Democritus Revived, or On Atoms

Creator: Jean-Chrysostome Magnen (Ioannes Chrysostomus Magnenus) | Date: 1646 | Notes: Original title: Democritus reviviscens, sive De atomis A systematic, demonstrative Latin treatise in natural philosophy, printed at Pavia in 1646 and dedicated to the Senate of Milan, that undertakes to rehabilitate the ancient atomism of Democritus as a rigorous and Christian-compatible physics. Organised into two chief parts—one on prime matter and one on atoms—it argues from within the scholastic tradition using a Euclidean apparatus of definitions, axioms, and postulates. It defines the atom as the root and beginning of material and physical extension, reduces the four elements to three (fire, water, and earth, with air demoted to a universal medium), rejects the void, holds that God composes all things from atoms, lodges substantial forms within individual atoms, treats sensible qualities as existing only by convention, defines color as internal refracted light, and refers local motion to impetus. It incorporates a free-fall experiment with wooden and iron globes and Galileo's odd-number law of fall, and appends a Vita Democriti and analytical indexes. 👉 <a href="https://tryleo.ai/collections/exlatinis/magnen-democritus-atomism-1646">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/iochrysostomimag00magn">View the original source file</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: Democritus Revived, or On Atoms
Creator: Jean-Chrysostome Magnen (Ioannes Chrysostomus Magnenus)
Date: 1646
Notes: Original title: Democritus reviviscens, sive De atomis A systematic, demonstrative Latin treatise in natural philosophy, printed at Pavia in 1646 and dedicated to the Senate of Milan, that undertakes to rehabilitate the ancient atomism of Democritus as a rigorous and Christian-compatible physics. Organised into two chief parts—one on prime matter and one on atoms—it argues from within the scholastic tradition using a Euclidean apparatus of definitions, axioms, and postulates. It defines the atom as the root and beginning of material and physical extension, reduces the four elements to three (fire, water, and earth, with air demoted to a universal medium), rejects the void, holds that God composes all things from atoms, lodges substantial forms within individual atoms, treats sensible qualities as existing only by convention, defines color as internal refracted light, and refers local motion to impetus. It incorporates a free-fall experiment with wooden and iron globes and Galileo's odd-number law of fall, and appends a Vita Democriti and analytical indexes. 👉 <a href="https://tryleo.ai/collections/exlatinis/magnen-democritus-atomism-1646">Read our introductory primer, full report, and finding guide here</a> 📜 <a href="https://archive.org/details/iochrysostomimag00magn">View the original source file</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: Democritus reviviscens, sive De atomis A systematic, demonstrative Latin treatise in natural philosophy, printed at Pavia in 1646 and dedicated to the Senate of Milan, that undertakes to rehabilitate the ancient atomism of Democritus as a rigorous and Christian-compatible physics. Organised into two chief parts—one on prime matter and one on atoms—it argues from within the scholastic tradition using a Euclidean apparatus of definitions, axioms, and postulates. It defines the atom as the root and beginning of material and physical extension, reduces the four elements to three (fire, water, and earth, with air demoted to a universal medium), rejects the void, holds that God composes all things from atoms, lodges substantial forms within individual atoms, treats sensible qualities as existing only by convention, defines color as internal refracted light, and refers local motion to impetus. It incorporates a free-fall experiment with wooden and iron globes and Galileo's odd-number law of fall, and appends a Vita Democriti and analytical indexes. 👉 Read our introductory primer, full report, and finding guide here 📜 View the original source file 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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AQUILA NON CAPTAT MUSCAS STILLMAN DRAKE LIBRARY of the UNIVERSITY of TORONTO

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The eagle does not catch flies STILLMAN DRAKE LIBRARY of the UNIVERSITY of TORONTO

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M 19 29 92 Galileo 230 253-4

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M 19 29 92 Galileo 230 253-4

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DE ATOMIS

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DE ATOMIS

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Digitized by the Internet Archive in 2024 with funding from University of Toronto https://archive.org/details/iochrysostomimag00magn

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Digitized by the Internet Archive in 2024 with funding from University of Toronto https://archive.org/details/iochrysostomimag00magn

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IO: CHRYSOSTOMI MAGNENI Burgundi, Philosophi, Medici, & in celeberrima Ticinensi Vniuersitate Regij Medicinæ Professoris DEMOCRITVS REVIVISCENS SIVE DEATOMIS Ad Excellentissimum SENATVM Mediolanensem. Addita est Democriti vita cum Indicibus necessarijs. PAPIÆ, Apud Io: Andream Magrium. Ann. M. DC. XLVI. SUPERIORVM PERMISSV.

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IO: CHRYSOSTOMUS MAGNENI Burgundian, Philosopher, Physician, and in the most celebrated University of Ticino Royal Professor of Medicine DEMOCRITUS REVIVING OR DE ATOMIS To the Most Excellent Senate of Milan. The life of Democritus, with the necessary indexes, is added. Pavia, אצל Io: Andrea Magri. Year 1646. With the permission of the Superiors.

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Opus philosophicum Doct. Medici Io: Chrysostomi Magneni Ticinensis Professoris, cui titulus est Democritus Reuiuiscens, ego infrascriptus attentè perlegi, & cùm nihil contineat, quod legibus aduersetur, quinimò singulari doctrina, subtilitate, ac eruditione sit refertum, ideò dignum censeo, vt Typis expressum in publicam prodeat vtilitatem, si ità videbitur Reuerendissimo Patri Inquisitori &c. Ego Io: Baptista Belcredius Doctor Collegiatus Regius Interpres Primarius in Gymnasio Ticinensi, & Sanctissimæ Inquisitionis Librorum Censor &c, Imprimatur Vicarius Sancti Officij Papiæ. Comes Maior agius pro Excellentissimo Senatu.

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The philosophical work of the physician Doctor Io: Chrysostomus Magnenus of Pavia, Professor, entitled Democritus Reuiuiscens , I, the undersigned, have carefully read, and since it contains nothing that is contrary to the laws, but rather is full of singular learning, subtlety, and erudition, I therefore judge it worthy to be printed and brought forth for the public benefit, if it shall so seem good to the Most Reverend Father Inquisitor, etc. I, Io: Baptista Belcredius, Doctor of the Royal College, Chief Interpreter in the University of Pavia, and Censor of Books of the Most Holy Inquisition, etc., Imprimatur. Vicar of the Holy Office of Pavia. Comes Maioragius for the Most Excellent Senate.

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EXCELLENTISSIMI SENATVS MEDIOLANENSIS ÆQVISSIMO PRÆSIDI D. OCTAVIANO PICENARDO I. C. CREMONENSI ILLVSTRISSIMIS CONSULTISSIMISQVE SENATORIBVS D. ALOYSIO BELCREDIO I. C. Ticinensi. D. IO: BAPTISTÆ BONETTO I. C. Cremonensi. D. PETRO PETRACINO I. C. Laudensi. D. IO: ARIAS MALDONATO I. C. Hispano. D. OTHONI CAIMO I. C. Mediolanensi. D. ANDREA ALIFERO I. C. Mediolanensi. D. MATTHÆO BIMIO I. C. Mediolanensi. D. IO: BAPTISTÆ CANTONO I. C. Alexandrino. D. ALFONSO DELRIO NORIEGA I. C. Hispano. D. FABIO FRANCISCO DVGNANO I. C. Mediol. D. GVIDOBONO CAVALCHINO I. C. Ticinensi. D. CAROLO PATELLANO I. C. Mediolanensi. D. AUGUSTINO NAVARROBVRENÆ I. C. Hisp. Io: Chrysostomus Magnenus immortalem gloriam P. 3

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To the most excellent Senate of Milan, to the most equitable president D. Octavian Picenardo, lawyer of Cremona, to the most illustrious and most learned senators, D. Aloysio Belcredio, lawyer of Pavia. D. Io: Baptista Bonetto, lawyer of Cremona. D. Peter Petracino, lawyer of Lodi. D. Io: Arias Maldonato, lawyer of Spain. D. Otho Caimo, lawyer of Milan. D. Andrea Alifero, lawyer of Milan. D. Matthæo Bimio, lawyer of Milan. D. Io: Baptista Cantono, lawyer of Alessandria. D. Alfonso Delrio Noriega, lawyer of Spain. D. Fabio Francisco Dugnano, lawyer of Milan. D. Guidobono Cavalchino, lawyer of Pavia. D. Carolo Patellano, lawyer of Milan. D. Augustino Navarroburenæ, lawyer of Spain. Io: Chrysostomus Magnenus, to immortal glory P. 3

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PATRES AMPLISSIMI. ONSECRO vestro nomini philoso- phiæ meæ primitias, quæ vobis prius de- stinatæ sunt quam natæ: ijs singulares vniuscuiusque vestrum adoraturus eram virtutes, at nunc insigne mihi à vestra munificentia collatum agniturus beneficium; quo scilicet me in emeritorum sub- sellia euexistis, dum Regium nominauistis Professorem, & honorario meritis meis maiori auxistis. Sentio satis tanto plus à me expectari quo gradus maior est in quo me esse voluistis; neque verò faustis vt ignauià otioq; torperem, sed quam ab vnoquoque vestrum grauissimam accepi adhortationem dum adiui singulorum domos, bene- ficientissimas in me manus venerabundè deliberaturus; vide- rem vt spei de me conceptæ responderent facta, exploremq; omni- um expectationem, hæc inquam admonitio ità insedit menti vt vires animosq; dederit ad referendos Elysios, rediuiuum vobisstituro Democritum, cuius sapientissima doctrina iam dudum interpretem sibi exposerbat vel apologiam. Reuerà cum amicorum suasionibus adductus fui vt ab physica qua- dam tractatione typos lacesserem, diù animo fui inter va- rias designationes fluctuante; Dum itaq; anceps animi con- silium meum excutio, id quod Seuerinus ille Boetius ordinis Sena-

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MOST DISTINGUISHED FATHERS. I consecrate to your name the first fruits of my philosophy, which were destined for you before they were born: to these I was about to adore the singular virtues of each one of you, but now I acknowledge the distinguished benefit bestowed on me by your munificence; by which, namely, you have raised me to the seats of the meritorious, when you named me Royal Professor, and increased my honor with a reward greater than my merits. I feel that so much more is expected of me, since the rank to which you wished me to be elevated is greater; and indeed I should not, through favor, grow dull in inactivity and idleness, but rather, from the most serious exhortation I received from each of you while I visited the houses of all, reverently considering your most beneficent hands toward me, I should see that my deeds corresponded to the hope conceived of me, and test the expectation of all. This admonition, I say, settled so deeply in my mind that it gave me strength and courage to present to you the Elysian, revived Democritus, whose most wise doctrine had long since been demanding an interpreter, or even an apology for itself. Indeed, when I was moved by the persuasion of friends to venture upon some treatment of physics, for a long time my mind wavered among various plans; and while I was thus trying to settle my doubtful purpose, that which that Severinus Boethius of the Sena-

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Senatorij, triumphantifq; togæ sapientissimum ferculum, sibi in carcere detento conrigisse finxit cum philosophia ipsa colloqui, id enim verò mihi in musæo pene accidit, veterum juniorumq; Sapientias audire disceptantes: illa quidem ob- soletis vestibus, obscuro vultu, vixq; humani quidquam ob- lutum, & squallorem retinente; hæc autem loquacior, com- ptula & factu pene tyranico superba; at vbi antiquior Se- niorq; sapientia plurimà aqua serenum sibi nariumq; vul- tum sorditie abiecta restituit, tunc enim maiestatis visa mi- hi est pene adorandæ, vnumq; pro se adduxit argumentum quod scilicet propior origini, æternæ scilicet veritati, ab ea minus aliquanto quam iunior sophia aberraret: atomorumq; opinionem veluti grande palmariumq; mentium humanarum opus produxit in medium, reliquitq; me in hac atomorum cogitatione defixum. Ea sanè digna visa est quæ ab ipsius antiquioris Sapientiæ ore prodiret, appositumq; vobis munusculum duxi, tum quod id opus à nullo hactenus fue- rit pertractatum (Sennertus si quidem qui vno capite de illis agit atomos nequaquam, sed minima physica dari probauit) tum etiam quod subtilissimæ indagationis, in præ- struendis principijs, & ad stabiliendam doctrinam, eliciendasq; consequentias, plurimum haberet. Res ardua est ve- tustis nouitatem dare; nouis autoritatem, obsoletis nitorem, ob- scuris lucem, fastiditis gratiam, dubijs fidem, omnibus verò na- turam, et naturæ sua omnia: itaque etiam non assecutis voluisse pulchrum est. Non explebo vnquam vel assequar exquisitissima Democriti sensa, sed sicuti pueri olim repandis vlnis Rhodij Colossi digitos metiebantur; ità vastas huius inge- niorum Pitænicis cogitationes veluti pumilo nisu ambiri à me perspicietis; Democritum itaq; luci nostræ restituere placuit, & tanto philosopho ad celeberrimum tot philosophis fæcu-

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Senator, with a triumphant toga, the wisest dish, pretending to himself that he had conversed with philosophy itself while detained in prison, and indeed this almost happened to me in my museum, to hear the Wisdom of the ancients and the younger sort disputing: the former indeed in worn garments, with a dark face, hardly retaining anything human, and its squalor; the latter more loquacious, trim and in manner almost tyrannically proud; but when the older and senior Wisdom, with much water, had restored to itself a serene countenance and nose, putting aside filth, then it seemed to me almost worthy of worship in its majesty, and it brought forward for itself one argument, namely that, being nearer to the origin, that is, to eternal truth, it wandered from it somewhat less than younger sophia: and it set forth the opinion of atoms as a great prize and the work of human minds, and left me fixed in this thought of atoms. It certainly seemed worthy to proceed from the mouth of Wisdom itself, and I judged it an appropriate little gift for you, both because that work has until now been handled by no one (for Sennertus, who in one chapter deals with them, by no means approved atoms, but proved that physical minima are given), and also because it would have much of the most subtle inquiry, both in laying down first principles and in establishing the doctrine, and drawing out consequences. It is a difficult thing to give antiquity novelty; to the new authority, to the obsolete brilliance, to the obscure light, to the despised grace, to the doubtful faith, but to all things nature, and to nature all things of its own: therefore it is also beautiful even not to have attained, but to have wished. I shall never exhaust, nor shall I attain, the most exquisite thoughts of Democritus; but just as once boys with outstretched arms measured the fingers of the Rhodian Colossus, so you will perceive that I with feeble effort am striving to encompass the vast Pythian thoughts of this genius; it pleased me therefore to restore Democritus to our light, and to present to so great a philosopher among so many celebrated philosophers a very small gift.

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fæculum esse admissionalis, vitam illi concessi posthumam, mixtasq[ue] minurissimis cineribus eius corporis atomos ab antiquorum runderibus, rogisque eruere sum conatus: imperfectum sanè spirat, lucisque huius vsuram ab vettræ protectionis aura sibi exposcit, cæteroqui si fauere destituatur vetro comburetur iterum, fatoq[ue] illi subiacebit acerbissimo, quod exsuscitatum impijs artibus ab Erichtone cadauer de quo eloquentissimus Poeta Lucanus Vadit defunctus ad ignes. Absit hoc omen: fouebitis enim virum legislatorem, Senatus abderitani præsidem, diuinæq[ue] si Herculem consecramus, nobilitatis; amplectentur Hippocratis amicum Medici, scientiæq[ue]; vniuersalis virum docti omnes apud quos id fortè promouero, vt illorum aliquis excultionis ingenij id perficiat, cui principium dedi. Vos interea, PATRES CONSCRIPTI, conatibus meis fauete, & dum alij cælos integros, fori contentiones, medelarumq[ue]; volumina vestris aris appendent, atomum etiam inter ea donaria adesse patiamini. Valete. Ticini Regij prid. Kal. Maij Anno M. DC. XLVI.

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As a dregs fit only for admission, I have granted it a posthumous life, and have tried to rescue the atoms of its body, mingled with its very smallest ashes, from the ruins and pyres of the ancients: it breathes indeed in an imperfect state, and asks for the benefit of this light under the protection of your favor; otherwise, if it is left without your support, it will be burned again and fall under that most bitter fate, of which the corpse, raised up by impious arts by Erichtho, the eloquent poet Lucan says: “The dead man goes to the flames.” May this omen be far away. For you will cherish a man who is a legislator, president of the Senate of Abdera, and, if we consecrate Hercules, the nobility of divinity; the doctors will embrace a friend of Hippocrates, and all the learned the friend of science and a universal man, among whom I may perhaps advance this work, so that some one of them may complete, by the cultivation of his genius, what I have begun. Meanwhile, YOU, CONSCRIPT FATHERS, favor my efforts, and while others hang up whole heavens, the contests of the forum, and volumes of remedies on your altars, allow this atom also to be among those gifts. Farewell. Pavia, the day before the Kalends of May In the year 1646.

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SYLLABVS Disputationum, & Propositionum de Atomis. PROLEGOMENA. DEMOCRITVS REVIVISCENSIVE DE ATOMIS, eadem reperiatur inesse, Fundamentum totius Operis eius tia vt sit ingenerabilis, & in- distributio, & methodus corruptibilis, quarta vt in ab elementis. ipsa corpora omnia per dissolu- Definitiones tione vltima resoluantur. 36 Principia Propositio II. Elementa sunt Postulata primum vniusquisq; corporis Caput I. Elementa esse mate- subiectum, in omnibus corpo- riam primam. ribus naturalibus eadem re- Propositio I. Quatuor sunt ma- periuntur inesse, sunt ingene- teriæ primæ proprietates ab ip- rabilia, & incorruptabilia, sa inseparabiles: prima vt sit quodlibet corpus in ipsa per primum vniusquisq; corporis dissolutionem vltimam reso- subiectum secunda vt in om- luitur. 37 nibus corporibus naturalibus Propositio III. Elementa sunt materia prima. 48 Pro-

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SYLLABUS of Disputations and Propositions on Atoms. PROLEGOMENA. DEMOCRITUS REVIVED ON ATOMS, the same is found to inhere, Fundamentum totius Operis eius namely, that it is ingenerable, and in- distribution, and method corruptible; fourth, that in from the elements. the bodies themselves all things are by Definitions final dissolution resolved. 36 Principles Proposition II. The elements are Postulates the first subject of each and every body, Chapter I. That the elements are they are found to be in all natural bodies matter first. the same, are ingenerable, and incorruptible, Proposition I. There are four pro- whatever body is resolved into them by perties of primary matter inseparable from it: the first, that it is the final dissolution. 37 first subject of each and every body; the second, that in all Proposition III. The elements are primary matter. 48 Pro-

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SYLLABVS. Propositio IV. Materia prima quam Aristoteles proponit ex Ægyptiorum mente, omni-no inutilis est, tum physico, tùm medico. 49 Caput II. De natura, numero, & proprietatibus elementorum, iuxta Democriti placita. 49 Propositio V. Quatuor sunt Neotericorum de Elementis opiniones præcipuæ. 50 Propositio VI. Elementa iuxta Democriti placita defini-re. 52 Propositio VII. Elementum non componitur ex materia, & forma. 54 Propositio VIII. In quousi elemento tria sunt primariò considera[n]da, primò moles substantialis corporea: secundò qualitas prima; tertio appetentiamixtionis. Secundariò autem elementa contemplanda sunt vt partes vniversi, & vt mobilia localiter. 56 Propositio IX. No[n] est satis probatum à philosophis dari quatuor elementa. 59 Propositio X. Aer non est elementum. | 65| Propositio XI. Dantur tria tantum Elementa, Terra, Aqua, Ignis. | 70| Propositio XII. Definitiones primarum qualitatum ab Aristotele traditæ, sunt impropriæ, quare alias afferre tentau, Democriti placitis conformes. | 72| Caput III. Satisfit obiectionibus contra superiorem Democriti doctrinam. | 76| Obiectiones contra incorruptibilitatem, & numerum Elementorum. | 77| Obiectiones contra ternarium elementorum numerum | 83| Propositio XIII. Aer caret gravitate, & leuitate. | 86| Obiectio contra aeris indifferentiam | 91| DISPUTATIO II. Deco[n]positione reru[m] ex atomis | 94| Definitiones. | 95| Principia. | 96| Postulata. | 98| Caput I. Sententiæ celebres de com-

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Syllabus. Proposition IV. The first matter which Aristotle proposes according to the mind of the Egyptians is wholly useless, both physically and medically. 49 Chapter II. On the nature, number, and properties of the elements, according to Democritus’s opinions. 49 Proposition V. There are four principal opinions of the moderns concerning the elements. 50 Proposition VI. To define the elements according to Democritus’s opinions. 52 Proposition VII. An element is not composed of matter and form. 54 Proposition VIII. In any element there are three things primarily to be considered: first, the substantial bodily mass; second, the primary quality; third, the appetite for mixture. Secondarily, however, the elements are to be contemplated as parts of the universe, and as locally movable. 56 Proposition IX. It has not been sufficiently proved by philosophers that there are four elements. 59 Proposition X. Air is not an element. | 65| Proposition XI. There are only three elements, Earth, Water, Fire. | 70| Proposition XII. The definitions of the primary qualities handed down by Aristotle are improper; therefore I have attempted to put forward others, conformable to Democritus’s opinions. | 72| Chapter III. Objections against the above doctrine of Democritus are answered. | 76| Objections against the incorruptibility and number of the elements. | 77| Objections against the ternary number of the elements | 83| Proposition XIII. Air lacks heaviness and lightness. | 86| Objection against the indifference of air | 91| Disputation II. On the decomposition of things from atoms | 94| Definitions. | 95| Principles. | 96| Postulates. | 98| Chapter I. Celebrated opinions about com-

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SYLLABVS: compositione continui 98 Propositio XIV. Continuum no[n] constat ex punctis mathematicis. 98 Propositio XV. Continuum no[n] co[n]ponitur ex partibus, et punctis mathematicis simul. 100 Propositio XVI. Continuum non co[n]stat ex simplici entitate ante diuisione indistincta. 101 Propositio XVII. Continuum non constat partibus syncategorematicè infinitis. 102 Propositio XVIII. Numerus partium continui non est sicuti numeri finiti possibiles. 102 Caput II. Quod omnia ex atomis constant. 104 Propositio XIX. Continuum co[n]ponitur ex atomis, siuè corpusculis finitis numero, adæquatè inter se distinctis, certæ & determinatæ arcæ. 104 Propositio XX. Atomi definitionem dare. 113 Caput III. De atomoru[m] proprietatibus. 116 Propositio XXI. Omnibus atomis conuenit triplex mobilitas primaratione Vniuersi, secun- daratione Vacui, tertia ratione mixti. | 116 Propositio XXII. Datur sympathia inter atomos. 118 Propositio XXXIII. De atomorum paruitate aliquid coniecturà assequi. 122 Propositio XXIV. Atomis aeris insitum est, & proprium cu[m] alijs Vniri nunquam. 125 Propositio XXV. Quomodo se habeant atomi igneæ, aqueæ, & terreæ ad Vnionem determinare. 126 Propositio XXVI. Atomis sua inest figura. 129 Examen doctrinæ Platonicæ de elementorum figuris. 130 Propositio XXVII. Atomis igneis figurâ assignare ex Democrito. 138 Propositio XXVIII. Atomorum terrearum figurâ ex Democrito determinare. 143 Propositio XXIX. Atomis aquearum figuram determinare. 149 Propositio XXX. De atomorum aerearum figura iuxta Democritu[m] pronuntiare. 153 Propo-

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SYLLABVS: On the composition of the continuum 98 Proposition XIV. The continuum does not consist of mathematical points. 98 Proposition XV. The continuum is not composed of parts and mathematical points together. 100 Proposition XVI. The continuum does not consist of a simple entity indistinct before division. 101 Proposition XVII. The continuum does not consist of parts infinitely syncategorematic. 102 Proposition XVIII. The number of parts of the continuum is not like the number of possible finite things. 102 Chapter II. That everything consists of atoms. 104 Proposition XIX. The continuum is composed of atoms, or of small bodies finite in number, adequately distinct from one another, of a certain and determinate size. 104 Proposition XX. To give a definition of the atom. 113 Chapter III. On the properties of atoms. 116 Proposition XXI. All atoms are endowed with a triple mobility, first by reason of the Universe, secon- dly by reason of the Void, thirdly by reason of the mixture. | 116 Proposition XXII. There is sympathy between atoms. 118 Proposition XXXIII. To arrive at something by conjecture concerning the smallness of atoms. 122 Proposition XXIV. It is inherent in, and proper to, the atoms of air never to be united with others. 125 Proposition XXV. To determine how the fiery, watery, and earthly atoms behave with regard to union. 126 Proposition XXVI. Each atom has its own figure. 129 An examination of the Platonic doctrine concerning the figures of the elements. 130 Proposition XXVII. To assign a figure to the fiery atoms according to Democritus. 138 Proposition XXVIII. To determine the figure of the earthy atoms according to Democritus. 143 Proposition XXIX. To determine the figure of the watery atoms. 149 Proposition XXX. To pronounce on the figure of the aerial atoms according to Democritus. 153 Propo-

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SYLLABVS. Propositio XXXI. Motus atomorum ad figuram potest explicari analogicè. 155 Caput IV. Demixtione, & dissolutione atomorum. 160 Propositio XXXII. Mundi genesim explicare per atomos iuxta Democritum. 160 Propositio XXXIII. Modus agendi atomorum est triplex: Primus per intrusionem sui in poros: Secundus per propagationem qualitatis in spatio libero: Tertius per inhibitione qualitatis contrariæ. 166 Propositio XXXIV. Modu[m] quo atomi miscetur explicare. 169 Propositio XXXV. Plures sunt mixtionum gradus, una ordinatur ad perfectiorem, & mixta simpliciora perfectiorum sunt materia, mixtisq[ue] plurimi insunt pori qui ab atomoru[m] seriatim positarum connexione ortum habent. 172 Propositio XXXVI. Explicatur dissolutio mixti ex Democriti principijs. 178 DEMOCRITVS Docens, siue, paradigmæ explicandi ardua quæuis per corpusculorum doctrinam. | 183| Thema Philosophicum. | 183| Status quæstionis. | 183| Inuestigatio generalis. | 183| Color, siue adaptatio. | 185| Resolutio quæstionis. | 186| Annotationes. | 186| Reflexio. | 187| Caput V. Difficultatum in quæstione continui solutio ex proprijs atomorum principis. | 188| Seminarium Responsionu[m] ad argumenta mathematica. | 188| Lemma I. Mathematica abstrahit ab omni materia, & subiecto reali. | 188| Lemma II. Diuisibilitas extrinseca non infert diuisibilitatem intrinsecam. | 189| Lemma III. Non sunt expendendæ actiones physicæ regulis geometricis. | 190| Obiectiones mathematicæ. | 191| Obiectio I. De triangulo. | 191| Obiectio II. De quadrato. | 191| Obiectio III. De circulis concentricis. | 193|

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SYLLABUS. Proposition XXXI. The motion of atoms toward form can be explained analogically. 155 Chapter IV. On the mixture and dissolution of atoms. 160 Proposition XXXII. To explain the genesis of the world through atoms according to Democritus. 160 Proposition XXXIII. The mode of action of atoms is threefold: First, by their intrusion into pores; Second, by the propagation of quality in free space; Third, by the inhibition of a contrary quality. 166 Proposition XXXIV. To explain the manner in which atoms are mixed. 169 Proposition XXXV. There are several degrees of mixture; one is ordered toward a more perfect one, and the simpler mixtures of the more perfect are their matter; and in mixtures there are many pores, which arise from the connection of atoms placed in sequence. 172 Proposition XXXVI. The dissolution of a mixture is explained from Democritus' principles. 178 DEMOCRITUS Teaching, or, paradigms for explaining difficult matters through the doctrine of corpuscles. | 183| Philosophical Theme. | 183| State of the question. | 183| General investigation. | 183| Color, or adaptation. | 185| Resolution of the question. | 186| Annotations. | 186| Reflection. | 187| Chapter V. Solution of the difficulties in the question of continuity from the proper principles of atoms. | 188| A nursery of responses to mathematical arguments. | 188| Lemma I. Mathematics abstracts from all matter and from the real subject. | 188| Lemma II. Extrinsic divisibility does not entail intrinsic divisibility. | 189| Lemma III. Physical actions are not to be weighed by geometric rules. | 190| Mathematical objections. | 191| Objection I. On the triangle. | 191| Objection II. On the square. | 191| Objection III. On concentric circles. | 193|

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SYLLABVS. Obiectio IV. De circuli tetra- pars B quàmaiores, & ma- tragonismo. i94 Propositio XXXVII. Pro- atomo ABC possumus as- blema. Meniscum, siuè lu- signare. 204 nulam quadrare. Obiectio I X. De motu rotę. 208 Obiectio V. De linea conchi- Obiectio X. De comparatione li. maioris, & minoris exten- 197 sionis. 209 Propositio XXXVIII. Dā- Obiectio XI. De luminis propa- tur lineæ quæ productę in infi- gatione, & figuratione. 210 nitum sumper magis, ac magis Obiectio XII. De illumin- acedunt, nunquam tamen atione globi. 212 vel intersecant se, vel se tan- Obiectio XIII. De continuo, gunt, & quamuis aliunde di- & tempore. 214 stent magis, & magis in infi- Obiectio XIV. De quantita- nitum, nunquam tamen ul- tis ratione. 214 tra certam distantiam à se in- Obiectio XV. De indiuisibili- vicem abese possunt. bus simul iunctis. 216 Scholium. Obiectio XVI. Argumentum Obiectio VI. De contactu glo- Zenonis. 216 bi, & plani. Obiectio XVII. Contra indi- Obiectio VII. De lineis inse- uisibilitatem atomoru[m]. 217 cabilibus. Caput VI. Respo[n]sa ad Obie- Propositio XXXIX. La- tiones singularem atomorum tus quadrati est incommensu- doctrinam impugnantes. 217 rabile longitudine cum diame- Obiectio I. Pro Aristotelis tex- tro sua. tu 66. 3. de cælo c[on]tra id quod Obiectio VIII. De angulo con- diximus proposit 26. tetrae- tactus, & angulo acuto. dran[n]o posse replere lucu[m]. 218 Propositio XXXX. In ato- Præpositio XLI. Tetraedran[n]o mo A B C potest designari replent

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SYLLABUS. Objection IV. On the tetra- gonism of the circle. the part B, as larger, and ma- 94 Proposition XXXVII. Prob- lem. To square the meniscus, or atom ABC we can des- ignate. 204 lune. Objection IX. On the motion of the wheel. 208 Objection V. On the cochlear line. Objection X. On the comparison of 197 greater and smaller extension. 209 Proposition XXXVIII. Deter- Objection XI. On the propagation of mined lines which, being produced to infi- light, and its figure. 210 nity, always draw nearer and nearer, Objection XII. On the illumination yet never intersect or touch one another, of the globe. 212 and although they are farther and farther Objection XIII. On the continuous, apart from one another into infinity, and time. 214 nevertheless they can never be at a Objection XIV. On the relation of quan- greater distance from one another than a certain one. tities. 214 Scholium. Objection XV. On indivisibles joined together. 216 Objection VI. On the contact of the glo- Objection XVI. Zeno's argument. 216 be and the plane. Objection XVII. Against the indivisibility of atoms. 217 Objection VII. On inseca- ble lines. Chapter VI. Replies to the objections attacking the singular doctrine of atoms. 217 Proposition XXXIX. The Objection I. From Aristotle's text 66. 3. De caelo, against what side of the square is incommensu- rable with its diagonal. we said in proposition 26, that a tetra- hedron can fill a space. 218 Objection VIII. On the angle of con- tact, and the acute angle. Proposition XLI. The tetrahedron fills Proposition XXXX. In the ato- m A B C can be designated

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SYLLABVS! replent locum solidum. 219 Obiectio II. De Atomis, & 223 vacuo Democriti. 223 Obiectio III De mixtionis imperfectione. 223 Obiectio IV. De motu, tempore, rarefactione c[on]d[e]satione-intensione, & remissione. 223 DISPUTATIO III. De consequentijs præcipuis ex 225 Democriti philosophia deductis. 225 Definitiones. 225 Principia. 226 Postulata. 227 Caput I. De motu locali atomorum. 228 Propositio XLII. Quamuis admitti debeat grauitas, & 228 leuitas popularis, nihilominus tamen no[n] datur grauitas neq[ue]; 228 leuitas strictè, & philosophicè dicta. 228 Propositio XLIII. Motus localis est entitas permanens, 228 tota simul in natura, & sucessua in connotatione, cuius causa productrix est solus impetus. 233 Obiectiones. Contra doctrinam Democriti de motu locali. 237 Obiectio I. De motu tardissimo, & velocissimo. 237 Obiectio II. De quietibus, & saltibus, siuè transmissione spatiorum non transeundo per medium. 238 Propositio XLIV. Circularis motus in volutatione tripliciter fertur, motu scilicet progressivo, motu regressivo, & circa centrum, maior autem est retrocessio in maiori circulo quam in minori. 240 Obiectio III. De successione motus. 244 Caput II. De rarefactione, & condensatione iuxta Democritum. 245 Propositio XLV. Rerum quotidianus vsus rarefactionis, & condensationis naturam ostendit. 245 Propositio XLVI. Vnica atomus siue rarefactione, sine inflatione aut reproductione potest naturaliter occupare maiorem, et maiorem locum in infinitum. 247 Propo-

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SYLLABUS! fills the solid place. 219 Objection II. On the atoms, & 223 the void of Democritus. 223 Objection III. On the imperfection of mixture. 223 Objection IV. On motion, time, rarefaction, c[on]d[e]nsation, intensification, & remission. 223 DISPUTATION III. On the principal consequences drawn from 225 the philosophy of Democritus. 225 Definitions. 225 Principles. 226 Postulates. 227 Chapter I. On the local motion of atoms. 228 Proposition XLII. Although popular gravity and 228 lightness ought to be admitted, nevertheless there is no gravity nor 228 lightness strictly and philosophically speaking. 228 Proposition XLIII. Local motion is a permanent entity, 228 all at once in nature, and successive in notation, whose productive cause is impetus alone. 233 Objections. Against the doctrine of Democritus concerning local motion. 237 Objection I. On the slowest, and fastest motion. 237 Objection II. On rests, and leaps, or transmission of spaces without passing through the middle. 238 Proposition XLIV. Circular motion in rolling is carried in three ways, namely by progressive motion, by regressive motion, and around the center; but the retreat is greater in the larger circle than in the smaller. 240 Objection III. On the succession of motion. 244 Chapter II. On rarefaction, and condensation according to Democritus. 245 Proposition XLV. The ordinary use of things shows the nature of rarefaction, and condensation. 245 Proposition XLVI. One atom, whether by rarefaction, without inflation or reproduction, can naturally occupy a greater, and greater place without limit. 247 Propo-

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SYLLABVS. Propositio XLVII. Quamuis 258 admitti debeat aliqua in natura

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SYLLABUS. Proposition XLVII. Although 258 something must be admitted in nature

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PROLEGOMENASIVE Anteloquia ad doctrinam Democriti de atomis autorandam, & meliùs intelligendam. VM primogenitam inter omnes sapientum sectas atomorum philosophiam restituere designauerim, eiusque opinionis famam mille calumnis obsoletam vindicare, operæ pretium visum est anteloquia quædam præmittere in quibus curiosus lector de vita, moribus, scriptis, ingenioq[ue] illius qui eam sententiam acuratissimè omnium pertractauit iudicare posset; adde quod necessarium fuit selectis autoritatibus ostendere legitima fuisse illius institutoris placita, quæ à me deducuntur, tum maioris claritatis gratià vniversam in synopsi tanquam in thesibus vnoq[ue] aspectu colligere opinionem, tandem in præfatione ad lectorem de huius temporis philosophis deq[ue] meo instituto pauca differere. Præcipuus atomorum patronus fuit Democritus quem Abderitem alij, alij Milesum vocauerunt hos inter fuit Blancanus in Chronologia mathematicarum. Ille est Democritus cui risum insanum affinxerè litteratorum plebs, huius vitam innocentissimam, mores probabiles, subtilissimos libros, stupenda inuenta, laudes, meritis minores, doctrinamq[ue] curiosam æquè ac facilem paucis his prolegomenis accipe. DE-

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PROLEGOMENA Preliminary notes for the doctrine of Democritus on atoms, to be treated and better understood. Since I have proposed to restore the philosophy of atoms, first born among all the sects of the wise, and to vindicate the reputation of that opinion, darkened by a thousand calumnies, it seemed worthwhile to add certain preliminary notes, in which the curious reader might judge the life, habits, writings, and character of the one who most carefully of all handled that doctrine; moreover, it was necessary to show, by selected authorities, that the teachings which I set forth derived from its rightful founder; then, for greater clarity, to gather the whole opinion into a synopsis, as if into theses, and with a single glance; finally, in the preface to the reader, to say a few words about the philosophers of this age and about my own undertaking. The chief patron of the atoms was Democritus, whom some called an Abderite, others a Milesian; among these was Blancanus in the Chronology of Mathematics. He is the Democritus to whom the common crowd of men of letters attached the name of insane laughter. His most innocent life, respectable conduct, most subtle books, astonishing discoveries, praises less than his merits, and his curious yet easy doctrine, accept in these few preliminary notes. DE-

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DEMOCRITI VITA. VANTVM authoritas hominum opinionibus imponit, tantum nosse interest authorem eorum, quæ adducuntur in medium; ob id plurimos de rebus à Democrito gestis, scriptis, dictisue consului, vt tùm meæ tùm aliorum cupiditati satisfieret. Omnes honorificam de eo faciunt mentionem: vt Hipocrates sibicoænus, Aristoteles, Theophrastus, Ælianus, Seneca, Constantinus Cæsar, Plinius, Iulianus, Lucretius, Plutarchus, Eustatius, Athenodorus, Athenæus, Diogenes Laertius, Lucianus, Apuleius, Petronius Arbiter, alijq[ue] minores litterarum Genij quos post tanta nomina laudare nefas sit. Ante annos bis mille supra 166., sexcentis, & octoginta post excidium Troianum annis, æternæ mentis Numen duo molitum est ædificia, Imperij scilicet Romani fundamenta iecit dictatore 1. qui Imperatores referret creato, & sapièriè collossum erexit in Thracia effuso in lucem Democrito; vt dum caput orbis cæterè genti humanæ iura diceret, Democritus regnaret in omnium ingenia. Non parum contulit ad erigendos eius animos natalium splendor, qui plerumq[ue] circumstantium pomparum familiaritate altas cogitationes inspirat designationesq[ue]; maiorum gloria non indignas. Inuenit cælestem nobilitatem domi; erat enim Herculis ex fratre nepos, vt testatur Abderite epistola ad Hippocraté ex Oenopidis familia; reperit opulentiam præterea, regios philosophos patris domesticos, penates Monarcharum hospitalitate inclytos celebres sapientum conventus foris, & vbiq[ue] addiscendi opportunitatem. A Cum

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THE LIFE OF DEMOCRITUS. Only as much authority does the reputation of men impose on opinions as it matters to know the author of the things brought forward into the open; for this reason I consulted many writings and sayings about the deeds of Democritus, so that both my own curiosity and that of others might be satisfied. All make honorable mention of him: Hippocrates of Cos, Aristotle, Theophrastus, Aelian, Seneca, Constantine Caesar, Pliny, Julian, Lucretius, Plutarch, Eustathius, Athenodorus, Athenaeus, Diogenes Laertius, Lucian, Apuleius, Petronius Arbiter, and other lesser geniuses of letters, whom after so many great names it would be wrong to praise. More than 2,166 years ago, six hundred and eighty years after the destruction of Troy, the divinity of eternal mind devised two works: it laid the foundations of the Roman Empire, creating a dictator who would reproduce the emperors, and it raised a colossal figure in Thrace, brought forth to light as Democritus; so that while the head of the world was proclaiming laws to the rest of humankind, Democritus might reign over all minds. Not a little did the splendor of his birth contribute to raising his spirit, for it often inspires high thoughts and noble designs through familiarity with the pomp of those around one; deeds not unworthy of the glory of his ancestors. He found a heavenly nobility at home; for he was the grandson of Hercules through a brother, as the letter of the Abderite to Hippocrates from the family of Oenopides attests; he also found wealth, royal philosophers in his father’s household, the household gods of monarchs made famous by hospitality, celebrated gatherings of sages abroad, and everywhere the opportunity for learning. A Cum

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2 Democriti Vita. Cum Xerxes apud Democriti patrem esset hospitatus, regio munere gratiam illi rependit; Is doctissimos Persas, quos ob reconditam sapientiam magos vocant, Caldæosq; astrologiæ peritissimos hospiti suo reliquit, qui Democritum diuinæ cælestisq; scientiæ mysterijs initiarunt, & cum viuacis ingenij iuueni admirationem sui fecissent, siuè sua reuisendi cupiditas consilium corrumperet, siuè quodominatione cumulatam sui discipuli sapiétiam optarent, exterorum ingesserunt curiositatem. Patre ergo demortuo hæreditas fratribus tribus diuisa est, quorum minimus natu Democritus minorem vltrò sibi poposcit portionem: Ea peregrinaturo erat accomodata, vt pote pecuniæ vis, quæ centum auri talenta, hoc est, iuxta plurimorum calculos, sexaginta aureorum millia facilè excederet. sed quamuis ea electio in fratrum commoda videretur, suspicione tamen vexârunt Democritum, quasi subdolosè moliretur aliquid; adeò ambigùè creditur ingenioso. Præceptoribus itaq; suis viæ ducibus, consuluit in Ægypto Gymno sophistas, sacerdotum geometriam audiuit, & ad interiora Aliæ scientiarum ingeniorumq; triumphator penetrans Caldæorum principes per totam Persidem inuestigauit; tum reflexit se ad Arabicum sinum, vbi sacra ciuilisq; doctrina felicioribus auspicijs excolebatur. Vidit in India quidquid magorum arx portenti clauderet, quam pene fabulosam nimio miraculo facit Philostratus: congressuq; cum litteratis hisce habito, lustrauit Æhtiopiam, & vbiq; perspicacis ingenij, honestæq; liberalitatis vestigia reliquit. Enim verò regressus in patriam omnium egens præterquam doctrinæ Damasum fratrem patricognominem, paterno in se animo est expertus; Ille enim fundi hæres paterni copiosissimo reditu sublimem. Oenopidis familię gradum alebat; dum purius patrimoniu[m], sed quod ideo facilius effluit, aurum scilicet cusum signatumq; paucis

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2. The Life of Democritus. When Xerxes had been entertained at the house of Democritus’s father, he repaid the favor with a royal gift. He left with his host the most learned Persians, whom, on account of their hidden wisdom, they call magi, and the Chaldeans, most skilled in astrology, who initiated Democritus into the mysteries of divine and heavenly knowledge; and when they had made him, a youth of lively genius, an object of admiration, either because a desire to revisit their own country troubled their plan, or because they wished to enrich the wisdom of their pupil with the reputation of their teaching, they stirred up his curiosity concerning foreign lands. After his father’s death, therefore, the inheritance was divided among the three brothers, and Democritus, the youngest, voluntarily asked for the smaller portion for himself. It was suited for travel, since it was a sum of money that would easily exceed a hundred talents of gold, that is, by the reckoning of most people, sixty thousand aurei. But although that choice seemed to benefit the brothers, they nevertheless vexed Democritus with suspicion, as if he were secretly plotting something; so ambiguous is genius judged. Taking his teachers, therefore, as guides on his journey, he consulted the Gymnosophists in Egypt, heard the geometry of the priests, and, pressing onward to the inner recesses and triumphs of the arts and minds, he sought out the leading Chaldeans throughout all Persia. Then he turned toward the Arabian Gulf, where sacred and civic learning flourished under happier auspices. In India he saw whatever prodigy the stronghold of the magi contained, which Philostratus makes almost fabulous by too great a marvel. And when he had conversed with these men of letters, he traversed Ethiopia, and everywhere left traces of a keen intellect and honorable liberality. Yet, returning to his homeland in want of everything except learning, he experienced the paternal spirit of his brother Damasus, surnamed after his father. For he, as heir of the paternal estate, sustained the lofty rank of the family of Oenopides with a most abundant income, while the purer patrimony—yet one that therefore slips away all the more easily, namely coined and stamped gold—[to a few].

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Democriti vita. 3 paucis annis Democritus exhaustisset. Quod mille minis, inuitâ Minerua, studium vix delibant pueri, id etiam adolescenti Democrito ità placuit vt in volu- ptuariam domum, quæ horto paternisq[ue]; ædibus ferè adhere- bat, secederet, vt commodius in eo silentio libris naturæq[ue]; con- templationi dederetur; reuera ità defixus erat in cogitatione animus, vt licet sacrificium iuxta Orphei præscripta Deo Pa- ni Pater appararet; non aduerterit nisi tùm demum cum mo- nitus fuit, facienti assisteret. Hoc excolendæ mentis studium quod voluptatis adoratio iuuentuti adeò incommoda, quod rei augendæ cupiditas quæ virilem ferè ætatem fascinat nulla ratione potuerunt minuere, ad extremam vsq[ue]; senectutem seruauit; tatum interest pulcherrimo otio à pueris assuescere. Auri pecuniarumq[ue]; contemptor quam qui maximè, diuitias enim, vt ait Seneca de prouidentia, tamquam onus bonæ mentis proiecit. Italicæ sectæ princeps fuit Pherecydes, cui Pythagoras, & deinde Telauges filius tanto parenti non impar in philosophico regno successit, sceptrum deinde Xenophani datum, postea caput renuntiatus est Parmenides, post hunc conscendit pul- pitum Zeno Eleates, deinde Leucippus qui moriens Democrito locum cessit: antequam tamen has partes obtineret rempu- blicam administrauit patrij consilij, arbiter, leges faxit, op- timasq[ue]; consuetudines inuexit; ita vt totius Ciuitatis curam oculosq[ue]; in se conuerteret, & instar cælestis cuiusdam numinis coleretur. Verum cum innata confirmataq[ue]; per tot anno- rum curricula discendi scribendiq[ue]; cupiditas e[ss]e publicis nego- tijs non rarò subtraheret, quæreretq[ue]; solitudines, sepulcris præterea frequentandis non abstineret, exploraret imagina- tionis vires, felicem specierum visibilium opinionem explica- ret, rarasq[ue]; vulgaribus ingenijs disciplinas crederet, in de- A 2 mentiæ

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The life of Democritus. 3 Democritus had spent a few years. That study, which boys scarcely taste under a thousand threats, against Minerva’s will, pleased even the young Democritus so much that he withdrew into a pleasure-house, which almost adjoined the garden and his father’s house, so that he might more conveniently devote himself there, in that silence, to books and the contemplation of nature; indeed his mind was so fixed in thought that, although he was preparing a sacrifice to God Pan Father according to the precepts of Orpheus, he did not notice it until he was at last warned to stand by the man performing it. This zeal for cultivating the mind, which is so detrimental to youth’s worship of pleasure, and the desire for wealth, which almost captivates mature age, could in no way diminish; he preserved it right up to extreme old age. Such is the importance of being accustomed from boyhood to the fairest of leisure. A despiser of gold and money as few others were; for riches, as Seneca says in On Providence , he cast off as though they were a burden to a noble mind. The leader of the Italian school was Pherecydes; after him Pythagoras, and then his son Telauges, no unworthy successor to so great a father in the kingdom of philosophy; the sceptre was then given to Xenophanes, afterward Parmenides was proclaimed head; after him Zeno the Eleatic ascended the platform, then Leucippus, who when dying yielded his place to Democritus. Before, however, he obtained these positions, he administered the commonwealth by his father’s counsel, acted as arbitrator, made laws, and introduced the best customs; so that he drew upon himself the care and attention of the whole city and was revered as though he were some heavenly deity. Yet since his inborn and long-confirmed desire to learn and write often drew him away from public business, and he sought solitude, and moreover did not refrain from frequenting tombs, examined the powers of imagination, explained the fortunate opinion of visible appearances, and held doctrines rare to ordinary minds, in derangement

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Democriti vita! mentiæ suspicionem venit: neq[ue] satis ab ea illum suspicione vindicauit Hippocrates, quin etiam Seneca populari errato sit assensus. Diuino senis nostri iudicio absolutus est, sapientiæq[ue] cumulatissimæ renuntiatus, quippe qui non seipsum modo, verum etiam si quem alloqueretur sapientissimum felici contagione faceret. In ea solitudine libros conscripsit quorum syllabum connectam; chymicis vacabat operationibus; naturæ explorabat in plantis vires; astrorum naturam motusq[ue]; contemplabatur: ibi specierum visibilium effusiones, quibus adeò ætas nostra gloriatur, adinuenit primus; neq[ue]; aliâ ratione frequentata ab ipso sepulcra crediderim, quam vt obscuritatis fauore imagines rerum melius detegeret; illa p[er]sæ enim per foramina in obscuru[m] species in oppositis parietibus albis produnt se se. Astrologiam calluit quam qui maximè, planetarumq[ue]; numerum septenario nô limitari pronunciauit, authore Seneca; nostrisq[ue]; ideo huius sæculi Keppleris, Galilæis, Scheineris, Reitenisq[ue]; palmam præripuit. Prædixit plurima quæ diuinitatis famâ honoresq[ue]; etiam conciliarunt, quod effectus naturales suis in causis futuros præcognosceret, & ea quæ nunc arcana pro plantis herbisq[ue]; fucandis, inscribendis foecundandisq[ue]; à plurimis tanquam noua venditantur, Democrito adscribi debent, teste Constantino Cæsare in lib. de agricultura: lac ab Hippocrate oblatum, capellæ quæ primò pepererat, & nigræ esse cognouit: diligentiæ curiosissimo miraculo. Imo vt aliqua à festiuo philosopho subdamus minus seuera, puellam Hipocratis comitem Virginem primo, sequenti verò die foeminam salutauit quod nocturnæ deflorationis vestigia in eius oculis perciperet; inuisâ generis humani dimidio sagacitate. Facundiæ erat gratissimæ quæq[ue]; animos deuinciret; qui ge- numus

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Democritus’s life! He came under suspicion of madness; nor did Hippocrates sufficiently vindicate him from that suspicion, and even Seneca agreed with the common error. By the divine judgment of our old man he was absolved, and declared endowed with the fullest wisdom, since by his happy contagion he made not only himself, but also anyone he addressed, most wise. In that solitude he wrote books, a list of which I shall set down; he was occupied with chymical operations; he investigated the powers of nature in plants; he contemplated the nature and motions of the stars. There he first discovered the emanations of visible species, by which our age greatly prides itself; nor do I believe that he frequented tombs for any other reason than that, with the aid of darkness, he might better detect the images of things; for those species pass through openings into the dark and appear on the opposite white walls. He understood astrology better than anyone, and declared that the number of the planets was not limited to seven, according to Seneca as author; and thus he snatched the palm from our age’s Kepplers, Galileos, Scheiners, Reitens, and the rest. He foretold many things that won him honors and even the reputation of divinity, because he would foreknow natural effects in their causes to come, and those things which are now sold by many as new secrets for coloring, inscribing, fecundating plants and herbs, ought to be attributed to Democritus, as Constantine Caesar testifies in book 1, On Agriculture: he recognized the milk offered by Hippocrates as black in the goat that had first given birth: a miracle of the most curious diligence. Indeed, to add something less severe from that cheerful philosopher, he greeted the daughter of Hippocrates, who accompanied him, first as a virgin and the next day as a woman, because he perceived the signs of nocturnal defloration in her eyes; with a sagacity hateful to half the human race. He was of the most pleasing eloquence, and he won over all hearts; which kind of...

