it is wrong to hide enviously what she has liberally entrusted to his care. FINIS.

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INDEX RERVM NOTABILIVM. EARVM PRÆSERTIM, QVÆ extra ordinem diuagantur. Numerus primus indicat Paginam, Secundus est marginalis singulis litteris proprius. A A Figuræ dignitas, & encomia, pag. 1. num. 1. Eam sus rostro delineauit humi, ibid. n. 2 A Phoenice in Græciam allata, ibidem In ea omnes figuræ, omnia Geometrica instrumenta velut in compendio continentur, ibid. n. 1 Abachi vocabulum vnde apud Italos deriuatum, 3. n 4 Abortum causant in feminis terræ motus, 305. n. 25 Abscissio luminis in Planetis quot modis fiat, 4 n. 8 Absidum mutationes magnas in Mundo mutationes indi- cant, 5. n. 9 Id quo modo intelligendum, ibidem Reiicitur Cardani commentum, ibid. Quid hac in re ex Philosophiæ principiis conjectari possit, ibid. Acerum diffusum optimum contra Turbinem tutamentum, 317. n. 78. Achates gemma Cani sidereo subest, 292. n. 64 Achronicè quæ sidera dicantur oriri pro re, & impropriè, 6. n. 16. Aconiti virus, & mira conditio, 292. n. 63 Adagium de Alcor Stellulæ. 19. n. 90 Adam an fuerit Astrolabij Inuentor, 70. n. 330 Ægri eur sæpè in Solis occasu deficiant, 37. n 180 Ædificia facienda in signis Fixis, 167. n. 10 Ægyptij non nisi per hieroglyph. res suas explicant, 235. n. 19

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INDEX OF NOTABLE THINGS. Especially of those which wander outside the order. The first number indicates the page, the second is the marginal one proper to each letter. A The dignity and praises of the figure, p. 1, no. 1. He drew it on the ground with his beak, ibid. no. 2. It was brought to Greece from the Phoenix, ibidem. In it are contained, as in a compendium, all figures and all geometric instruments, ibid. no. 1. Whence the word Abacus was derived among the Italians, 3, no. 4. Earthquakes cause miscarriages in women, 305, no. 25. The extinction of light in the planets, in how many ways it happens, 4, no. 8. The changes of the apogees indicate great changes in the world, 5, no. 9. How this is to be understood, ibidem. Cardano’s notion is rejected, ibid. What in this matter may be conjectured from the principles of philosophy, ibid. The scattering of ashes is the best protection against a whirlwind, 317, no. 78. The gem Achates lies beneath the starry dog, 292, no. 64. Which stars are said to rise achronically, properly and improperly, 6, no. 16. The poison of aconite, and its marvelous nature, 292, no. 63. A saying about the Little Star of Alcor, 19, no. 90. Whether Adam was the inventor of the astrolabe, 70, no. 330. Why the sick often fail at sunset, 37, no. 180. Buildings should be constructed in fixed signs, 167, no. 10. The Egyptians explain their things only through hieroglyphs, 235, no. 19.

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INDEX Ægyptiorum finium ratio philosophicè probata, 10. n. 164 & p. 495. n. 19 Æquinoctij tempus obseruare quam difficile, 11. n. 34 Id assequi diffusus est Ptolæmeus. Eo tempore Pituita in hominibus crescit, ibid. Aeria, & succosa tunc sumenda, ibid. Æquinoctiorum sedes à Gregorio XIII. suo tempore restituta, 86. n. 16 Aër an animatus, 305. n. 86. Mo[n]uetur ad motum vniuersitatis, 13. n. 39 In tres Regiones tribuitur, 12. n. 37, Media Regio à Dæmonibus inhabitata, 12. n. 38 Firmamenti nomine in saeris paginis appellatus, 191. n. 19 Spiritus Mundi, & Coelestium qualitatum vehiculum, 208. n. 14 Ob sui facilitatem, & continuitatem cùm Coelo, subito recipit Coelorum impressiones, ibid. Ejusde substantiæ cù reliqua Ætheris regione, 115. n. 139 Aëris infallibiles mutationes sub certis siderum conventionibus, 51. n. 238 Aër cur antequam illucescat obscurior fiat, 129. n. 189 Æstas quæ anni pars dicatur, 13. n. 44 Sub Æquatore duplex, ibid. & 535. n. 10 Mirior, ac minus feruens quam hyems. ibid. Æstiuale Solstitium aquas prolectat, & quare, 462. n. 85 Hyemale Solstitium vt plurimum seium affert, ibid. Eo tempore Aleyones in littore Maris nidificant, ibid. In Æstiuali filix vno die florem profert, & fructum, ibidem. Æstus major sub Tropicis, quam sub Æquatore, 536. n. 11 Æsopicæ vulpeculæ lepidum scomma, 203. n. 44 Ætas Lunæ quomodo per Epactam inueniatur. 176. n. 52 Ætates hominum singulis Planetis tributæ, 103. n. 85 Ætheris nomine quid veniat, 14. n. 45 Cuius substantiæ, ibid. & 129. n. 189 Æfricus ventus procellis nimius, 14. n. 48 In Lusitania facit Equas concipere, ibid. Ægens quodcunque operatur intra determinatam sphæram actiuitatis. Digress. Quæst. 1. n. 17. Quando nam requirat certam distantiam ad hoc vt agat, ibid. b. 14. & 19 An dari possit actio indistans, Quæst. 1. n. 21. & Quæst. 3. n. 11.

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INDEX The boundary of Egypt, philosophically demonstrated, 10. n. 164 & p. 495. n. 19 How difficult it is to observe the time of the Equinox, 11. n. 34 Ptolemy explains this at length. At that time phlegm increases in men, ibid. Then airy and succulent foods are to be taken, ibid. The seat of the Equinox, restored in its own time by Gregory XIII, 86. n. 16 Whether air is animate, 305. n. 86. It is moved by the motion of the universe, 13. n. 39 It is divided into three regions, 12. n. 37, the middle region inhabited by demons, 12. n. 38 Called by the name of the Firmament in sacred pages, 191. n. 19 Spirit of the World, and vehicle of celestial qualities, 208. n. 14 Because of its ease and its continuity with the heavens, it immediately receives the impressions of the heavens, ibid. Of the same substance as the rest of the region of Ether, 115. n. 139 The unfailing changes of air under certain conjunctions of the stars, 51. n. 238 Why the air becomes darker before it grows light, 129. n. 189 What part of the year is called summer, 13. n. 44 Twofold under the Equator, ibid. & 535. n. 10 More pleasant, and less burning than winter. ibid. The summer solstice draws up the waters, and why, 462. n. 85 The winter solstice usually brings hail, ibid. At that time Halcyons nest on the seashore, ibid. In summer, fern on one day brings forth flower and fruit, ibidem. The greater tide under the Tropics than under the Equator, 536. n. 11 The witty jest of the Aesopic fox, 203. n. 44 How the age of the Moon is found by the Epact. 176. n. 52 The ages of men assigned to the several planets, 103. n. 85 What is meant by the name of Ether, 14. n. 45 Of what substance it is, ibid. & 129. n. 189 The Etesian wind, excessively stormy, 14. n. 48 In Lusitania it causes mares to conceive, ibid. An agent operates whatever it does within a determinate sphere of activity. Digress. Quæst. 1. n. 17. When indeed it requires a certain distance in order to act, ibid. b. 14. & 19 Whether action at a distance can exist, Quæst. 1. n. 21. & Quæst. 3. n. 11.

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RERVM MOBILIVM. 383 Agentia Naturalia cæteris paribus fortius agunt passio approximata, quam longiùs constituta, Qu.1. n.14: & seq. Non omnis eorum virtus nobis comperta est, ibidem. n.38 Alcis vngula aduersus morbum comitialem, Qu 3. n.29 de Alcot stellula ad caudam Vrsæ adagium apud Arabes, 19. n.90 Allio complantata Rosa cur odoratior, Quæst.3. n.13 Alcyones in Hyemali solstitio Maris in littore nidificant, 462. n.85 Almugea Planetarum ad luminaria quid sit, 24. n.139 Eius ratio naturæ consona, ibid. Alstedij error circa figuram sexdecim laterum, 190.16 Altitudinis prærogatiua naturali ratione probata, 28. n.158. Vide etiam in Verbo Exaltatio. Amorem conciliant Musicæ Notæ, 313. n.100 Amor, & nexus partium Mundi anima est, secundùm Pla- tonem, 242. n.32 Amphiscij populi qui audiunt, 34. n.174 Eorum regio temperantissima, n.175 Amussis, seu Quadræ graphicæ descriptio, 1. n.1 In ea omnia instrumenta Mathematica continentur, ibidem. Eius consideratio est Mathematicarum omnium disci- plinarum compendium, ibid. Analogia Corporum Cælestium cum terrestibus, Qu.3. n.4 Macrocosmi cum Macrocosmo, ibid & 303. n.92 Anæreta quid sit, & eius ratio quibus competar, 38. n.186 Andromeda sidus infaustum, 278. n.12 Eius significata in Horoscopo, 40. n.195 Angulus quid sit, 41. n.198. eius divisiones, n.199. & variæ acceptiones, ibidem Animal nullum moritur in Maris refluxu, 37. n.180 Animal an dici possit Mundus, 310. n.92. Aqua; 311. n.93. Terra, 498. 21. Cælestia corpora, 116. n.140 Animalia bruta an sint corporibus Cælestibus nobiliora, 311. n.94 Anni diuersæ acceptiones, ac species, 42. n.202 Annus periodicus Imperijs, & Monarchijs fatalis, 44. n.210 Eius ratio vnde sumenda, ibidem Eam in certam numeri harmoniam refert Plato, ibid. Anni Climacterici, seu schalares, 142. n.35 Annis Lunaris & Solaris, vtriusq; diuisiones, 42. n.203. & seq.

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OF MOVABLE THINGS. 383 Natural agents, ceteris paribus, act more strongly when the passion is nearer than when it is placed farther away, Qu. 1. n. 14: & seq. Not all of their power is known to us, ibidem. n. 38 The hoof of an elk against the falling sickness, Qu. 3. n. 29 The saying among the Arabs concerning the little star near the tail of the Bear, 19. n. 90 Why a Rose planted with Garlic is more fragrant, Quæst. 3. n. 13 Alcyones nest on the seashore at the winter solstice, 462. n. 85 What Almugea of the planets with respect to the luminaries is, 24. n. 139 Its reason is in agreement with nature, ibid. Alsted’s error concerning the figure of a sixteen-sided body, 190. 16 The prerogative of altitude proved by natural reason, 28. n. 158. See also under the word Exaltatio. Musical notes conciliate love, 313. n. 100 Love, and the bond of the parts of the world, is the soul according to Plato, 242. n. 32 The people called Amphiscij, who hear on both sides, 34. n. 174 Their region is most temperate, n. 175 What Amussis, or the description of the graphic square, is, 1. n. 1 In it all mathematical instruments are contained, ibidem. Its consideration is a compendium of all mathematical disciplines, ibid. The analogy of celestial bodies with terrestrial ones, Qu. 3. n. 4 Of Macrocosm with Macrocosm, ibid. & 303. n. 92 What Anæreta is, and the reason with which it is connected, 38. n. 186 The star Andromeda, unfortunate, 278. n. 12 Its meaning in the horoscope, 40. n. 195 What an angle is, 41. n. 198. its divisions, n. 199. & various meanings, ibidem No animal dies in the ebb of the sea, 37. n. 180 Whether an animal can be called a world, 310. n. 92. Water; 311. n. 93. Earth, 498. 21. Celestial bodies, 116. n. 140 Whether brute animals are nobler than celestial bodies, 311. n. 94 The various meanings and species of years, 42. n. 202 The periodic year is fatal to empires and monarchies, 44. n. 210 Whence its reason is to be taken, ibidem Plato refers it to a certain harmony of number, ibid. Climacteric, or stair-like years, 142. n. 35 The divisions of lunar and solar years, of both, 42. n. 203. & seq.

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21 INDEX Antecanis cur dictus Procyon, seu Canis Minor, 47. n. 224 Antipathiæ vis vnde sit, 50. n. 232. & 242. n. 32. & 245. n. 36. 488. n. 1. & in Qu. vniuersè, & fusè in V. Sympathia. Antipathiæ quarundam Plantarum ad inuicem, Quæst. 3. n. 13 Iiem & Animalium, Qu. 3. n. 1. & seq. Sanguinis cum Calchanto, Qu. 1. n. 37 Antipodes olim admittere hæreticum habebatur, 46. n. 210. & 221 Eos deridet D. Augustinus, ibidem Iam modò eos negare non possumus, ibid. Antiquitas olim Arithmeticæ ignara, in numerando calculus vtebatur, 2. n. 4 Antiscia quæ dicantur, & eorum noua Doctrina Naturæ, & rationi consona, 48. n. 227 Verius Paralleli dicendi, 49. n. 230 & 361. n. 17 Antiscia in Mundi situ etiam considerata: ibidem Nec minoris efficaciæ, ibid. n. 18 Antiscij Populi qui, 49. n. 131 Antonij Pomæ Cler. Reg. de Zona Torridæ testimonium, 537. n. 15 Apheta, seu viæ dator, qui Planeta dicendus, 51. n. 238 An plures constituendi sint, ibidem Apheta in gradibus intermedijs signorum fixorum euadit valdè debilis, & quare, 80. n. 369 Apostolorum nominibus Zodiacus appellatus, 159. n. 68. &c 334. n. 22 Apulia ab Iapygè, & Coro ventis infesta, 126 n. 181 Aqua vnde dicta, 55. n. 162. An maior Terra, 18. n. 270. an Animata, ibid. n. 169 In Oceanum iugiter defluens cur non redundet, 56. n. 264 In Puteis ebulliens, ac tetrum odorem immittens Terræ motus indicium, 504. n. 27 Aqua in vniuerso perinde ac sanguis in homine, 57. n. 269 Aqua solem sequuntur in Tropicis, 56. n. 267 Aquas prolectat solstitium Æstiuale, 462. n. 85 Aqua nunquam intereunt qui sub Cabe Sirlo oriuntur, 21. n. 111 Aquilæ in Horoscopo significata, 59. n. 273 Aquilo ventus vnde dictus, 59. n. 174. eius natura, ibid. Aranea pars superior Astrolabij, vnde dicta, 176. n. 80 Arborus odoratiores sunt, si in eas Iris incubauerit, 251. n. 51 Arborum,

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21 INDEX Why Procyon, or Canis Minor, is called Antecanis, 47. n. 224 The force of antipathy, whence it arises, 50. n. 232. & 242. n. 32. & 245. n. 36. 488. n. 1. & in Qu. generally, & at length in V. Sympathia. The antipathy of certain Plants to one another, Quæst. 3. n. 13 Likewise of Animals, Qu. 3. n. 1. & seq. Of Blood with Calchanto, Qu. 1. n. 37 That to admit Antipodes was once held heretical, 46. n. 210. & 221 St. Augustine derides them, ibidem Now we can no longer deny them, ibid. The ancients, ignorant of Arithmetic, used a pebble in counting, 2. n. 4 What are called Antiscia, and their new Doctrine consonant with Nature and reason, 48. n. 227 More properly called Parallels, 49. n. 230 & 361. n. 17 Antiscia also considered in the position of the World: ibidem Nor of less efficacy, ibid. n. 18 What peoples are Antiscij, 49. n. 131 The testimony of Antonius Poma, Cler. Reg., concerning the Torrid Zone, 537. n. 15 Apheta, or giver of the way, who should be called a Planet, 51. n. 238 Whether more are to be constituted, ibidem An Apheta in the intermediate degrees of the fixed signs becomes very weak, and why, 80. n. 369 The Zodiac called by the names of the Apostles, 159. n. 68. &c 334. n. 22 Apulia harassed by the winds Iapyx and Corus, 126 n. 181 Whence water is so called, 55. n. 162. Whether it is larger than the Earth, 18. n. 270. whether animated, ibid. n. 169 Why, flowing continually into the Ocean, it does not overflow, 56. n. 264 Boiling in wells, and emitting a foul smell, a sign of an earthquake, 504. n. 27 Water in the universe as blood in a man, 57. n. 269 Waters follow the sun in the Tropics, 56. n. 267 The summer solstice draws on the waters, 462. n. 85 Water never perishes in those who are born under Cabe Sirlo, 21. n. 111 Eagles signified in the Horoscopus, 59. n. 273 Whence the wind Aquilo is so called, 59. n. 174. its nature, ibid. The upper part of the Astrolabe, whence it is so called, 176. n. 80 Trees are more fragrant if Iris has lain upon them, 251. n. 51 Of trees,

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Rerum Mobilium. 63 Arboretum, & Satorum quorundam mira Sympathia, atque Antipathia, Qu. 3. n. 13 Archimedis Sphæra vitrea memorabilis, 77. n. 361 Arcturus Stella informis circà crura Bootis, 61. n. 283 Cum Ioue diuitias pollicetur, 87. n. 19 Ei subjacet Iaspis, 292. n. 64 Arcus vnde dicitur Argumentum, 63. n. 295 Argentei Cometæ natura, & significata, 62. n. 288 Arisabium Vrbs in Asia, cui magis proximum est verum Orientis punctum, 331. n. 11 Armilla militare ornamentum, quo victores è bello milites donabantur, 66. n. 302 Arietis in Horoscopo significata, 63. n. 298. & 240. n. 18 In eo iuncti malefici perniciè affectunt Ouibus 489. n. 6 Aristoteles maris æstum intelligere non valens in mare se metuit, 35. n 178 Arithmeticæ laudes atque officia, 3. n. 4. & 64. n. 301 Angelica disciplina, 328. n. 37 Artemisia herba Ioui subest, 292. n. 64 Ascones Cometæ portenta, 68. n. 315 Aselli stellæ duæ in Cancro potentissimæ, & quare, ibid. n. 316 Eorum significata in Horosc. ibid. Aspectus varij Planetarum, ijdemque noui, & musicis consonantijs comprobati, 68. n. 310. & 86. n. 15 An in Aspectibus seruanda sit latitudo, 419. n. 6 Aspectus omnes sunt in genere familiaritatu, 68. n. 320 Astra Coeli Rosæ, 125 n. 176 Astra omnia lumen à Sole participant, 275. n. 50 Habent tamen aliquam lucem sibi propitiam, ibid. Quæ est ratio scintillationis in fixis, 193. n. 23 Agunt in hæc inferiora per solum lumen, ibid. Non sunt animantia, 116. n. 140 Viuunt tamen vitæ mundi vniuersali longè inferioribus superiore, 310. n. 91 Qua ratione cum sensu, & vegetatione careant, vitam animantibus tribuant, ibid. An vllam activitatè habeant in opera artificiara, 239. n. 25 Non sine magno consilio, & conuenientia ipsis nomina ex fabulis attributa, 212. n. 18 Astledij error circa figuram sex decim laterum, 190. n 16 Astrologia in quo ab Astronomia differat, 70. n. 338 Ad quælicitè se extendunt eius præditiones, 71. n. 342 Quodnam sit eius objectum, ibid.

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Movable things. 63 The Arboretum, and the marvelous sympathy and antipathy of certain plants, Qu. 3. n. 13 Archimedes’ memorable glass sphere, 77. n. 361 Arcturus, the shapeless star near the legs of Bootes, 61. n. 283 It promises riches with Jupiter, 87. n. 19 Jasper is subject to it, 292. n. 64 The bow, whence the argument is called, 63. n. 295 The nature and signification of silver comets, 62. n. 288 Arisabium, a city in Asia, to which the true point of the Orient is nearest, 331. n. 11 The military armlet, with which victorious soldiers from war were rewarded, 66. n. 302 The signification of Aries in the horoscope, 63. n. 298. & 240. n. 18 In it, joined malefics harm the sheep with destruction, 489. n. 6 Aristotle, unable to understand the tide of the sea, feared to enter the sea, 35. n. 178 The praises and offices of arithmetic, 3. n. 4. & 64. n. 301 Angelic discipline, 328. n. 37 Artemisia herb is under Jupiter, 292. n. 64 Cometary portents of Ascones, 68. n. 315 The two stars, the Asses, most powerful in Cancer, and why, ibid. n. 316 Their signification in the horoscope, ibid. Various aspects of the planets, and new ones likewise, confirmed by musical consonances, 68. n. 310. & 86. n. 15 Whether latitude should be observed in aspects, 419. n. 6 All aspects are, in general, of familiarity, 68. n. 320 The stars of the heaven are roses, 125 n. 176 All stars receive light from the Sun, 275. n. 50 Yet they have some light proper to themselves, ibid. What is the reason of scintillation in fixed stars, 193. n. 23 They act upon these lower things by means of light alone, ibid. They are not living creatures, 116. n. 140 Yet they live with the universal life of the world, far above lower things, 310. n. 91 Since they lack sense and vegetation, by what means do they grant life to animals, ibid. Whether they have any activity in artificial works, 239. n. 25 Their names, taken from fables, were assigned to them not without great design and suitability, 212. n. 18 Astledius’ error concerning the figure of the sixteen-sided body, 190. n. 16 In what way astrology differs from astronomy, 70. n. 338 To what extent its predictions extend, 71. n. 342 What its object is, ibid.

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66 INDEX Astrologicæ interrogationes fictitiæ, ac superstitiosæ, 251. n. 47 Electiones è contrà licitæ, ac naturales, 165. n. 18 Astronomicæ, vt vocant, Imagines an vllam superstitionem sapiant, 237. n. 23 Ahlantis Insula in Oceanum per Terræmotum mersa, 305. n. 29 Atmosphæta quæ dicatur, 74. n. 347 Auges singuli Planetarum, 78. n. 364 Aurea Regula quid. 263. n. 33 Aureus numerus quid sit, & vndè dictus, 75. n. 356 Eius commoda, ibid. Aurotæ Cometes portenta, 76. n. 359 Ante Auroram cur tenebræ intendantur, 128. n. 188 Auges singuli Planetarum, 78. n. 364 Eorum mutatio, an rerum mutationes inducat, 5. n. 10 Auster infensissimus hortis, 77. n. 360 Visum hebetat, & alia mala adducit, ibid. Trans Æquatorem salutaris, & naturam Boreæ induit, & quare, ibid. & 321. n. 15. 16 Axes quot in Mundo concipiendi. 79, n. 356 Azimech nomen genericum stellas omnes de natura generis complectens, 80. n. 370 Azorum Insulæ celebres ob verum Occidens in ijs situm, 81. n. 373. B Baltheus, seu cingulus Orionis in Horosc. facit ingeniosum, 83. n. 3 Cum Ioue facit tempus turbidum, & obscurum, ibid. Beibeniæ Stellæ quæ dicantur, 84. n. 8 Bellatrix Stella in sinistro Orionis humero atdentissima, ibid. n. 7 Mirè ad bella inclinat, ibid. Ad Lunam directa adducit repentinum iter, ibid. Beneuentum Ciuitas vnde dicta, 105. n. 89 Berenices Coma oculis infensa, 84. n. 9 Beryllus gemma Cani Sidereo subest, 292. n. 64 Bicorporea signa geminatum foetum præsignant, 85. n. 13 Biquintilis radius de nouo inuentus, quis, & cujus efficacix, ibid. n. 15 Bissextilis annus vnde exortus, 86. n. 16 Fius Inuentor fuit Cæsar Dictator. ibid. Quomodo in posterum instituenda eius ratio ad Æquinoctij, & Solstitiorum rationem non perturban-

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66 INDEX Astrological interrogations are fictitious and superstitious, 251. n. 47 Elections, on the contrary, lawful and natural, 165. n. 18 Whether Astronomical, as they are called, Images savor of any superstition, 237. n. 23 The Island of Atlantis, sunk into the ocean by an earthquake, 305. n. 29 What an Atmosphæta is, 74. n. 347 The several Apses of the Planets, 78. n. 364 What the Golden Rule is. 263. n. 33 What the Golden Number is, and whence it is so called, 75. n. 356 Its advantages, ibid. Comets at dawn as portents, 76. n. 359 Why darkness is prolonged before sunrise, 128. n. 188 The several Apses of the Planets, 78. n. 364 Whether their change induces changes in things, 5. n. 10 The south wind most unfriendly to gardens, 77. n. 360 It blunts the sight, and brings other evils, ibid. Crossing the Equator, it is beneficial, and takes on the nature of Boreas, and why, ibid. & 321. n. 15. 16 How many axes are to be conceived in the World. 79, n. 356 Azimech, a generic name embracing all stars of that nature, 80. n. 370 The Azores Islands, famous because the true West is situated in them, 81. n. 373. B The Belt, or girdle of Orion, in a Horoscopic figure makes one ingenious, 83. n. 3 With Jupiter it makes the weather stormy and dark, ibid. What the Beibeniæ stars are, 84. n. 8 Bellatrix, a star on the left shoulder of Orion, very hot, ibid. n. 7 It inclines greatly to war, ibid. Directed to the Moon, it brings about a sudden journey, ibid. The city of Beneventum, whence so called, 105. n. 89 Berenice’s Hair, inimical to the eyes, 84. n. 9 Beryllus, a gem under the Dog Star, 292. n. 64 Double-bodied signs foretell a twin birth, 85. n. 13 What a biquintile ray is, newly discovered, and what its efficacy is, ibid. n. 15 The leap year, whence it arose, 86. n. 16 Its inventor was Julius Caesar the Dictator. ibid. How its method is to be established in future so as not to disturb the reckoning of the Equinoxes and Solstices

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Rerum Mobilium. 67 dam, ibid. Bombardarum explosio contra turbinem vulis, 517. n. 78 Bona fortunæ cur naturaliter significet Lunaris Horoscopus; 216. n. 42. Boreas in Chile Regno calidus, & humidus, 87. n. 10 & 521. n. 15. Brastæ Terræmotus species, 302. n. 26 Brunæ rempore Origanum aridum efflorescit, 88. n. 25 Etiam Murium iccora eo tempore augentur, ibid. Ex Brumæ qualitate coniectatur qualitas totius Hyemis, ibid. C Cæcias Ventus contra naturam Ventorum ad se attrahit nubes, 89. n. 7 Cæsar Dictator Anni Bissextilis inuentor, 86. n. 16 Calculis in numerando olim vtebatur Antiquitas. 9. n. 4 Cancer sidus vnde dictum, 90. n. 12 Sub eo nari statura breues sunt, & ampli pectore, ibid. Canariæ Insulæ olim celebres ob primum meridianum in ipsis constitutum, 81. n. 373 Canis Minor cur dictus Procyon, 47. n. 224 Canis Sirius Stella fixa aliquibus Sole maior, 91. n. 14. & alibi sæpè. Canis Coelestibus cum Sole exorientibus, terrestres aguntur in rabiem, 2. 6. n. 20 Canicularis dies vnde dicti, & quo incipiant tempore, 912. n. 15 Carbones in Ædium fundamentis iniecti, eas à terræ moti- bus immunes reddunt, 304 n. 28 Caroli V. Sphera memorabilis, 78. n. 362 Canopus Stella in Argonavi Melitæ incipit radere horizon- tem, 92. n. 16 In Rhodo Insula saris conspicua, ibid. Cantharides manu præsse exulcerant illæsa manu, Qu. 1. n 36 Capur Medusæ Stella funerea à D. Thoma dicta, 211. n. 27 Luminaribus violentum exirum portendit, ibid. Cassiopæ noua Stella an fuerit Cometes, 94. n. 33 Moscouiæ verticalis exuitit, 96. n 36 Eius Directio vsque ad annum 1632. ibid. Catalogus nouus Ciuitatum iam denuò fabricandus ob ve- rum Occidens alibi quam in Canarjs situm, 82 n. 374 Cauda Capricorni in Horoscopo dat morum gravitatem, 97, n. 47 e ij

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Movable Things. 67 dam, ibid. The explosion of bombs against a turbine of wheels, 517. n. 78 Why good fortune naturally signifies the lunar horoscope; 216. n. 42. Boreas in the Kingdom of Chile is warm and humid, 87. n. 10 & 521. n. 15. Earthquake species of Brastæ, 302. n. 26 At the time of winter, dry oregano flowers, 88. n. 25 Also the livers of mice increase at that time, ibid. From the quality of winter one conjectures the quality of the whole winter, ibid. C Cæcias, a wind that against the nature of winds draws clouds to itself, 89. n. 7 Caesar the Dictator, inventor of the leap year, 86. n. 16 In antiquity, people used pebbles for counting, 9. n. 4 Cancer, why the constellation is so called, 90. n. 12 Under it, the nostrils are short in stature, and the chest broad, ibid. The Canary Islands were once celebrated because the first meridian was established in them, 81. n. 373 Canis Minor, why called Procyon, 47. n. 224 Canis Sirius, a fixed star by some greater than the Sun, 91. n. 14. & elsewhere often. When the celestial Dogs rise with the Sun, earthly dogs are driven mad, 2. 6. n. 20 Dog days, why so called, and at what time they begin, 912. n. 15 Charcoal thrown into the foundations of buildings makes them immune from earthquakes, 304 n. 28 The memorable sphere of Charles V, 78. n. 362 Canopus, the star on the ship Argo, begins to graze the horizon in Malta, 92. n. 16 In the island of Rhodes it is clearly visible, ibid. Cantharides, if pressed by hand, blister the hand that remains unharmed, Qu. 1. n. 36 Caput Medusæ, a funereal star, so called by St. Thomas, 211. n. 27 It portends a violent end to the luminaries, ibid. Whether the new star of Cassiopeia was a comet, 94. n. 33 It appears vertical at Moscow, 96. n. 36 Its declination up to the year 1632, ibid. A new catalogue of cities must now be made again, because the true west is located elsewhere than in the Canaries, 82 n. 374 The tail of Capricorn in the horoscope gives seriousness of character, 97, n. 47 e ij

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63 INDEX Cauda Ceti dat periculum submersionis, ibid. n. 49 Cauda Cygni mirè humores adauger, potissimè sperma, 79. n. 366 Est verticalis Florentiæ Bononiæ alijsque sinitimis Ciuitatibus, ibid. Cauda Leonis dat optimum ingenium, atque honores, 97. n. 53 Ceginus sinister humerus Bootis verticalis Regno Neapol. 99. n. 59 Centiloquij Author an Ptolemæus, ibid. 63 Hali sibi contrarius de Centiloquij Authore, ibid. Illud approbat D. Thomas, ibid. n. 64 Centrum Mundi duplex, 100. n. 65 Solis, & siderum Terræ, ibid. & 500. n. 23 A Centro Telluris sit dimensio siderum à Mathematicis; 100. n. 65 Cepheus in Horoscopo quid significet, 101 n. 67 Ceratias Cometa apparens anno 1618. quot mala intulerit, ibid. 68 Chasma falsò à Plinio in genere Cometaru[m] positu[m] 102. n. 73 Chamæleon sidus directè oppositum Vrsæ, ibid. 78 Chele cur dicantur Stellæ in lancibus libræ, ibid. n. 74 Chile Regnum Ventorum naturam habet nobis contrariam, 76. n. 360 Vbi Auster frigidus, & siccus. Boreas contra calidus, & humidus, ibid. Choreutæ cur dictæ Stellæ du r extremæ circa Polaré, 103. n. 81 Christiani Danix Regis memorabile dictum, 78. n. 362 Chronocatores qui sint, 103. n. 85. Cicuta hominibus exitialis, Sturnis verò commodum pabulum, Qu. 1. n. 16 Cur frigiditate non interimat, non Nix, aut Glacies, 191. n. 62 Aduersus eam præsens Antidotum Vinum, ibid. Cingulus Orionis in Horoscopo ingeniosos facit, 83. n. 3 Circini Geometrici Galilæi laus, 2. n. 3 Circius Ventus vnde dictus, 104. n. 89 Eius qualitates, ibid. Circulus quid, & in quo differat ab Ellipsi, 105. n. 92 Circuli quadratura an dari possit, & in quovere consistat, 408. n. 9. & seq. Circumstantiæ multæ superstitiosæ reperiuntur apud aliquos in compositione, & vsu Vnguenti Armarij, Qu. 1. n. 1. & seq. Non tamen per hoc spermendum, ibid. Climata quot co[n]stituerint Antiqui, quot receptiores, 107. n. 103

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63 INDEX The Tail of Cetus gives danger of drowning, ibid. n. 49 The Tail of Cygnus greatly increases humors, especially semen, 79. n. 366 The vertical is at Florence, Bologna, and other neighboring cities, ibid. The Tail of Leo gives the best understanding and honors, 97. n. 53 The left shoulder of Bootes is vertical in the Kingdom of Naples, 99. n. 59 Whether the Author of the Centiloquium was Ptolemy, ibid. 63 Haly, contrary to himself, on the Author of the Centiloquium, ibid. That is approved by St. Thomas, ibid. n. 64 The Center of the World is twofold, 100. n. 65 Of the Sun, and of the Earth and stars, ibid. & 500. n. 23 That the measurement of the stars by mathematicians should be from the center of the Earth, 100. n. 65 What Cepheus signifies in the horoscope, 101 n. 67 How much evil the comet appearing in the year 1618, Ceratias, brought about, ibid. 68 Chasma falsely placed by Pliny among the kinds of comets 102. n. 73 The star Chamæleon directly opposite the Bear, ibid. 78 Why the stars in the scales are called Chele, ibid. n. 74 The kingdom of Chile has a nature of winds contrary to ours, 76. n. 360 Where the south wind is cold and dry; the north wind, on the contrary, warm and humid, ibid. Why the two extreme stars around the Pole are called Choreutæ, 103. n. 81 A memorable saying of the King of Denmark, Christian, 78. n. 362 Who the Chronocatores are, 103. n. 85. Hemlock is deadly to men, but to starlings a useful food, Qu. 1. n. 16 Why it does not kill by cold, nor snow or ice, 191. n. 62 Against it, the immediate antidote is wine, ibid. The Belt of Orion in the horoscope makes people ingenious, 83. n. 3 The praise of Galileo’s geometric compass, 2. n. 3 The wind Circius, whence it is so called, 104. n. 89 Its qualities, ibid. What a circle is, and wherein it differs from an ellipse, 105. n. 92 Whether the quadrature of the circle can be given, and in what it consists, 408. n. 9. & seq. Many superstitious circumstances are found among some in the composition and use of the Armourer’s Ointment, Qu. 1. n. 1. & seq. Nevertheless, it is not to be despised for this reason, ibid. How many climates the ancients established, how many the later authorities, 107. n. 103

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RERVM MOBILIVM. 64 Totidem constiuenda trans Æquarorem, 110. n. 128 Quodnam sit. Clima cæteris temperatius, ibid. n. 119 Climaterici dies, & anni vnde exorti, 111. n. 132 Cloaca Vniuersi Infernus, 240. n. 39 Cælos quot constituerar Antiqui, quot Recentiores, 113 n. 135 Vnum constituendum, & eiusdem substantiæ cum aere, 115. n. 137. 139 Eius materialis partirio ex Astris, 115. n. 135 Quinque Coelorum proprietares, ibid. n. 134 An per motum vocalem sonum edant, 115. n. 138 Eorum motus noua doctrina, 1. 4. n. 136 An detur vllum Coelum Anastron. 298. n. 75 Eius substantia tenuissima, & quoad omnes partes fluida, 115. n. 139 An sit animarum, 116. n. 140. & 306. n. 87 Cælestium Corporum cum terrestribus connexio & sympathia, Qu. 3. n. 4 Vitam Animantibus tribuunt, 310. n. 91 Colæ piscis, seu vralij vocâr Orbis, mira natura se ad spirantem ventum verientis, 512. n. 18 Vnde hæc affectio oriarur, ibid. Coluri quid sint, & eorum munia, 117. n. 144 Combusta via quæ dicenda, & quare, 1 8. n. 147 Combustus Planetæ cur debilis, 117. n. 146 An malesici combusti deteriores fiant, ibid. n. 147 Cometæ quid sint, cuiusque substantiæ, 118. n. 149 An præter aëreos detur etia[m] siderei, 118. n 150. p. 375. n. 59 Eorum diuisiones, ibid. De ijs salsa Democriui opinatio, 119. n. 152. & 376. n 60 Comites Siellas an habeant omnes Planetæ, 440. n 13 Conceptionis tempus indagandi an derur certa methodus, ac naturæ conformis, 515. n. 73 Congressus luminarium cum beneficis producit mixta, & animalia humano generi opportuna, cum maleficis aduersantia, 267. n. 42 Consilio Astris nomina ex Fabulis, & animantibus indita, 212. n. 28 Conuersa directio, non eadem quæ directa, 112. n. 166 Reijcitur Argolus, ibid. Qui significatores per eam dirigi possint, ibid. Cor Hydræ Stella venenata contrarijs qualitatibus prædita, 124. n. 171 Cor Leonis Stella Regia, 124. n. 172 Est tamen abscinden is naturæ, ibid. e iij

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Of movable things. 64 As many are to be established beyond the Equator, 110. n. 128 What it is. The climate temperate beyond the others, ibid. n. 119 Climacteric days, and whence the years arose, 111. n. 132 The sewer of the universe, Hell, 240. n. 39 How many heavens the Ancients established, how many the Moderns, 113 n. 135 That one is to be established, and of the same substance as the air, 115. n. 137. 139 Its material partition from the stars, 115. n. 135 The properties of the five heavens, ibid. n. 134 Whether they emit sound by vocal motion, 115. n. 138 A new doctrine concerning their motion, 1. 4. n. 136 Whether there be any heaven of the astrons, 298. n. 75 Its substance very subtle, and fluid in all its parts, 115. n. 139 Whether it be for souls, 116. n. 140. & 306. n. 87 The connection and sympathy of heavenly bodies with earthly ones, Qu. 3. n. 4 They grant life to living things, 310. n. 91 Colæ, a fish, or vralij called Orbis, of wondrous nature, turning itself toward the blowing wind 512. n. 18 Whence this affection arises, ibid. What the coluri are, and their offices, 117. n. 144 What a combust way is to be called, and why, 1 8. n. 147 Why a combust planet is weak, 117. n. 146 Whether malicious combust ones become worse, ibid. n. 147 What comets are, of what substance each is, 118. n. 149 Whether besides aerial ones there are also sidereal ones, 118. n 150. p. 375. n. 59 Their divisions, ibid. Democritus' false opinion about them, 119. n. 152. & 376. n 60 Whether all planets have companion stars, 440. n 13 Whether there is a certain method, conformable to nature, for investigating the time of conception, 515. n. 73 The conjunction of the luminaries with the benefics produces mixed things, and animals suitable to the human race; with the malefics, contrary ones, 267. n. 42 By design, names have been given to the stars from myths and animals, 212. n. 28 The converse direction is not the same as the direct, 112. n. 166 Argolus is rejected, ibid. Which significators may be directed by it, ibid. The Heart of Hydra, a venomous star endowed with contrary qualities, 124. n. 171 The Heart of Leo, a royal star, 124. n. 172 Yet it is of a cutting nature, ibid. e iij

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70 INDEX In Horoscopo semper affert aliquam corporis discræ tiam, ibid. Cum luminaribus magnam fortunam adducit. ibid. Sola inter fixas habet, & recipit a pectus ad Planetas, 83. n. 4. & 426. n. 54. In Corde Solis cur Planeta euadat fortis, cum alias com- bustus aut sub radijs euadat debilis, 98. n. 58 Cor Scorpii, Stella fixa Regia, sed violenta, 124. n. 173. & 46. n. 216 Eius significata in Horosc. ibid. Est directè opposita Pallilitio, ibid. Coro Vento infestissima est Apulia, 126. n. 181 Coronæ aeræ, Quæ. 126. n. 179 Coronæ Septentrionalis in Horoscopo significata, 125. n. 176 Sidus est omnium nobilissimum, ibid. Cæli pupilla, & flos coelestis cur dicta, 26. n. 151 Est tamen sidus tempestuosum, ibid. n 152 Corpora Planetarum, & Globi quare non concaui, sed con- uexi, 120. n. 157 Corpora Platonica, Quæ. 131. n. 8 Cosmicè Astra impropriè dicuntur oriri, 126. n. 181 Cosmographia, eius munus, & quomodo differt à Geogra- phia, 127. n. 184 Crateris sidus in Horoscop. significata, 128. n 186 Crepusculum quid dicatur, 128. n. 187 Noua solis in Crepusculis existentis dirigendi metodus, ibid. n. 188 In spatio Crepusculorum sol constitutus semper vitæ moderationem obtinet, ibid. In Noruegia semper Crepusculi, ibid. Critici dies qui, & vnde exorti, 130. n. 190 Eorum maxima ratio à Medico habenda, ibid. Obseruandi etiam Indicatiui, qui formantur ab aspecti- bus imperfectis, ibid. Crux sidus Australium Cynosura, 132 n. 194 Culmen seu medium Cæli naturalis Actionum significator, 132. n. 197 Cuspis quæ dicatur, 133. n. 202 Cyclo vtebatur Ecclesia ante Gregorianam correctionem, 133. n. 104 Cygnus in Horosc. quid significet, 79. n. 366 In eo noua Stella apparuit anno 1600. 134. n. 209 Quæ tandem euanuit relicto quodam hiatus in loco, ibid. Cynocephalus horarum inuentor, 232. n. 34

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70 INDEX In a horoscope it always brings some bodily difference, ibid. With the luminaries it brings great fortune, ibid. Among the fixed stars alone it has, and receives from, the Pectus of the Planets, 83. n. 4. & 426. n. 54. In the Heart of the Sun, why a planet becomes strong, while otherwise, when combust or under the rays, it becomes weak, 98. n. 58. Cor Scorpii, a fixed royal star, but violent, 124. n. 173. & 46. n. 216. Its significations in the horoscope, ibid. It is directly opposite to the Pallitium, ibid. Coro is most hostile to the wind in Apulia, 126. n. 181. Aërial crowns, what they are, 126. n. 179. The significations of the Northern Crown in the horoscope, 125. n. 176. It is the noblest of all stars, ibid. Why it is called the pupil of heaven, and the flower of the sky, 26. n. 151. Yet it is a stormy star, ibid. n. 152. Why the bodies of the planets and the globes are not hollow, but convex, 120. n. 157. What the Platonic bodies are, 131. n. 8. The stars are improperly said to rise cosmically, 126. n. 181. Cosmography, its office, and how it differs from Geography, 127. n. 184. The signification of the star of the Crater in a horoscope, 128. n. 186. What is meant by twilight, 128. n. 187. A new method of directing the sun existing in twilights, ibid. n. 188. In the interval of twilight the sun, when placed there, always maintains moderation of life, ibid. In Norway there is always twilight, ibid. Critical days: what they are, and whence they arose, 130. n. 190. Their greatest importance is to be considered by the physician, ibid. Also to be observed are the significators, which are formed from imperfect aspects, ibid. The Cross, the southern Cynosura, 132 n. 194. The Culmen, or midheaven, a significator of natural actions, 132. n. 197. What the cusp is called, 133. n. 202. The Church used the cycle before the Gregorian correction, 133. n. 104. Cygnus: what it signifies in a horoscope, 79. n. 366. A new star appeared in it in the year 1600, 134. n. 209. Which at last vanished, leaving a certain gap in its place, ibid. The Cynocephalus, inventor of hours, 232. n. 34.

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R E R V M MOBILIVM. 71 In luminariam coitus, nec cibum sumit, nec videt, 460. n. 81 Cynosura, 61. n. 282 D Amnarorum corpora in Inferno etunt tanquam muria- tici pisces in dolio, 246. n. 39 Dæmon maxima quæque naturæ bona gestit suis tricis co- rumpere, aut suspecta reddere, Qu. 1. n. 26 Quæ ipse agit, & nos agere valeremus, si eamdem quam ipse habet rerum notitiam haberemus, Qu. 2. n. 29 Dæmon meridianus cur dicta sagitta sidus, 135. n. 3 Dæmones secundam Aëris regionis inhabitant, & quare, 12. n. 38 Debilitatis gradus an dentur in signis, & qui nam ij sint, 79. n. 367 An fictitia, ibid. Decanorum prærogatiua, Quæ. 135. n. 7 Declinatio quid sit, 136 n. 10 Quid commodi ex ea eliciatur, ibid. Decubitus figura, an ad indagandum morbi progressum, & qualitates licitè erigatur, 136. n. 11. 12 An erigenda sit initio morbi, an potius à puncto quo quis à morbo prostatus tandem in lecto decumbit. ib. Defectiones luminarium pro qualitate signorum in quibus incidunt, auspicandæ, 235. n. 20 In Arietis signo occurrentes, Arietibus, & pecudi pestem inducunt, ibid. Delphinus cum Planetis exoriens quid indicet, 137. n. 15 Diameter Mundi quæ dicatur, 138. n. 22 In ea eius magnetica se directè ad polum vertit, 81. n. 374 Dies quid. & vnde à diuersis Nationibus computari, incipiat 140. n. 26 Dies Caniculares vnde dicti. & quo tempore incipiant, 91. n. 15 Dies Critici. vide Critici dies. Dies vbi maiores, 107. n. 104. & seq. Digiti Ecliptici quot constituantur in disco Solari, quot in Lunari, 140. n. 28. Dignitates Planetaru[m] alièq[ue] essentiales, alièq[ue] accidètales, 141. n. 30 Quæ potiores, & cur ita dicantur, ibid. Directionis motus quis sit, & an realis, 142. n. 35 Quomodo fiat, & quando compleatur. 143 n. 36 Directio conuersa. vide, conuersa directio. Noua doctrina dirigendi solem in spatio crepusculorum e liij

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ON MOBILE THINGS. 71 In conjunction with the luminary, it takes neither food nor sees, 460. n. 81 Cynosura, 61. n. 282 D The bodies of the dead in hell are like salted fish in a barrel, 246. n. 39 The Demon strives to corrupt with its tricks whatever goods are greatest in nature, or to make them suspect, Q. 1. n. 26 What it itself does, and what we also would be able to do, if we had the same knowledge of things that it has, Q. 2. n. 29 The midday demon: why is the arrow called a star, 135. n. 3 Demons inhabit the second region of the air, and why, 12. n. 38 Whether there are degrees of weakness in the signs, and which they are, 79. n. 367 Whether they are fictitious, ibid. The prerogative of the decans, Q. 135. n. 7 What declination is, 136 n. 10 What advantage is drawn from it, ibid. The figure of the decubitus, whether it may lawfully be erected in order to investigate the progress and qualities of the disease, 136. n. 11. 12 Whether it should be erected at the beginning of the disease, or rather from the point at which one, having been afflicted by the disease, finally lies down in bed. ib. Eclipses of the luminaries are to be forecast according to the quality of the signs in which they occur, 235. n. 20 Those occurring in the sign of Aries bring plague to the rams and to cattle, ibid. What is indicated by the Dolphin rising with the planets, 137. n. 15 What is called the diameter of the world, 138. n. 22 In it, its magnetic nature turns directly toward the pole, 81. n. 374 What a day is, and whence, by different nations, the counting of it begins, 140. n. 26 Why the dog days are so called, and at what time they begin, 91. n. 15 Critical days. See critical days. Where the days are longer, 107. n. 104. & seq. How many ecliptic digits are constituted in the solar disk, how many in the lunar, 140. n. 28. The dignities of the planets are partly essential, partly accidental, 141. n. 30 Which are the principal ones, and why they are so called, ibid. What the motion of direction is, and whether it is real, 142. n. 35 How it is made, and when it is completed. 143 n. 36 Reversed direction. See reversed direction. A new doctrine for directing the sun in the space of the crepusculars e liij

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72 INDEX existentem, 118. n. 137 Directus Planeta cur validior quam retrogradus, aut stationarius, 74. n. 348 & 148. n. 42. & 417. n. 37 Dispositor alicuius loci quis Planeta dicatur, 149. n. 46 Diurnus, ac Nocturnus Planeta dicitur in ordine ad qualitates actiua, aut passiuas, 149. n. 49 Domicilij prærogatiua in Planetis Philosophicè probata, 150. n. 52 & 495. n. 19 Dominus Horæ, seu Diepon. 139. n. 25 Dominus Nouenariæ quis, 39. n. 193 Dominus Terminorum, 20. n. 102 Dominus annuæ profectionis an sit Astrologorum fig-mentum, 152. n. 54 Dominus Genituræ an astruendus. Quinam dicendus, 152. n. 55. & seq. Quas prærogatiuas habere debeat, ibid. Variæ Astrologorum sententiæ, ibid. Auctoris opinio Naturæ, & experimentis conformis, 153. n. 56 An Luminaria ab hac prærogatiua sint excludendi, ibid. 57 An Planeta combustus, cadens, aut sub Solis radijs con-stitutus, ibid. Dominum Horæ obseruare in rerum electionibus an super-stitiosum, 155. n. 59 Domorum Coelestium, quoad situm mundi congruens na-turæ distributio, 151. n. 53 Domum ædificare Scorpion in Horosc. existente, ipsa Scor-pionum nidus euadet, 445. n. 27 Drago volens Cometæ genus, 158. n. 67 Dnbia superstitiosa ne sint an naturalia, naturalia censenda sunt. Qu. 1. n. 29 In Dubijs tutior pars eligenda. Qu. 1. n. 25 Quomodo id intelligi debeat, ibid. Duodecim signa singula singulis membris humanis præsunt, 453. n. 64 E Eclipse quid, & vnde dicta, 161. n. 8 Eclipse Solis à Lunari diuersitas, ibid. Eclipse Solis potius dicenda Telluris Eclipse, ibid. Eclipsantur etiam Planetæ superiores, 163. n. 7 Eclipse Louis anni 1648. quid orbi induxerit, ibid. Eclipses quid in singulis signis occurrentes portendant, ibid. & 235. n. 20

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72 INDEX existing, 118. n. 137 Direct Planet, why it is stronger than retrograde or stationary, 74. n. 348 & 148. n. 42. & 417. n. 37 The ruler of a place: which planet is so called, 149. n. 46 A planet is called diurnal or nocturnal in relation to active or passive qualities, 149. n. 49 The prerogative of domicile in the planets, philosophically proved, 150. n. 52 & 495. n. 19 Lord of the Hour, or of the day, 139. n. 25 Lord of the Nine, which, 39. n. 193 Lord of the Terms, 20. n. 102 Whether the lord of annual profection is a figment of astrologers, 152. n. 54 Whether there is a Lord of the Nativity. Who he is to be called, 152. n. 55. & seq. What prerogatives he ought to have, ibid. Various opinions of astrologers, ibid. The author's opinion, in conformity with nature and experience, 153. n. 56 Whether the luminaries are to be excluded from this prerogative, ibid. 57 Whether a combust planet, falling, or placed under the rays of the Sun, ibid. Whether observing the Lord of the Hour in elections of things is superstitious, 155. n. 59 The distribution of the celestial houses, with regard to the position of the world, in harmony with nature, 151. n. 53 To build a house with Scorpio in the Ascendant, the house itself will become a nest of scorpions, 445. n. 27 A dragon flying: a kind of comet, 158. n. 67 Whether doubtful things that are superstitious are to be held as natural, they are to be judged natural. Q. 1. n. 29 In doubtful matters the safer part is to be chosen. Q. 1. n. 25 How this ought to be understood, ibid. The twelve signs each preside over individual human members, 453. n. 64 E Eclipse: what it is, and whence the word is derived, 161. n. 8 The difference between a solar and a lunar eclipse, ibid. A solar eclipse should rather be called an eclipse of the Earth, ibid. The superior planets are also eclipsed, 163. n. 7 What the eclipse of the Moon in the year 1648 brought upon the world, ibid. What eclipses occurring in each sign portend, ibid. & 235. n. 20

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R E R V M M O B I L I V M. 73 Eclipsis Solis anni 1651. in Ariete, & altera in Leone 1654. 162. n. 6 A præcedentibus Luminarium Eclipsibus Nupera Italiæ pestilentia ortum habuit, ibid. Eclipses non afficiunt ea loca in quibus non apparent, ibid. Eclipsis portentosa quæ erit anno 1681. qua totum cor- pus solare obscurabitur, quæ mala indicet, 141. n. 19 Eclipses non tam malorum, quam maximorum bonorum sunt causæ, 163. n. 6 Eclipsæ duæ, 163. n 9 Eneasias Ventus longè ab cæteris diuersus, 164. n. 10 Eius descriptio ex Aristotele, ibid. Electiones Astrologiæ quid, 165. n 18 An licitè fiant, ibid. Sunt in duplici differentia, ibid. Elementa omnia præter terram mouentur motu vniuersitatis, 169. n. 24 Ea negat Auersa quam benè? ibid. Elementa Geometriea, Quæ. 170. n. 25 Elevatio siderum super sidera in quo consistat, 170 n. 26 Malè explicata à Pontano, n. 27 Variæ aliorum explicationes expenduntur, ibid. & seq. Auctoris iudicium, n. 30 Elevationis dignitas an consistat in eo quod Planeta sit eminentior situ in Epicyelo, 23. n. 131 Empirei magnitudo, 174. n. 44 Engonasis in Horoscopo significata, 175. n. 46 Enneatiei dies Naturæ infensi. vide Critici dies. Epacta quid. Eius inueniendi ratio, & quando deficiat, 176 n. 52. & seq. Ephemerides, seu Annotationes, 23. n. 130 Equus in Horoscopo inclinat ad Poësima. 179. n. 63 Equicruia figura quid. vide in V Figura. Eridani Stellæ tempestuosæ, 179. n. 66 Etesiæ Venti quo tempore in diuersis orbis partibus spirent, 180. n. 69 Eurus Ventus vitibus exitialis quonam pacto huic malo oc- curatur, 181. n. 77 Exaltatio Planetarum in quo consistat. 181. n. 79 An sit potior iure domicilij, ibid. Exasteron dicuntur Pleiades, qua ratione, 183. n. 81

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R E R V M M O B I L I V M. 73 Solar eclipse of the year 1651 in Aries, and another in Leo, 1654. 162. n. 6 From the preceding eclipses of the luminaries, the recent plague of Italy arose, ibid. Eclipses do not affect those places in which they do not appear, ibid. A portentous eclipse which will occur in the year 1681, in which the entire body of the sun will be obscured; what evils it indicates, 141. n. 19 Eclipses are not so much causes of evils as of the greatest goods, 163. n. 6 Two eclipses, 163. n. 9 Aneasias, a wind far different from the others, 164. n. 10 Its description from Aristotle, ibid. What astrological elections are, 165. n. 18 Whether they may lawfully be made, ibid. They are of a twofold difference, ibid. All the elements except earth are moved by the motion of the universe, 169. n. 24 What does he deny to Auersa? ibid. Geometric elements, what they are, 170. n. 25 Elevation of the stars above the stars, in what it consists, 170. n. 26 Badly explained by Pontanus, n. 27 Various explanations of others are examined, ibid. and following The author’s judgment, n. 30 Whether the dignity of elevation consists in this, that a planet is more eminent in position in the epicycle, 23. n. 131 The size of the empyrean, 174. n. 44 Engonasis signified in the horoscope, 175. n. 46 Enneatic days hostile to nature. See Critical days. What an epact is. The method of finding it, and when it fails, 176 n. 52 and following Ephemerides, or annotations, 23. n. 130 The horse in the horoscope inclines to poetry. 179. n. 63 What the equicrural figure is. See under the letter V. The tempestuous stars of Eridanus, 179. n. 66 The Etesian winds: at what time they blow in different parts of the world, 180. n. 69 The Euroas wind, fatal to vines; in what way this evil is prevented, 181. n. 77 In what the exaltation of the planets consists. 181. n. 79 Whether it is superior by right of domicile, ibid. The Pleiades are called Exasteron; for what reason, 183. n. 81

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74 INDEX F Familiaritas inter sidera in quo consistat, 185. n. 3 Fam duplex ratio contrahendi, & in Mundo, & in Zodiaco, ibid. Inter eas conumeranda sunt etiam Antiscia, 186. n. 6 Omnes Aspectus sunt in genere familiaritatu[m], 68. n. 310 Familiaritatum species ex modis musicis auspicantur, 186. n. 5 Fata Imperiorum, & Monarchiarum vnde, 44. n. 210 Fauonius Ventus in Lusitania an verum sit quod Equas faciat concipere, 14. n. 48 Genitalis Mundi spiritus dicitur, 186. n. 7 Est Venationi contrarius, & quare, 333. n 5 Felices gradus, & infelices in signis an dentur. vide Gradus. Felis abortus ad masculi occisionem vnde sequatur, Qu 3. n 16 Feralia signa sunt feris affinia, 187. n. 9 In Horoscopo faciunt monstra, ibid. Feretrum Lazari quid. 510. n. 47 Fidicula Lucida Stella, excepto Sirio, omnium maxima, & potenior, 187. n. 13 Eius significata in Horoscopo, ibid. Figura sexdecim laterum, quæ dicatur, 188. n. 16 Alstedij in eius explicatione palmalis error, ibid. Figura Æquicuria foetum mortuum excludit, aut diu viuere non permittit, 9. n 30 Explicatur in quo ea consistat, ibid. Figuræ Isoperimentræ quæ dicantur ab Geometris- 188. n. 15 Figuræ decubitus opportunæ in morborum initijs eriguntur, 136. n. 18 In quo puncto ea erigenda sint, ibid. n. 12 Figurarum, ac nominum ex Fabulis in Stellis fixis appinxio, quam ritè, 213. n. 29 Filix vno die florem profert, & fructum, 462. n. 85 Fines. vide Termini. Finitor quid sit, & quotuplex, 190. n. 18 Firmamenti nomine in sacris paginis appellatur Aër. 191. n. 19 Quid eo nomine communiter veniat, ibid. Firmamentum in quo fixæ consistunt an sit solidum, 191. n. 19 Vnde dictum, ibid. Quanra sit eius crassities. ibid. n. 20 Antiqui ob motus tarditatem ipsum à primo mobili non distinguebant, ibid. n. 21

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74 INDEX F Familiarity among the stars, what it consists in, 185. n. 3 A twofold way of contracting familiarity, both in the World and in the Zodiac, ibid. Among them are also to be reckoned Antiscia, 186. n. 6 All Aspects are in general among the familiarities, 68. n. 310 The kinds of familiarities are derived from the musical modes, 186. n. 5 The fates of Empires and Monarchies, whence, 44. n. 210 Whether the West Wind in Lusitania truly causes mares to conceive, 14. n. 48 It is called the spirit of the Genital World, 186. n. 7 It is contrary to Hunting, and why, 333. n. 5 Whether happy and unhappy degrees in the signs are given. See Degrees. The miscarriage of a female cat follows from the killing of a male, whence, Qu. 3. n. 16 Feralia signs are akin to wild beasts, 187. n. 9 In the Horoscope they produce monsters, ibid. What the bier of Lazarus is, 510. n. 47 Fidicula, a bright star, except for Sirius, the greatest and most powerful of all, 187. n. 13 Its significations in the Horoscope, ibid. What is meant by a figure with sixteen sides, 188. n. 16 A notable error of Alstedius in its explanation, ibid. The Equicurious figure produces a dead fetus, or does not allow it to live long, 9. n. 30 It is explained in what it consists, ibid. What figures of equal perimeters are called by geometers, 188. n. 15 Positions of the body suitable at the beginnings of diseases are raised up, 136. n. 18 At what point they should be raised, ibid. n. 12 The annexing of figures and names from fables onto fixed stars, how it should be done, 213. n. 29 The fern produces flower and fruit in one day, 462. n. 85 Fines. See Terms. What a Finitor is, and how many kinds there are, 190. n. 18 Under the name of Firmament, Air is called in sacred pages. 191. n. 19 What is commonly meant by that name, ibid. Whether the firmament, in which the fixed stars are situated, is solid, 191. n. 19 Whence it is so called, ibid. What its thickness is. ibid. n. 20 The ancients, because of the slowness of its motion, did not distinguish it from the first moved, ibid. n. 21

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R E R V M M O B I L I V M. 79 Qui primi eius motum peculiarem obseruaverint, ibid, Vitam animantibus tribuir, ibid. n. 20 Firmius Latinè m. .gis, quam Philosophicè scripsit, 153. n. 55 Eius scripta quare ab Ecclesia permissa, ibid. Fixa signa quæ dicantur, 192. n. 22 Opportuna ad ædificandum, ibid. & 167. n. 20 Fixæ vnde dictæ Stellæ in Firmamento, 193. n. 23 An digniores Erraticis, ibid. Habent hoc peculiare, quod scintillent, quod non est in Planetis, ibid. Earum scintillandi ratio varie explicata vide scintillatio, 443. n. 23 Auctoris opinio, 444. n 25 Fixæ admirabiles, & repentinas dignitates afferunt, quas sæpè calamitatibus insigniunt, 193. n. 24 Earum magnitudo quomodo colligenda, ibid. An omnes in eadem sint à Tel'ure distantia, ibid. Quomodo fereno Coelo dignosci possint, 195. n. 26 Quor numero sint, ibid. n. 20 & 469. n. 107 Solæ Pleiades Telescopio detectæ sunt numero, 50. 195. n. 25 Num earum aliqua sit Sole grandior, 91. n. 14. p. 194. n. 25. & 267. n. 41 Flos Coeli cur dicta sit Lucida Coronæ Gnostiæ, 26. n. 151 Fluuiorum repentina exsiccatio euidens Terræ motus signum, 505. n. 29 Item eorumdem in conatariam partem conuersio, ibid. Fluxus. & Resfluxus maris vnde, & quotuplex, 35. n. 178 Fœminæ abortum patiuntur in Terræ motibus, 505. n. 29 Fœminini, & Masculini Planetæ, & signa an detut, 196. n. 29. 30 In quo consistat hæc diversitas, ibid. & seq. Fœmineus nè sit an Masculus foetus in vteto clausus quomodo præuideri possit, 197. n. 31 Fœmineus Planeta num aliquando dicendus sit Mars, 281. n. 23. & 196. n. 29 Fœtus vtero exclusus quando incipiat Coelorum influxibus subijci, 30. n. 164 Fomahand Stella in exitu Aquarij dat nominis immorralitatem, 197. n. 32 Formicæ Luna silente Otiosæ, 452. n. 63 Fortunæ quare dicantur Venus, & Iupitet, 197. n. 33 Fortunæ pars quare dicatur Horoscopus Lunaris, 198. n 34. & 226. n. 41 An, & quomodo sit naturalis bonorum fortunæ significa-