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Democriti vita. genuinus est eloquentiæ character; vnde in priuatis etiam ser- mocinationibus ea afferebat sermonis condimenta, vt omne fastidium abesset, arteq[ue] fuit adeò mirabili, vt quod naturæ vires superat, mortuam Darij Regis coniugem ad vitam reuo- care lugenti principi, consolationemq[ue]; omnem respuenti pro- miserit: audiuit magna cupiditate audax propositum Darius recepitq[ue]; daturu[m] se quidquid ad inferos referandos esset opus; petijt à Rege, trium nomina qui luxissent nunquam: tractabilio- remq[ue]; Regis animum ea propositione, quæ communem homi- num sortem explicat, ità solatus est, vt quietè deinceps deside- rium coniugis pertulerit nihil ingeniosius eo artificio adinue- nit vnquam Rhetorica, hæc Iulianus in epistola ad Amerinum Mo- rum præterea integritas pudicitiaq[ue]; tanta vt rationibus exem- ploq[ue]; rarum veneris vsum commendaret, vt post Plinium, ait Rodericus à castrol. 3. c. 4. de natura mulierum: vnicum è coniuge filium suscepit Protagoram Abderitem, qui à patris sapientia abfuit quantum à viro puer vt testatur Ælianus lib. 1. c. 23. fa- tetur equidem Laertius, Protagoram, Democriti auditorem, sed parentem assignat, Artemonem, Apollodorus, & Dion in Persicis Mæandrum. Protagoras tamen quamuis tantum à præcepto- ris, vel Patris sui Democriti abfuerit sublimitate, Sapientia, vo- cabatur teste Phauorino, elogio planè insigni quod vnicæ infor- matum viuentemq[ue]; sapientia celebrat; eumq[ue]; valdè suspexit. Plato qui ei dialogum inscribit, & Apuleius in apolog. & in flor. l. 3. Natus erat ad amicitias Democritus, vnde, & Hippocrati medicorum Principi percarus, quo etiam nomine veneratio- nem apud præcipuos medicinæ vindices meretur: Philola[us] vsus est familiarissimê, cum Leucippo doctissimam amicitiam coluit: at verò non nihil simultatis fouit in Anaxagoram, quem insecutus est publicè quod sibi opiniones de sole, & luna arro- garet A 3

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Democritus’s life. This is the genuine mark of eloquence; whence, even in private conversations, he brought to speech such pleasant seasoning that all weariness was absent, and he was so marvelous in art that what surpasses the powers of nature he promised to do: to call back to life the dead wife of King Darius for a mourning prince who rejected all consolation. Darius heard the bold proposal with great eagerness and accepted it, saying that he would give whatever was needed to bring her back from the underworld; he asked the king for the names of three men who had never mourned. And by that proposition, which explains the common lot of mankind, he so consoled and softened the king’s mind that afterward he bore his wife’s loss quietly. Never did Rhetoric devise anything more ingenious than that device, says Julian in a letter to Amerinus Morus. Moreover, his integrity and chastity were so great that by argument and example he recommended the rare use of Venus; as after Pliny, says Rodericus a Castro, 3. c. 4. De natura mulierum. He had one son by his wife, Protagoras of Abdera, who was as far removed from his father’s wisdom as a boy is from a man, as Aelian testifies, book 1, c. 23. Laertius indeed admits that Protagoras was a hearer of Democritus, but assigns as his father Artemon; Apollodorus and Dion in the Persian histories name Maeandrus. Yet Protagoras, although he fell so far short of the sublimity, wisdom, and learning of his teacher, or father Democritus, was called wise, according to Phavorinus, with a title truly distinguished, for he alone fashioned a living wisdom; and Plato, who dedicates a dialogue to him, greatly admired him, as did Apuleius in the Apology and in the Florides, book 3. Democritus was born for friendships; hence he was very dear even to Hippocrates, prince of physicians, by which name also he deserves veneration among the foremost defenders of medicine. He was most intimate with Philolaus; with Leucippus he cultivated a most learned friendship. But indeed he fostered some enmity toward Anaxagoras, whom he openly attacked because he arrogated to himself opinions about the sun and the moon

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Democriti vita. 6 garet quas à Democrito mutuas tantum habuerat, easq; à priscis ad se deriuanas ingenuo famæ contemptu confessus est: dignus planè cuius gloriæ consultum sit qui ità antiquorum dignitati fauit: cæterum præter eam simultatis occasionem aliâ referunt; Anaxagoras ab tanti viri consortio auram captans popularem illum ijs horis adiuit quibus necessitas vnumquam libet officiosis urbanitatibus deesse cogit; excusatum ergo colloquium est; quam repullam iniquè ferens Anaxagoras in sui contemptum reflecti existimauit; sed præter stilorum digladiationes nihil cruenti hæc inimicitia peperit: plurium præterea familiaritatem fouit, quod seueritatem vitæ, scientiarumq; profundissima arcana, miris leporibus condiret, & facetissimus idem idemq; grauissimus videretur: præterea tot gentibus lustratis, tot ingeniorum concursatione cicur, excultusq; animus, facillimè ad aliorum genium inflectebat se se: duo enim sunt, quæ præter institutionem à puero urbanum flexibilemq; reddunt, gerere vel sua vel aliorum negotia ciuilia, & nationes lustrare. Socratis ambiuit culloquium, & cum lycæi contentiones fecissent Athenis nomen, illuc occultus ingeniorum doctrinæq; explorator penetrauit, gloria quam in illo litteratorum theatro tulisset spreta; voluptatem præterea maledicentiæ quæ viros in litteris illustres non rarò titillat, ita auersatus est vt innoxijs facetijs solum modo luderet, serenoq; potius vultu prodiret in publicum quam (licet aliquantulo tempore id ab eo sit factum) vt effuse riserit semper, quod ineptè quidam existimarunt hoc enim viro in Ciuitate sua Præsidi, Legislatori, Principi, Philosopho omnem abstitulisset authoritatem, & qui ob secessum solitudinisq, amorem dementiæ est accusatus ob ridendi sine ansa consuetudinem stultissimus leuissimulq; mortalium esset æstimatus; tantum abest, vt sapientia,

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Democritus’ life. 6 He confessed, with a noble contempt for fame, that the things he possessed as loans from Democritus, and which he had derived from the ancients, were his own; truly worthy of being cared for in his glory, who thus favored the dignity of the ancients: however, besides that occasion for hostility, they report another; Anaxagoras, seeking the popular breeze from the company of so great a man, visited him at those hours when necessity requires that a courteous call should never be absent; the interview was therefore excused; Anaxagoras, bearing this rebuff unfairly, thought it reflected contempt upon himself; but apart from verbal sparring this enmity produced nothing bloody: moreover, it fostered the intimacy of many others, because he tempered the severity of his life and the deepest secrets of the sciences with marvelous charm, and was seen to be at once most witty and most grave; furthermore, having traversed so many nations, and his mind, tamed and refined by the meeting of so many talents, most easily bent itself to the character of others: for there are two things which, besides upbringing from childhood, make a person urbane and pliant, namely, to conduct either one’s own or other men’s civil affairs, and to travel among nations. He sought Socrates’ conversation, and when the disputes of the Lyceum had made Athens famous, he entered there as a hidden scout of minds and learning, despising the glory he might have won in that theater of scholars; moreover, he so shunned the pleasure of mockery, which not rarely tickles men distinguished in letters, that he would play only with harmless jests, and would rather appear in public with a serene countenance than, although for a little while this did happen to him, to laugh immoderately forever, as some foolishly supposed; for this, in a man who was the guardian, lawgiver, prince, philosopher of his city, would have taken away all authority, and he who, because of his retreat and love of solitude, was accused of madness, because of his habit of laughing without cause would have been judged the stupidest and lightest of mortals; so far is it from the case that wisdom,

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Democriti vita. vta, corpus sapientiæ, Philosophia, in scientijs pentathlos, ab Hipocrate, Abderitanis quos inter degebat, & Anaxagora esset salutatus, alijsq[ue] nobilissimis honestatus vbiq[ue] fuisset elogijs: furorem potius quam risumipsi Athenæus, & Seneca adscripsere deditq[ue] inter alios Aristoteli occasionem tantum tribuendi in problematibus bili vtriq[ue] pro præstantioribus ingenijs. Defecisse senio testatur Laertius; pene furentem sub vitæ vltimam periodum scripsit Atheneus, & ille quidem odore panis triduò vitam protraxisse, dum Cerealia celebrarentur, ne eius forores funeris causa ab cætero mulierum conuentu abessent; hic autem aereo melle fouisse vitam narrat in sapientum cænis lib. 2. c. 3. reuera melle Pythagoricorum more delectabatur Democritus, Pythagorei enim præter mel pani adhibebant omnino nihil; Rogatusq[ue] Democritus quomodo sanitati prouidendum esset, si exteriora, inquit, oleo, interiora melle irrigentur. Suam experientia valde fauorabili confirmauit opinionem, vita ad centesimum nonum annum prorogata. Sed enim lege cautum erat ne qui patrimonium consumperat sepeliretur, viuens itaq[ue] sibi iustorum funebrium ius recuperauit Democritus, recitato publicè eximio palmarioq[ue] opere suo quod diacosmum magnum seu de mundorum systematibus composuerat, vnde non sepulturæ modo ius, verum etiam quinque aureorum millia pro lecturæ suæ honorario abstulit; eiq[ue] positæ sunt statuæ quib[us] peculiaris honor habebatur, eusiq[ue] in eius honorem nummi. Senatus populiq[ue] Abderitani publico luctu ingenti pompa elatus est. Hæc fuit Democriti vita, hic finis. Quoad eius personam habitumq[ue] corporis vt hoc annotationis demus Physiognomicis, & Metoposcopicis pauca annotauit. Ipse Democritus (ait Hippocrates in epistola ad Damagetum) Sub ampla, ac humilima platano fedebat in veste crassa; citra humeros desinente, solus, discalceatus, super lapidea fede, valde palli- A 4 dus

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The life of Democritus. Life, the very body of wisdom, philosophy, the pentathlete in the sciences, was by Hippocrates, among the Abderitans with whom he lived, and by Anaxagoras, and by others of the noblest sort, everywhere honored with eulogies: Athenaeus and Seneca ascribed to him rather madness than laughter, and among others this gave Aristotle occasion to assign black bile, in the Problems, to both as superior minds. Laertius testifies that he declined through old age; Athenaeus wrote that he was almost frenzied in the last period of his life, and indeed that he prolonged his life for three days by the smell of bread while the Cerealia were being celebrated, so that his sisters might not be absent from the customary gathering of women because of his funeral; Athenaeus, however, in book 2, ch. 3, says that he sustained his life with honeyed air in the banquets of the wise. Truly Democritus delighted in honey, after the manner of the Pythagoreans; for the Pythagoreans used nothing at all with bread except honey. And when Democritus was asked how health should be cared for, he replied: if the outer parts are moistened with oil, the inner with honey. Experience confirmed his judgment very favorably, his life being prolonged to his 109th year. But since the law provided that no one who had consumed his patrimony should be buried, Democritus, while still living, recovered for himself the right to a lawful funeral by publicly reciting that remarkable and excellent work of his, which he had composed on the great arrangement of the worlds, the Diacosmum Magnum, or On the Systems of the Worlds; from this he obtained not only the right of burial, but also five thousand gold pieces as a fee for his reading; and statues were set up to him, with special honor paid to them, and coins were struck in his honor. He was carried out by the senate and people of Abdera with a great public mourning and splendid procession. Such was the life of Democritus, such his end. As to his person and bodily appearance, so that we may give something of this to physiognomists and metoposcopists, a few notes have been made. Democritus himself (says Hippocrates in the letter to Damagetus) sat beneath a broad and low plane tree, dressed in a thick garment ending above the shoulders, alone, barefoot, upon a stone seat, very pallid...

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Libri à Democrito scripti. dus ac macilentus promissabarba. Lusciosis oculis fuisse videtur indicare Poeta vetus apud Gellium, Democriti enim oculos dicit luscificatos fuisse; frone fuit mediocr, lineis constanti tractu sulcatis sed modice longis, minusq; profundis, naso inter aquilum, & simum sed simo magis, labris tantisper hulcis, statura quam diuitem vocant: solitudini deditus vbi solus nonnumquam subridebat: in arguendo audax plusquam decuit vt patet in epistola ad Hippocratem; Ingenio quoad mores priuatos seu monasticam raro, quoad ciuilem saryrico, ad politicam serio, ad oeconomicam indifferenti, in physicis præcelluit, herbarum præsertim magiæq; naturalis, vt vocant, arcana pleraq; prodidit quod testantur Seneca, Plinius, Constantinus Cæsar. temperamento herculeo fuit ex bile, & melancholia, hæc constantem, illa viuidum prumptumq; reddidit. Floruit maximè sub Peloponesiaco bello 300. anno ab V. C. vt refert Plinius l. 30. c. 1. Scripsit autem Moralia, Physica, Mathematica, Philologica, & Mechanica, hæ sunt quinq; eius operum classes hi verò libri quorum plerosq; à Diogene Laertio accepi; reliquos cum suo teste laudo. MORALIA. 1 Pythagoras. 2 De affectu sapientis. 3 De his quæ sunt apud inferos. 4 Tritogenia, hoc est quod omnia ex tribus fiant quæ omnia humana contineant. 5 De probitate seu virtute. 6 De copiæcornu. 7 De sedatione animi, hoc est de tranquillitate, eius libri mentio- nem fecit Seneca. 8 Com-

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Books written by Democritus. Thin and meager, with a long beard. He seems to have had weak eyes, as an ancient poet apud Gellius appears to indicate, for he says that Democritus’ eyes were clouded; his forehead was middling, with lines furrowed by a steady course, though moderately long and somewhat shallow, his nose between aquiline and snub, but more snub, his lips somewhat hollowed, in stature what they call a tall man: devoted to solitude, and when alone he would sometimes smile. In arguing he was bolder than was fitting, as appears from the letter to Hippocrates; in genius, as to private morals or the monastic life, he was rare; as to civic matters satirical; as to politics serious; as to household matters indifferent; in physics he excelled, and he revealed most of the hidden secrets of herbs and of natural magic, as they call it, as Seneca, Pliny, and Emperor Constantine testify. He had a Herculean temperament, from bile and melancholy; the latter made him steadfast, the former lively and prompt. He flourished especially during the Peloponnesian War, in the 300th year from the founding of the City, as Pliny relates, book 30, chapter 1. Now he wrote Moral Works, Physics, Mathematics, Philology, and Mechanics: these are the five classes of his works; the books themselves, the greater part of which I have taken from Diogenes Laertius, I list; the rest I cite with their own testimony. MORAL WORKS. 1. Pythagoras. 2. On the Affection of the Wise Man. 3. On Things That Are Among the Dead. 4. Tritogenia, that is, that all things are made from three things, which contain all human things. 5. On Honesty, or Virtue. 6. On the Horn of Plenty. 7. On the Quieting of the Mind, that is, On Tranquility; Seneca made mention of this book. 8. Com-

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Libri à Democrito scripti. 9 8 Commentariorum vel domorum, id est de oeconomica disciplina. 9 Euesto, de felicitate seu felici statu perierat iam Thrasylitempore hic liber. 10 Scripsit etiam librum cuius titulus erat, Sermo operis vmbra vt videtur innuere Anaxagoras. 11 Legales causæ. PHYSICA. 1 Magnus diacolmus, palmarium Democritiopus in 12. saltem libros diuisum, quod tamen Leucippo adscribit Theophrastus, sed enim illum publice recitauit, vt ait Antisthenes, citaturq; à pluri- bus antiquis tanquam legitimus Democriti partus vt ab Epicuro epist. ad Herodot. 2 Paruus diacolmus: hic, superior de mundi machina agebat, si titulus idem dat libri; hic tamen de huius mundi compositione, alter verò de mundo isto deq; alijs quos innumeros sibi persuadebat. 3 Cosmographia. Lustratas à se prouincias complectebatur siquidem maximam orbis partem viderat. 4 De sideribus vagis seu planetis: in isto libro alios planetas præter septem vulgatos asserebat quod postea nuntij sideres prodiderunt: id extra dubium ponit Senecal. 7. nat. q. c. 3. 5 Denatura. 6 Denatura hominis siue de carne, hic liber consecratus est Hippocrati à Democrico extat enim epistola ea de re apud Hippocratem no. 37. qua quam floridè scripserit Democritus manifestè apparet. 7 De mente. 8 De sensibus. 9 De anima. 10 De liquoribus. 11 De

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Books written by Democritus. 9 8. Commentaries, or Houses, that is, on economic discipline. 9. Euesto, on happiness or a happy state; this book had already perished in the time of Thrasyllus. 10. He also wrote a book whose title was, Speech the shadow of the work, as Anaxagoras seems to suggest. 11. Legal causes. PHYSICS. 1. The Great Diacosmos, Democritus’ chief work, divided into at least 12 books; yet Theophrastus assigns it to Leucippus, but he, as Antisthenes says, published it openly, and it is cited by several ancient writers as the legitimate offspring of Democritus, as by Epicurus in his letter to Herodotus. 2. The Small Diacosmos: the former dealt with the machine of the world, if the same title is given to the book; this one, however, with the composition of this world, the other with that world and with others, innumerable as he believed them to be. 3. Cosmography. It comprised the provinces he had traveled through, since he had seen a great part of the world. 4. On the wandering stars, or planets: in this book he asserted that there were other planets besides the seven commonly recognized, which later the messenger-stars revealed; Seneca makes this beyond doubt, Nat. Q. 7, ch. 3. 5. On Nature. 6. On the nature of man, or On flesh; this book was dedicated to Hippocrates by Democritus, for there is a letter on this matter among Hippocrates, no. 37, in which it clearly appears how eloquently Democritus wrote. 7. On the mind. 8. On the senses. 9. On the soul. 10. On liquids. 11. On

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10 Libri à Democrito script. 11 De coloribus. 12 De differentibus fragoribus hoc est de sono. 13 Iudicium rerum naturalium. 14 De imagine seu præuidentia. 15 De pestibus. 16 Normę seu canones: hoc est principia, & axiomata totius philosophiæ naturalis. 17 De ambiguis, seu dubiorum libri tres. 18 Cælestes causæ siue de influxibus. 19 Aeriæ causæ siue de meteorologicis. 20 Phanæ causæ id est de sole vel apparentijs, quo in locolucis, & umbræ naturam explicuit, & sub apparentijs solares maculas complexus, est. Est autem sol apud Macrobiu[m] phana, & phanes vt apud Orpheum amor ità vocatur, quia ex Chao apparuit primus: sol autem quod maximè appareat, & quotidie oriatur dicitur phanes. 21 De igne, & de his quæ sunt in igne, Causæ. 22 Vocum causæ. 23 De causis plantarum, de semine, arbore fructu, qua in parte quantum excelluerit conijce ab eius industriarum fragmentis quæ collegit in suo libro de agricultura Constantinus Cæsar, & Plinius alijq[ue]. 24 De causis animalium. 25 De causis æquiuocis seu promiscuius. 26 De lapidibus, hic etiam doctissimus fuit Democritus, primus enim liquandi lapides, fingendi smaragdos, & quemlibet infundendi colorem rationes adinuenit, vt ait Seneca lib. 14. epistola 91. ebur mollire nouerat aliaq[ue] innumera. 23 De atomis scripsit librum quem sibi Epicurus adscribebat vt ex Halicarnasseo est autor Laertius lib. 10. in Epicuri vita. 28 De imaginatione reliquit imperfectu[m] opus quamuis illius vires diu explorasset. 29 Præ-

Transcription: Translated (English)

10 Books written by Democritus. 11 On colors. 12 On different sounds, that is, on sound. 13 Judgment of natural things. 14 On image, or providence. 15 On pestilences. 16 Rules or canons: that is, principles and axioms of the whole philosophy of nature. 17. On ambiguities, or three books of doubtful matters. 18. Celestial causes, or on influences. 19. Aerial causes, or on meteorological matters. 20. Phanae causes, that is, on the sun or on appearances, in which place he explained the nature of light and shadow, and under appearances included solar spots. Now the sun is phana, and phanes, as love is so called in Orpheus, because it appeared first out of Chaos; but the sun is said to be phanes because it appears most clearly and rises daily. 21. On fire, and on those things which are in fire, Causes. 22. Causes of sounds. 23. On the causes of plants, of seed, tree, fruit; from which part, how much he excelled, may be inferred from the fragments of his researches which Constantine Caesar collected in his book on agriculture, and Pliny and others. 24. On the causes of animals. 25. On equivocal or mixed causes. 26. On stones; here too Democritus was most learned, for he first invented the methods of liquefying stones, forming emeralds, and infusing any color whatsoever, as Seneca says, book 14, epistle 91. He knew how to soften ivory and countless other things. 23. He wrote a book on atoms, which Epicurus claimed as his own, as Laertius is the author from Halicarnassus, book 10, in the life of Epicurus. 28. He left an unfinished work on imagination, although he had long investigated its powers. 29. Pre-

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Libri à Democrito scripti. II 29 Prænotiones medicinæ de ratione victus. 30 Intempestiuorum, & tempestiuorum causæ. 31 De febre. 32 De excretis per tussim. 33 De insania, hunc enim librum scribebat eo ipso tempore cum eum insanum iudicabant Abderitæ, inuenitq[ue]; illi operi incumbente[m] Hip- pocrates in epistola ad Damagetum num. 21. ipse autem Democri- tus de polis ac sphæris tunc commentarios scripsisse refert in epist. ad Hippocratem, duo fortasse opera habens præ manibus. 34 De simulacris vagantibus seu speciebus visibilibus: id opus à se scriptum ait Democritus apud Hippo. in epist. nu. 28. MATHEMATICA. 1 De contactu circuli, & sphæræ. 2 De sententiæ differentijs, siue in quibus mathematici inter se differant. 3 De geometria. 4 De geometricorum numeris, hoc est de soluendis per numeros geometricis problematibus. 5 De mutis, ac solidis lineis; has Euclides, & pleriq[ue] mathema- tici comparabiles, & incommensurabiles vocant, nomenq[ue]; muti, ac solidi relinquunt arithmetica. 6 Explicationes. 7 Magnus annus, siue astronomia, complectens vniuersam cæli machinam, cum ea planetarum omnium ratione, vt à puncto vnde primo moueri ceperunt ad idem redeant omnes: Et magnum qui- dem annum Democritus, alij Platonicum dixere, nonnulli vniuer- salem, Cicero in somnio Scipionis eleganter annum vertente[m] vocat. 8 Parapegma. Instrumentum astronomicum quo ortus occasusq[ue] syderum tempestatumq[ue]; significationes cognoscuntur, & inueniun- tur: dicitur parapegma quod ex multis partibus sit compactum, & comin-

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Books written by Democritus. II 29 Medical preliminaries on the regimen of diet. 30 Causes of untimely and timely things. 31 On fever. 32 On discharges by coughing. 33 On madness; for he was writing this book at that very time when the Abderites judged him mad, and Hippocrates found it, the man being occupied with that work, in letter 21 to Damagetus. Democritus himself, however, reports in the letter to Hippocrates that he had then written commentaries on poles and spheres, perhaps having two works in hand. 34 On wandering images or visible forms: Democritus says that this work was written by him in Hippocrates, epist. no. 28. MATHEMATICS. 1 On the contact of the circle and the sphere. 2 On differences of opinions, or in what mathematicians differ among themselves. 3 On geometry. 4 On geometric numbers, that is, on solving geometrical problems by numbers. 5 On straight and solid lines; Euclid and most mathematicians call these comparable and incommensurable, and leave the name of straight and solid to arithmetic. 6 Explanations. 7 The Great Year, or astronomy, comprising the entire machine of the heavens, with the whole arrangement of all the planets, so that from the point from which they first began to move they all return to the same point: and Democritus called this indeed the great year, others the Platonic, some the universal; Cicero, in the Dream of Scipio, elegantly calls it a turning year. 8 Parapegma. An astronomical instrument by which the rising and setting of the stars and the signs of the weather are known and found: it is called parapegma because it is made up of many parts, and comin-

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12 Libri à Democrito scripti. concinnatum, ut ait Suidas, eiusq[ue] instrumenti meminit Vitruvius l. 9. c. 7. respondet fortasse ipsi quonunc utimur astrolabio; vel planisphærio aut armillari sphæræ: nisi forte sphaera Chaldeorum fuit quæ plurimum abest à sphæris Ptolomæi, Longomontani, Orontij Finæi, vulgariq[ue]; Ille analemna inuenit; Longomontanus lib. 1. sphæricorum c. 4. sphaeram habet 9. circulis æqualibus compactam, Orontius 4 magnos circulos cum uno quadrante lib. 5. cosmog. c. 3. & aliam è tribus tantum circulis in lib. horolog. vulgaris tropica, & minores circulos habet. Chaldaica autem homo centricis quibusdam unoq[ue]; horizonte constat alijsq[ue]; A Caldaës astrologiam didicerat. 9 Certamen clepsydræ: siue examen motus clepsydræ cum motu cæli; quem librum subtilissimum fuisse oportet, agebat enim de motuum, & temporum commensuratione, & comparabilitate. Sunt clepsydræ horologia ex aqua. 10 Cæli descriptio: hoc est asterismi, & constellationes. 11 Terræ descriptio. 12 Poli descriptio. 13 Radiorum descriptio siue de projectionibus opticis, & geometricis, & propagatione linearum physicarum. 14 De concentu, & harmonia. 15 De quaternario scripsisse ait Plinius sed in quibusdam exemplaribus Demetrium autorem legi in alijs Democritum l. 28. c. 6. PHILOLOGICA. 1 De Poesi. 2 De carminis venustate. 3 De Homero siue de versuum rectitudine. 4 De consonis, & dissonis rebus id est de sympathy, & antipathia. 5 De

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12 Books written by Democritus. constructed, as Suidas says, and Vitruvius mentions this instrument in book 9, chapter 7. perhaps it corresponds to the astrolabe we now use; or to the planisphere or armillary sphere: unless perhaps it was the Chaldean sphere, which differs greatly from the spheres of Ptolemy, Longomontanus, Orontius Finaeus, and the common one. The latter invented the analemma; Longomontanus, in book 1 of the Sphaerics, chapter 4, has a sphere made up of 9 equal circles; Orontius, in book 5, chapter 3 of the Cosmography, has 4 large circles with one quadrant, and another made of only three circles in the book on ordinary horologes; the tropical one, and it has smaller circles. The Chaldean sphere, however, consists of certain concentric circles and one horizon, and other things as well. He had learned astrology from the Chaldeans. 9 Contest of the clepsydra: or examination of the motion of the clepsydra with the motion of the heavens; this must have been a most subtle book, for it dealt with the measurement and comparability of motions and times. Clepsydras are water clocks. 10 Description of the heavens: that is, of asterisms and constellations. 11 Description of the earth. 12 Description of the poles. 13 Description of rays, or of optical and geometric projections, and the propagation of physical lines. 14 On concord and harmony. 15 Pliny says that he wrote on the quaternary, but in some copies the author is read as Demetrius, in others Democritus, book 28, chapter 6. PHILOLOGICAL. 1 On poetry. 2 On the beauty of verse. 3 On Homer, or on the correctness of verses. 4 On concordant and discordant things, that is, on sympathy and antipathy. 5 On

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Libri à Democrito scripti. 13 5 Delinguis. 6 De carmine. 7 De verbis, & nominibus. 8 De Sacris in Babylone litteris, hoc est hyerogliplycoru[m] lectura. 9 De his quæ sunt in Meroe. 10 Oceani nauigatio. 11 Historia Chaldaica. 12 Historia Phrygia. 13 Chirocinera scripsit, id est de rerum magia seu miraculis naturalibus. Vt ait Plinius lib. 24. c. 17. Vbi Pythagoræ, & Cleempo ro medico illius gloriam aufert voluminis; aitq[ue] Democriti certè esse constat. MECHANICA, ET MISCELLANEA. 1 De architectura, cuius legibus adinuenit modum concamerationum, & fornicum, quamuis Seneca lib. 14. epist. 91. frigidissimo argumento id neget, quod ante Democritum pontes fierent; equidem sed non erant fornicati, & per arcus inflexi ità Vt esset totius operis vnicaclaus, Vt ante Europæorum aduentum in America constructierant in rapidissimis fluiijs pontes, sed nihil erat concamerati. 2 De agricultura, in qua quantum excelluit testis est Constantinus Cæsar, qui pulcherrima inuenta Democrito adscripta refert plusquam quadraginta dispersa per omnes suos agriculturæ libros. 3 De pictura. 4 De re militari, & armis, machinisq[ue] præclarum mechanicæ scientiæ argumentum. 5 Problemata quæ Chernica vocantur à Laertio, quod vocabulum nuspiam inuenire potui: an legere deberemus potius Choenica? (modica enim est differentia) & sic sensus huius tituli esset. Problemata, hoc est questiones quæ Choenicæ vocantur seu conuiuales Chænix enim diurna esca est, Vt ait Laertius lib. 8. in Pytagora, vel

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Books written by Democritus. 13 5. On languages. 6. On poetry. 7. On words and names. 8. On sacred letters in Babylon, that is, on the reading of hieroglyphics. 9. On the things that are in Meroë. 10. Navigation of the Ocean. 11. Chaldaean History. 12. Phrygian History. 13. He wrote Chirocinera, that is, on the magic of things, or natural wonders. As Pliny says, book 24, chapter 17, where he takes this volume away from the glory of Pythagoras and the physician Cleemporus; and says that it is certainly Democritus’s. MECHANICAL AND MISCELLANEOUS. 1. On architecture, by whose laws he devised the manner of vaulting and arches, although Seneca, book 14, letter 91, denies this on a very weak argument, namely that bridges were made before Democritus; indeed they were, but they were not arched, nor curved through arches so that there would be a single bond of the whole work, as before the arrival of the Europeans in America they had constructed bridges over the swiftest rivers, but there was nothing vaulted about them. 2. On agriculture, in which he excelled so greatly that Emperor Constantine is witness, who reports more than forty of the finest inventions attributed to Democritus, scattered through all his books on agriculture. 3. On painting. 4. On military affairs and arms, and machines, a notable proof of mechanical science. 5. Problems which Laertius calls Chernica, a word which I have nowhere been able to find: ought we rather to read Choenica? (for the difference is slight) and so the meaning of this title would be, Problems, that is, questions which are called Choenica, or convivial; for chenix is the daily food, as Laertius says, book 8, in Pythagoras, or

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14 Libri à Democrito scripti. ra: vel potius cum Chænices fuerint pedicæ quædam, ligna scilicet crassa rotunda instar Chænicis (quod Paulo Æginetæ mensuræ no- men est) in quæ crura immitebantur, dici posset problemata Chæ- nica fuisse quæstiones ità difficiles vt respondentem caperent, & involuerent ijs difficultatibus quibus se non posset extricare veluti qui in Chænicis seu vinculis detinetur. 6 Composuit etiam de herbis vt ait Plinius l.25.c.2. nisi forte liber iste sit idem atq[ue] is quem de agricultura aut de plantarum causis re- censuimus superius. 7 Videtur etiam Commentaria, & elucidationes edidisse in libros Apollonicis Capridentis, et Dardani Phænicij: vt colligimus ex Pli- nio l.30.c.1. Vbi ait hos authores à Democrito illustratos. Hos verò libros omnes Democriti memoriæ inuidens Plato comburete statuerat, vt ait Aristoxenus in historicis comen- tarijs apud Laertium, cumq[ue] maximam exemplarium copiam magno sumptu maiori diligentia congregasset, ab hac impia designatione abductus est Amyclæ, & Cliniæ Pythagoricorum monitis; quod apud plerosq[ue] diffusi essent huiusmodi libri: af- sentitur Aristoxeno Laertius, silentiumq[ue]; Platonis de Democri- to grandem facit sceleris suspicionem: non audebat, vt ait La- ertius, contra optimum philosophorum inite certamen neq[ue]; vero flo- renti adeo nomini suis laudibus voluit suffragari. At quod Plato designauerat exequutus est Alexandri ope Aristoteles, quasi parum esset Alexandro si se monarcham red- deret Asic, nisi Aristoteli ius in philosophos daret, qui quod sua tantum de tot antiquis monumenta superesse voluit, tyrannidem in ingenia videtur affectasse, ea rarione qua Turcarum Dominus fratres necat suos, vt ne in paterni imperij posse- sione quenquam riualem habeat: aut eorum exemplo poti- us qui cruentam legitimorum principum purpuram iniustè sibi arrogant: dum itaq[ue] Regum fortunas vnicæ vincendi libi- dine

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14 Books written by Democritus. ... or rather, if there were certain fetters called Chænices, that is, thick round pieces of wood like a Chænicis (which is a measure named by Paulus Aegineta), into which the legs were thrust, it might be said that the Chænic questions were questions so difficult that they would catch the respondent, and entangle him in such difficulties that he could not extricate himself, like one held fast in Chænices, or bonds. 6 He also composed a work on herbs, as Pliny says, book 25, chapter 2, unless perhaps that book is the same as the one we noted above, On Agriculture, or On the Causes of Plants. 7 He also seems to have published commentaries and explanations on the books of Apollonicis Capridentis and of Dardanus the Phænician, as we gather from Pliny, book 30, chapter 1, where he says that these authors were illuminated by Democritus. But Plato had determined to burn all these books of Democritus, as Aristoxenus says in his Historical Commentaries in Laertius; and when he had gathered a very great number of copies at great expense and with even greater diligence, he was turned away from this impious design by Amyclæ and Cliniæ, by the admonitions of the Pythagoreans; because such books were widely circulated among many. Laertius agrees with Aristoxenus, and by his silence regarding Plato makes a strong suspicion of a crime against Democritus; for he did not dare, as Laertius says, to enter into a contest against the best of philosophers, nor indeed did he wish to support by his praises so flourishing a name. But what Plato had planned, Aristotle carried out with Alexander’s help, as if it were not enough for Alexander to make himself monarch of Asia unless he also granted Aristotle authority over the philosophers; for he seems to have aimed at tyranny over minds, since he wished that only his own writings should survive out of so many ancient monuments, in the same way that the Turkish ruler kills his brothers so that he may have no rival in the possession of his father’s empire: or rather like those who unjustly arrogate to themselves the bloody purple of legitimate princes. Thus, therefore, by the single desire of conquering the fortunes of kings

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Libri à Democrito scripti. 15 dine ductus euerteret Alexander, superbissimo furore ambitiosus nominis Aristoteles in philosophorum Principes est debacchatus, vnoq[ue] incendio congesta triginta sex seculis tot sapientiæ diuitias absumpsit, & si quæ voluit superesse funeri, ea omnium ludibrio dicterijsq[ue] lacessenda tradidit posteris, dum in optimorum bona inuectus abscissis perditisq[ue] sapientiæ statuarum capitibus, suu[m] imposuit singulis: neq[ue] obscure literarij peculatus reum facit Aristotelem curiosissimus Plinius in præfat. ad D. Vespasianum Imp. Sed nihil egisti Aristoteles Democritus enim etsi libris nuspiam, vbiq[ue] tamen inclyto nomine est; Viuit viuetq[ue] in doctissimorum monumentis, & du[m] philosophia aliquo in honore erit, comitem æui sui laudem Democriti trahet, omnisq[ue] posteritas etiam scripta quæ non extant mirabitur, tuum vero in eum factum execrabitur. Testimonia de Sapientia, & doctrina Democriti. Hippocratis, & Abderitarum Democriti Ciuium. Hippocrates in epist. Somnium Hippocratis. Ipsa quidem veritas, apud Democritum manet, Opinio verò apud Abderitas habitat. Quam autem ob causam dementiæ fuerit insimulatus à suis, videre est apud Hipp. in epist. nu. 5. Hic præ multa quæ detinet ipsum sapientia ægrotat, vt timor sit, ne nostra vrbs Abderitarum pessum detur si Democritus mente fuerit motus. Etenim oblitus sui omniumq[ue] vigilans, & noctu, & interdiu, & omnia deridens totamq[ue] vitam nihil faciens vitam agit, ridetq[ue] si quem videt aut hilarem aut moestum. Idolis aerem plenum esse dicit, volucrum voces explorat, seque aliquando in rerum immensitatem proficisci dicit, & Democritos esse similes sibi ipsi innumerabiles, corpusq[ue] cum mente corrumpit. Anima

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Books written by Democritus. 15 If Alexander, driven on by a certain impulse, overthrew it, the very ambitious Aristotle, in a most haughty frenzy, raged against the princes of the philosophers; and with one conflagration he consumed the riches of so much wisdom gathered over thirty-six centuries, and whatever he allowed to survive the funeral, he handed down to posterity to be mocked and assailed with taunts, while, attacking the goods of the best men, he placed his own name over the broken and destroyed heads of the statues of wisdom; and Pliny, most inquisitive, in the preface to Emperor Vespasian, plainly makes Aristotle guilty of literary plunder. But you achieved nothing, Aristotle: for Democritus, though nowhere in books, is nevertheless everywhere with his illustrious name; he lives and will live in the monuments of the most learned, and so long as philosophy is held in any honor, the praise of Democritus will accompany the age that was his own, and all posterity will wonder even at the writings that no longer exist, while it will execrate your act against him. Testimonies concerning the wisdom and learning of Democritus. From Hippocrates and the citizens of Abdera, Democritus’ fellow townsmen. Hippocrates in the letter, The Dream of Hippocrates: Truth itself indeed remains with Democritus, but Opinion dwells among the Abderites. And for what cause he was accused of madness by his own people may be seen in Hippocrates, epistle no. 5. Here, possessed by much wisdom, he is ill, so that there is fear our city of the Abderites may be brought to ruin if Democritus should be out of his mind. For, forgetting himself and everyone else, awake both by night and by day, and mocking everything and spending his whole life in doing nothing, he lives; and he laughs if he sees anyone either cheerful or sad. He says that the air is full of images, investigates the cries of birds, and says that at times he goes forth into the immensity of things, and that there are innumerable Democrituses like himself, and he corrupts body together with mind. Soul

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Testimonia de Democrito. Animæ autem Democriti gratia etiam si Vrbs aurum esset dederetur. Leges putamus ægrotare ò Hipp. adsis optimè Vir curaturus Virum insignem. Non medicus sed conditor sacratiorem Ionia murum circumdabis, Ciuitatem Senatumq; curabis: Serua corpus sapientiæ, & ipsam ad te supplicem mitti doctrinam puta; gratificaberis etiam futuro sæculo, si non destitueris Democritum propter veritatem cuius primas se laturum sperat: tu enim genere, & arte coniunctus es Æsculapio: hic verò Herculis est ex fratre nepos: hæc aliaq; complura ad Hipp. Abderitæ deprecati, vt Democritum ab insania liberaret. Respondit Hipp. Epistolam vestram legi, & admiratus sum quod ob Vnum hominem, vt si ipse Vnus Ciuitas esset, turbati estis. Et beati profecto sunt populi qui, sciunt bonos viros sua esse munimenta, non autem turres aut muros sed sapientum consilia: audio autem Democritum grauibus ac solidis moribus præditum esse, & Vrbis Vestræ ornamentum. Et ad Philopæmonem; Vna sapientiæ cura alias exigit mente, vt dum tumultuantibus ancillis hera apparet conquiescunt, sic sapietiatæ conspectu reliquæ affectiones velut famulæ decedunt: in veritatis regione quam sapientia collustrat non est pater, nec mater vxorue aut cognati, non liberi nec fratres neq; famuli fortunaq; vel aliud ex bis quæ tumultum faciunt. Democritus illuc præ sapientia commigrauit, & insania teneri creditur ob solitudinis amorem. Et ad Dionysium Excellentia, morbi opinionem de se præbet, propter iudicantium imperitiam. Iuit ad Democritum Hippocrates decem talentis æstimata visitatione, siue mille, & ducentis nummis aureis Pphilippicis. Scripsitq; quid sibi cum Democrito contigisset in epist. ad Damagetum nu. 21. Hoc erat illud, Damagete, quod coniectabamus, non insanit Democritus sed super omnia sapit, & nos sapientiores effect, & per nos omnes homines; vide sis curiosissimam hanc Hipp. epist. quæ quod longior sit à me tantum defloratur. Ridebat itaq; Democritus hominum insaniam qui vicissitudinis rerum ignavi veluti

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Testimonies concerning Democritus. And indeed, for the sake of Democritus’s soul, even if the City were offering gold. Laws we think to be sick. O Hipp., be present, most excellent man, you who will cure an outstanding man. Not a physician but a founder: you will surround the more sacred wall of Ionia; you will care for the City and the Senate; preserve the body of wisdom, and think that doctrine itself is sent to you as a suppliant; you will also do a favor to future ages, if you do not abandon Democritus on account of the truth, whose first place he hopes to take: for you are united by both birth and art to Aesculapius: this man, indeed, is the grandson of Hercules through his brother. These and many other things were written to Hipp. by the people of Abdera, begging that he would free Democritus from madness. Hipp. replied: I read your letter, and I marveled that on account of one man, as if he alone were the City itself, you were thrown into confusion. And truly blessed are those peoples who know that good men are their fortifications, not towers or walls, but the counsel of the wise. But I hear that Democritus is endowed with grave and solid character, and is an ornament of your City. And to Philopæmon: One concern of wisdom requires others with the mind, as when, while the maidservants are making a commotion, the mistress appears, they grow quiet; so too, at the sight of wisdom the remaining affections withdraw as if they were servants. In the realm of truth, which wisdom illumines, there is no father, nor mother, wife or kinsman, not children nor brothers nor servants nor fortune, nor anything else from among those things that make a disturbance. Democritus migrated there because of wisdom, and is believed to be held by madness because of his love of solitude. And to Dionysius: Excellence shows an opinion of sickness about itself, because of the ignorance of those judging. Hippocrates went to Democritus, the visitation being valued at ten talents, or a thousand and two hundred gold Philippic coins. And he wrote what had happened to him with Democritus in the letter to Damagetus, no. 21. This was that very thing, Damagetus, which we had conjectured: Democritus is not mad, but is wise beyond all things, and made us wiser, and through us all men. See, I pray, this most curious letter of Hipp., which, because it is longer, I merely abridge here. Thus Democritus was laughing at the madness of men, who, ignorant of the vicissitudes of things, were as if

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Testimonia de Democrito. 17 ri veluti firma, ac stabilis sua vita fortunaq[ue]; esset, multis cala- mitatibus repentinis opprimebantur. Terram fodientes argen- tum quærunt, argento reperto terram emunt, empta terra fructus vendunt, fructibus venditis argentum accipiunt eaq[ue]; agitatione ve- luti rota semper circumvoluti nullo cupiditatibus fine imposito. . . . . . . Quæso te Hipp[ocrito] non ridere debeo plorantem propter amorem, eo quod voluptate sua exclusus est? Intra sufficientiam se feræ continent; Quis enim leo aurum occuluit? quis taurus vberioris alimenti gratiæ pugnauit? quam pardalim insatiabilitas cæpit? sitit aper vsq[ue]; ad aquæ appetentiam, Lupus deuorato alimento necessario quiescit, an- nuorum temporum ordo brutis terminus est ad coitum: at homo perpe- petuo ingluuiei libidinisq[ue]; æstro stimulatur. . . . . . . . Quem admo- dum optimus corporis habitus periculosus, ità successuum fortunæ ma- gnitudo periculosa, quorum præuidentiam cæci ex aliorum malis habere debuerant. Hisq[ue]; qui benefacere cogitant fulminis ictum pro gratia- rum actione accipiunt vt tuus ille progenitor Æsculapius: videtur enim, & mundus ipse hominibus infensus. Totus homo ex natuita- te morbus est; dum educatur inutilis alienæ opis egens, dùm crescit pro- teruus, & insipiens pædagogo coercendus, dùm viget audacia abripi- tur, dùm decrescit miserabilis. . . . . . . . Vtinam facultas esset nobis vniuersorum habitacula revelare, singulaq[ue]; actionum humanarum momenta perpendere, videremus &c. Hæc autem cum diceret sub- videbat, & mihi, à Damagete, diuina specte apparebat, & velut qui priorem suam formam exuisset. Et ego, multa, à Democrite, sapien- tiæ admiratione me impleuisti: Discedo veritatis tuæ præco. . . . . . vidi Democritum virum sapientissimum qui solus potentissimus est homines prudentes facere; & num. 31. optimum naturæ ac mundi in- terpretem vocat Democritum. Hoc Hipp[ocrito] testimonium eo lucu- lentius est quod ab homine falli penenescio, & Democriti co- æuo procedit. B Anaxa-

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Testimonia of Democritus. 17 ... or as firm and stable as his own life and fortune; yet they were overwhelmed by many sudden calamities. Those who dig the earth seek silver; having found silver, they buy land; the land bought, they sell the fruits; the fruits sold, they receive silver, and in this movement, as if turned always around a wheel, no limit is set to their desires. . . . . . . Do I ask you, Hipp[ocrates], ought I not to laugh at one who is weeping because of love, because he has been shut out from his pleasure? Wild beasts keep themselves within what is sufficient; for what lion has hidden gold? what ox has fought for the sake of richer food? what leopard has been captured by insatiability? the boar thirsts only up to the desire for water; the wolf, having devoured the necessary food, rests; the course of the yearly seasons is for brute animals the limit of mating. But man is continually driven by the frenzy of gluttony and lust. . . . . . . Just as the best bodily condition is dangerous, so too the greatness of prosperous success is dangerous, and the blind ought to have foreseen this from the misfortunes of others. And those who think of doing good receive the stroke of lightning as the reward of their services, like your ancestor Aesculapius: for the world itself seems hostile to men. Man in his entirety is by nature sickness; while he is brought up, useless and needing another’s help; while he grows, headstrong and foolish, to be restrained by a tutor; while he is in vigor, he is seized by audacity; while he declines, he is wretched. . . . . . . Would that we had the power to lay open the habitations of all men and to weigh each moment of human actions; we would see, etc. But while he said these things he was looking askance, and to me, from Damagetes, he appeared with a divine expression, as if he had laid aside his former form. And I said: “Democritus, you have filled me with admiration for wisdom. I depart as a herald of your truth.” . . . . . . I saw Democritus, a most wise man, who alone is most powerful in making men prudent; and at no. 31 he calls Democritus the best interpreter of nature and the world. This testimony of Hipp[ocrates] is all the more clear because it comes from a man who knows not how to deceive, and from the contemporary of Democritus. B Anaxa-

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Testimonia de Democrito ANAXAGORÆ. Anaxagoras cu[m] Socrates de Democrito locutus, hic (inquit) philosophus similis est quinq[ue]; certaminum victori, nam naturalia, mathematica, politiores litteras, mechanicarumq[ue]; peritiam omnem callebat: vnde & omniscium appellat Laertius. ARISTOTELIS. Ab inuido laudes expressit Democriti virtus: Sic enim ille 1. 1. de gen. t. 5. Democritus videtur omnia curasse, & principia supposuisse, quæ ad omnia accomodari possunt, & ad alios motus. Eustat. 1. 2. moral. c. 1. Id quod de Democrito alibi ait Aristotel. qui aptè quasi in natura inhabitasset naturalia pertractaret, & non vt Pythagoræi, qui cum omne in mathematicis studium collocarent, de rebus naturalibus loquentes, imperitè suis eas rationibus, non eis suas dissertationes accomodabant. Et cap. 2. 1. 1. de gen. Ad summum de nulla mutatione, nisi superficiè tenus quicquam alius definiuit, præterquam Democritus, cui omnia curæ videntur fuisse; Hoc Aristotelis testimonium vt Democrito fauet, ità multis iniuriosum est, quasi verò omnia superficie tenus scripserit Hipp. à quo optima quæque veterum spoliator accepit, & in furto maluit depræhendi quam bona fides suum cuique reddere: nusquam enim Hippocratis meminit, quod Andreæ Laurentio lectissimi ingenij medico bilem mouit l. 8. anat. q. 30. SENECÆ, PLINI, CELSI. Seneca Sapientissimus ille Hispanus nat. q. 1. 7. c. 3. antiquorum omnium subtilissimum vocat Democritum, & alibi antistitem litterarum, sapientiæ caput, naturæq[ue] linguam. Plura Democriti admirator optimus Plinius; l. 28. c. 6. l. 18. c. 28. l. 30. c. 1. & alibi. Cornelius Celsus medicorum Cicero in pref. Multos ex

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Testimonies concerning Democritus ANAXAGORAS. When Anaxagoras spoke with Socrates about Democritus, he says: this philosopher is like a victor in five contests; for he was skilled in natural philosophy, mathematics, polite letters, and all mechanical knowledge; whence Diogenes Laertius also calls him “all-knowing.” ARISTOTLE. The virtue of Democritus drew forth praise even from the envious: for thus he says, 1. 1. de gen. t. 5. Democritus seems to have investigated everything, and to have assumed principles which can be applied to all things, and to other motions. Eustat. 1. 2. moral. c. 1. This is what Aristotle elsewhere says of Democritus, that he handled natural things aptly, as though he had almost lived within nature, and not, like the Pythagoreans, who, while placing all their study in mathematics, when speaking about natural things, awkwardly adapted them to their own reasonings rather than adapting their dissertations to them. And cap. 2. 1. 1. de gen. In sum, none defined any change except so far as the surface, except Democritus, for whom all things seem to have been a concern. This testimony of Aristotle, while favoring Democritus, is also in many ways offensive, as though Hippocrates had written everything only superficially—he from whom that excellent spoiler of the ancients took the best things, and preferred to be caught in theft rather than in good faith rendering to each his own: for nowhere does he mention Hippocrates, which irritated Andreas Laurentius, a physician of the finest intellect, l. 8. anat. q. 30. SENECA, PLINY, CELSUS. Seneca, that very wise Spaniard, nat. q. 1. 7. c. 3. calls Democritus the most subtle of all the ancients, and elsewhere the leader of letters, the head of wisdom, and the tongue of nature. Pliny, Democritus’s greatest admirer, has many things [to say of him]; l. 28. c. 6. l. 18. c. 28. l. 30. c. 1. and elsewhere. Cornelius Celsus, the Cicero of physicians, in the preface, Many from

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Testimonia de Democrito. 19 tos ex sapientiæ professoribus peritos medicinæ fuisse accepimus, clarif- simos verò ex his Pythagoram, & Empedoclem, & Democritum, huius autem vt quidam crediderunt discipulus Hipp. Cous. Sed De- mocriti nequaquam discipulus fuit Hippocrates, erat enim. iam Senex cum illum primò cognouit vt patet in epistola ad ipsum Demoricitum nu. 31. PETRONII, LVCIANI, APVLEII. Petronius Neronis deliciarum Arbiter, quiq; vt ait Tacit- tus, erudito fuit luxu, in suo satyrico, Itaq; hercule inquit, om- nium herbarum succos Democritus expressit: & ne lapidum virgul- torumq; vis lateret ætatem inter experimenta consumpsit. Lucianus nulli philosophorum præterquam Democrito parcit, & admi- randa ab illo scripta esse testatur. Apuleius in apol. Democri- tum inter precipuos rerum naturæ patronos recenset, & Flor. 1. 3. Protagoras sophista fuit longè multificius, & cumprimis Rhetoricæ repertis perfacundus: Democriti physici cuius æquæuus: inde et sup- peditata doctrina est. Hæc mitiorum ingeniorum testimonia adducere volui post seueriores viros, vt omnibus Democri- tum arrisisse ostenderem. LVCRETII, IVVENALIS. Lucretius qui academiam in parnassum deduxit nusquam Democriti sine honore meminit vt l. 3. & iterum l. 3. Democriti quod sancta viri sententia penit. Ingeniosissimus poëtarum Iunius luuenalis in votorum fa- tyra 10. sic de Democrito. Tunc quoq; materiam risus inuenit ad omnes Occursus hominum, cuius prudentia monstrat, Summos posse viros, & magna exempla daturos, Veruecum in patria, crassoq; sub aerenasci. B 2 Sapien-

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Testimonies concerning Democritus. 19 We have learned that among the professors of wisdom there were some skilled in medicine, and among these the most famous were Pythagoras, Empedocles, and Democritus; and, as some believed, Hippocrates of Cos was his disciple. But Hippocrates was by no means a disciple of Democritus; for he was already an old man when he first became acquainted with him, as is clear from the epistle to Democritus himself, no. 31. PETRONIUS, LUCIAN, APULEIUS. Petronius, Neronis deliciarum arbiter, who, as Tacitus says, was learned in luxury, in his Satyrica says, “Itaque hercule,” he says, “Democritus extracted the juices of all herbs; and, lest the power of stones and plants should remain hidden, he spent his life in experiments.” Lucian spares no philosopher except Democritus, and testifies that admirable writings were composed by him. Apuleius, in the Apology, counts Democritus among the foremost champions of natural philosophy, and in Flor. 1. 3. says that Protagoras the sophist was a very multifaceted man, and especially eloquent in rhetoric; as a contemporary of Democritus the physicist, from whom also his doctrine was supplied. I wished to adduce these testimonies of gentler minds after the more severe men, in order to show that Democritus pleased everyone. LUCRETIUS, JUVENAL. Lucretius, who led the academy into Parnassus, nowhere mentions Democritus without honor, as in book 3, and again in book 3: “Of Democritus, whose holy judgment went deep.” The most ingenious of poets, Junius Juvenalis, in the satire on vows, 10, thus speaks of Democritus: “Then too he found material for laughter at every encounter with men, whose prudence shows that the highest men, and those who are to give great examples, may be born in their homeland under a rough roof.” B 2 Sapi-

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Testimonia de Democrito. Sapientem vocat, summum virum quiq[ue]; magna exempla dederit: è Thracia fuit Democritus quod barbarum solum suo ortu nobilitauit. Ad hæc testimonia subnecto vnum quo summa. Democriti felicitas pateat; vulgaris est ingenij addiscere, felicis, & commodi inuentis addere, at paucissimis inuenire concessum. Democritus tamen diuino præditus ingenio plurima adinuenit, qua illum veterum omnium gentilium sapientissimum doctissimumq[ue]; reddunt, ita vt eorum nulli ingenium vastius fuisse putem. 1 Species visibiles à corporibus omnibus fluere deprehedit. 2 Primus ostendit cæli, et terræ societate[m], artemq[ue], te[m]pestates, abundantiam penuriamq[ue]; prædicendi aperuit, teste Plinio, qui coemptum omne tractus vnius oleum à Democrito dixit, ignorantibus mirantibusq[ue]; cuiibus, qui paupertatem, et quietem doctrinaru[m] sciebant imprimis cordi esse, atq[ue]; vt apparuit causa, et ingens diuitiarum cursus, restituisse mercedem anxiæ dominorum penitentiæ, contentum ità probasse opes sibi, preuisa rerum caritate, in facili cum vellet fore l. 18. c. 18. vide præteterea historiam metentis Damasi Constant. l. 5. c. 41. 3 Magiam inuexit naturalem vnde Plin. l. 30. c. 1. plenum miraculi, et hoc pariter vtrasq[ue]; artes efloruisse, medicinam dico magicenq[ue]; eadem ætate illam Hippocrate, hanc Democrito illustrantibus. 4 Concameratorum fornicum rationem architectonicam adinuenit, teste Seneca, pontesq[ue]; in fluuijs è lapidibus eo præscribente constructi primum. 5 Lapides liquare, ebur molliro, quemlibet fingere lapillum pretiosum, & ad libitum colore suo tingere nouerat. 6 Instrumenta mathematica excogitauit quibus non stellarum modo cursus, verum etiam futurarum tempestiuitatum ratio-

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Testimonies concerning Democritus. He is called wise, the greatest of men, and he has given great examples: Democritus was from Thrace, because he ennobled that barbarous soil by his birth. To these testimonies I add one, by which the highest happiness of Democritus may be made clear: it is common for genius to learn, for happiness and advantage to add to inventions; but it is granted to very few to invent. Yet Democritus, endowed with divine genius, invented very many things, which make him, of all the ancient pagan sages, the wisest and most learned; so that I think none of them had a more vast intellect. 1. He discovered that visible species flow from all bodies. 2. He was the first to show the partnership of heaven and earth, and the art of predicting storms, abundance, and scarcity, opening the way, as Pliny attests; who said that the whole tract of one district was bought up by Democritus, to the wonder of those who did not know, and of those who did; for he knew that poverty and the quiet of study were especially dear to him, and that, as the reason appeared, the great course of riches had restored the reward of the masters’ anxious repentance, and that he approved wealth only as contentment, since the dearness of things was foreseen, and it would be easy for him whenever he wished. l. 18. c. 18. See moreover the history of the reaper Damasus Constant. l. 5. c. 41. 3. He introduced natural magic, whence, as Pliny says, l. 30. c. 1, it is full of wonder; and likewise both arts flourished together, I mean medicine and magic, Hippocrates illustrating the one and Democritus the other in that age. 4. He discovered the architectural principle of vaulted arches, as Seneca attests, and bridges in the rivers were first built of stone, he having prescribed it. 5. He knew how to liquefy stones, to soften ivory, to shape any little precious stone whatsoever, and to dye it at will with its own color. 6. He devised mathematical instruments by which not only the courses of the stars, but also the calculation of future weather

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Testimonia de Democrito. 21 rationes acuratè exponebat: ignes inextinguibles nisi lacte, speculaq; portentosa finxit. 7 In agricultura fuit peritissimus ex Constantino Cæsare Pogonato, qui multa à Democrito transcribit pulcherrima arcana. 8 In plantarum, & lapidum non historia modo, verùm quod maius est, experimentis viribusq; fuit versatissimus ex Petronio. 9 Omnem fontium habuit peritiam, tum inueniendorum sicubi sub terra laterent, tum deducendorum vt videre est apud Const. 1. 2. c. 5. & alios. 10 Effluvia corporum, atomosq; comperit, & inuexit omnium primus ex Laertio: quod vnum tanti apud me est, vt cogellas omnium Philosophorum laudes vel exæquet vel su- peret. Synopsis doctrinæ Democriti quæ ad atomos pertinet. Omissis ijs opinionibus quæ ad præsens institutum non fa- ciunt, ex vno fere Aristotele, qui suis operibus optimas De- mocriti lacinias intexuit, doctrinam quæ ad atomos spectat ad- ductis autoritatibus delibabo. I. Ex lib. 1. phys. t. 6. agens de principijs corporum; Et si infinita aut sic, vt Democritus, genere quidem vnum, figura verò vel specie differentia aut etiam contraria. hoc est: principia corporum conueniunt in genere atomi differunt autem aliqua specie, & figura. II. Lib. 3. phys. t. 27. Quicumq; autem infinita faciunt ele- menta, quemadmodum Anaxagoras, & Democritus, ille quidem ex ijs quæ sunt similibus partium, hic autem, & omnifeminario figura- rum B 3

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Testimonia concerning Democritus. 21 he set forth the reasons accurately: he devised inextinguishable fires unless by milk, and portentous mirrors. 7 In agriculture he was most skilled, according to Constantine Caesar Pogonatus, who transcribes many most beautiful secrets from Democritus. 8 In plants and stones he was thoroughly versed, not in history only, but, which is greater, in experiments and powers, according to Petronius. 9 He had complete knowledge of springs, both of discovering them if anywhere they lay hidden under ground, and of bringing them forth, as may be seen in Const. 1. 2. c. 5. and others. 10 He discovered the effluvia of bodies and atoms, and was the first to introduce them, according to Laertius: which alone is of such value to me that it either equals or surpasses the praises of all philosophers. Synopsis of the doctrine of Democritus which pertains to atoms. Passing over those opinions which do not serve the present purpose, from Aristotle almost alone, who in his works interwove the best fragments of Democritus, I shall select, with authorities cited, the doctrine that concerns atoms. I. From book 1 of the Physics, text 6, speaking of the principles of bodies; And if they are infinite, or thus, as Democritus says, one in kind indeed, but different in figure or species, or even contrary. That is: the principles of bodies agree in kind; the atoms differ, however, in some species and in figure. II. Book 3 of the Physics, text 27. But whoever makes the elements infinite, as Anaxagoras and Democritus do, the former indeed from those things which are of similar parts, the latter however, and omnifeminario of shapes B 3

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22 Synopsis doctrinæ Democriti. rum tactu, continuum infinitum esse dicunt, siue vt vertit Auerrois interpres Mantinus, Democritus verò ex illo quod vocat radicem omnis figuræ, & semen omnis figuræ. PANSPERMIAM. Infinitum etiam est quodlibet continuum ex Democriti sententia, sed tantum extrinsecè, & designatiuè, vt videbimus inferius. III. lib. textu 29. Democritus autem nullum aliud ex alio fieri primorum dixit, sed tamen ipsum commune corpus omnium esse principium, magnitudine secundum partes figuraq[ue]; differens: siue vt melius ex græco colligitur, ratio corporis diuersa est in speciebus, partibus, quantitate, & figura. IV. Lib. 8. t. 10. Democritus monstrat quod impossibile est omnia facta esse, tempus enim ingenitum esse, & t. 15. Democritus non quæsiuit eorum quæ semper essent causam. Vide l. 2. de gen. animal. c. 4. V. Lib. 4. de cælo t. 42. disputans de causa grauis, & leuis refert Democriti sententiam, qui existimabat stricta corpora descendere quod pauca ipsis resistant, lata verò ascendere super aquam: addit instantiam Democriti t. 43. deberet enim in aere hoc etiam fieri, sed soluit molliter (Democritus) ait enim non in vnum impetum facere soun, vocans soun motum eorum, quæ sursum mouentur corporum. Sou autem est vox abigentis aues apud Aristoph. in com[m]odia de Vespis. crediderim à sono quê edunt in aere corpora vsurpatam à Democrito, nam quæ fortius aerem secant e[ss]e edunt sonu[m]. Soluit aute instantia Democritus non molliter, sed nervosè negando paritatem, est enim maxima differentia inter motus qui fiunt in aqua, & eos qui in aere; quam verò commodè respondeat Democritus ostendemus suo loco. VI. Lib. 1. de gen. t. 1. Democritus autem, & Leucippus ex corporibus induisibilibus alia componi inquiunt: hæc autem infinita, & multitudine, & formis esse, ipsa autem à seipsis differre his, ex quibus sunt

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22 Synopsis of the doctrine of Democritus. by touch, they say that the continuum is infinite; or, as the interpreter of Averroes, Mantinus, translates it, Democritus from that which he calls the root of every figure, and the seed of every figure. PANSPERMIA. An infinite continuum also, according to Democritus’ opinion, but only extrinsically and by designation, as we shall see below. III. Book 3, text 29. Democritus, however, said that nothing else is made from another among the first principles, but nevertheless that the common body of all things is itself the principle, differing in magnitude according to parts and in figure; or, as may better be gathered from the Greek, the nature of body is different in species, parts, quantity, and figure. IV. Book 8, text 10. Democritus shows that it is impossible for all things to have been made, for time is ungenerated; and text 15. Democritus did not inquire for the cause of those things that always were. See book 2 On the Generation of Animals, ch. 4. V. Book 4 On the Heavens, text 42, discussing the cause of the heavy and the light, he reports Democritus’ opinion, who thought that compact bodies descend because few things resist them, but broad bodies ascend over water. He adds Democritus’ reply at text 43: for it ought also to happen in air, but he answers gently: Democritus, he says, makes not one single impulse, calling sound the motion of those bodies that are moved upward. But sou is a cry of one driving away birds in Aristophanes’ comedy The Wasps. I would believe that Democritus used it from the sound which bodies make in the air, for those that cleave the air more strongly produce sound. Democritus does not solve the objection gently, but forcefully, by denying the parity; for there is a great difference between motions that occur in water and those that occur in air. But how suitably Democritus replies we shall show in its proper place. VI. Book 1 On Generation, text 1. Democritus and Leucippus say that other things are compounded from indivisible bodies: these are infinite both in multitude and in forms, and they themselves differ from one another in these respects, from which they are made.

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Synopsis doctrinæ Democrini. 23 sunt, et positione, et ordine horu[m] expressè in græco, ex atomis, quæ infinitæ figuris, et multitudine sunt: earum autem positionem ordinemq; inducere differentias voluit. VII. lb. t. 5. Democritus videtur omnia curasse, et principia supposuisse quæ ad omnia accomodari possunt, et ad alios motus ..... Democritus autem, et Leusippus facientes figuras alterationem, et generationem ex his faciunt segregatione quidem, et congregatione generationem, et corruptionem, ordine autem, et positione alterationem. Quoniam autem existimabant verum esse in apparendo, contraria autem sunt, et infinita quæ apparent, figuras infinitas fecerunt, ita vt transmutationibus ipsius compositi idem videatur contrarium alij, et alij, et transmutetur paruo immisto, et omnino aliud appareat uno transmutato, ex eisdem enim tragædia, et comædia fit litteris. Ex hoc textu colligimus quantus fuerit Democritus, qui principia adeo commoda adinuenerit: eius præterea de generatione, corruptione, accretione, alteratione sententiam claram apertamq; habemus. VIII. lb. t. 56. 57. Actionem, et passionem fieri dixerunt, ijsdem Democritus, & Leucippus, per meatus insensibiles. Unde Empedocles miseri ea voluit quorumcunq; meatus ad inuicem sunt mensurati, qua via maximè, et de omnibus uno sermone determinaverunt Leucippus, et Democritus, principium cum fecerunt secundum naturam quod est. Voluit autem duo tantum esse absolutè Democritus, atomum & vacuum quo nomine intelligit aerem, quod clarè colligimus ex Galeno de theriaca ad Pisonem c. 2. Sintem ex atomis, et vacuo, sicut Democritus, et Epicurus asserunt, omnia constitissent, vel vt Aselepiades medicus, inquit, molibus, et vacuo seu meatibus, nam eandem quam illi de rerum natura sententiam cum retineat, nominibus tantum mutatis, atomos moles, vacuum meatus appellat. Ex quibus patet quodnam sit Democriti inane vel vacuum, aer icilicet qui poros implet. B 4 IX. Lib.

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Synopsis of the doctrine of Democritus. 23 are, and in position, and in order of these things expressly in Greek, from atoms, which are infinite in figures, and in multitude: but he wished their position and order to introduce differences. VII. lb. t. 5. Democritus seems to have attended to everything, and to have assumed principles which can be adapted to everything, and to other motions ..... But Democritus and Leucippus, making figures, produce alteration and generation from these; by segregation indeed, and congregation, generation and corruption, but by order and position alteration. And since they thought the true to be in appearance, but the things that appear are contrary, and infinite, they made infinite figures, so that by the transmutations of the composite itself the same thing may seem contrary to another thing, and to another, and may be transformed by a small admixture, and, one thing being wholly changed, something altogether different may appear; for from the same letters tragedy and comedy are made. From this text we gather how great Democritus was, who devised principles so suitable for all things: moreover we have a clear and open statement of his opinion concerning generation, corruption, increase, and alteration. VIII. lb. t. 56. 57. They said that action and passion come to be by the same things, Democritus and Leucippus, through insensible passages. Whence Empedocles wished those things to be unfortunate whose passages are measured to one another, in which way especially, and with regard to all things, Leucippus and Democritus determined in one account, when they made as a first principle according to nature that which is. But Democritus wished there to be absolutely only two things: the atom and the void, by which name he means air, which we clearly gather from Galen, On Theriac to Piso, ch. 2. If all things were constituted from atoms and void, as Democritus and Epicurus assert, or as Asclepiades the physician says, from masses and void or passages, for while he retains the same opinion as they have concerning the nature of things, with names changed only, he calls atoms masses, void passages. From these it is clear what Democritus’ void or empty space is, namely air, which fills the pores. B 4 IX. Lib.

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Synopsis doctrinæ Democriti. IX. Lib. 1. de anima t. 20. Democritus ignem quendam, & calorem dicit esse animam, infinitis enim existentibus figuris, & atomis quæ speciei rotundæ, ignem & animam dicit, (vt in aere quæ vocantur ramenta, quæ videntur in radijs qui per fenestras eunt) quarum omni seminarium elementa dicit Democritus totius naturæ: similiter autem, & Leucippus: horum autem Sphærica animam, propterea quod maximè possunt per totum penetrare huiusmodi figuræ, & mouere reliqua, cum moueantur, & ipsa: arbitrantes animam esse id, quod dat animalibus motum. Ex quibus videre est atomos igneas Democrito fuisse sphæricas, & animam ex illis constare, verum alium quendam ignem pro anima componenda intelligebat quam elementarem; quam opinionem repetit Aristotel. textu 30. 44. 68. 71. 73. lib. 1. de anima, & lib. de resp. c. 6. X. Ex lib. de sensu, & sensili c. 4. Album quidem, & nigrum hoc quidem asperum dicit esse, hoc verò læue; ad figuras autem reducit sapores. Vide Gal. 1. 1. de elementis c. 2. quantum autem mysterij sit in his paucis verbis aduertemus disp. 3. c. vltimo huius libri cum de colorum generatione erit sermo. Hæc pauca ex Aristotele annotasse sit satis: alias eius opiniones inuenies apud Diogenem Laertium, Senecam, Plinium, Theophrastu[m], Galenum, & alios veteres. XI. Diogenes itaq; ei dat tres opiniones pulcherrimas: Prima generationes fieri ex atomorum concurfu, quarum motus cietur à vertigine cæli; imò & vniuersum mundum atq; adeò mundos innumeros fortuito atomoru[m] coalitu generatos, vertiginem verò cæli vocat necessitatem. Secunda visionem ex allapsu imaginum ab obiectis in oculum missis fieri, quam ei sententiam adscribit Aristotel. 1. de sens. & sensili c. 2. Tertia fine hominis, seu beatitatem in hac vita esse quietum statum, seu animi tranquillitatem XII. Plinius 1. 7. c. 55. de resurrectione mortuorum refert senten-

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Synopsis of the doctrine of Democritus. IX. Book 1. De anima t. 20. Democritus says that a certain fire and heat is the soul; for since there exist infinitely many figures and atoms of a round shape, he says that fire and soul are the same, as in the air those things called motes, which are seen in the rays that pass through windows. Of these, Democritus says that the seed of all the elements of nature consists; and likewise Leucippus. He says that the soul is spherical because such figures can most easily penetrate through everything and move the rest, while they themselves are also moved; they thought the soul to be that which gives animals motion. From this it can be seen that Democritus’s fiery atoms were spherical, and that the soul consisted of them; but he understood a certain other fire to be composed for the making of the soul, different from the elemental fire; Aristotle repeats this opinion in text 30, 44, 68, 71, 73, Book 1 De anima , and in De respiratione ch. 6. X. From De sensu et sensili ch. 4. He says that white is rough and black is smooth; and he reduces tastes to figures. See Galen, 1. 1. De elementis ch. 2. But how much mystery there is in these few words we shall observe in dispute 3, in the last chapter of this book, when the generation of colors is discussed. Let these few things from Aristotle be enough to have noted; you will find his other opinions in Diogenes Laertius, Seneca, Pliny, Theophrastus, Galen, and other ancients. XI. Diogenes therefore assigns him three very beautiful opinions: First, that generations arise from the conjunction of atoms, whose motion is stirred by the whirl of the heavens; indeed, the whole world and even innumerable worlds were generated by the fortuitous union of atoms, while he calls the whirling of heaven necessity. Second, that vision arises from the influx of images sent from objects into the eye, which opinion Aristotle attributes to him in Book 1 De sensu et sensili ch. 2. Third, that the end of man, or blessedness in this life, is a calm state, or tranquility of soul. XII. Pliny, Book 7, ch. 55, relates concerning the resurrection of the dead senten-

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Synopsis doctrinæ Democriti. 25 sententiam Democriti quâ, cultissimus ille sed impius irridet. Puerilium, inquit, ista deliramentorum, auidæq[ue] nunquam desinere mortalitatis commenta sunt. Similis de asseruandis corporibus hominum, ac reuiuiscendis promissa à Democrito vanitas, qui non re- uixit ipse. XIII. Censuit dari mundos infinitos, vt docet Hipp[ocrates] epist. ad Damagetum, quam opinionem eleganter expressit Clau- dianuspan. Manl. Ille ferox, vnoq[ue] tegi non passus olympe Immensum per inane volat, finemq[ue] perosus Parturit innumeros angusto pectore mundos. Vide Lucret. l. 2. qui omnem hanc doctrinam luculenter explicat. Secundò mundum coaluisse digladiantibus, & se se inuicé per inane quærentibus, tridentibusq[ue] atomis; vnde Virgil. Democriti affecla ecloga. 6. siue in Sileno. Nanque canebat vti magnum per inane coacta Semina, terrarumq[ue] animæq[ue] marisq[ue] fuissent, Et liquidi simul ignis, vt his exordia primis Omnia, & ipse tener mundi concreuerit orbis. Tertiò videtur Claudianus illum impietatis accusare l. 1. in Ruffinum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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Transcription: Translated (English)

Synopsis of the doctrine of Democritus. 25 the opinion of Democritus, which that most polished but impious man ridicules. “These are childish fancies,” he says, “and inventions of a greedy immortality that never ceases.” The promise made by Democritus concerning the preservation of human bodies and their revival was equally vain, since he himself did not revive. XIII. He judged that there were infinite worlds, as Hippocrates teaches in the letter to Damagetus, an opinion elegantly expressed by Claudianus Pan. Manl. That fierce one, who would not allow himself to be covered by a single heaven, flies through the immeasurable void, and, hating an end, breeds countless worlds within his narrow breast. See Lucretius, book 2, who explains all this doctrine clearly. Secondly, that the world coalesced from atoms contending with one another, and seeking one another through the void, and from their three-pronged motions; whence Virgil, the companion of Democritus, Eclogue 6, or in Silenus. For he was singing how seeds, gathered through the great void, had been the beginning of earth and sea and air, and of liquid fire as well, so that from these first origins all things, and the tender sphere of the world itself, had come together. Thirdly, Claudian seems to accuse him of impiety, book 1 against Rufinus.

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Transcription: ATR-1

26 Synopsis doctrinæ Democriti. Omissis ergo erroribus qui Democritum vt alios gentiles deturparunt, hæc sunt legitima illius placita quæ mihi explicanda stabiliendaq[ue] proposui, ex quibus tota atomorum doctrina veluti compendio quodam percipi potest. I. Censuit materiam primam esse elementa, cum vocat illa seminarium figurarum, text. 20. l. 1. de an. II. Existimauit elementa non transmutari inuicem, 3. phys. tex. 29. clarèq[ue] id testatur Diogenes Laertius in eius vita l. 9. cum dicit ex mente Democriti ob firmitatem, & soliditatem passioni, & mutationi non esse obnoxia elementa: idq[ue] Empe- docles statuit l. 2. de gen. & corrupt. tex. 37. III. Vocat elementa ignem, aquam, terram de quibus mentionem fecit l. meteor. de anim. de resp. Aeris ab eo non fit mentio tan quam de elemento propriè dicto: imo l. de resp. facit aerem aliarum atomorum receptaculum, ac proinde ad illas erit omnino indifferens. Vide Galen. dethr. ad Pison. c. 11. Arist. l. 1. de gen. t. 1. lib. 1. de an. t. 20. & Lueret. l. 6. IV. Negare videtur aeri grauitatem, & leuitatem 4. cæli t. 43. imo aerem, & vacuum seu inane Democriti superius statuimus idem esse ex Arist. Galen. Virgilijq[ue] authoritate. V. Omnia ex atomis componi voluit. VI. Atomis infinitas esse figuras l. 1. de anim. t. 20. l. 3. phys. t. 29. l. 1. de gen. t. 1. VII. Atomis mutabiles esse figuras: probatur l. 3. phys. t. 29. vbi corpus commune nihil aliud est quam elementorum compages, & l. 1. de an. t. 20. vocatur omniseminarium figurarum, radixq[ue] figurarum. VIII. Igneas atomos voluit esse sphæricas l. 1. de an. t. 20. 44. 30. & alibi. IX. Atomi in Democriti sententia indiuisibiles sunt modo communi, & non proprio ex Aucrroe 1. phys. comment. 35. Id est ato-

Transcription: Translated (English)

26. Synopsis of the doctrine of Democritus. Therefore, setting aside the errors that disfigured Democritus, like the other pagans, these are the legitimate opinions of his which I have proposed to explain and establish, from which the whole doctrine of atoms may be understood, as it were, in summary form. I. He judged the first matter to be the elements, since he calls them the seed-bed of shapes, text. 20, l. 1. de an. II. He thought that the elements are not transformed into one another, 3. phys. tex. 29; and Diogenes Laertius clearly testifies to this in his Life, l. 9, when he says that, according to the mind of Democritus, because of their firmness and solidity the elements are not subject to passion and change: and Empedocles laid down the same, l. 2. de gen. & corrupt. tex. 37. III. He calls the elements fire, water, and earth, of which he made mention in l. meteor. de anim. de resp. He makes no mention of air as a truly and properly so-called element: indeed, in l. de resp. he makes air the receptacle of the other atoms, and therefore it will be wholly indifferent to them. See Galen, dethr. ad Pison. c. 11; Arist. l. 1. de gen. t. 1; lib. 1. de an. t. 20; and Lucretius, l. 6. IV. He seems to deny gravity and lightness to air, 4. cæli t. 43; indeed, we have stated above that air and vacuum, or void, in Democritus are the same thing, on the authority of Aristotle, Galen, and Virgil. V. He wanted all things to be composed from atoms. VI. He held that atoms have infinite figures, l. 1. de anim. t. 20; l. 3. phys. t. 29; l. 1. de gen. t. 1. VII. He held that the figures of atoms are changeable: this is proved by l. 3. phys. t. 29, where the common body is nothing other than the compages of the elements, and by l. 1. de an. t. 20, where it is called the seed-bed of all forms, and the root of forms. VIII. He wanted fiery atoms to be spherical, l. 1. de an. t. 20, 44, 30, and elsewhere. IX. Atoms, in the opinion of Democritus, are indivisible in the common sense, and not in the proper sense, according to Averroes, 1. phys. comment. 35. That is, ato-

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Synopsis doctrinæ Democriti. 27 est atomus vna non potest secari realiter ità vt ex vna fiant duæ, sed tamen est diuisibilis modo Mathematicis proprio, si- ue per designationem, per intellectum, extrinsecè. Vocat autem modum communem diuisionem realem, quia ità vulgus intelligit, diuisionem autem mathematicam vocat propriam, quod atomis ea propria sit: Vnde, & continuum vocauit infi- tum, quod mathematicè posset in infinitum diuidi, quamuis physicè esset finitum. His quatuor verbis tanta inest vis vt to- tam atomorum doctrinam sustineat. X. Congregatione atomorum fieri generationem, segre- gatione corruptionem voluit. 1. 1. de ortu t. 5. XI. Ex paucis mutatis totum mutari, imo ex eisdem aliter dispositis fieri diuersum quid, vt ex eisdem literis fit tragædia, & comædia. l. 1. de ortu, & inter. t. 5. ex qua etiam complica- tione varios emergere colores censuit l. de sens. & sensili c. 4. XII. Alterationem fieri per meatus pronuntiauit, corpus- culis siue atomis proportionatos sibi poros subeuntibus l. 1. de gen. t. 56. 57. quam sententiam sequitur Democriti lingua Lucretius l. 2. & l. 6. XIII. Intensionem, & remissionem qualitatum per ordi- nationem, & positionem seriatim atomorum explicuit l. 1. de ortu. t. 5. XIV. Motum omnem impetu fieri dixit l. 4 cælit. 42. 43. Hæ sunt legitimæ Democriti opiniones de quibus nulli du- bium erit quin ad eum spectent cum necessaria ratiocinationis colligatione hæreant, & si qui dubium cupiam esset num ità censuerit Democritus, legat diligenter Aristotelem, Gale- num, Diogenem Laertium, & maximè Lucretium, planumq; erit quam sedulò eius sensa perquisuerim quamq; sincere ex- ponam. Annotaui præterea de alia Democriti scientia com- plures opiniones quas breui curiositati publicæ dabo, veteraq; noua videbuntur. DEMO-

Transcription: Translated (English)

Synopsis of the doctrine of Democritus. 27 an atom cannot really be cut so that from one two are made, but it is nevertheless divisible in the manner proper to mathematicians, that is, by designation, by the intellect, externally. He calls the common mode real division, because the crowd understands it in that way; but he calls mathematical division proper, because that belongs to atoms: whence he also called the continuum infinite, because it could be divided to infinity mathematically, although physically it was finite. In these four words there is such force that they uphold the whole doctrine of atoms. X. He held that generation arises from the aggregation of atoms, and corruption from their separation. 1. 1. de ortu t. 5. XI. From a few things changed, he said, the whole is changed, indeed from the same things differently arranged something different is produced, as from the same letters tragedy and comedy are made. l. 1. de ortu, & inter. t. 5. from which also by this compounding he judged that various colors emerge l. de sens. & sensili c. 4. XII. He declared that alteration takes place through passages, the particles or atoms entering pores proportioned to themselves l. 1. de gen. t. 56. 57. which opinion Lucretius follows, Democritus's tongue, l. 2. & l. 6. XIII. He explained the intensification and remission of qualities through the arrangement and serial position of atoms l. 1. de ortu. t. 5. XIV. He said that all motion occurs by impulse l. 4 cælit. 42. 43. These are the legitimate opinions of Democritus, concerning which there will be no doubt that they belong to him, since they adhere with the necessary linkage of reasoning; and if anyone should wish to doubt whether Democritus really held such views, let him carefully read Aristotle, Galen, Diogenes Laertius, and especially Lucretius, and it will be clear how diligently I have investigated his views and how sincerely I set them forth. I have furthermore noted concerning another branch of Democritus's science several opinions, which I shall soon give to the public as a curiosity; and the old will seem new. DEMO-

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Transcription: ATR-1

DEMOCRITVS REVIVISCENS, SIVE DE ATOMIS. Præfatio ad lectorem. TRIPLEX philosophantium genus in lucem, nostra ætas effudit alij enim certo cuidam autori sunt addicti, cuius verbis veluti catena quadam adamantina alligantur, vnde totum suum ponunt studium vt sensus principi suo fauorabiles inue- niant, excogitent illi tuendo subterfugia, & si aperto Marte propugnare non liceat, stratagematis vtantur. Ità sunt nunc peripatetici, qui vni vacantes Aristoteli non intelligunt, quid intersit autorem explanare vel eius adhærere placitis. Inge- niosum est sacramentum philosophicum dicere, & in verba, magistri conceptis verbis adigi, & quantus sit Aristoteles vix vllus fauorabilius, quam ego, iudicauit. Ad hanc philoso- phorum sectam reducimus omnes eos qui alicuius insistentes vestigijs, scriptis alienis explanandis incumbunt, quales sunt qui Scotum adorant, qui Ræmundum Lullum colunt, qui Paracelsi portentosa mirantur deliria. Alij sunt libertatis philosophicæ vindices qui nullius auto- ritatem, & omnium rationes ponderant, seq; veluti naturæ, & Lycæi vel arbitros faciunt vel restitutores: Illi nouis sectis principium faciunt, siue veram habeant sapientiam, siue am- bitioso errore sint præcipites. Ità Sebastianus Basso qui noua aduersus Aristotelem inuexit. Ità Paracelsus Hippocrati, Galeno, & Auicennæ iniuriosissimus ebrius. Sic Thomas Campanella propriam sibi physiologiam vulgauit, artemq; medicinalem ex proprijs principijs descripsit. Sic Fluddus, Crollius innumerabilesq; chymici. Hosq; optimè in varias classes

Transcription: Translated (English)

DEMOCRITVS REVIVISCENS, OR ON ATOMS. Preface to the reader. A threefold kind of philosophers has our age brought forth into the light. For some are attached to a certain author, to whose words they are bound as by some adamantine chain; wherefore they devote all their study to finding notions favorable to their master, inventing subterfuges for his defense, and, if they may not fight in open battle, they employ stratagems. Such now are the Peripatetics, who, clinging to Aristotle alone, do not understand what it is to explain an author or to adhere to his doctrines. It is, as it were, a philosophical sacrament to say, and to be compelled into the words of the master by set formulae; and how great Aristotle is, scarcely anyone has judged more favorably than I. To this sect of philosophers we refer all those who, following in someone else’s footsteps, labor in expounding others’ writings, such as those who worship Scotus, who honor Ræmundus Lullus, who marvel at the monstrous delusions of Paracelsus. Others are the vindicators of philosophical liberty, who weigh the authority of no one and the arguments of all, and make themselves, as it were, either judges or restorers of Nature and of the Lycæum. These are the men who give rise to new sects, whether they possess true wisdom or are driven headlong by ambitious error. Thus Sebastianus Basso brought forward new things against Aristotle. Thus the drunken Paracelsus was most injurious to Hippocrates, Galen, and Avicenna. Thus Thomas Campanella published a physiology of his own and described the art of medicine according to his own principles. Thus Fludd, Crollius, and countless chemists. And these most suitably into various classes

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PRÆFATIO. 29 classes distinxeris, quidam enim nouorum curiosi sunt, conscij quam parum in vulgata philosophia certitudinis sit: alij fac- tionum capita dici ambiunt; pauci nullius retinentes sententiæ, imo ne suæ quidem, soli veritati locum dant, veterum imitatores, inuentoribus conditoribusq[ue] scientiarum annu- merandi qui posita experientia philosophantur, quales fue- runt nostro sæculo Tychones Kepleri, Galilæi, Scheineri qui immixtas philosophiæ mathematicas illustrarunt, & nullo pe- ne plagiatu sunt vsl. Istis esse semper debuit pro emblemate pura lux, pro anima verò; Amicus Plato, amicus Aristoteles, magis amica Veritas. Tertium philosophoru[m] genus adolescentioribus placitis vel spretis vel iam deliberatis ad philosophiam anum vetulamq[ue]; re- gressi quærunt ecquidna[m] decoris firmitatisq[ue]; suo tempore ha- berit quæ nunc collapsa in cineribus fax est. Sic Samij Ari- starchi Astrologiam deduxit Copernicus, Platonis doctrinam celebrauit cum suis Florentinis Marsilius Ficinus, & à multis sæculis obsoletâ pene Empedoclis philosophiam ex parte ce- cinit cultissimus Lucretius, restituereq[ue]; in hoc opere tentamus Democriti. De tribus hisce sectis si iudicium à me quæris, dicam, om- nibus suum honorem deberi, potissimamq[ue]; esse quæ vnum veritatis solem adorat: At pro iuuentutis institutione satius est Aristotelem prælegere, quod eius methodus, & sensa omni sint exceptione maiora, tum etiam quia meliori Philosopho care- mus absumptis veterum libris, Platoneq[ue]; qui solus cum Aristo- tele superuixit, in scientia naturali valdè parconec ordinato. Vnde grauissimo omnium pene populorum consensu sancta, & inuiolabilis est in Academijs peripateticorum principis maie- stas, vt maiori diligentia illi studeat iuuentus, quem à veteranis quibusq[ue]; vident scrupulosissimè coli. Quare cum Democriti phi-

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PREFACE. 29 you have distinguished classes, for some are curious about novelties, being aware how little certainty there is in received philosophy; others seek to be called the leaders of factions; few, retaining no opinion at all, indeed not even their own, give room only to truth, imitators of the ancients, to be numbered among the founders and discoverers of the sciences, who philosophize on the basis of observation, such as in our age Tycho, Kepler, Galileo, Scheiner, who illuminated the mathematics intermingled with philosophy, and were in almost no way plagiarists. For these there should always have been as emblem, pure light; and for their soul, “Friend is Plato, friend is Aristotle, but more a friend is Truth.” A third kind of philosophers, having despised or already discarded more recent doctrines, have returned to philosophy, old and very old, and seek whether it has at its time any dignity or firmness, which now, fallen into ashes, is a torch. Thus Copernicus drew forth the astronomy of the Samian Aristarchus; Marsilius Ficinus celebrated the doctrine of Plato together with his Florentines; and Lucretius, the most polished of men, in part sang the philosophy of Empedocles, long since nearly obsolete; and we attempt to restore that of Democritus in this work. If you ask my judgment about these three sects, I shall say that honor is due to each, and especially to that which worships the one sun of truth. But for the education of youth it is better to lecture on Aristotle, because his method and doctrines are beyond all exception; and also because we lack a better philosopher, the books of the ancients having been destroyed, and Plato alone surviving, alongside Aristotle, who in natural science was very sparing and not systematic. Hence, by the gravest agreement of almost all peoples, the majesty of the prince of the Peripatetics is sacred and inviolable in the Academies, so that youth may devote themselves to him with greater diligence, whom they see to be most scrupulously honored by all experienced scholars. Therefore, since Democritus phi-

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30 PRÆFATIO. philosophia à me restitui debere censui, id primò veritatis desiderio ingenijq[ue] exercendi causa susceptum à me est opus, deinde cum in philosophicis nulla possit esse præscriptio non abs re fore duxi in integrû restituere sententias que primò viguerunt. Si verum attigimus, optatis potimur, sin minus, à nostris deuiationibus alteri factioni non parum accedit autoritatis. Hæc tamen priuato studio continebuntur placita, neq[ue] alius mecum è philosophis cathedram ascendet regiam, præterquâ Aristoteles, in publicis enim prælectionibus iuuentutis institutioni non autem genio nouitatiue est iudulgendum. Vnum insuper moneo, breuitatis consilio multas è meis ratiocinationibus emergentes difficultates vel omisas vel abscissas, cum doctis apertum sit, in acurata sententiæ explicatione omnium obiectionum solutiones, tanquam in seminario quodam contineri. Aliquis fortasse expectabit pro Democrito argumenta quæ aduersarium vel mutum vel desperatum reddant. Eluduntur omnia philosophorum tela præsertim in scientia naturali, in qua omnes cæcutimus, & promittere ratiocinationes demonstratiuas in physicis vel temerarij est, vel ignari lubrica esse sophistarum ingenia, & nullo pacto vinciri posse. Id tamen sanctè seruaturum me spondeo, nullas difficultates à me in aciem malignè deducendas, sed potius omni ratione nitar vt robur suum habeant. Interea mi lector si Democritum produce dedignaris, nec ipse curabit, & tibi benignus arri- debit. DEMO-

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30 PREFACE. I judged that philosophy ought to be restored by me; first undertaken from a desire for truth and for the exercise of my intellect, and then because in philosophical matters no prescription can be valid, I thought it would not be out of place to restore intact the opinions that first flourished. If we have touched the truth, we attain our desire; if not, by our deviations authority is not a little added to the other party. Yet these doctrines will be confined to private study, nor shall any other philosopher ascend the royal chair with me, except Aristotle; for in public lectures one must cater not to novelty of genius, but to the instruction of youth. One thing further I would warn: for the sake of brevity, many difficulties arising from my reasoning have been either omitted or cut away, since it is plain to the learned that, in an accurate explication of a doctrine, the solutions of all objections are contained as in some seedbed. Someone perhaps will expect arguments on behalf of Democritus that would render an opponent either dumb or hopeless. All the weapons of philosophers are avoided, especially in natural science, in which we are all blind; and to promise demonstrative reasonings in physics is either rash, or shows ignorance that the minds of sophists are slippery and can in no way be bound. Nevertheless, I solemnly promise this: that I shall not maliciously bring forward any difficulties in attack, but rather shall strive by every means that they retain their own force. Meanwhile, my reader, if you disdain to produce Democritus, he himself will not care, and he will smile upon you kindly. DEMO-

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DEMOCRITVS REVIVISCENS SIVE DE ATOMIS; Fundamentum totius operis, eius distri- butio, & methodus. Væstioni de compositione continui omnibusque annexis hoc est toti pæne philosophiæ naturali, tot incubant tenebræ, vt fatendum sit nos aliquid latere principium è quo toti disputationi lumen esset mutuandum: maximæq[ue]; fiunt à veritate peregrinationes dum prætermisssis quibusdam necessarijs, falsisuè subsumptis errores in consequentibus multiplicari contingit, error enim in principio leuis, maximus est in fine. Ab hoc ergo vel malè præsupposito, aut omisso principio motus, tempus, alteratio, intensio, temperamentum, rarefactio, condensatio, mixtio, augmentatio, nutritio, propagatio rerum aliaq[ue]; innumera sic inuoluuntur vt diligentissimum quemque confundant. Suspicor in tribus esse posse nostram circa illud principium ignorationem; primò quidem in distinctione vera materialis, & spiritualis quam à diuisibilitate alij, alij aliunde petunt; secundò in essentia quantitatis assignanda, quam non pauci materiæ primę diuisibilitatem dixerunt afferre. Sed tertium mihi potius omnium difficultatum origo videtur, ignoratio verę materię primę. Ratio meę coniecturę hæc est: forma præsupponit materiâ vt ab alijs etiam accidentibus præsupponitur subiectum, ergo vt erit materia, ità & continuitas: forma enim, & accidentia quę educuntur debent sequi naturam materię, cum

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DEMOCRITUS REVIVED OR ON ATOMS; The foundation of the whole work, its distribution, and method. On the question of the composition of the continuous, and everything connected with it—that is, nearly the whole of natural philosophy—so many obscurities lie upon us that we must admit that some principle is hidden from us, from which light for the whole discussion must be borrowed; and great wandering from the truth results whenever, certain necessary points having been omitted or false assumptions introduced, errors are multiplied in the consequences; for an error in the beginning is slight, but in the end it is great. From this, then, whether through an ill-supposed or omitted principle, motion, time, alteration, intensity, temperament, rarefaction, condensation, mixture, augmentation, nutrition, propagation of things, and countless other matters are so involved that they confuse even the most diligent. I suspect that our ignorance concerning that principle may be in three things: first, in the true distinction between the material and the spiritual, which some derive from divisibility, others from elsewhere; secondly, in assigning the essence of quantity, which not a few have said brings with it the divisibility of prime matter. But a third seems to me rather the source of all the difficulties: the ignorance of true prime matter. The reason for my conjecture is this: form presupposes matter, just as among other accidents a subject is presupposed; therefore, as matter will be, so also will continuity be. For form and the accidents that are drawn forth ought to follow the nature of matter, since

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De atomis, fundamentum. cum quidquid recipitur per modum recipientis recipiatur, ergo accidentia nihil ad continuitatis rationem possunt afferre, materia enim prius est continua quam frigida quantaue; hoc principium dissimularunt ij qui in hæc absurda impegerunt clarissimi cæteroqui scriptores; Materia spoliata quantitate est tota in toto, & tota in qualibet parte, & totius mundi materia in punctum mathematicum conflueret si quantitate spoliaretur; ità Valquez, & alij. Primùm itaq[ue] inuestigandam mihi esse duxi materiam primam, quam deinde atomis constare contendo, sicq[ue] duæ sunt primæ huius libri partes prima de materia prima, altera de atomis, quibus tertia subnecti debuit consequentiarum, cum nec atomos sine motu stabilire, nec opus abiq[ue] rarefactionis difficultate explanata complere potuerim. Ecce itaq[ue] libri tripartitam diuisionem. Quoad methodum; tentau nobilissimam Euclidis consuetudinem, maioris claritatis causa, à geometrico puluere in lycaum inuehere, definitiones axiomata, & postulata præstruens propositionibus; deinde cum mille in rebus mathematicarum scientiæq[ue] naturalis compererim societatem, data occasione, demonstrationes geometricas, & arithmeticas admiscui; multu[m] itaq[ue] interest mathematicis, elementis saltem Euclidis esse initiatum, nihil enim magni in philosophia faciet, qui mathesim ignorat, atomorum certè subtilissimam scientiam nullo modo percipiet, nedum ad illius suprema mysteria deuehetur.

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On atoms, the foundation. Since whatever is received is received according to the mode of the receiver, therefore accidents can contribute nothing to the notion of continuity; for matter is continuous before it is cold or extended in quantity. This principle was concealed by those most distinguished writers, otherwise, who have run into these absurdities; matter, stripped of quantity, is entire in the whole, and entire in each part, and the matter of the whole world would flow together into a mathematical point if it were stripped of quantity; thus Valquez, and others. First, therefore, I thought that I must investigate primary matter, which I then maintain is composed of atoms; and so there are two principal parts of this book, the first concerning primary matter, the second concerning atoms, to which a third on consequences ought to be added, since I could neither establish atoms without motion, nor complete the work without explaining the difficulty of rarefaction. Behold, then, the threefold division of the book. As for the method; I attempted to introduce the most noble custom of Euclid, for the sake of greater clarity, bringing into the Lyceum from geometric dust definitions, axioms, and postulates before the propositions; then, since I discovered in many matters a kinship with mathematical and natural science, when occasion offered I intermingled geometric and arithmetical demonstrations; there is therefore much advantage for mathematicians in at least having been initiated into Euclid’s Elements; for he who is ignorant of mathematics will accomplish nothing great in philosophy, and will certainly in no way grasp the most subtle science of atoms, much less be led up to its highest mysteries.

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De Atomis. Disput. I. DISPVTATIO I. An detur materia prima diuersa ab elementis. Ribus capitibus hanc dissertationem expediâ, ostesu- r[um] primò iuxtà Democritum nullam dari materiam primam diuersam ab elementis; Secundò de eorum natura numero, & proprietatibns secundum atomoru[m] doctrinam tractabo; Tertiò obiectiones diluam. Quæ disputatio necessariò premitti debuit vt primas atomorum species possemus distinguere. Sed vt meam fidem liberem, methodica Euclidis consuetudine ordiar à definitionibus, tùm verborum, tùm etiam rerum, ne vlla subsit æquiuocatio. DEFINITIONS. I. Elementi nomine intelligo corpus simplex ad mixtorum compositionem concurrens quodq; sit purè homogeneum. II. Subiectum primarium est illud, quod qualitatum à se immediatè promanantium sedes est, & principium materiale, aut efficiens: sic ignis caloris à se diffusi subiectum est primarium. III. Subiectum secundarium est illud quod recipit accidens ab extrinseco agente transmissum: vt aer est subiectum secundarium caloris ignis. IV. Subiectum denominationis illud est quod denominatiuè tantum tale est, à potiori scilicet parte denominatione sumpta. Huius distinctionis fundamentum sumitur à natura mixtionis, quà sic partes inter se miscentur, vt nulla ad sensum sit amplius distinguibilis ab alia, ac proinde totum denominatur ab eo, quod inq[ui]s percipitur, cæteris qualitatibus latentibus, & sub imperio oppressis. V. Subiectum inhæsionis est illud, cui strictè, & formaliter C acci-

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On Atoms. Disputation I. DISPUTATION I. Whether there is a first matter distinct from the elements. In three chapters I shall unfold this dissertation, showing first, according to Democritus, that no first matter distinct from the elements is given; secondly, I shall treat of their nature, number, and properties according to the doctrine of atoms; thirdly, I shall answer objections. This disputation had necessarily to be premised, so that we might be able to distinguish the primary species of atoms. But in order to free myself from blame, I shall begin in the methodical manner of Euclid, from definitions, both of words and of things, lest any ambiguity remain. DEFINITIONS. I. By the name of element I understand a simple body contributing to the composition of mixed bodies, and which is purely homogeneous. II. The primary subject is that which is the seat of qualities immediately flowing from it, and the material or efficient principle: thus fire is the primary subject of the heat diffused from it. III. The secondary subject is that which receives an accident transmitted from an external agent: thus air is the secondary subject of the heat of fire. IV. The subject of denomination is that which is such only by denomination, namely from the more powerful part, the denomination being taken from it. The foundation of this distinction is taken from the nature of mixture, in which the parts are so mingled with one another that no part is any longer distinguishable from another to the senses, and therefore the whole is denominated from that which is perceived in the inquiry, the other qualities lying hidden and suppressed under its rule. V. The subject of inherence is that to which, strictly and formally, an accid-

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De Atomis. Disput. I. 34 accidens inest. Ita terra est formaliter subiectum inhæsionis frigoris, homo autem subiectum denominationis, neq[ue] enim animus algore vexari potest. V I. Elementu[m] symbolum est, quod vna qualitate cum alio consentit; vt aer, & ignis ex Aristotele, qui vtriq[ue] calorem assignat. V I I. Elementa dissymbola sunt, quæ in nulla qualitate co[n]ueninut, vt aqua, & ignis ex Aristot. PRINCIPIA. I. Ex nihilo nihil fit: hoc est agentia naturalia exigunt subiectum vt agant, & materiam circa quam versentur. II. Mundus destrui non potest per causas naturales vi propria, & naturaliter applicatas: secus si virtute diuina applicentur passo. Sic enim sæculi consummatione ignis omnia vastabit, & erit cælum, terraq[ue] noua: apoc. c. 21. v. I. III. Agentium naturalium actio iuuatur ab extensione dummodo sit ea absq[ue], dispersione virtutis: pariter, & resistentia passi iuuatur ab extensione virtuti suæ actiuæ proportionata. Ità magnus ignis plus agit quam paruus, & centum libræ glaciæ diutius resistent æstui, quam selibra. IV. Sublata parte essentiali perit totum, siuè pars illa se habeat ex parte materiæ, efficientis, formę, finisue, nihil enim absq[ue]; hisce causis esse potest in natura. V. Quinq[ue]; sunt mundi partes principes, & essentiales terra, aqua, aer, ignis, se habentes ex parte materiæ. VI. Vbi contrarietas datur inter agens, & passum ibi necessariò est alteratio successiua præcedens passi destructionem substantialem. VII. Natura semper intendit quod perfectissimum est. VIII. Non potest introduci forma sine præuijs dispositionibus, & vbi sunt dispositiones omnes ibi est forma. IX.

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On Atoms. Disputation I. 34 an accident inheres. Thus earth is formally the subject of the inherence of cold, but man is the subject of denomination, for the mind cannot be afflicted by cold. VI. An element is a symbol, which agrees with another in one quality; as air and fire, according to Aristotle, who assigns heat to both. VII. Elements are dissimilar, which agree in no quality, as water and fire according to Aristotle. PRINCIPLES. I. Nothing comes from nothing: that is, natural agents require a subject on which to act, and matter with respect to which they operate. II. The world cannot be destroyed by natural causes by their own power, and when applied naturally; otherwise if they are applied to the patient by divine power. For thus at the consummation of the age fire will lay waste all things, and there will be a new heaven and a new earth: Apoc. c. 21. v. 1. III. The action of natural agents is aided by extension, provided that it be without the dispersion of power; likewise, the resistance of the patient is aided by extension proportioned to its active power. Thus a large fire acts more than a small one, and a hundred pounds of ice resist heat longer than a half-pound. IV. When the essential part is removed, the whole perishes, whether that part is on the side of matter, efficient cause, form, or end; for nothing can exist in nature without these causes. V. There are five principal and essential parts of the world: earth, water, air, and fire, which are on the side of matter. VI. Where contrariety exists between agent and patient, there must necessarily be a successive alteration preceding the substantial destruction of the patient. VII. Nature always tends toward what is most perfect. VIII. Form cannot be introduced without prior dispositions, and where all the dispositions are present there is form. IX.