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R E R V M M O B I L I V M. 79 Who first observed its peculiar motion, ibid. It attributes life to living beings, ibid. n. 20 He wrote more firmly in Latin than philosophically, 153. n. 55 Why his writings were permitted by the Church, ibid. The fixed stars called by what name, 192. n. 22 Suitable for building, ibid. & 167. n. 20 Why the fixed stars in the Firmament are so called, 193. n. 23 Whether they are more worthy than the wandering stars, ibid. They have this peculiarity, that they scintillate, which is not in the planets, ibid. The reason for their scintillation is explained in various ways; see scintillation, 443. n. 23 The author's opinion, 444. n. 25 The fixed stars, admirable, and bring sudden dignities, which they often distinguish with calamities, 193. n. 24 How their magnitude is to be gathered, ibid. Whether all are at the same distance from the Earth, ibid. How they may be recognized in a clear sky, 195. n. 26 How many there are, ibid. n. 20 & 469. n. 107 Only the Pleiades have been discovered by telescope in number, 50. 195. n. 25 Whether any of them is greater than the Sun, 91. n. 14. p. 194. n. 25. & 267. n. 41 Why the Flower of Heaven is called the Bright One of the Gnostic Crown, 26. n. 151 The sudden drying up of rivers is a clear sign of an earthquake, 505. n. 29 Likewise their turning toward the opposite direction, ibid. The flux and reflux of the sea, whence, and how manyfold, 35. n. 178 Women suffer miscarriage in earthquakes, 505. n. 29 Female and male planets, and whether there are signs, 196. n. 29. 30 In what this difference consists, ibid. & seq. How it may be foreseen whether the fetus enclosed in the womb is female or male, 197. n. 31 Whether the female planet should at any time be called Mars, 281. n. 23. & 196. n. 29 When the fetus brought forth from the womb begins to be subject to the influences of the heavens, 30. n. 164 The Fomahand star, at the exit of Aquarius, confers immortality of name, 197. n. 32 Ants at rest when the Moon is silent, 452. n. 63 Why Venus and Jupiter are called fortunate, 197. n. 33 Why the fortunate part is called the lunar horoscope, 198. n. 34. & 226. n. 41 Whether, and how, there is a natural signification of the good fortune of

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75 INDEX trix, Error communis Astrologorum eam in partibus Zodiaci computandi, Non ea in Zodiaco, sed in situ Mundi constituenda, Debet vncio naturali die aspectus omnes ad Lunam, & alios occursantes habere, quod, si in Zodiaco constituetur, obtinere non posset, Vera eam in suo situ reali constituendi ratio, ac metodus, Veteribus etiam nota, Noua eam dirigendi metodus, Quomodo in Zodiaco locus definiatur, Fouca Planetarum cur dictum sit imum Coeli, Fridariæ quæ, & quotuplex, Frigus intensior sub Aurora, quouis anni tempore, quam in cæteris noctis vigilijs, Fulgura rara in hyeme præterquam in Campania, Funerea Stella, ac Naturæ maximè infensa est potissima in Gorgonis Capite, 211. n. 27. G Galaxia quid sit, De ea Philosophi, & Antiquorum error, Est minutarum Stellarum congeries, Nouorum Phænomenatum in Coelo apparentium subiectum, & seminarium, Gallinæ quomodo futurum Terræ motum indieret. Gaudium Planetarum quot modis accipiatur, Eius ratio ex Philosophiæ principijs eruta, Gemelli à bicorporibus signis originem habent, Genethliacum Thema erigere an, & quousque sit licitum, Quid ex eo naturaliter coniectari possit, Ad quod temporis momentum erigi debeat. Geodæsia quid. & in quo à Geometria differat, Geometriæ laudes, Gibbosi nascuntur, qui habent Lunam in Nodis cum maleficis, Globus in quo differat à Sphera & Orbe, Gorgonis Caput. ac Stellæ in eo funereæ ex D. Thoma. Est verticalis Regno Neapolis, vt olim Greciæ. Quot malorum auctor extiterit, Quæ longe ante Argolus prænuntiauit, Vide in V. Medusa.

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75 INDEX trix, The common error of astrologers in calculating it in the parts of the Zodiac, It is not to be placed in the Zodiac, but in the position of the World, By its natural conjunction it must have all aspects to the Moon, and to the others that meet it, which, if it were placed in the Zodiac, it could not obtain, The true method and way of placing it in its real position, Known also to the Ancients, The new method of directing it, How the place in the Zodiac is defined, The lower part of the Planetary sphere, why it is so called, Fridaria, what it is, and how many kinds there are, Cold more intense at dawn, at any season of the year, than in the other watches of the night, Lightning rare in winter except in Campania, The funereal star, and especially hostile to Nature, is most powerful in the Head of Medusa, 211. n. 27. G Galaxy, what it is, Concerning it, the error of the philosophers and of the ancients, It is a cluster of tiny stars, The subject and seedbed of new phenomena appearing in the heavens, How the hen foretold an earthquake to come. The joy of the planets, in how many ways it is understood, Its explanation drawn from the principles of philosophy, Gemini have their origin from double-bodied signs, Whether it is lawful to erect a genethliac figure, and how far, What may be naturally conjectured from it, At what moment of time it ought to be erected. Geodesy, what it is, and in what it differs from geometry, The praises of geometry, Hunchbacks are born who have the Moon in the Nodes with malefics, A globe, how it differs from a sphere and a orb, The Head of Medusa, and the funereal stars in it, from St. Thomas. It is vertical to the Kingdom of Naples, as once to Greece. How many evils it has been the author of, What Argolus foretold long beforehand, See under M. Medusa.

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Rerum MobiliVM 77 Gradus apud Astronomos quid. 213. n. 19 Idem proportionaliter, ac Geometricè in terra consi- derati, ibid. Quot millaria in terra singuli comprehendant. ibid. Diuersa eorum denominatio, ibid. n. 30 An, & quinam reales sint, ibid. Eorum aliqua ratio elucet ex Stellis fixis in ijs constitutis, ibid. Iam nunc vel ex eo euadunt erroribus multis obnoxij, ibid. Felicium, & Infelicium subtilis ratio ex Cardano, ibid. Gradus contermini finibus beneficarum felices, maleficiarum verò infelices; ibid. Gradus intermedij signorum fixorum infelices, & quare ibi debilis ad modum euadit Aphera, 80. n. 379 Tabula Graduum augenrium fortunam, 215. n. 32 Lucidorum, & Tenebrosorum. n. 33. Putealium, n. 35 Vacuorum, & Plenorum. n. 36. & Debilitatis, 79. n. 367 H HAlon quid memorabilis visus tempore Augusti. 217. n. 314. Hædi Stellulæ in Aurigæ tempestuosæ, 218. n. 11 Eorum significata in Horoscopo, ibid. Hircus Stella Nautis infesta, 221. n 25 Quid in Horoscopo indicet, ibid. Quibus locis sit verticalis, ibid. Historia memorabilis de Naso adscititio, Qu. 3. n. 16 De muliere solo attactu podagram concipiente, ibid. n. 22 Cuiusdam Medici solis pulueribus ex humano corpore comparatis omnes morbos curantis, ibid. n. 26 Pediculorum sub linea Occidentis morienrium, 82. n. 374 Homines cuiter ni forent, & immortales si ab Albo Planeta- rum eraderentur Mars, & Saturnus, 440. n. 15 Hora quid, & vnde dicta, 222. n. 34 Horarum inuentio, & distributio ex Cynocephalo, ibid. Earum diuersitas, ibid. & seq. Horæ inæquales seu Planetariæ, Quæ. ibid. Quomodo singulis diebus extrahi possint, 139. n. 25 Horæ opportunitarem in rebus agendis contemnere, est potius arbitrij præcipitatio, quam libertas. vide in V. Diepon. Horaria tempora Planearum Latirudinem habentium, quomodo facile extrahantur, 223. n. 35 Horizontis officia, 225. n. 38

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Rerum Mobilium 77 The degrees among astronomers, see q. 213, no. 19 The same, proportionally and geometrically considered on earth, ibid. How many miles each contains on earth, ibid. Their different denomination, ibid. no. 30 Whether they are real, and which ones, ibid. Some rationale for them is made clear from the fixed stars set in them, ibid. They now indeed are, from this very fact, liable to many errors, ibid. A subtle reckoning of fortunate and unfortunate degrees from Cardano, ibid. The bordering degrees at the limits of the benefic houses are fortunate, those of the malefic ones unfortunate; ibid. The intermediate degrees of the fixed signs are unfortunate, and why there the sphere becomes extremely weak, 80. no. 379 Table of the fortunate degrees of the ascendant, 215. no. 32 Of the bright and the dark, no. 33. Of the well-like, no. 35 Of the empty and the full, no. 36. And of debility, 79. no. 367 H A halo, a memorable one, was seen in the time of Augustus, 217. no. 314. The little stars in Auriga, the Hædi, are stormy, 218. no. 11 Their significations in the horoscope, ibid. The Goat Star, hostile to sailors, 221. no. 25 What it indicates in the horoscope, ibid. At what places it is vertical, ibid. A memorable story about an adopted nose, Qu. 3. no. 16 About a woman who, by mere touch, conceived gout, ibid. no. 22 Of a certain physician who cured all diseases only with powders made from the human body, ibid. no. 26 Of lice dying under the line of the West, 82. no. 374 Men would be weavers if there were not, and immortal if Mars and Saturn were erased from the white planet, 440. no. 15 What an hour is, and whence it is so called, 222. no. 34 The invention and division of hours from the Cynocephalus, ibid. Their diversity, ibid. and following. Unequal hours, or planetary hours, what they are, ibid. How they may be extracted for each day, 139. no. 25 To despise the opportune time of hours in affairs, is rather a rashness of judgment than freedom. see under V. Diepon. How the hourly times of planets having latitude are easily extracted, 223. no. 35 The offices of the horizon, 225. no. 38

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78 INDEX Horologia Solaria absque Gnomone, 443. n. 38 Horoscopus quomodo sit naturalis vitæ significator, 325. n. 40 Humana signa cum natura humana consensum, & Sympathiam habent, 227. n. 44 In ijs Luminarium defectiones, aut maledicorum coitus incidentes pestilentiam, aliaque mala hominibus portendunt, ibid. Probatur id nupera Italix experientia. ibid. Humani Corporis mira consensio, & simetria, 473. n. 121 Eiusdem cum coelestibus ordo, ibid. Humidi radicalis auctrix, & fatrix Luna, 207. n. 12. & p. 270. n. 47 Hyades Stellæ pluuiosæ, 227. n. 46 Earum significata in Horoscopo, ibid. Hybernia à Terræmotus libera, 303. n. 26 Hydrargiti miræ qualitates, 291. n. 62 Hydræ Stellæ Venenosæ, 228. n. 47 Hyemale Solstitium cur fecè semper serenum, 462. n. 85 Hyems quæ apud Veteres, quæ nunc, 228. n. 50 Sub Pollis continua, ibid. Sub Æquatore duplex, ibid. Fulgura rara in Hyeme, præterquam in Campania, ibid. I I Aspis gemma Arcturo subest, 262. n. 64 Ex occulta qualitate habet sanguinem sistere, ibid. &c Qu 1. n. 35 Icosaëdrum vnum ex quinque generibus corporum regula- rium, 230. n. 8 Dicuntur etiam ab aliquibus Corpora Platonica, 231. n. 8 Ignis nè fæcundus, an sterilis, 231. n. 10 An detur Sphæra ignis in concauo Lunæ, ibid. n. 11 Num sit ousalis, an Sphærica, n. 12 Argoli rationes ignis Sphæram post Aërís regionem constituendam, de medio tollentis inefficaces, ibid. n. 11 Num sit vitalis, n. 14 Num in Inferno sit tanquam in propria Sphæra, n. 13. & 247 n. 40 Ignis castitatis symbolum, 231. n. 10 Ignis fatuus, ibid. n. 15 Cur fugientes Insequatur, insequentes fugiat, ibid. Ignis lambens, & eius miræ conditiones, ibid. n. 16 Ignis in Inferno an Lumine, & cæteris qualitatibus ignis elementaris sit præditus, 247. n. 40

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78 INDEX Solar clocks without a gnomon, 443. n. 38 The horoscope as how it is a natural significator of life, 325. n. 40 Human signs have agreement and sympathy with human nature, 227. n. 44 In these, eclipses of the luminaries, or conjunctions of malefics, portend pestilence and other evils to mankind, ibid. This is proved by recent experience in Italy. ibid. The wondrous agreement and symmetry of the human body, 473. n. 121 Its order with the celestial bodies, ibid. The Moon, author and maker of the radical moisture, 207. n. 12. & p. 270. n. 47 The Hyades, rainy stars, 227. n. 46 Their significations in the horoscope, ibid. Ireland free from earthquakes, 303. n. 26 The wondrous qualities of mercury, 291. n. 62 Hydra, venomous stars, 228. n. 47 The winter solstice, why it is almost always clear, 462. n. 85 Winter, what it was among the ancients, what now, 228. n. 50 Continual under the poles, ibid. Double under the equator, ibid. Lightning rare in winter, except in Campania, ibid. I The gem Aspis is beneath Arcturus, 262. n. 64 By an occult quality it stops bleeding, ibid. &c Qu 1. n. 35 The icosahedron, one of the five kinds of regular bodies, 230. n. 8 It is also called by some Platonic bodies, 231. n. 8 Whether fire is fertile or sterile, 231. n. 10 Whether there is a sphere of fire in the hollow of the Moon, ibid. n. 11 Whether it is oval or spherical, n. 12 Argoli's reasons for establishing a sphere of fire after the region of air, and removing it from the middle, are ineffective, ibid. n. 11 Whether it is vital, n. 14 Whether in Hell it is as in its own sphere, n. 13. & 247 n. 40 Fire, symbol of chastity, 231. n. 10 Ignis fatuus, ibid. n. 15 Why it pursues those who flee, and flees those who pursue, ibid. Lambent fire, and its wondrous conditions, ibid. n. 16 Whether the fire in Hell is endowed with light and the other qualities of elemental fire, 247. n. 40

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RERVM MOBILIVM. 79 Ignis inter omnia agentia naturalia maxime actiuis. Qu. 1. n. 30 Imaginatiuæ vis in rebus timorem incutientibus, Qu. 3. n. 3 Imagines Astronomicæ an licitæ, 237. n. 23 Quonam pacto ijs iuuò, ac sine scrupulo vti possimus, ib. Imagines Coelestes instituendi quæ ratio, 234. n. 19 Cur è fabulis potissimum excerptæ, ibid. Cur tanta earum diuersitas, ibid. n. 20 Cur in vna plures, & disparatæ, ibid. Melius nunc cognita plenè Stellarum natura instituiu[m] possent, 333. n. 20 Schilleius easdem in Diuorum Imagines piè commuta- uit, quæ recensentur, 236. n. 20 & 334. n. 21 An non iua appositè, & cum plausu, ibid. Imagines Coelestes an occultam Philosophiam contineant, 236. n. 20 In magna Aula Patauina depictæ, 237. n. 22 An in primo mobili vllæ sint Imagines, & characteres, ibid. & 294. n. 69 Imperatorum, & Monarchiarum fata vnde sint, 44. n. 210 Imum Coeli cur Fouca ab Astronomis appelletur, 202. n. 42 Incidentiæ scrupula in Eclipsibus, quid sint, 162. n. 3 Inconiuncta signa sunt causa Antipathiæ rerum in hisce infe- rioribus, 242. n. 32 Indictio quid sit, & vnde dicta, 245. n. 37 Quomodo singulis annis competens facilè inueniatur, ibid. Indorum vanitas circa Horas coniunctionis Planetarum, 17. n. 79 Inferiora ista à superioribus tanquam à causis vniuersalibus reguntur, Qu. 2. n. 13 Infernus vnde dictus, 246. n. 39 Ex eo verus siderum locus obseruari posset, ni Telluris obstaret crassities, ibid. Quanta sit eius amplitudo, ibid. Tria in se continet receptacula, ibid. Quanium singula diffent à superficie terræ, ibid. An in eo verus ignis corporeus existat, ibid. n. 40 An eiusdem rationis cum nostro, ibid. An sit lumine, alijsque qualitatibus ignis elementaris prædius, ibid. n. 41 Quomodo terqueat Daemones, & animas separatas, ibid. Quare ignis Inferni sit nostro longè velocior, ibid. An montes Igniuiomi sint Inferni spiracula, è quibus

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OF MOVABLE THINGS. 79 Fire, among all natural agents, is the most active. Q. 1. n. 30 The force of imagination in things that inspire fear, Q. 3. n. 3 Astronomical images: whether they are lawful, 237. n. 23 In what way we may use them helpfully and without scruple, ib. The method of establishing celestial images, 234. n. 19 Why they are taken chiefly from fables, ibid. Why there is so great a variety among them, ibid. n. 20 Why several, and diverse, are in one, ibid. Could they not now, with a full knowledge of the nature of the stars, be instituted more suitably, 333. n. 20 Schilleius piously changed the same into images of the saints, which are listed, 236. n. 20 & 334. n. 21 Was not this done appropriately and with approval, ibid. Whether celestial images contain occult philosophy, 236. n. 20 Painted in the great Paduan Hall, 237. n. 22 Whether there are any images and characters in the first mobile, ibid. & 294. n. 69 Whence the fate of emperors and monarchies arises, 44. n. 210 Why the lower pole of the heavens is called Foucà by astronomers, 202. n. 42 What the scruples of incidence are in eclipses, 162. n. 3 Inconjunct signs are the cause of the antipathy of things in these lower regions, 242. n. 32 What an indiction is, and whence the term is derived, 245. n. 37 How the corresponding one for each year may easily be found, ibid. The vanity of the Indians concerning the hours of the conjunction of the planets, 17. n. 79 These lower things are governed by the higher as by universal causes, Q. 2. n. 13 Whence hell is called, 246. n. 39 From this the true position of the stars could be observed, if the thickness of the Earth did not obstruct it, ibid. How great its extent is, ibid. It contains three receptacles, ibid. How much each differs from the surface of the earth, ibid. Whether in it there exists a true corporeal fire, ibid. n. 40 Whether it is of the same nature as our fire, ibid. Whether it is endowed with light and other qualities of elemental fire, ibid. n. 41 How it torments demons and separated souls, ibid. Why the fire of Hell is far swifter than ours, ibid. Whether volcanoes are the vents of Hell, from which

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80 INDEX naturaliter euaporet Ignis, ibid. 5. 40 Historia de quadam horrisona Voragine in Turingia, n. 41 De Puteo Sancti Patricij in Hybernia, ibid. Cur Deus hæc Inferni ostia pluribus, ac diuersis in locis apparuerit, ibid. Ingressus Planetarum quid sint. n. 250. n. 44 Vaient ad actuandos effectus in radice præordinatos, ibid. Duplicates alij actiui, alij passui, ibid. Instans Natiuitatis elicere quam difficile, 207. n. 12. & seq. Quomodo artificiosè indagari possit, 30. n. 164. & seq. Quodnam dicendum sit verum instans Natiuitatis, 208. n. 14 Instrumentum Gnomonicum, 39. n. 187 Inter lunium quantum temporis amplectatur, 250. n. 46 Inter lunij tempore si sata serantur non sunt vermiculis obnoxia, ibid. Formicæ eo tempore otiosæ 452. n. 63 Interrogationes Astrologicæ an licitæ, 251. n. 47 Iris quid sit, 251. n. 49 Formatur tam à Sole quam à Luna, ibid. Nunquam conspicua in Meridie, nisi in hyeme, & quare, ibid. Eius præsagia, ibid. n. 50 Est serenitatis prænuntia, & quide naturaliter, ibid. n. 51 Cur manè pluuiam, vesperè serenum indicet, ibid. Si in Arbores incubauerit eas odoratiores facit, ibid. Iris Lunæ in quo à Solari differat, n. 49 Est Christi Domini humanitatis symbolum, n. 52 Iuglandis Vmbra cur dormientibus obsit. Qu. 1. n. 16. Iugularum nomine quæ Stellæ veniant, 254. n. 60 Iupiter vnde dictus, 254. 65. eius natura, ibid. In Pharmacis sumendis non est adeò idoneus, & quare, 167. n. 20 Eius astrum duabus Zonis conspicuum, 255. n. 63 Habet suos stipatores, ibid. 284. n. 31 Iouis mira obscuratio anno 1648. 163. n. 7 Quid portendat. ibid. L Lacus quidam cur salsedine præditi, 56. n. 264 Gæteri, etsi vastissimi, qua de re non sint salsi, ibid. n. 265 Latlap

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80 INDEX naturaliter euaporet Fire, ibid. 5. 40 History of a certain fearsome whirlpool in Thuringia, n. 41 Of the Well of Saint Patrick in Ireland, ibid. Why God has appeared in several and different places as the gates of Hell, ibid. Ingressus Planetarum, what they are. n. 250. n. 44 They tend to produce effects preordained in the root, ibid. Duplicates, some active, some passive, ibid. How difficult it is to determine the instant of Nativity, 207. n. 12. & seq. How it may be skillfully investigated, 30. n. 164. & seq. Which should be called the true instant of Nativity, 208. n. 14 Gnomonic instrument, 39. n. 187 How long the interlunar period lasts, 250. n. 46 If seeds are sown during the interlunium, they are not vulnerable to worms, ibid. At that time ants are idle 452. n. 63 Whether astrological interrogations are lawful, 251. n. 47 What the rainbow is, 251. n. 49 Formed by both the Sun and the Moon, ibid. Never visible at midday, except in winter, and why, ibid. Its omens, ibid. n. 50 It is a forerunner of fair weather, and indeed naturally so, ibid. n. 51 Why in the morning it indicates rain, in the evening fair weather, ibid. If it has settled on trees it makes them more fragrant, ibid. How the Moon’s rainbow differs from the solar one, n. 49 It is a symbol of the humanity of Christ the Lord, n. 52 Why the shade of the walnut tree is harmful to sleepers. Qu. 1. n. 16. What stars are meant by the name of the “neck” stars, 254. n. 60 Jupiter, whence so called, 254. 65. its nature, ibid. In medicines to be taken it is not so suitable, and why, 167. n. 20 Its star visible in two zones, 255. n. 63 It has its attendants, ibid. 284. n. 31 The amazing obscuration of Jupiter in the year 1648. 163. n. 7 What it portends. ibid. L Certain lakes, why endowed with saltness, 56. n. 264 Others, though most vast, for what reason are not salty, ibid. n. 265 Latlap

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INDEX 81. Laclaps Ventus. 237. n. 3 Lapides pretiosi vnde propriam virtutem, 292. n. 64 Lapidum pluuia ex Turbine, 317. n. 78 Latitudo quot modis accipiatur, 258. n. 13. & seq. An eius ratio habenda in directionibus, p. 113. n. 36 An in Aspectibus, p. 419. n. 6 Lazari Feretrum quid. p. 530. n. 47 Leones Febre laborant, Sole eiusdem nominis signum ingresso, 160 n. 16. & p. 236. n. 21 Sole in Leone existente potiones sumere, aut sanguinem mittere malum, ibid. Imago Leonis in Auro contra Cardiacam, p. 237. n. 23 Vestes non sub Leone scindendæ, aut tendendæ. p. 239 n. 25 Eius rei conveniens ratio. ibid. Cauda Leonis in Horoscopo dat ingenium atque honores amplissimos, p. 97 n. 53 Cor Leonis, vide Basiliscus, Regulus. Lepus in Horoscopo facit hominem miræ agilitatis, p. 260 n. 18. Libra quale signum, p. 261. n. 24 Sub Libra nati, an mortis suæ causa sint. p. 533. n. 6 Ratio Pontani expenditur, & rejicitur. ibid. Cum libra olim Scorpij sidus confundebatur, p. 83. n. 376 Limbus SS. Patrum, & Puerorum vide, Infernus, & Sinus Abrahæ. Linea quid sit apud Geometros, p. 262. n. 38 Linea incidentiæ, p. 162. n. 3 Linea Fiduciæ, seu Dioptra, p. 142. n. 33 Lippirudo oculorum ex luminatium congressu cum stellis nebulosis. p. 84. n. 9 Liquor è Coelo manans. Vide, Manna. Locus verus partis Fortunæ, p. 199. n. 35. Logistica quid sit, p. 264. n. 34 Longitude apud Astronomos quotaplex, p. 265. n. 35 A Longitudine auspicatur Orientalitas, & Occidentalitas locorum 16. idem n. 36. & seq. Ludorum Olympicorum Au[n]ctor quis fuerit. Vide Olympiades. Lumen est præcipuum siderum instrumentum, p. 265. n. 38 In singulis Planetis proprium, ibid. An sidera agant per luminis intentionem, vel extensionem, ibid. n. 39 An per veram, vel apparentem, ibid. f

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INDEX 81. Laclaps Ventus. 237. n. 3 Precious stones, whence their proper virtue comes, 292. n. 64 A shower of stones from a whirlwind, 317. n. 78 How many ways latitude is taken, 258. n. 13. & seq. Whether it should be taken into account in directions, p. 113. n. 36 Whether in aspects, p. 419. n. 6 What the bier of Lazarus is. p. 530. n. 47 Lions suffer from fever when the Sun enters the sign of the same name, 160 n. 16. & p. 236. n. 21 When the Sun is in Leo, it is bad to take potions or to let blood, ibid. The image of a Lion in gold against cardiac trouble, p. 237. n. 23 Clothes are not to be cut or stretched under Leo. p. 239 n. 25 The proper reason for this matter. ibid. The tail of the Lion in the horoscope gives talent and the highest honors, p. 97 n. 53 The heart of the Lion, see Basiliscus, Regulus. The hare in the horoscope makes a man of amazing agility, p. 260 n. 18. Libra, what sign it is, p. 261. n. 24 Those born under Libra, whether they are the cause of their own death. p. 533. n. 6 Pontanus’s argument is examined and rejected. ibid. In former times Libra was confused with the star of Scorpio, p. 83. n. 376 The limbo of the Holy Fathers and of children, see Hell and Abraham’s bosom. What a line is among geometers, p. 262. n. 38 The line of incidence, p. 162. n. 3 The line of confidence, or Dioptra, p. 142. n. 33 Blearing of the eyes from the meeting of luminous bodies with nebulous stars. p. 84. n. 9 A liquid flowing from heaven. See, Manna. The true place of Part of Fortune, p. 199. n. 35. What logistica is, p. 264. n. 34 How manyfold longitude is among astronomers, p. 265. n. 35 From longitude are inferred the easternness and westernness of places 16. same n. 36. & seq. Who was the author of the Olympic games. See Olympiades. Light is the chief instrument of the stars, p. 265. n. 38 Proper to each of the planets, ibid. Whether the stars act through the intention or extension of light, ibid. n. 39 Whether through real or apparent light, ibid. f

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Rerum Mobilium. Eorum luminis intensio, & ex ensio causat actiua. & passiuas qualitates in inferioribus, ibid. Vide, Lux Luminaria quæ dicantur, p. 267. n. 41 An per accessum, & recessum sint causa orius, & interius rerum, ibid. n. 40 Sunt causæ rerum vniuersales & æquiuocæ, ibid. n. 42 Cum diuersis Planetis congruidentia diuersi generis mixta, & animalia producunt, ibid. Quæ Luminarium defectiones pestilentiam, & alia mala adducant, ibid. Quam benè D Dionysius Areopagita, ex miro illo, ac formidabili luminarium defectu in Christi morte, mundi defectionem arguerit, ibid. Luminaribus si fortior, & supra ipsa Planeta eleueretur Satellitium Planeta cedet, p. 440. n. 13 Luna vnde dicta. Eius encomia ex S. Ambrosio, p. 268 n. 44 Efficacia ipsius in hæc inferiora, ibid. & p. 470. n. 113 Agit per lucis extensionem, ibid. Præest Picuitæ, & humido radicali, ibid. & 207 n. 12 Rorem affluenter adducit, 44 n. 53 Cum primum apparet illuminatur ex terræ reflexione, p. 269. n. 45 Triplex Mensis Lunæ. Periodicus, Synodicus, & apparitionis, p. 268. n. 44 Eius diameter quanta, p. 270. n. 47 Quid sin in eius disco maculæ, p. 269. n. 45 Lunæ stationes quæ, p. 271. n. 48 Phases quæ, ibid. An sit locus habitationi congruus, p. 270. n 46 An in eius superficie constituenda sit Paradisus Terrestris, ibid. & p. 355. n. 9. & seq. per 10:um. ibid. An ibi Henochi, & Elias, Si quis in Luna constitueretur ea omnia videret in superficie terræ, quæ nos in Luna conspicimus, p. 168 n 2. Lunæ Eclipsis, Vide Eclipsis, In Lunari Eclipsi Cyclosæpè deceptus, p. 218. n. 4 Lunaria herba Lunæ mutationes seruat, qu 1. n 20 Lusitani ob Aeris diversitatem in India diù viuere nequeunt, nisi eò pergant adolescentes, p. 111. n 131 Lustium quid sit, p. 245. n 37 Lux quid sit, & in quo à Lumine differat, p. 175. n. 50 Quibus corporibus competat lux, quibus lumen, ibid.