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C. I. Elementa esse materiam primam. 35 IX. Causa principalis debet continere effectum suum vel formaliter, vel eminenter. X. Idem est finis actionum, & essentiæ, nam esse est prop- ter operari. XI. In ijs quæ sub sensum cadunt posita experientia oportet philosophari, sensibilia enim per sensus iudicanda sunt. XII. Existentia rei dignosci potest à tribus, primò ex causæ necessariæ aut effectus necessarij existentia, vt ignis est, ergo etiam calor, dies est, ergo sol lucet. Secundò ex proportione, & reciprocatione actionum, & connexione cum alio externo existente, rerum enim non existentium nulla est actio. Tertiò cum est ad totius vniuersibonum. XIII. Magis, & minus non faciunt differre essentialiter. POSTVLATA. I. Concedatur dari materiam primam quæcunq[ue] tandem sit, & formas substantiales. II. Concedatur dari elementa, de eorum autem natura, numero proprietatibusq[ue] nihil postulo. III. Consideremus elementa in sua puritate, non autem quatenus mixta sunt aut alterata. CAPVT PRIMVM. Elementa esse materiam primam: Mirabile vtiq[ue] Aristotelis ingenium in quatuor potissimu[m] rebus enituit, primò in formis syllogisticis: dem de moraliu[m] lib. præsertim polit. 1. 5. tertio in mechanicis quæstionibus 4. in methodo qua vsus est ad autorandâ nobile[m] materiæ primæ fabulam, quam ab Ægyptijs ad Græcos esse derivatam testatur Laertius I. 1. Vtq[ue] in primo excultissimæ ra- tioci- C 2

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C. I. Elements are the primary matter. 35 IX. The principal cause ought to contain its effect either formally or eminently. X. The end of actions and of essences is the same, for being is for the sake of acting. XI. In those things which fall under the senses, one must philosophize by observation; for sensible things are to be judged through the senses. XII. The existence of a thing can be recognized from three things: first, from the existence of a necessary cause or necessary effect, as fire is, therefore also heat; it is day, therefore the sun shines. Second, from the proportion and reciprocity of actions, and from connection with some other external existent, for things that do not exist have no action. Third, when it is for the good of the whole universe. XIII. More and less do not make things differ essentially. POSTULATES. I. Let it be granted that there is primary matter, whatever it may finally be, and substantial forms. II. Let it be granted that there are elements; but concerning their nature, number, and properties I ask nothing. III. Let us consider the elements in their purity, not however insofar as they are mixed or altered. CHAPTER ONE. That the elements are primary matter: Indeed, Aristotle's marvelous genius shone forth above all in four matters: first, in syllogistic forms; then in moral matters, especially in political ones; third, in mechanical questions; fourth, in the method he used to devise the noble fiction of primary matter, which Laertius testifies was derived from the Egyptians to the Greeks. And as in the first of the most cultivated ratio- C 2

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De Atomis. Disput. I. 36 tiocinationis se fuisse ostendit, in secundo ciuile animal rebus humanis aptissimum, in tertio subtilitatis mathematicæ scientissimum, in quarto certè, dum antiquis parum tribuit, hominem se, qui falli posset, patefecit: vtq[ue] in primo excolit intellectum, in secundo voluntatem, & mores, in tertio imaginationem, cuius palmarium opus est mechanica, ità in quarto suo partu non satis auertit se ab illa facultate animi, quam Platonici quidam eleganti nomine Erraticam appellant. Materiam certè primam dari negabit nullus, at an sit inanis illa potentia de qua certant inter se Peripatetici nunc est inquirendum, eruenda à fundamentis veritas, neq[ue] aduersariorum defectus dissimulandi, vel tantum tribuendum autoritati, vt ipsi ratio, & experientia cedant. PROPOSITIO I. Quatuor sunt materiæ primæ proprietates ab ipsa inseparabiles: prima vt sit primum uniuscuiusq[ue]; corporis subiectum, secunda vt in omnibus corporibus naturalibus eadem reperiatur inesse, tertia vt sit ingenerabilis, & incorruptibilis, quarta vt in ipsa corpora omnia per dissolutione vltimam resoluantur. P Rima proprietas est veluti conceptus materiæ primæ essentialis, & assentitur Aristotel. in primo phys. Secunda sequitur necessariò ex prima, cum enim sit primum omnium rerum subiectum, debet etiam intelligi inesse. Ratio à priori est, quia modus agendi materiæ est per sui communicationem vt etiam formæ, aliarum verò causarum est vel per influxum, vel per intentionem, aut directionem, vt patet in efficiente, finali, & idæali: cum ergo materia agat tantum per sui communicationem quæ propria est agendi ratio causarum internarum, sequitur eius absentiam cum sui effectus seu compositi subsi-

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On Atoms. Disputation I. 36 it showed itself to have been from reasoning, in the second a civil animal most suited to human affairs, in the third most skilled in the science of mathematical subtlety, in the fourth certainly, while he assigns too little to the ancients, he disclosed himself as a man who could be mistaken: and just as in the first he cultivates the intellect, in the second the will and morals, in the third the imagination, of which the chief work is mechanics, so in his fourth production he did not sufficiently turn away from that faculty of the soul which certain Platonists with an elegant name call the Wandering faculty. That there is certainly a first matter, no one will deny; but whether there is that empty power about which the Peripatetics dispute among themselves is now to be inquired into: truth must be drawn from the foundations, nor must the shortcomings of opponents be concealed, nor must so much be granted to authority that reason itself and experience yield to it. PROPOSITION I. There are four properties of first matter inseparable from it: the first, that it is the primary subject of every body; the second, that it is found to be present in all natural bodies; the third, that it is ingenerable and incorruptible; the fourth, that all bodies are finally reduced into it by dissolution. The first property is, as it were, the essential concept of first matter, and is assented to by Aristotle in the first book of the Physics. The second follows necessarily from the first; for since it is the primary subject of all things, it must also be understood to be present in them. The reason a priori is this: because the mode of acting of matter is through communication of itself, as also of form, whereas the other causes act either through influx, or through intention, or direction, as is evident in the efficient, final, and ideal cause. Since therefore matter acts only through communication of itself, which is the proper mode of action of internal causes, it follows that its absence, together with the absence of its effect or composite subsi-

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C.1. Elimenta esse materiam primam. subsistentia nullo modo posse intelligi, ergo in omnibus eadem reperietur inesse. Tertia proprietas probatur ab Aristotele primò phys. c.5. & sequitur euidenter ex premissis: si enim esset generabilis vel fieret ex subiecto vel sine subiecto, si primum, non esset ma- teria prima quandoquidem assignatur prior, si secundum, neq[ue] pariter erit necessaria ad generationem cum sine subiecto fiat: deinde daretur creatio naturaliter contra princip. I. Quarta conditio vt in ipsam omnia resoluantur est etiam Aristotelis qui ait, si quid corrumpitur in eam Vltimo resoluitur, & probatur ratione, quia vt est compositio, ità & resolutio in opposita ratione, sed in co[n]positione corporis materia est pri- mum quod supponitur, ergo in resolutione erit Vltimum, vis enim resolutionis incipit ab eo quod primum in compositione fuit. Conuenit ergo cum Democrito Aristoteles in eo, qua- tuor esse materiæ primæ characteres essentiales, quod erat of- tendendum. PROPOSITIO II. Elementa sunt primum Vniuscuiusq[ue] corporis subiectum, in omnibus corporibus naturalibus eadem reperiuntur inesse, sunt inge- nerabilia, & incorruptabilia, quodlibet corpus in ipsa per dissolutionem Vltimam resoluitur. Hæc propositio est minor syllogismi cuius precedens ma- ioris locu[m] obtinet, quâ si probauero acta res est. Et primò quidem nullus dubitat de secunda nostræ propositionis parte, quod scilicet omnibus mixtis eadem insint elementa, id enim eorum resolutione patet: totius rei cardo vertitur in asserenda prima materiæ primæ proprietate, quâ est primùm vniuscuius- que corporis subiectum, nam ex illa dependent tertia, & quar- ta. Et quamuis id probare difficillimum sit, neq[ue] à Peripate- ticis C 3

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C.1. It makes this the first matter. subsistence cannot in any way be understood; therefore it will be found to be the same in all things. The third property is proved by Aristotle first in Physics, c. 5, and it clearly follows from the premises: for if it were generable, it would either come to be from a subject or without a subject; if the first, it would not be first matter, since it is assigned as prior; if the second, then it would likewise not be necessary for generation, since it comes to be without a subject: then there would be natural creation, against principle I. The fourth condition, that all things are resolved into it, is also Aristotle's, who says that if anything is corrupted, it is ultimately resolved into it, and it is proved by reason, because as there is composition, so also is resolution in the opposite order; but in the composition of a body matter is the first thing presupposed, therefore in resolution it will be the last, for the force of resolution begins from that which was first in composition. Therefore Aristotle agrees with Democritus in this, that there are four essential characters of first matter, which was to be shown. PROPOSITION II. The elements are the first subject of every body; they are found to be present in all natural bodies, they are ingenerable, and incorruptible; every body is resolved into them by ultimate dissolution. This proposition is the minor premise of the syllogism, whose preceding one occupies the place of the major; if I prove that, the matter is done. And first, indeed, no one doubts the second part of our proposition, namely that the same elements are in all mixed bodies, for this is clear from their dissolution: the whole crux of the matter turns on asserting the first property of first matter, namely that it is the first subject of every body, for the third and fourth depend on that. And although it is very difficult to prove this, nor by the Peripatetics C 3

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38 De Atomis. Disput. I. ticis hactenus satis probatum sit dari illam potentiam puram, seu materiæ primæ inanitatem, tamen in arduis ausum suam laudem meretur. Probatur itaq[ue] prima proprietas per tertiam. Elementa sunt ingenerabilia, & incorruptabilia, ergo sunt primum vni- uscuiusq[ue]; corporis subiectum. Consequentia est euidens, nam si daretur aliud subiectum, daretur illorum generatio, & cor- ruptio, si autem sunt ingenerabilia, & incorruptabilia sequitur in ipsa per dissolutionem vltimam cuncta resolui, neq[ue] enim in incorruptibili vlterior datur resolutio. Ex tertia itaq[ue] proprie- tate, siue ab antecedenti posito omnes aliæ asseruntur, pro- batur ergo antecedens, Primò à priori: Elementorum finis est certis quibusdam prefinitisq[ue]; generationibus in natura presidere, si autem gene- rabilia essent, & corruptabilia nequaquam id fieret, quia ex mutatis principijs consequentias mutari necesse est, atq[ue] vt doctissimus cecinit Lucretius l. 1. circa medium. ............................................ si primordiarerum Commutari aliqua possent ratione reuincta, Incertum quoq[ue]; iam constet, quid possit oriri. Quid nequeat........................................ Nec toties possent generatim sæcla referre Naturam, motus, victum, moresq[ue]; parentum. Quia scilicet imminuta parte essentiali natura non po- test amplius suis insistere vestigijs neq[ue]; iuxta suas regulas intendere quod optimum est, quale in omnibus est tempera- mentum ad iustitiam, diminutioni scilicet vel corruptioni su- biacentibus elementis: ergo cum sit adeo proprium naturæ perfectius intendere ex p. 7. etiam medium illius intentionis elementorum firmitas, & inuariata natura supponi debuit. Probatur secundò. Si eleméta essent corruptabilia, & gene- rabilia

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38 On the Atoms. Disput. I. thus far it has been sufficiently proved that there is that pure potency, or the emptiness of first matter, yet in difficult matters boldness deserves its praise. Therefore the first property is proved by the third. The elements are ingenerable and incorruptible; therefore they are the first subject of every body. The consequence is evident, for if another subject were given, their generation and cor- ruption would be given; but if they are ingenerable and incorruptible, it follows that in them all things are resolved by ultimate dissolution, for in the incorruptible no further resolution is given. From the third property, therefore, or from the antecedent posited, all the others are asserted; the antecedent is therefore proved. First, a priori: the end of the elements is to preside over certain predetermined generations in nature; but if they were generable and corruptible, this would by no means happen, because from changed principles it is necessary that consequences be changed, and as the most learned Lucretius sings, book 1, around the middle: ............................................ if the first things of things could be changed by some bound rationally tied, then also it would already be uncertain what could arise. What could not........................................ Nor could the generations of the ages so often reproduce nature, motions, food, and the habits of parents. Because, namely, with an essential part diminished, nature cannot any longer follow its own tracks nor, according to its rules, direct what is best, as in all things is the temperament for justice, namely when the elements are subject to diminution or corruption: therefore, since it is so proper to nature to aim at what is more perfect, from p. 7. even the middle of that intention, the firmness of the elements and their unchanged nature had to be assumed. Second, it is proved. If the elements were corruptible and generable

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C. 1. Elementa esse materiam primam. 39 rabilia mundus destrui posset per causas naturales vi propria applicatas, contra prin. 2. quod sumptum est à Pytagora, & Platone, qui mundum à Deo solo creatum, & ab ipso solo dis- soluendum dixere apud Valles de Sacra phil. c. 1. & quidem rectè, perennant enim opera Dei vel per indiuiduoru[m] successio- nem aut per eorum immortalitatem; neq[ue]; verò potest mundi machina alteratione quadam successua dissolui, vna enim parte essentiali sublata reliquum redderetur innutile, ac pro- inde annihilandum, Deus enim, & natura nihil frustra faciunt. Si autem per causas naturales fieret huiusmodi interitus sensim fieret, & eo prorsus modo, quo videmus indiuiduorum dissolutiones contingere; ergo per eas fieri nequit ob residua- rum partium inutilitatem. Natura autem sapientis oeconomi instar nihil deperdit, omnia conseruat, & quamuis cæcis ob- scurisq[ue]; effluuijs imminui videatur, quod tamen abit, nullo modo corrumpitur, sed ad suam originem, veluti penum quan- dam redit, quod probauit mirus Hipp. de nat. humana, cuius relegens vestigia Lucretius ità cecinit l. 2. sub finem. Nam sua cuiq[ue]; locis ex omnibus omnia plagis Corpora distribuuntur, & ad sua sæcla recedunt. Humor ad humorem, terreno corpore terra Crescit, & ignem ignes producunt, ætheraq[ue]; æther. Sicuti in typis contingit prælo finito characteres singulos suis in loculis distribui, vnde iterum ad alias formas explendas re- sumantur; quibus ità explicatis. Probatur major, quæ ità se habet, si elementa essent corrup- tribilia mundus destrui posset per causas naturales vi sua appli- catas. Supponamus enim ignem mutasse in se vnum aeris cu- bitum; nonne plusaget virtus ignis noua illa extensione au- cti, quam antea, ex p. 3. minusq[ue]; alteri sui corruptioni resistere poterit aer, ex p. eodem? ergo poterit aliam aliamq[ue]; portione[m] C 4 aeris

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C. 1. The elements are the prime matter. 39 the world could be destroyed by natural causes applied through their own force, contrary to principle 2, which was taken from Pythagoras and Plato, who said that the world was created by God alone, and to be dissolved by Him alone, as in Valles, De Sacra Phil. c. 1; and indeed rightly so, for the works of God endure either through the succession of individuals or through their immortality; nor can the machine of the world, by some successive alteration, be dissolved, for if one essential part were removed, the rest would be made useless, and therefore to be annihilated; for God and nature do nothing in vain. But if such destruction were brought about by natural causes, it would happen gradually, and precisely in the same way that we see the dissolutions of individuals occur; therefore it cannot happen through them, because of the uselessness of the remaining parts. Nature, like a wise steward, loses nothing, preserves everything, and although it may seem to diminish through blind and obscure effluences, whatever departs is not corrupted in any way, but returns to its origin, as it were to a kind of storehouse; this Hippocrates wonderfully proved in De nat. humana, whose traces Lucretius, following, thus sang, book 2, near the end. For from every place all things are distributed to each in their own ways and return to their own ages. Moisture grows from moisture, earth from terrestrial body, fires produce fires, and ether ether. Just as in printing, when the press is finished, the individual characters are distributed into their own compartments, whence they are taken up again to fill other forms; these things having thus been explained. The major premise is proved, which stands thus: if the elements were corruptible, the world could be destroyed by natural causes applied through their own force. For let us suppose that fire has transformed into itself one cubit of air; would not the force of fire, now increased by that new extension, be more active than before, according to p. 3, and would not air be able to resist the corruption of another portion of itself less, according to p. the same? therefore it will be able [to corrupt] another and another portion of air C 4 air

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40 De Atomis. Disput. I. aeris transmutare: totoq[ue] aere è natura eliminato mundum perire necesse erit ex p.4. & 5. Confirmatur, quia hactenus eo statu res se continuerunt, vt nullam huiusmodi corruptionem deprehendamus, ergo signu[m] est à posteriori elementa esse ingenerabilia, & incorruptibilia. Dices primo clades vtrimq[ue] æquari, & dispendia aeris nouis in igne victorijs co[n]pensari, quare geometrica proportione sic iacturæ, & lucra computantur vt nihil hic aeris pereat quin alibi tantumdem ignis corrumpatur, vt si sub torrida zona deperit aer crescitq[ue]; ignis, sub circulis polaribus vincit aer, & ventorum agitatione semper æqualis manet sibi similis regio. Sed contra primò: hæc compensatio iacturarum fabulam redolet: secundò, si velint zone torridæ exemplo vti, legant Iosephum Acostam de natura noui orbis videbuntq[ue]; quam inani fundamento ista in medium adducantur, ibi enim non, vt voluit Aristoteles perpetuo ardent arenæ steriles, sed temperata multis in locis aeris aspiratione fru[n]tur fertilitateq[ue]; supra spe. Dices secundò interitum terris à sole imminere qui ideò descendit vt terram comburat, 80., nempè terrestris globi diametris depressiorem solem dicunt esse astrologi quam ante annos bis mille, ergo eo tandem vicini veniet, vt incendia misceat, sicq[ue] mundus suis viribus aduretur. Sed contra primò quamuis enim sol suam mutet declinationem ab æquatore, nihilominus tamen illum depressiorem fieri dubitatione non vacat, ratio est, quia eadem puncta tropicorum in sphæris armillaribus vmbram Solis in cancro, vel capricorno siti recipiunt inuariabili ratione, ergo signum est ipsum sensibili adeò deuiatione non deprimi, nam quo Stella humilior est eo longiores vmbras projcit vt probat Claius c.1. in sphæram Io. de Sacrobosco, quod si dicas in eadem omnino circulisectione remanere, vnde & pares in alpectu an- gulos

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40 On Atoms. Disputation I. to transform air; and with all the air eliminated from nature, the world must necessarily perish, from pp. 4 & 5. It is confirmed, because hitherto things have continued in such a state that we detect no corruption of this kind; therefore it is a sign a posteriori that the elements are ingenerable and incorruptible. You will say first that losses are balanced on either side, and that the losses of air are compensated by new victories of fire; wherefore, by geometric proportion, losses and gains are thus reckoned so that nothing of air perishes here unless elsewhere just so much fire is corrupted, as if under the torrid zone air is lost and fire increases; under the polar circles air prevails, and by the agitation of the winds the region always remains equal to itself and like itself. But against this, first: this compensation of losses smells of fiction; second, if they wish to use the example of the torrid zone, let them read Joseph Acosta on the nature of the New World, and they will see with what empty foundation these things are brought forward in support; for there, not as Aristotle wanted, do sterile sands burn perpetually, but temperate places enjoy fertility through the breathing of the air in many places; above hope. You will say second that destruction threatens the earth from the sun, which therefore descends in order to burn the earth, 80; namely, astrologers say that the sun is lower than the terrestrial globe by the diameter of two thousand years ago, therefore at last it will come so near that it will mingle fires, and thus the world will be burned up by its own forces. But against this, first: although the sun does change its declination from the equator, nevertheless it is not free from doubt that it becomes lower; the reason is that the same points of the tropics in armillary spheres receive the shadow of the sun in Cancer or Capricorn with unchanging proportion; therefore it is a sign that it is not lowered by such a perceptible deviation, for the lower a star is, the longer shadows it casts, as Clavius proves, ch. 1, in the sphere of Joannes de Sacrobosco; but if you should say that it remains altogether in the same section of the circle, whence also equal angles in view on-

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C.1. Elementa esse materiam primam. 41 gulos faciet vt facilè demonstrari potest ex 5. & 6. primi Eu- clidis, tamen sensibile esset caloris augmentum, cum tamen contrarium experiamur sæuientibus hyemibus, æstatibusq; impurissimis. Senescit fortasse Sol, & virtutis effoetæ annum suis terminis non amplius coercere potest. Phaetonem è sole facere contendunt sydus hominum commodis natum; si itaq; descendit sequetur suas in perigæo periodos, quarum puncta vbi primum attigerit, nostræ incolumitati consulens ad apog- um reuertetur. Prob. secundò idem antecedens, nempe elementa esse inge- nerabilia, & incorruptibilia, ratiocinatione sumpta ab igne, cuius corruptionem maximè sensibilem, & ipsa luce clariorem, nec nisi ab impudente negâdam aduersa Democrito Stoa pro- fitetur: Sed tollant mihi hunc scrupulum Peripatetici. Cor- ruptio ignis non potest fieri in instanti, sed extinctio ignis fit in instanti, ergo extinctio ignis non est eius corruptio; vnica au- tem extinctio sensibus subiacet quam ipsi cum corruptione confundunt. Minor syllogismi patet sensu experientiaq; , ex sufflata enim vel suffocata candela statim, ignis extinguitur, quod nec aquæ aut aeri terræue contingit. Ad maioris pro- bationem quod corruptio ignis non possit fieri in instanti, sup- pono corruptionem vnius esse alterius generationem, vnde sic argumentor. Si ignis corrumperetur dùm extinguitur vel mutaretur in elementum symbolum, vel dissymbolum, aut aliquod mixtum, nullum ex his dici potest, ergo non corrumpitur. Maior est adæquatę diuisionis ex qualicet argumentari negatiuè. Pro- batur minor. Non potest mutari in elementum symbolum quin adsit pugna inter qualitates cõtrarias, multò minus in dissymbolum, neq; itidem in mixtum quin retundantur, & alteren- tur eius vires, sed in omni contrarietate est alteratio, & omnis alteratio

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C.1. That the elements are the first matter. 41 they will make insensible; as can easily be demonstrated from the 5th and 6th of the first book of Euclid; yet an increase of heat would be sensible, whereas we experience the contrary in the most violent winters and the most impure summers. Perhaps the Sun grows old, and, exhausted of strength, can no longer restrain the year within its bounds. They contend that Phaethon was made from the sun, a star born for the convenience of mankind; if therefore it descends, it will follow its periods in perigee, and when it has first reached those points, caring for our safety, it will return to apogee. Secondly, let the same antecedent be proved, namely that the elements are ingenerable and incorruptible, by reasoning taken from fire, whose corruption, most perceptible and clearer than light itself, the Stoic, opposed to Democritus, admits cannot be denied except by an impudent man. But let the Peripatetics remove this difficulty for me. The corruption of fire cannot take place in an instant, but the extinction of fire takes place in an instant; therefore the extinction of fire is not its corruption. Only one extinction is subject to the senses, and they confuse this with corruption. The minor premise of the syllogism is clear from sense and experience; for from a blown out or smothered candle, fire is immediately extinguished, which does not happen to water, air, or earth. To prove the major premise, namely that the corruption of fire cannot take place in an instant, I assume that the corruption of one thing is the generation of another, whence I argue thus. If fire were corrupted while it is extinguished, or were changed into a symbolical element, or a dissymbolical one, or into some mixed body, none of these can be said; therefore it is not corrupted. The major is an adequate division, from which one may argue negatively of any thing. The minor is proved. It cannot be changed into a symbolical element without there being a conflict between contrary qualities; much less into a dissymbolical one, nor likewise into a mixed body, unless its powers are blunted and altered; but in every contrariety there is alteration, and every alteration

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42 De Atomis. Disput. I. alteratio sit successiuè, si præsertim plurium sit graduum, edo- mantur enim prius aliquè partes, tùm intentionis, tùm exten- sionis, & succedunt aliæ, donec adeam moderationem quali- tates deueniant, quæ alterius formæ inclinationi sufficiat, ergo cum corruptio ignis non possit fieri in instanti, propter dispositionem alij formæ introducendæ necessariam, extinctio autem ignis fiat in instanti, sequitur quod extinctio ignis non est corruptio ignis. Et reuera extinctio dicit tantum remotionem lucoris ab humido pingui fluentis, corruptio verò re- spicit generationem nouæ substantiæ, & alterius destructione. Dices extinctionem fieri successiuè, sed contra, illud non perit successiuè quod desinit totum simul, sed per extinctione, ignis desinit lucere totus simul, ergo extinction non sit successiuè, cæteroqui deberet paulatim perire lux, & sensim obtene- brari aer, dùm tandem tota candelæ flamma perisset, quod ad- uersarius non potest dicere, cum sensibus repugnet. Sed pro- batur vlterius ignis incorruptio sequenti ratiocinatione quæ de igne, & de aqua potest intelligi, cuius mutationem in aeré oculis patere credunt: quam transmutationem vt fieri non posse ostendam, Obseruo primò in via Aristotelis elementa componi ex ma- teria, & forma substantialibus, neque formam absq; dispositionum conuenienti apparatu introduci posse. Obseruo secundò plura requiri ad primam formæ introdu- ctionem, quam ad eius conseruationem in subiecto, quod foetuum experientia patet, aliarumq; generationum in quibus fit tàm delicatus accidentium apparatus, & tam elaborata dispo- sitio, quæ deinde sine substantiæ detrimento certos limites intensionis, & diminutionis pati potest; Quod quidem, & ratione, & experientia comprobari potest, ratione quidem, nam ad id vt introducatur forma talis determinata, prærequi- runtur

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42 On the Atoms. Disputation I. alteration is successive, especially if it be of several degrees; for certain parts are first brought under control, then as to intensity, then as to extension, and others follow in succession, until the qualities come to that degree of moderation which suffices for the inclination of another form; therefore, since the corruption of fire cannot take place in an instant, on account of the disposition necessary for the introduction of another form, but the extinction of fire does take place in an instant, it follows that the extinction of fire is not the corruption of fire. And indeed extinction signifies only the removal of brightness flowing from the moist and fatty substance; corruption, however, has regard to the generation of a new substance and the destruction of another. You will say that extinction occurs successively, but on the contrary, that does not perish successively which ceases all at once; but by extinction fire ceases to shine all at once, therefore extinction is not successive, otherwise the light ought to perish little by little, and the air to grow dim gradually, until at last the whole flame of the candle had vanished, which the opponent cannot say, since it conflicts with the senses. But the incorruptibility of fire is further proved by the following reasoning, which may be understood of fire and of water, whose change into air they believe is evident to the eyes: that I shall show that this transmutation cannot take place. I note first, in Aristotle’s way, that the elements are composed of material and substantial form, and that the form cannot be introduced without the suitable arrangement of dispositions. I note secondly that more is required for the first introduction of a form than for its preservation in the subject, as is clear from the experience of embryos and other generations, in which such a delicate arrangement of accidents and such an elaborate disposition are found, which afterward without detriment to the substance can endure certain limits of increase and decrease; and this indeed can be confirmed by reason and experience. By reason, namely, because in order that such a determinate form may be introduced, there are required

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C.1. Elementa esse materiam primam. 43 runtur sigilla quædam accidentium, quæ ipsi proportionatum omnino domicilium præparent, at dum in ipso dominatur cor- pore, potest se se tueri aliquatenus contra insultus contrario- rum, suis scilicet qualitatibus vel occultis vel apertis, quas ex se immediatè profundit; & quæ elementaribus legem faciunt; deinde quod vinculum formæ cum materia non ità facilè dis- solui possit, ob insitum rebus omnibus perennandi amorem; nam omnia fugiunt interitum, neq[ue] solum esse cupiunt com- modamq[ue]; durationem habere, verum etiam diuturnam. Ex- perientia clara est in embryone, qui dubio procul moreretur si persentiret h yemale frigus, quod pueri impune tolerant. Vt pullulet è grano spica, tantus requiritur apparatus, vt gentilis superstitio spicæ procreandæ duodecim Deos præfecerit, ma- turis frugibus vnicum. His positis. Probatur aquam non mutari in aerem. Primò experientia, vaporum, qui iterum in aquam resoluuntur nubium rorisq[ue]; forma, aut certè insensibili madore vt exprimit Lucretius l.1. qui ait vestes vuescere insensibiliter si aquaru habeant viciniâ: In paruas igitur partes dispergitur humor. Deinde experimentis chymiæ quotidianis, quibus aquæ li- quorumq[ue]; metamorphoses innumeræ eo tandem deducuntur, vt exprimatur sub vaporum forma defæcata aqua, liquorq[ue]; purior. Probatur secundò ad hominem contra eos qui dicunt aerem esse frigidum. Raritas est dispositio ad formam aeris, sed ra- ritas est effectus caloris quo aer caret ex te, ergo ab aere non introducetur raritas in aquam; deinde introducendo calorem in aquam vt rarescat, impedies ne fiat aer; qui ex te frigi- dus est. Probatur tertiò idem antecedens. Maior est resistentia, aquæ, quàm sit actiuitas aeris, nam aquæ resistentia juuatur ab humidi-

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C.1. The elements are the first matter. 43 certain signs of accidents are formed, which prepare for it a dwelling altogether proportioned to it; yet while it dominates in its body, it can defend itself to some extent against the attacks of opposites, namely by its qualities, whether hidden or manifest, which it immediately sends forth from itself; and which give law to the elements. Moreover, the bond of form with matter cannot so easily be dissolved, because of the innate love of all things for continuance; for all things flee destruction, and do not merely desire to be and to be at ease, but also to endure for a long time. This is clear from experience in the embryo, which would undoubtedly die if it sensed the wintry cold that boys endure unharmed. That an ear of grain should sprout from a kernel requires such great preparation that pagan superstition appointed twelve Gods for the generation of the ear, but only one for ripened crops. These points being established. It is proved that water is not changed into air. First, by experience: vapors, which are again resolved into water, have the form of clouds and dew, or certainly of imperceptible moisture, as Lucretius expresses it, book 1, where he says that garments become wet imperceptibly if they have water nearby: thus moisture is dispersed into small parts. Then by the daily experiments of chemistry, by which the countless metamorphoses of waters and liquids are brought at last to this, that purified water is expressed under the form of vapors, and a purer liquid. Secondly, it is proved ad hominem against those who say that air is cold. Rarity is a disposition toward the form of air, but rarity is an effect of heat, which air lacks, in your account; therefore rarity will not be introduced from air into water. Then, by introducing heat into water so that it becomes rarefied, you will prevent it from becoming air, which, according to your view, is cold. Thirdly, the same antecedent is proved. The resistance of water is greater than the activity of air, for the resistance of water is aided by humidi-

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De Atomis. Disp. I. 44 humiditate, cui tam propria est adhesio partium cum partibus, & à densitate sibi congenita, actiuitas verò aeris imminuitur tum ab eius raritate, tum quod vis actiua aeris quæ in calore sita est, minor est aliquanto eius humiditate si quam habet: ergo aer non potest introducere in aquam dispositiones transmutationi aquæ in aerem proportionatas. Dices mediante igne hanc mutationem futuram. Sed contra: Ignis non est formaliter neq[ue] eminenter aer, ergo ignis non potest esse causa principalis generatiua aeris ex principio 9. In pari enim dignitatis gradu sunt elementa vnde nullum ab alio eminenter continetur; sed neq[ue] formaliter, sunt enim contraria, ergo nullum produci poterit ab alio. Qnè ratiocinatio vt in meliorem diem ponatur, annotandæ sunt quatuor regulæ quibus rerum dignitas expendi, & conferri potest. Regula prima logica est: Illud est nobilius alio quod de meliori, & nobiliori specie, & differentia participat ità equus nobilior est lapide, quia hic sub Mixto, ille sub Viuente reperitur. Cum ergo omnia elementa sint sub eodem prædicato corporis simplicis, habeantq[ue] vltimas differentias sine vllo excessu alterius in alterum, sequitur quod nullum continet aliud eminenter, & quod in eodem dignitatis gradu sunt posita. Regula secunda est metaphysica. Contrariorum positiuè, & propriè eadem est dignitas absoluta. Dixi positiuè, nam in contrarijs priuatiuis ignobilius est non Ens ipso Ente, sic tenebræ luci, vmbra lumini, mors vitæ concedunt. Addidi propriè vt contraria relatiuè excluderem, Dominus enim seruo, Pater filio, Præceptor discipulo dignior est, subiunxi digni tamen absolutam, respectiuè enim potest fieri vt aliquid alio sit optabilius. Dices alexipharmacum potius esse veneno digniusq[ue] absoltè, & tamen sunt in positiua contrarietate. Res- pondeo

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On the Atoms. Disp. I. 44 from humidity, to which the adhesion of parts with parts is so proper, and from its innate density; but the activity of air is diminished both by its rarity, and because the active power of air, which is situated in heat, is somewhat less than its humidity, if it has any: therefore air cannot introduce into water dispositions proportioned to the transmutation of water into air. You will say that this change will take place by means of fire. But on the contrary: fire is not formally nor eminently air, therefore fire cannot be the principal generative cause of air from principle 9. For the elements are in an equal rank of dignity, so that none is eminently contained by another; but neither are they formally so, for they are contraries; therefore none can be produced by another. And so that this reasoning may be set aside for a better day, four rules are to be noted by which the dignity of things can be weighed and compared. The first rule is logical: that is nobler than another which participates in a better and nobler species and difference; thus a horse is nobler than a stone, because the latter is found under the Mixed, the former under the Living. Therefore, since all the elements are under the same predicate of simple body, and have the ultimate differences without any excess of one over another, it follows that none contains another eminently, and that they are placed in the same rank of dignity. The second rule is metaphysical. In positive and proper contraries the same is the absolute dignity. I said positively, for in privative contraries non-Being is less noble than Being itself; thus darkness yields to light, shadow to brightness, death to life. I added properly, to exclude relative contraries, for a master is more worthy than a servant, a father than a son, a teacher than a pupil; I added, however, absolute dignity, for relatively it may happen that something is more desirable than another. You will say that an alexipharmic is rather more worthy than poison and more worthy absolutely, and yet they are in positive contrariety. I answer

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C. 1. Elementa esse materiam primam. 45 pondeo negando esse contrarietatem politiuam sed tantum respectiuam, mediatam, & impropriam; alexipharmacum enim veneno aduersatur, venenum autem homini non verò alexipharmacaco. Cum ergo elementa ex Stagyritis sint propriè contraria, sequitur illa in pari dignitatis gradu esse constituta, quamuis secundum situm, locum, & alia respectiua, nonnulla digniora videantur. Regula tertia physica est. Vbi actiones qualitatum non extrahuntur extra competentiam aut contrarietatem, tùm in intentione, tùm in ratione categorica, ibi substantiarum est æqualis dignitas; quam ab actionibus tantum nosse possumus: sed actiones elementorum nunquam sunt extra contrarietatem, & competentiam, suntq[ue] in eadem serie, ergo etiam substantiæ elementorum paris, & æqualis erunt dignitatis, ac proinde nullum alterius causa esse poterit: neq[ue] calor frigore nobilior censendus, cæteroqui sui contrarij perpetuo victor esset, quod est contra experientiam. Regula quarta est geometrica. Vbicunq[ue] eiusdem rationis sunt numeri ibi est æqualitas, sed in via Aristotelis æquales sunt numeri in qualitatibus elementorum, ergo inter ea pura interuenit æqualisq[ue] ratio. Ita ignis ex Circumambulonum placitis est calidus vt 8. Siccus vt 4. Aer calidus vt 4. humidus vt 8. Aqua humida vt 4. frigida vt 8. Terra frigida vt 4. sicca vt 8. Cum ergo paribus momentis contrariè ille qualitates sint distributæ, sequitur ad hominem æqualis dignitas, parq[ue] vndiq[ue], & geometrica æqualitas. Confirmatur hæc doctrina, quia nulla qualitas prima continet aliam primam vel formaliter vel eminenter, ob contrarietatis rationem, ergo sequitur neq[ue] eam præeminentiam eorum formis substantialibus esse concedendam. Dices ignem esse omnium nobilissimum ratione actiuitatis, effe-

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C. 1. The elements are the primary matter. 45 I reply by denying that there is a positive contrariety, but only a relative, mediated, and improper one; for alexipharmacum is opposed to poison, but poison is not opposed to man, but rather to alexipharmacum. Therefore, since the elements among the Aristotelians are properly contraries, it follows that they are placed in a rank of equal dignity, although according to position, place, and other relative respects, some may seem more worthy. The third physical rule is this: where the actions of qualities are not taken outside their proper capacity or contrariety, both in intention and in categorical sense, there the substances have equal dignity; and this we can know only from their actions. But the actions of the elements are never outside contrariety and capacity, and they are in the same series; therefore the substances of the elements will also be of equal and equal dignity, and consequently none can be the cause of another. Nor should heat be judged nobler than cold; otherwise it would perpetually conquer its contrary, which is contrary to experience. The fourth rule is geometrical: wherever numbers are in the same ratio, there is equality. But in Aristotle’s system the numbers in the qualities of the elements are equal; therefore between them there intervenes a pure and equal ratio. Thus fire, according to the doctrines of the Circumambulones, is hot as 8 and dry as 4; air is hot as 4 and moist as 8; water is moist as 4 and cold as 8; earth is cold as 4 and dry as 8. Since, therefore, with equal weights those qualities are distributed in contrary ways, it follows for man that there is equal dignity, equal rank everywhere, and geometrical equality. This doctrine is confirmed, because no primary quality contains another primary quality either formally or eminently, on account of the nature of contrariety; therefore it follows that this pre-eminence must not be conceded to their substantial forms. You will say that fire is the noblest of all by reason of its activity, eff-

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De Atomis. Diput. I. 46 effectuum, loci & imperij quod habet in natura. Sed contra. Sequitur ergo ignem esse ingenerabilem, & incorruptibilem cum non sit assignabilis causa vel nobilior vel æquè nobilis quæ illum vel generet vel corrumpat: quis enim vnquam Peripateticorum concessit ignem frigefieri, & tamen id de aqua concedunt, obliti sui principij quod contrariorum eædem sunt passiones? Dices eam mutationem fieri à causis æquiuocis. Sed contra, eæ enim causæ sine certis dispositionibus formæ introduciori non præsunt, cum autem nihil sit quod in ignem introducat aquæ dispositiones, sequetur ignem non posse vnquam mutari in aquam, neq[ue] aquam in aerem. Contraria enim se se potius expellunt quam generent, & inimicitia elementorum, vt mixtis prodest, sic ipsis necessariam affert sterilitatem. Cum ergo aqua nec ab aere nec ab igne mutari possit, multò minus id à terra fiet, cum è diametro aduersetur: ingenerabilia itaq[ue] & incorruptabilia sunt elementa. Confirmatur primò, quia nullum inanimatum habet vim productiuam sui similis, sed hoc viuentibus proprium est, ergo neq[ue] ignis ignem, neq[ue] aqua, aut terram terra generabit, quod si in mixtis animo carentibus hanc sterilitatem animaduertimus, sintq[ue] illorum causæ æquiuocæ, quanto magis in elementis concedi debet, tùm ob ignobiliorem sui conditionem, tùm quod generare sibi simile perfectius sit quam nutriri vel augeri, viuentia enim nisi certum attigerint perfectionis gradum femine carent. Adde quod, hæc sterilitate mundi totius tutelę cautum esse debuit, ob insanam elementorum extensionem, quare virtute assimilatiua carent, quæ etiam ipsis eo nomine est deneganda, quod cum finis essentię, & actionum sit idem, esse enim est propter operari, vt loquuntur metaphysici, ergo essentia se habet in ratione analoga medij ad finem: sequitur elementis nullam nisi mixtorum gratia com- petere

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On the Elements. Disputation I. 46 of their effects, the place, and the dominion which it has in nature. But on the contrary. It follows, therefore, that fire is ingenerable and incorruptible, since there is no assignable cause, either nobler or equally noble, that can either generate it or corrupt it. For who among the Peripatetics ever admitted that fire is cooled, and yet they concede this of water, forgetting their own principle that the passions of contraries are the same? You will say that this change is brought about by equivocal causes. But on the contrary, such causes do not act without certain dispositions introducing the form; but since there is nothing that introduces the dispositions of water into fire, it will follow that fire can never be changed into water, nor water into air. For contraries rather drive one another out than generate one another, and the enmity of the elements, while useful in mixtures, brings upon the elements themselves a necessary barrenness. Since, therefore, water cannot be changed either by air or by fire, much less will this be done by earth, since it is directly opposed to it: the elements are therefore ingenerable and incorruptible. This is first confirmed, because no inanimate thing has the power to produce something like itself, but this is proper to living beings; therefore neither fire will generate fire, nor water, nor earth earth. If in mixed things, lacking soul, we observe this barrenness, and if their causes are equivocal, how much more ought this to be granted in the elements, both because of the baser condition of their state, and because to generate something like oneself is more perfect than to be nourished or increased. For living beings, unless they have reached a certain degree of perfection, lack the female principle. Add to this that by this barrenness the safety of the whole world ought to have been provided for, on account of the excessive extension of the elements; wherefore they lack the assimilative power, which also must be denied them for this reason, that since the end of essence and of actions is the same—for to be is for the sake of acting, as the metaphysicians say—therefore essence stands in an analogous relation as a means to an end: it follows that nothing belongs to the elements except for the sake of mixtures.

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C. 1. Elementa esse materia primam. 47 petere actionem, at mixtis transmutatio illa omnino inutilis est, ergo non datur transmutatio inter elementa, sunt ergo in- generabilia, & incorruptibilia. Confirmatur secundò ex princip. I I. posita experientia, oportet philosophari, sed in omni corruptione mixtorumq; dis- solutione videntur superesse elementa, terra in cineribus, qui nullo igne flamma fiunt, aqua in vaporibus denuò in guttas reformatis, cur ergo de igne aliter philosophabimur quam ill- lum cineribus, & rogo suo superesse immortalem? Probatur quartò elementa esse ingenerabilia, & incorrup- tibila. Elementa esse formaliter in mixto existimat tota fere iuniorum schola, quod placitum licet non habeat expressas Principum nostrorum leges, tamen Fernelius l.2. de elem. c. 6. veterum esse contendit, fuit enim Democriti, Empedoclis, Leucippi, Epicuri, Platonis, Pythagore, Lucretij &c. Hanc certè sequutus est Auicenna l. I. Fen. I. doct. 3. videturq; faue- re Hipp. l. de natura humana: Gal. autem l. I. methodic. 2. de his definire superuacaneum medico esse censet. Aristoteles l. I. meteor. sum. I. c. 2. negatiuam sequi videtur; vt vt sit affir- matiuam admitto supponoq; stabilitam apud Fernel. loc. cit. [sulphur] in l. de abditis. Dandium, Iandunum, Ioubertum aliosq; qui vt prudentissimè formas admisere partiales, & elementa formaliter in mixto, ità non video quanam ratione loquantur consequenter, dùm corrupi transmutariq; concedunt. 1. Quia transmutatio, & corruptio inutilis est vbi integra, puraq; requirûtur elementa, atqui in mixto debent esse forma- liter, cum ergo ex principio I o. omnes elementorum actiones sint propter mixta, vt omnia serui commoda pro domino, ne- quaquam corrupentur aut transmutabuntur. 2. Si admittunt minima in elementis quomodo corrupi explicabunt? Sit enim minimum terræ B. illud ex aduersario diuidi

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C. 1. Elements are the primary matter. 47 to seek action; but in mixed things that transmutation is altogether useless, therefore there is no transmutation among the elements; therefore they are un- generated and incorruptible. This is confirmed secondly from the principle I. I. established by experience: we ought to philosophize; but in every corruption of mixed things and dis- solution the elements seem to remain behind, earth in ashes, which by no fire are made flame, water in vapors again formed into drops; why then shall we philosophize otherwise about fire than that it remains immortal in its ashes and on its own pyre? It is proved fourthly that the elements are ingenerable and incorrupt- ible. That the elements exist formally in the mixed thing is held by almost the whole school of the later writers, which opinion, although it does not have the express laws of our Princes, nevertheless Fernelius, l. 2. de elem. c. 6., contends is the view of the ancients; for it was held by Democritus, Empedocles, Leucippus, Epicurus, Plato, Pythagoras, Lucretius, etc. Certainly Avicenna followed this, l. 1. Fen. 1. doct. 3., and Hippocrates also seems to favor it, l. de natura humana: Galen, however, l. 1. methodic. 2., thinks it superfluous for a physician to determine these things. Aristotle, l. 1. meteor. sum. 1. c. 2., seems to follow the negative view; but whether he did so or not, I admit the affirmative and suppose it established with Fernelius, loc. cit. [sulphur] in l. de abditis. Dandius, Iandunus, Joubertus, and others, who most prudently admitted partial forms and the elements formally in the mixed thing, I do not see by what reasoning they speak consistently, while they grant corruption and transmutation. 1. Because transmutation and corruption are useless where whole and pure elements are required; but in the mixed thing they ought to be formally present. Since then, according to principle I. all the actions of the elements are for the sake of mixed things, as all servants are for the advantage of their master, they will by no means be corrupted or transmuted. 2. If they admit minima in the elements, how will they explain corruption? Let the minimum of earth be B; that, according to the adversary, to be divided

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48 De Atomis. Disput. I. diuidi potest, diuidatur ergo in partes duas A. C. sequitur vel materiam esse spoliatam omni forma naturaliter, quod negant fieri posse, vel dari annichilationem naturalem quod nullus admittit, vel in partibus A. C. remanere formam elementaré, proinde B. non esse minimum physicum in quo forma posset subsistere, contra suppsitionem. 3. Si elementa sunt corruptibilia quomodo erunt in mixto formaliter? nam ibi debet corrumpi ignis vbi caret dispositionibus necessarijs, & conditionibus ad existentiam connaturalibus, quales sunt latitudo medij, alimentum extra sphærâ, intensio certa qualitatum suarum, quibus omnibus in congelato saxo caret, vbi sine calore actuali, sine alimento, sine spatio, angustijs coarctatus est, ergo vel ibi vel nuspiam corrumpi debet: remanet autem in saxo in statu adeò violento, & quidem diutissimè, sequitur ergo esse incorruptibilem, & ingenerabilem. Elementa itaq[ue] perennia sunt, & ingenerabilia; erunt proinde primum vniuscuiusq[ue]; rei subiectum, omnibus mixtis inerunt, & per vltimam dissolutionem in ea mixta omnia resoluentur, quod erat instituti nostri probare. PROPOSITIO III. Elementa sunt materia prima. Hæc propositio conclusio est syllogismi cuius duæ præcedentes propositiones premissarum loco se habent. Illud est materia prima, quod est primum subiectum, ex quo in existente sit vnum per se, & in quod si quid corrumpitur vltimò resoluitur; sed hæc conueniunt elementis, nam sunt primum subiectum, vt pote ingenerabilia, & incorruptabilia, inexistunt in mixitis, ex his, & forma substantiali sit vnum per se, & in omni corruptione resolutio sit in elementa, ergo sunt materia prima, quod erat demonstrandu[m]. Pro-

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48 On Atoms. Disputation I. it can be divided; let it therefore be divided into two parts A. C. it follows either that matter is stripped of every form naturally, which they deny can be done, or that a natural annihilation is granted, which no one admits, or that in the parts A. C. the elemental form remains, and consequently B. is not the smallest physical thing in which the form could subsist, contrary to the supposition. 3. If the elements are corruptible, how will they be formally in the mixture? for there fire must be corrupted where it lacks the necessary dispositions and the conditions connatural to its existence, such as the width of the medium, food outside the sphere, a certain intensity of its qualities, all of which it lacks in frozen stone, where, without actual heat, without nourishment, without space, compressed within narrow confines, it is held; therefore either there or nowhere must it be corrupted: yet it remains in the stone in a condition so violent, and indeed for a very long time; therefore it follows that it is incorruptible and ungenerated. Therefore the elements are perpetual, and ungenerated; they will therefore be the first subject of each thing; they will be in all mixed bodies, and by the ultimate dissolution all things mixed in them will be resolved, which was the aim of our undertaking to prove. PROPOSITION III. The elements are prime matter. This proposition is the conclusion of a syllogism whose two preceding propositions stand in the place of premises. That is prime matter which is the first subject, out of which in the existing thing there is one thing per se, and into which, if anything is corrupted, it is ultimately resolved; but these apply to the elements, for they are the first subject, inasmuch as they are ingenerated and incorruptible, they inhere in mixed bodies, from these, and from substantial form there is one thing per se, and in every corruption the resolution is into the elements; therefore they are prime matter, which was to be demonstrated. Pro-

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C. I. Elementa esse materiam primam. 49 PROPOSITIO IV. Materia prima quam Aristoteles proponit ex Ægyptiorum mente, omnino inutilis est, tùm physico, tùm medico. PRobatur primò, quia ea omissa facilius explicantur omnia, vt patebit inferius: deinde quia eleméta ad omnimodam mixturem sufficiunt; tertio quia medicus elementa tantum incorporibus contemplatur, physicus autem nullam materiæ primæ Aristotelicæ necessitatem ostendere potest, quare cum nihil in natura frustra sit, eam materiam non dari concludendum. Reuera Arabum Medicorum Sultanus Auicenna nullam præter elementa agnouit materiam, quem multi è peritioribus medicis sequuntur. Neq[ue] verò mihi inutilis tantum, sed etiam impossibilis videtur, & in terminis contradictionem inuoluere; certè illius conceptum idæamq[ue]; animo nunquam potui adaptare, quibus autem fundamentis nitatur perpendemus capite 3. huius disp[ens]a cum aduersariorum retundemus tela, obiectiones enim nisi explicatæ acuratius Democriti sententiæ subdi non debuerunt, ne ordo confunderetur doctrinæ. CAPVT SECUNDVM. De natura, numero; & proprietatibus elementorum, iuxta Democriti placita. NOLO hic fusè de elementis pertractare, sed quantum ad præsens institutum de atomis necessarium est, prætermis curiosissimis quæstionibus, de igne artificiali, aereo, subterraneo; de luce igni insita: de atmosphæra, de spiritibus aereis, & igneis, de mutatione, & phaëbus æris;

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C. I. The elements are the first matter. 49 PROPOSITION IV. The first matter which Aristotle proposes, according to the mind of the Egyptians, is altogether useless, both physically and medically. This is proved first, because if it is omitted, everything is more easily explained, as will appear below; secondly, because the elements are sufficient for every kind of mixture; thirdly, because the physician contemplates only the elements in bodies, whereas the physicist can show no necessity for Aristotle’s first matter; wherefore, since nothing in nature is in vain, it must be concluded that that matter does not exist. Indeed, the Sultan of Arab physicians, Avicenna, acknowledged no matter besides the elements, and many of the more experienced physicians follow him. Nor indeed does it seem to me not only useless, but also impossible, and to involve a contradiction in terms; certainly I have never been able to fit its notion and idea to my mind. On what foundations it rests, however, we shall consider in chapter 3 of this discussion, when we shall blunt the weapons of our adversaries; for objections ought not to have been set down unless the doctrine of Democritus had first been explained more accurately, lest the order of teaching be confused. CHAPTER SECOND. On the nature, number, and properties of the elements, according to the views of Democritus. I do not wish to treat at length here of the elements, but only so far as is necessary for the present undertaking concerning atoms, setting aside the most curious questions: about artificial fire, aerial fire, subterranean fire; about the light innate in fire; about the atmosphere, about aerial and fiery spirits, about the alteration, and the phaëbus of the air;

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De Atomis. Disput. I. 50 ris: De aquis mineralibus, & bituminosis, defontium miraculis præsertim quæ in Indijs vtrisq; à nouis Argonautis sunt reperta: de virtute magnetica terræ, de centro grauium, de quiete terræ, de terrarum varietate; his inqua alijsq; omissis me cöfero ad ea quæ lumen dicédis afferre necessariò debeant. PROPOSITO V. Quatuor sunt Neotericorum de Elementis opiniones præcipuæ. Prima opinio sic elementum definit; Corpus simplex formali- ter existens in mixto, vt principium materiale ex tribus veluti- có pactum humore, succo, & solida substantia. Prima pars defini- tionis vsq; ad id ex tribus veluti &c. aperta est, sentitq; cum Democrito dum vocat elementum principium materiale: at verò quis succus ignis, quis terræ humor, quæ soliditas aquæ aut aeri adscribi potest? An ignis humidus est, & succi ple- nus? humor. n. supponit humiditatem, succus misionem cum concoctione ex Theophrasto l. 1. hist. plant. c. 19. De solidita- te nihil disputo illa enim mathematicè penes dimensiones, phy sicèq; penes plenitudinem potest explicari. Is tamen, qui hu- ius opinionis est caput, adscribit igni sic citatem in summo, sicuti etiam terræ, vbi ergo erit humor succusue qui semper de genere liquoris est, licet addensari possit? vnde videtur sibi ipsi parum consentiens; Sed cum nemo non auditus damnandus sit, ab hac opinione exagitanda supersedeo, cuius nudam so- lummodo thesim vidi editam Lugduni. Secunda opinio sic elementum definit. Corpus simplex mix- torum basis, & materia è duobus coalescens, mole scilicet, & influxio fixo. Ità nobilis Hungarus quem forte fortuna in itinere bi- duò comitem habui cum secundò in Italiam venirem. Influxum dicebat esse portionem ætheream ipsi elemento congenitam quæ cum orbe superiori, & cælestibus mixta singula con- iunge-

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On the Elements. Disput. I. 50 ...: On mineral waters, and bituminous waters, on the miracles of springs, especially those which in both Indies have been discovered by the new Argonauts; on the magnetic virtue of the earth, on the center of gravities, on the rest of the earth, on the variety of lands; these things, and others omitted, I turn myself to those which must necessarily bring light to the matter to be discussed. PROPOSITION V. There are four principal opinions of the Neoterics concerning the Elements. The first opinion defines an element thus: a simple body formally existing in a mixture, as a material principle compounded of three things, as it were: moisture, juice, and solid substance. The first part of the definition, up to “of three things as it were,” etc., is clear, and it agrees with Democritus when he calls an element a material principle; but what juice is that of fire, what moisture that of earth, what solidity can be ascribed to water or air? Is fire moist, and full of juice? For moisture presupposes humidity; juice involves mixture with concoction, according to Theophrastus, Hist. Plant. l. 1, c. 19. I say nothing about solidity, for that can indeed be explained mathematically by dimensions, and physically by fullness. Yet he who is the head of this opinion assigns to fire dryness in the highest degree, as also to earth; so where then will there be moisture or juice, which is always of the nature of liquid, although it can be thickened? Hence it seems somewhat inconsistent with itself. But since no one is to be condemned unheard, I refrain from attacking this opinion, of which I have seen only the bare thesis published at Lyons. The second opinion defines an element thus: a simple body, the basis of compounds, and matter consisting of two things, namely mass and fixed influx. So said a noble Hungarian, whom by chance I had as a companion for two days on the journey when I was returning to Italy. He said that influx was an ethereal portion inherent in the element itself, which, mixed with the higher sphere and the heavenly bodies, joins individual things together...