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Rerum Mobilium. Their intensity of light, and extension, causes active and passive qualities in lower things, ibid. See Lux What things are called luminaries, p. 267, n. 41 Whether by approach and recession they are the cause of the origin and interior of things, ibid. n. 40 That they are universal and equivocal causes of things, ibid. n. 42 How different kinds of mixed things and animals are produced by the harmony of different planets, ibid. Which eclipses of the luminaries bring pestilence and other evils, ibid. How well D. Dionysius the Areopagite, from that wonderful and dreadful eclipse of the luminaries at Christ’s death, argued the downfall of the world, ibid. If the satellite were stronger than the luminaries, and were raised above the planets themselves, the satellite would prevail over the planet, p. 440. n. 13 The Moon, whence so called. Its praises from St. Ambrose, p. 268 n. 44 Its efficacy in these lower things, ibid. & p. 470. n. 113 It acts by the extension of light, ibid. It presides over moisture and radical humidity, ibid. & 207 n. 12 It abundantly brings dew, 44 n. 53 When it first appears it is illuminated by reflection from the earth, p. 269. n. 45 The Moon’s threefold month: periodic, synodic, and of appearance, p. 268. n. 44 Its diameter, how great, p. 270. n. 47 What the spots on its disk are, p. 269. n. 45 The Moon’s stations, what they are, p. 271. n. 48 What its phases are, ibid. Whether it is a suitable place for habitation, p. 270. n. 46 Whether the Terrestrial Paradise is to be placed on its surface, ibid. & p. 355. n. 9. & seq. per 10:um. ibid. Whether there are Enoch and Elijah there, If someone were placed in the Moon, he would see on the surface of the earth all those things which we behold in the Moon, p. 168 n. 2. Lunar eclipse, see Eclipse, Often deceived by Cyclos in a lunar eclipse, p. 218. n. 4 The lunar herb preserves the changes of the Moon, qu 1. n 20 The Portuguese, on account of the diversity of the air in India, cannot live long unless they go there as young men, p. 111. n. 131 What lustium is, p. 245. n. 37 What light is, and in what it differs from lumen, p. 175. n. 50 To which bodies light belongs, and to which lumen, ibid.

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INDEX 83 Lyra fidus, quid cum Planetis præstet in Aeris mutationibus, p. 275. n. 53 Eius in Horoscopo significata, ibid. & p. 187. n. 13 Est Italix verticalis, ibid. Est maioribus fixis maior, excepto Sirio, ibid. M M Acelenti quare vt plurimum in maris recessu moriuntur, p. 37. n. 180 Maculæ in disco Lunari quid sint, p. 169. n. 45 Quid in Sole, p. 459. n. 78 Maculæ in Linteis ex Arborum fructibus contractæ, non deterguatur nisi ad foliorum ex ipsis decisionem, q. 1 n. 18 Magia quid sit, & vnde dicta, p. 276. n. 1 Ab Arabibus deprauata, ibid. Naturalis ex Medicina, Astrologia, & Religione coalescit, ibid. Magistralis ventus vnde dictus, p. 88. n. 22. & p. 276. n. 2 Magnetica vulnerum curatio, in digress. ad V. Sympar. per totum, Ea non est supra Naturæ vires, qu. 1. n. 23 Magneticæ curationis excellentia. qu. 3. n. 18 Magnetica curatio sit à Natura immediatè per aliquid excitara, qu. 3. n. 13 Magorum stella an fuerit Cometa, p. 95. n. 34 An eadem quæ in Cassiopea visa est anno 1572. ibid. &c p. 375. n. 39 Mala Fortuna, p. 256 n. 2 Maleficarum coniunctio in signo humano pestem indicat, p. 227. n. 44 Maleuentum cur olim appellata fuerit Vrbs Beneuentum, Malus Genius, p. 88. n. 2 p. 277. n. 3. & p. 105. n. 90 Manna quid sit, p. 434. n. 54. & seq. In Calabria lectissimum, ibid. eius productio. ibid. Manna Israëliticum an fuerit eiusdem rationis cum nostro, ibid. & p. 277. n. 8 Mare cur non redundet ad tantam Fluviorum accessionem, p. 56. n. 264. Margaritas cur soluat acetum, non aqua fortis, qu. 1. n. 16 Martis Planetæ qualitates, p. 279. n. 17 Effæminatus, ibid. & p. 196. n. 29 In Perigeo sub Sole sit, & magnum æstum facit, p. 179. n. 18 Sua habet Phases vt Luna, ibid. f ij

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INDEX 83 Lyra fidus, what it does with the Planets in changes of the air, p. 275. n. 53 Its signification in the Horoscope, ibid. & p. 187. n. 13 It is the vertical of Italy, ibid. It is greater than the greater fixed stars, except Sirius, ibid. M M Acelenti, why they most often die in the ebbing of the sea, p. 37. n. 180 What spots in the lunar disk are, p. 169. n. 45 What in the Sun, p. 459. n. 78 Stains on linens contracted from the fruits of trees are not washed away except by the falling off of the leaves themselves, q. 1 n. 18 What magic is, and whence it is so called, p. 276. n. 1 Corrupted by the Arabs, ibid. Natural magic is composed of Medicine, Astrology, and Religion, ibid. What the magistral wind is called from, p. 88. n. 22. & p. 276. n. 2 Healing of wounds by magnetism, in the digression to V. Sympar. throughout, It is not above the powers of Nature, qu. 1. n. 23 The excellence of magnetic healing. qu. 3. n. 18 Whether magnetic healing is brought about by Nature immediately through something aroused, qu. 3. n. 13 Whether the star of the Magi was a comet, p. 95. n. 34 Whether it was the same as that seen in Cassiopeia in the year 1572, ibid. &c. p. 375. n. 39 Bad Fortune, p. 256 n. 2 The conjunction of witches in a human sign indicates pestilence, p. 227. n. 44 Why the city Beneventum was formerly called Maleventum, Evil Genius, p. 88. n. 2 p. 277. n. 3. & p. 105. n. 90 What manna is, p. 434. n. 54. & seq. In Calabria very choice, ibid. its production. ibid. Whether the manna of the Israelites was of the same kind as ours, ibid. & p. 277. n. 8 Why the sea does not overflow with so great an influx of rivers, p. 56. n. 264. Why vinegar dissolves pearls, but not aqua fortis, qu. 1. n. 16 The qualities of the planet Mars, p. 279. n. 17 Effeminate, ibid. & p. 196. n. 29 It is in perihelion beneath the Sun, and makes great heat, p. 179. n. 18 It has phases like the Moon, ibid. f ij

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Rerum Mobilium. Aliquando pro Venere acceptus, p. 525. n. 24 Tycho in eius obseruatione fatiscens, ibid. An suos Stipatores habeat, vt Saturnus, & Iupiter, p. 279. n. 19 Est in fortuna minor & quare, p. 180. n. 20 Mars, & Saturnus si in Cælo non essent, homines immortales forent, p. 440. n. 15 Masculini, & Fæminini ratio in Planetis, & signis Philosophicè probata, p. 180. n. 22. & seq. Mathematica vnde dicta, p. 282. n. 27 Eius diuisiones, ibid. Medicamenta vulgaria sunt ad instar Lixirij, quæ naturam purgant quidem, sed simul eneruant, qu. 3. n. 10 Non sic extracta, & alia sublimiora, ibid. Medicamentum non est absolutè relinquendum, eo quod superstitiosis circumstantijs implicetur, si modò alias naturalem vim ad curandum habeat, qu. 2. n. 19 Medicæ stellæ quæ, & vnde denominatæ, p. 184. n. 31. & p. 255. n. 64 Medicus Naturæ sub fæmulatur, qu. 3. n. 10 Semper Ephemeridas præ manibus habere debet, p. 130. n. 191 Medusæ Caput Stella perniciosissima, verticalis olim Græcix, nunc Regno Neapolitano, p. 21. n. 108 Mel præcipuus siderum fructus, p. 185. n. 36. & p. 435. n. 35 Sub Cane Sirio salutaris, ibid. Mensium, & Signorum sympathia, & Antipatia, p. 245. n. 36 Mercurius Planeta omnium minimus, p. 185. n. 40 Est naturæ promiscu[m], ibid. Quæ de eo circumferuntur minus certa sunt, quàm quæ de Planetis reliquis, & quare, ibid. n. 41 In domo Saturni profundam dat rerum intelligentiam, ibid. n. 40 Motor ventorum, p. 520. n. 13 Meridiani quot in Cælo concipiendi, p. 286. n. 42 Primus vbi constituendus, ibid. & p. 75. n. 365 Meteora sunt siderum fructus, p. 288. n. 50 Sunt mixta imperfecta, ibid. n. 51 Miles Cometa, quid sua apparitione portendat, p. 189. n. 56 Milliaria quot comprehendant singuli gradus in æquatore, p. 213. n. 29 Minutum quid apud Astronomos, p. 289. n. 57

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Movable things. Sometimes taken for Venus, p. 525. n. 24 Tycho, wearied in observing it, ibid. Whether it has attendants, like Saturn and Jupiter, p. 279. n. 19 It is smaller in fortune, and why, p. 180. n. 20 If Mars and Saturn were not in the heavens, men would be immortal, p. 440. n. 15 The ratio of the masculine and feminine in the planets and signs, proved philosophically, p. 180. n. 22. & seq. Mathematica, whence so called, p. 282. n. 27 Its divisions, ibid. Common medicines are like Elixir, which indeed cleanse nature, but at the same time weaken it, qu. 3. n. 10 Not so the extracted and other more sublime ones, ibid. Medicine is not absolutely to be abandoned because it is involved in superstitious circumstances, if otherwise it has a natural power to cure, qu. 2. n. 19 What the healing stars are, and whence they are so named, p. 184. n. 31. & p. 255. n. 64 The physician is a servant of Nature, qu. 3. n. 10 He ought always to have almanacs at hand, p. 130. n. 191 Medusa’s Head, a most pernicious star, formerly vertical in Greece, now in the Kingdom of Naples, p. 21. n. 108 Honey, the chief fruit of the stars, p. 185. n. 36. & p. 435. n. 35 Under the Dog-star Sirius, salutary, ibid. The sympathy and antipathy of months and signs, p. 245. n. 36 Mercury, the smallest of all the planets, p. 185. n. 40 It is of mixed nature, ibid. What is circulated about it is less certain than what is said of the other planets, and why, ibid. n. 41 In the house of Saturn it gives a profound understanding of things, ibid. n. 40 Mover of the winds, p. 520. n. 13 How many meridians are to be conceived in the heavens, p. 286. n. 42 Where the first is to be established, ibid. & p. 75. n. 365 Meteors are the fruits of the stars, p. 288. n. 50 They are imperfect mixtures, ibid. n. 51 What a comet portends by its appearance, p. 189. n. 56 How many miles each degree in the equator contains, p. 213. n. 29 What a minute is among astronomers, p. 289. n. 57

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INDEX 85 Mixta quæ dicantur, p. 290. n. 60 Num eorum miræ qualitates purè Elementares sint, an verò ex coelestibus derivaræ, ibid. n. 33 Mixta quædam occulta quadam qualitate operantur, quæ longè Elementaribus præstar, q. 1. n. 32 Quare sola mixta perfecta sint congrua alimenta viuentium, p. 290. n. 60 Mobilia signa quæ & vnde dicantur. p. 292. n. 65 Sunt omnis mutabilitatis origines, ibid. Moderatores rerum qui sint dicendi ibid. n. 66 Se habent vt subjectum passibile respectu Astrorum, ibid. Significant genera rerum, ibid. An quinque tantum sint assignandi, ibid. & seq. Momentum Nariuitaris quodnam dicendum, p. 108. n. 14, Monstra Bicorporea, Gemelli nascuntur sub signis communibus, p. 120. n. 154 Montes igniuomi an sint inferni spiracula, p. 249 n. 41 Montium prominentiæ in Telluris globo perinde ac tuberculi in Aurantij poino, p. 33. n. 262 Morbi difficile curantur sub Procyone, p. 21. n. 109 Morbum comitialem pellit per sympathiæ vim Alcis vngula, qu. 3. n. 19 Moræ dimidiæ scrupula in Eclipsibus, quæ dicantur, p. 162 n. 5 Motus Coelorum quotuplex, p. 298. n 74. & seq. An morus Coelorum sit causa efficiens productionis rerum, p. 297. n. 72 Vtrum sit causa caloris in sublunaribus, ibid. n. 73 An sit Armonicus, p. 115. n. 138 Motus Diurnus Planetarum spiralis, p. 466. n. 98 Motus Coelorum est sicut motus cordis in animali, p. 310. n. 91 Octo genera morus retræmoti. p. 302. n. 26 Mundi nomine propriè quid veniat, p. 302. n. 81 An eo perfectior, & perfectior creari possit, p. 303 n. 83 Quo tempore creatus sit. ibid. n. 84 An potuerit esse ab æterno, ibid. Vnde cuidenter probetur eius initium, & desirio, p. 4. 8 n. 21 Quantum sit duraturus, p. 304. n. 85 An sit animarus, ibid. n. 86 An habeat saltem propriam formam substantialem, ibid. f iij

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INDEX 85 What mixed things are called, p. 290, n. 60 Whether their wonderful qualities are purely elementary, or rather derived from the heavenly bodies, ibid., n. 33 Certain mixed things operate by a hidden quality, which is far superior to elementary qualities, q. 1, n. 32 Why only perfect mixed things are suitable nourishment for living things, p. 290, n. 60 What are called movable signs, p. 292, n. 65 They are the origins of every kind of change, ibid. Who should be called moderators of things, ibid., n. 66 They stand as a passive subject in relation to the stars, ibid. They signify the kinds of things, ibid. Whether only five should be assigned, ibid. and following What is meant by the moment of nativity, p. 108, n. 14 Bicorporeal monsters, twins are born under common signs, p. 120, n. 154 Whether fiery mountains are the vents of hell, p. 249, n. 41 The prominences of mountains on the globe of the earth are like the little swellings on an orange, p. 33, n. 262 Difficult diseases are cured under Procyon, p. 21, n. 109 The hoof of a stag drives away epilepsy by the power of sympathy, q. 3, n. 19 What half-minutes of delay in eclipses are called, p. 162, n. 5 How many kinds of motion of the heavens there are, p. 298, n. 74 and following Whether the motion of the heavens is the efficient cause of the production of things, p. 297, n. 72 Whether it is the cause of heat in sublunary things, ibid., n. 73 Whether it is harmonic, p. 115, n. 138 The daily motion of the planets is spiral, p. 466, n. 98 The motion of the heavens is like the motion of the heart in an animal, p. 310, n. 91 Eight kinds of retrograde motion, p. 302, n. 26 What properly comes under the name of the world, p. 302, n. 81 Whether it can be created more and more perfect, p. 303, n. 83 At what time it was created, ibid., n. 84 Whether it could have been from eternity, ibid. By what means its beginning and origin are clearly proved, p. 4, 8, n. 21 How long it will endure, p. 304, n. 85 Whether it is animate, ibid., n. 86 Whether at least it has its own substantial form, ibid. f iij

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Rerum MobiliVM. 86. Mundi Natalis Thema, ibid. n. 83. & p. 43. n. 104 Mundus Vniuersus nobilissima vita præditus, p. 38 n. 89 Mundus Archetypus Deus, p. 303. n. 83 Mures naturali instinctu incumbentes terræ præsentiunt, p. 514. n. 27 Eorum iescora augentur in Bruma, p. 88. n. 25 Musicae vis in affectibus concitandis, p. 313. n. 100 Mutilata signa quæ, & vnde dicantur. p. 315. n. 105 N Natale solum cunctis animantibus dulcius, arque accom- modatius, p. 30 n. 164 Nati, sub Cane sirio exoriente, aqua nunquam intereunt, p. 21. n. 111 Natiuitatis Thema erigere, & inde hominis affectiones, & accidentia auspicare, an, & quousque sit licitum, p. 207 n. 12. & seq. Natiuitatis Thema erigendi modus ex D. Thoma, p. 30. n. 164 Natura omnis repatitur Cane Sirio exoriente, p. 21. n. 111 Naturæ nomine quid veniat, p. 316. n. 7 Qui distinguat:ur ab arte, ibid. Quonam pacto eius opera excitari possint, coadiuari, aut etiam præuerti, p. 318. n. 8 Natura Morborum vnica medicatrix, qu. 3. n. 10 Natura Arte suffulra breui tempore perficere porest quod se sola longum tempus exquirit, qu. 1. n. 24. Naturæ Arcana admirari potius nobis darum est, quam comprehendere, qu 2. n. 25 In Natura dantur diuersi generis Sympathiæ, p. 476 n. 116 Naturalium rerum virtutes non omnes nobis compertæ, qu. 1. n. 38 Navigatio cur citius in Occidentem, quam in Orientem fiat, p. 56. n. 267 Contra Helenæ fidus nauigantibus perniciosissimum, ridiculum Solini remedium, p. 233. n. 17 Neapolitanum Regnum terræ motibus obnoxium, p. 503 n. 26 Nebulosæ stellæ quæ dicantur, p. 319. n. 13 Cum luminaribus oculorum vitia adducunt, ibid & p. 230. n. 1. Nigræ Cometæ significata, p. 320. n. 21 Noctis variæ diuisiones, p. 327. n. 35

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Movable Things. 86. Theme of the World’s Nativity, ibid. n. 83. & p. 43. n. 104 The Whole World endowed with a most noble life, p. 38 n. 89 The Archetypal World, God, p. 303. n. 83 Mice, by natural instinct, foreseeing the earth beneath them, p. 514. n. 27 Their intestines increase in winter, p. 88. n. 25 The power of music in arousing the affections, p. 313. n. 100 Mutilated signs, what they are, and whence so called. p. 315. n. 105 N Native soil is sweeter and more suitable to all living creatures, p. 30 n. 164 Those born under the rising Dog Star never drown in water, p. 21. n. 111 Whether it is lawful to erect the Theme of Nativities, and from it to prognosticate a man’s dispositions and accidents, and how far, p. 207 n. 12. & seq. The manner of erecting the Theme of Nativities, from St. Thomas, p. 30. n. 164 Nature of all things suffers when the Dog Star rises, p. 21. n. 111 What is meant by the name of Nature, p. 316. n. 7 How it is distinguished from art, ibid. By what means its operations may be stirred up, aided, or even prevented, p. 318. n. 8 Nature of diseases is the sole physician, qu. 3. n. 10 Nature assisted by Art can in a short time accomplish what by itself it requires a long time to do, qu. 1. n. 24. It is given to us to admire the secrets of Nature rather than to comprehend them, qu. 2. n. 25 In Nature there are sympathies of different kinds, p. 476 n. 116 The virtues of natural things are not all known to us, qu. 1. n. 38 Why navigation is quicker to the West than to the East, p. 56. n. 267 Against Helen’s rope, most harmful to sailors, the ridiculous remedy of Solinus, p. 233. n. 17 The Kingdom of Naples is subject to earthquakes, p. 503 n. 26 What nebular stars are called, p. 319. n. 13 With the luminaries they bring on defects of the eyes, ibid. & p. 230. n. 1. The significance of black comets, p. 320. n. 21 The various divisions of the night, p. 327. n. 35

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INDEX 87 Nodi Lunares cum Luminaribus gibosos faciunt, & defor- mes, p. 325. n. 27 Nomina stellis fixis apposita, quam appositè, p. 194. n. 25 & p. 235. n. 19. p. 212. n 28 Nona domus naturalis itinerum, ac studiorum significatrix, p. 50. n. 6 Quomodo ad Religionem inclinet, ibid. Nona domus esti cadens nobilior est cæceris domibus, præter angulos, p. 80. n. 3 In Noruegia continui sunt crepusculi, p. 129 n. 189 Notarum Arithmecarum mirum inuenium, ac proportio, p. 3. n. 4 Notoria ars infamis, & aperiè superstitiosa, p. 296 n 70 Notus Ventus vnde dictus, p. 326. n 30 Si diu flauerit pestilentiam adducet, & quonam pacto, ibid. Nouenariæ Planetarum fictitiæ, p. 39. n. 193 Nouilunij præcisum tempus, qua arte obseruare possimus, p. 327. n 33 Quomodo per Epactam inueniatur, ibid. n 34 Nubecula Sereno Coelo in longum protensa, terræ morus signum, p. 304. n. 27 Numerales calculi antiquitus, pro numeris adhiberi soliti, p. 1. n. 4 Numerica proportio, p. 263. n. 33 Numerus Arithmericæ objectum. p. 328. n. 37 Olim ad censum millia tantum pertingebat, ibid. Angelica disciplina, ibid. n. 37 Numerus aureus, Vide Aureus Numerus, O Obesi decumbentes in Maris accessa vt plurimum moriun- tur, p. 37. n. 180 In Oceano Mari sex morus diuersi, p. 36. n. 206 Occidens ex Antiquis vbi constituitur, p. 330. n. 11 Vbi verius nunc temporis constituendus, p. 31. n. 373 & p. 287. n. 44 Cur citius in Occidentem, quam in Orientem fiat navi- gatio, p. 36. n. 267 Occursantes qui dicantur apud Astronomos, p. 311. n 14 Ab eis duplex in illis virtus consideratur, ibid n 15 Octaua, & Duodecima Coeli Domus, cur ineptæ, & mali omi- nis habeantur, p. 177. n. 55 Octaua Sphæra quæ sit. p. 133. n. 19 Eius imaginum distributio, ibid. f iiiij

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INDEX 87 The lunar nodes, when they are with the luminaries, make them gibbous and deformed, p. 325, n. 27 The names applied to fixed stars, how aptly, p. 194, n. 25 and p. 235, n. 19; p. 212, n. 28 The ninth house, natural significator of journeys and studies, p. 50, n. 6 How it inclines to Religion, ibid. The ninth house, although succedent, is more noble than the other houses, except the angles, p. 80, n. 3 In Norway the twilight is continual, p. 129, n. 189 The wonderful invention and proportion of arithmetical notations, p. 3, n. 4 The art of notory, infamous and openly superstitious, p. 296, n. 70 The Notus wind, from what it is so called, p. 326, n. 30 If it blow for a long time it will bring pestilence, and by what means, ibid. The fictitious ninefold divisions of the planets, p. 39, n. 193 The exact time of the new moon, by what art we may observe it, p. 327, n. 33 How it may be found by the epact, ibid., n. 34 A small cloud stretched out for a long time in a clear sky, a sign of an earthquake, p. 304, n. 27 Counting stones, formerly used for numbers, p. 1, n. 4 Numerical proportion, p. 263, n. 33 Number, the object of arithmetic, p. 328, n. 37 Formerly it barely reached the census of thousands, ibid. Angelical discipline, ibid., n. 37 The golden number, see Golden Number, O The obese, when lying down, for the most part die at the tide's advance, p. 37, n. 180 In the Ocean Sea there are six different tides, p. 36, n. 206 The West, where it was placed by the ancients, p. 330, n. 11 Where it ought more truly to be placed in the present time, p. 31, n. 373 and p. 287, n. 44 Why navigation is made sooner toward the West than toward the East, p. 36, n. 267 What are called occidents among astronomers, p. 311, n. 14 From these a twofold virtue is considered in those things, ibid., n. 15 Why the Eighth and Twelfth Houses of Heaven are held to be unfitting and of evil omen, p. 177, n. 55 What the Eighth Sphere is, p. 133, n. 19 The distribution of its images, ibid. f iiiij

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RERVM MOBILIVM. Melius oppldò institui posset, ibid. n. 16 Octi mestris partus cur non superuiuat, p. 241. n. 34. & seq Oppositio an sit semper radius Hostilis, p. 340. n. 32 Op. ima quæque sunt magis corruptioni obnoxia, qu. 1. n. 19 Orbis in quo defferat à Globo, & à Sphæra, p. 341. n. 34 Singulorum Planetarum o[mn]es, ibid. n. 35 Orbis piscis mira natura, quæ se ad spirantem ventum con- uertit vel mortuus, & vndè hæc affectio oriatur, p. 313. n. 18. & seq. Origanum aridum appensum, in Brumâ cur reslorescat, p. 38 n. 25 Orion sidus tempestuosum, p. 343. n. 42 In Horoscopo quid significet, ibid. Ostensorum quæ in sublimi aere videntur tria genera, p. 119 n. 152 Quid singula portendant, ibid. & in V. Pseudostella, Olympiades vnde, p. 337. n. 26. & seq. P Palilitium cur dicta sit stella in oculo australi Tauri consti- tura, p. 345. n. 1 Paracelsus vnguenti Armarij primus inuentor, qu. 2. n. 5 Ante ipsum tamen apud Antiquos aliqua eius notitia habira, ibid. Paracelsus à maledictis vindicatus, ibid. n. 27. & seq. Paradisus Terrestris an modò erter, & vbi constituatur, p. 270 n. 46. & seq. & p. 346. n. 4. & seq. Parados quid sit, p. 33. n. 248 Parallaxis quid sit, p. 360. n. 15 Quæ sidera Parallaxim habeant, ibid. n. 16 Paralleli declinationis qui sint, & quantæ efficacix, p. 361 n. 17. & p. 48. n. 217 Paralleli Cosmici, siue in mundo ad instar Antisciorum nuper inuenti, non minoris potentiæ. p. 363. n. 18 & seq. Item Paralleli Ascensionales, quorum ratio, & vis ex- plicatur, p. 361. n. 18 Parelia cur signa sint imminentis pluvix, p. 367. n. 25 Pars Fortunæ, Vide Fortuna, & in V. Lunaris Horosc. Fius noua, & subtilis consideratio, ibid. Partes Arabum an admittendæ, p. 367. n 29. & p. 201 n. 41. Parrus Masculinus, & Fæmininus, an, & qua ratione præ- uideri possit, p. 197. n. 30 Partus Septimestris, cur superuiuat, nunquam tamen

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OF MOVABLE THINGS. It could be better established in a town, ibid. n. 16 Why an eight-month birth does not survive, p. 241. n. 34. & seq. Whether opposition is always a hostile ray, p. 340. n. 32 The lowest things are the more liable to corruption, qu. 1. n. 19 How an orbit differs from a globe and from a sphere, p. 341. n. 34 The orbs of individual planets, ibid. n. 35 The wondrous nature of the fish-orb, which turns itself toward the breathing wind even when dead, and whence this property arises, p. 313. n. 18. & seq. Why dry marjoram hung up blossoms again in winter, p. 38 n. 25 The stormy star Orion, p. 343. n. 42 What it signifies in a horoscope, ibid. The three kinds of apparitions seen in the upper air, p. 119 n. 152 What each of them portends, ibid. & in V. Pseudostella, Olympiads, whence, p. 337. n. 26. & seq. P Why the star in the southern eye of Taurus was called Palilitium, p. 345. n. 1 Paracelsus, the first inventor of the pomade of the armory, qu. 2. n. 5 Yet before him some knowledge of it had existed among the ancients, ibid. Paracelsus vindicated from curses, ibid. n. 27. & seq. Whether the Earthly Paradise now exists, and where it is situated, p. 270 n. 46. & seq. & p. 346. n. 4. & seq. What a paradox is, p. 33. n. 248 What parallax is, p. 360. n. 15 Which stars have parallax, ibid. n. 16 What parallels of declination are, and how effective they are, p. 361 n. 17. & p. 48. n. 217 Cosmic parallels, or parallels recently discovered in the world in the likeness of antiscia, no less powerful. p. 363. n. 18 & seq. Likewise ascensional parallels, whose rationale and force are explained, p. 361. n. 18 Why parhelia are signs of impending rain, p. 367. n. 25 Part of Fortune, see Fortune, and in V. Lunar Horoscope. Its new and subtle consideration, ibid. Whether the Arabian Parts are to be admitted, p. 367. n. 29. & p. 201 n. 41. Whether the male and female birth can, and by what means, be foreseen, p. 197. n. 30 Why a seven-month birth survives, though neveretheless

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INDEX octimestris, p. 241. n. 34. & seq. Parauij in Magna Aula Monomæriæ depictæ, p. 237. n. 22 Sancti Patriitij puteus admirabilis in Hybernia, p. 249. n. 41 Pauones quomodo futurum terræ motum indicent, p. 504 n. 27 Pediculorum Historia sub linea Oceidentis morientium, p. 82. n. 374 Pegasus in Horoscopo facit Poëtam, p. 179. n. 63 Perihelium punctum quid, p. 52. n. 239 Perigæa Planetarum, sicut & Apogæa non semper fixa, p. 53 n. 250 Periscij, & Periæci populi qui dicantur, p. 370. n. 41. & 45 Persei sideris in Horoscopo significata, p. 372. n. 47 Perticæ Cometæ apparciis portenta, p. 374. n. 50 Pestilentia naturaliter sequitur terræ motum, p. 503. n. 26 Phalangij Apuli, seu tantulæ mira natura, qu. 3. n. 8 Eius variæ affectiones, & ictorum ab eo ad ecrtos sonos, ac saltus propensio explicantur, ibid. & seq. Phoenice cur dicta Polaris stella, p. 374. n. 56. & p. 27 n. 154 Phoenomena liber à quibus è Græco in Latinum translatus, p. 60. n. 277 Phoenomena sæpiùs in Coelo visa cuius substantiæ, p. 373 n. 59 Singulis bis mille annis insigne aliquod Phoenomenum apparere solitum, p. 96. n. 38 Piscium signi in Horoscopo significata, p. 379. n. 76 Pisces multi pulmone præditi, p. 513. n. 19 Piscis Orbis mira affectio, qua se ad spirantem ventum conuertit, ibid. n. 18 Vnde hæc affectio, vel in mortuo oriatur, ibid. Kircheri speculatio rejicitur, ibid. Auctoris sententia, ibid. Piscibus vniuersis Ventus nimium importunus, ibid. n. 19 Pithetes Cometæ genus, p. 379. n. 81 Planeta quando dicatur Posthetes, p. 52. n. 241 Planeta in Genethliacis vitæ rationem inhiens, p. 51 n. 238 Quas conditiones habere debeat, ibid. Planeta combustus cur debilis, p. 117. n. 146 An malesici combusti deteriores fiant, ibid. Planetæ quæ stellæ dicantur, p. 379: n. 81 Planetæ se mutuò respicientes contrahunt familiarita-

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INDEX octimestris, p. 241. n. 34. & seq. Parauij in Magna Aula Monomæriæ depictæ, p. 237. n. 22 Sancti Patriitij puteus admirabilis in Hybernia, p. 249. n. 41 How peacocks indicate an impending earthquake, p. 504 n. 27 History of lice dying under the line of the West, p. 82. n. 374 Pegasus in the horoscope makes a poet, p. 179. n. 63 What the point of perihelion is, p. 52. n. 239 The perigees of the planets, as well as the apogees, are not always fixed, p. 53 n. 250 Periscii and Periæci, what peoples they are called, p. 370. n. 41. & 45 Signification of the star of Perseus in the horoscope, p. 372. n. 47 Portents from the appearance of the comet Perticæ, p. 374. n. 50 Pestilence naturally follows an earthquake, p. 503. n. 26 The Apulian phalangium, or tiny creature, of wonderful nature, qu. 3. n. 8 Its various affections, and its propensity to strike at certain sounds, and to leap are explained, ibid. & seq. Why Phoenice is called the Pole Star, p. 374. n. 56. & p. 27 n. 154 The book Phoenomena, translated from Greek into Latin by whom, p. 60. n. 277 Of what substance the phenomena often seen in the sky are, p. 373 n. 59 An outstanding phenomenon used to appear every two thousand years, p. 96. n. 38 Signification of the sign of Pisces in the horoscope, p. 379. n. 76 Many fishes endowed with lungs, p. 513. n. 19 The wonderful affection of the Piscis Orbis, by which it turns itself toward the blowing wind, ibid. n. 18 Whence this affection arises, even in a dead one, ibid. Kircher's speculation is rejected, ibid. The author's opinion, ibid. The wind is too troublesome for all fishes, ibid. n. 19 Pithetes, a kind of comet, p. 379. n. 81 When a planet is called Posthetes, p. 52. n. 241 A planet, in genethliacs, considering the plan of life, p. 51 n. 238 What conditions it ought to have, ibid. A combust planet, why weak, p. 117. n. 146 Whether evil planets, when combust, become worse, ibid. What stars are called planets, p. 379: n. 81 Planets, when looking at one another, contract familiarita-

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Rerum Mobilium. tem, p. 85. n. 15 Plantæ multæ ad aliquarum viciniam læduntur, ad aliarum oblectantur, & viuidius efflorescunt, qu. 1. n. 13 Plantæ, quibus iris incubauerit, odoratiores redduntur, p. 251. n. 31 Platonica corpora quæ, p. 231. n. 8 Pleiades stellæ vnde dictæ, p. 38. 1 n. 89 Quot numero sinr, p. 183. n. 81 Earum in Horoscopo significata, p. 381. n. 89 In Pleniiunio Luna sup[er]ta Horizontem cum Sole sæpius visa, p. 424. n. 25 Eius rei rario, ibid. n 26 Pluuiæ iuges in Æstate mira naturæ prouidentia sub Zona torrida habitantibus opportunæ, p. 537. n. 14 Pluuijs Ver cur semper infestum, p. 526. n. 24 Polaris stella cur Phoenice dicta, p. 374. n. 56. & p. 27 n. 154 Olim Nautarum directrix, ibid. Nunc temporis non distat à Polo Mundi plusquam tribus gradibus, ibid. Num aliquando accidat, vt in Polum ipsum coincidat, p. 27. n. 115 Sub Polis nunquam tenebræ, p. 119. n. 118. & p. 516 n 12 Sub Polaribus Regionibus, an eadem sit aëris amoenitas, quam in nostris, ibid. Plinij assertum rejicitur, ibid. Est tamen ibi tolerandum frigus, ibid. Pontanus, Poëta magis, quam Astrologus, p. 383. n. 89 Præsepis stellæ in Horoscopo significata, p 386. n. 101 Sub Procyone difficiles admodum morborum curationes, p. 388. n. 108 Profectionum nomine apud Astronomos quidnam veniat, ibid. n. 110 Earum noua doctrina Philosophiæ consona, ibid. n. 111 Proportionalitatis diuisiones, p. 391. n. 115. & seq. Prorogatores qui dicantur, p. 391. n. 113 Prouincia nulla in Orbe quæ non sit commodè habitabilis, p. 337. n. 15 In hoc mira Numinis prouidentia commendatur, ibid. Puluis Sympathicus quid sit, & quomodo præparetur, qu. 1 n. 3 Vulneribus curandis ad miraculum factus, ibid. Prodest vel ipsis linceaminibus vulneratorum sanguine infectis, quantumuis loco dissitis applicatus, ibid.

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Of Mobile Things. tem, p. 85. n. 15 Many plants are harmed by the vicinity of some, delighted by others, and bloom more vigorously, qu. 1. n. 13 Plants on which iris has lain are made more fragrant, p. 251. n. 31 What the Platonic bodies are, p. 231. n. 8 From what the stars of the Pleiades are so called, p. 38. 1 n. 89 How many they are, p. 183. n. 81 What is signified by them in the Horoscope, p. 381. n. 89 At full Moon, the Moon above the Horizon together with the Sun has often been seen, p. 424. n. 25 The reason for this, ibid. n 26 Constant rains in Summer, by a wondrous provision of nature, are beneficial to those living under the torrid Zone, p. 537. n. 14 Why Spring is always troubled by rains, p. 526. n. 24 Why the Pole Star is called Phoenice, p. 374. n. 56. & p. 27 n. 154 Formerly the guide of sailors, ibid. At present it is no more than three degrees distant from the Pole of the World, ibid. Whether it ever happens that it coincides with the Pole itself, p. 27. n. 115 Under the Poles there is never darkness, p. 119. n. 118. & p. 516 n 12 Under the Polar Regions, whether the pleasantness of the air is the same as in ours, ibid. Pliny’s assertion is rejected, ibid. Yet the cold there must be endured, ibid. Pontanus, more a poet than an astrologer, p. 383. n. 89 What significance the stars of the Crib have in the Horoscope, p 386. n. 101 Under Procyon, cures of diseases are very difficult, p. 388. n. 108 What is meant among astronomers by the name of Profections, ibid. n. 110 Their new doctrine agrees with philosophy, ibid. n. 111 Divisions of proportionality, p. 391. n. 115. & seq. Who are called prorogators, p. 391. n. 113 There is no province in the world that cannot be conveniently inhabited, p. 337. n. 15 In this the wondrous providence of God is commended, ibid. What the sympathy powder is, and how it is prepared, qu. 1 n. 3 Made almost miraculous for healing wounds, ibid. It is useful even when applied to linen cloths infected with the blood of the wounded, however far away they may be from the place, ibid.

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INDEX. An idipsum præstet immediatè adhibitur: n. 9 An superstitionem vllam contineat, n. 10 An iuta conscientia adhiberi possit, ibid. & seq. per totam. Eius naturalis efficacia fusè probatur, ibid. q. 3 per totam. Pupilla Coeli cur dicta sit Lucida stella Coronæ Gnost. p. 26 n. 151 ibid. Eius significata in Horoscopo, ibid. Est tamen sidus tempestuosum, ibid. Puteales gradus apud Astrologos qui vide, Gradus. ibid. An fictitij, Q ibid. Qvadræ Lesbiæmira constructio, & effectus. p. 4. n. 5 Quadrantes Geometrici vsus, & officia, p. 403 n. 4. 5 Quadratus Aspectus quis, p. 406. n. 7. An semper Hostilis, ibid. & in V. Oppositio, Semi quadrati aspectus consideratio, p. 447. n. 39 De quadrati natura imperfectè participat, ibid. & seq. Eius ratio in Morbis tantum, & in aëris mutationibus auspicandis habenda, ibid. & p. 51. n. 238 Item in Aphetæ constitutione inter vndecimam, & duodecimam domum, ibid. Quadratura circuli quæ verè audiat, p. 408. n. 9 An dari possit, ibid. & seq. Qvæstiones, seu interrogationes Astrologicæ an licix, p. 251. n 47 Qualitas quid sit apud Philosophos, p. 410. n. 11 Qualitates acti suas facit intensio Lucis, passi suas extensio, ibid. & seq An dentur qualitates totius substantiæ, ibid. Qualitates mixtorum num sint Elementares, an potiùs eælestes, ibid. & in V. Mixta. An admittenda vlla qualitas occulta in Astris, p. 265 n. 38 Qualitas morbifica in quibusdam Zodiaci gradibus, an ex recessu aliquarum stellarum ab ijs locis recesserit, p. 50. n. 368 Qualitas Vindemiæ à die S. Urbani auspicanda, p. 388 n. 109 Quantitas quæ nam sit Mathesis objectum, p. 414. n. 17 Diuerso modo eam considerat Philosophus, & Mathe- maticus, ibid. Quintilis Aspectus de nouo agnitus, & eius ratio rationj

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INDEX. Whether the same thing is immediately applied: n. 9 Whether it contains any superstition, n. 10 Whether it can be used with a good conscience, ibid. & seq. throughout. Its natural efficacy is fully proved, ibid. q. 3 throughout. Why the Pupilla Coeli is called the Lucida stella Coronæ Gnost. p. 26 n. 151 ibid. Its meaning in the Horoscope, ibid. Yet it is a stormy star, ibid. The Puteales degrees among Astrologers; see Degree. ibid. of fictitious ones, Q ibid. Qvadræ Lesbiæ: its remarkable construction and effect, p. 4 n. 5 Quadrants: the use and functions of the geometric, p. 403 n. 4. 5 Quadrate Aspect: what it is, p. 406 n. 7. Whether it is always hostile, ibid. & in V. Oppositio, Consideration of the semiquadrate aspect, p. 447 n. 39 It participates imperfectly in the nature of the square, ibid. & seq. Its ratio is to be considered only in diseases, and in prognosticating changes of the air, ibid. & p. 51 n. 238 Likewise in the constitution of the Apheta between the eleventh and twelfth house, ibid. Quadrature of the circle: what it truly means, p. 408 n. 9 Whether it can be demonstrated, ibid. & seq. Qvæstiones, or astrological interrogations, whether lawful, p. 251 n. 47 Quality: what it is among philosophers, p. 410 n. 11 The qualities of the agent are made so by the intensity of light; those of the patient by extension, ibid. & seq. Whether there are qualities of the whole substance, ibid. Whether the qualities of mixed bodies are elemental, or rather celestial, ibid. & in V. Mixta. Whether any occult quality should be admitted in the stars, p. 265 n. 38 Morbific quality in certain degrees of the Zodiac: whether it has receded from the retreat of certain stars from those places, p. 50 n. 368 Quality of the vintage to be prognosticated from the day of St. Urban, p. 388 n. 109 Quantity: what its object is in mathematics, p. 414 n. 17 The philosopher and the mathematician consider it in different ways, ibid. Quintile Aspect newly recognized, and its ratio to ratio

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Rerum MobiliVM. consona, p. 417. n. 21 Biquintilis euanidus, p. 85. n. 15 Quotiens in numeris quis dicatur, p. 417. n. 22 R R adius quot modis accipiatur, p. 418. n. 2 Radij Hostiles, an aliquando benefici, Vide. Op- positio, R adius Quintilis, p. 416. n. 21 Rationalis methodus erigendi Coelestem figurat[ur], irrationa- lis, p 421 n. 5. In Recessu Maris Macilenti, vt plurimum moriuntur, in ac- cessu obesi, p. 37. n. 180 Eius rei ratio à Natura de sumpta, ibid. Reflexionis descriptio, & miracula, p. 423. n. 21 Eius beneficio habemus quot in Coelo sunt sidera, ibid. Refractiones quæ sint, & quæ modo fiant, p. 423. n. 24 & seq. Refractiones nullæ in meridie, ibid. Neque vllæ accidunt in Regione Etherea, ibid. Ob Refractiones sepè ambo luminaria supra horizontem conspiciuntur, cum infra sint, ibid. n. 25 Eam ob causam in plenilunio passim videntur ambo Luminaria supra horizontem, ibid. Regiæ stellæ quæ dicantur, p. 425. n. 28 Regio nulla inhabitabilis, p. 537. n. 15 Regio in regra ob terræ motum cum suis habitatoribus in mare translata; ibique per mensem integrum super- natans, p. 505. n. 29 Regulæ aureæ efficia & commoda, Vide. Aurea Regula, Regulus stellarum fixarum efficacissima, p. 426. n. 33. & 34 Solus inter fixas aspectus ad Planetas facit, & recipit, ibid. Remediorum inuentio omnis ex sympathiæ; aut antipathiæ consideratione desumpta, qu. 3. n. 24 Repletionis scrupula in Eclipsibus quæ sint, p. 62. n. 3 Respiratio prima viuentium operatio, p. 108 n. 14 Retrogradatio in Planetis quid sit, p. 427. n. 37 An in Malesicis bona, vel mala, ibid. n. 38 Quibus potissimum conueniat, ibid. & seq. Num verè vel apparenter, ibid. Reuolutio quid sit, p 428. n. 43 Quot modis accipiatur, ibid. n. 48 Nouus annuarum reuolutionum instituendarum modus; ibid. n. 42

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Of movable things. consona, p. 417. n. 21 Biquintilis euanidus, p. 85. n. 15 When one is said to be in numbers, p. 417. n. 22 R Radius, in how many ways it is taken, p. 418. n. 2 Hostile rays, whether they are ever beneficial, see Opposition, Radius Quintilis, p. 416. n. 21 Rational method of erecting the celestial figure, irrational, p. 421. n. 5. In the recession of the thin sea, the lean mostly die; in the approach, the fat, p. 37. n. 180 The reason for this is taken from Nature, ibid. Description of reflection, and its wonders, p. 423. n. 21 By its help we know how many stars are in heaven, ibid. What refractions are, and in what way they are produced, p. 423. n. 24 and following There are no refractions at midday, ibid. Nor do any occur in the ethereal region, ibid. Because of refractions, both luminaries are often seen above the horizon, when they are below it, ibid. n. 25 For that reason, at full moon both luminaries are commonly seen above the horizon, ibid. What are called royal stars, p. 425. n. 28 No region is uninhabitable, p. 537. n. 15 A region in Russia, transferred with its inhabitants into the sea because of an earthquake; and floating there for a whole month, p. 505. n. 29 The effects and advantages of the golden rules, see Golden Rule, The fixed star Regulus is most effective, p. 426. n. 33 and 34 Among the fixed stars alone, its aspect acts upon the planets, and receives from them, ibid. The discovery of remedies is entirely drawn from the consideration of sympathy or antipathy, qu. 3. n. 24 What the scruples of replenishment in eclipses are, p. 62. n. 3 Breathing, the first operation of living beings, p. 108. n. 14 What retrogradation in planets is, p. 427. n. 37 Whether it is good or bad in malevolent planets, ibid. n. 38 To which it chiefly belongs, ibid. and following Whether truly or apparently, ibid. What revolution is, p. 428. n. 43 In how many ways it is taken, ibid. n. 48 A new method of instituting annual revolutions, ibid. n. 42

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INDEX Adriani Negusantij nobile circa eius inuentum, ibid. 46. & seq. Ros quid sit, & quomodo fiat, p. 433. n. 31. & seq. Eius descriptio ex Aristotele, ibid. Est Serenitas indicium, ibid. Est Pecoribus in opportunus, ibid. Larga Roris cur Luna appelliterut, ibid. Rosa Allio complantata sit odoratior, qu. 3. n. 13 Rubrarum rerum vel solo intuitu sanguis accenditur, ibid. n. 11 Ruminantia signa quæ, p. 436. n. 62 Si po iones in iis fiant vomitum excitant, ibid. Rupes in Cyrene quam nefas sit atirectare, p. 316. n. 30 S Sagitta dicta Daemon meridianus, p. 135. n. 3 Saliua Canis reerrestris mortifera est hominibus, cum Ca- nis Coelestis sit salutaris. p. 435. n. 15 Sanguis in humano corpore perinde ac aër in Mundo, p. 308 n. 89 Mouetur circulariter circa cor, ibid. Sanguis ad conspectum rubrarum rerum accenditur, qu. 3. n. 22 In sanguine quamuis exciso, & exsiccato semper aliquid remanet primitivæ substantiæ, ibid. n. 23 Sanguis ex occisi corpore cur produat ad occisoris præ- sentiæm, ibid. n. 32 Sæpè etiam effunditur ad præsentiam gentilium, & ami- corum, ibid. n. 35 Ad sanguinem emittendum quæ tempora sint importuna, quæue opportuna, p. 167. n. 20 Sapphirus contra pestem singulare præsidium, qu. 3. n. 30 Sata si interlunij tempore lerantur non sunt vermiculis ob- noxia, p. 250. n. 46 Satellitium Planetarum ad Luminaria quid sit, p. 439 n. 12 & seq. In quo verè consistat, ibid. n. 13 Eius rei uariæ explicationes, vide. Doriphoria, Satellitium aliquando à Luminaribus ad Planetam tran- sit, si illis inuentus fuerit fortior, & super ipsa eleva- tum, ibid. Satellitium proprium habet Iupiter, & Saturnus, ibid. An reliqui Planetæ, ibid. Venus, & Mercurius sunt veluti solis Satellites, & stipa- tores, ibid.

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INDEX Adriani Negusantij, noble concerning his invention, ibid. 46. & seq. What dew is, and how it is formed, p. 433. n. 31. & seq. Its description from Aristotle, ibid. It is an indication of serenity, ibid. It is useful for livestock, ibid. Why a copious dew is called Moon, ibid. Whether garlic-planted roses are more fragrant, qu. 3. n. 13 At the mere sight of red things, blood is stirred, ibid. n. 11 What signs ruminants have, p. 436. n. 62 If potions are made in them, they provoke vomiting, ibid. The rock in Cyrene which it is sacrilegious to touch, p. 316. n. 30 S The dart called the midday demon, p. 135. n. 3 The saliva of the terrestrial dog is deadly to humans, whereas the Celestial Dog is salutary. p. 435. n. 15 Blood in the human body is just as air is in the world, p. 308 n. 89 It moves circularly around the heart, ibid. Blood is stirred at the sight of red things, qu. 3. n. 22 In blood, even when cut and dried, something of the primitive substance always remains, ibid. n. 23 Why blood from the body of the slain is produced at the presence of the killer, ibid. n. 32 It is often also shed in the presence of gentiles and friends, ibid. n. 35 At what times it is unfitting, and at what times fitting, to let blood, p. 167. n. 20 Sapphire, a singular safeguard against pestilence, qu. 3. n. 30 If seeds are sown during the new moon, they are not exposed to worms, p. 250. n. 46 What the satellite-system of the planets in relation to the luminaries is, p. 439 n. 12 & seq. In what it truly consists, ibid. n. 13 Various explanations of this matter, see Doriphoria, Sometimes the satellite-system passes from the luminaries to a planet, if a stronger one is found by them, and is raised above them, ibid. Jupiter and Saturn have their own satellite-system, ibid. Whether the remaining planets do, ibid. Venus and Mercury are as it were the satellites and attendants of the sun, ibid.

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54 RERVM MOBILIVM. Sarutnus Planeta Maleficus, p. 440. n. 15 Est cæteris Planetis cui su velocior, p. 114. n. 137 Eius qualitates explicantur, p. 440. n. 15 An sit calidus, & humidus, ibid. n. 16 Quid cum singulis Planetis associatus producat, ibid. Si Saturnus, & Mars non essent in Coelo, homines immortales forent, ibid. Scientiæ ope Daemonis comparatæ licitus imposterum erit vsus, qu. 1. n. 28 Sciethia à fulgure cur immunis, p. 229. n. 50 Scorpij signum fallax, p. 445. n. 27 Duo complectitur sidera, ibid. Olim cum Libra confundebatur, p. 33. n. 376 Scorpij imago in Bezaar certo tempore sculpta, an licitè adhibeatur aduersus Scorpionis iactus, p. 237. n. 23 Selenites Lunæ phases, ac mutationes exhiber, qu. 1. n. 20 Secundinæ puerperarum malè habitæ, ac sordido loco dejectæ immania symptomata ipsis pariunt, qu. 1. n. 8 Sensatio an absolutè sit gradus vitæ perfectiæ, p. 311. n. 93 Semi quadratus Aspectus an efficax, p. 447. n. 39 In morbis habet indicare de futura Crisi, ibid. In Lunationibus magnam vim obtinet ad faciendas aëris mutationes, ibid. n. 40 Eius ratio habenda est in electione Aphetæ constituti inter vndecimam, & duodecimam domum, ibid. Semisextilis aspectus euanidus, p. 241. n. 31 Septentrio Venius omnium saluberrimus, p. 59. n. 174 Septimestris Partus cur superuiuat, nunquam tamen Octimestris, p. 241. n. 34 Serpentis imago in Deserto an naturaliter ab ignitis Serpentibus iactus opitularetur, p. 236. n. 24 Sesquiquadratus aspectus de nouo obseruatus quanix sit efficacix, p. 450. n. 54 Quandoque vitam abscindendi vim habet, ibid. Sidera an influere habeant in opera artificiata, p. 239. n. 25 Signa Imperantia, vide Imperantia, sic intuentia, sic inconjuncta, Significatores quid apud Astrologos, p. 454. n. 67 An plures quam quinque instituendi, ibid. Singulis bis mille annis insigne aliquod sidus apparere solitum, p. 95. n. 35 Sinus Abrahæ an modò extet, & num in inferno, p. 455 n. 71 Sido ex oriente tota ferè natura concutitur, p. 21. n. 118

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54. MOVABLE THINGS. Saturn, Malefic Planet, p. 440. n. 15 It is the slowest of the other Planets, p. 114. n. 137 Its qualities are explained, p. 440. n. 15 Whether it is hot and humid, ibid. n. 16 What it produces when associated with the individual Planets, ibid. If Saturn and Mars were not in the heavens, men would be immortal, ibid. Whether, with the aid of science acquired from a demon, the use hereafter will be lawful, qu. 1. n. 28 Why Scythia is immune from lightning, p. 229. n. 50 The sign of Scorpio is deceptive, p. 445. n. 27 It comprises two stars, ibid. Formerly it was confused with Libra, p. 33. n. 376 Whether an image of Scorpio carved in bezoar at a certain time may be lawfully applied against the sting of a scorpion, p. 237. n. 23 Selenite shows the phases and changes of the Moon, qu. 1. n. 20 The afterbirths of women in labor, badly handled and thrown into a filthy place, produce terrible symptoms in them, qu. 1. n. 8 Whether sensation is absolutely a degree of perfect life, p. 311. n. 93 Whether the semi-quadrate aspect is effective, p. 447. n. 39 In diseases it has to indicate a future crisis, ibid. In lunations it has great power for causing changes in the air, ibid. n. 40 Its consideration must be taken into account in choosing the Apheta placed between the eleventh and twelfth house, ibid. The semi-sextile aspect is vanishing, p. 241. n. 31 The North Wind is the healthiest of all, p. 59. n. 174 Why the seven-month child survives, but never the eight-month child, p. 241. n. 34 Whether an image of a serpent in the desert would naturally help against attacks from fiery serpents, p. 236. n. 24 How effective the sesquiquadrate aspect newly observed is, p. 450. n. 54 It sometimes has the power to cut short life, ibid. Whether the stars influence works of artifice, p. 239. n. 25 Directive Signs, see Imperantia, likewise intuentia, likewise inconjuncta, What significators are among astrologers, p. 454. n. 67 Whether more than five are to be established, ibid. That a notable star is accustomed to appear every two thousand years, p. 95. n. 35 Whether Abraham's bosom still exists, and whether it is in hell, p. 455. n. 71 From the East almost all nature is shaken, p. 21. n. 118

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INDEX 93 Qui sub eo nascuntur nunquam aqua interiisse comper- ti sunt, ibid. Sirius an Sole maior, p. 94. n. 14. p. 194. n. 25. & p. 267. n. 41 Smaragdus virtutes à spica Virginis accipit, p. 192. n. 64 Solis encomia, p. 458. n. 75 Centrum omnium Planetarum, excepta Lunâ, non alio- rum siderum, ibid. Eius substantia formaliter ignea, ibid. n. 76 Eius figura Elliptica propè Horizontem, & quare, ibid. n. 79 Quid sint maculæ in eius disco conspicæ, ibid. n. 78 Eius magnitudo, ibid. n. 80 Sol vitalis potentia fons, & origo, p. 241. n. 34 Venus, & Mercurius sunt veluti Solis Satellites, & sti- patores, p. 439. n. 13 Solstitium quid & quotuplex, p. 461. n. 84 Aestiuale aqua prolectat, Hyemale è contra Serenum adducit, ibid. Sonum vllum an edant Coelestia corpora se mouentia, p. 115 n. 138 Sphæra vitrea Archimedis memorabilis, p. 77. n. 361 Alia longè insignior Christiani Danix Regis, p. 78 n 362 Spica Virginis Stella benignissima ad morum suauitatem, ac pietatem, naturaliter inclinans, p. 466. n. 98. & in V. Aluazel, Azimech. Splendor in quo differat à radio, & à Luce, p. 467. n. 102 Splendor Planetis tribuitur, Soli autem radius, ibid. Stellæ quot numero sint, p. 469. n. 107 Stella noua in Cassiopea an fuerit Cometes, p. 94. n. 33 Stella noua in pectore Cygni anno 1600. apparens, du- ransque vsque ad annum 1621. teliæto in loco quodam hiatu, quid significet, p. 449. n. 51. & p. 21. n. 116 Stella in genu Serpentarij apparens quid indicauerit, ibid. Stella in Aequatore perficit in hora, quantum velocis- simus cursor perficeret spatio annorum, 290. p. 5. n. 29 Stella Polaris cur olim Phoenice dicta, p. 27 n. 154 Olim Nautarum directrix, ibid. Stellæ in Orionis humero calores intendunt, p. 84. n. 7 An aliquando debent in ipsum Polum recidere, ibid. Stellæ nebulosæ offendunt oculos, ac ipsam potentiam visuam, ibid. n. 9

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INDEX 93 Those born under it are found never to have perished by water, ibid. Sirius, whether greater than the Sun, p. 94. n. 14. p. 194. n. 25. & p. 267. n. 41 The emerald receives its virtues from the Spike of Virgo, p. 192. n. 64 Encomiums of the Sun, p. 458. n. 75 The center of all the planets, except the Moon, not of other stars, ibid. Its substance formally fiery, ibid. n. 76 Its elliptical figure near the horizon, and why, ibid. n. 79 What the spots seen on its disk are, ibid. n. 78 Its magnitude, ibid. n. 80 The Sun, source and origin of vital power, p. 241. n. 34 Venus and Mercury are as it were the Sun’s satellites and attendants, p. 439. n. 13 What a solstice is, and how many kinds there are, p. 461. n. 84 In summer it attracts water; in winter, on the contrary, it brings clear weather, ibid. Whether heavenly bodies moving of themselves give off any sound, p. 115 n. 138 The memorable glass sphere of Archimedes, p. 77. n. 361 Another, far more distinguished, of King Christian of Denmark, p. 78 n. 362 The Spike of Virgo, a very benevolent star, naturally inclining to sweetness of character and piety, p. 466. n. 98. & in V. Aluazel, Azimech. How splendor differs from a ray and from light, p. 467. n. 102 Splendor is attributed to the planets, but a ray to the Sun, ibid. How many stars there are in number, p. 469. n. 107 Whether the new star in Cassiopeia was a comet, p. 94. n. 33 The new star appearing in the breast of Cygnus in the year 1600, lasting until the year 1621, by a certain gape of the sky in that place, what it signifies, p. 449. n. 51. & p. 21. n. 116 What the star appearing in the knee of Serpentarius indicated, ibid. A star in the Equator accomplishes in an hour what the swiftest runner would accomplish in the space of years, 290. p. 5. n. 29 Why the Pole Star was once called Phoenice, p. 27 n. 154 Once the guide of sailors, ibid. Stars in the shoulder of Orion intensify the heat, p. 84. n. 7 Whether at some time they ought to fall upon the Pole itself, ibid. Nebulous stars offend the eyes, and even the power of sight itself, ibid. n. 9

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RERVM MOBILIVM. Stellam Magorum indicat Plinius, p. 62. n. 288 Subsolanus, seu Eurus, p. 50. n. 235 Sympathiæ, & Antipathiæ rerum ratio in quo consistat, p. 474 n. 122. & seq. Sympathia inter homines nascitur ex locis figuræ permutatis, p. 488. n. 1. Sympathiæ rerum ex naturali connexione, aut similitudine, vide in verbo Sympathia, & in Quæstionibus passim, Aliquando obseruatur in rebus, natura, tempore, & loco dissitis, q. 3. n. 2. & 5. Triplex Sympathiæ genus in humano corpore, & in mundo, ibid. n. 7 Adhuc alia rerum mirabilis Sympathia, quæ ad tria hæc capita reduci non potest, ibid. n. 8 Veræ Sympathiæ, Antipathiæque affectiones enumerantur, atque expenduntur in V. Sympathia P. totum & qu. 3. à n. 8. in fine. T. Tabula graduum Masculinorum, & Fæminorum in signis, p. 197 n. 31 Tabula moræ foetus in vtero Matris, p. 516. n. 73 Tabula signorum inconiunctorum, p. 242. n. 32 Tarantulæ mira Symptomata, quæ parit in ictis, q. 3. n. 5. & seq. Ea vitreo olim loculo inclusa subsilire ad certos sonorum numeros visa, ibid. Tauri signum in Horoscopo quid significet, p. 488. n. 5 In tauro Coniunctio maleficarum celebrata, perniciem affert armatis, p. 489. n. 6 Sub tauro nati, taurorum naturam præseferunt, p. 236 n. 20 Tempus quid sit, p. 490 n. 10 An in primo mobili constituendum, ibid. Singulæ siderum circulationes, singulas temporum dimensiones præsignant, ibid. n. 11 An constet ex instantibus indivisibilibus, ibid. n. 12 & seq Temporum certæ mutationes in certis siderum sizigijs, p. 50. n. 236 Tempus accommodatum humores purgandi, p. 167 n 10 Tempus itineris, & navigationis, quale improprium, ibid. n. 19 Tenebræ

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OF MOVABLE THINGS. Pliny indicates the star of the Magi, p. 62. n. 288 Subsolanus, or Eurus, p. 50. n. 235 On what the rationale of Sympathy and Antipathy in things consists, p. 474 n. 122. and following. Sympathy among men arises from the exchange of the positions of figures, p. 488. n. 1. The sympathy of things from natural connection, or similarity, see under the word Sympathy, and in the Questions throughout, It is sometimes observed in things far apart in nature, time, and place, q. 3. n. 2. & 5. The threefold kind of Sympathy in the human body, and in the world, ibid. n. 7 Another wondrous Sympathy of things, which cannot be reduced to these three heads, ibid. n. 8 The true affections of Sympathy and Antipathy are enumerated and examined in V. Sympathia P. throughout & qu. 3. from n. 8. at the end. T. Table of masculine and feminine degrees in the signs, p. 197 n. 31 Table of the duration of the foetus in the mother's womb, p. 516. n. 73 Table of inconjunct signs, p. 242. n. 32 The wondrous symptoms of the tarantula, which it produces in its bites, q. 3. n. 5. & following. It was once seen enclosed in a glass case to leap at certain numbers of sounds, ibid. What the sign of Taurus in the Horoscope signifies, p. 488. n. 5 A conjunction of witches celebrated under Taurus brings ruin to armed men, p. 489. n. 6 Those born under Taurus display the nature of bulls, p. 236 n. 20 What time is, p. 490 n. 10 Whether it should be placed in the prime mobile, ibid. The individual revolutions of the stars presage the individual measures of time, ibid. n. 11 Whether it consists of indivisible instants, ibid. n. 12 & following Certain changes of times in certain syzygies of the stars, p. 50. n. 236 The time suitable for purging the humors, p. 167 n. 10 The time of travel and navigation, when improper, ibid. n. 19 Darkness