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C.2. De Elementis iuxa Democritum. 51 iungeret mediante ipso elemento, & singula ad suos planetas referret, vt planetę ad stellas fixas, & ipsi referuntur analogia mundana. Volebat elementa esse septem, terram, aquam, ignem, spiritum, seu ventum, essentiam, regulam, numerum, quæ septem in singulis mixtis reperiuntur. Terram diluit aqua, aquam distribuit spiritus, spiritum vegetat ignis, ignem eleuat essentia, seu radicalis ros mixtorum cui insire sunt, & veluti radicatæ proprietates, totum certa figura coercet regula, & numerus partibus modum ponit. Regula autem, & numero substantias intelligebat, improprijs ad eum sensum vocabulis. Terram Saturno, aquam Lunę, ignem Ioui, Spiritum Mercurio, regulam Marti, numerum Veneri, essentiam Sol non absurde componebat. Sed cum de planetis Iouialibus fieret à me certior, vnde & adinuenienda quatuor elementa sympathica igni pro stellis Medicæis, & duo sympathica terre, nam Saturni stella tribus globis deinceps positis dicitur componi; Respondit ea se habere per modum vnius: gratis audiui que gratis dicerentur, nec mihi ad alia festinati tot refellere vacat, vel tunc scholastica contentione curiosas confabulationes corrumpere. Tertia opinio est multorum Chymicorum è quorum numero, & superiorem fuisse puto. Illi duo dari volunt elementa, Terram quam damnata, maledictam, & caput mortuum vocant, & Aquam vel insipidum phlegma, quæ omni sale, mercurio, & sulphure careat. Quorundam Chymicorum absonę sententię etiam vocabulis, quibus nitor, & claritas adesse semper debet, magnam authoritatis partem suę arti abstulerunt, quid enim de ijs censendum est quam quod Lucret. 1. 1. de Heraclito pronuntiat, Clarus ob obscuram linguam, magis inter inanes, Quam grauior Græos, inter qui verarequirunt: D 2 Omnia

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C.2. On the Elements according to Democritus. 51 he would join by means of the element itself, and refer each thing to its proper planet, just as the planets are referred to the fixed stars by the world’s analogy. He wished there to be seven elements: earth, water, fire, spirit, or wind, essence, rule, number; which seven are found in each mixture. Earth is diluted by water, water is distributed by spirit, spirit is enlivened by fire, fire is raised up by essence, or the radical dew of mixed things, in which they are rooted and, as it were, rooted properties; rule constrains the whole within a certain figure, and number sets a measure to the parts. By rule and number, however, he understood substances, using words improperly in that sense. Earth he fittingly matched with Saturn, water with the Moon, fire with Jupiter, Spirit with Mercury, rule with Mars, number with Venus, essence with the Sun. But when I had informed him more certainly about the Jovian planets, and thus about finding the four sympathetic elements for fire in the Medicean stars, and the two sympathetic elements for earth, for Saturn’s star is said to be composed of three globes placed one after another, he replied that these matters were held in the manner of a single one. I gladly heard things that were said freely, and I had no leisure, driven to other matters, to refute so many objections, or then to corrupt curious conversations with scholastic contention. The third opinion is that of many Chymists, among whom I think the one above was also counted. They wish there to be two elements: Earth, which they call damned, accursed, and a dead head, and Water, or tasteless phlegm, lacking all salt, mercury, and sulphur. The strange opinions of certain Chymists have, even by the very words with which brightness and clarity ought always to be present, taken away a great part of authority from their art; for what is to be judged of these things except what Lucretius pronounces concerning Heraclitus, book 1: Famous because of his obscure language, more among the worthless, Than among the weightier Greeks, among whom they seek the truth? D 2 All things

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52 De Atomis. Disput. I. Omnia enim stolidi magis admirantur, amantque, Inuersis quæ sub verbis latitantia cernunt. Chymicorum plurimi à suis officinis egressi ab alambici fulcris tanqua[m] ab Apollinis tripode, reuelata sibi arcana iactant, & ea loquuntur quæ nec ipsimet intelligant. Naturæ mysteria etiam si mille facibus reuelentur, arbitrantium oculis nunquam tota excipientur, restabit semper quod quæras, & quo plus scies, eo plura à te ignorari miraberis. Quarta opinio sic definit elementum, corpus simplex à nullo naturaliter dissolubile, constans substantià, qualitate acerrimà, & mobilitate primarià simplici. Verum quidem est, in ratione qualitatum sensibilium elementares esse omnium acerrimas vincuntur tamen in actiuitate ab ijs quæ à formis substantialibus mixtorum immediatè promanant. Admittit hæc sententia quinq; elementa ignem, seu æthera, aquam, terram, influxum quem astra rerum, & stellarum particulas vocat, & gultinosum tartarum ad omnium vnionem necessarium. Prima opinio fundatur in proportione eorum quæ ad mixtum videntur accomodata. Secunda nititur analogia maioris, & minoris mundi, & relatione quam sublunaria habent cum celestibus, quam quisq; ad libitum explicat. Tertia prætendit experientiam, & sensibus nititur. Quarta vt nouum quidpiam afferret astrorum fragmentis nos ditauit, sed illa exhibet Chymicus. PROPOSITIO VI. Elementum iuxta Democriti placita definire. Elementa definiuntur à Galeno l. I. de elementis c. I. quæ natura prima, & simplicissima sunt, quæque in alia non amplius dissolui queunt; in quam definitionem recidit Auicennę definitio l. I. Fen. I. doctrina 2. cum dicit; Elementa sunt corpora sim- plicia

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52 On the Elements. Disputation I. For all the foolish admire and love all the more those things which they see hidden under inverted words. Most of the alchemists, having gone forth from their workshops, boast of secrets revealed to them, as though from the supports of Apollo’s tripod, and they speak of things which not even they themselves understand. Even if the mysteries of nature are revealed by a thousand torches, they will never be fully taken in by the eyes of observers; there will always remain something for you to seek, and the more you know, the more you will marvel that is ignored by you. The fourth opinion defines an element thus: a simple body, naturally dissoluble by nothing, consisting of substance, of a very sharp quality, and of a simple primary mobility. It is indeed true, in respect of sensible qualities, that the elements are the sharpest of all; yet in activity they are surpassed by those which proceed immediately from the substantial forms of mixed bodies. This view admits five elements: fire, or ether, water, earth, the influence which it calls the force of things and the particles of the stars, and a gummy tartar necessary for the union of all things. The first opinion is founded on the proportion of those things which seem suited to the mixed body. The second relies on the analogy of the greater and lesser world, and on the relation which sublunary things have with the heavenly, which each person explains as he pleases. The third appeals to experience, and relies on the senses. The fourth, as though to bring forth something new, has enriched us with the fragments of the stars; but the Chemist presents that. PROPOSITION VI. To define an element according to the views of Democritus. Elements are defined by Galen, book I, On the Elements, chapter I, as those things which are first and most simple by nature, and which can no longer be dissolved into others; into which definition falls Avicenna’s definition, book I, Fen. I, doctrine 2, when he says: Elements are simple bodies

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C.2. De elementis iuxta Democritum. 53 plicia, et partes primæ corporis humani, et aliorum, quæ in corpora diuersarum formarum diuidi minimè possunt ex quarum commixtione species diuersæ generatorum fiunt. Aristoteles autem 5. met. t. 4. Elementum dicitur ex quo inexistente indiuisibili secundum speciem in aliam speciem, aliquid componitur; quæ definitio metaphysica est & vniuersalissima, sed deinde ab eodem Aristotele restringitur ad elementa corporum, cum vocat vltima in quæ corpora diuiduntur, illa verò non amplius in alia specie differentia corpora, et siue vnum, siue plura huiuscemodi sint, hæc elementa aiunt, & in fine textus ibid. omnibus verò elementi acceptionibus commune est illud cuiusq[ue]; esse elementum quod primum cuiq[ue]; inest; ex quibus manifestum est vnicum elementorum characterem in quo tres isti litteraru[m] legislatores conueniunt, esse perfectam homogeneitatem. Definiri autem posset elementum; Corpus simplex seu purè homogeneum natura sua institutum vt in mixtorum compositionem veniat; quæ definitio datur per causam finalem, & respectum transcendentalem, quo ab alijs distinguitur. Hæ definitiones optimè sunt neq[ue]; Democriti sensibus vlla ratione contrariè, imò potius fauorabiles, si præsertim addamus pronuntiatum Aristotelis 5. metaphys. t. 4. Parum, simplex, indiuisibile elementum dicitur. Nihilominus tamen aliam colligo Democriti definitionem ex l. 1. phys. & ex Lucretiol. 5. Elementa sunt seminariu[m] primu[m] atomoru[m] simpliciter figuraturu[m], et vnigenarum secundu[m] quarum variationem, et vnitionem diuersam mixta quæuis generantur, et in quæ omnia vltimò resoluuntur. Dixi seminarium primum, quia dantur figuræ, & minima secundæ sortis quæ à forma substantiali, cæli vertigine, alijsq[ue] causis ad mixtorum obsequium variam obtinent figuram. Dixi simpliciter, quia co[m]positione omni caret. Vocavi vnigenas, hoc est, figuræ aut atomi aqueæ omnes sunt eiusdem rationis, idem deterreis igneisq[ue]; iudicium esto; Cætera plana erunt ex se- quen-

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C.2. On the elements according to Democritus. 53 simple, and the first parts of the human body, and of other things, which can in no way be divided into bodies of different forms, from whose mixture different species of generated things arise. But Aristotle in Metaphysics 5, text 4, says: An element is that from which, while remaining indivisible in species, something is composed in another species; which definition is metaphysical and most universal, but then is restricted by the same Aristotle to the elements of bodies, when he calls those the ultimate things into which bodies are divided, those things which are no longer bodies differing in another species; and whether such elements be one or many, they say these are elements, and at the end of the text in the same place. But common to all acceptions of element is this: that of each thing, that is its element which is first present in it; from which it is manifest that the single character of the elements, in which these three legislators of language agree, is perfect homogeneity. Now an element could be defined as: a simple body, or one purely homogeneous by its nature, instituted so that it may come into the composition of mixed things; which definition is given through the final cause, and through a transcendental relation, by which it is distinguished from others. These definitions are best, and in no way contrary to Democritus’ views; indeed rather favorable, especially if we add the statement of Aristotle, Metaphysics 5, text 4: an element is called small, simple, indivisible. Nevertheless, however, I derive another definition of Democritus from Physics book 1 and from Lucretius book 5. Elements are the first seedbed of atoms simply formed, and of single kinds, according to whose variation and diverse union all mixtures are generated, and into which all things are ultimately resolved. I said “first seedbed,” because there are figures, and secondary minima of another sort, which, from substantial form, the turning of the heavens, and other causes, obtain a varying figure for the service of mixed things. I said “simply,” because it lacks all composition. I called them “of single kind,” that is, all watery figures or atoms are of the same nature; the same judgment applies to earthy and fiery ones; let the rest be plain from the fol-

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De Atomis. Disput. I. 54 quentibus. Confirmatur hæc doctrina à Lucretio qui dicit omnia corpuscula terrea adunata in vnum, & de alijs elemen- tis ità similiter docet l. 5. Quippe etenim primum terrai corpora quæq; Propterea quod erant grauia, & perplexa, coibant. In medioq; imas capiebant omnia sedes. Definiuimus ergo elementum secundum Democritum, quod erat propositi nostri. PROPOSITIO. VII. Elementum non componitur ex materia, & forma. Hæc conclusio necessariò sequitur ex prop. 2. & 3. Illud enim non componitur ex materia, & forma quod est in- generabile, & incorruptibile, sed elementa sunt huiusmodi per prop. 2. ergo non componuntur ex materia, & forma. Maior euidés est, incorruptio enim absoluta, & omnimoda, qualé da- mus elementis, non potest stare cum illa compositione quæ se- parationem materiæ, & formæ facit possibilem. Verùm non est hic dissimulanda difficultas quæ exurgit à definitione cor- poris naturalis ab Aristotele tradita, quamq; omnes adorant philosophi. Corpus naturale est compositum substantiale (ex mate- ria, & forma) habens principium motus, & quietis sensibilis; quæ sententia elicitur ex 1. & 2. physicæ auscult. & ex cap. 4. l. 5. metaphys. ad quam difficultatem soluendam, & ponendum. Democriti placitis stabile fundamentum, Obseruo primò: rationem corporis vniuersalissimam ab- strahere ab omni compositione vt colligimus ex Aristotel. l. 1 3. metaphys. c. 2. & probatur ex eiusdem philosophi doctri- na, qui materiam primam vocat substatiam corpoream seu cor- pus, & tamen omni forma caret. Adde quod ratio corpo- ris apud Mathematicos aliud importat, vnde definitur corpus ab ipsis

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On Atoms. Disputation I. 54 The following confirms this doctrine from Lucretius, who says that all earthy corpuscles, gathered into one, and similarly teaches of the other elements in book 5. For indeed at first all the bodies of the earth Because they were heavy and entangled, came together. And in the middle they all took their lowest seats. We have therefore defined the element according to Democritus, which was the object of our proposal. PROPOSITION VII. An element is not composed of matter and form. This conclusion necessarily follows from propositions 2 and 3. For that which is ingenerable and incorruptible is not composed of matter and form; but elements are of this kind by proposition 2; therefore they are not composed of matter and form. The major premise is evident, for absolute and complete incorruptibility, such as we grant to elements, cannot stand with that composition which makes separation of matter and form possible. But here one must not conceal the difficulty which arises from the definition of a natural body handed down by Aristotle, which all philosophers adore. A natural body is a substantial composite (of matter and form), having the principle of sensible motion and rest; this opinion is derived from book 1 and 2 of the Physics and from chapter 4 of book 5 of the Metaphysics. To resolve this difficulty and to lay a firm foundation for Democritus’ views, I observe first: the most universal notion of body abstracts from every composition, as we gather from Aristotle, book 1 3 of the Metaphysics, chapter 2, and it is proved from the doctrine of the same philosopher, who calls primary matter a corporeal substance or body, and yet it lacks every form. Add that the notion of body among mathematicians implies something else, whence body is defined by them

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C. 2. De elementis iuxta Democritum. 55 ab ipsis pro figura solida, vt sit habens longitudinem, latitudinem, & crassitiem, & pro extremitate superficiem, ità Eucl. 1. 10. elem. definitione, 1. & 2. quæ tres dimensiones sumuntur penes perpendicularem, quæ omnium linearum mensura est quia est vna, breuissima, & inuariabilis, vt demonstrauit Proclus, in 16. & 17. primi elem. Euclidis, vnde, & ratio corporis apud Mathematicos sumitur tantum extensiùè vel quantitatiuè, & reuerà ipsi abstrahunt à materia, vt docet Aristotel. 1. 13. metaphys. summa 1. c. 3. Obseruo secundò differentiam essentialem corporis physici, sumi penes intrinsecum illud principium immanens motus, & quietis sensibilis primò & per se, non per accidens, quare corpus prout abstrahit à simplici, & composito (nam mathematicorum corpus est figura tantum solida, & æquiuocè corpus quale ab ipsis vmbrarum terminis effingitur) definiri inquam debet. Substantia materialis quantitatis, & extensionis exigitiua; diuideturq; in corpus simplex, & compositum. Corpus simplex, est substantia materialis homogenea exigitiua quantitatiuæ extensionis, habens principium motus, & quietis sensibilis primò, & per se & non per accidens. Corpus verò compositum. Est corpus naturale, seu substantia materialis completa heterogenea exactu substantiali, & materia composita, habens principium motus, & quietis primò, & per se non per accidens. Cum ergo ratio corporis vniuersaliter sumpta no[n] importet secum essentialiter compositionem ex materia, & forma, sitque alia ratio corporis simplicis, & alia mixti quæ ab homogeneitate, & heterogeneitate tanquam à proprijs sigillis distinguitur ab Auicenna, sequitur ex hoc capite nihil offici, quo minus demonstratum sit, materiam & formam elementis non inesse, quoderat faciendum. D 4 PRO-

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C. 2. On the elements according to Democritus. 55 by them as a solid figure, that is, as having length, breadth, and thickness, and as surface for its extremity; thus Euclid, book 1, definition 10 of the Elements, 1 and 2, in which these three dimensions are taken with respect to the perpendicular, which is the measure of all lines, because it is one, shortest, and invariable, as Proclus demonstrated, in 16 and 17 of the first book of Euclid's Elements; whence the notion of body among Mathematicians is taken only extensively or quantitatively, and in truth they abstract from matter, as Aristotle teaches, Metaph. 1, 13, summa 1, c. 3. I observe secondly that the essential difference of physical body is taken with respect to that intrinsic and immanent principle of motion and sensible rest, primarily and per se, not accidentally, wherefore body, insofar as it abstracts from the simple and the composite (for the body of the mathematicians is only a solid figure, and equivocally a body, such as is fashioned by them from the very boundaries of shadows), must, I say, be defined thus: a material substance, demanding quantity and extension; and it is divided into simple body and composite body. A simple body is a homogeneous material substance, demanding quantitative extension, having a principle of motion and sensible rest primarily, and per se and not accidentally. But a composite body is a natural body, or complete material substance, heterogeneous by substantial completion, and composed of matter, having a principle of motion and rest primarily, and per se, not accidentally. Since therefore the notion of body, taken universally, does not necessarily imply composition from matter and form, and there is one notion of simple body and another of mixed body, which is distinguished by homogeneity and heterogeneity as by their proper seals, according to Avicenna, it follows from this point that nothing is lacking to prevent it from being demonstrated that matter and form do not inhere in the elements, which was the thing to be done. D 4 PRO-

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56 De Atomis. Disput. I. PROPOSITIO. VIII. In quous elemento tria sunt primariò consideranda, primò moles sub- stantialis corporea: secundò qualitas prima; tertiò appetentia mixtionis. Secundariò autem elementa contemplanda sunt vt partes vniuersi, & vt mobilia localiter. Explicatur, & probatur propositio. Moles substantialis corporea est ens substantiale simplex corporeum sub tribus dimensionibus comprehensum longitudine, latitudine, & altitudine, cum exigentia quantitatis quà fiat impenetrabile. Nomine qualitatis, quæ est secunda elementi ratio, intelligo qualitates primas quas adinuenit omnium primus noster Hippocrates ex Galeno l. 1. methodi c. 2. calorem, frigus, humiditatem, & siccitatem: Molis autem substantialis exigentia, est nota, & character eius essentialis, nam moles ignis à mole aquæ in eo differt primò, quod ista humiditatem, illa calorem exigat. Et sicuti in alijs omnibus philosophi essentiam nunquam constituunt in actu secundo, sed tantum in actu primo qui est potentia respectu secundi vt ait Aristoteles l. 2. de anima cap. 5. Ita moles substantialis aquæ est in potentia ad humiditatem, quare elementum metaphysicè componitur ex mole, & exigentia qua ponitur in actu primo ad illam qualitatem quam moles prior naturà, ex se profundit: itaq; exigentia illa est veluti actus metaphysicus quæ molem sub certa specieponit. Dices nonnullos existimare in philosophia Democriti nullâ dari qualitatem primam, & adducere possent pro se Lucretium qui varias atomorum figuras modo frigus modo calorem gignere dicit. l. 2. Sedne

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56. On Atoms. Disputation I. PROPOSITION VIII. In every element, three things are primarily to be considered: first, its corporeal substantial bulk; second, the first quality; third, an appetite for mixture. Secondarily, however, the elements are to be contemplated as parts of the universe, and as locally movable. The proposition is explained and proved. Corporeal substantial bulk is a simple substantial corporeal being comprehended under three dimensions, length, breadth, and height, together with the requirement of quantity whereby it becomes impenetrable. By the term quality, which is the second reason of an element, I mean the first qualities which our very first Hippocrates, from Galen, introduced: in book 1 of the Method, chapter 2, heat, cold, humidity, and dryness. But the requirement of substantial bulk is its sign and essential character; for the bulk of fire differs from the bulk of water in this first respect, that the latter requires humidity, the former heat. And just as in all other things philosophers never constitute the essence in the second act, but only in the first act, which is potency with respect to the second, as Aristotle says in book 2 of On the Soul, chapter 5, so the substantial bulk of water is in potency for humidity; wherefore the element is metaphysically composed of bulk and a requirement by which it is placed in first act toward that quality which the prior bulk in nature of itself produces. Thus that requirement is, as it were, a metaphysical act by which the bulk is placed under a certain species. You will say that some think that in the philosophy of Democritus no first quality is given, and they could cite Lucretius for themselves, who says that the various shapes of atoms now produce cold, now heat. Book 2. But not

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C.2. De Elementis iuxta Democritum. 57 Sed ne forte putes solo spoliata colore. Corpora prima manere, etiam secreta teporis Sunt ac frigoris omnino, calidiq; Vaporis Et sonitu sterilia, & succo ieiuna feruntur. Et libro quarto vbi qualitates sensibiles explicat per figuras, & meatus excipientes; Verùm tantum abest vt sit Democriti sensus, vt ipse quidem secundas, tertias, quartasq; qualitates à proportione secundarum, tertiarum, quartarumq; atomorum oriri existimet, at primas influxu vero diffundi posse censet; Lucretius quide[m] Empedoclis sententiam sequitur, nos autem Democriti. Sed de his fusius dicemus disp. 2. Deinde dico vnam atomum seorsum sumptâ non posse frigefacere, aut calefacere, quia actiones physicè construuntur vti pyramides quarum basis est in agente, vertex in passo, atqui vbi tantum est punctum non potest fieri basis, quę lineà indiget physicà, ergo neq; ab vna atomo potest vlla actio sensibilis promanare. Appetentia verò formarum, & mixtionis omnibus elementis est essentialis quatenus sunt principium materiale, & subiectum formarum, moles itaq; , exigentia qualitatis, & appetentia mixtionis sunt essentialiter in quouis elemento, & sicuti varia est in singulis qualitatu[m] exigetia, ità dici potest, appetentiam formæ omnibus elementis co[m]munem, ad vnumquodq; contrahi per peculiare subiectionem qua formę subseruiunt, nam aliter ignis, aliter aqua, & terra ad mixtionem veniunt quamuis simul sumpta faciant vnicam materiam primam co[m]pletam. Quæ doctrina adoratur ab Auicenna l. 1. Fen. 1. doctrina 2. cum ait. Terræ vsus est ad retentione[m] fixationem, & ad conservatione[m] figuræ, & formæ; aqua extendit, & suscipit figuras; aer subleuat, & attenuat; Ignis maturat, permiscet eiusq; penetratione currit substantia aerea, & vt duorum elementorum grauium frigidorumq; puram frigiditatem frangat, & vt de elementaria pro- prietate

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C.2. On the Elements according to Democritus. 57 But lest perhaps you should think that the primary bodies remain stripped of color alone. They are also altogether devoid of the heat of warmth and of cold, and they are carried along barren of sound and lacking juice. And in the fourth book, where he explains sensible qualities through figures and receiving passages, however far this is from the meaning of Democritus: for he himself indeed thinks that second, third, and fourth qualities arise from the proportion of second, third, and fourth atoms, but he judges that the first qualities can be diffused by true influx; Lucretius, however, follows the opinion of Empedocles, while we follow Democritus. But we shall speak more fully of these things in disputation 2. Then I say that one atom, taken by itself, cannot cool or heat, because physical actions are constructed like pyramids, whose base is in the agent and whose apex is in the patient; but where there is only a point, a base cannot be made, and a base requires a physical line; therefore no sensible action can proceed from a single atom. But the appetite for forms and for mixture is essential to all the elements insofar as they are the material principle and the subject of forms. Thus bulk, the demand of quality, and the appetite for mixture are essentially in every element, and just as the demand for qualities is various in each, so it may be said that the appetite for form common to all elements is drawn down to each one through a particular subjection by which they serve forms; for otherwise fire, water, and earth come into mixture in one way or another, although taken together they make one complete prime matter. This doctrine is honored by Avicenna, book 1, Fen. 1, doctrine 2, when he says: Earth is used for retention, fixation, and for the preservation of figure and form; water extends and receives figures; air raises up and attenuates; fire matures, mixes together, and by its penetration the airy substance runs through it, and so that it may break the pure coldness of the two heavy, cold elements, and so that from the elementary pro-

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58 De Atomis. Disp. I. prietiate ad complexionalitatem redeat. Duo autem grauia plus iu- uant ad menbrorum generationem, et eorum quietet: & duo leuia ad spiritus, motionemq; tum spirituum tum membrorum: licet motus no[n] sit nisi ab anima; hæc doctissimus Princeps, quæ videbis eluci- datius exponi prop. 12. huius disp. Differunt autem appetitio, & potentia recipiendi formas eo quod appetitus connotet tendentiam ad sui perfectionem, potentia verò solam recipiendi capacitatem videatur signifi- care: sunt autem duæ formalitates resq; vnica. Quoad alia, quæ secundariò consideranda dixi, nempè de mobilitate, & quatenus sunt vniuersi partes, reiectis ad disp. 3. quæ ad motum pertinent, Obseruo elementis triplicem inesse mobilitatem, prima quatenus sursum deorsumue proprijs nutibus feruntur, secunda est superioris ordinis nempè ad bonum commune, quod vt magis promoueant frequenti generatione sunt locis permixta omnibus elementa, neq; terram, aut aquam puram habemus sed omnia sunt immixta ad vniuersi bonum, præsertim quæ in atmosphæra circa terram reperiuntur. Tertiæ mobilitati cedunt duæ iam explicatæ, nam ista ordinatur ad generalissimum vniuersi bonum ad fugam penetrabilitatis, & vacui. Corpora enim simplicia, vt potè machinæ mundanæ fundamenta debent fouere connexionem vniuersalem, & omnia loca replere. Prima mobilitas oritur à densitate, raritate, latitudine, & copaginatione, aut grauitate leuitateq; . Secunda ex appetentia mixtionis, & formarum. Tertia ad totius commodum cui priuata subseruiunt, vt in Repub. ità in natura. Ob primam mobilitatem elementa mouentur lineis perpendicularibus ad centrum vel circumferentiam. Ob secundam obliquè mouëtur dùm quærunt mixtionis locum aggregatiuum, in ipso autem actu mixtionis nullum motum respuunt. Ob tertiam verò omni

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58 On Atoms. Disp. I. …returns to complexionality. Moreover, two heavy things contribute more to the generation of the limbs and to their rest; and two light things [contribute] to spirits and to motion, both of the spirits and of the limbs: although motion is not except from the soul; these are the words of that most learned Prince, which you will see explained more clearly in proposition 12 of this disputation. But appetite and the power of receiving forms differ in this: appetite connotes a tendency toward its own perfection, whereas power seems to signify only the capacity for receiving; yet they are two formalities and one thing. As for the other points, which I said were to be considered secondarily, namely concerning mobility, and insofar as they are parts of the universe, setting aside to Disputation 3 the matters pertaining to motion, I observe that a threefold mobility inheres in the elements. The first is insofar as they are carried upward or downward by their own impulses. The second is of a higher order, namely with respect to the common good; in order that they may promote this more effectively by frequent generation, the elements are mixed together in all places, and we have neither pure earth nor pure water, but all things are intermingled for the good of the universe, especially those found in the atmosphere around the earth. To the third mobility yield the two already explained, for this one is ordered to the most general good of the universe, namely to flee penetrability and emptiness. For simple bodies, as the foundations of the world-machine, ought to foster universal connection and fill all places. The first mobility arises from density, rarity, breadth, and coposition, or heaviness and lightness. The second arises from an appetite for mixture and for forms. The third is for the advantage of the whole, to which private things are subordinate, as in a republic, so in nature. On account of the first mobility the elements are moved in perpendicular lines toward the center or the circumference. On account of the second they are moved obliquely while they seek the aggregative place of mixture; but in the very act of mixture they reject no motion. On account of the third, however, every…

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C.2. De elementis iuxta Democritum. 59 rò omni motu per omnem lineam cientur, his ità explicatis. Probarur propos. elementum est substantia materialis simplex exigitiua quâtitatis, est enim de ratione corporis vt sit impenetrabiliter in loco: deinde vult poni sub certis dimensionibus, vt pote ens finitum, & determinatum: Exigit præterea. suas qualitates quibus agere possit ad extra, cum enim eius essentia sit pro alio nempè pro mixto, actio etiam elementi debet esse pro alio, ergo extrinseca est, & transiens, actio autem transiens non potest fieri nisi per qualitatem, ergo elementum illam exigit. Appetitus formæ est essentialis principio primo materiali, conuenitq[ue] elemento mobilitas, vt melius naturæ institutis subseruiat, ergo hæc omnia in elementis sunt agnoscenda, quod erat nobis propositum demonstrare. PROPOSITIO IX. Non est satis probatum à philosophis dari quatuor elementa. PRobatur ex confutatione rationum Aristotelis, Auicennæ, Galeni, & aliorum. Aristoteles ità argumentatur in l. de cælo, & meteor. Tot sunt corpora simplicia quod sunt motus simplices, sed sunt quinq[ue]; motus simplices, sursum secundum quid, & simpliciter, deorsu simpliciter, & secudu quid, & motus circa cætrum, ergo erunt quinq[ue]; corpora simplicia, quibus hi motus conveniunt, cælum, ignis, aer, aqua, terra. Maior probatur quia cum natura sit principium motus, & cum sint quinq[ue]; motus illi primarij, & simplices motus, sequitur dari quinq[ue]; prima naturæ corpora; minor argumenti primi est adæquatæ diuisionis, & inductio experientia confirmatur, ergo sunt quatuor elementa præter ætherem. Respondere posset Democritus Aristotelem supponere tria valde dubia, & quærere ignotu per ignotius, primùm de principio motus localis intrinseco corporum, secundò motus cælorum

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C.2. On the elements according to Democritus. 59 are moved by every motion through every line, these things being thus explained. The proposition is proved: an element is a simple material substance, requiring quantity; for it belongs to the nature of a body to be impenetrably in a place. Next, it is to be placed under certain dimensions, as being a finite and determinate being. It further requires its own qualities, by which it may act outwardly; for since its essence is for another, namely for the mixed body, the action of the element also ought to be for another, therefore it is extrinsic and transient; but transient action cannot take place except through a quality; therefore the element requires that quality. The appetite for form is essential to the first material principle, and mobility likewise belongs to the element, so that it may better serve the institutions of nature. Therefore all these things are to be acknowledged in the elements, which it was our purpose to demonstrate. PROPOSITION IX. It has not been sufficiently proved by the philosophers that there are four elements. This is proved from the refutation of the arguments of Aristotle, Avicenna, Galen, and others. Aristotle argues thus in the book On the Heaven and in the Meteorologica: There are as many simple bodies as there are simple motions, but there are five simple motions, upward in a certain respect and absolutely, downward absolutely and in a certain respect, and motion around the center; therefore there will be five simple bodies to which these motions belong: heaven, fire, air, water, earth. The major premise is proved because, since nature is the principle of motion, and since there are five primary and simple motions, it follows that there are five primary bodies of nature; the minor premise of the first argument is an adequate division, and the induction is confirmed by experience; therefore there are four elements besides ether. Democritus could reply that Aristotle assumes three very doubtful things, and seeks the unknown through what is more unknown: first, concerning the intrinsic principle of local motion in bodies, second, the motion of the heavens

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De Atomis. Disp. I. 60 lorum ad rationes antiquorum astronomoru[m] expensos. Tertiò de natura centri grauium. Verum ne videamur difficultatibus nouis hanc obiectionem inuolutam eludere, aut totius philosophiæ naturalis fundamenta vni diluendo syllogismo conuellere, transeat motus elementorum à grauitate, & leuitate oriri, secundò transeat in cælis dari homocentrica omnia vt explicuit Fracastorius, tertiò transeat cælos moueri à propria forma, hæc enim ab Aristotelis argumento supponuntur, nam excentrici, & epicycli quos inuenit omnium primus ex Arist. I. 12. metaphys. t. 47. Calippus astrologus, non mouentur circa centrum grauium: deinde si cæli sunt fluidi, neq[ue] planetæ mouentur circa centrum cum habeant varietatem cur sus sui adeò variam vt annotarunt astrologi, & si intelligentia cælos astraq[ue] mouet vt ipse Aristoteles docet I. 12. metaphys. t. 48. quid convincet ab illo motu qui externa vi imprimitur? His ità dissimulatis. Respondeo in forma transeat maior, ne- go minorem; sunt enim tantum tres motus simplices sursum deorsum, & circa centrum, alter à grauitate, alter à leuitate, tertius à vi motrice innominata; magis enim, & minus non faciunt differentiam essentialem vnde deorsum simpliciter, & secundum quid nullatenus differunt specificè, neq[ue] verò absolutè loquendo datur vllus motus deorsum secundum quid, nam aqua, cui ille motus abscribitur, per viam breuissimam ad centrum vsq[ue]; pergeret nisi præpediretur, sicuti terra non descendit dato obstaculo. Dices motus specificari à termino ad quê qui quadruplex est pro elementorum sedibus. Respondeo primò hos terminos ad libitum constitui, nam illos vt lubebit multiplicabo, in aere enim tres sunt regiones ergo tres termini ad quem. Vnus est autem grauium terminus ad quem, centrum mundi ad quod licet non perueniant, illuc tamen collimant, & per accidens est, si nutu suo defraudentur, deinde quotus- quisq[ue]

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On Atoms. Disputation I. 60 from the calculations of the ancient astronomers examined. Thirdly concerning the nature of the center of gravity. But lest we seem to evade this objection by wrapping it in new difficulties, or by overturning the foundations of all natural philosophy by a single syllogism, let it pass that the motion of the elements arises from gravity and levity; secondly, let it pass that all things in the heavens are homocentric, as Fracastorius explained; thirdly, let it pass that the heavens are moved by their own form, for these are assumed from Aristotle's argument. For the eccentric circles and epicycles, which Calippus the astronomer, the first of all to discover them, found from Arist. I. 12. metaphys. t. 47, are not moved around the center of gravity. Then, if the heavens are fluid, the planets too are not moved around the center, since they have such a varied course, as the astrologers have noted; and if intelligence moves the heavens and the stars, as Aristotle himself teaches in I. 12. metaphys. t. 48, what will be proved by that motion which is impressed by external force? These things being thus set aside. I answer, in form: let the major premise pass; I deny the minor. For there are only three simple motions: upward, downward, and around the center; one by gravity, another by levity, the third by an unnamed moving force. For more and less do not make an essential difference, so that downward simply and downward in a qualified sense differ in no specific way; nor, speaking absolutely, is there any motion downward in a qualified sense, for water, to which that motion is attributed, would proceed by the shortest path to the center, unless it were impeded, just as earth does not descend when an obstacle is given. You will say that motion is specified by the terminus ad quem, which is fourfold according to the abodes of the elements. I reply first that these termini are established at will, for I shall multiply them as I please; in the air, for instance, there are three regions, therefore three termini ad quem. But there is one terminus ad quem of heavy bodies, the center of the world, to which, although they do not reach it, they nevertheless aim; and it is accidental if they are deprived of it by their own will. Then how many

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C.2. De elementis iuxta Democritum. 61 isq[ue] admittit ignem in concauo lunæ, quem multi pabuli gratia vagari credunt? ijs tamen tanquam suppositionibus nititur Aristotelis ratiocinatio. At suppositio vel nunquam fallax es- se debet, qualis est mathematicorum, vel certa experientiâ, aut alibi demonstrata. Vis autem corporum motrix quam parum habet apud philosophos in sui notitia conuenientiæ? dum alij grauitatem tantum, leuitatem præterea alij, nonnulli solum impetum, mechanici extrusionem, Aristarchi Sectatores qui Copernici stipendia merent, virtutem magneticam, nonnulli virtutem motricem indifferentem, alij antipathiam, sympa- thiamq[ue]; Lucretius, & Empedocles primorum corporum cur- sitationes in meatibus, alij alia comminiscuntur? Cum ergo tam dubia pro certis supponat philosophus, & conclusio se- quatur deteriorem partem, dicamus eius propositionem paru[m] veritatis minusq[ue]; certitudinis habere. Hipocrates vt ait Gal. 1. 1. de elementis c. 9. Videtur pri- mus omnium naturæ elementa excogitasse atq[ue]; quantum satis esse possit demonstrasse, & ipse Aristoteles ex Gal. 1. 1. de elem. c. 5. Videtur in suarum rationum forma Hippocratem imitatum fuisse. Diuinus itaq[ue]; senex 1. de carnibus textu primo vbi ostendit quomodo ex elementis quatuor variè immixtis homo sit generatus, hanc adducit rationem pro elementorum nume- ro. Datur corpus intelligentiæ particeps siue calidum immor- tale quod vocantæthera; datur quod occupat medium mundi locum, infimum, & supra illud infimum, humidissimum quid ac crassissimum, ergo sunt quatuor elementa ratione sui situs satis distincta, hanc autem rationem deduxit suo modo Aristo- tele illi[us]; satisfecimus. Verum in tenebris natus Hipp. ijs er- roribus hic scatet, quos Christiani in admirabile lumen vocati deridemus, hominem scilicet ex putri natum, deinde animam, & ignem calidum esse, quod Democrito etia[m] placuit, quare sua sponte ruit Hipp. ratiocinatio. Gale-

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C.2. On the elements according to Democritus. 61 and does he not admit fire in the hollow of the moon, which many believe wanders for the sake of pasture? Yet Aristotle’s reasoning relies on such things as suppositions. But a supposition ought either never to be deceptive, as is the case with the mathematicians, or else to be established by certain experience or demonstrated elsewhere. How little agreement do the moving force of bodies and its proper understanding have among philosophers! While some attribute only heaviness, others also lightness; some only impulse; the mechanicians expulsion; the followers of Aristarchus, who deserve Copernicus’s pay, magnetic power; some an indifferent moving power; others antipathy and sympathy; Lucretius and Empedocles the courses of primary bodies through passages; others invent other explanations. Since, then, the philosopher assumes as certain things so doubtful, and the conclusion follows on the worse side, let us say that his proposition has little truth and less certainty. Hippocrates, as Galen says in 1.1 On the Elements, c. 9, seems to have been the first of all to devise the elements of nature and to demonstrate them as far as may be enough; and Aristotle himself, from Galen 1.1 On the Elements, c. 5, seems to have imitated Hippocrates in the form of his arguments. Therefore the divine old man, in 1 On Flesh, the first text, where he shows how man is generated from the four elements variously mixed together, brings forward this reasoning for the number of the elements: there is a body that is a participant in intelligence, namely the hot and immortal thing which they call ether; there is that which occupies the middle place of the world, the lowest, and above that lowest, the very moist and thick thing; therefore there are four elements sufficiently distinguished by reason of their position. Aristotle, in his own way, derived this same reasoning from that source; we have made our point. But Hippocrates, born in darkness, is here full of those errors which we Christians, called into marvelous light, laugh at: namely, that man is born from putrefaction, and then that the soul and fire are hot, which also pleased Democritus; for this reason Hippocrates’ reasoning falls of its own accord. Gale-

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Galenus l. 1. de elementis c. 5. sic argumentatur ex Hipp[ocrates] placitis. Corpora quæ rerum vniuersitatem componunt, & ex quibus omnia fiunt, sunt elementa, sed sunt quatuor huiusmodi, regionibus, qualitatibusq[ue] distincta, ergo sunt quatuor elementa, quæ, & ipse recenset terram, aquam, aerem, ignem omnium prima, & simplicissima. Responderi potest ex Democriti placitis concedendo maiorem, & negando minorem, nam licet dentur hæc quatuor corpora, negabit tamen ex ijs omnibus propriè mixta fieri, vt fusius explicabitur inferius, & qualitates primas singulis inesse. Auicenna l. 1. Fen. 1. d. 2. sic argumentatur à causa finali. Non potest fieri coporis naturalis generatio quin adsit fixio quædam, extensio, & dilutio partium, permeatio, & subtilisatio, deinde mixtio cum motu. Atqui fixationem terra præstat, extensionem, & dilutionem aqua, permeabilitatem, & tenuitatem aer, motum verò mixtionis ignis promouet, ergo cum hæc quatuor ad generationem omnem concurrant, sequitur esse elementa. Hæc ratiocinatio doctissimi Arabis plus apud me est quam Aristotelis. Concedo itaq[ue] requiri hæc omnia ad generationem perfectam, concedo etiam ab quatuor istis corporibus aliquid horum fieri, concedo aeris beneficio poros esse permeabiles, at nego attenuare aerem, cum vnus ignis ad hoc munus sufficiat: aer enim non figitur vt dicemus inferius, estq[ue] alijs elemétis impermiscibilis, vt voluit Democritus, qui illum confudit cum inani, corpora enim ex tribus elementis componi censuit quæ facerent molem, meatus autem ab aere, quare licet optimè Princeps Auicenna probet dari quatuor corpora, quæ concurrant ad generationem, non probat tamen satis illa esse elementa propriè, & peripateticè dicta. Quidam insuper ità probant dari elementa quatuor primò. Tot

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Galen, book 1, On the Elements, chapter 5, argues thus from the doctrines of Hippocrates: The bodies which make up the universe of things, and from which all things are made, are elements; but there are four such bodies, distinguished by regions and qualities; therefore there are four elements, which he also enumerates as earth, water, air, and fire, the first and simplest of all things. It can be replied, from the doctrines of Democritus, by granting the major premise and denying the minor; for although these four bodies are admitted, he will nevertheless deny that any truly mixed things are made from all of them, as will be explained more fully below, and that the primary qualities are present in each. Avicenna, book 1, Fen. 1, d. 2, argues thus from the final cause. No generation of a natural body can take place unless there is some fixation, extension, and dilution of the parts, permeation, and subtilization, and then mixture with motion. But earth provides fixation, water extension and dilution, air permeability and thinness, and fire promotes the motion of mixture; therefore, since these four contribute to every generation, it follows that they are elements. This reasoning of the most learned Arab is worth more to me than Aristotle’s. I therefore grant that all these things are required for perfect generation, I also grant that something of these results from those four bodies, I grant that by the help of air the pores are permeable, but I deny that air itself is attenuated, since one fire is sufficient for this task; for air is not fixed, as we shall say below, and it is impermixable with the other elements, as Democritus wished, who confused it with the void. For he held that bodies are composed of three elements which would make up mass, but the passages are from air; therefore, although Prince Avicenna very well proves that there are four bodies which concur in generation, he does not prove sufficiently that these are elements properly and in the Peripatetic sense. Some others likewise prove that there are four elements, first. So many

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C.2. De Elementis iuxta Democritum 63 Tot sunt elementa quot sunt anni tempora, sed sunt quatuor anni tempora, veri respondet aer, æstati ignis, autumnus terre, hyems aque: ergo sunt quatuor elementa, 2. Adde quod dantur quatuor signorum triplicitates in zodiaco, 3. quatuor humores in corpore qui quatuor elementis respondent, 4. quatuor humorum motus, 5. quatuor in die naturali differen- tiæ 6. quatuor morborum tempora, 7. quatuor qualitatum or- dines, 8. quatuor in extractionibus chymicis rerum differen- tiæ, 9. quatuor in rebus quæ subsident regiones, ergo debent admitti elementa quatuor. Respondet ridens Democritus ad primum, rectè proponi hanc obiectionem in Europa sub zona temperata, Peruanorum Yncas, Malabarum Brachmanes, Sumatræ logues minorem negabunt, quod patet ex cursu solis, his enim prouincijs sub zona æquidiali 6. mensium est æstas, 6. mensium hyems vtraq; duplex eo quod sphæram habeant rectam. In Brasilię tracti- bus quibusdam ver est perpetuum ex Beretario. Cur non di- xit potius dantur 12. menses, ergo & totidem elementa, sunt enim qualitatum sensibiliter diuersarum, aut cum Hungaro dantur 7. planetæ, ergo & 7. elementa. Ad 2. de signorum triplicitatibus quatuor concedo eas dari at negro ex ijs probari elementa quatuor, imo supponunt probata. Ad 3. Respon- deo primò soluendum esse S. Thomæ, & Stoicis qui negant ae- rem esse calidum, & humidum, Vallesio qui nobiscum est, alijsq; deinde negabitur absolutè consequentia, cur enim non dixit potius dantur tres principes hominis partes, cerebro res- pondet aqua ob humiditatem, nam vt ait Hipp. 1. de carnibus t. 4. Cerebrum est, metropolis frigidi, & glutinosi. Cordi ignis ob calorem, calidum enim, vt ait Ibid. Hipp. pinguis sedes est, pingue autem igni dat pabulum. Hepari respondet terra, in eo enim venæ arborum, & herbarum instar implantantur. Ad 4. negro

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C.2. On the Elements according to Democritus 63 So many are the elements as there are seasons of the year; but there are four seasons of the year: to spring corresponds air, to summer fire, to autumn earth, to winter water; therefore there are four elements. 2. Add that there are four triplicities of the signs in the zodiac. 3. Four humors in the body which correspond to the four elements. 4. The four motions of the humors. 5. The four differences in the natural day. 6. The four times of diseases. 7. The orders of the four qualities. 8. The differences in things in chemical extractions. 9. The four things that settle into regions; therefore four elements must be admitted. Democritus, laughing, replies to the first that this objection is rightly proposed in Europe under the temperate zone; the Inca Peruvians, the Brachmans of Malabar, the logues of Sumatra will deny the lesser, as is clear from the course of the sun, for in these provinces under the equinoctial zone there is a summer of six months and a winter of six months, both double, because they have a right sphere. In some parts of Brazil there is perpetual spring, according to Beretarius. Why did he not rather say that there are twelve months, and therefore so many elements, since there are qualitatively different things? Or, with the Hungarian, that there are seven planets, and therefore seven elements? To 2, concerning the triplicities of the signs, I grant that there are four of them, but I deny that from these the four elements are proven; indeed, they presuppose what has already been proved. To 3, I answer first that we must deal with St. Thomas and the Stoics, who deny that air is hot and moist, with Vallesius, who agrees with us, and others; then the consequence will be denied absolutely, for why did he not rather say that there are three principal parts of man? To the brain corresponds water on account of humidity, for, as Hippocrates says, 1. De carnibus t. 4, the brain is the metropolis of the cold and glutinous. To the heart, fire on account of heat; for the heart, as Hippocrates says there, is a fat seat, and fat provides fuel to fire. To the liver corresponds earth, for in it the veins are implanted in the manner of trees and herbs. To 4, I deny

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64 De Atomis. Diput. I. 4. nego ab vitalibus moribus ad elementales esse argumentandu[m]. Ad 5. 6. dico nihil illis concludi. Ad 7. concedo has qualitatum differentias ex Galeno simp[er] med[icinam] fac. l. 5. Sed nego oriri ab elementis, vt satis à me probatu[m] est l. de manna cap. 1 3. de tabaco Exercit. 3. & ex professo l. 1. de purgatib[us] prælectione 7. Ad 8. dico plurimos chymicos admittere tres tantum differentias rerum, alios quinq[ue]; quas vocant fæces, phlegma, oleum, essentiam, æthera qui verò tres, dicunt esse salem, sulphur, mercurium, Ad 9. Nego in ijs quæ subsident quatuor apparere regiones sed aliquando quinq[ue]; aliquando tres pro variorum corporum differentia. Mihi arrisisset magis argumentum à Timæo Platonis sumptum, Corpora propter ignem videri ait, propter terram tangi: addo propter aquâ gustari, vehiculum enim saporum est humidum, quod diluit salium differentias, ex quibus oritur sapor, sonum edere propter aerem: ergo propter elementum quintum odoratui sunt proportionata; dabuntur ergo quinq[ue]; elementa. Verum his minus seueris omissis alias perpendamus ratiocinationes. Tres aliæ supersunt viæ inuestigandi numerum elementorum, prima per qualitates primas, secunda ex natura mixtionis, tertia à motu locali mixtorum. Pro prima sic fit argumentum. Tot sunt elementa quot sunt possibiles primarum qualitatum combinationes, sed sunt quatuor, ergo totidem elementa; maior probatur, quia à positione proprietatis diuersæ, sequitur positio naturæ diuersæ, ergo cu[m] dentur h[uius] qualitates, vt patet experiétia, sequitur earum combinationes reperiri. Sunt autem quatuor tantum possibiles, calidum, & siccum, calidum, & humidum, humidum, & frigidum, frigidum, & siccum, ergo sunt quatuor eleméta. Pro secunda. Sublato quolibet ex elementis sequitur inæ- qualitas

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64 On the Elements. Disput. I. 4. I deny that, from vital qualities, one is to argue to elemental ones. As to 5 and 6, I say that nothing is concluded by them. As to 7, I grant that these differences of qualities are taken from Galen, Simp. med. fac. l. 5. But I deny that they arise from the elements, as has been sufficiently proved by me in the book De manna, ch. 1, and De tabaco, Exercit. 3, and more fully in book 1, De purgativis, lecture 7. As to 8, I say that many chemists admit only three differences of things, others five; which they call feces, phlegm, oil, essence, ether; but those who hold three say that they are salt, sulphur, mercury. As to 9, I deny that in those things which settle four regions appear, but sometimes five, sometimes three, according to the difference of bodies. I would rather have liked the argument taken from Plato’s Timaeus, in which he says that bodies seem by fire to be seen, by earth to be touched; I add, by water to be tasted, for the vehicle of flavors is moisture, which dilutes the differences of salts, from which flavor arises; by air to emit sound: therefore, on account of the fifth element, they are proportioned to smell; therefore five elements will be granted. But setting aside these less severe arguments, let us consider other reasonings. There remain three other ways of investigating the number of elements: the first through the primary qualities, the second from the nature of mixture, the third from the local motion of mixed bodies. For the first, the argument runs thus: there are as many elements as there are possible combinations of the primary qualities; but there are four; therefore, the same number of elements. The major premise is proved because from the position of a different property there follows the position of a different nature; therefore, since these qualities are granted, as experience shows, it follows that their combinations are found. Now there are only four possible combinations: hot and dry, hot and humid, humid and cold, cold and dry; therefore there are four elements. For the second: if any one of the elements is removed, inequality follows

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C. 2. De elementis iuxta Democritum. 63 qualitas miscibilium quæ mixtioni contraria est, duo enim fri- gida vincent vnum calidum, & duo calida vnum frigidum, er- go superest vt sint duo calida, & duo frigida ad mixtionis per- fectionem, quæ ratio elicitur ab Auicenna loc. cit. Pro tertia. Mixta vt ait Arist. 2. de gen. t. 40. mouentur ad motum elementi præualentis: cum ergo quadruplex motus depræhendatur in mixtis erunt quatuor elementa, sic ignea, sursum feruntur, terrea deorsum, aerea aquis innatant, flui- da termina[n]tur alienis terminis, & expanduntur vt aqua: quod patet in flamma, plumbo, lignis, & liquoribus, ergo cum illi motus sint quadruplices, & pendeant ab elemento prædomi- nante, sequitur dari quatuor elementa. Responderi potest ad primum, soluendam esse eam diffi- cultatem S. Thomæ, Senecæ, Vallesio, Stoicis omnibus, ip- siq[ue]; Galeno qui omnes aerem calidum esse negant. Seneca certè l. 2. nat. q. c. 10. aer frigidus per se est, obscurus, lumen illicolorq[ue]; aliunde sunt, & in fine cap. Natura enim aeris gelida est. Quæ assertio Stoicorum etiam est: Valles. in 4 meteor. Galenus 8. de vsu partium c. 3. falsam vocat Aristotelis assertionem, aerem esse calidum. Deinde quid probat contra illum qui dice- ret dari tantum tres qualitates primas, calorem, humidita- tem, frigus? siccitas enim priuatio est cum vix vlla eius actio deprehendi possit quæ à solo calore non possit explicari dissipa[n] te humorem, at verò frigus sensibile est. Præterea negabunt hasce combinationes, sed corpori simplici, simplicem, & vni- cam qualitatem actiuan assignabunt, quare ignem calidum, terram frigidam, aquam humidam faciunt, ponuntq[ue] humi- ditatem tanquam medium contraria duo frigus, & calorem connectens, cum vtroq[ue] enim sibi bene conuenit, ignem frige- fieri, terram calcieri, aquam humiditate carere posse negant: sed horum actiones vel retundi vel admixtis particulis confun- di, ità

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C. 2. On the elements according to Democritus. 63 the quality of the mixables, which is contrary to mixture; for two cold things will overcome one hot, and two hot things one cold. Therefore it remains that there be two hot and two cold things for the perfection of mixture, a reason drawn from Avicenna, loc. cit. For the third. Mixtures, as Aristotle says in De generatione 2, text 40, are moved according to the motion of the prevailing element: since, then, a fourfold motion is perceived in mixtures, there will be four elements. Thus fiery things are borne upward, earthly things downward, airy things float upon waters, fluids are bounded by alien limits and are expanded, as water is: which is clear in flame, lead, wood, and liquids. Therefore, since those motions are fourfold and depend on the predominant element, it follows that four elements are given. To the first it may be replied that that difficulty must be solved in St. Thomas, Seneca, Valesius, all the Stoics, and Galen himself, all of whom deny that air is hot. Seneca certainly, in Natural Questions 2, ch. 10, says that air is cold by itself, dark; light and color are from elsewhere, and at the end of the chapter: “For the nature of air is cold.” This is also the assertion of the Stoics: Vales. in Meteor. 4. Galen, in De usu partium 8, ch. 3, calls Aristotle’s assertion that air is hot false. Next, what does it prove against one who should say that there are only three primary qualities, heat, humidity, and cold? For dryness is a privation, since scarcely any action of it can be perceived that cannot be explained by heat alone, which disperses moisture; but cold, on the other hand, is perceptible. Moreover, they will deny these combinations, but to each simple body they will assign a simple and unique active quality; thus they make fire hot, earth cold, water moist, and place humidity as a kind of middle term connecting the two contraries, cold and heat; for with both it is equally compatible, nor do they deny that fire can be cooled, earth warmed, or water deprived of moisture: but they say that these actions are either weakened or confused by the admixture of particles, so that

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64 De Atomis. Disput. I. di, ità ad sensum terram apparere calidam cum id spiritibus igneis tribuendum sit. Cum ergo hæc prima via multa supponat aut valde controuersa, aut falsa de numero, & combinatione elementorum, & qualitatum, nihil per eam confici posse necessarium est. Et reuerà Valles. in 4. meteor. Arist. c. 1. hanc rationem vocat leuissimam. Ad secundam rationem. Respondeo etiam si sint tantum tria elementa nihil impedit quo minus ea ratione possint dispensari, vt alterius copia aliorum numerum excedat. Sit enim corpus cui necessaria sit humiditas vt 3. calor vt 5. nonne ità dispensabuntur elementa vt sint ignis portiones 5. aquæ 3. terræ tres, illudq; corpus etiamsi vno constet calido, tamen calidis in primo annumerandum erit. Ad tertium argumentum. Responderi potest primò vtsupra, deinde retorqueo argumentu. Nullum enim mixtum sursum fertur, ergo vel in nullo præualet ignis, quod aduersarius non dicet, vel ignis non mouetur sursum naturaliter, & per se, sed tantum per accidens, imò videmus mixta cuiuscunq; sint leuitatis centrum petere, metalla, fossilia quæuis, ligna omnis generis, liquores, fructus, & etiam agaricum, suber, spongias &c. Quæ autem aquis innatant non alia id ratione faciunt quam quod porosa sint corpora, multo aere tumida, quare non ità innatant vt sola sui superficies aquam tangat, sed tantumdem in aquam deprimuntur quantum aquæ necessarium esset æquiponderando suo corpori. Sic nauis centum millium pondo eum sibi in aqua defodit locum, & eo vsq; deprimitur, dum hinc, & inde centum millia librarum aquæ extruserit, vnde, & ars nautica sibi sumpsit fundamentum, & regulam quæ onera nauibus certa proportione præscribit imponenda. Et hac inductus experientia non existimo improbabilem eam esse sententiam, quæ omnia corpora mixta æqualis esse

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64 On Atoms. Disputation I. Thus, then, does the earth appear warm to the senses, when this must be attributed to fiery spirits. Since, therefore, this first way assumes many things either highly controversial or false concerning the number and combination of the elements and qualities, it is necessary that nothing can be accomplished by it. And indeed Valles, in 4. Meteor. Arist. c. 1, calls this reasoning the weakest. As to the second reason, I answer that even if there are only three elements, there is nothing to prevent them from being distributed in such a way that the abundance of one exceeds the number of the others. Let there be, for example, a body that requires humidity in amount 3 and heat in amount 5; surely the elements will be so distributed that there are 5 portions of fire, 3 of water, and 3 of earth, and that body, although it consists of one hot element, will nevertheless be counted among hot things in the first place. As to the third argument, it may be answered first as above; then I turn the argument back upon it. For no mixed body is carried upward; therefore either fire does not prevail in any mixed body—which the opponent will not say—or fire is not moved upward naturally and of itself, but only by accident. Indeed, we see that mixed bodies of whatever lightness seek the center: metals, all kinds of fossils, woods of every sort, liquids, fruits, and even agaric, cork, sponges, and so on. And those things that float on water do so for no other reason than that they are porous bodies, swollen with much air; wherefore they do not float in such a way that only their surface touches the water, but they are pressed down into the water just as much as would be necessary for the water to counterbalance their body. Thus a ship of one hundred thousand pounds sinks into the water to such a depth, and is depressed until it has displaced on this side and that one hundred thousand pounds of water; from this the art of navigation drew its foundation and rule, prescribing for ships the burden to be imposed in a certain proportion. And being led by this experience, I do not consider improbable that opinion which says that all mixed bodies are of equal...