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Rerum Notabilium. 97 Tenebræ nullæ sub polis. p. 129. n. 18. & p 516. n 12. Tenebræ ante auroram cur magnopere intendantur, ibidem n 189 Terella quid sit. p. 501. n 24. Termini Planetarum apud Astrologos qui sint. p. 495. n. 19 & p. 190. n. 17 Probantur magis Ægyptii, quam Ptolemaici Ibidem. Eorum efficacia Philosophicè comonstratur ibidem. Terra Vniversi alterum cenrum p. 497. n. 21. Sessi [e]n[im] complanationem affectat. ibidem. Inde mundi initium, & finis evidenter ostenditur. Ibidem. Eam magnum aliquod animal dixit Keplerus. p. 501. n. 24. Eius stabilitas probata. Ibidem n 22. Illuminatur à Sole perinde ac altera Luna. Ibidem. n 25. Terræ motus quid sit. p 502. n. 26. Signa Terræ notum indicantia. Ibidem. n. 17. Quæ loca Terræmotibus sint obnoxia. Ibidem. n. 28. Quo tempore potissimum gerentur. Ibidem. Terræmotum lequitur Pettilentia. Ibidem. n. 19. An vllum contra ipsum remedium. Ibidem n 28. Thematis Natalitij rectificandi nova ratio Naturæ consona. p. 10. n. 164. Thyco in Lunaris Ecclipsis observatione sæpè deceptus p. 218 n. 9. In maris observatione satiscens. p. 515. n. 23. Trajanus legem sanvit ne domus edificandæ certos altitudinis pedes excederent. p. 505 n. 28. Transitus Planetarum qui sint, & quantæ potentiæ. p. 509 n. 54. In quo differant ab ingressibus, Ibidem An sint directionibus validiores Ibidem 5. Eorum a ij activi, alij passivi. Ibidem. Trini Radij esti acia. p 513. n. 66 Habet respondentiam ad quintam. Ibidem. Eius bonitatis ratio in quo consistat. Ibidem. n 67. Trisagium contra Terræmotem. p 503. n. 26. Sub Tropicis cur major Æstus sit, quam sub lineâ æquinoctiali 535. n. 11. Tropei venti Italiæ nimis infensi. p 514 n. 71. G

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Notable Things. 97 Darknesses are nowhere under the poles. p. 129. n. 18. & p. 516. n. 12. Why darkness before dawn is greatly intensified, ibid. n. 189 What a terella is. p. 501. n. 24. What the terms of the planets among astrologers are. p. 495. n. 19 & p. 190. n. 17 The Egyptian rather than the Ptolemaic are proved. Ibid. Their efficacy is demonstrated philosophically. Ibid. The Earth is the other center of the universe. p. 497. n. 21. It aims at flattening, indeed. Ibid. Hence the beginning and end of the world are clearly shown. Ibid. Kepler said it was a great animal. p. 501. n. 24. Its stability proved. Ibid. n. 22. It is illuminated by the Sun just as another Moon is. Ibid. n. 25. What the motion of the Earth is. p. 502. n. 26. Signs indicating the movement of the Earth. Ibid. n. 17. What places are subject to earthquakes. Ibid. n. 28. At what time they chiefly occur. Ibid. Pestilence follows an earthquake. Ibid. n. 19. Whether there is any remedy against it. Ibid. n. 28. A new method of correcting the natal figure, consonant with nature. p. 10. n. 164. Tycho often deceived in observing a lunar eclipse. p. 218 n. 9. Sufficiently accurate in observing the sea. p. 515. n. 23. Trajan enacted a law that houses to be built should not exceed a certain number of feet in height. p. 505 n. 28. What the transits of the planets are, and how powerful they are. p. 509 n. 54. In what they differ from ingresses. Ibid. Whether they are more powerful than directions. Ibid. 5. Some of them active, others passive. Ibid. The three rays of the spear. p. 513. n. 66 It has a correspondence to the fifth. Ibid. Wherein its goodness consists. Ibid. n. 67. Trisagion against an earthquake. p. 503. n. 26. Why there is greater heat under the tropics than under the equinoctial line. 535. n. 11. The Tropic winds of Italy, too hostile. p. 514 n. 71. G

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R E R V M Trutina Hermetis quid, Ibidem. n. 73 An quicquam soliditatis habeat, Ibidem. Turbo quid p. 117 n. 78 In quo differat ab Ecnephia, Ibidem. Insigne contra turbinem tutamentum, Ibidem. Typho Ventus in quo differat à turbine, p. 518 n. 80 Quanta sit ejus vis, Ibidem. n. 81 Ex eo portentosæ non semel saxorum pluuix exortæ, Ibidem. V V Apos quid sit, p. 288 n. 52 Vegetatio per se loquendo non est gradus vitæ perfectior, p. 311 n. 9. Ventus quid sit, p. 119 n. 11 An acr commotus, Ibidem. n. 12 Quomodo generetur, n. 13 Ventorum species numerus, & nomenclario, n 16 Omnes ex sui natura ejusdem sunt rationis, & qualitatis, n. 14 A Regionibus vnde spirant, & per quas transeunt novas qualitates accipiunt, Ibidem. Omnes lateraliter mouentur, n. 13 Eorum commoda, n. 17 Numinis prouidentia in Ventorum distributione, Ibidem. Ventorum natura mutatur in Regno Chile, p. 76 n 360 Ventus piscibus importunus, p. 513 n. 19 Ad eam partem vbi spirat naturaliter vestitur piscis Orbis, Ibidem. Vndesit talis affectio, Ibidem. Venus omnium stellarum pulcherrima, p. 524 n. 20. Est Terra minor, Ibidem. Vnbram facit, & easdem Phases habet quas Luna, Ibidem. Quantum distet à Terra, Ibidem. Voluptatem asterie in membro, cui præest signum, in quo ipsa reperitur natiuitatis tempore, Ibidem. n. 21 Eius natura, Ibidem. An soli contraria, Ibidem. n. 22

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THINGS What the “Trutina Hermetis” is, ibid. n. 73 Whether it has any solidity, ibid. What a turbo is, p. 117 n. 78 How it differs from ecnephia, ibid. An outstanding protection against a whirlwind, ibid. Typho: in what the wind differs from a whirlwind, p. 518 n. 80 How great its force is, ibid. n. 81 From it, prodigious showers of stones have not once arisen, ibid. V What Vapos is, p. 288 n. 52 Vegetation, speaking properly, is not a higher degree of life, p. 311 n. 9. What wind is, p. 119 n. 11 Whether it is agitated air, ibid. n. 12 How it is generated, n. 13 The kinds, number, and nomenclature of the winds, n. 16 All are by their nature of the same kind and quality, n. 14 From the regions from which they blow, and through which they pass, they acquire new qualities, ibid. They all move sideways, n. 13 Their advantages, n. 17 Divine providence in the distribution of the winds, ibid. The nature of the winds is changed in the kingdom of Chile, p. 76 n. 360 The wind is troublesome to fish, p. 513 n. 19 On that side where it naturally blows, the fish is clothed with the orb, ibid. Whence such an affection arises, ibid. Venus, the most beautiful of all the stars, p. 524 n. 20. It is smaller than the Earth, ibid. It casts a shadow and has the same phases as the Moon, ibid. How far it is from the Earth, ibid. Astrological pleasure in the member over which the sign presides, in which it is found at the time of nativity, ibid. n. 21 Its nature, ibid. Whether contrary to the Sun, ibid. n. 22

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NOTA BILIVM. 59 An aliquando colorem, magnitudinem, vigutam, motum mutauit, n. 23 Tychonis in ejus obseruatione deceptio, ibidem. Ver sumendis portionibus opportunum, p. 167 n. 20 Veris qualitates, p. 515 n. 24 In Vere mundus creatus, ibidem. Vestes non sunt sub Leone scindendæ, p. 239 n. 25 Vigiles cur dictæ stellæ in Cynosura, p. 517 n. 35 Vindemi Vbertas, aut raritas à die S. Urbani auspicatur, p. 388 n. 109 Vindemiator cur dicta stella in ala Virginis, p. 518 n. 36 Vinum, Cicuræ antidotum, p. 291 n. 61 Vinum indoliis fluctuat sirio exoriente, p. 31 n. 111 Violemia signa, & stellæ quæ sint, p. 517 n 37 Quos effectus pariant, ibidem. Virgæ quid sint, p. 518 n. 38 In quo differant ab Itide, ibidem. Pluuiæ ingruentis manifestum judicium, ibidem; Vita Mundi altruitur, & probatur, p. 307 n. 89 Et est perfectior vita omnium animantium, p. 311 n. 94 Vita duplex in homine intellectualis, & animalis, ibidem Vitriolum habet naturalem antipathiam cum sanguine, qu. 1. n. 17 Vmbra in locis Antisciis, Amphisciis, ac Perisciis multi- plex, p. 49 n. 231 Vmbra vbi versatilis, p. 110 n. 117 Vnguenti Armarij descripso, & virtus, Qu. 2 à n. 4 & seq. Eius aliquam notitiam habuerunt Antiqui, ibidem. n. 3 Diuersimodè à diversis Auctoribus traditur, ibidem. n. 22 & seq. Ab aliquibus non sine superstitionis admixtione, ibi- dem. Quomodo naturaliter operetur, qu. 3. per totam. Vngula Aleis aduersus morbum comitialem, qu. 3. n. 19 Vniones quare soluat Acetum, non Aqua fortis, q. 1. n. 36 Vomitum excitant rumiantia signa, p. 436 n. 61 Vorago in Turingia horisona, p. 249 n. 41 Vrinæ ardorem contrahit ad Siluestrem vrticam mingens; qu. 1. n. 16 Vrla duplex in Cælo, p. 519 n. 47 g ij

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NOTA BILIVM. 59 Whether it ever changed color, magnitude, force, motion, no. 23 Tycho’s error in his observation of it, ibid. Spring, fitting for taking portions, p. 167 n. 20 Qualities of spring, p. 515 n. 24 The world created in spring, ibid. Clothes are not to be cut under Leo, p. 239 n. 25 Why the stars called Vigiles are in the Cynosura, p. 517 n. 35 Fruitfulness, or scarcity of the vintage, is foretold from St. Urban’s day, p. 388 n. 109 Why the star in Virgo’s wing is called Vindemiator, p. 518 n. 36 Wine, the antidote to Cicuræ, p. 291 n. 61 Wine in casks swells with Sirius rising, p. 31 n. 111 Violemia signs, and what stars they are, p. 517 n. 37 What effects they produce, ibid. What the Virgæ are, p. 518 n. 38 In what they differ from the Ictis, ibid. Manifest judgment of an approaching rain, ibid.; The life of the world is nourished, and proved, p. 307 n. 89 And it is the more perfect life of all living creatures, p. 311 n. 94 A twofold life in man, intellectual and animal, ibid. Vitriol has a natural antipathy with blood, qu. 1. n. 17 Shadow in places of Antiscians, Amphiscians, and Periscians, manifold, p. 49 n. 231 Where the shadow is movable, p. 110 n. 117 Description and virtue of the Armary unguent, Qu. 2 from n. 4 and following The ancients had some knowledge of it, ibid. n. 3 It is variously handed down by different authors, ibid. n. 22 and following By some, not without a mixture of superstition, ibid. How it works naturally, qu. 3. throughout. Goat’s hoof against the falling sickness, qu. 3. n. 19 Why vinegar dissolves pearls, but not aqua fortis, q. 1. n. 36 Ruminating signs excite vomiting, p. 436 n. 61 A whirlpool in Thuringia full of sound, p. 249 n. 41 Urine contracts burning by urinating on the wild nettle; qu. 1. n. 16 A double Urla in the sky, p. 519 n. 47 g ij

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RERVM NOTABILIVM. Vrsa minor naturarum directrix, ibidem. Vrsamajor Helice dicta, p. 119 n. 13 Vulturnus ventus vnde dictus, p. 530 n. 11 Eius qualitates perniciosæ, ibidem. Reddit objecta oculis majora, quam verè sint, ibid. Vnde id oriatur, ibidem, & seq. X X Yphiæ cometes, natura, & significata, p. 531 n. 1 Z Z Enit apud Arabes idem ac punctus verticalis, p. 532 n. 3 In costellæ maximæ sunt efficaciæ, ibidem. Caput Medusæ nunc temporis Regno Neapolis Verticalis, ibidem. Zephirus ventus vnde dictus, ibidem, n. 4 Est Venationi contrarius, ibidem, n. 5 Zischas Hæreticus quo consilio sibi mortuo detrahi pellem mandauit & ex catympanum confici. qu. 3. n. 38 Zodiacus vnde dictus, p. 533 n. 7 Duplex est sensibilis, & imaginarius, p. 534 n 8 Sensibilis sensim ab imaginario recessit, ibidem. Quod ideò quæ de signis Zodiaci ab Antiquis tradita sunt nunc temporis, minus veritati respondent, ibid. Zonæ quot sint, ibidem. n. 9 An omnes commodè habitabiles, p. 535 n. 10 An sub Æquatore sit jucundissima habitatio, p. 535 n. 11 In Æstare sub Æquatore, & sub tropicis juges pluuix, p. 537 n 14 Antonij Pomæ Missionarij celebre de hac re testimonium, ibidem, n. 15 Cur id accidat naturaliter, demonstratur, ibidem. Dei in hoc summa prouidentia commendatur, ibidem. FINIS.

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NOTABLE THINGS. Ursa Minor, the directrix of natures, ibidem. Ursa Major, called Helice, p. 119 n. 13 The wind Vulturnus, from whence so called, p. 530 n. 11 Its harmful qualities, ibidem. It makes objects seen by the eyes appear greater than they truly are, ibid. Whence this arises, ibidem, & seq. X X Yphia’s comet, its nature and significance, p. 531 n. 1 Z Z Enit among the Arabs is the same as the vertical point, p. 532 n. 3 In the greatest constellations there are powers, ibidem. The Head of Medusa, now in the Kingdom of Naples, vertical, ibidem. Zephirus, the wind, from whence so called, ibidem, n. 4 It is contrary to hunting, ibidem, n. 5 Zischas the heretic, for what purpose he ordered his skin to be stripped from his dead body and made into a tambourine. qu. 3. n. 38 Zodiac, from whence so called, p. 533 n. 7 It is twofold, sensible and imaginary, p. 534 n. 8 The sensible gradually withdrew from the imaginary, ibidem. For this reason, the things concerning the signs of the Zodiac handed down by the Ancients nowadays correspond less to the truth, ibid. How many zones there are, ibidem. n. 9 Whether all are conveniently habitable, p. 535 n. 10 Whether habitation under the Equator is most pleasant, p. 535 n. 11 In summer under the Equator, and under the tropics, continual rains, p. 537 n. 14 The celebrated testimony of Antonij Poma, missionary, on this matter, ibidem, n. 15 Why this happens naturally, is demonstrated, ibidem. Herein the highest providence of God is commended, ibidem. THE END.

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INDEX INSIGNIORVM QVÆSTIONVM, quæ in hoc Opere ex occasione examinantur. Numerus appositus & marginalis singulis literis proprius, & cuivis editioni accomodatus. AN Aqua sit terra maior. A. num. 270. An sit Animata A. 269. & M. 38. An moueatur motu vniversitatis A. 267. & 180. & M. 73. An sub Æquatore sit temperatissimum Clima. C. 119. & Z. 10. An sub Æquatore hyems sit æstate, calidior. Z. 10. Per quid Astragant in hæc inferiora. L. 38. An Astravel potius cælu in quo sunt moueantur. M. 76. An præter motum vniversitatis habeant suum peculia- rem motum. M. 75. & seq. An ullam activitatem habeant in opera artificata I. 23 Astrologicæ Questiones, seu interrogationes an licite. I. 47. Qua ratione Astracum sensu, & vegetatione careant vitam sensibilibus ac vegetabilibus tribuant. M. 93. An Calorum substantiasit diversa à sublunarium C 19. & S. 113. An Cali per motum Vocalem sonum edant. C. 138. An sint Animati C. 140. & M. 18. An per motum causent calorem in sublunaribus. M. 73.

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INDEX OF THE MORE IMPORTANT QUESTIONS, which in this Work are examined as they arise. The number placed in the margin is proper to each letter, and adapted to every edition. Whether water is greater than the earth. A. no. 270. Whether it is animate. A. 269. & M. 38. Whether it is moved by the motion of the universe. A. 267. & 180. & M. 73. Whether under the Equator the climate is most temperate. C. 119. & Z. 10. Whether under the Equator winter is colder than summer. Z. 10. By what they are conveyed into these lower regions. L. 38. Whether the stars rather move in the heavens in which they are. M. 76. Whether, besides the motion of the universe, they have their own particular motion. M. 75. & seq. Whether they have any activity in artificial works. I. 23. Astrological questions, or inquiries, whether they are lawful. I. 47. By what reason the stars, lacking sense and vegetation, grant life to things endowed with sense and to plants. M. 93. Whether the substance of the heaven is different from that of the sublunary things. C. 19. & S. 113. Whether the heavens by vocal motion emit sound. C. 138. Whether they are animate. C. 140. & M. 18. Whether by motion they cause heat in sublunary things. M. 73.

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INDEX. Quodnam si Climacteris temperatius. C. 129. Quænam sit substantia Cometarum. C. 149. ß seq. p. 59. Quid ß quotuplex sit Directionis motus, ß an Realis D. 35. ß seq. Decubitum momentum computari ne debeat ab initio morbi, an potius à posizione decumbentis in letto, D. 11. An comets non tam malorum, quam bonorum sint naturales significatores. p. 129. ß seq. Qua ratione culmen sit naturalis actionum significator. C. 98. Dierum Criticorum ratio vnde exorta. C. 191. Domicilij ratio in Planetis naturaliter probata. D. 51. ß T. 19. Quænam ex Dignitatibus Planetarum sint efficaciores essentiales ne an verò accidentales. D. 30. Electiones ex Asbris an licitæ. E. 18 ß seq. Quid sit Elenatio siderum super sidera. E. 26. ß seq. An in Planetis prærogatina exaltationis sit potior jure Domicilij. E. 79. ß seq. Quot genera familiaritatum Philosophica ratione inter Astra constituenda. A. 320. ß F. 3. ß seq. Vnde fata Imperiorum ß Monarchiarum A. 210. Finium ratio apud Ægyptios ß Chaldaos vnde probata. F. 17. ß T. 19. Firmamentum num solidum sit an fluidum. F. 20. Fixæ an sint Planetis validiores. F. 23. ß seq. An sint propria luce præditæ, quàm nullatenus à sole participent. Ibid. ß S. 24. Quinam dicendus sit Genitura vel Anni Dominus. D. 55. ß seq. An insignis dentur gradus fortitudinis, aut debilitatis. A. 168. An Fidelitæ sint cæteræ graduum distinctiones in fæmini,

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INDEX. What the climacteric should be if more temperate. C. 129. What the substance of comets may be. C. 149. and following, p. 59. What, and of how many kinds, the motion of Direction is, and whether it is real. D. 35. and following. Whether the moment of lying down should not be calculated from the beginning of the disease, or rather from the position of the patient lying in bed, D. 11. Whether comets are not natural significators of good things as much as of evil. p. 129. and following. By what reasoning the culminating point is the natural significator of actions. C. 98. Whence the system of critical days arose. C. 191. The reason for domicile in the planets, naturally demonstrated. D. 51. and T. 19. Which of the dignities of the planets are the more effective, essential or rather accidental. D. 30. Whether elections from the stars are lawful. E. 18 and following. What the elevation of the stars above the stars is. E. 26. and following. Whether in the planets the prerogative of exaltation is by right superior to domicile. E. 79. and following. How many kinds of familiarities are to be established among the stars by philosophical reasoning. A. 320. and F. 3. and following. Whence the fates of empires and monarchies. A. 210. The reason of bounds among the Egyptians and Chaldeans, whence proved. F. 17. and T. 19. Whether the firmament is solid or fluid. F. 20. Whether fixed stars are stronger than planets. F. 23. and following. Whether they are endowed with their own light, in no way participating from the sun. Ibid. and S. 24. Who ought to be called the Lord of the Nativity or of the Year. D. 55. and following. Whether there are notable degrees of strength or weakness. A. 168. Whether there are other distinctions of degrees in females,

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INDEX. nos, [Sol] Masculinos plenos [Sol] vacuos [Sol]c. F. 19. [Sol] G. 30. An [Sol] quæ ratione Horoscopus sit naturalis Vitæ significator. H. 40. Ignis sphæra an detur [Sol] vbi constituenda. L. 11. 12. [Sol] 41. Num dicendus sit foecundus an sterilis. I. 10. Num ejus figuræ sit onalis vel Sphærica. L. 12. Ignis gehennæ an sit corporeus, [Sol] ejusdem rationis cum nostro. L. 40. An luce atque ijsdem qualitatibus ignis elementaris sit præditus. Ibid. Quanta sit inferni Diameter [Sol] amplitudo. I. Ibidem. An montes igninomini sint inferni spiracula. Ibidem. 41. Imagines Astronomicæ an naturali vi præditæ, ac licitè adhiberi possint. L. 23. [Sol] seq. Imagines Cælestes an ullam cum terrestribus connexionem habeant. G. 28. [Sol] L. 19. [Sol] seq. An laudabiliter in Divorum imagines commutatæ. L. 24. [Sol] O. 23. Iris cur mane apparens indicet pluviam Vespere autem serenum. I. 51. Latitudinis ratio num habenda sit in Moderatoribus ad siderum radios dirigendis. R. 6. Cur luminarium defectus pestilentiam, [Sol] alia mala naturaliter indicent. P. 6. An sint bonorum etiam Autores, [Sol] signa E. 6. Lumen astrorum an operetur per sui extentionem veram vel apparentem. L. 39. Luna an sit habitabilis. L. 46. Quidnam sint maculæ in Disco Lunari. L. 45. An Mars sit Planeta Masculus, vel femineus. F. 29. M. 17. [Sol] 22. Cur Vespere post Crepusculum, [Sol] mane ante Auro} é ij

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INDEX. nos, [Sun] Masculine full [Sun] empty [Sun] c. F. 19. [Sun] G. 30. Whether the Horoscopus is by what reason the natural significator of Life. H. 40. Whether the sphere of Fire is granted [Sun] where it is to be placed. L. 11. 12. [Sun] 41. Whether it ought to be called fertile or sterile. I. 10. Whether its figure be oval or spherical. L. 12. Whether the fire of Gehenna is corporeal, [Sun] of the same nature as ours. L. 40. Whether fire endowed with light and the same qualities as elementary fire. Ibid. What the diameter [Sun] extent of hell may be. I. Ibidem. Whether the burning mountains are the vents of hell. Ibidem. 41. Whether Astronomical Images are endowed with natural force, and can lawfully be used. L. 23. [Sun] seq. Whether Heavenly Images have any connection with earthly things. G. 28. [Sun] L. 19. [Sun] seq. Whether they are laudably changed into images of the Saints. L. 24. [Sun] O. 23. Why the rainbow appearing in the morning indicates rain in the evening, but clear weather. I. 51. Whether account should be taken of latitude in instruments directed toward the stars’ rays. R. 6. Why defects of the luminaries naturally indicate pestilence, [Sun] and other evils. P. 6. Whether they are also causes of good things, [Sun] signs E. 6. Whether the light of the stars acts by its true or apparent extension. L. 39. Whether the Moon is habitable. L. 46. What the spots in the lunar disc may be. L. 45. Whether Mars is a masculine or feminine planet. F. 29. M. 17. [Sun] 22. Why in the evening after twilight, [Sun] in the morning before Auro} é ij

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INDEX. ram tenebræ intendantur. C. 189. An suos stipatores habeat, vt saturnus, & Jupiter. M. 19. An Mare sit altius Terra. A. 263 & T. 21. Cur exconstituta aquarum accessione non redundet. A. 264. Quanam sit causa æstui Maris. A. 178. An, & qua ratione verum sit quod ait Plinius nullum Animal nisi in maris recessu expirare. A. 180. An Mixtorum qualitates purè elementares sint, an potius à cælestibus derivatæ. M. 61. & Q. 13. & seq. An & cur Mixta sola sint alimenta Viventem. Ibidem. Quo tempore creatus sit mundus. M. 84. An naturaliter ostendi possit ipsum non fuisse ab æterno nec in æternum duraturum. T. 21. Quanto tempore conjecturaliter duraturus sit. M. 24. & A. 201. An habeat propriam formam substantialem. M. 87. An sit Vitâ præditus. M. 88. & seq. An per hoc dici possit Magnum quoddam Animal. M. 92. Mutationes absidum Planetarum an ullam in Mundo mutationem naturaliter indicent. A. 10. & 11. Quodnam dicendum sit verum Natiuitatis momentum; seu Quando Astra incipiat influere infætum natum. C. 13. & seq. Modi Lunares an ullam activitatem habeant in isthac inferiora. C. 23. In quamam Orbis parte constituendum sit verum occidens. A. 373. Unde oriatur naturalis affectio piscis Orbis se jugiter ad spirantem ventum vertentis. V. 18. Pars Fortunæ nùm in Zodiaco an potius in situ Mundi constituenda. F. 34

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INDEX. When darkness is extended. C. 189. Whether it has its own attendants, like Saturn and Jupiter. M. 19. Whether the Sea is higher than the Earth. A. 263 & T. 21. Why it does not overflow from the established influx of waters. A. 264. What the cause of the tide of the Sea is. A. 178. Whether, and in what way, what Pliny says is true: that no animal expires except at the ebb of the sea. A. 180. Whether the qualities of mixed things are purely elemental, or rather derived from the heavenly bodies. M. 61. & Q. 13. & seq. Whether, and why, mixed things alone are nourishment for the living. Ibidem. At what time the world was created. M. 84. Whether it can be naturally shown that it was not from eternity, nor will endure eternally. T. 21. For how long it is conjectured to endure. M. 24. & A. 201. Whether it has its own substantial form. M. 87. Whether it is endowed with life. M. 88. & seq. Whether by this it can be called a certain great Animal. M. 92. Whether the changes of the apsides of the Planets indicate any natural change in the World. A. 10. & 11. Which should be called the true moment of Nativity; or when the Stars begin to influence the infant born. C. 13. & seq. Whether Lunar modes have any activity in these lower things. C. 23. In what part of the Sphere the true west is to be established. A. 373. Whence arises the natural inclination of the fish Orbis, which continually turns itself toward the blowing wind. V. 18. Whether the Part of Fortune is to be established in the Zodiac, or rather in the position of the World. F. 34

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INDEX. Præditiones Astrologicæ quousque licitè ac naturaliter extendantur. A. 332. O N. 7. Primum mobile an verè ac realiter sit Imaginibus, O Characteribus insignitum. I. 22. O M. 69. An Nouæ stellæ in Calo apparentes sint è materia. Cælesti de novo genitæ, an vero è sublunari regione illuc transcendant. P. 59. Cur Planetæ aucti, Lumine, O Numero sint cæteris validiores. A. 348. O seq. Cur Planeta in Corde Solis dicatur fortior, cum alioqui combustus, aut sub radis sit debilior. C. 58. An Pleiades visæ sint numero septem vel sex. E. 81. An Polaris stella aliquando sit in ipsum Polum recisura. A. 155. An dentur Qualitates totius substantiæ. Q. 13. An Retrogradatio Maleficarum bona sit, vel mala. R. 38. O seq. Unde sit Maris falsedo. A. 264. In quo consistat ratio satellitij ad Luminaria. S. 13. Quænam sit causa scintillationis in Astris. S. 23. Sinius Abrahæ vbi situs. S. 71. An Sol sit formaliter ignem. S. 77. Quid sint Maculæ in Disco solari. Ibidem. Cur solstitium hiemale sit ferè semper serenum, æstimale verò sit plusium. S. 84. An spheræ, seu Orbes cælestes, eorumque motus venerà sit vnus vel multiplex. S. 96. C. 135. M. 71. O seq In quo consistat ratio sympathiæ O antipathiæ rerum in uniuersa Natura. S. 122. O seq. An Terrasit Mundi. Centrum. T. 22. An sit altera Luna. T. 25. Vegetatio, æ sensatio, an sint gradus vitæ perfectiores. M. 88. é iij

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INDEX. How far astrological predictions are lawfully and naturally extended. A. 332. O N. 7. Whether the Primum Mobile is truly and really marked with Images and Characters. I. 22. O M. 69. Whether the new stars appearing in the sky are generated anew from heavenly matter, or whether they ascend there from the sublunary region. P. 59. Why the planets, being increased in light and number, are stronger than the rest. A. 348. O seq. Why the planet is said to be stronger in the heart of the Sun, although otherwise, being burnt, or under the rays, it is weaker. C. 58. Whether the Pleiades were seen as seven in number or six. E. 81. Whether the Pole Star will at some time be cut down to the very Pole itself. A. 155. Whether qualities of the whole substance are to be granted. Q. 13. Whether the retrogradation of witches is good or bad. R. 38. O seq. Whence the sea’s saltness arises. A. 264. In what the reason of the satellites to the luminaries consists. S. 13. What the cause of the scintillation of the stars is. S. 23. Where Abraham’s bosom is situated. S. 71. Whether the Sun is formally fire. S. 77. What the spots in the solar disk are. Ibidem. Why the winter solstice is almost always serene, but the summer solstice is more rainy. S. 84. Whether the celestial spheres, or orbs, and their motions are truly one or multiple. S. 96. C. 135. M. 71. O seq. In what the reason of sympathy and antipathy of things in universal Nature consists. S. 122. O seq. Whether the Earth is the center of the world. T. 22. Whether there is another Moon. T. 25. Whether vegetation and sensation are more perfect degrees of life. M. 88. é iij

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INDEX. Quid sit ventus. V. 11. ß seq. An Veneris Astrum aliquando formam, lumen, & motum mutavit. V. 23. An omnes Zona sint æque & commode habitabiles. Z. 10. An detur resolu:io vsque ad materiam primam in cor- ruptione compositi. Digress. quæst. 3. n. 23. ß seq. Quid sit Tempus. T. 10. An reuerà conslet ex atomis indivisibilibus. T. 12. In quo formaliter consistat ratio vitæ. M. 8. An Terra extrà aquam constituta sit in statu violento. T. 21. Cur lacus & stagna aquarum, etsi amplissima non sint salsa. A. 265. Paradisus terrestris vbi sit, & vbi constituenda. P. 4. & seq. Tru:ina Hermetis pro indagando ex conceptione vero Nativitatis , an quidquam soliditatis habeat. T. 73. Au stella Magorum fuerit Cometes, & an eadem, quæ anno 1572. apparuit in sede Cassiopeæ. A. 88. & C. 33 Au & cur Nona Domus sit naturalis memoriæ, ac pietatis significatrix. T. 36. Vita hominis quousque naturaliter protrahi possit. Q 8. & T, 65. Centiloquij Autor an Ptolemens. C. 63. Transitus Planetarum an sint directionibus validiores. T. 55. Bruta Animantia an sint astris nobiliora. M. 93. Præditiones ex Astris ad quid naturaliter se extendant. A. 312. Annorum scholarium, seu Climaticorum ratio unde habeatur. C. 131, & seq. & 1. 31. Cur Partus Octimestris non superuiuat. I. 34.

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INDEX. What wind is. V. 11. & seq. Whether the Star of Venus ever changed form, light, and motion. V. 23. Whether all the Zones are equally and conveniently habitable. Z. 10. Whether there is a resolution all the way down to first matter in the corruption of a compound. Digress. quæst. 3. n. 23. & seq. What Time is. T. 10. Whether it truly consists of indivisible atoms. T. 12. In what the formal notion of life consists. M. 8. Whether the Earth, placed outside the water, is in a violent state. T. 21. Why lakes and pools of water, though very large, are not salt. A. 265. Where the earthly Paradise is, and where it is to be placed. P. 4. & seq. The Hermetic balance for investigating from conception the true Nativity, whether it has any solidity. T. 73. Whether the star of the Magi was a comet, and whether it was the same as that which appeared in the year 1572 in the seat of Cassiopeia. A. 88. & C. 33. Whether and why the Ninth House is the natural signifier of memory and piety. T. 36. How far a human life may naturally be prolonged. Q. 8. & T. 65. Whether the author of the Centiloquium was Ptolemy. C. 63. Whether the passages of the planets are more powerful than directions. T. 55. Whether brute animals are more noble than the stars. M. 93. To what extent predictions from the stars naturally extend. A. 312. Whence the rule of scholastic, or climatic, years is obtained. C. 131, & seq. & I. 31. Why an eight-months-born child does not survive. I. 34.

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INDEX. Quando puer ex utero egrediens nasci dicatur. G.17. O seq. An sic possibilis Quadratura circuli, & an ullus illum atim quadraverit. Q.9. An Manna Israeliticum fuerit ejusdem rationis cum nostro. R.14. An Puluis sympathicus, linteaminibus vulneratorum sanguine infettis applicatus licitè adhiberi possit in Vulnerum curatione Digress. Physiotheol. Qu.1. An pari ratione vnguenti armarijvsus in Vulnerum curatione sit licitus. Ibid. qu. est.2. Quonam patto puluis sympathicus, Unguentum Armarium, & cætera hujusmodi medicamenta conferant ad vulnerum aliormoque morborum curatio- nem. Ibid. qu.3. FINIS.

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INDEX. When a child, coming forth from the womb, may be said to be born. G.17. See seq. Whether the Squaring of the Circle is possible, and whether anyone has so far squared it. Q.9. Whether the Israelite Manna was of the same nature as ours. R.14. Whether sympathetic powder, applied to cloths of the wounded stained with blood, may lawfully be used in the curing of wounds. Digress. Physiotheol. Qu.1. Whether, for the same reason, the use of armary ointment in the curing of wounds is lawful. Ibid. qu. est.2. In what way sympathetic powder, Armary Ointment, and other such medicines contribute to the curing of wounds and other diseases. Ibid. qu.3. FINIS.

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ERRATA CORRIGENDA. Pag. 2. lin. 1. tentissimæ, lege, potissima. lin 3 tabse l. ab eo. p. 4. lin. 39. Ausis, l. Augis. p. 5. lin. 4. Quod, l. Qui. lin. 20. hac in se, l. hac in re. p. 7. lin. 28. Caigni, l. Cygni. p. 8. lin. 34. Hermann. l. Germanici. ibid. in Arab, l. in Arati. lin. 39. comperiantur, l. comperiuntur. p. 9. lin. vlt. Quodcumque, l. Quandocumque. p. 10. lin. 3. orchogonicum, l. orthogonicum. lin. 16. aut suprà, l. vt suprà. lin. vlt. Iunctiuius, l. Iunctinus. p. 11. lin. 5. Indecimæ, l. Duodecimæ. lin. 41. comperuit, l. comperiit. p. 13, lin. 23. Blazanum, l. Blancanum. p. 14. lin. 21. Heleg. l. Hileg. lin. 37. Foemilias, l. Equas. p. 16. lin. 23. Hayr, l. Hayz. lin. 30. spicitur, dele. p. 16. lin. 15. Quadring, l. Quadrip. lin. 17. Mercurius? dele? lin. 21. Alxiæ, l. Alxia. p. 19. lin. 38. aunc, l. nunc. lin. 41. tunc, l. nunc. p. 21. lin. 11. tunc, l. nunc. lin. 81. tunc, l. nunc. p. 22. lin. 14. Alhadida, l. Alhidada. p. 28. lin. 12. sit, l. sit. p. 32. lin. 22. culminans, l. culminantem. p. 34. lin. 37. quæ, l quam. lin. 43. infringantur, l. infringuntur. p. 35. lin. 14. à græcis, l. punctis. lin. 24. Adriatiao, l. Adriatico. lin. 34. Trabene, l. Strabonem. p. 36. lin. 21. restuit, l. refluit. p. 38. lin. 24. Caropricia, l. Catoptrica. lin. 25. Anaclatica, l. Anaclastica. p. 42. lin. 2. Parallelogram, l. Parallelogrammum. p. 43. lin. 7. in annis 4900. l. in annis 49000. p. 44. lin. 25. ex redecim, l. ex tredecim. p. 45. lin. 4. bis Toucan, l Toucan. p. 47. lin. 20. exspicari, l. expiscari. lin. 26. Insulæ, l. Insula. lin. 26. Americæ l. America. lin. 36. completur directi, l. complet. directionem. lin. 40. octivum, l. octavo. lin. 41, min...

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ERRATA CORRIGENDA. Pag. 2. lin. 1. tentissimæ, lege, potissima. lin. 3. tabse l. ab eo. p. 4. lin. 39. Ausis, l. Augis. p. 5. lin. 4. Quod, l. Qui. lin. 20. hac in se, l. hac in re. p. 7. lin. 28. Caigni, l. Cygni. p. 8. lin. 34. Hermann. l. Germanici. ibid. in Arab, l. in Arati. lin. 39. comperiantur, l. comperiuntur. p. 9. lin. vlt. Quodcumque, l. Quandocumque. p. 10. lin. 3. orchogonicum, l. orthogonicum. lin. 16. aut suprà, l. vt suprà. lin. vlt. Iunctiuius, l. Iunctinus. p. 11. lin. 5. Indecimæ, l. Duodecimæ. lin. 41. comperuit, l. comperiit. p. 13, lin. 23. Blazanum, l. Blancanum. p. 14. lin. 21. Heleg. l. Hileg. lin. 37. Foemilias, l. Equas. p. 16. lin. 23. Hayr, l. Hayz. lin. 30. spicitur, dele. p. 16. lin. 15. Quadring, l. Quadrip. lin. 17. Mercurius? dele? lin. 21. Alxiæ, l. Alxia. p. 19. lin. 38. aunc, l. nunc. lin. 41. tunc, l. nunc. p. 21. lin. 11. tunc, l. nunc. lin. 81. tunc, l. nunc. p. 22. lin. 14. Alhadida, l. Alhidada. p. 28. lin. 12. sit, l. sit. p. 32. lin. 22. culminans, l. culminantem. p. 34. lin. 37. quæ, l. quam. lin. 43. infringantur, l. infringuntur. p. 35. lin. 14. à græcis, l. punctis. lin. 24. Adriatiao, l. Adriatico. lin. 34. Trabene, l. Strabonem. p. 36. lin. 21. restuit, l. refluit. p. 38. lin. 24. Caropricia, l. Catoptrica. lin. 25. Anaclatica, l. Anaclastica. p. 42. lin. 2. Parallelogram, l. Parallelogrammum. p. 43. lin. 7. in annis 4900. l. in annis 49000. p. 44. lin. 25. ex redecim, l. ex tredecim. p. 45. lin. 4. bis Toucan, l. Toucan. p. 47. lin. 20. exspicari, l. expiscari. lin. 26. Insulæ, l. Insula. lin. 26. Americæ l. America. lin. 36. completur directi, l. complet. directionem. lin. 40. octivum, l. octavo. lin. 41, min...

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1. min.40. lin.44. Cnacti, 1. Cancri. p. 48. 1. vlt. Cnari, 1. Cancri. p. 66. 1. 4. manducat, 1. manuducat. p. 67. 1. 12. initatiua, 1. initiatiua. p. 72. 1. 18. agricolatinem, 1. agricolationem. p. 142. 1. 42. alterum ad alterum, 1. alter ad alterum. p. 206. 1. 10. bonus gedius, 1. bonus genius. p. 208. 1. 9. erudissime, 1. eruditissime. p. 209. 1. 39. tostro, 1. nostro. p. 211. 1. 35. beneficia, 1. benefica. p. 212. 1. prima. indi. 1. indicat. p. 229. 1. 34. mobibilis, 1. mobilis. p. 249. 1. vlt. leo est ium 1. esse locum p. 253. 1. 5. Christopolitanus, 1. Chrisopolitanus.. p. 346. 1. 22. initio, 1. irrito, p. 358. 1. 15. fons 1. fon. tem, p. 453. 1. penult. dispescitur 1. diuiditur p. 486. 1. 20. probere 1. probare.

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1. min.40. lin.44. Cnacti, 1. Cancri. p. 48. 1. vlt. Cnari, 1. Cancri. p. 66. 1. 4. manducat, 1. manuducat. p. 67. 1. 12. initatiua, 1. initiatiua. p. 72. 1. 18. agricolatinem, 1. agricolationem. p. 142. 1. 42. alterum ad alterum, 1. alter ad alterum. p. 206. 1. 10. bonus gedius, 1. bonus genius. p. 208. 1. 9. erudissime, 1. eruditissime. p. 209. 1. 39. tostro, 1. nostro. p. 211. 1. 35. beneficia, 1. benefica. p. 212. 1. prima. indi. 1. indicat. p. 229. 1. 34. mobibilis, 1. mobilis. p. 249. 1. vlt. leo est ium 1. esse locum p. 253. 1. 5. Christopolitanus, 1. Chrisopolitanus.. p. 346. 1. 22. initio, 1. irrito, p. 358. 1. 15. fons 1. fon. tem, p. 453. 1. penult. dispescitur 1. diuiditur p. 486. 1. 20. probere 1. probare.

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INDEX LOCORVM ET Verborum quæ in hoc opere ord:ne Alphabetico ex instituto examinatur. A. Figura Aëquidium, & Abàculi. Aëquidiale. Abalàntica. Æguinòctiù. Abén Ràs. Æquilaterum. Abradàleus. Aër. Abscissio luminis. Aërea signa. Absis. Æròbo. Abterrànei. Æestas. Acàrnàr. Æethier. Acèntacer. Afeta. Actinobòlium Æhalén. Achrònicus. Africus. Achelàl. Agaticâ. Acontiæ. Agothodæm[ón]. Acùtus Angulus. Agglutinàtio. Adalòr. Ahàrph. Adigège. Aichàrd. Adoringèn. Aiz. Adòncado. Alaazèl. Agipan. Ægòceros. Allacàf. Æquàtor, & Alacantabùt. Æquinociûlis Alagabàl, Ala- Æquicrûriafigura. hòre. Alaim. Alamàc, Asa- lìth. Alângue. Alànthica. Alathà. Alatràb. Alayôth. Albàhurim. Albètatran. Albègala. Albìrèo. Albòaran. Albuzìch. Alìhatis. Alchenìb. Alchetìb. Alchià Dàpha. Alchìnera. Alchitòt. Alesbòl. Alcocòden. Alcòr. Alcyònii dies. Aldèbaran. Alderaimìn. Aldhàfera. Alfàntia. A

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Index of places and words which in this work are examined in alphabetical order according to the established plan. A. Figure Aëquidium, & Abàculi. Aëquidiale. Abalàntica. Æguinòctiù. Abén Ràs. Æquilaterum. Abradàleus. Aër. Abscissio luminis. Aërea signa. Absis. Æròbo. Abterrànei. Æestas. Acàrnàr. Æethier. Acèntacer. Afeta. Actinobòlium Æhalén. Achrònicus. Africus. Achelàl. Agaticâ. Acontiæ. Agothodæm[ón]. Acùtus Angulus. Agglutinàtio. Adalòr. Ahàrph. Adigège. Aichàrd. Adoringèn. Aiz. Adòncado. Alaazèl. Agipan. Ægòceros. Allacàf. Æquàtor, & Alacantabùt. Æquinociûlis Alagabàl, Ala- Æquicrûriafigura. hòre. Alaim. Alamàc, Asa- lìth. Alângue. Alànthica. Alathà. Alatràb. Alayôth. Albàhurim. Albètatran. Albègala. Albìrèo. Albòaran. Albuzìch. Alìhatis. Alchenìb. Alchetìb. Alchià Dàpha. Alchìnera. Alchitòt. Alesbòl. Alcocòden. Alcòr. Alcyònii dies. Aldèbaran. Alderaimìn. Aldhàfera. Alfàntia. A

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INDEX. Alfazìm. Almanach. Alfèua. Almanàr. Alféta. Almanèm. Alfridârie. Almauerèth. Algebàr. Almegramèth. Algebra. Almicâtharâth Algebûbatàr. Almogiza. Algèdi Denèb. Almàcedeme. Algèmmee. Almìdhebir. Algenìb. Almugèa. Algènsis. Almuri. Algèti. Almusechele't. Algòl. Almustêuli. Algonèysa. Almûthen. Algoràb. Alnisigrèf. Alhàbor. Alosaph. Alhàbor. Alphantia. Alhaisèth. Alphàrd. Alhàntica. Alpheua. Alhàdida. Alpheràtz. Alhùrto. Alphèta. Alìbd. Alramèch. Alichèl. Alràkaba. Alicòrab. Altalisùm. Alicìtisal. Altàni. Alìoth. Aluehczît. Alkàir. Alynthiæ signu[m] Alkìa Dapha. Alzimòn. Alkìndus. Amblygòniu[m]. Alkinìra. Amfrocraciator. Alkinirèm. Annimodar. Allûre. Amphicyrtos. Almagèstum.

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INDEX. Alfazìm. Almanach. Alfèua. Almanàr. Alféta. Almanèm. Alfridârie. Almauerèth. Algebàr. Almegramèth. Algebra. Almicâtharâth Algebûbatàr. Almogiza. Algèdi Denèb. Almàcedeme. Algèmmee. Almìdhebir. Algenìb. Almugèa. Algènsis. Almuri. Algèti. Almusechele't. Algòl. Almustêuli. Algonèysa. Almûthen. Algoràb. Alnisigrèf. Alhàbor. Alosaph. Alhàbor. Alphantia. Alhaisèth. Alphàrd. Alhàntica. Alpheua. Alhàdida. Alpheràtz. Alhùrto. Alphèta. Alìbd. Alramèch. Alichèl. Alràkaba. Alicòrab. Altalisùm. Alicìtisal. Altàni. Alìoth. Aluehczît. Alkàir. Alynthiæ signu[m] Alkìa Dapha. Alzimòn. Alkìndus. Amblygòniu[m]. Alkinìra. Amfrocraciator. Alkinirèm. Annimodar. Allûre. Amphicyrtos. Almagèstum.

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LOCORVM ET VERBORVM. lunisolaris. Apis. Annus magnus Apus. metonicus. Aplanes. Annus perio- Aplane. dicus. Apocâstasis. Anomalia. Apodéate. Anser. Apogæum. Anser Ameri- Apogæi. cânus. Apollo. Antâcticus. Aporrhæa. Antares. Aporrogas. Antascônes. Apotelêsma. Antigene. Apòtome. Antichthones. Apòtome. Antipodes. Appârétiæ. Antazônes. Applicàtio. Antecânis. Apullîa. Antica. Aqua. Antincus. Aquàrius. Antiscia. Aqueta signa. Antîscij. Aquila. Antipathîa. Aquilo. Antôeci. Ara. Apâretias. Arànea. Apeliôtes. Arathêa Spæ- Aperitio por- ta. tarum. Archatàpias. Aphænêtæ. Architectûra. Aphêta. Arciterens. Aphêlium. Arctòphilax. Aphêretæ. Arctos. Aphêtes. Arctûrus. Aphrûimis. Arcus. Aphut. Areâ. Area Meteorô. Aredir. Argèntum seu Argéticomus. Argèstes. Argetenàr. Argìon. Argonàuis. Argumètum. Argumentum. luitudinis lu- næ. Ariàdnæ Coro- na. Ariaméch. Aridèd. Aries. Ario. Arista. Arithmètica. Armilla. Armillâris sphæra. Arnig. Aròlabum. Arpien. Artûrus. Asànges. Asbìa. Ascèndens. Ascensiones, & descensiones. Ascensionàlis differentia. A ij

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Of Places and Words. lunisolar. Apis. Great year Apus. metonic. Aplanes. Periodic year Aplane. periodic. Apocâstasis. Anomaly. Apodéate. Goose. Apogæum. American goose. Apogæi. Antâcticus. Apollo. Antares. Aporrhæa. Antascônes. Aporrogas. Antigene. Apotelêsma. Antichthones. Apòtome. Antipodes. Apòtome. Antazônes. Appârétiæ. Antecânis. Applicàtio. Antica. Apullîa. Antincus. Water. Antiscia. Aquàrius. Antîscij. Water-bearing signs. Antipathîa. Eagle. Antôeci. Aquilo. Apâretias. Altar. Apeliôtes. Spider. Opening of the gates. Arathêa Spæ- tarum. Archatàpias. Aphænêtæ. Architecture. Aphêta. Arciterens. Aphêlium. Arctòphilax. Aphêretæ. Arctos. Aphêtes. Arctûrus. Aphrûimis. Arcus. Aphut. Area. Meteor area. Aredir. Silver or Argéticomus. Argèstes. Argetenàr. Argìon. Argonàuis. Argument. Argument. Length of the moon. Ariadne's coro- na. Ariaméch. Aridèd. Aries. Ario. Spike. Arithmetic. Armilla. Armillary sphere. Arnig. Aròlabum. Arpien. Artûrus. Asànges. Asbìa. Ascèndens. Ascensions, and descensions. Ascensional difference. A ij

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Transcription: ATR-1

INDEX Aschere aliè- Auctus lumine. min. Aucto numero Asconi[n]as. Auellèr. Aselli. Auis. Asicàth. Auis Paradisiaca. Asiccàn. Aulàx. Asidà. Aurea regula. Aspèctus. Augentes fortunam. Assabe. Aura. Assànge, Arnig. Aurea regula. Assub. Astucus. Aùrea numerus. Aster. Astiro. Aùreus numerus. Astrabister. Auriga. Astræa. Aurora. Astroôcynos. Aurora Come[n]tes. Astrolabium, Austron. Auster. Astrothêmata. Autômata. Astrothêsia. Autùmnus. Astrum, seu Asterismus. Aux. Asymetria. Axis. Atàbulus. Azèlfage. Atazîr. Azimèch. Atèmbui. Azimùth. Aterêchinis. Azôni. Atùn Eltaùr. Azòrum insulæ Athale. Azûbenè. Athorâye, seu B. Altorich. B. Attestationes. Baculus Astronomi- Atmosphæra. .

Transcription: Translated (English)

INDEX Aschere aliè- Auctus lumine. min. Aucto numero Asconi[n]as. Auellèr. Aselli. Auis. Asicàth. Auis Paradisiaca. Asiccàn. Aulàx. Asidà. Aurea regula. Aspèctus. Augentes fortunam. Assabe. Aura. Assànge, Arnig. Aurea regula. Assub. Astucus. Aùrea numerus. Aster. Astiro. Aùreus numerus. Astrabister. Auriga. Astræa. Aurora. Astroôcynos. Aurora Come[n]tes. Astrolabium, Austron. Auster. Astrothêmata. Autômata. Astrothêsia. Autùmnus. Astrum, seu Asterismus. Aux. Asymetria. Axis. Atàbulus. Azèlfage. Atazîr. Azimèch. Atèmbui. Azimùth. Aterêchinis. Azôni. Atùn Eltaùr. Azòrum insulæ Athale. Azûbenè. Athorâye, seu B. Altorich. B. Attestationes. Baculus Astronomi- Atmosphæra. .

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Transcription: ATR-1

LOCORVM ET VERBORVM. C. Catægis. C Aballus. Cataphoræ. C Cacodæ- Cathalze. C mon. Catogæum. Càdens. Cachetus Cæcias. incidentiæ. Cænaculum, Cathetus reflexionis. Calbèz. Cachetus reflexionis. Calculator. Catôptrice. Calippica Periodus. Casus. Càmmarus. Cauda Capricorni. Cancer. Cauda Cygni. Canis maior. Cauda Ceti. Canis minor. Cauda draconis sideris. Canopus. Cauda delphi-ni. Capella. Cauda leonis. Caper. Cauda Vrsæ maioris. Caput draconis. Cauda Vrsæ minoris. Caput & cauda draconis. Cauda Vrsæ minoris. Caput Apollo. Cauda Vrsæ minoris. Caput Herculis. Cazimi. Caput seu se- Cegînus. ctio Equi. Centilòquium. Caput Medusæ Centra domorum. Caput Ophiuci Cæpheus. Carcinos. Ceràtias. Carpèncum. Cèrados. Casmòn. Cetus. Cassiopêa. Chakitichi. Catabibazon. Chamæleo Chásma. Chélæ. Chélis. Cheleùb. Chelidònius. Chenèn. Chìron. Chórda. Chorographîa. Chriseus. Chrònicus. Chronocrâtor. Cingulus orio-nis. Cignus. Cìrcius Ven-tus. Circitòtes. Circulus. Circul[us] rectus Circulus obli-quus. Circuli altitu-dinum. Circuli horarij Circuli posi-tionum. Circuli verti-cales. Circumferen-tia. Circuallàtio. A ij

Transcription: Translated (English)

PLACES AND WORDS. C. Catægis. C Aballus. Cataphoræ. C Cacodæ- Cathalze. C mon. Catogæum. Càdens. Cachetus Cæcias. incidentiæ. Cænaculum, Cathetus reflexionis. Calbèz. Cachetus reflexionis. Calculator. Catôptrice. Calippica Periodus. Casus. Càmmarus. Tail of Capricorn. Cancer. Tail of Cygnus. Canis maior. Tail of Cetus. Canis minor. Tail of the Dragon star. Canopus. Tail of Delphinus. Capella. Tail of Leo. Caper. Tail of Ursa Major. Caput draconis. Tail of Ursa Minor. Caput & cauda draconis. Tail of Ursa Minor. Caput Apollo. Tail of Ursa Minor. Caput Herculis. Cazimi. Caput seu se- Cegînus. ctio Equi. Centiloquium. Caput Medusæ Centers of houses. Caput Ophiuci Cephæus. Carcinos. Ceratias. Carpèncum. Cerados. Casmòn. Cetus. Cassiopêa. Chakitichi. Catabibazon. Chameleon Chásma. Chélæ. Chélis. Cheleùb. Chelidònius. Chenèn. Chìron. Chórda. Chorographîa. Chriseus. Chrònicus. Chronocrâtor. Cingulus orio-nis. Cignus. Cìrcius Ven-tus. Circitòtes. Circulus. Circul[us] rectus Circulus obli-quus. Circuli altitu-dinum. Circuli horarij Circuli posi-tionum. Circuli verti-cales. Circumferen-tia. Circuallàtio. A ij

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INDEX Cirnecir. Cónus. Clima. Cor cæli. Climactericus. Cor hydræ. Cælum. Cor leonis. Coitus. Cor scorpij. Colubramèr. in Corde solis. Columba. Coróna Austriana. Colûri. Coróna Septentrionalis. Coma Berenices. Coróna. Combustus. Coróna Me- Combusta via. Coróna Meteoron. Cométa. Corpus. Commèxtio. Córus. Communia si- Coruus. gna. Cósmicus. Competèntes Cómographia gradus. Còzimon. Complementum Cràter. arcus. Crêter. Còncauum. Crepusculum. Concèntricum Critici dies. Conditionà- Cròtus. rium. Crux. Confinium. Cùbus. Congressus. Cùlmen. Conòdromus. Cursu vacuus. Constellàtio. Cursu velox. Contactus. Cruilèncum. Contàratos. Cùspis. Contrantiscia. Cyclus. Conuèrsa di- Cyclus solaris. rectio. Cycluus luna- Conuèxum. tis. Cyclus aurei numeri. Cyclus Epac- tarum. Cygnus. Cylinder. Cynosura. D. Dapha Al- chia. Dapha aredèr. Dæmon Meri- dianus. Dasim. Dath Elkàrsi. Dàulo. Decàni. Decuriônes. Declinatio. Decùbitus fi- gura. Dèferens. Delàpsus. Delphìnus. Dèlteton. Denèb. Descensio. Detrimentum. Diagonius.. Diagramma. Diameter. Diasàccora.

Transcription: Translated (English)

Index Cirnecir. Cónus. Clima. Cor cæli. Climactericus. Cor hydræ. Cælum. Cor leonis. Coitus. Cor scorpij. Colubramèr. in Corde solis. Columba. Coróna Austriana. Colûri. Coróna Septentrionalis. Coma Berenices. Coróna. Combustus. Coróna Me- Combusta via. Coróna Meteoron. Cométa. Corpus. Commèxtio. Córus. Communia si- Coruus. gna. Cósmicus. Competèntes Cómographia gradus. Còzimon. Complementum Cràter. arcus. Crêter. Còncauum. Crepusculum. Concèntricum Critici dies. Conditionà- Cròtus. rium. Crux. Confinium. Cùbus. Congressus. Cùlmen. Conòdromus. Cursu vacuus. Constellàtio. Cursu velox. Contactus. Cruilèncum. Contàratos. Cùspis. Contrantiscia. Cyclus. Conuèrsa di- Cyclus solaris. rectio. Cycluus luna- Conuèxum. tis. Cyclus aurei numeri. Cyclus Epac- tarum. Cygnus. Cylinder. Cynosura. D. Dapha Al- chia. Dapha aredèr. Dæmon Meri- dianus. Dasim. Dath Elkàrsi. Dàulo. Decàni. Decuriônes. Declinatio. Decùbitus fi- gura. Dèferens. Delàpsus. Delphìnus. Dèlteton. Denèb. Descensio. Detrimentum. Diagonius.. Diagramma. Diameter. Diasàccora.

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Transcription: ATR-1

LOCORVM ET VERBORVM. Dichotomos. poris. Diepon. Doryphorîa. Dies. Doza Almogiza. Differentia Ascensionalis. Draco. Dìgitus Eclipticus. Draconis lunæ caput & cauda. Dignitas. Draco volans. Dimantarcoris. Dabhè. Dimètiens. Ductio. Diòptra. Ductoria. Directio. Duodenària Directus. Planetarum. Discus. Dysis. Disceus. Diùsor. Diùrnus. Dòcus. E Dodecaêdrum. Eclipsis. Dodecatemoron. Ecliptica. Domicilium. Ecptôsis. Dòmus. Edelen. Dominus anni. Edùb. Dominus genituræ. Effluxus. Dominus Orbis. Elathi. Dominus Horæ. Eldegiagûl. Dominus radiorum. Elei[n]et. Dominus tèm- Elementum. Elementa Geometrica. Eleuàtio. Elhabòr. Elhamnèl. Elhaut. Elgèdi. Elkaùs. Elkèrd. Elkleischèmal. Ellipsis. Eltanin. Eluàrad. Elzegiàle. Embolismus. Embolismica lunatio. Empireum. Engonâsis. Enif alferi[n]ts. Eniochus. Ennàgone. Enneàtici dies. Eòsphorus. Epàcta. Ephèmeris. Epicatàphora. Epicyclus. Epigius. Epima. Epitrion. Epocha. Eptàgonum. Equiculus. Equus alàtus. Erègbuo. A iii

Transcription: Translated (English)

Of places and words. Dichotomos. poris. Diepon. Doryphorîa. Dies. Doza Almogiza. Differentia Ascensionalis. Draco. Dìgitus Eclipticus. Draco’s moon’s head & tail. Dignitas. Flying dragon. Dimantarcoris. Dabhè. Dimètiens. Ductio. Diòptra. Ductoria. Directio. Duodenary Directus. Of the planets. Discus. Dysis. Disceus. Diùsor. Diùrnus. Dòcus. E Dodecaêdrum. Eclipsis. Dodecatemoron. Ecliptica. Domicilium. Ecptôsis. Dòmus. Edelen. Dominus anni. Edùb. Dominus genituræ. Effluxus. Dominus Orbis. Elathi. Dominus Horæ. Eldegiagûl. Dominus radiorum. Elei[n]et. Dominus tèm- Elementum. Elementa Geometrica. Eleuàtio. Elhabòr. Elhamnèl. Elhaut. Elgèdi. Elkaùs. Elkèrd. Elkleischèmal. Ellipsis. Eltanin. Eluàrad. Elzegiàle. Embolismus. Embolismica lunation. Empireum. Engonâsis. Enif alferi[n]ts. Eniochus. Ennàgone. Enneàtici days. Eòsphorus. Epàcta. Ephèmeris. Epicatàphora. Epicyclus. Epigius. Epima. Epitrion. Epocha. Eptàgonum. Equiculus. Equus alàtus. Erègbuo. A iii

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Transcription: ATR-1

Eriethônius. Figura sexdecim laterum. Eridanus. Geographia. Erigone. Geometria. Erraticæ stellæ Fines. Etesiæ. Globus. Eteroscij. Finetes. Eudamon. Gnasch, Gnomon, Gnomé, Geometricu. Euchens. Gnomonica. Eugonius. Gnostia Eugrammas. Foca. Eurus. Gorgónis caput. Exagonum. Fortùna. Exaltatio. Gradus. Existeron. Græcus. Exalatio. Grus. Exhilma. H Excetra. Adio. Exercsimus. G F. Galacèn. Facies. Galascia. Falco. Hammel. Familiaritas. Galgàl. Fauònius. Galina. Fèra. Garbinus. Feralia. Gaudium. Feralis. Gèmini. Ferdariæ. Gènesis. Ficares. Genethliacum. Fidiculæ. Geniculàtor. Figura. Gènna. Figuræ isoperimétræ. Gènyahar. Geodâlia. Hercules.