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C. 2. De elementis iuxta Democritum. 65 esse grauitatis existimauit, differre autem ratione pororum seu meatuum quos infercit aer. Si ergo ratione elementi prædominantis corpora quædam innatant, vt vult aduersarius, quare in naui aurea, & argentea tutò nauigari potest, vt norunt hi qui libros Archimedis de his quæ vehuntur in aqua, salutarunt è limine, aut qui hydraulicæ, staticæ, nauticæq; principia delibarunt? Orontius Finæus in hydraulico horologio regio l. 2. horol. p. 17. nauim cupream adhibuit, & integram machinam Henrico I I. Galliarum Regi obtulit, eaq; aquis innatabat, ergo non ratione elementi prædominantis sed ratione potius aeris in poris vel sinubus inclusi vel positi innatant aut mer guntur mixta. Idem quod in alijs videre poteris in oleo, quod si in vasto effuderis vase tantum in aquam deprimetur quantum mole eiis haber cum mole aquæ in ratione ponderis proportionem, quod si nimia sit olei copia neq; via sit extrusioni, tunc instar operimenti superincumbet, qua ratione succos in phialis asseruant pharmacopolæ. Ex quibus patet non probari sufficienter à philosophis dari quatuor elementa quod erat ostendendum, nunc audiamus in te tam graui Democritum. PROPOSITIO. X. Aer non est elementum. PRobatur primò. Quod caret qualitatibus primis illud non est elementum, sed aer caret qualitatibus primis, ergo nô est elementum, maior est euidens, & si à quopiam negetur quæstio erit de nomine, nam si elementum esse velit, corpus simplex cum reliquis rerum vniuersitatem constituens, concedam in eo sensu aerem esse elementum sed ipsi rationes alias elementis essentiales inesse nego: probatur itaq; minor. Si aer haberer qualitates primas ineptus esset ad id munus cui destinatus est à natura, quæ illum constituit mediatorem in- ter E 2

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C. 2. On the elements according to Democritus. 65 to be of gravity, but to differ by reason of the pores or passages which air fills. If therefore, by reason of the predominant element, certain bodies float, as the adversary wishes, why in a golden and silver ship can one sail safely, as know those who have saluted from the threshold the books of Archimedes on those things that are borne in water, or who have perused the principles of hydraulics, statics, and navigation? Orontius Finæus in the royal hydraulic clock, l. 2. horol. p. 17. employed a copper ship, and presented the entire machine to Henry II, King of the French, and it floated on the waters; therefore it floats or sinks mixed, not by reason of the predominant element but rather by reason of the air enclosed or placed in the pores or cavities. The same thing you will be able to observe in other cases in oil, which if you pour it into a large vessel will be sunk into the water only in such measure as it will have a proportion to the mass of the water in the ratio of weight; but if there be too much oil and there be no way for extrusion, then it will lie on top like a covering, by which means apothecaries preserve juices in vials. From these things it is clear that the philosophers do not sufficiently prove that there are four elements, which was to be shown; now let us hear in you, so grave a Democritus. PROPOSITION X. Air is not an element. It is proved first. That which lacks the primary qualities is not an element; but air lacks the primary qualities, therefore it is not an element. The major is evident, and if anyone should deny it, the question will be one of name; for if he wishes it to be an element, that is, a simple body constituting the universe together with the rest of things, I will grant air to be an element in that sense, but I deny that other reasons essential to elements are present in it: therefore the minor is proved. If air had the primary qualities it would be unfit for that office for which it was assigned by nature, who constituted it the mediator be- tween E 2

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66 De Atomis. Disp. 1. ter cælum, & terram, vehiculum specierum, actionum, influxuum, & accidentium transportatorem; locum vbi sphæræ actiuitatis non mutilantur; sensibilium cognitionum, & imaginum intentionalium sincerum fideiustorem; quare ob motus locales fecit facilè diuisibilem, ob species intentionales purissimum, & sine crassitie diaphanum; propter oculum sine colore, & aliorum sensuum gratia sine sono, sapore, odore, & tangibilitate, quod in aere quieto sinceroq[ue]; patet; vt actiones propaget cuiusuis externæ impressionis, est susceptibilis, atq[ue] vt ait Frismegistus in Asclepio; Aer est organum vel machina omnium per quam omnia fiunt. Quæ qualitates, & officia, cum in aqua, terra, igniue non reperiantur, videtur nobis ansa porrigi aliter de aere, quam de alijs philosophandi. Cuius insuper fluiditas vacuo impediendo, tenuitas poris subeundis, subtilitas dilatandis vaporibus crassis, rarefactioniq[ue]; corporum ob calorem adiuvandæ aptissima est, & vbiq[ue]; non tam sua, quam naturæ totius negotia pertractare aptus natus est aer. Vnde sic argumentor. Medium naturale, & proprium inter agens, & patiens de neutro participare debet, sed aer est huiusmodi, ergo de nullius agentis patientisue qualitatibus participat. Sit enima aer frigidus, vt volunt Stoici, sic licebit ratiocinari. Sicut non potest ignis actiuitas peruenire ad passum cum intermediat glacies, ità neq[ue]; ignis calor persentir i potest intermediante aere: quanam enim ratione pura actio calidi vt 6. vel 5. perueniet ad nos per medium fridigium vt 7? Dices raritate aeris eius reactionem præpediri. Sed contra, intensio qualitatis etiam in subiecto raro resistit subiectioni contrariæ, ità flamma stuparum, & palearum, sic ignis aquæ vitæ quamuis sit rarus, numquam tamen frigori cedet, ità vt frigus in eadem parte sui sit cum calore; pariter si aer dicatur calidus humidusue, corrumpet, retun- -det,

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66 On Atoms. Disp. 1. by which heaven and earth are transported, the vehicle of species, actions, influences, and accidents; the carrier; the place where spheres of activity are not mutilated; the faithful guarantor of sensible cognitions and intentional images; wherefore, on account of local motions, it has been made easily divisible, on account of intentional species most pure, and without grossness diaphanous; on account of the eye without color, and for the sake of the other senses without sound, taste, smell, and tangibility, as is clear in calm and pure air; so that it may propagate the actions of whatever external impression it is susceptible of, and, as Frismegistus says in the Asclepius: Air is the organ or machine of all through which all things are done. Since these qualities and offices are not found in water, earth, or fire, it seems to us that the occasion is offered to philosophize about air otherwise than about the others. Its fluidity, besides, is most suited to preventing a vacuum; its fineness, to the passage of pores; its subtlety, to the dispersing of thick vapors, and to the rarefaction of bodies assisted by heat, and everywhere air is suited not so much to manage its own affairs as those of the whole of nature. Whence I argue thus. The natural and proper medium between agent and patient ought to partake of neither; but air is of this kind, therefore it partakes of the qualities of neither agent nor patient. For if air were cold, as the Stoics wish, then the reasoning would be allowed. Just as the activity of fire cannot reach the patient when ice intervenes, so neither can the heat of fire be perceived through air intervening; for by what reasoning would the pure action of the hot, as 6 or 5, reach us through a cold medium, as 7? You will say that the reaction of the air is impeded by its rarity. But contrariwise, the intensity of a quality even in a rare subject resists a contrary subjection; thus the flame of tinder and straw, and fire of aqua vitae, although rare, nevertheless will never yield to cold, so that cold is in the same part of itself as heat; likewise, if air be said to be hot or moist, it will corrupt, blunt,

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C. 2. De elementis iuxta Democritum. 67 det, & adulterabit actiones frigidas, & siccas: ergo necessariò concludendum est, ob illud vniuersale aeris officium median- di, nullam ipsi qualitatem actiuam inesse: neq[ue] enim concipi potest quanam tandem ratione minoris virtutis agentium vis, in medio sibi penitus contrario non pessum detur. Confirmatur ex officio aeris replendi locum, & poros subeundi, natura enim debuit huiusmodi corpus omnino innoxium creare, ne sua subtilitate, & quousi tendendi licentià, alijs corporibus officeret. Vnde Vallesius in 4. meteor. Aristotel. c. 1. commentario primo cum ostendisset, quam parum probasset suam de primarum qualitatum combinatione sententiam Dux Peripateticorum; An non melior (inquit) ratio est aerem, à quo homines, & perfectissima animantia erant perpetuò perpessura, in agentium qualitatum nulla, mediocritatem excedere, sed temperatum esse, vt illa mediocriter afficeret? Ego quidem arbitror atq[ue] proinde sentio quod in controuersijs confirmavi, aerem neq[ue] calidum neq[ue] frigidum esse, sed in hac oppositione temperatum. Nam præter dicta quod aliqua qualitate est natura præditum, difficile trahitur ad contrariam, sed aere nihil est quod citius mutetur, de calore ad frigus, & contra de frigore ad calorem, vsq[ue]; adeò vt eadem die calidus, & frigidus, & vtrumq[ue] impensè frequenter sit, ergo neq[ue] calidus neq[ue] frigidus est. Hæc viri extra omnem doctrinæ aleam positi sententia, quamuis nostræ faueat, tamen nobiscum non est, in eo quod temperatum aerem faciat, hoc est de frigore, caloreq[ue] moderatè participantem, Sed etiam si haberet quatuor gradus caloris tantum, & totidem frigoris, difficile trahe- retur ad septem, quia resisterent alij gradus; ergo neq[ue] calidus neq[ue] frigidus est natura sua. Confirmatur secundò, quia nihil certi à sensibus haurire possemus, si agentium qualitates in medio vel fauorabili, vel vires addente, aduersante, & imminuente perciperemus. E 3 Probatur

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C. 2. On the elements according to Democritus. 67 it would destroy and adulterate cold and dry actions; therefore it must necessarily be concluded that, because of that universal office of the air of mediating, there is in it no active quality at all; for it cannot even be conceived by what reasoning the force of agents of lesser power should not be utterly lost in a medium wholly contrary to them. This is confirmed by the office of the air in filling space and entering pores; for nature ought to have created such a body wholly harmless, lest by its subtlety and, as it were, license to extend itself, it should hinder other bodies. Hence Valesius, in the 4th book of Aristotle’s Meteorologica, c. 1, in the first commentary, after showing how little the Leader of the Peripatetics had approved his opinion on the combination of the primary qualities, says: “Is it not a better reason,” he says, “to make the air, through which men and the most perfect animals were to suffer continually, have no quality among active qualities, but rather to be moderate, so that it may affect them moderately?” I myself judge and therefore hold, as I have confirmed in the controversies, that the air is neither hot nor cold, but tempered in this opposition. For, besides what has been said, if it is endowed by nature with some quality, it is difficult to draw it to the contrary; but in the air there is nothing that changes more quickly, from heat to cold and from cold to heat, and indeed so much so that on the same day it is often hot and cold, and both intensely; therefore it is neither hot nor cold. This opinion of a man placed outside every risk of doctrine, although it favors ours, nevertheless is not with us, in that it makes the air tempered, that is, participating moderately in cold and heat. But even if it had only four degrees of heat and as many of cold, it would be difficult to draw it to seven, because the other degrees would resist; therefore it is neither hot nor cold by its own nature. Secondly, this is confirmed because we could draw nothing certain from the senses if we perceived the qualities of agents in the medium either as favorable, or as adding force, opposing, and diminishing it. E 3 It is proved

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68 De Atomis. Disp. I. Probatur secundò propositio. Illa non est qualitas insita, & effluens à corpore, cuius licet causam ab extrinseco assignare, sed in aere nulla est qualitas prima cuius causa nô sit extrinseca, nam calescit a sole, frigescit à terra, humesit ab aqua, lacubus, vligine, paludibus, fossis, nubibus inficitur, non respuit fodinarum halitus, pestilentes vapores, cadauerum fætorem, mutatur ventis, influxibus siderum, & tamquam Proteus omnium agentium impressionibus versatilis est, ergo nullam habet qualitatem innatam. Confirmatur 1. quia omnibus elementis alijs insitam vbiq; eandé primariâ qualitate videmus, ità terra vbiq; frigida est, aqua humida, ignis nullibi calidus non est, aer tamen nuspiam sibi in qualitate prima similis, nam variatur tum à cæli aspectibus, & certis plagis, tum ab vicinia ignis subterranei, qui vbiq; maxima portione terræ immixtus est ex Hipp. 1. de carrib. t. 1. & sub eodem æquatore torretur in Monomotapa, riget in Peruuiæ montibus, temperatus est in Brasilia, mutatur ventis, maris viciniâ, orientis meridieiq; afflatu, & infinitis alijs variatatibus à causa extrinseca ortis subiacet, ergo nullam habet qualitatem insitam sibi. Dices has omnes mutationes fieri successiuè continuè, vbiq; aerem esse humidum; & à tribus tantum rebus aerem immutari in instanti ex Gal. 1. de oculis, particula secunda c. 6. Hæc tria sunt quæ aerem sine ullo temporis spatio immutant, lumen solis, fulgidus color, & lumen visibilis spiritus. Quod autem aer vbique humidus sit patet ex sua consistentia, & humidi definitione, nam facile alienis terminis continetur, successio verò alterationis ostendit resistentiam insitæ qualitatis. Sed contra. Illa mutatio non fit continuè successiuè, nisi quòd præexistat in aere contraria qualitas, si enim aer nulla aduentitia re esset præalteratus sed sincerus esset, calefieret in instan-

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68. On Atoms. Disputation I. Second proposition is proved. It is not an innate quality, and flowing from the body, although its cause may be assigned from without, but in air there is no first quality whose cause is not external; for it is warmed by the sun, chilled by the earth, made moist by water, lakes, marshes, swamps, ditches, and clouds, it is tainted, it does not reject the fumes of mines, pestilential vapors, the stench of corpses; it is changed by winds, by the influences of the stars, and, like Proteus, it is versatile under the impressions of all agents. Therefore it has no innate quality. This is confirmed, first, because in all the elements we see the same primary quality innate everywhere in the others: thus earth is everywhere cold, water moist, fire nowhere is not hot; but air nowhere is similar to itself in its primary quality, for it is varied both by the aspects of the heavens and by certain regions, and by the proximity of subterranean fire, which everywhere is mixed with a great portion of earth, according to Hippocrates, 1 De morbis, t. 1. and under the same equator it is scorched in Monomotapa, it freezes in the mountains of Peru, it is temperate in Brazil; it is changed by winds, the vicinity of the sea, the breath of the east and south, and it is subject to infinite other varieties arising from external causes; therefore it has no innate quality belonging to itself. You will say that all these changes take place successively, and that the air is everywhere humid; and that the air is changed instantly only by three things, according to Galen, 1 De oculis, part two, ch. 6. These three things are what alter the air without any interval of time: the light of the sun, a shining color, and the light of a visible spirit. But that the air is everywhere humid is clear from its consistency and the definition of the humid; for it is easily contained within foreign boundaries, but the succession of alteration shows the resistance of an innate quality. But on the contrary. That change does not take place continuously and successively unless there already exists in the air a contrary quality; for if the air had no adventitious thing by which it were pre-altered, but were pure, it would be heated in an instant

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C.2. De Elementis iuxta Democritum. 69 instanti: at verò cum à terra noctu sit frigidus factus, à sole paulatim sensimq[ue] calefit. Ad rationem aute[m] humid, verum quidem est aerem vbiq[ue] liquidum esse, humidum verò nequa- quam, hæc enim definitio liquidi est, vt videbimus prop. 12. Confirmatur secundò, quia mutatio omnis quæ formæ in- clinationi contraria est transit, & momento durat, ingenua, natiuàq[ue] qualitate redeunte, atqui nulla qualitas ab aere re- paratur, ergo nulla ipsi est insita. Probatur tertiò eadem propositio. Illud non est elemen- tum quod non potest venire in compositionem mixti. Sed aer non potest venire in compositionem mixti, ergo aer non est elementum. Maior est certa, cum enim elementa sint ad mix- tum faciendum, sequitur quod quæ ad eum scopum minimè attingere possunt, non sunt elementa, cum natura nihil frustra faciat. Probatur itaq[ue] minor; Illud non potest venire in com- positionem mixti quod refugit vnionem cum alijs, sed aer re- fugit vnionem, nam neq[ue] in aqua, neq[ue] in terra aut igne figi- tur hæretue, videmus enim in globulum se se colligere vt maria diuidat, liquores ab eodem secari, & si à visciditate impe- diatur, tamen sine adhæsione in illis carceribus manebit, dum auolandis locus detur. Contrariâ verò ratione se se habent alia elementa, ignea enim corpuscula terræ miscentur, quod patet in fictilibus, & ferro candente, aqua verò, & terra quam faci- le, quam subtiliter in limum coalescunt? ignis etiam intrudit spiritus in mediam aquam; Ergo cu[m] neque aer cum alijs ele- mentis vniatur, neq[ue] ipsi conueniant qualitates vilæ ex primis, sequitur illi elementi nomen non conuenire, quod erat osten- dendum. E 4 PRO-

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C.2. On the Elements according to Democritus. 69 immediately; but when at night it has been made cold by the earth, it is by the sun gradually and little by little heated. As to the reasoning from humidity, it is indeed true that air is everywhere liquid, but by no means humid; for this is the definition of liquid, as we shall see in prop. 12. Secondly, it is confirmed because every change that is contrary to the inclination of the form passes away, and lasts only for a moment, the native and innate quality returning; but no quality is restored by air, therefore none is inherent in it. Thirdly, the same proposition is proved. That is not an element which cannot come into the composition of a mixed body. But air cannot come into the composition of a mixed body, therefore air is not an element. The major is certain, for since elements are for the making of a mixed body, it follows that those which cannot in the least attain that end are not elements, since nature does nothing in vain. Therefore the minor is proved: that cannot come into the composition of a mixed body which shuns union with others, but air shuns union; for it is fixed neither in water, nor in earth, nor in fire, nor does it adhere there, since we see it gather itself into a little globe so as to divide the seas, and liquids to be separated by it; and if it is hindered by viscosity, nevertheless it will remain there without adhesion in those prisons, as long as there is room for it to fly away. By a contrary reasoning, the other elements behave in this way: fiery corpuscles mingle with earth, as is clear in pottery and glowing iron; and water and earth, how easily, how subtly do they coalesce into mud? Fire also drives spirits into the middle of the water. Therefore, since air is joined neither with the other elements, nor do low qualities from the first belong to it, it follows that the name of element does not belong to it, which was to be shown. E 4 PRO-

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70 De Atomis. Disput. I. PROPOSITIO XI. Dantur tria tantum Elementa, Terra, Aqua, Ignis. S Equitur hæc propositio tanquam Corollarium præcedentis nihilominus tamen vlterius Probatur primò. Tot sunt elementa quot reperiuntur in corporum dissolutione, sed tria tantum reperiuntur, vt Chymicis est manifestum qui sulphur, mercurium, & salem in omnibus mixtis reperiunt, agnosce in sulphure ignem, aquam in mercurio, in sale terram: quamuis enim tria hæc sint mixta, nihilominus in singulis ità predominantur sua elementa vt id potissimum esse videantur cuius potiores partes habet. Ignis ergo copiosissimus est in sulphure, aqua in mercurio qui totus in fumos abit, & à vaporibus iterum in mercurium coalescit; In terra sal, quod à pòdere conijci potest æquè ac alijs rationibus sumptis à lib. meteor. Arist. & lib. de sensu, & sensili: sal enim se habet ad terram vulgarem vt 106. ad 92. Aqua marina se habet ad terram, vt 90. ad 93. quæ aqua marina immixto sale grauior est dulci, ad eam enim se habet vt 92. ad 74. ergo cum terra sit ponderosissima, sequitur quod vbi maximum est pondus ibi etiam illa prædominetur ex aduersario, ergo sal ad terram refertur. Adde quod in resolutione quotidiana mixtorum, & sine arte parata, sunt tantum tria, cineres, fumus, flamma, agnosce in cineribus terram, in fumo vapores aqueos, in flam[m]a spiritus igneos, quod clarius exponâ c.4. d.2. Illustrari posset hæc ratio Pythagoræorum placitis, nam internario foecunditatis symbolum, quæ elementis conuenit animaduertunt, est enim imparium primus ex paritate vna, & vnitate coalescens &c. sed pro his vide doctissima Bungi commentaria in mysterijs numerorum; hìc enim, non philologum, sed philosophum agere decreui. Proba-

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70 On Atoms. Disputation I. PROPOSITION XI. There are only three Elements, Earth, Water, Fire. This proposition follows as a corollary from the preceding one; nevertheless it is further proved first. There are as many elements as are found in the dissolution of bodies; but only three are found, as is manifest to chemists, who find sulfur, mercury, and salt in all mixed bodies; recognize in sulfur fire, in mercury water, in salt earth. For although these three are mixed, nevertheless in each one its own element predominates so much that it seems to be chiefly that of which it has the greater parts. Fire therefore is most abundant in sulfur, water in mercury, which wholly passes into fumes and from vapors again coalesces into mercury; in salt, earth, which may be inferred from weight, as well as from other reasons taken from the 4th book of Aristotle’s Meteorologica and from the book De sensu et sensili: for salt stands to common earth as 106 to 92. Sea water stands to earth as 90 to 93; this sea water, with salt mixed in, is heavier than fresh water, for it stands to it as 92 to 74. Therefore, since earth is the heaviest, it follows that where the greatest weight is, there also that element predominates as the opposite term; therefore salt is referred to earth. Add that in the ordinary resolution of mixed things, both and those prepared without art, there are only three: ashes, smoke, flame. Recognize in the ashes earth, in the smoke watery vapors, in the flame fiery spirits, which I shall explain more clearly in c. 4, d. 2. This reasoning could be illustrated by the doctrines of the Pythagoreans, for the ternary, symbol of fertility, which suits the elements, they observe; for it is the first of the odd numbers, arising from parity as one and from unity, and so forth. But for these matters see Bungo’s most learned commentaries on the mysteries of numbers; for here I have resolved to act not as a philologist, but as a philosopher. Proba-

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C.2. De Elementis iuxta Democritum. 71 Probatur secundò de singulis. Terra in sua puritate consi- derata habet summum frigus, magnum pondus, densitatem crassam, diaphana est secundum quid, suis terminis facilè, dif- ficilè alienis coercetur, aspera & diuisionibus resistit, facilè tamen cum alijs elementis vnitur, nam ad eorum contactus fit friabilis, que cum elementi naturam exhibeant sequitur terrâ esse elementum. Aqua humidissima, terrę se se facilè insinuat, alienis terminis facilius quam suis continetur, fluida est, diaphana, densa, satis facilè diuisibilis, facillimè vnibilis, mi- xtis diluendis aptissima, ergo est elementu. Ignis calidus, flui- dus, agilis, rarus, vagus, permeans, spirituosus, actiuitatis magnæ, facilè vnibilis, auctà luce gaudens, facilè diuisibilis, disgregatius, seù dissolutius dùm multum viget, congrega- tiuus, & vnitius si moderatiùs agat, colorum omnium ra- dix, corporum expetita portio, astrorum syngenis, aquæ, & terræ acceptissimus hospes, vitæ instrumentum: Ex quibus ignem esse elementum statuo. Sed hæc tria ad mixtionem sufficiunt, terra enim corpus vel in figura coercet, aut solidiorem ipsi dat crasim: aqua terrâ diluit, & cum prædominatur certa quadam ratione colliqua- ta, & colata mixtum fluidum facit: ignis benigno calore vtrumq; fouet, liquidu & transpirabile corpus reddit, & aquæ innatans ne congeletur à terra præpedit; ignis tamen, & terræ vinculum videtur aqua ob humiditatem frigoris, & caloris a- micam; vnde cum aer sit ad mixtionem inutilis, hæcq; tria sint satis, sequitur dari tantum tria Elementa, quod erat demon- strandum. PRO-

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C.2. On the Elements according to Democritus. 71 It is proved secondly from the individual elements. Earth, considered in its purity, has the greatest cold, great weight, thick density, is transparent in a certain respect, is easily contained within its own bounds, with difficulty within others; it is rough and resists division, yet it readily unites with the other elements, for upon contact with them it becomes friable; and since these qualities show the nature of an element, it follows that earth is an element. Water is most humid, easily insinuates itself into the earth, is more easily contained within alien boundaries than within its own, is fluid, transparent, dense, quite easily divisible, most easily capable of union, most suited to diluting mixtures; therefore it is an element. Fire is hot, fluid, agile, rare, wandering, penetrating, spiritual, of great activity, easily capable of union, delighting in increased light, easily divisible, more separating, or more dissolving when it is very vigorous, unitive, and more closely joined if it acts more moderately, the source of all colors, the desired portion of bodies, the companion of the stars, most welcome to water and earth, the instrument of life: from which I conclude that fire is an element. But these three are sufficient for mixture, for earth either confines a body in shape or gives it a more solid constitution; water dilutes earth, and when it predominates in a certain proportion, made somewhat thick and strained, it makes the mixture fluid; fire with kindly warmth nourishes both, renders the body liquid and capable of transpiration, and, floating upon the water, prevents it from freezing from the earth; fire, however, seems to be the bond of water and earth on account of the humidity of cold, and the friendliness of heat; whence, since air is useless for mixture, and these three are sufficient, it follows that only three Elements are given, which was to be demonstrated. PRO-

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De Atomis. Disp. I. PROPOSITO XII. Definitiones primarum qualitatum ab Aristotele traditæ, sunt im- propriæ, quare alias afferre tentaui, Democriti placitis conformes. Aristoteles in definitionibus fuit mirabilis; Plato illius que- stionis æstimator quæ dicitur, quid est? totum terrarum orbem pro accurata definitione intelligenda peragrasset, plu- res sanè habemus descriptiones quam definitiones, quod inde colligere licet, quòd plurima absoluta per transcendentes res- pectus exponamus. Sic itaq[ue] primas qualitates definiuit, Sta- girita. Calor est qualitas tactilis congregans homogenea, & disgregans heterogenea. 2. de gen. t. 8. Frigus est qualitas tactilis congregans heterogenea. Ibid. Siccitas est qualitas tactilis qua corpora facilè suo termino, difficile alieno terminantur. 2. de gen. t. 9. & 4. meteor. c. 1. Humiditas verò, est qualitas tactilis qua corpora difficile suis alie- nis verò terminis facilè continentur. Ibid. At cur illa particula tactilis in singulis definitionibus poni- tur, vt scilicet in definitione postea potentiæ sensitiuæ vitiosus fiat circulus, definitur enim potentia in ordine ad obiectum, & hoc obiectum habet aliquid specificationis à potentia, quod nullo modo admittendum est: deinde nonne calor moderatus congregat heterogenea in coctionibus naturalibus, & artifi- ciosis? & frigoris vis etiam homogenea congregat, & nimia etiam eius intensio diuidit, & separat, & homogenea, & hæ- terogenea, vnde frigore disrumpi arbores in hercinia sylua, & saxa ipsa lacerari ferunt, fitq[ue]; tantum per accidens vt frigus in aqua gelu concreta compingat lignis lapidibusq[ue]; carcerem: quæ adunatio est tantum localis, non physica: melius autem fuisset definire has qualitates in ordine ad modu[m] operandi in- mixtione,

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On Atoms. Disp. I. PROPOSITION XII. The definitions of the primary qualities handed down by Aristotle are im- proper; wherefore I have attempted to propose others, in conformity with the opinions of Democritus. Aristotle was marvelous in definitions; Plato, that estimator of the question, as it is called, “what is it?”, if he had traversed the whole globe to understand an accurate definition, we certainly have more descriptions than definitions, which may be gathered from this, that we explain many things in an absolute way by transcendent respects. Thus, then, the Stagirite defined the primary qualities. Heat is a tactile quality joining homogeneous things and separating heterogeneous things. 2 de gen. t. 8. Cold is a tactile quality joining heterogeneous things. Ibid. Dryness is a tactile quality by which bodies are easily bounded by their own limit, and with difficulty by an alien one. 2 de gen. t. 9. & 4 meteor. c. 1. Humidity, however, is a tactile quality by which bodies are with difficulty contained by their own and indeed easily by alien limits. Ibid. But why is that particle tactile placed in each definition, namely so that later, in the definition of the sensitive power, a vicious circle may arise; for the power is defined in relation to the object, and this object has something of specification from the power, which must in no way be admitted: furthermore, does not moderate heat unite heterogeneous things in natural and artificial concoctions? and does the power of cold not also gather homogeneous things, and its excessive intensity even divide and separate both homogeneous and heterogeneous things, whence they say that trees in the Hercynian forest are broken by cold, and rocks themselves torn apart, and that in truth cold does this only accidentally, as when ice in water, frozen by frost, compacts a prison for logs and stones: which union is only local, not physical. It would have been better, however, to define these qualities with regard to the mode of operating in mixture,

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C.2. De Elementis iuxta Democritum 73 mixtione, & generatione corporum, nam cum ad illam ordi- nentur, perfectiorem notitiam inde oriri par est. Adde quod definitorio humidi sumitur tantum in ordine ad locum, & con- uenitèquè igni, ac aeri, vel aque, facile enim terminatur ignis alienis terminis, quare dicendum est humidi, definitionem co- uenire tantum fluido, & definitionem sicci solido, nam coelum ex Aristotele caret qualitatibus primis, tamen alienis terminis non coercetur, ergo coelum est siccum, quod implicat ad homi- nem. Proponam in re adeò difficili meos conceptus, alio- rum si potiores sint admissurus non inuitè, sic itaq[ue] definiret Democritus. Calor est qualitas prima rarefactiua corporum quibus est extrinse- ca, instituta à natura, vt formarum actiuitatem proriret, & mixtu[m] in vigore detineat, moueatq[ue] primò atomos ad mixtionem. Frigus est qualitas prima condensatiua corporum quibus est ex- trinseca, instituta à natura vt formæ imperium in corpore firmet, ef- fluxus nimios impediat partesq[ue] ad mixtionem venientes figat. Siccitas est qualitas prima quà corpora vnionem cum alijs refugi- unt, comminutaq[ue] difficile coalescunt, instituta à natura ad vincula partium modificanda, & partes ipsas suo in situ, & figura conveni- enti coercendas. Humiditas est qualitas 1. à qua corpora habent vt vnione cu[m] alijs facilè admittant adhæreantq[ue] & diuisa facilè coalescant, instituta à natura ad vincula partium modificanda, & partes ipsas laxandas, prout formæ fuerit opportunum. Hæ definitiones fundatæ suut in modo agendi qualitatum, videmus enim calorem rarefacere cum ab extrinseco agit in aliud corpus, sic calor ignis aquam rarefacit, & soluit in va- pores; at dum calor ille est intrinsecus, & naturalis alicui rei illam non rarefacit, sic cor à calore sibi insito non rarefit, neq[ue] piper quod calidum sit ideò rarum est: deinde calore est veluti prin-

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C.2. On the Elements according to Democritus 73 mixture, and the generation of bodies; for when things are ordered toward that, it is fitting that a more perfect knowledge should arise from it. Add that the definition of moist is taken only with respect to place, and it agrees equally with fire, and with air, or with water; for fire is easily bounded by foreign limits. Wherefore it must be said that the definition of moist pertains only to the fluid, and the definition of dry to the solid, for heaven, according to Aristotle, lacks the primary qualities, yet it is not confined by foreign limits; therefore heaven is dry, which implies to man. I shall present my own thoughts on so difficult a matter, ready to admit those of others if they are better; thus, then, Democritus would define it. Heat is the primary quality of bodies, extrinsic to them, instituted by nature so that it may promote the activity of forms, and maintain the mixed body in vigor, and first move the atoms to mixture. Cold is the primary quality of bodies, extrinsic to them, instituted by nature so that it may strengthen the rule of form in the body, prevent excessive effluxes, and fix the parts that come together for mixture. Dryness is the primary quality by which bodies reject union with others, and when broken up coalesce only with difficulty, instituted by nature to regulate the bonds of the parts, and to restrain the parts themselves in their proper position and figure. Moisture is the primary quality by which bodies, by union with others, readily admit and adhere, and when divided readily coalesce, instituted by nature to regulate the bonds of the parts, and to loosen the parts themselves, as may be fitting for form. These definitions are founded on the mode of acting of the qualities, for we see that heat rarefies when it acts from outside upon another body; thus the heat of fire rarefies water and dissolves it into vapors. But when that heat is intrinsic and natural to a thing, it does not rarefy it; thus the heart, by heat innate in itself, is not rarefied, nor is pepper, because it is hot, therefore rare. Next, by heat it is as it were the prin-

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De Atomis. Disput. I. 74 principium motu[m] in natutâ si loquamur de motu ad substantiam, vnde hyeme nullæ pene generationes, appetente verè calor dominans naturam mouet, & excitat omnia. Pariter neq[ue] frigus insitum, & naturale cuipiam rei, illam condensat, sed tatum id agit in ea corpora quibus ab extrinseco, & veluti violenter communicatur, facit tamen ne nimia fiant effluua, vnde, & impedita illa spirituum difflatione, & effluxu de quo Aristoteles l. 2. de plantis c. I. firmius inter mixta inanimata, & diuturnius reddit formæ dominium, quo fit vt durent diutius frigida, calidis subinde pereuntibus, sic marmor, saxa, lapides pretiosi vix mutantur, cum tamen aluminosa, & bituminosa terrarumq[ue]; genera vltra certum tempus vsui in remedica esse non possint: deinde calor mouet, frigus verò motum figit quem non inuitè generationis amore sequebatur: fit enim vt paulatim eius influxu partes constipentur, & cùm adsit calor in mixtione, coalescant cum sapientia, quæ naturæ motus dirigit; opus enim naturæ, opus intelligentiæ. Siccitatis verò, & humiditatis definitiones à solido, & fluido distinguntur satis, neq[ue] ignem humidum esse concedam, cum ignis vnionem respuat cum multis neq[ue]; vt humidis contingit adhæreat, nam si digitum miseris in aquam madidum retrahes, si per ignem duxeris non adhærebunt partes igneæ. Deinde siccitas, & humiditas vinculis partium seu vnionis rationi modum ponunt; quare cum hæ definitiones petantur à fine ad quem à natura qualitates illæ institutæ sunt, videntur magis aptæ quam quæ vulgò Stagiritæ proponuntur, quæ ab effectis accidentalibus, vel à modo quo sunt in loco petitæ videntur, cum indistinctione ab alijs rebus: cum tamen definitio rei naturam explicare debeat, ac proinde rem illam à qualibet alia distinguere, nam per illud idem res est per quod differt ab omni alio, vt aiunt metaphysici. Quod

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On Atoms. Disputation I. 74 If we speak of motion in nature with respect to substance, there is the principle of motion; hence in winter there are scarcely any generations, but in spring, as it approaches, heat rules, moves nature, and excites all things. Likewise, neither cold implanted and natural in some thing does condense it, but it acts only on those bodies to which it is communicated from without, and, as it were, violently; yet it makes them not become too dissipated, whence, by the hindering of that diffusion and outflow of the spirits, of which Aristotle speaks, book 2 of Plants, chapter 1, it renders the rule of form firmer among inanimate mixtures and more enduring, so that cold things last longer, while hot things in turn perish; thus marble, rocks, precious stones are scarcely altered, whereas aluminous and bituminous things, and the kinds of earth, cannot be fit for use in remedies beyond a certain time. Then heat moves; cold, however, fixes the motion which it had not unwillingly followed for love of generation. For it happens that little by little, by its influx, the parts are compacted, and when heat is present in the mixture they cohere with that wisdom which directs the motions of nature; for the work of nature is the work of intelligence. As for dryness and humidity, their definitions are sufficiently distinguished from solid and fluid, nor shall I admit that fire is humid, since fire rejects union with many things, nor does it adhere as humid things do; for if you dip your finger in water you will draw it out wet, but if you pass it through fire the fiery parts do not adhere. Then dryness and humidity set a limit to the bonds of the parts, or to the reason of union; wherefore, since these definitions are sought from the end for which those qualities were instituted by nature, they seem more suitable than those commonly proposed by the Stagirite, which seem to be taken from accidental effects, or from the manner in which they are in a place, with no distinction from other things; yet definition ought to explain the nature of a thing, and therefore to distinguish that thing from every other, for by the same thing a thing is what it is by which it differs from everything else, as the metaphysicians say. What

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C.2. De Elementis iuxta Democritum. 75 Quod spectat ad modum agendi qualitatum, etsi in omni- bus mixtis admittamus effluuia corporum quæ Aristoteles lo- co citato à Democrito didicit, & celebrat passim Lucretius, medicinæq; patroni vno ore vindicant, ità vt in eo vix vllum dubium sit, in elementis tamen an ea dentur dubitatione non vacat, si quidem pura elementa poris carere probabile est quamuis Basso l. 2. de cælo intent. 2. art. 4. illis poros tribuat, qui planè necessarij sunt ad illam agendi rationem, nam mea- tibus indigent effluuia corporum siue aporroiæ. Verùm hæc controversia facilè solui potest, meatus enim ex parte passi, effluuium est ex parte agentis; ac primò quidem elementis adesse illa effluuia patet in igne qui paleas logè dissitas naph- tamq; inuisibilibus scintillis accendit, terra exhalat, aquæ va- pores tolluntur sursum, magno naturæ consilio quæ ea ratione generationes promouet. Atq; vt id concedatur in Demo- criti philosophia ita clarum non est an agant eleméta per pro- pagationem suæ qualitatis; dico itaq; vt nudam responsio- nem, omissa prolixitate, afferam, omnibus elementorum qua- litatibus dari propagationem sui per acerem, qui omnis qualita- tis capax est, quia nullam habet, quę cum contrarietate sit con- iuncta. Calor ergo in agendo magnam habet sphæram actiuitatis; frigus exiguam, nam frigida immediato pene contactu opus habent vt sentiantur: Sennertus certè experientia sibi coeper- tum esse dicit, nulli glaciem nisi palpet manu innotescere, si verò clausis oculis rem probet, fore vt nesciat an lignum an li- brum aliudue socius admoueat: at contrarium expertus sum, licet enim, fateor, id à modico inter uallo distingui possit, per- sentitur tamen obscurum frigus absq; contactu, resq; in niuis glacieiq; cellis probari potest; Humiditas sola partium hu- midarum adhæsione madefacit, siccitas autem obscuram ha- bet

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C.2. On the Elements according to Democritus. 75 As regards the mode by which qualities act, although in all mixed bodies we admit the effluvia of bodies, which Aristotle in the passage cited learned from Democritus and which Lucretius everywhere celebrates, and the defenders of medicine unanimously uphold, so that on this point there is scarcely any doubt, yet whether such things are found in the elements is not free from uncertainty; for it is probable that pure elements are without pores, although Basso, l. 2. de caelo, intent. 2, art. 4, attributes pores to them, which are plainly necessary for that mode of action, since they require passages for the effluvia of bodies, or aporrhoiae. But this controversy can easily be resolved: for passages, on the part of what is acted upon, are effluvia on the part of the agent. And first, indeed, the presence of such effluvia in the elements is evident in fire, which ignites straw lying far away and naphtha with invisible sparks; the earth exhales, vapors are drawn upward from the waters, with the great design of nature, which in this way promotes generations. And although this is granted in the philosophy of Democritus, it is not so clear whether the elements act by the propagation of their quality. I therefore say, to give a brief reply and omit prolixity, that all the qualities of the elements have the power to propagate themselves through the air, which is capable of every quality because it has none of its own joined with contrariety. Therefore heat, in acting, has a great sphere of activity; cold a small one, for cold things require almost immediate contact in order to be felt. Sennertus certainly says that by experience he has learned that ice is not recognized by anyone unless he touches it with the hand; but if, with eyes closed, he were to test the matter, he would not know whether a piece of wood or a book or some other object were being brought near. Yet I have found the contrary: for although, I admit, it may be distinguished from a small distance, nevertheless a dim cold is perceived without contact, and the thing can be tested in rooms of snow and ice. Humidity alone moistens by the adhesion of wet parts, but dryness has a faint

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CAPVT TERTIVM. Satisfit obiectionibus contra superiorem De- mocriti doctrinam. D Iximus elementa esse materam primam, eaq[ue] ingenerabilia & incorrumptibilia, dempsimus ex elemento- rum numero aerem quod qualitatibus primis careat aliasq[ue];

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CHAPTER THREE. Objections against the above doctrine of Democritus are answered. We said that the elements are prime matter, and that they are ungenerated and incorruptible; we excluded air from the number of the elements, because it lacks the primary qualities and the others;

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C. 3. Obiectiones contra Elementa Democriti. 77 aliasq[ue] consequenter adstruximus assertiones ex Democrito, quas vt hactenus munire sumus conati, nunc tuendæ sunt. OBICTIONES Contra incorruptibilitatem, & numerum Elementorum. Obijcitur primò. Incredibile est tantam ignis copiam in li- gno esse, quantam ab eius combustione promi videmus, ergo sequitur generari, ac proinde elementa non esse ingene- rabilia. Respondeo hanc difficultatem soluendam omnibus illis qui dicunt elementa esse formaliter in mixto, si enim ignis ad sui co[n]seruationem indiget calore actuali, pabulo, & latitudine medij, quomodo poterit esse in saxo? si non indiget qua de causa corrumpetur? soluo tamen difficultatem ex proprijs De- mocriti principijs, & vt mea solutio leniùs admittatur, aduerto experiêtiâ sæpe repetitâ edoctus sphærâ igneam decies ter mil lies octogentesies vigesies quater maiore ab vno pulueris ni- trati grano effici quam sit ipsum granum: cuius rei habes de- monstrationem in his numeris. Grani integri diameter 2. Radix Circulus planus 4. Planus numerus Sphæra solida 8. Cubus Grani accensi diameter 48. Radix Circulus planus 1304. Planus numerus Sphæra solida 110592. Cubus At numerus 8. seu cubus grani no[n] accesi co[n]tinetur 13924. in numero 110592. seu cubo accensi, vt patet per diuisionis arithmeticæ, & algebraæ regulas, ergo sphæra solida accensi decies ter millies octingentesies xxiv. continet sphæram soli- dam non accensi, quod erat demonstrandum: neq[ue] cuiquam in hisce

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C. 3. Objections against the Elements of Democritus. 77 and consequently we have previously established other assertions from Democritus, which, having so far tried to defend, are now to be upheld. OBJECTIONS Against the incorruptibility and number of the Elements. First objection. It is incredible that there should be so much fire in wood as we see issued from its combustion; therefore it follows that it is generated, and consequently that the elements are not ingenerable. I reply that this difficulty is to be solved for all those who say that the elements are formally in the mixture; for if fire, for its preservation, needs actual heat, fuel, and width of medium, how can it be in a stone? If it does not need these, for what reason will it be destroyed? Nevertheless, I solve the difficulty from Democritus's own principles, and so that my solution may be more gently received, I note, having been taught by frequently repeated experience, that a fiery sphere, made from a single grain of saltpeter, is ten thousand three hundred and eighty-four times greater than the grain itself: of which matter you have the demonstration in these numbers. Diameter of the whole grain 2. Root Plane circle 4. Plane number Solid sphere 8. Cube Diameter of the ignited grain 48. Root Plane circle 1304. Plane number Solid sphere 110592. Cube But the number 8, or the cube of the unignited grain, is contained 13,924 times in the number 110,592, or the cube of the ignited grain, as is clear by the rules of arithmetic division and algebra; therefore the solid sphere of the ignited one contains the solid sphere of the unignited one ten thousand three hundred and eighty-four times, which was to be demonstrated; nor to anyone in these things

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78 De Atomis. Disput. I. hisce numeris dubium erit qui Eucl. 1. 12. elem. perceperit, sic enim ille prop. 2. Circuli eam inter se rationem habent, quam des- cripta adiametris quadrata, & prop. 18. Sphæræ inter se rationem hibent suarum diametrorum triplicatam. Tanta itaq[ue] ignis copia quanam oritur ratione? R. eam non esse tantam, videri tamen 1. quia idem ignis in pluri- bus locis videtur ratione motus, & refractionis: sic vna scintilla sursum ascendens lineam ducêre in aere videtur, & si baculum ignitum giraueris circulum igneum credes, quod ergo in his motibus cōtingit idem inflamma aceidere par est credere; superficiê scilicet igneorumq[ue]; spiritu[m] exiguu[m] numeru[m] multi- plicem apparere, & eo copiosiorê quo motus velocior est, na[m] tardus in paucioribus locis videtur: præterea in omni flamma datur oleaginositas quæ refractione[m] facit, & diuersu[m] situm quo fit vteo etia nomine idê in pluribus locis multiplici distractaq[ue]; specie appareat. Quod si è grano pulueris nitratitanta ignis vis erumpere videtur, cum tamen illi generando desint apparatus in omni generatione requisiti, quod dispositionibus quæ sensim introduci debent non sit tempus, quanto maior ignis copia in lignorum strue delitescet, dein de cum ignis sit lucidus sit vt omnis flamma ignis esse censeatur, vt pote luce tincta, cum tamen res ità se non habeat, quare illud omne quod à sensibili magis caloris lucisq[ue]; prædominio rectè denominatur ignis, magnam aquæ terræ, & aeris portionem immixtam habet. Quod si hæc non satisfaciant aduersario: quæret Democritus vt quid tanta vaporu[m] copia ex vno aquæ cyatho emergit; num aqua de nouo generatur? rarefieri dicent, quod itidem de igne in ligno delitescente concedemus: quare ignis est in mixtis veluti compactus, statim autem, ac in latitudinem medij aeris potest erumpere rarefit, & magnum occupat locu[m]: & dissolutio sensim facta, sensim etiam ignem prodit, itq[ue]; vt ea diu-

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78 On Atoms. Disputation I. he who has understood the above numbers will have no doubt, if he has grasped Euclid, Elem. I, prop. 12; for thus he, in prop. 2, says that circles bear to one another the ratio which the squares described on their diameters bear to one another, and in prop. 18 that spheres bear to one another the ratio of the cubes of their diameters. Whence then does so great a quantity of fire arise? Answer: it is not so great as it appears; nevertheless it seems so 1) because the same fire is seen in many places by reason of motion and refraction: thus a single spark rising upward seems to trace a line in the air, and if you whirl a burning stick you will believe you see a circle of fire, and therefore what happens in these motions to the same flame it is fitting to believe happens here also; namely, that the very small number of fiery surfaces and spirits appears multiple, and the swifter the motion, the more abundant it appears, for a slow motion is seen in fewer places; moreover, in every flame there is an oily nature which causes refraction, and by the different position by which it is produced, it comes about that under the same name it appears in several places as multiplied and dispersed in diverse forms. If from a grain of nitre powder so great a force of fire seems to burst forth, although there is lacking in it the apparatus required in every generation for producing it, since there is no time for the dispositions that ought gradually to be introduced, how much greater a quantity of fire will lie hidden in a heap of wood; and then, since fire is luminous, so that every flame is thought to be fire, as being tinged with light, although the matter is not in fact so, therefore all that which is rightly called fire from a more sensible predominance of heat and light has a great portion of water, earth, and air mixed with it. And if these things do not satisfy the opponent, Democritus will ask why so great a quantity of vapors rises from a single cup of water; is the water generated anew? They will say it is rarefied, which we shall likewise concede concerning fire concealed in wood; wherefore fire is in mixed bodies as it were compacted, but as soon as it can burst out into the width of the surrounding air, it becomes rarefied and occupies a great space; and the dissolution, being effected gradually, also reveals the fire gradually, and so that the sea-

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C.3. Obiectiones contra elementa Democriti. 79 ea diuturnitate maior censeatur eius copia, cum potiùs lentus motus æstimari deberet: quanam aute ratione fiat ea dissolutio explicabimus in calce disput. 2. Obijcitur secundò multiplex experientia. 1 Aqua ex Æolypilo Vitruij exit in ventum mutata. 2 In maris medio vi remorum ignis scintillæ emicant, quia interceptus aer in ignem mutatur. 3 Ignis extinguitur, neq; vlli spiritus ignei supersunt etiam in vase hermeticè clauso. 4 Vbicunq; est ignis ibi est lux, ergo extincto igne nihil ignis superesse fatendum est, quia nulla lux residua est, ergo corruptio ignis secuta est eius extinctionem. 5 Dantur ignes qui aquâ nutriuntur, & in Delphinatu ad Gratianopolim fons est qui aqua sua nutrit ignem, vnde & fons igneus, illi nomen inditum: cuius fontis meminit S. Aug. de Ciuit. Dei. 6 Sol eleuat vapores qui non semper soluuntur in pluuias, superest ergo vt caloris vi, mutentur in aerem. Quibus experientijs alijsq; videtur conuinci elementa inter se transmutari, ac proinde malè stabiliri à Democrito ea esse ingenerabilia, & incorruptibilia. Experientiæ succedit ratio Aristotelis l.2. de gen. c.6. qui ità agit contra Empedoclem qui cum Democrito sentiebat. Elementa (inquit) possunt comparari inter se ex quantitate, ergo habent aliquid commune ratione cuius mutari possunt. Hoc argumentum Aristotelis futile est si non penitus enucleetur, forte autem, & validum si latens exquiratur medulla. Quantitas enim est accidens, ergo adheret alteri, sed in singulis elementis est quantitas, ergo in singulis est aliquid cui adhæreat, ergo illud subiectum est commune omnibus, ac proinde secundum illud mutari inuicem poterunt. Et idem

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C.3. Objections against the elements of Democritus. 79 That by reason of its greater duration its quantity may be judged greater, whereas it ought rather to be estimated as a slow motion: in what manner, however, that dissolution takes place we shall explain at the end of disputation 2. Secondly, a manifold experience is objected. 1. Water from Vitruvius’ aeolipile comes out transformed into wind. 2. In the middle of the sea, by force of the oars, sparks of fire flash forth, because the enclosed air is changed into fire. 3. Fire is extinguished, and no fiery spirit remains even in a hermetically sealed vessel. 4. Wherever there is fire, there is light; therefore, once fire is extinguished, it must be admitted that nothing of the fire remains, because no light remains; therefore the corruption of fire follows upon its extinction. 5. There are fires nourished by water, and in the Dauphiné near Grenoble there is a spring which nourishes fire with its water; whence also it is called the fiery spring, a name given to it; St. Augustine makes mention of this spring in City of God . 6. The sun raises vapors which are not always dissolved into rain; therefore it remains that, by the force of heat, they are changed into air. By these experiences and others it seems to be proved that the elements are mutually transformed into one another, and consequently that Democritus wrongly establishes that they are ingenerable and incorruptible. To the experience succeeds Aristotle’s reasoning, book 2 of On Generation , ch. 6, where he argues thus against Empedocles, who agreed with Democritus. The elements (he says) can be compared with one another in quantity; therefore they have something common by reason of which they can be changed. Aristotle’s argument is futile if it is not thoroughly unfolded; but perhaps it is valid and strong if the hidden core is sought out. Quantity is an accident, therefore it adheres to another thing; but in each element there is quantity; therefore in each there is something to which it adheres; therefore that subject is common to all, and consequently according to it they will be able to be changed into one another. And the same

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80 De Atomis. Disp. I. Et idem Stagirita cap. 5. sic arguit, quæcunq[ue] mutuo sunt contraria possunt inuicem transmutari, sed elementa sunt inter se contraria, ergo inter se transmutabuntur, maior est clara ex definitione contrariorum, nam contraria sunt quæ sub eodem genere posita inter se maximè differunt, & ab eodem subiecto saltem successiuè, ac proinde ex vnius corruptione alterius admittitur generatio: elementa verò contraria esse patet sensu. Affero instantia. Omnis alteratio est propter generationem substantialem, sed si ignis, verbi gratia, in terram agit eam alterat, ergo vt faciat aliquid substantiale: atqui omnium agentium finis est assimilare sibi effectum, ergo sine suo non debet priuari, præsertim cum sit prius igni propter se agere quam propter mixta. Cum itaq[ue] ignis terram alteret, & alteratio sit via ad generationem, debeatq[ue]; passum assimilari agenti, sequitur terram ab igne corrumpi, & ratio à priori peti potest à p.7. nam alteratione ponuntur dispositiones ad formam, ergo cum ignis in terram introducat dispositiones, & qualitates ignis sequitur etiam ignis formâ debere succedere: adde quòd contrariæ qualitates debent posse inhærere subiecto eidem, ergo qualitates ignis possunt esse in materiali subiecto qualitatum aquæ, ergo & ipsa ratio specifica ignis siue forma substantialis. Hæc sunt meo judicio maioris momenti contra elementorum incorruptionem argumenta, quæ in suum diem ponere sum conatus, ne (quod in Aristotele damnamus qui malignè doctrinam aduersariorum adducit in medium) viderer præuaricari. Respondeo ad primam experientiam, aquam in Æolypilo Vitruuij violēter, & artificiosè intrusam, ob tenuius foramen, exire non posse nisi in vapores attenuetur, qui deinde in aquâ resoluuntur iterum, atqui vapor est formaliter aqua, ergo nulla ibi sit aquæ corruptio. Ad

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80 On the Atomists. Disputation I. And the same Stagirite in chapter 5 argues thus: whatever things are mutually contrary can be mutually transformed into one another; but the elements are contrary to one another; therefore they will be transformed into one another. The major premise is clear from the definition of contraries, for contraries are those which, being placed under the same genus, differ most from one another, and from the same subject at least successively; and therefore, from the corruption of one, the generation of the other is admitted: but that the elements are contrary is evident to the senses. I bring forward an instance. Every alteration is for the sake of substantial generation; but if fire, for example, acts upon earth, it alters it, therefore in order to make something substantial. Now the end of all agents is to assimilate the effect to itself; therefore it ought not to be deprived of its own end, especially since it is prior for fire to act for its own sake than for the sake of mixtures. Since, then, fire alters earth, and alteration is the way to generation, and since the patient ought to be assimilated to the agent, it follows that earth is corrupted by fire, and the reason a priori can be sought from p. 7. For by alteration dispositions are laid down for form; therefore, since fire introduces into earth the dispositions and qualities of fire, it follows also that the form of fire ought to succeed. Add that contrary qualities must be able to inhere in the same subject; therefore the qualities of fire can be in the material subject of the qualities of water, and therefore also the specific nature of fire, that is, the substantial form. These are, in my judgment, the arguments of greatest weight against the incorruptibility of the elements, which I have tried to place on their proper day, lest I should seem to be acting unfairly (as we condemn in Aristotle, who maliciously brings the doctrine of his opponents into the middle). I reply to the first experience: water violently and artfully forced into Vitruvius’s Æolipile, because of the smaller opening, cannot come out unless it is attenuated into vapors, which afterward are again resolved into water; but vapor is formally water, therefore there is no corruption of the water there. To

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C.3. obiectiones contra elementa Democriti. 81 Ad secundam, respondeo vi remorum, ignis scintillas posse emicare, quia elementa sunt immixta locis, deinde vel è remis prodijsse dicam, sicut ex ligno lauri arctiùs constricto emicat, vt è saxo; vel illum ignem in aere ipso extitisse aut in aqua. Ad 3. & 4. dico plures requiri conditiones igni ad id vt luceat: in flamma certè necessarium est humidum pingue, & aliqua partium ignearum adunio: Atomi autem spiritusq[ue] ignei omné chymicoru[m] solertiam, pororum beneficio fallunt. Ad quintam, nego vllum ignem aqua nutriri, qua de re videbis in mea Theorica militari lib.4. Theor.5. Ad fontem illum igneum qui à me tantùm non est visus, respondeo sulphureos halitus vndiquaq[ue] emergere qui aquas allambunt. Ad sextam dico vapores illos vel asportari aliò à ventis vel in pluuias infensibiles solui, vt in rorem, aerem quem serotinum dicunt, qui ferè ros est vespertinus, in guttas noctu decidentes, in humorem illum qui in herbas, & alia allabitur, ergo nulla experientia probatum est elementa transmutari. Ad rationem Aristotelis respondeo ipsi philosopho esse soluendam, Cælum enim quod ex ipsius placitis incorruptibile est habet quantitatem, ergo potest comparari cum elementis, ergo habet aliquid commune secundu[m] quod transmutari possit. Sed ex proprijs Democriti principijs soluo argumentum in forma. Elementa possunt comparari inter se penes quantitatem concedoant. ergo habent aliquid commune specificè nego, genericè concedo: at qui ad transmutationem requiritur communio specifica eiusdem subiecti: nam moles substantialis ignis differt specificè à mole substantiali terræ, ac proinde nihil est commune inter illa duo, nisi genericè, sic coeli materia si diuersa esset à materia terræ, certissimum est coelum nunqua[m] in terram commutari posse, quia nihil est vtriq[ue] commune nisi genericè, neq[ue] obstat quod singulis elementis inhæreat quantitas F 2

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C.3. objections against Democritus’s elements. 81 To the second, I reply that by means of the oar-blades, sparks of fire can flash forth, because the elements are mixed in with the places; then I shall say that they either came out from the oars, as from laurel wood more tightly compressed a spark leaps forth, as from a stone; or that that fire existed in the air itself or in the water. To the 3rd and 4th, I say that more conditions are required for fire so that it may shine: in flame, certainly, a fatty moisture is necessary, and some combination of fiery parts. But fiery atoms and spirits deceive all the skill of chemists, by the help of pores. To the fifth, I deny that any fire is nourished by water; concerning this you will see in my Military Theorics, book 4, Theor. 5. To that fiery fountain, which I myself have almost not seen, I reply that sulfurous vapors arise everywhere, which lap up the waters. To the sixth I say that those vapors are either carried elsewhere by the winds or dissolved into imperceptible rains, as into dew, the air which they call evening air, which is almost evening dew, into drops falling by night, into that moisture which falls upon herbs and the like; therefore by no experience has it been proved that the elements are transmuted. To Aristotle’s argument I reply that the philosopher himself must be refuted; for heaven, which according to his doctrines is incorruptible, has quantity; therefore it can be compared with the elements; therefore it has something in common, according to which it may be transmuted. But from Democritus’s own principles I solve the argument in form. The elements can be compared with one another as to quantity: I grant it. Therefore they have something in common specifically: I deny it; generically: I grant it. But for transmutation there is required a specific commonality of the same subject; for the substantial bulk of fire differs specifically from the substantial bulk of earth, and therefore nothing is common between those two except generically. Thus if the matter of the heavens were different from the matter of the earth, it is most certain that heaven could never be changed into earth, because nothing is common to both except generically; nor is it an objection that quantity inheres in each element. F 2

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82 De Atomis. Disput. I. -titas, vnde concludet aduersarius, quòd erit subiectum specifi- cè idem: nam in ijs quæ toto etiam genere differunt videmus non rarò eadem accidentia, & qualitates: equidem debuerat ostendere Stagirita suæ materiæ proprietates ab ipsa insepara- biles, & quas vocant quarto modo, ijsq; stabilitis, & demon- stratis potuisset à posteriori ostendere vbinam ea materia, reperiretur. Ad secundam rationem. Contraria possunt inuicem tran- smutari, nego maiorem ad probationem maioris quod contra- ria se se expellant ab eodem subiecto, respondeo distinguendo, se expellunt à subiecto primario inhæsionis nego, à subiecto denominationis, & subiecto secundario inhæsionis concedo. Explico meum responsum, non existimo ab vllo philosopho admitti frigus in igne puro, & defecato posse inesse, ità vt ignea pars possit euadere frigida vt 6. si ergo in igne videatur hoc improbandum, cur in aqua concedetur, cum sit vtrobiq; par ratio, & contrariorum eadem sit philosophia? quare nega- ui contraria expellere se à subiecto primario inhæsionis quod explicui def 2. 3. 4. Contrarijs idem est subiectum inhæsionis in aere, vnde se se mutuo expellunt qualitates sibi infensæ; In mixtis autem est tantum subiectum denominatiuè idem, nam à potiori denominatio sumitur, ibi enim est ignis, & aqua, sed pro alterutrius ad sensum dominatu mixtum dicetur calidum vel humidum aut frigidum, quamuis multæ particulę aliter se se habeant. Pro instantia vltimò adducta explico duo principia quibus innititur. I. Omne agens intendit sibi assimilare effectum: si sit agens vniuocum, & nulli alteri subordinetur tanquam instrumentum causæ principali, verissimum est axioma, at si sit æquiuocum vel instrumentum tantum alterius, est falsum, sic enim sol non intendit facere alium solem dum concurrit ad gene-

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82 On Atoms. Disputation I. -ties, from which the adversary will conclude that the subject will be specifically the same: for in things that differ even in genus we often see the same accidents and qualities. Indeed, the Stagirite ought to have shown the properties of his matter to be inseparable from it, and what are called inseparable in the fourth mode; and once these had been established and demonstrated, he could have shown a posteriori where that matter might be found. To the second reason. Contraries can be mutually transmuted, I deny the major. In proof of the major, that contraries drive one another out from the same subject, I reply by distinguishing: they drive one another out from the primary subject of inherence, I deny; from the subject of denomination, and from the secondary subject of inherence, I concede. I explain my reply thus: I do not think that any philosopher admits that cold can be in pure and refined fire in such a way that the fiery part can become cold, as in 6. If therefore this is to be disapproved in fire, why should it be granted in water, since the reason is equally applicable in both, and the philosophy of contraries is the same? Hence I denied that contraries expel one another from the primary subject of inherence, which I explained in defs. 2, 3, 4. For contraries have the same subject of inherence in air, and from this they mutually expel qualities hostile to them; but in mixed things there is only the same subject denominatively, for denomination is taken from the predominant element: for there is fire and water there, but according to which of the two predominates to the senses the mixture will be called hot, or humid, or cold, although many particles may behave otherwise. For the last instance adduced, I explain the two principles on which it rests. I. Every agent intends to assimilate the effect to itself: if it be an univocal agent, and subordinated to no other as an instrument of the principal cause, the axiom is most true; but if it be equivocal, or only the instrument of another, it is false. For thus the sun does not intend to make another sun when it concurs in the gene-

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C.3. Obiectiones contra Elementa Democriti. 83 generationem auri, & dolabra statuam dissecans non intendit facere dolabram, quia est instrumentum ideæ quam habet artifex in mente, & ratio huius rei à priori peti potest à naturâ finis, qui ab omnibus medijs intenditur: quare, & huic axiomati inter philosophica datus est locus; Causæ instrumentales, & subordinatæ agunt in gratiam principalis agentis. 11. Autem principium, implicante fine frustra adhibentur media, verissimum est, & facit à nobis; finis enim elementorum, & suarum actionum vnus est, nam esse est propter operari, quare cum elementa sint propter mixta, etiam omnis generatio fiet in gratiam mixti, vnde non est prius igni assimilare sibi effectum, sed verus ordo est, vt ignis agat propter mixtum cui subordinatur: ex quibus patet solutio. Ad confirmationem R.1. distinguendo vt supra de subiecto inhæsionis primario, & secundario & de subiecto denominationis: R.2. transeat posse frigus in igne, calorem in terra subiectari, nego sufficere huiuscemodi dispositiones, cum aduersarius etiam concedat eleméta formaliter in saxo vbi ignis calore pene omni caret, & tamen est formaliter ignis, præterquam quod hæc argumenta procedunt à suppositione quod detur materia prima diuersa ab elementis quod Democritus negauit. OBIECTIONES Contra ternarium elementorum numerum. Obijcitur primò. Vnum vni est contrarium, sed datur vnu[m] frigidum, & siccum, nempè terra, ergo debet dari calidum, & humidum, nempe aer. Respondeo primò, hoc argumérum soluendum esse S. Thomæ, Stoicisq; cum quibus Seneca in q. nat. ait aerem esse frigidum, Vallesio qui temperatum facit. Respondeo secundò negando F 3

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C.3. Objections against Democritus’ Elements. 83 the generation of gold, and when a man with a spade cuts up a statue he does not intend to make a spade, because it is an instrument of the idea which the craftsman has in his mind, and the reason for this matter can be sought a priori from the nature of the end, which is intended by all means: wherefore, to this axiom also a place has been given among philosophical matters; instrumental causes, and subordinate ones, act for the benefit of the principal agent. 11. But the principle that means are used in vain if they involve an end is most true, and holds for us; for the end of the elements, and of their actions, is one, for being is for the sake of acting, wherefore, since the elements are for the sake of mixts, every generation also will take place for the benefit of the mixt, whence it is not first for fire to assimilate the effect to itself, but the true order is that fire acts for the sake of the mixt to which it is subordinated: from which the solution is clear. In confirmation of R.1, by distinguishing, as above, between the primary and secondary subject of inherence, and the subject of denomination: R.2. let it pass that cold in fire, heat in earth can be subjectated, I deny that such dispositions are sufficient, since the adversary also grants the elements formally in stone, where fire is almost entirely lacking in heat, and yet it is formally fire; besides, these arguments proceed from the supposition that there is a first matter different from the elements, which Democritus denied. OBJECTIONS Against the ternary number of elements. First objection. One thing is contrary to one thing, but there is one thing cold and dry, namely earth; therefore there ought to be one thing hot and moist, namely air. I answer first, that this argument must be solved by St. Thomas and by the Stoics, with whom Seneca in the Questions on Nature says that air is cold, and by Vallesius, who makes it temperate. I answer secondly, by denying F 3

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De Atomis. Disput. I. 84 negando maiorem, nam vni plura sunt contraria, sic opio contraria sunt alexipharmacæ, castorium, assa, semen rutæ, origanum. Bezahar indistinctè venenis datur ex Auicenna in Canticis, parte tertia, numero 5 1. & 1. 4. Fen. 6. t. 1. c. 5. Respondeo tertiò, vnum vni est contrarium hoc est vna qualitas vni qualitati transeat maior, concedo minorem, nego consequentiam: nam in syllogismo fit transitus à qualitate ad substantiam cui nihil est contrarium. Eodem recidit argumentum à quatuor primis contrarietatibus petitum de quo supra egimus. Obijcitur secundò. Grauitas, & leuitas oriuntur à qualitatibus primis, sed aer est grauis, ergo habet qualitatem à primis ortam, & consequenter primas, nam ab effectu necessario cognoscitur existentia causæ per princip. 1 2. Minor itaq[ue] probatur primò à Mathematicis qui de aeris pondere scripserunt, inueneruntq[ue]; eius ponderis momenta, 2. à Francisco de Mendoça qui in suo viridario p[ro]blema instituit, an in aere nauigari possit, 3. à descensu lapidum, & aliorum grauium quæ aeris pondere prægrauata vrgent suum descensum, & velocius in fine quam principio mouentur, 4. experimento adducto à Balsone qui follem inflatum citius descendere ait quam aere vacuum, ob additum aeris pondus 1. de motu intent. 1. art. 3. Respondeo primò negando maiorem, prius enim est elementum esse mobile localiter quam calidum vel frigidum, nam corporis definitio motus importat principium quod grauitatem esse volunt. Responderi posset secundò neglectâ maiori negando minorem, quæ est contra Aristotelem qui vult aerem esse leuem in 1. 4. meteor, & 1. de cælo, 1. de ortu, & alibi, verum siue leuem siue grauem dicat aerem, manet argumenti vis, quare distinguenda est maior: grauitas, & leuitas in nixtis oritur ab ele- men-

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Concerning Atoms. Disputation I. 84 by denying the major, for in one thing there are several contraries, thus to opium there are contraries: alexipharmacæ, castorium, assa, rue seed, oregano. Bezahar is given indiscriminately against poisons according to Avicenna in the Canticis, part three, number 5 1. & 1. 4. Fen. 6. t. 1. c. 5. I answer thirdly, one thing is contrary to one thing, that is, one quality passes to one quality; I grant the major, I deny the minor: for in a syllogism there is a transition from quality to substance, to which nothing is contrary. The argument taken from the four first contrarieties, which we discussed above, comes to the same point. It is objected second. Gravity and levity arise from the first qualities, but air is heavy, therefore it has a quality arising from the first qualities, and consequently the first qualities themselves, for from the effect the existence of the cause is necessarily known, according to principle 12. The minor is therefore proved first by the Mathematicians who wrote about the weight of air, and found the measures of that weight; secondly by Francisco de Mendoça who in his Viridarium proposed the problem whether navigation in the air is possible; thirdly by the descent of stones and other heavy bodies, which, weighed down by the weight of the air, press on their descent and move more rapidly at the end than at the beginning; fourthly by the experiment cited by Balson, who says that an inflated bellows descends more quickly than one emptied of air, on account of the added weight of the air, 1. de motu intent. 1. art. 3. I answer first by denying the major, for it is prior for an element to be locally movable than to be hot or cold, since the definition of a body implies motion, which they wish to be the principle of gravity. Secondly one might reply, while neglecting the major, by denying the minor, which is contrary to Aristotle, who holds air to be light in 1. 4. Meteor., and 1. de Caelo, 1. de Ortu, and elsewhere; yet whether he call air light or heavy, the force of the argument remains, therefore the major must be distinguished: gravity and levity in mixts arise from the ele-

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C.3. Obiectiones contra Elementa Democriti. 85 mentis, & eoru[m] crasi concedo, in simplicibus corporibus nego. Ad primam probatione[m] Respondeo à mechanicis plerisq[ue]; admitti pro virtute motrice omnium corporum solam grauitatem vt per extrusionem deinde motus suos explicent, verùm de sua hypothesi cura non est mathematico, & reuera illam probare alterius est facultatis, vt ait Aristoteles, ponderare autem aere, diligentiâ non superat humanâ, licet enim exigere videretur spatium corpore leuiori plenum vt esset ignis regio, tamen, & in ipso aere, & in aqua examinari potest, leuior enim aer citiùs extruditur sursum, ponderosior tardiùs, dataq[ue]; motuum proportione de ipso pondere iudicari potest; In aere autem puriori impurus aer potest examinari, vt si magnum vtrem aere iniercias ex valle desumpto, alium paris ponderis montano, videbis in aere sereniori alterum altero preponderare, quæ animaduersio vt in aquarum generibus non inutilis est medicinæ, leuiores enim probamus ex Hipp. & Galeno, ità, & aeris examen ex bilance non est spernendum crassus enim aer deterior; Verùm hæc nihil faciunt contra nos quia argumentum procedit de elementis impuris contra postulatum 3. Ad secundum Respondeo Mendoçam loqui ex supositione quod detur ignis in lunæ concauo, elicereq[ue]; consequentiam illustrandis veris Luciani historijs appositam: sint enim naues sinus amplissimi in aeris conuexitate positæ, negat eas ad centrum mundi casuras quia leuissima ignis substantia aere leuiori replebuntur, vnde, & expansis velis remigioq[ue]; in aeris conuexa superficie poterit nauigari: quæ Mendoçæ curiositas luxus plurimum, parum autem contra nos roboris obtinet. Ad tertium Respondeo negando impelli lapidem ab aere sed mobile colligit impetum in descensu cuius proportionem certis regulis digesserunt mechanici, quas fauente cælo videbis in mea Theorica militari. 1. 1. à Theor. 1. ad 20, F 4 Ad

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C.3. Objections against the Elements of Democritus. 85 of mind, and their mixture I concede; in simple bodies I deny it. To the first proof I answer with most of the mechanicians: that they admit as the motive force of all bodies only gravity, so that by extrusion thereafter they explain their motions; but the mathematician need not concern himself with his hypothesis, and truly to prove it belongs to another faculty, as Aristotle says; moreover, to weigh with air is beyond human diligence, for although it might seem necessary to require a space filled with a lighter body, so that it might be the region of fire, yet it can be tested both in air itself and in water, for the lighter air is driven out upward more quickly, the heavier more slowly, and, given the proportion of the motions, the weight itself can be judged from it; in air however, the purer the air, the impure air can be tested, as if you put a large bladder full of air taken from a valley, another of equal weight from the mountains, you will see in the clearer air the one outweigh the other; which observation, as it is not useless in the kinds of waters for medicine— for we test the lighter ones from Hippocrates and Galen—so the testing of air by the balance is not to be despised, for thick air is worse; but these things do nothing against us because the argument proceeds from impure elements against postulate 3. To the second I answer that Mendoza speaks from the supposition that there is fire in the hollow of the moon, and draws a consequence suited to illustrating the true histories of Lucian: let there be ships placed in the very broad bays within the convexity of the air, he denies that they will fall to the center of the world because they will be filled with the lightest substance of fire, lighter than air, whence, with sails spread and oars too, it will be possible to sail on the convex surface of the air: which curiosity of Mendoza contains much luxury, but little strength against us. To the third I answer by denying that the stone is pushed by the air, but the mobile body gathers impetus in its descent, the proportion of which the mechanicians have set out according to certain rules, which, with heaven’s favor, you will see in my Military Theory. 1. 1. from Theor. 1. to 20, F 4 To

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86 De Atomis. Disput. I. Ad quartum nego experientiam Bassonis veram esse, sed ipsum ex coniectura loqui assero, neq; à se factum illius rei ex- perimentum scripsit; imo expertus sum æqualibus momentis vacuum plenumq; follem descendere, quod vt melius expli- cetur, & vt solidissimum Democriticis assertionibus fundame[n] tum ponâ, sequentem instituo ratiocinationem ex princip. I I. PROPOSITIO XIII. Aer caret grauitate, & leuitate. S I experientia quam affero omni caret errore peripateticam philosophiam ruisse existmo. Sæpius expertus sum diuer- sæ grauitatis, figuræ, molis pondera æquè velociter ab editio- ribus locis ad terram peruenire: lignum, & ferreum globum eodem momento ex eade[m] horizontali linea pari altitudine de- misi, & vtrumq; pari velocitate ad terram delatum est, saxum, & glebam, librum, & plumbi globum, pilam lusoriam, glo- bum ferreum, vesicam inflatam iunxi diuersis locis, & tem- poribus, nihil tamen vel minimæ differentiæ potui deprehendere, licet ab editissimis turribus experimenta repetiuerim: & id in aere sensi quod in inani contingere canit doctissimus Lucretius l. 2. Omnia quapropter debent per inane quietum Aequè ponderibus non æquis concita ferri. Cuius experimenti rationem à priori ità reddere possumus, omnis virtus corporum inanimatorum oritur à primis corpori- bus; Sed prima corpora sunt æqualiter mobilia, ergo omnia corpora ab ipsis orta, maior admittitur disertè ab Aristote- le cù ait corpora moueri pro ratione elementoru[m], prob. minor. Ibi debet esse eade[m] vis motrix vbi par est illius necessitas, alio- qui natura quæ ditissima est deficeret in sui primordijs, atqui par est exigentia vt omnia elementa paribus momentis moue- antur,

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86 On Atoms. Disputation I. To the fourth I deny that Bassonius’ experience is true, but I affirm that he speaks from conjecture, nor did he write that he had made the experiment of that matter himself; indeed, I myself have experienced that a vacuum and a full bellows descend with equal moments, which, that it may be better explained, and that I may lay down a very solid foundation for the Democritic assertions, I set up the following reasoning from principle II. PROPOSITION XIII. Air lacks gravity and lightness. If the experience which I bring is free from all error, I think the Peripatetic philosophy is overthrown. I have often experienced weights of different gravity, shape, and bulk arriving equally quickly from higher places to the earth: I let down a piece of wood and an iron globe at the same moment from the same horizontal line at equal height, and both were brought to the earth with equal speed; a stone and a clod, a book and a leaden globe, a playing ball, an iron globe, an inflated bladder, I joined in different places and at different times, yet I was able to detect nothing, not even the slightest difference, although I repeated the experiments from the loftiest towers. And in air I sensed what the most learned Lucretius sings of as occurring in emptiness, book 2: For all things ought therefore through the quiet void To be borne onward with equal speed, though not with equal weights. The reason for this experiment can be given a priori thus: all force of inanimate bodies arises from the first bodies; but the first bodies are equally movable, therefore all bodies arising from them are too. The major premise is expressly admitted by Aristotle, when he says that bodies move according to the ratio of the elements; proof of the minor: the same moving force ought to be where the need for it is equal; otherwise nature, which is most bountiful, would fail in its own beginnings. But the demand is equal that all elements be moved with equal moments,

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C.3. Obiectiones contra Elementa Democriti. 87 antur, cum ad idem munus sint destinata mixtorum scilicet generationi, ergo debent paribus momentis ferri ad locum vbi perfectæ fiunt generationes qui est centrum mundi, & regio circa centrum posita. Quibus ità positis, Probatur propositio. Si aer haberet grauitate aut leuitatem faueret quibusdam corporibus in descensu, alia verò præpediret, atqui id non facit vt experientia patet, ergo aer caret grauitate, & leuitate, maioris sequelam perpendens Lucretius loco citato sic ait, posita scilicet in medio grauitate, & leuitate. Nam per aquas quæcunq[ue] cadunt, atq[ue] aera deorsum. Hæc pro ponderibus casus celerare necesse est. Probatur itaq[ue] maior. Vt se habet grauitas aquæ adea quæ per ipsam descendunt ità se habet grauitas aeris. Sed grauitas aquæ remoratur leuiora, ergo idem deberet facere grauitas aeris. Idem de leuitate iudicium esto, pirum tardius fertur per aquam quam plumbeus globus, & si duas pilas ferreas diuersi pôderis vt altera sit vnc.2. altera lib.6. minor citius ad aquæ fûdum perueniet. Quo enim corpus acutius est eo facilius diuidit resistentiam medij, vnde cunei quo acutiores eo melius diuidunt, & acutior cultri acies promptius secat: at minor globus facit angulum contactus cum aquæ plano magis dehiscentem; Sit enim globus maior F. globus minor E. aquæ superficies A B. angulus contactus à maiori circulo C A B. linea directionis motus à centro grauitas D sit diameter F D A. Dico primo angulum contactus à maiori circulo cum superficie aquæ esse acutiorem, quâ à minori, ac proinde globum minorem faciliùs promptiùsq[ue] cæteris paribus diuidere aquam. cum

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C.3. Objections against the Elements of Democritus. 87 are carried, since they are intended for the same office, namely the generation of mixed bodies; therefore they ought to be borne by equal forces to the place where perfect generations are completed, which is the center of the world, and the region situated around the center. These things being thus set forth, The proposition is proved. If air had gravity or levity, it would favor certain bodies in descending and hinder others; but in fact it does not do this, as experience shows; therefore air lacks gravity and levity. Considering the consequence of the major premise, Lucretius in the place cited says thus, namely, placed in the middle with gravity and levity. For by whatever waters things fall, and down through the air. These things necessarily hasten the fall because of their weights. The major premise is therefore proved. As the gravity of water behaves toward those things that descend through it, so the gravity of air behaves. But the gravity of water delays lighter bodies; therefore the gravity of air ought to do the same. The same judgment should be made about levity. A pear is carried more slowly through water than a leaden ball, and if two iron balls of different weight are taken, so that one is 2 ounces and the other 6 pounds, the smaller will reach the bottom of the water more quickly. For the sharper a body is, the more easily it divides the resistance of the medium; hence wedges, the sharper they are, divide better, and the sharper edge of a knife cuts more readily. But a smaller ball makes the angle of contact with the plane of the water more open. Let the larger ball be F, the smaller ball E, the surface of the water A B, the angle of contact of the larger circle C A B, the line of the motion's direction from the center of gravity D; let the diameter be F D A. I say first that the angle of contact of the larger circle with the surface of the water is sharper than that of the smaller one, and therefore the smaller ball, all other things being equal, divides the water more easily and more readily.

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cum enim lineæ D A, A B. faciant angulum rectum B A D. qui in duos angulos B A C, C A D. per circumferentiam A. C. diuiditur, sequitur quod acutiori facto angulo B A C. sit obtusior remanens D A C. vt patet ex communibus notionibus primi elementorum, atqui est anguli D A C diuidere, constituitur enim ex linea directionis, & superficie corporis ergo tardius diuidet: quod autem in minori circulo angulus contactus sit obtusior facili negotio comprobatur ex principio 9. 1. Euclid. se habet enim vt totum ad partem, ergo remanens angulus ex peripheria, & linea directionis acutior erit, quoderat demonstrandum. Magnus item globus superficiem habet à plano minus remotam, minor autem recedit statim multumq[ue] distat à plano: quare, & aqua minus resistit minori. Confirmatur quia vterq[ue] globus F & E. sibi defodiunt in aqua alueum quo ferantur, est autem in concauitate aquæ ambientis E magis præceps via, minusq[ue]; à linea directionis aliena, ergo minor globus promptiùs per aquam, & aliud medium resistens feretur. Cur ergo idem in aere non contingit inæqualibus præsertim ponderibus: si enim vt ait Euclides l. de leui, & ponderoso di- uersæ

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For since the lines D A, A B make a right angle B A D, which is divided into two angles B A C, C A D by the circumference A. C. it follows that, when the sharper angle B A C is made, the remaining angle D A C is the more obtuse, as is plain from the common notions of the first Elements. But since it is the business of the angle D A C to divide, for it is constituted of a line of direction and the surface of a body, therefore it will divide more slowly. That in a smaller circle the angle of contact is more obtuse is easily proved from proposition 9 of the first book of Euclid, for it stands as the whole to the part; therefore the remaining angle, from the circumference and the line of direction, will be sharper, which was to be demonstrated. Likewise a large globe has a surface less remote from the plane, but a smaller one immediately recedes and is much farther from the plane; wherefore water resists the smaller one less. This is confirmed because each globe, F and E, digs for itself in the water a channel through which it may be carried; but in the concavity of the surrounding water there is for E a steeper path, and one less removed from the line of direction; therefore the smaller globe will be carried more readily through the water, and through any other resisting medium. Why then does the same thing not happen in air, especially with unequal weights? For if, as Euclid says in the book On Light and Heavy, the different…

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C.3. Obiectiones contra Elementa Democriti. 89 uerse potentię diuersi contingunt motus, vt quid eiusdem ma- gnitudinis globi duo alter ligneus libræ vnius, alter plumbeus librarum 50. per aerem æqualibus momentis feruntur: debe- rent enim per Theorema 2. habere differentes motiones ità vt dum vnum pedem emetiretur ligneus globus, quinquaginta petransiret plumbeus? An quia aer sustinet omnino nihil; at prægrandes aues in aere librantur. An quia leuis est aer absq; vlla grauitate ac proinde grauibus quibuscunq; cedit? at certè deberet ea leuitas grauioribus facilius cedere; ergo cum omnia perpendiculari motu æqualibus momentis per aerem ferantur signum est neq; grauem neq; leuem esse. Quod cognoscens Democritus apud Aristotelem l. 4. coeli t. 42. soluit hanc difficultatem quæ maximi hoc in loco pon- deris est; Democritus itaq; existimabat, teste philosopho, stri- cta corpora descendere quod pauca ipsis resistant, lata verò ascendere, super aquam. Subdit instantiam à Democrito ad- ductam textu 43. deberet enim in aere hoc etiam fieri, sed soluit molliter, ait enim non in vnum impetum facere SOVN, vocans SOVN motum eorum quæ sursum mouentur corporum, quæ solu- tio non mollis est sed neruosa, negat enim paritatem Democi- tus, cum ait, non fieri motum in vno, & eodem medio; aqua enim resistit ob grauitatem humiditatemq; , aer autem nullius est resistentię quia grauitate, & leuitate omni caret. Quid ve- rò intelligat per vocem SOVN innuit philosophus, at illam particulam sursum intelligede omni motu qui in aere fit, aer enim respectiuè ad aquam superior videtur, absolutè autem nihil datur sursum deorsumq; vt probatur à nobis in astrologia Democriti, SOV autem est vox abigentis aues apud Aristo- phanem in Vespis: delata enim violento motu pondera eum sonum edunt. Hæc autem experientia de pari ponderum omnium ad ter- ram

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C.3. Objections against the Elements of Democritus. 89 by various powers, diverse motions occur; for example, two balls of the same size, one wooden, of one pound, the other leaden, of 50 pounds, are carried through the air with equal moments: for according to Theorem 2 they ought to have different motions, so that while the wooden ball travels one foot, the leaden one would travel fifty? Or is it because the air sustains absolutely nothing? Yet very large birds are supported in the air. Or because air is light, without any gravity, and therefore yields to heavy things of any kind? But certainly that lightness ought to yield more easily to heavier things; therefore, since all bodies are carried through the air in downward motion with equal moments, it is a sign that air is neither heavy nor light. Perceiving this, Democritus, as Aristotle says in book 4 of the De caelo , text 42, resolved this difficulty, which in this place is of the greatest weight. Democritus therefore thought, according to the philosopher, that compact bodies descend because little resists them, but broad bodies ascend, over water. He adds the objection brought by Democritus in text 43: “this ought to happen in air as well,” but he resolves it gently; for he says that they do not make one impulse, calling SOVN the motion of bodies moved upward. This solution is not gentle but forceful, for Democritus denies equality when he says that motion does not occur in one and the same medium; for water resists because of its heaviness and moisture, but air has no resistance because it lacks both heaviness and lightness altogether. But what the philosopher means by the word SOVN he indicates, namely that little word “upward,” understood of every motion that takes place in the air; for air, relatively to water, seems higher, but absolutely there is no up and down, as we prove in the astronomy of Democritus. And SOV is a word used by Aristophanes in the Wasps to drive away birds; for weights carried off by violent motion produce that sound. This experience, however, concerning the equal weight of all things toward the earth

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90 De Amtomis. Disp. I. ram descensu nullâ habitâ molis, figuræ, grauitatis excedentis ratione, aut aliorum quæ motum vel accelerare, vel præpedire possent, peripateticis omnibus contra sensum est neganda si suam stare velint doctrinam, cæteroquin mirum quantum Democriti sententiæ fauet, & Stagiritæ nocet: nam si virtus motrix deorsum est maior in saxo quam in ligno, cur lignum æquè cito descendit? si vtrobiq[ue]; par est cur saxum maioris est grauitatis? certè admissâ semel grauitate, & leuitate nullo modo concedi potest id fieri, quod tamen oculis ipsis depræhendimus. Scio quosdam negare ab satis edito loco factam experientiam, dicereq[ue]; nonnullum quod si ab orbe lunæ deciderent huiusmodi pondera fore vt depræhenderetur diuersitas; sed contra; sensibilis diuersitas virtutis, imo ità diuersa vt altera sit in centupla proportione, debet effectum facere sensibiliter diuersum in spatio satis conuenienti, sed nulla vnquam depræhenditur differentia quæ vel vnius cubiti imo palmæ sensibilis esset ergo nulla est vitutis differentia. Scribit Campanella quæst. 32. a. 1. physiologiæ expertum se citius pilam vnius vnciæ cadere, quam ferream 6. librarum, subditq[ue]; rationem quòd aer plus sustineat: at etiam plures sunt partes quæ resistentiam vincunt: neq[ue] enim retardantur suis partibus pondera; cum vnicuiq[ue]; parti vis sua motrix insita sit: moles enim vim intrinsecam nô præpedit, cum ea paribus cum corpore crescat incrementis, quare æqualis est vtrimq[ue]; virtus respectiuè ad partes quibus respondet, si enim maior globus 20. partes habet deuehendas, ipsi concessa sunt 20. virtutis motricis momenta, & minori globo qui 4. constat momentis totidem correspondent partes: quare in medio non resistenti omnia æquè cito descendent. Verùm nec mihi nec Campanellæ fides sit, pro voco ad experientiam, quam adeò facilem, & proptam tot vbiq[ue]

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90 On the De Amtonis. Disp. I. ...in the descent, with no account taken of mass, shape, excess of weight, or of other things that could either accelerate or impede motion, must be denied by all the Peripatetics, if they wish their doctrine to stand; otherwise it strangely favors the opinion of Democritus and harms that of the Stagirite. For if the moving power downward in a stone is greater than in wood, why does the wood descend just as quickly? if in both it is equal, why is the stone of greater weight? Certainly, once gravity and levity are admitted, it can in no way be granted that this happens, though we perceive it with our own eyes. I know that some deny the experiment made from a sufficiently elevated place, and say that if such weights were to fall from the orbit of the moon, a difference of this kind would be perceived; but on the contrary, a sensible difference in the power, indeed so different that one is in a hundredfold proportion, ought to produce a sensibly different effect in a sufficiently suitable space; but no difference is ever perceived that would be perceptible even by one cubit, nay even by one palm; therefore there is no difference of power. Campanella writes, quest. 32, a. 1, of physiology, that he has tested that a ball of one ounce falls faster than one of iron of 6 pounds, and he adds the reason, that the air supports more; but there are also more parts that overcome resistance: for weights are not retarded by their own parts, since in each part its own moving force is inherent; for mass does not impede intrinsic force, since it increases with the body by equal increments; therefore the force is equal on both sides respectively in relation to the parts to which it corresponds. For if the larger globe has 20 parts to be carried down, 20 moments of moving force have been allotted to it, and to the smaller globe, which consists of 4 moments, the same number of parts correspond; therefore in a medium offering no resistance, all things will descend at the same speed. Yet let neither I nor Campanella be trusted; I appeal to experience, which is so easy and ready, among so many everywhere

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C.3. Obiectiones contra Elementa Democriti. 91 vbiq[ue] turres editioraq[ue] loca faciunt. Atq[ue] vt omne suffugiu[m] tollatur aduersario, qui propter angulorum opticorum perpendicularem pene allapsum negat ab eo qui sursum est posse discrimen deprehendi, adsint inferius qui ponderum casum explorent, & qui superius est rationem habeat, vt vtriusq[ue] ponderis superficies sit in eadem linea horizonti parallela, & bina eiusdem instanti demittantur, veritatis inuestigandæ causâ. Sæpius cum alijs, & solus, in aquam, in terram varijsq[ue] ponderibus experientiam repetij, neq[ue] vnquam vel latum vnguem abfuerunt à simultate cursus, videndum tamen ne ventus reflet, si enim aer non sit tranquillus, deuiabunt à linea perpendiculari pondera, & hâc illâcq[ue] rapientur, sed quecunq[ue] perpendiculariter cadent, ea porro nullo discrimine ad terram eodem instanti peruenisse deprehendes. Ergo aer grauitate, & leuitate caret, etiam ex suppositio- ne quod ex qualitates dentur in rerum natura qua de re infra Democritus d.3.c.1. Videbis Theoricam meam militarem lib. 1. Theor. 12. OBIECTIO Contra aeris indifferentiam. Obijcitur tertiò: Si aer careret qualitatibus primis inutilis esset respirationi ad quam potissimum à natura est ordi- natus: neq[ue] enim humectaret vel refrigeraret cor. Vt huic obiectioni fiat satis. Obseruo 1. nô ideò moueri pul- mones, quia succedit aer, sed ideo aerem succedere quia pul- mo mouetur, principium enim motus est à viuento. Obseruo 2. humanum genus in ea regione aeris viuere, que à vulgo infima regio aeris, à doctis dicitur atmosphæra, hoc est vapida regio de quâ Clauius lib. de crepusculis, Scheine- rus in refractionibus celestibus, & in rosa vrsina, Kepplerus in- para-

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C.3. Objections against the Elements of Democritus. 91 where towers and higher places are made. And so that every escape may be removed from the adversary, who, on account of the perpendicular fall of optical angles, denies that any difference can be perceived by the one who is above, let there be those below who examine the fall of weights, and let the one above take care that the surface of both weights be in the same line parallel to the horizon, and let two be let down at the same instant, for the sake of investigating the truth. More often, with others and alone, I repeated the experiment in water, on land, and with various weights, nor did they ever differ by the breadth of a nail from a simultaneous course; yet attention must be paid lest the wind blow back, for if the air is not calm, the weights will deviate from the perpendicular line and be carried hither and thither; but whichever fall perpendicularly, you will moreover perceive that they have reached the earth at the same instant, without any difference. Therefore air lacks heaviness and lightness, even on the supposition that qualities of the first kind are given in the nature of things, concerning which below, Democritus d.3.c.1. You will see my military theory, book 1, Theor. 12. OBJECTION Against the indifference of the air. Third objection: If air were lacking primary qualities, it would be useless for respiration, for which it is chiefly ordered by nature; nor indeed would it moisten or cool the heart. To satisfy this objection, I observe 1. that the lungs are not moved because air succeeds, but rather air succeeds because the lung is moved, for the principle of motion is from the living being. I observe 2. that the human race lives in that region of the air which by the common people is called the lowest region of air, but by the learned is called the atmosphere, that is, the vaporous region, concerning which Clavius in his book On the Twilights, Scheiner in Celestial Refractions, and in the Rose of Ursula, Kepler in-

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92 De Atomis. Disput. I. paralipomenis ad Vitelionem, eamq[ue] non in terra modo sed etiam in stellis probabiliter admittit Galilæus, ob illud proflu- uim corporum quod in singulis pene deprehendimus. Hanc 52. milliaribus penes perpendicularem commensuratis sursum exporrectam, quousq[ue] scilicet ascendunt vapores facilè cen- suerim, cum mathematica instrumenta id inferre videantur: quamuis ea inæqualiter diffusa est, cùm alibi crassores aut fre- quentiores vapores ex halationesue fundantur, vnde, & aeris diuersitas oritur, alibi verò infrequentiores, & subtiliores: quo fit vt crepuscula septentrionalia meridionalibus sint longiora, non ideò tantum quia obliquiores solis radij perueniunt illuc, verùm etiam id à vaporu[m] densitate exhalationibusq[ue] densiori- bus oriri par est. Quapropter, & contra sphæræ rationes Hol- landi in celebri illa nauigatione, quâ vltimò iter ad Sinas per septentrionis glacies tentarunt, 22. dies solem citius spe vide- runt, quia refractione ingenti factum est, vt sol qui multis gra- dibus infra horizontem latebat, supra horizontem conspicuus fieret. Clauius re[m] mihi incredibilem de proportione quam ha- bent elementa refert in cap. 1. sphæræ Sacrobosci; cum ait ignis sphærâ habere proportionem maiorem cum terra, quàm 38289. ad 1. & ad aerem maiorem habere quam 865803. ad 1. globus verò ex terra, & aqua coalescenseode[m] autore se habet ad aeré vt 23. ad 1. sed tatu[m] abest vt sectatores habeat, quin etia[m] plurimi existiment aerem vsq[ue]; ad firmamenti concauum por- rigi. In eo itaq[ue] Clauius videtur hallucinatus, quod vaporum ascensum ab igne occurrente prohiberi crederet, vnde cum 52. milliaribus tantum ascendant, coniecit non vlterius aerem exporigi: Sed ideò sistuntur quia radius primarius reflectio- nis solaris non extenditur vlterius, quare vehiculo luminis, & caloris destituti vapores colligunt, se ad statum suum natium reddunt, & condensati resoluuntur in pluuias, ex quibus, Resp.

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92 On Atoms. Disputation I. in the additions to Vitellio, and Galilei likewise admits it as probable, not only on earth but also in the stars, on account of that flow of bodies which we perceive in almost each one. I should think this is extended upward to 52 miles, measured along the perpendicular, as far, that is, as vapors ascend, since mathematical instruments seem to indicate this: although it is unevenly dispersed, since elsewhere thicker or more frequent vapors are emitted from exhalations, whence also arises a diversity of air, while elsewhere they are less frequent and more subtle: hence northern twilight is longer than southern, not only because the sun’s rays reach there more obliquely, but also because this is fittingly derived from the density of the vapors and thicker exhalations. Wherefore, and contrary to the principles of the sphere, the Hollanders in that celebrated voyage, in which they last attempted the route to China through the ice of the north, saw the sun 22 days sooner than they had hoped, because by a great refraction it came about that the sun, which lay many degrees below the horizon, became visible above the horizon. Clavius reports to me an incredible thing about the proportion that the elements have in chapter 1 of Sacrobosco’s Sphere: when he says that fire has a greater proportion to earth than 38289 to 1, and to air a greater one than 865803 to 1; but that the globe composed of earth and water, according to the same author, stands to air as 23 to 1. Yet he is so far from having followers that many even think that air extends all the way to the concavity of the firmament. In this matter, then, Clavius seems to have been mistaken in thinking that the ascent of vapors is prevented by the fire encountered, whence, since they ascend only 52 miles, he concluded that air does not extend farther: but they stop because the primary ray of solar reflection does not extend farther; wherefore, deprived of the vehicle of light and heat, the vapors collect, return to their natural state, and, becoming condensed, are resolved into rains, from which, Resp.

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C.2. Obiectiones contra Elementa Democriti. 93 Resp[ondeo] argumento, negando maiorem, non enim respiramus aerem, vt est purè aer, sed quatenus vapores dilutos secum ve- hit quibus atmosphæra plena est: aer. n. purus à vaporibus in- utilis est respirationi, vnde sicut aqua suffocat, ità aer subtilior est ex suaptenatura, quâ vt sit pulmonibus aptus: mixtus aute[m] vaporibus respirationi aptissimus redditur. Aer itaq[ue] loquelę pulmonum motui, & refrigerationi vsui est, quia ob terræ, & aquæ viciniam frigus quoddam habet, vapores autem hume- ctant ne lingua aut palatum exsiccetur. Quod confirmatur experientiâ, in montibus enim Peruiæ altissimis nisi vapo- ribus à spongia madida ori nasoq[ue] admotâ aer diluatur, ne scilicet benignis vaporibus incomitatus pectus petat, pericu- lum vitæ manifestum est, & qui hoc spongiæ præsidio destituti, in transitu asthmatici tantum fiunt, secum verò præclarè actu[m] existimant. Ergo vtilior est multò respirationi aer sine qua- litatibus primis quam si eas haberet, quia nociuum semper es- set haurire humidum vel frigidum in summo: benigniùs aute[m] insinuant se aeri vapores, & cu[m] illo immixti pectori conducunt. Dices si aer frigidus non est cur ergo ventilamur æstate? Resp[ondeo] in æstu ad solem non sentiri ventilationem eamq[ue] esse inutilem, in vmbra autem vbi aer modicè est refrigeratus vti- lis est, & quod nouæ semper succedant aeris partes, ijs quæ no- stro contactu incaluerant amotis. Reliquas obiectiones si quæ sunt ex doctrina, & adducta, & adducenda nullo negotio diluere quivis poterit.

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C.2. Objections against the Elements of Democritus. 93 I answer the argument by denying the major premise; for we do not breathe air as pure air, but insofar as it carries with it diluted vapors with which the atmosphere is full. Pure air, indeed, is useless for respiration apart from vapors; hence, just as water suffocates, so air by its very nature is thinner, that it may be fit for the lungs. But mixed with vapors it becomes most suited to respiration. Air, therefore, is useful for speech, for the movement of the lungs, and for cooling, because by reason of its proximity to earth and water it has a certain coldness; the vapors, moreover, moisten it so that neither the tongue nor the palate may dry out. This is confirmed by experience: for on the highest mountains of Peru, unless the air is diluted by vapors from a moist sponge applied to the mouth and nose, lest it enter the chest without benign vapors accompanying it, there is manifest danger of death; and those who are deprived of this help of the sponge become asthmatic merely in passing through, yet they think they are very much in possession of their full faculties. Therefore air without the primary qualities is far more useful for respiration than if it possessed them, because it would always be harmful to inhale moisture or cold in the extreme; but vapors insinuate themselves more kindly into the air, and mixed with it they are beneficial to the chest. You will say: if air is not cold, why then do we take air in summer with fans? I answer: in the heat, when exposed to the sun, fanning is not felt and is useless; but in the shade, where the air is moderately cooled, it is useful, because fresh portions of air are continually succeeding one another, after those that had grown warm through contact with us have been removed. Any remaining objections, if there are any, anyone will be able to refute without difficulty from the doctrine, both what has been cited and what is to be cited.