Transcription: Translated (English)

Eriethônius. Figure of sixteen sides. Eridanus. Geography. Erigone. Geometry. Erraticæ stellæ Boundaries. Etesiæ. Globe. Eteroscij. Finetes. Eudamon. Gnasch, Gnomon, Gnomé, Geometricu. Euchens. Gnomonica. Eugonius. Gnostia Eugrammas. Foca. Eurus. Head of Gorgon. Exagonum. Fortuna. Exaltatio. Degree. Existeron. Greek. Exalatio. Crane. Exhilma. H Excetra. Adio. Exercsimus. G F. Galacèn. Facies. Galascia. Falco. Hammel. Familiaritas. Galgàl. Fauònius. Galina. Fèra. Garbinus. Feralia. Joy. Feralis. Gemini. Ferdariæ. Genesis. Ficares. Genethliacum. Fidiculæ. Geniculator. Figura. Gènna. Figuræ isoperimétræ. Gènyahar. Geodâlia. Hercules.

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Transcription: ATR-1

LOCORVM ET VERBORVM. Oculus Tauri. Panselene. Olor. Parabola. Ophiucus. Paradisus terestris. Opora. Parallase. Oporinum sidus. Parallaxis. Oppositio. Paralleli. Optica. Parallelo grāmum. Orbis. Parallelo pèura. Orbita. Parallelo pèu-ra. Oricrator. Parallelo pipê-dum. Oriens. Parallelo pipê-dum. Orientales domus, Parètia. Orientalis Planeta. Paraselene. Orion. Pars fortunæ. Orizon. Partes aliæ. Ornithias. Partilis radicis. Oroaser. Passer. Orthogonius. Pauo. Ortographiæ. Pàtera. Ortus, & occasus sideum. Pegasus. Ostensor. Peregrinus. Os piscis. Perigæum. Ouàlis figura. Perimêtrum. Oxygòmum. Periæci. P. Peripheria. Pallilitium. Perpendiculu[m]. Palmà serpentarij. Perseus. Perspectiuæ. Perspectiuæ. Pèrtica. Pèrtica. Persebre. Persebre. Pharmàz. Pharmàz. Phàses. Phaenix ventus Phaenix sidus. Phaenix sidus. Phenicoptê-rus. Phenicoptê-rus. Phaenômena. Phaenômena. Phaenon. Phaenon. Phaeton. Phaeton. Phòsphoros. Phòsphoros. Pholèx. Pholèx. Phthinûsa. Phthinûsa. Phuonisie. Phuonisie. Pica brasilica. Pica brasilica. Picatàphora. Picatàphora. Pinnæ. Pinnæ. Pinacin. Pinacin. Piothânatos. Piothânatos. Piscis. Piscis notius. Piscis volans. Piscis volans. Pistria. Pistria. Pithètes. Pithètes. Planètæ. Planètæ. Planisphæ-rium. Planisphæ-rium. Planum. Planum. Plàticus aspe-ctus. Plàticus aspe-ctus. Plàustrum si- Plàustrum si-

Transcription: Translated (English)

Of places and words. Oculus Tauri. Panselene. Olor. Parabola. Ophiucus. Paradisus terestris. Opora. Parallase. Oporinum sidus. Parallaxis. Oppositio. Paralleli. Optica. Parallelo grāmum. Orbis. Parallelo pèura. Orbita. Parallelo pèu-ra. Oricrator. Parallelo pipê-dum. Oriens. Parallelo pipê-dum. Orientales domus, Parètia. Orientalis Planeta. Paraselene. Orion. Pars fortunæ. Orizon. Partes aliæ. Ornithias. Partilis radicis. Oroaser. Passer. Orthogonius. Pauo. Ortographiæ. Pàtera. Ortus, & occasus sideum. Pegasus. Ostensor. Peregrinus. Os piscis. Perigæum. Ouàlis figura. Perimêtrum. Oxygòmum. Periæci. P. Peripheria. Pallilitium. Perpendiculu[m]. Palmà serpentarij. Perseus. Perspectiuæ. Perspectiuæ. Pèrtica. Pèrtica. Persebre. Persebre. Pharmàz. Pharmàz. Phàses. Phaenix ventus Phaenix sidus. Phaenix sidus. Phenicoptê-rus. Phenicoptê-rus. Phaenômena. Phaenômena. Phaenon. Phaenon. Phaeton. Phaeton. Phòsphoros. Phòsphoros. Pholèx. Pholèx. Phthinûsa. Phthinûsa. Phuonisie. Phuonisie. Pica brasilica. Pica brasilica. Picatàphora. Picatàphora. Pinnæ. Pinnæ. Pinacin. Pinacin. Piothânatos. Piothânatos. Piscis. Piscis notius. Piscis volans. Piscis volans. Pistria. Pistria. Pithètes. Pithètes. Planètæ. Planètæ. Planisphæ-rium. Planisphæ-rium. Planum. Planum. Plàticus aspe-ctus. Plàticus aspe-ctus. Plàustrum si- Plàustrum si-

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INDEX. Linea. Malfelcare. Linea incidentiæ. Mamareth. Linea medij motus. Mandebula ceri. LAbanach. Manipulus spicarum. Lactea via. Linea veri motus. Lælaps. Logarithnica. Làmpas. Logarithmi. Làmpades. Logìstica. Lancea. Lōgitudo apud Astronomos. Lar. Lōgitudo apud Geographos. Larpitio. Lucifer. Làterculus. Lumen. Laterônes. Luminaria. Latio. In suo Lumine. Latitudo apud Geographos. Luna. Latidudo ortiua. Lunæ mensiones. Lelaps. Lupus. Leo. Lux. Lepus. Lybicus. Lesath. Lybànotos. Leucònoti. Lyra. Leuis. Libànotus. M Liberàlitas. Libra. Magia. Limbus Magistralis ventus. Limbus SS. Patrum. Maleuentum. Linda. Malèficæ.

Transcription: Translated (English)

INDEX. Line. Bad augury. Line of incidence. Mamareth. Line of mean motion. Mandebula ceri. Labanach. Sheaf of ears of grain. Milky Way. Line of true motion. Lælaps. Logarithmic. Lamp. Logarithms. Lamps. Logistics. Spear. Length among Astronomers. Lar. Length among Geographers. Larpitio. Lucifer. Little brick. Light. Torches. Lights. Movement. In its own light. Length among Geographers. Moon. Rising latitude. Moon's measurements. Lelaps. Wolf. Leo. Light. Hare. Libyan. Lesath. Libanus. North-west winds. Lyra. Light. Libanus. M Generosity. Libra. Magic. Limbus Main wind. Limbus of the Holy Fathers. Maleventum. Linda. Wicked ones.

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LOCORVM ET VERBORVM. Mercurius. Musica. Meridianus. Muta signa. Mèrops. Mutàtil. Mesanguo. Mututlum. Mescimàch. Mutilàta signa. Mèsen. N. Mesaquelo, &c N. Metèora. O. Metonicus annus. N Micromèsa, Naásch, Muros cetàratos. Nadir. Miles. Nahar.Alcharnèr. Minùtum. Naris ceti. Mirach. Natiuitas. Mixta. Natura. Mobilia signa. Nauis. Moderatòres. Nabolassid. Monomeniæ. Nebulosæ stel- Ægyptiorum. læ. Mosclèk. Nemèr. Motus. Neomànum. Primum Mobi-le. Nèpa. Secundi Mo-biles. Nescher. Mòtlatum. Nigèr. Moznàin. Nigra. Mundus. Nitàch. Mumir. Nodi. Musator. Nona sphæra. Musca. Notapeliores. Mùscida equi. Notolybicus. Notus. Nòtius piscis. Nouenàriæ. Nouilùnium. Nox. Nubes. Numerus. O. O. O Obedien-tiasigna. Obiaculàri. Obliquus An-gulus. Obliquus Cir-culus Obliqua signa. Obliquatio. Obscuræ stel-læ. Obscuræ stel-læ. Obsessio. Obsessio. Obrusus angu-lus. Obrusus angu-lus. Occidens. Occidens. Occidentales domus. Occidentales domus. Occidentalis Occidentalis Planeta. Planeta. Occursi[n]antes. Occursi[n]antes. Oceànus. Oceànus. Octuêdum. Octuêdum. Octuagulus. Octuagulus. Octauasphæra. Octauasphæra.

Transcription: Translated (English)

Of Places and Words. Mercurius. Music. Meridianus. Mute signs. Mèrops. Mutable. Mesanguo. Mututlum. Mescimàch. Mutilated signs. Mèsen. N. Mesaquelo, &c N. Metèora. O. Metonicus annus. N Micromèsa, Naásch, Muros cetàratos. Nadir. Miles. Nahar.Alcharnèr. Minùtum. Naris ceti. Mirach. Natiuitas. Mixta. Nature. Mobilia signa. Ship. Moderatòres. Nabolassid. Monomeniæ. Nebulous stars. Ægyptiorum. Mosclèk. Nemèr. Motus. Neomànum. Primum Mobi-le. Nèpa. Secundi Mo-biles. Nescher. Mòtlatum. Black. Moznàin. Black. Mundus. Nitàch. Mumir. Knots. Musator. Ninth sphere. Musca. Notapeliores. Mùscida equi. Notolybicus. Notus. Nòtius fish. Nouenàriæ. New moon. Nox. Clouds. Numerus. O. O. O Obedien-tiasigna. Obiaculàri. Obliquus An-gulus. Oblique circle Obliqua signa. Obliquation. Obscuræ stel-læ. Obscure stars. Obsessio. Obsessio. Obrusus angu-lus. Obrusus angu-lus. Occidens. Occident. Occidentales domus. Western houses. Occidentalis Occidental Planeta. Planet. Occursi[n]antes. Occursi[n]antes. Oceànus. Ocean. Octuêdum. Octuêdum. Octuagulus. Octuagulus. Octauasphæra. Octauasphæra.

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Transcription: ATR-1

LOCORVM ET VERBORVM. Hermippus. Hypogæum. Hesperus. Hypothenûsa. Heteròscij. Hyppcus. Hexagonum. I Hinniculus. I Hiêrezim. I Hircus. I Hircus Meteoron. I Hircus æquoris. I Holomêtrum. I Homocentricu. I Homoch. I Homôzena. Ignis. Hóra. Ignis fatuus. Horària tempora. Ignis l'ambens. Horinæum. Imàgines cælestes. Horizon. Imàgines Astronomicæ. Horoscopus. Imàgines Astronomicæ. lunaris. Imum Cæli. Horoscòpium. Inathêdes. Humàna signa. Inconiuncta signa. Huzìmethon. Inconiuncta signa. Hydra. Imperantia signa. Hydrus. Imperantia signa. Hydrographia. Intuëtia signa. Hyems. Indictio. Hylig. Indus. Hylegialia loca. Infernus. Hypaùgus. Ingeniculus. Ingressus. Ingressus. Interluniu m. Interluniu m. Interrogationes Interrogationes Astrologicæ. Inuena: if. Inuena: if. Iris, irina. Iris, irina. Isla: hmi. Isla: hmi. Isagónius. Isagónius. Isoperimêtræ Isoperimêtræ figutæ. Isomæùnos. Isomæùnos. Isis. Isis. Isosceles. Isosceles. Iugula. Iugula. Iugulas. Iugulas. Iugum. Iugum. Iùpiter. Ixiònis rota. K K K, Abàr. Abàr. Kchitichì. Kchitichì. Kàlb. Kàlb. Kaytos. Kaytos. Kaluròps. Kaluròps. Kènen. Kènen. Kertho: Kertho. Kesil. Kesil. Ketpholt. Ketpholt. Kimàch. Kimàch. Kollàsmenon. Kollàsmenon. Kûs. Kûs.

Transcription: Translated (English)

Of places and words. Hermippus. Hypogæum. Hesperus. Hypothenûsa. Heteròscij. Hyppcus. Hexagonum. I Hinniculus. I Hiêrezim. I Hircus. I Hircus Meteoron. I Hircus æquoris. I Holomêtrum. I Homocentricu. I Homoch. I Homôzena. Ignis. Hóra. Ignis fatuus. Horària tempora. Ignis l'ambens. Horinæum. Imàgines cælestes. Horizon. Imàgines Astronomicæ. Horoscopus. Imàgines Astronomicæ. lunaris. Imum Cæli. Horoscòpium. Inathêdes. Humàna signa. Inconiuncta signa. Huzìmethon. Inconiuncta signa. Hydra. Imperantia signa. Hydrus. Imperantia signa. Hydrographia. Intuëtia signa. Hyems. Indictio. Hylig. Indus. Hylegialia loca. Infernus. Hypaùgus. Ingeniculus. Ingressus. Ingressus. Interluniu m. Interluniu m. Interrogationes Interrogationes Astrologicæ. Inuena: if. Inuena: if. Iris, irina. Iris, irina. Isla: hmi. Isla: hmi. Isagónius. Isagónius. Isoperimêtræ Isoperimêtræ figutæ. Isomæùnos. Isomæùnos. Isis. Isis. Isosceles. Isosceles. Iugula. Iugula. Iugulas. Iugulas. Iugum. Iugum. Iùpiter. Ixiònis rota. K K K, Abàr. Abàr. Kchitichì. Kchitichì. Kàlb. Kàlb. Kaytos. Kaytos. Kaluròps. Kaluròps. Kènen. Kènen. Kertho: Kertho. Kesil. Kesil. Ketpholt. Ketpholt. Kimàch. Kimàch. Kollàsmenon. Kollàsmenon. Kûs. Kûs.

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Transcription: ATR-1

LOCORVM ET VERBORVM. dus, Protrigêtes. Pléiades Pseudostellæ. Plenilunium. Pulsatio. Pliathis. Punctum. Pogoniàs. Puteus. Pollux. Pureàles gradus. Polus. Radius. Polichrônium. Pyràmis. Poliêdum. Pyroys. Poligònius. Pychètes. Polygràmmus. Python. Ponderòsus. Q. Præsèpe. Q. Præster. Q. Præuentionâlis. Q Primum mobile. Quadràngulus. Principatus. QuadransGeometricus. Prisma. Quadrantes. Procella. Quadràtus. Pròcyon. Quadratura. Profectiones. Circuli. Prohibitio luminis. Quadripartitum. Promissòres. Quàlitas. Proportionaliitas. Quàntitas. Pròpus. Quæstiones astrologicæ. Prorogitòres. Quintilis radius. Proscatheron. Quòtiens. Prosthaphæresis R. Prothànatos. R. R Abdæ. R Radius. R Radius apud Astronomos. R Radius apud Geometras. R Radius Astronomicus. R Radius satinus. R Ràdix. R Ramphètes. R Ras. R Rationàlia signa. R Rationàlis quantitas. R Rationalis via. R Rectum. R Rectàngulum. R Rectilineum. R Rectirùdo. R Redditus luminis. R Rèditus. R Refractiones. R Refranàtio. R Règiæ,stellæ,signa, &c. R Règula. R Règula aurea R Règula harmonica.

Transcription: Translated (English)

Of Places and Words. dus, Protrigêtes. Pléiades Pseudostellæ. Plenilunium. Pulsatio. Pliathis. Punctum. Pogoniàs. Puteus. Pollux. Pureàles gradus. Polus. Radius. Polichrônium. Pyràmis. Poliêdum. Pyroys. Poligònius. Pychètes. Polygràmmus. Python. Ponderòsus. Q. Præsèpe. Q. Præster. Q. Præuentionâlis. Q Primum mobile. Quadràngulus. Principatus. QuadransGeometricus. Prisma. Quadrantes. Procella. Quadràtus. Pròcyon. Quadratura. Profectiones. Circuli. Prohibitio luminis. Quadripartitum. Promissòres. Quàlitas. Proportionaliitas. Quàntitas. Pròpus. Quæstiones astrologicæ. Prorogitòres. Quintilis radius. Proscatheron. Quòtiens. Prosthaphæresis R. Prothànatos. R. R Abdæ. R Radius. R Radius apud Astronomos. R Radius apud Geometras. R Radius Astronomicus. R Radius satinus. R Ràdix. R Ramphètes. R Ras. R Rationàlia signa. R Rationàlis quantitas. R Rationalis via. R Rectum. R Rectàngulum. R Rectilineum. R Rectirùdo. R Redditus luminis. R Rèditus. R Refractiones. R Refranàtio. R Règiæ,stellæ,signa, &c. R Règula. R Règula aurea R Règula harmonica.

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Transcription: ATR-1

INDEX. Regulares figuræ. Samèh. Regulus. Sartài Mesarthia. Remuneratio. Sartàn. Réte. Satellitium. Retrogradus. Satèllites. Reuolutio. Saturnus. Rhombus. Scalènua. Rhomboides. Scheàt. Riforitas dùnnatu. Schedèr. Régel. Sciographia. Ros. Sciothèrium. Rosa Come- Scintillàtio. tes. Sciron. Rósch Halli- Scorpio. lièh. Scotomenia. Rota Ixiònis. Scyphônes. Rubail. Sècans. Ruuabàh. Sector Circuli. Ruminàntia si- Segmentum circuli. gna. Sidera discurentia. Rythmus. Sectio equi. S. Secundi mobiles. Saclàteni. Sedùlli. Sacrarium. Selas. Sàgen. Semicirculus. Sagàtta sidus. Semilunium. Sagitta sinus. Semiquadràtus Sagittàrius. Sénacher. Salchadài. Sencinèr. Saltàtor. Separàtio. Sephîna. Septangulus. Septentriones. Septentriona- le. Septentrio vé- tus. Serpens. Serpentàrius. Sertù pupillæ. Serucuth. Sesquiquadrà- tus. Sexingulus. Sexagenària di- uisio. Sextans Astro- nomicus. Sextilis radius. Sidus. Sidera discu- rentia. Sideràtio. Silens luna. Signa. Signifer. Significatòres Simplasis. Sinaphia. Sinus. Sinus Abrahæ. Sirius. Sithacèr. Soail samuni.

Transcription: Translated (English)

INDEX. Regulares figuræ. Samèh. Regulus. Sartài Mesarthia. Remuneratio. Sartàn. Réte. Satellitium. Retrogradus. Satèllites. Reuolutio. Saturnus. Rhombus. Scalènua. Rhomboides. Scheàt. Riforitas dùnnatu. Schedèr. Régel. Sciographia. Ros. Sciothèrium. Rosa Come- Scintillàtio. tes. Sciron. Rósch Halli- Scorpio. lièh. Scotomenia. Rota Ixiònis. Scyphônes. Rubail. Sècans. Ruuabàh. Sector Circuli. Ruminàntia si- Segmentum circuli. gna. Sidera discurentia. Rythmus. Sectio equi. S. Secundi mobiles. Saclàteni. Sedùlli. Sacrarium. Selas. Sàgen. Semicirculus. Sagàtta sidus. Semilunium. Sagitta sinus. Semiquadràtus Sagittàrius. Sénacher. Salchadài. Sencinèr. Saltàtor. Separàtio. Sephîna. Septangulus. Septentriones. Septentriona- le. Septentrio vé- tus. Serpens. Serpentàrius. Sertù pupillæ. Serucuth. Sesquiquadrà- tus. Sexingulus. Sexagenària di- uisio. Sextans Astro- nomicus. Sextilis radius. Sidus. Sidera discu- rentia. Sideràtio. Silens luna. Signa. Signifer. Significatòres Simplasis. Sinaphia. Sinus. Sinus Abrahæ. Sirius. Sithacèr. Soail samuni.

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Transcription: ATR-1

LOCORVM ET VERBORVM. Sol. Stròbilus. Solicitium. Sublunària. Solicitùdo planetæ. Subsolanus. Siretæ. Sùhel. Solidum. Superficies. Sòlidus numerus. Superiòres. Solstitium. Sydus. Syderatio. Sors. Symmetria. Sòssos. Sympathia. Sòchis. Symphasis. Sotia. Synehon. Sothiaca periodus. Synodus. Sphæniscus. Syròccus. Sphæra. Systêma. Sphæra materialis. Syth. Sphæra lucis. Syzigiæ. Spica Virginis. T. Spicarum manipulus. Tàngens. Spiræ. Tanin. Splendor. Taraopòz. Spòrades. Taurus. Statio. Telescòpium. Stationarius Telum. Planeta. Temperamentum. Stella. Tempus. Stereometria. Tenaculum. Stilpon. Tenebròsi padus. Stilpòntes. Tenebròsi padus. Stripatòres. Trapoidis. Tepisatòsoa. Tepisa cràs. Tepiscuch. Ternuèlles. Terra. Terræmòtus. Terrèlla. Tèrrea signa. Testudo. Thàmyris. Tetraêdrum. Thèos. Tetràgonus. Thèma. Teù Vazàzene. Themeso. Thesogàr. Thopibici. Thopitus. Thràscias. Thronum. Thorquetum. Thùimis. Toueàn. Thùimis. Trabis. Traicctione. Trapoidis.

Transcription: Translated (English)

Of places and words. Sol. Stròbilus. Solicitium. Sublunària. Solicitùdo planetæ. Subsolanus. Siretæ. Sùhel. Solidum. Superficies. Sòlidus numerus. Superiòres. Solstitium. Sydus. Syderatio. Sors. Symmetria. Sòssos. Sympathia. Sòchis. Symphasis. Sotia. Synehon. Sothiaca periodus. Synodus. Sphæniscus. Syròccus. Sphæra. Systêma. Sphæra materialis. Syth. Sphæra lucis. Syzigiæ. Spica Virginis. T. Spicarum manipulus. Tàngens. Spiræ. Tanin. Splendor. Taraopòz. Spòrades. Taurus. Statio. Telescòpium. Stationarius Telum. Planeta. Temperamentum. Stella. Tempus. Stereometria. Tenaculum. Stilpon. Tenebròsi padus. Stilpòntes. Tenebròsi padus. Stripatòres. Trapoidis. Tepisatòsoa. Tepisa cràs. Tepiscuch. Ternuèlles. Terra. Terræmòtus. Terrèlla. Tèrrea signa. Testudo. Thàmyris. Tetraêdrum. Thèos. Tetràgonus. Thèma. Teù Vazàzene. Themeso. Thesogàr. Thopibici. Thopitus. Thràscias. Thronum. Thorquetum. Thùimis. Toueàn. Thùimis. Trabis. Traicctione. Trapoidis.

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Transcription: ATR-1

INDEX. Transitus. Vagiâh. Translàtio luminis. Velzàgora. Trapèziæ. Vazalzene. Trapezoides. Vectox. Triada. Velox cursu. Triches. Vêter draconis Trigonum. Ventus. Trigonocràtor Venus. Trigonometria. Ver. Vera. Tritàterum. Veràsua. Trimôrion. Vergiliæ. Trinus radius. Vertex. Trìquetrum. Vespèrta. Trìquetrum Vespertilio. Ptolemæi. Vesperùgo. Tropæi recti. Via combusta. Trópici. Via lactea. Trùtina Hermetis. Vigiles. Tsamàngadu. Vindimiàtor. Tuberòn. Violenta signa. Turbo. Virgæ. Turbo ventus. Virgo. Tympana. Vmbilicus Andromedæ. Typhon. Vociferator. V. Voluellum. V Acuus Vortex. cursu. Vraniscos. FINIS. Vrna. Vrsa. Vvega. Vultur cædens. Vultur volans. Vultùrns. Y. X Iphias Cometes. Xiphias sidas. Y Y Pàfricus. Z. Z Amoëtàr. Zàdaron. Zenith. Zèphirus. Zigeàtus. Zodiacus. Zonæ. Zoodòtes. Zophomenia. Zozàcus. Zubeneschemali.

Transcription: Translated (English)

INDEX. Transitus. Vagiâh. Translàtio luminis. Velzàgora. Trapèziæ. Vazalzene. Trapezoides. Vectox. Triada. Velox cursu. Triches. Vêter draconis Trigonum. Ventus. Trigonocràtor Venus. Trigonometria. Ver. Vera. Tritàterum. Veràsua. Trimôrion. Vergiliæ. Trinus radius. Vertex. Trìquetrum. Vespèrta. Trìquetrum Vespertilio. Ptolemæi. Vesperùgo. Tropæi recti. Via combusta. Trópici. Via lactea. Trùtina Hermetis. Vigiles. Tsamàngadu. Vindimiàtor. Tuberòn. Violenta signa. Turbo. Virgæ. Turbo ventus. Virgo. Tympana. Vmbilicus Andromedæ. Typhon. Vociferator. V. Voluellum. V Acuus Vortex. cursu. Vraniscos. FINIS. Vrna. Vrsa. Vvega. Vultur cædens. Vultur volans. Vultùrns. Y. X Iphias Cometes. Xiphias sidas. Y Y Pàfricus. Z. Z Amoëtàr. Zàdaron. Zenith. Zèphirus. Zigeàtus. Zodiacus. Zonæ. Zoodòtes. Zophomenia. Zozàcus. Zubeneschemali.

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Transcription: ATR-1

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Transcription: Translated (English)

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Transcription: ATR-1

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Transcription: Translated (English)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 112 112 113 113 114 114 115 115 116 116 117 117 118 118 119 119 120 120 121 121 122 122 123 123 124 124 125 125 126 126 127 127 128 128 129 129 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 150 150 151 151 152 152 153 153 154 154 155 155 156 156 157 157 158 158 159 159 160 160 161 161 162 162 163 163 164 164 165 165 166 166 167 167 168 168 169 169 170 170 171 171 172 172 173 173 174 174 175 175 176 176 177 177 178 178 179 179 180 180 181 181 182 182 183 183 184 184 185 185 186 186 187 187 188 188 189 189 190 190 191 191 192 192 193 193 194 194 195 195 196 196 197 197 198 198 199 199 200 200 201 201 202 202 203 203 204 204 205 205 206 206 207 207 208 208 209 209 210 210 211 211 212 212 213 213 214 214 215 215 216 216 217 217 218 218 219 219 220 220 221 221 222 222 223 223 224 224 225 225 226 226 227 227 228 228 229 229 230 230 231 231 232 232 233 233 234 234 235 235 236 236 237 237 238 238 239 239 240 240 241 241 242 242 243 243 244 244 245 245 246 246 247 247 248 248 249 249 250 250 251 251 252 252 253 253 254 254 255 255 256 256 257 257 258 258 259 259 260 260 261 261 262 262 263 263 264 264 265 265 266 266 267 267 268 268 269 269 270 270 271 271 272 272 273 273 274 274 275 275 276 276 277 277 278 278 279 279 280 280 281 281 282 282 283 283 284 284 285 285 286 286 287 287 288 288 289 289 290 290 291 291 292 292 293 293 294 294 295 295 296 296 297 297 298 298 299 299 300 300 301 301 302 302 303 303 304 304 305 305 306 306 307 307 308 308 309 309 310 310 311 311 312 312 313 313 314 314 315 315 316 316 317 317 318 318 319 319 320 320 321 321 322 322 323 323 324 324 325 325 326 326 327 327 328 328 329 329 330 330 331 331 332 332 333 333 334 334 335 335 336 336 337 337 338 338 339 339 340 340 341 341 342 342 343 343 344 344 345 345 346 346 347 347 348 348 349 349 350 350 351 351 352 352 353 353 354 354 355 355 356 356 357 357 358 358 359 359 360 360 361 361 362 362 363 363 364 364 365 365 366 366 367 367 368 368 369 369 370 370 371 371 372 372 373 373 374 374 375 375 376 376 377 377 378 378 379 379 380 380 381 381 382 382 383 383 384 384 385 385 386 386 387 387 388 388 389 389 390 390 391 391 392 392 393 393 394 394 395 395 396 396 397 397 398 398 399 399 400 400 401 401 402 402 403 403 404 404 405 405 406 406 407 407 408 408 409 409 410 410 411 411 412 412 413 413 414 414 415 415 416 416 417 417 418 418 419 419 420 420 421 421 422 422 423 423 424 424 425 425 426 426 427 427 428 428 429 429 430 430 431 431 432 432 433 433 434 434 435 435 436 436 437 437 438 438 439 439 440 440 441 441 442 442 443 443 444 444 445 445 446 446 447 447 448 448 449 449 450 450 451 451 452 452 453 453 454 454 455 455 456 456 457 457 458 458 459 459 460 460 461 461 462 462 463 463 464 464 465 465 466 466 467 467 468 468 469 469 470 470 471 471 472 472 473 473 474 474 475 475 476 476 477 477 478 478 479 479 480 480 481 481 482 482 483 483 484 484 485 485 486 486 487 487 488 488 489 489 490 490 491 491 492 492 493 493 494 494 495 495 496 496 497 497 498 498 499 499 500 500 501 501 502 502 503 503 504 504 505 505 506 506 507 507 508 508 509 509 510 510 511 511 512 512 513 513 514 514 515 515 516 516 517 517 518 518 519 519 520 520 521 521 522 522 523 523 524 524 525 525 526 526 527 527 528 528 529 529 530 530 531 531 532 532 533 533 534 534 535 535 536 536 537 537 538 538 539 539 540 540 541 541 542 542 543 543 544 544 545 545 546 546 547 547 548 548 549 549 550 550 551 551 552 552 553 553 554 554 555 555 556 556 557 557 558 558 559 559 560 560 561 561 562 562 563 563 564 564 565 565 566 566 567 567 568 568 569 569 570 570 571 571 572 572 573 573 574 574 575 575 576 576 577 577 578 578 579 579 580 580 581 581 582 582 583 583 584 584 585 585 586 586 587 587 588 588 589 589 590 590 591 591 592 592 593 593 594 594 595 595 596 596 597 597 598 598 599 599 600 600 601 601 602 602 603 603 604 604 605 605 606 606 607 607 608 608 609 609 610 610 611 611 612 612 613 613 614 614 615 615 616 616 617 617 618 618 619 619 620 620 621 621 622 622 623 623 624 624 625 625 626 626 627 627 628 628 629 629 630 630 631 631 632 632 633 633 634 634 635 635 636 636 637 637 638 638 639 639 640 640 641 641 642 642 643 643 644 644 645 645 646 646 647 647 648 648 649 649 650 650 651 651 652 652 653 653 654 654 655 655 656 656 657 657 658 658 659 659 660 660 661 661 662 662 663 663 664 664 665 665 666 666 667 667 668 668 669 669 670 670 671 671 672 672 673 673 674 674 675 675 676 676 677

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Transcription: ATR-1

I-3.

Transcription: Translated (English)

I-3.

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Transcription: ATR-1

1 2

Transcription: Translated (English)

1 2