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DISPUTATIO II. De compositione rerum ex atomis. Ræ suppositâ de materiali corporum principio doctrinâ, illud idem materiale contemplaturus est Democritus quatenus ex ipso cætera componûtur, siue vt cōtinuum, & mixtû. Prius quæstio quid sit, fuit faciêda quâ quæstio qualis sit. Vasquez materiâ primâ aristotelicâ existimabat esse totâ in toto, & totâ in qualibet parte, & à quâtitate superueniête fieri diuisibile. Sed pace tanti viri prius subiectu diuisibile est quâ sit quâtâ, na radix originaria distinctionis est indiuiduitas quę separatione seper patitur, radix autę diuisionis actualis est vnio; Quâ titas verò reddit corpus impenetrabile hoc est ità vt cùalijs eode[m] in locoesse no[n] possit, ac proinde diuisibilitate[m] mechanicâ inducit quę manu fit aut ferro, at verò sine quantitate, Angelus materiale principiu[m] corporu[m] posset optimè diuidere, cum partes indiuidualiter differant. Nunc ex his principijs quæ fusiùs comprobare metaphysicorum est, pergo ad maximum Democriticæ philosophiæ mysterium, scilicet ad demonstrationes quod omnia ex atomis sint compacta: progressus in infinitum, indeterminatas productiones, partium confusionem impossibilia sunt nedum quæ satis concipi possint. Equidem damnandus Democritus quod fortuito atomorum concursu mundos infinitos dixerit esse productos, damnandus quod eximiu[m] adeò opus naturæq[ue]; vniuersitatem fortunæ potius cecis impetibus quam prouidentiæ sapientibus mometis dispensari crediderit. Sed si dicamus Deum opt. maximum atomis omnia composuisse verisimiliorem doctrinam sectabimur, planiorem certò, & multò compendiosiorem; quam vt melius insinuem sex ca- pitibus

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DISPUTATION II. On the composition of things from atoms. Given the doctrine of the material principle of bodies, Democritus will contemplate that same material principle insofar as the other things are composed from it, whether as continuous or as mixed. The first question, what it is, must be made before the question what sort it is. Vasquez thought the Aristotelian prime matter to be wholly in the whole, and wholly in any part, and to become divisible through supervening quantity. But with due respect to so great a man, the subject is first divisible insofar as it is quantitative; for the original root of distinction is individuality, which after separation admits of separation, the root of actual division however is union; but quantity makes a body impenetrable, that is, so that with other bodies it cannot be in the same place, and consequently it introduces mechanical divisibility, which is effected by hand or by iron; but without quantity, an Angel could divide the material principle of bodies most excellently, since the parts differ individually. Now from these principles, which it belongs to metaphysics to prove more fully, I proceed to the greatest mystery of Democritean philosophy, namely to the demonstrations that all things are compacted from atoms: progress into infinity, indeterminate productions, confusion of parts are impossible, not to mention what can scarcely be conceived. Indeed Democritus is to be condemned because he said that worlds infinite in number were produced by the fortuitous concourse of atoms; he is to be condemned because he believed that so outstanding a work of nature, and the universe itself, was governed rather by chance’s blind impulses than by the wise motions of providence. But if we say that God, the best and greatest, composed all things from atoms, we shall follow a more probable doctrine, certainly a clearer one, and much more concise; and to explain it better I shall do so in six chapters.

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De compositione rerum ex atomis. 95 pitibus digessi. Primò ne alij non auditi damnétur præcipuas opiniones de continui compositione paucis expendo. Secundò atomis omnia componi probare conor. Tertiù caput in atomorum distinctione specifica, & proprietatibus singularum specierum versatur. Quartum considerat atomos vt in mixtionem veniunt. Quintò, & sextò obiectionibus communibus nobisq[ue] peculiaribus fit satis: mathematicorum autem more vt superius feci definitiones, & principia præmitto. DEFINITIONS. I. Pars determinata est ea quæ habet magnitudinem terminis assignabilibus finitam II. Pars indeterminata est ea quæ nullis terminis assignabilibus finitur. III. Pars communicans est quæ habet aliquid commune cum alia, sic semipalmus est pars communicans palmi. IV. Linea incommensurabilis longitudine cum alia dicitur ea, quæ non est ad aliam vt numerus ad numeru[m], hoc est, de qua institui non potest comparatio per numeros, vt si dicatur linea A...B se habet ad lineam C—D vt 2. ad 4. V. Linea commensurabilis potentia est ea cuius quadratu[m] est commensurabile cum quadrato alterius: sic diameter quadrati, quæ est incommensurabilis longitudine cum costa, est tamen commensurabilis potentiâ, nam quadratum quod ex diametro fit, duplu[m] est quadrato costæ vt patet ex 47. propos. I. Eucl[is] ergo se habent in proportione dupla quæ his numeris efferri potest 4. 8. 16. V 1 Diuisibilitas mathematica, diuisibilitas extrinsecæ, diuisibile designatiuè, per imaginationem, per intellectum penes spatium extrinsecum, sunt terminis synonimi apud Democritum. G VII. Di

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On the composition of things from atoms. 95 I have arranged the chapters as follows. First, so that others who have not been heard should not be condemned, I briefly examine the principal opinions on the composition of the continuum. Second, I try to prove that all things are composed of atoms. Third, the chapter deals with the specific distinction among atoms and the properties of each species. Fourth, it considers atoms as they enter into mixture. Fifth and sixth, common objections and those peculiar to us are answered; but, as is the custom of mathematicians, as I did above, I first set down definitions and principles. DEFINITIONS. I. A determinate part is one which has magnitude limited by assignable boundaries. II. An indeterminate part is one which is not bounded by any assignable limits. III. A communicating part is one which has something in common with another; thus a half-palm is a communicating part of a palm. IV. A line is said to be incommensurable in length with another when it is not related to the other as number to number, that is, when no comparison by numbers can be established, as if one were to say that line A...B is to line C—D as 2 to 4. V. A line is commensurable by power when its square is commensurable with the square of another; thus the diameter of a square, which is incommensurable in length with a side, is nevertheless commensurable by power, for the square produced from the diameter is double the square of the side, as is clear from proposition 47, Book I of Euclid. Therefore those are in double proportion, which can be expressed by these numbers: 4, 8, 16. V 1 Mathematical divisibility, divisibility of the extrinsic, divisible designatively, by imagination, by intellect, in respect of external space, are synonymous terms among Democritus. G VII. Di

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De Atomis. Disput. 2. 96 VII. Diuisibile verò physicè, & realiter est quod ità solui potest vt vnio vel vinculu[m] soluatur ità vt ambæ partes existant separatæ, vel si altera partium sit modus, is pereat, remanente absoluto, sic diuiditur physicè lignum, & carta. VIII. Minimum naturale est minima, extenso sub qua potest corpus aliquod connaturaliter existere: dicitur etiam atomus secundaria. IX. Atomi simplices sunt elementorum indiuisibiles par- ticulæ, & linearum physicarum radices. X. Linea physica est atomorum simplicium adunata series, siue longitudo physica latitudinis physicæ expers, hoc est quæ physicè penes latitudinem sit indiuisibilis, quamuis mathe- maticè etiam secundum latitudinem diuidi possit in infinitum, vt etiam secundum longitudinem. Tot autem eius longitu- tudo patitur diuisiones reales physicasq; quod atomis linea componitur. XI. Superficies physica est extenso in longum, & latum profunditatis physicæ expers, siue est prima veluti atomorum instratio. XII. Figura est quæ sub aliquo vel aliquibus terminis co- præhenditur. XIII. Partes mathematicæ sunt eæ quæ sequuntur diui- sibilitatem mathæmaticam de qua definit. 6. PRINCIPIA I. Ex eo quod res est vel non est potest dici esse vel non es- se. Conceptus enim mensura est rei entitas, mensura autem vocis est conceptus, & ipsa res. II. Radice distinctionis adequatæ in creatis est indiuidua- tio, cuius nota vnica, & infalibilis est diuersa existentia, nam. III. Per illud idem res distinguitur ab omni alia per quod constituitur in suo esse. 4. Eorum

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On Atoms. Disputation 2. 96 VII. What is physically and really divisible is that which can be dissolved in such a way that the union or bond is dissolved, so that the two parts exist separated, or, if one of the parts is a mode, it perishes while the absolute remains; thus wood and paper are physically divided. VIII. A natural minimum is the smallest extension beneath which some body can exist connaturally; it is also called a secondary atom. IX. Simple atoms are the indivisible particles of the elements, and the roots of physical lines. X. A physical line is an assembled series of simple atoms, or a physical length lacking physical breadth, that is, one which, physically speaking, is indivisible with respect to breadth, although mathematically it can also be divided infinitely according to breadth, and likewise according to length. And its length admits so many real and physical divisions as there are atoms by which the line is composed. XI. A physical surface is extension in length and breadth, lacking physical depth, or it is as it were the first arrangement of atoms. XII. A figure is that which is contained under some one or more boundaries. XIII. Mathematical parts are those which follow the mathematical divisibility of which he defines in 6. PRINCIPLES I. From the fact that a thing is or is not, it can be said to be or not to be. For the concept is the measure of the thing’s entity, but the measure of speech is the concept, and the thing itself. II. The root of adequate distinction in created things is individuation, whose one and infallible mark is different existence, for. III. By that same thing a thing is distinguished from every other by which it is constituted in its own being. 4. Of their

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De compositione rerum ex axiomis. 97 IV. Eorum quæ identificantur non datur distinctio realis neq; separatio. V. Non potest concipi quanam ratione id quod tangit secundum se totum possit facere maius, si non habeat virtualiter partes, ac proinde verum est Aristotelis effatum: indiuisibile iunctum indiuisibili non potest facere maius. VI. Natura abhortet processus in infinitum. VII. Qui dat esse dat etiam consequentia ad esse. VIII. Res naturales conantur semper redire ad naturalem suum statum quem primò, & per se appetit natura vt sibi magis conuenientem. IX. Qui appetit finem, appetit etiam media ad illum necessaria. X. Eadem est ratio totius homogenei, & omnium eius partium. XI. Opus naturæ opus intelligentiæ. XII. Similia facilius adunantur, vnde sympathiarum, & amicitiarum paranymphus est similitudo, amor enim similes vel inuenit vel facit, ignis ignem trahit, nam si candelam admoueas foco videbis ad ipsum inclinari candelæ flammam. XIII. Non sunt expendendæ actiones physicæ regulis strictè geometricis. XIV. Sensibilia per sensus sunt iudicanda, nam illius est potentiæ iudicare de re perquam res cognoscitur, neq; fides omnis sensibus deneganda. XV. Positâ experentiâ oportet philosophari, & experientias acuratè factas tanquam principia per se nota admittere. XVI. Vnio siue sit modus realis siue connotation est essentialiter plurium vnio. XVII. Tempus, locus seu spatium, & motus sunt analoga. G 2 POSTV-

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On the composition of things from axioms. 97 IV. Of things that are identified, no real distinction nor separation is given. V. It cannot be conceived by what reason that which touches the whole by itself can make it greater, if it does not have parts virtually, and therefore Aristotle’s saying is true: the indivisible joined to the indivisible cannot make anything greater. VI. Nature abhors a process into the infinite. VII. Whoever gives being also gives the consequences of being. VIII. Natural things always strive to return to their natural state, which nature first, and of itself, desires as more fitting for itself. IX. Whoever desires the end, also desires the means necessary for it. X. The reason of the whole homogeneous thing is the same as that of all its parts. XI. The work of nature is the work of intelligence. XII. Similar things are more easily joined together; hence the likeness of things is the go-between of sympathies and friendships, for love either finds or makes similar things; fire draws fire, for if you bring a candle near a hearth, you will see the flame of the candle incline toward it. XIII. Physical actions are not to be weighed by strictly geometric rules. XIV. Sensible things are to be judged through the senses, for it belongs to that faculty to judge of the thing by which the thing is known, nor is all trust to the senses to be denied. XV. Once experience has been set down, one ought to philosophize, and carefully made experiences to admit as principles known in themselves. XVI. Union, whether it be a real mode or by connotation, is essentially the union of several things. XVII. Time, place or space, and motion are analogous. G 2 POSTV-

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98 De Atomis. Disp. I. POSTVLATA I. Cuiuscunq[ue] motus assignare spatium, & tempus. II. Quolibet assignato numero maiorem assignare, & quælibet linea data, maiorem ducere. III. Quidquid magnitudinem habet, finitamq[ue] extensionem, si pluribus dimensionibus substat concedatur illi suam inesse figuram. CAPVT PRIMVM Sententiæ celebres de compositione continui. PERÆpretium non est singulorum diuersa de continui compositione placita referre aut eorum discutere fundamenta, difficultates proponere, & vniuscuiusq[ue]; iugula manifestis argumentis petere, pauca quædam per synopsum retulisse satis erit instituto meo, qui omni plagiatu abstinere proposui: adeat Aristotelis explanatores philosophiæ candidatus, perlegat Suarem in metaphys. Auersam, Complutenses infinitosq[ue]; alios qui in hac quæstione plurimùm insudarunt, breuiter se se expediet Democritus. PROPOSITIO XIV. Continuum non constat ex punctis mathematicis. Definiuit Euclides punctu mathematicum, cuius pars nulla sit, caret, enim omni dimensione, longitudine scilicet latitudine, & profunditate, & consequenter etiam figurâ nullâ præditum est. Ex punctis mathematicis omnia componi ex antiquis complures, è recentioribus pauci voluerunt, hos inter Ariaga ingenuâ sed tamen nô probabili philosophis confessione

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98 On Atoms. Disputation I. POSTULATES I. To assign space and time to any motion. II. To assign a greater number to any number assigned, and to draw a greater line from any given line. III. Whatever has magnitude and finite extension, if it subsists in several dimensions, let it be granted that it has its own figure. CHAPTER ONE Famous opinions on the composition of the continuous. It is not worthwhile to report the various views of individuals concerning the composition of the continuous, or to discuss their foundations, propose difficulties, and seek the destruction of each by manifest arguments; it will be enough for my purpose, since I have resolved to abstain from all plagiarism, to mention a few things by way of synopsis. Let the student of philosophy consult Aristotle’s interpreters, read Suárez on the Metaphysics, Aversa, the Complutensians, and countless others who have toiled greatly in this question; Democritus will quickly be brought to an end. PROPOSITION XIV. The continuous does not consist of mathematical points. Euclid defined the mathematical point as that of which no part exists; it lacks all dimension, namely length, breadth, and depth, and consequently is also endowed with no figure. That everything is composed of mathematical points was held by many among the ancients, by a few among the more recent, among them Ariaga, in a candid though not a probable confession of philosophers.

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C.1 Seneentiæ de compositione continui. 99 fessione, eam dum pro viribus tuetur, nonnunqua[m] obiectionibus à se fieri satis non posse dicit. Qui punctis mathematicis subscribunt triplicis sunt factionis, alij enim finita simpliciter, & determinatè, alij finita secundum quid seu indeterminatè, alij verò infinita simpliciter puncta in continuo quantumuis paruo admittunt. Qui admittunt finita negant illud axioma Aristolelis, punctum puncto additum non potest facere maius, afferuntq[ue] exemplum è quantitate discreta, vnitas enim addita vnitati facit maius, ad probationem illius maioris quod scilicet punctum tangat secundum se totu[m] ergo non potest facere maius, concedunt antecedens negant conseq[ue]r. Qui autem infinita puncta admittunt in continuo ij cum Platone infinita duo admittunt magnum, & paruum. Vide Arist. 3. phys. t. 27. & isti quidem facilius soluunt argumenta mathematica, quorum 1. hypothesis est postul. 1. huius; nam quomodo diuidetur bifariam linea quinq[ue] punctorum, vel enim intermedium peribit vel alterutri parti adhærebit, si 1. est contra 1. postulatum, si 2. est contra Euclid. lib. 1. prop. 9. Verùm quidquid tandem subterfugij exquirant, clarè eam conuicit fallitatis, & impossibilitatis Aristoteles toto pene lib 6. phys. vbi ostendit motum, tempus, & spatium esse analoga, quare si componeretur continuum ex punctis mathematicis nullus motus altero velocior esset. Scio Arriagâ, vt hanc cæteroqui non solubilem difficultatem eluderet, excogitasse genus quoddam motus quem morulis aut quiete interpolata distinguit: vnde omnia æqualiter moueri vult, sed motus ideò est lentus, quòd mobile sæpius, idemtidem, & diutius quiescat, motus verò ideò censetur velox, quod infrequentiùs mobile quiescat, formica lentius mouetur quanqua quia quod hæc breuioribus pausis suum motum distinguat, illa longioribus: longissimis verò ijsq[ue] frequentibus mouetur animal G 3 illud

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C.1 Opinions on the composition of the continuum. 99 confession, while he defends it to the best of his ability, says that he can by no means sufficiently answer the objections made against him. Those who subscribe to mathematical points are of three factions: for some admit finite points simply and determinately; others finite points in a qualified sense, or indeterminately; others again admit infinite points simply in the continuum, however small it may be. Those who admit finite points deny that axiom of Aristotle, “a point added to a point cannot make a greater”; and they bring forward an example from discrete quantity, for one added to one makes a greater number. In proof of that greater thing, namely that a point touches the whole in itself, therefore it cannot make a greater, they grant the antecedent and deny the consequence. But those who admit infinite points in the continuum, with Plato admit two infinities, the great and the small. See Aristotle, Physics III, text 27. And these indeed more easily solve the mathematical arguments, the first hypothesis of which is the first postulate of this work; for how is a line of five points divided in half? For either the middle point will disappear, or it will adhere to one of the two parts; if the first, it is against the first postulate; if the second, it is against Euclid, book I, proposition 9. But whatever escape they may seek, Aristotle clearly refutes it as false and impossible throughout nearly the whole of book VI of the Physics, where he shows that motion, time, and space are analogous; therefore, if the continuum were composed of mathematical points, no motion would be faster than another. I know that Arriaga, in order to evade this otherwise unsolvable difficulty, devised some kind of motion which he distinguishes by pauses or intermittent rest; hence he wants all things to move equally, but motion is therefore slow because the moving thing rests more often, the same thing again and again, and for longer; motion is judged swift because the moving thing rests less often. An ant moves more slowly, although because it distinguishes its motion with shorter pauses, that one with longer pauses: but the animal moves with the longest and those frequent pauses, that

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De Atomis. Disput. II. illud americanu[m] cui à lento infessu pigritiæ nomen est factum, duobus enim diebus totidemq[ue] noctibus non conficiet iter 10. passum. Qui ergo huic de punctis mathematicis sententiæ subscribunt concedunt. 1. punctum puncto additum facere maius. 2. non darimotum successium sed tantum discretum. 3. motus omnes æqualis esse velocitatis, sunt enim puncta minimum quod pertransiri possit, & quies quæ in his motibus inesse fingitur, non est motus, 4. Tempus etiam ex instantibus componut, 5. debet necessariò concedere rotam dissolui dum mouetur circa axem, nam cum circulus ad axem lentius moueatur debet quiescere d[omi]ni circulus maior in circumferentia constitutus mouetur, ergo cum saltem vno puncto circulus exterior præcedat sequitur puncta eadem punctis ijsdem non correspondere: quod est absurdum, & incredibile, ergo continuum non constat ex punctis mathematicis. PROPOSITIO XV. Continuum non componitur ex partibus, & punctis mathematicis simul. SVarez hanc tuetur sententiam in metaphys. disput. de quantitate, vbi dicit dari puncta quæ partes partibus iungant, sed præterquam quod easdem difficultates habet quas opinio superior, nouis insuper implicatur dùm partes admittit, quanam enim ratione intelligi possunt vnit[ur] aut terminat[ur] nisi puncta adæquentur partibus? deinde cum puncta illa entia sint modalia vt volunt, nonne concedere debet partes entia scilicet absoluta sine ijs esse posse? amplius cum nô detur pars ultima quomodo dabitur punctu[m] ultimum id est terminatiu[m]? præterea vel inter vnum indiuisibile, & alia indiuisibilia intermediat aliquid vel nihil, si primum erit ergo pars sine punctis, si se-

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On Atoms. Disputation II. that American to whom, from a sluggish attack, the name of laziness has been given, for in two days and as many nights he will not complete a journey of 10 paces. Therefore those who subscribe to this opinion concerning mathematical points grant: 1. that a point added to a point makes something larger. 2. that there is not a continuous motion, but only a discrete one. 3. that all motions are of equal speed, for points are the least thing that can be traversed, and the rest which is supposed to be in these motions is not motion. 4. Time also is composed of instants. 5. One must necessarily grant that a wheel is dissolved while it moves around an axis; for since the circle moves more slowly toward the axis, the outer circle placed in the circumference ought to be at rest; therefore, since the outer circle is ahead by at least one point, it follows that the same points do not correspond to the same points: which is absurd and incredible; therefore the continuum does not consist of mathematical points. PROPOSITION XV. The continuum is not composed of parts and mathematical points together. Suárez defends this view in the Metaphysical Disputations on Quantity, where he says that points exist which join parts to parts; but besides the fact that it has the same difficulties as the previous opinion, it is further involved in new ones while it admits parts; for by what reason can they be understood as united or terminated unless points are made equal to parts? Then, since those points are, as they wish, modal beings, must he not concede that parts, namely absolute beings, can exist without them? Moreover, since no last part is given, how will there be a last point, that is, a terminal one? Furthermore, either between one indivisible and other indivisibles there intervenes something, or nothing; if the first, then there will be a part without points,

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C. I. Sententia de compositione continui. 101 si secundum totum constabit indiuisibilibus. Hæc Suaris opinio, omnium difficillima est, omnium enim obiectiones suas facit, & nulla vitat argumenta quæ sint alicuius momenti. PROPOSITIO XVI. Continuum non constat ex simplici entitate ante diuisionem indistincta. Albertinus huius factionis caput est negat enim partes continui ante diuisionem actualem esse distinctas inter se Eamq[ue] dicendi rationem excogitauit vt difficultati de partium distinctione occurreret. Contendit is distinctionem omnem pendere ab extrinseco hoc est per designationem vel diuisione actualem. Sed vnico argumento quod instar omnium est, refelli potest. Quæ possunt existere actu separata distinguntur realiter, sed partes possunt existere actu separatæ, ergo distinguntur realiter etiam ante diuisionem, diuisio enim non dat eis entitate[m], & indiuiduationem quæ ipsis est intrinseca, & est radix distinctionis. Maior syllogismi est vnica distinctionum regula quâ si neget Albertinus quomodo probabit Aristotelem à Platone distingui? minor est certa etiam sensu, pars enim A est sine parte B quamuis antea vnum continuum facerent, quod autem radix distinctionis sit propria entitas prob. ex princip. 3. per illud idem res distinguitur ab omni alia per quam constituitur in suo esse, sed singulæ constituuntur in suo esse per sua[m] entitatem ergo per illam distinguntur à quauis alia, deinde non potest dici pars A est pars B ergo pars A distinguitur realiter à parte B quæ ex 1. 2. 3. & 4. principio nota sunt. G 4 PROPO-

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C. I. Opinion on the composition of the continuum. 101 if according to the whole, it will consist of indivisibles. This opinion of Suaris is the most difficult of all; for it raises objections against everyone, and avoids no arguments that are of any weight. PROPOSITION XVI. The continuum does not consist of a simple entity indistinct before division. Albertinus is the head of this faction; for he denies that the parts of the continuum, before actual division, are distinct from one another. And he devised this way of speaking in order to meet the difficulty about the distinction of parts. He maintains that every distinction depends on something extrinsic, that is, on designation or actual division. But this can be refuted by a single argument, which is worth all the rest. Things that can exist actually separated are really distinct; but parts can exist actually separated; therefore they are really distinct even before division, for division does not give them entity and individuation, which are intrinsic to them and are the root of distinction. The major premise of the syllogism is the only rule of distinctions; if Albertinus denies it, how will he prove that Aristotle is distinguished from Plato? The minor premise is certain even by the senses, for part A exists without part B, although they formerly made one continuum; and that the root of distinction is proper entity is proved by principle 3. By that same thing a thing is distinguished from every other by which it is constituted in its being; but singular things are constituted in their being by their own entity; therefore by that entity they are distinguished from any other. Next, it cannot be said, part A is part B; therefore part A is really distinct from part B, which are known from principles 1, 2, 3, and 4. G 4 PROPO-

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102 De Atomis Disp. II. PROPOSITIO XVII. Continuum non constat partibus syncategorematicè infinitis. H Anc opinionem vulgus philosophorum nunc docent: sed quàm malè ingenia torqueat norunt studiosi omnes: suu[m] fundamentum duplex est, primum sumitur ab Aristotele lib. de lineis insecabilibus vbi argumentis mathematicis probat nullam dari lineam indiuisibilem. Secundò inducuntur in hanc sententiam ex ratione motus localis, & temporis quod cum semper fluat nullamq[ue]; habeat partem totam simul sitq[ue]; in infinitum diuisibile sequitur eius etiam partes infinitas esse syncategorematicè; Sed facilè his rationibus suo loco satisfaciemus, dum ipsi in spinis defixi hærebunt, sic enim inuoluuntur in numero, distinctione, diuisione, comparabilitate, & motu, vt quę responsa nunquam percipere potui aut argumétis nitidissimis commodè aptare, neq[ue]; etiam illis quidquam dare possim probabilitatis, cum optimus veritatis character sit lux, & claritas, in illis autem meras tenebras reperi. V. Arriagam, Complutenses, Ouiedum, Sua- rem, aliosq[ue]; PROPOSITIO XVIII. Numerus partium continui non est sicuti numeri finiti possibiles. Hæc opinio nititur ingeniosissimo analogismo quantitatis discretę ad continuam. I. Sicuti tota collectio numerorum finitorum possibilium est finita, sed limitibus incertis, ità tota collectio partium finita est sed indeterminatè. II. Sicuti numerorum finitorum maximus assignabilis non est, ità neq[ue]; in partibus assignari nequit minima. III. Omnis numerus finitus est secundu[m] quid distinctus, & secundum quid indistinctus: nam idem numerus terna-

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102 On Atoms, Disputation II. PROPOSITION XVII. A continuum does not consist of syncategorematically infinite parts. This opinion is now taught by the common run of philosophers; but all students know how badly it troubles minds. It has a double foundation: first, it is taken from Aristotle, Book On Indivisible Lines, where by mathematical arguments he proves that no indivisible line can be given. Secondly, they are led to this view from the reasoning of local motion, and of time, which, since it always flows and has no whole part all at once and is divisible into infinity, it follows that its parts too are syncategorematically infinite. But we shall easily answer these reasons in their proper place, while they themselves, fixed on thorns, remain entangled; for thus they become involved in number, distinction, division, comparability, and motion, so that the answers which I could never discern or conveniently fit to the most polished arguments, nor could I give them anything of probability, since the best mark of truth is light and clarity, but in those matters I find only darkness. See Arriaga, the Complutenses, Oviedo, Sua- rez, and others. PROPOSITION XVIII. The number of parts of a continuum is not like the numbers of possible finite things. This opinion rests on a most ingenious analogy of discrete quantity to continuous quantity. I. Just as the whole collection of possible finite numbers is finite, but with uncertain limits, so too the whole collection of parts is finite, but indeterminately. II. Just as among finite numbers there is no assignable greatest, so also among parts there is no assignable least. III. Every finite number is in one respect distinct and in another respect indistinct: for the same number is terna-

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C. I. Sententiæ de compositione continui. 103 ternarius potest comparari cum alio ternario à quo distingui- tur realiter adæquatè, vel potest comparari cum binario quem includit, & ab illo distinguitur realiter inadæquatè, vel potest comparari cum tribus vnitatibus collectiùè sumptis, & sic di- tinguitur tantùm secundum precisiuam intellectus formalita- tem. Sic palmus distinguitur adæquatè ab alio palmo, inadæ- quatè à semipalmo sui, & formaliter tantùm à duobus semipal- mis. IV. Sicuti numeri finiti possibiles dicuntur secun- dum quid indeterminati, communicantes, inassignabiles; ità & partes continui quæ necessariò in alijs includuntur: nullaq[ue]; communicans est quæ suis partibus non constet quarum respe- ctu est totum. V. Sicuti per intellectum numeri finiti possibi- les ponuntur extra causas, ità intellectus vi pars indetermina- ta, & communicans fit totum determinatum, sublata habitu- dine quam cum alijs habebat. Destruo hanc opinionem. I. Numeri finiti constant indi- uisibilibus vnitatibus suntq[ue]; entia formaliter intentionalia, & de omnibus numeris licet habere communem mensuram, id est vnitatem, atqui ex aduersario continuum non constat ex indi- uisibilibus, partes continui sunt omnes à parte rei, neq[ue]; cuiusuis magnitudinis datur mensura communis ex Euclide l. 10. vbi lineas incommensurabiles dari ostendit, ergo vitiosus est analo- gismus. II. Implicat omnes numeros finitos possibiles poni simul extra causas, quare cum non possint esse ne quidem per intellectum collectiùè, quomodo concedit aduersarius esse rea- liter à parte rei, materialiter enim existerent si vera esset eius opinio. III. Tot erunt partes in grano coriandri quot in to- rius terræ globo, vtrobiq[ue]; sicuti numerorum finitorum colle- ctio, quod est contra primam notionem Eucl. totum maius est sua parte. Quod cognoscens accutissimus Lucretius l. 1. ità argumentatur. Ergo

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C. I. Sentences on the composition of the continuum. 103 A ternary can be compared with another ternary from which it is really and adequately distinguished, or it can be compared with a binary which it includes, and from which it is really and inadequately distinguished, or it can be compared with three units taken collectively, and thus it is distinguished only according to the precise formal consideration of the intellect. Thus a palm is adequately distinguished from another palm, inadequately from half a palm of itself, and formally only from two half-palms. IV. Just as finite possible numbers are said in a certain respect to be indeterminate, communicable, inassignable, so also are the parts of the continuum, which necessarily are included in others: and there is no communicable thing which does not consist of its parts in relation to which it is a whole. V. Just as, by means of the intellect, finite possible numbers are posited outside their causes, so, by the intellect, a part that is indeterminate and communicable becomes a determinate whole, when the relation it had to others is removed. I reject this opinion. I. Finite numbers consist of indivisible units and are entities formally intentional, and a common measure, that is, unity, may be had for all numbers; but in the opponent’s view the continuum does not consist of indivisibles, the parts of the continuum are all in reality, and no common measure of any magnitude is given according to Euclid, book 10, where he shows that incommensurable lines can exist; therefore the analogy is faulty. II. It implies that all finite possible numbers are simultaneously posited outside their causes; wherefore, since they cannot be even by the intellect collectively, how does the opponent concede that they are really on the side of the thing? For they would exist materially if his opinion were true. III. There will be as many parts in a grain of coriander as in the globe of the whole earth, and in both cases as in the collection of finite numbers, which is contrary to the first notion of Euclid: the whole is greater than its part. Recognizing this, the most acute Lucretius, book 1, argues thus: Therefore

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CAPVT SECUNDVM. Quod omnia ex atomis consent. Oruissem quadraginta duas de compositione cõtinni referre sententias, in quibus noua inuenta nouis, & inextricabilibus fruticant difficultatibus, sic vt hydre videantur quibus dissecta capita ex proprio interitu exitiali fænore nascendi, & multiplicandi se se ius habent. Nunc sepultam in puteo veritatem Democriti auspicijs hauriamus. PROPOSITIO XIX. Continum componitur ex atomis, siue corpusculis finitis numero, adæquatè inter se distinctis, certæ & determinatæ areæ. Hanc opinionem probabo cum aliquid ordine methodico de nomine atomi premisero. ATOMOS vocabulum, est grecum à radice temno, & verbali TOMH, id est sectio, quare atomos idem est atq[ue] indiuisibile. Sumitur diuersimodè nam ludorus 1. 13. etymolog. c. 2. agnoscit atomos incorpo- re,

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CHAPTER TWO. That all things consist of atoms. I had intended to relate forty-two opinions concerning the composition of the continuous, in which new inventions sprout with new, and inextricable, difficulties, so that they seem like hydras, whose severed heads have the right, by their own ruinous death-payment, to be born again and multiply themselves. Now let us draw from the well the truth buried there under Democritus’s auspices. PROPOSITION XIX. The continuous is composed of atoms, or of little bodies finite in number, adequately distinct from one another, within a certain and determinate area. I shall prove this opinion after first premising something in orderly method about the name of atom. The word ATOM is Greek, from the root temno, and the verbal TOMH, that is, cutting; wherefore atomos means the same as indivisible. It is taken in different senses, for Ludorus, in book 1, chapter 13 of the Etymologicon, recognizes atoms incorpore-

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C.1. Sententiæ de compositione continui. 105 re, tempore, numero, & littera. Deinde vulgus minutiorem puluerem volantesq[ue]; in aere festucarum laciniolas atomos vocat cum tamen mixta sint. Tertiò, quamuis nominis ATO- MOS derivatio oriatur à radice temno, vt ait Isidorus, Plu- tarchus, Scapula, Budæus, & alij, tamen dici posset cum Hesychi generari à radice ATMOS, quod significat flatum, halitum, vaporem, fumum, præcipuorum naturæ corporum aeris, terræ, aqueæ, & ignis corollaria, & à mixtione ad dissolu- tionem, vel ab interitu ad generationem pergentium sympto- mata, vt scilicet hac etymologia habeamus veluti ansam du- bitandi, an diuini illi Nomenclatores, quos apprimè laudauit Plato in Cratylo, omnia ex atomis componi crediderint, cùm huiuscemodi vocabulum cum elementorum dispersione, quæ per corpuscula fieret, nonnihil habeat similitudinis; quapro- pter atomus istis, idem sonabat quod nobis vaporum aut fumi particulæ, nomen certè atmos etia apud Plutarchu[m] in eo sensu sumitur non semel. Tertiò propriè, & clarè nihil est aliud quâ corpusculum tantæ paruitatis eiusq[ue]; genij vt nullatenus diuidi possit, differtq[ue]; à puncto mathematico quod huius nulla sit pars neq[ue]; intrinseca neq[ue]; per designationem, eademq[ue]; sui vir- tualitate qua spectat orientem, occidenti adspirat, neq[ue]; vllor modo concipi potest quacunq[ue]; dimensione donatum, atomus autem suas habet dimensiones, suas virtualitates correspon- dentes spatio sed cum perfecta indiuisibilitate, & quamuis fi- gurâ coerceatur non ideò tamen physicam diuisionem pati vnquam poterit. His ità præexplicatis, adduci possunt octo fundamenta, quibus hæc Democriti princeps opinio propu- gnari posset. Primum fundamentum. Natura ex princip. 6. omnem re- fugit infinitatem, ergo eius principiu[m] materiale non est infini- tas: sed si continuum haberet partes infinitas vel categorema- ticè

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C.1. Opinions on the composition of the continuous. 105 in number, time, and letter. Then the common people call the finer dust and the little floating strips of straw in the air atoms, although they are mixed things. Third, although the derivation of the name ATOMOS comes from the root temno, as Isidore, Plutarch, Scapula, Budé, and others say, it could nevertheless be said, with Hesychius, to be generated from the root ATMOS, which means breath, exhalation, vapor, smoke, the corollaries of the principal natural bodies of air, earth, water, and fire, and symptoms proceeding from mixture to dissolution, or from destruction to generation; so that by this etymology we may have, as it were, a handle for doubting whether those divine Nomenclators, whom Plato especially praised in the Cratylus, believed that all things are composed of atoms, since this kind of word has some similarity to the dispersion of elements, which would be made through little bodies; wherefore, to those people, atomus sounded the same as for us the particles of vapor or smoke, and the name atmos itself is also taken in this sense not once in Plutarch. Thirdly, properly and clearly, it is nothing other than a little body of such smallness and nature that it can in no way be divided, and it differs from a mathematical point, because the latter has no part, neither intrinsic nor by designation, and with the same virtuality by which it looks toward the east it breathes toward the west; nor can it in any way be conceived as endowed with any dimension. But an atom has its dimensions, its corresponding virtualities, with respect to space, yet with perfect indivisibility; and although it is bounded by shape, it cannot on that account ever undergo physical division. These things having thus been previously explained, eight foundations can be adduced by which this chief opinion of Democritus could be defended. First foundation. Nature, according to principles 6, rejects all infinity; therefore its material principle is not infinity. But if the continuous had infinite parts, either categorically

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106 De Atomis Disp. II. ticò vel indeterminatè eius principium materiale esset vagum, & indeterminatu[m], ergo partes continui non sunt infinitæ neq[ue] numeri indeterminati, ergo datur prima, & vltima, quod admitti non potest quin atomi consequenter admittâtur, quâ- doquidem euidentes sunt contra puncta mathematica præsertim finita demonstrationes. Ordo qui ità naturæ, & sapienti rerum omnium architecto Deo cordi est, sine numero seruari non potest, qui quidé numerus finitus est absolutè sic vt suis mensuris contineatur. Secundùm fundamentum. Auicenna in 1. Fen. doctrina 1. c. 1. sic definit temperamentum, vt sit, qualitas quæ oritur ex mutua actione, & passione contrariarum qualitatum elementorum quorum partes ità ad minima sunt redactæ, vt cujusque earum plurimum contingat, plurimum alterius prouerit, cum enim ità mutuò patiuntur, & agunt &c. Vnde sic argumentor. Elementa constant ex minimis, ergo constant ex indiuisibilibus, sed elementa ex præmissis sunt materia prima, ergo materia prima constat ex puris indiuisibilibus, hoc est atomis, prob. antecedens. Conditiones intrinsecæ ad agendum necessariæ annumerantur inter dispositiones ad formæ introductionem aut rei conseruationem, ratio est quia cum esse sit propter operari, neq[ue] sine illis conditionibus possit esse agens in actu 1. ad operandum, sequitur etiam neq[ue]; vllò modo sic esse posse connaturaliter. Conditiones autem illæ ad agendum necessariæ dicuntur intrinsecæ cum se tenent ex parte agentis, extrinsecæ cum ex parte medij vel passi, atqui inter conditiones intrinsecas ad agendum necessarias est extensio certa, & determinata, infra quâ si restringatur agens, nullam omnino actionem parere poterit, ergo neq[ue]; vt sic, poterit existere, quare philosophi communi fere consensu etiam in elementis admiscere minima, quæ alijs termini paruitatis, ab alijs

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106 On Atoms, Disp. II. if, whether it be determinately or indeterminately, its material principle were vague, and indeterminate, therefore the parts of the continuum are not infinite nor of an indeterminate number, therefore there is a first and a last, which cannot be admitted unless atoms consequently be admitted, since demonstrations against mathematical points, especially finite ones, are evident. The order which is thus dear to nature, and to the wise architect of all things, God, cannot be preserved without number, which number indeed is finite absolutely, so that it is contained within its own measures. Second foundation. Avicenna, in 1. Fen. doctrine 1. c. 1, defines temperament thus, that it is a quality which arises from the mutual action and passion of the contrary qualities of the elements, whose parts are reduced to the smallest, so that as much of each of them as comes into contact with the other benefits the other as much; for when they thus mutually undergo and act, etc. Whence I argue thus. The elements consist of minima, therefore they consist of indivisibles; but the elements, from the premises, are prime matter; therefore prime matter consists of pure indivisibles, that is, atoms. Proof of the antecedent. The intrinsic conditions necessary for acting are counted among the dispositions for the introduction of form or the preservation of a thing; the reason is that since being is for the sake of acting, neither without those conditions can there be an agent in act 1. for acting, it follows also that neither in any way can it be so by nature. But those conditions necessary for acting are called intrinsic when they pertain to the side of the agent, extrinsic when from the side of the medium or the patient; but among the intrinsic conditions necessary for acting there is a certain and determined extension, below which if the agent is restricted, it will be able to produce absolutely no action at all; therefore neither, as such, will it be able to exist, wherefore philosophers by almost common consent also in the elements admit minima, which by some are called limits of smallness, by others

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C. 2. Omnia componi ex atomis. 107 alijs termini extensiui, ab alijs minima quod sic, ab alijs diminutę entitates à Virgilo in physica sua allegorica, hoc est in Si- leni Ecloga, semina rerum, à Democrito nostro atomi, & radi- ces corporum nominantur, his ità stabilitis, Probatur cons. primi argumenti minima scilicet illa esse atomos Democriticas, hoc est corpuscula diuisionis omnis inca- pacia. Primò quidem contra eos qui negant materiam primâ peripateticam posse esse sine forma cum tamen minima dari confiteantur, sit minimum ignis A, peto vt diuidatur: debent ipsi ex suis principijs admittere hypothesim, & concedere igne destruendum, quod scilicet nulla deinceps forma subitura sit, tùm quod non sint dispositiones, tùm quod omnium formaru[m] simplicissima sit elementaris quę cum ibi subsistere non possit, multò minus de alia concedi debet. Ergo vel materia erit de- stituta omni forma vel dabitur annihilatio naturalis, quod ad- uersarius negauerat antea: restat ergo huiuscemodi minima elementalia esse indiuisibilia. Probatur secundò etiam ad hominem, materia est propter formas sed formæ non possunt esse in minori extensione quàm habent minima, ergo neq; materia potest in minorem particu- lam diuidi, quod si supponatur diuisa, illi non conueniet de- finitio materiæ primæ, erit enim vt sic, formæ omni inepta, ergo ex minimorum doctrina redditur probabile dari atomos. 111. Fundamentum sumitur à ratione creationis: Tot sunt creationes in materia prima quot sunt indiuidua sed nul- lum indiuiduum est indeterminatum ergo nulla creatio pariter erit indeterminata, sequitur itaq; quod omnes partes continui sunt adæquatè distinctæ à quibuslibet alijs, ergo sunt indiuisi- biles, & ratio à priori est, quia nihil ponitur extra causas nisi in indiuiduo, quidquid autem est in indiuiduo distinguitur adæ- quatè à quous alio per princip. 3. IV. Fun-

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C. 2. All things are composed from atoms. 107 by others extended terms, by others minima, as it were, by others diminished entities called by Virgil in his allegorical physics, that is, in the Silenus Eclogue, seeds of things; by our Democritus atoms, and roots of bodies. These things being thus established, it is proved by the conclusion of the first argument that the minima are those Democritean atoms, that is, little bodies incapable of all division. First, indeed, against those who deny that primary Peripatetic matter can exist without form, while nevertheless they admit that minima are given: let the smallest fire be A; I ask that it be divided. They themselves, according to their own principles, ought to admit the hypothesis and concede that the fire is to be destroyed, namely that no form is thereafter to be received, both because there are no dispositions and because the simplest of all forms is the elementary one, which since it cannot remain there, much less ought it to be conceded of another. Therefore either matter will be deprived of every form, or natural annihilation will be granted, which the opponent had previously denied. It remains, then, that minima of this sort are indivisible. It is proved secondly, also ad hominem: matter exists for the sake of forms, but forms cannot be in a smaller extension than the minima have; therefore matter too cannot be divided into a smaller particle. And if it be supposed divided, the definition of primary matter will not fit it; for it will be, as such, unfitted for every form. Therefore from the doctrine of minima it is made probable that atoms are given. 111. The foundation is taken from the notion of creation: as many creations are there in primary matter as there are individuals, but no individual is indeterminate; therefore no creation likewise will be indeterminate. It follows, then, that all parts of the continuum are adequately distinct from any others; therefore they are indivisible. And the reason a priori is that nothing is posited outside its causes except in an individual; but whatever is in an individual is adequately distinguished from any other by principle 3. IV. Fun-

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De Atomis. Disp. II. IV. Fundamentum sumitur à natura vnionis, ad cuius intelligentiam suppono ens modale eius esse naturæ vt iungatur semper absoluto neq[ue]; sine ipso possit subsistere. Sic, exempli gratia, intellectio sine intellectu non potest esse, quamuis intellectus esse possit sine intellectione; vnio non potest esse sine partibus quamuis partes esse possint sine vnione. Vnde sic argumentor. Illud tantum quod fit independenter à subiecto est terminus creationis, sed vnio non fit independenter à subiecto, ergo vnio nô est terminus creationis. Cum ergo terminus creationis in materia prima careat omni vnione, sequitur quod est ex indiuisibilibus, diuisibilitas enim oritur ab vnionis solutione. Confirmatur ex princip. 7. subiectum vnde elicitur aliud prius est natura illo quod elicitur, sed partes materiæ primæ sunt subiectum vnde elicitur vnio, ergo sunt prius natura omni vnione, ergo in illo priori naturæ debent intelligi sine vlla vnione, ac proinde indiuisibiles. Dices non posse intelligi sine vnione aliqua implicita. Sed contra. Illud quod non est de essentia rei non ingreditur conceptum rei, sed vnio non est de essentia partium materiæ primæ ergo non ingreditur earum conceptum; Maior est certa ex princip. 1. probatur minor, nullus modus actualis est de essentia rei, sed vnio est modus actualis partium, ergo non est de essentia neq[ue]; de illarum conceptu, si ergo partes concipiuntur sine vnione intelliguntur indiuisibiles: dixi modum actualem, quia modus quatenus abstrahit ab existentia est de essentia aliquarum potentiarum quæ ab illo specificantur: sic intellectus dicit essentialem ordinem ad intellectionem, actualitas tamen intellectionis non est de eius essentia, alioqui necessariò semper intelligeret actu. Cum ergo in illo priori naturæ vel temporis partes materiæ primæ intelligantur sine vlla vnione sequitur

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On Atoms. Disp. II. IV. The foundation is taken from the nature of union, for the understanding of which I suppose that a modal being is of such a nature that it is always joined to an absolute being, nor can it subsist without it. Thus, for example, intellection cannot be without intellect, although intellect can be without intellection; union cannot exist without parts, although parts can exist without union. Whence I argue thus. That alone which comes to be independently of a subject is the term of creation, but union does not come to be independently of a subject; therefore union is not the term of creation. Since therefore the term of creation in prime matter lacks all union, it follows that it is composed of indivisibles, for divisibility arises from the dissolution of union. This is confirmed by principle 7: the subject from which something else is elicited is by nature prior to that which is elicited; but the parts of prime matter are the subject from which union is elicited; therefore they are by nature prior to every union; therefore in that prior state of nature they must be understood without any union, and consequently as indivisible. You will say that they cannot be understood without some implicit union. But on the contrary. That which is not of the essence of a thing does not enter into the concept of the thing, but union is not of the essence of the parts of prime matter; therefore it does not enter into their concept. The major premise is certain from principle 1. The minor is proved: no actual mode is of the essence of a thing, but union is the actual mode of the parts, therefore it is not of their essence nor of their concept; if therefore the parts are conceived without union, they are understood as indivisible. I said actual mode, because a mode, insofar as it abstracts from existence, is of the essence of certain powers which are specified by it: thus the intellect indicates an essential order to intellection, yet the actualization of intellection is not of its essence; otherwise it would necessarily always be actually understanding. Since therefore in that prior state of nature or time the parts of prime matter are understood without any union, it follows

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C.2. Omnia componi ex atomis. 109 sequitur eam etiam intelligi constare ex atomis neq; dicas posse carere hæc vel illa vnione non tamen omni, quia cum vnio siue distributiue siue collectiue, siue determinatè, aut indeterminatè intelligatur, educatur è partibus, sequitur partes esse priores naturà, ac proinde in illo priori intelliguntur sine vlla vnione, ergo indiuisibiles. Hoc certè fundamentum satis est pro Democrito validum. V. Fundamentum sumitur ab impossibilitate partium infinitarum in continuo. Tot sunt extensiones quantitatiuæ quot sunt physicæ partes, sed nemine cogitante sunt infinitæ syncat gorematicè, erunt ergo totidem extensiones, atqui impossibile est vt infinitæ actu existentes extensiones faciant tantum vnam finitam, ergo etiam est impossibile finitam extensionem constare ex infinitis actu existentibus. Dices primò esse tantum syncategorematicè infinitas. Sed contra, nihil est hìc in potentia, ergo omnes sunt actu, sed infinitum syncategorematicum dicit aliquid actu, aliud in potentia, ergo hìc non sunt infinitæ syncategorematicè, cùm enim nulla sit quæ non augeat continuum sequitur esse incrementa actu infinita. Dices secundò argumentum transire à partibus indeterminatis ad determinatas. Sed contra. Nulla est quæ non existat, ergo nulla est indeterminata, quidquid enim existit, existit in indiuiduo, omne autem indiuiduum est determinatum. Dices tertio à distributiuo ad collectiuum non valere. Sed contra, si hoc argumentum non concludat, sunt extensiones actu infinitæ, ergo totum resultans est infinitum in extensione: quomodo probabunt infinitis cubitis fieri infinitum categorematicum in extensione. VI. Fundamentum. Rationibus istis accedunt experien- tiæ

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C.2. All things are composed from atoms. 109 it follows that it too is understood to consist of atoms; nor should you say that this or that union may be lacking, though not every union, because when union, whether distributively or collectively, whether determinately or indeterminately, is understood to be drawn from the parts, it follows that the parts are prior by nature, and consequently in that prior state they are understood without any union, therefore indivisible. This certainly is a foundation sufficiently strong for Democritus. V. The foundation is taken from the impossibility of infinite parts in a continuum. There are as many quantitative extensions as there are physical parts, but by no one thinking of them they are infinite syncategorematically; there will therefore be just as many extensions, yet it is impossible that infinitely many actually existing extensions make only one finite one, therefore it is also impossible for a finite extension to consist of infinitely many actually existing things. You will say first that they are only syncategorematically infinite. But on the contrary, nothing here is in potency, therefore all are in act; but the syncategorematic infinite says one thing in act, another in potency, therefore here they are not syncategorematically infinite, since there is none that does not increase the continuum, it follows that there are actually infinite increments. You will say secondly that the argument passes from indeterminate parts to determinate ones. But on the contrary. There is none that does not exist, therefore none is indeterminate; for whatever exists, exists in an individual, and every individual is determinate. You will say thirdly that the transition from distributive to collective does not hold. But on the contrary, if this argument does not conclude, there are actually infinite extensions, therefore the resulting whole is infinite in extension: how will they prove that by infinite cubits an infinite categorematic thing is made in extension. VI. Foundation. To these reasons are added experiences

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De Atomis. Disput. II. tiæ Chymicorum quas videbis apud Danielem Sennertum in hyponeumate 3. c. 2. vbi de atomis illo vnico capite tractat, quod illibatum tibi relinquo in fonte videndum. Curiosiorem habeo experientiam, & naturali miraculo propiorem ex Iacobo Gafarello in suis curiositatibus inauditis. Illam paucis expono quod scilicet in ea tanquam in speculo, Democriticæ philosophiæ mysterium omne refulgeat. Narrat, ille oculatosq; testes appellat suo nomine, viros graues, & suæ domi fatis notos, qui in Poloni Medicinumusco phialas complures viderunt, in quarum fundo pulueres ex arte præparati florum animas in cineribus conseruabant, viuebantq; veluti suis in vnis. Spectaculum hospitibus gratum exhibiturus doctissimus ille chymicus, accensam candelam detentæ in aere phialæ qua rose cineres preparati asseruabantur certâ distantiâ supponit, vix calor se se in vitrum insinuaverat, cum ecce tibi mo- ueri corpusculorum puluerisq; populos, cinerem illum leniter agitari, dum tandem post horę fere interuallum totus ille puluis collecto calore in media phialæ area suspensus, varijs deinceps confusisq; motibus vndiquaq; cieri cepit: sicut dum apes alucaria mutantes in aeris medio in nubem coactę confuso volatu hinc, & inde per sua castra volitant: tandem varijs agitationibus, quasi se se atomi ad vnionem queritarent, paulatim in rosam perfectissimam corpuscula illa coaluerunt, cui neq; in folijs ordo, neq; color, neq; meditullium croceum deessè videbatur. Sed spectaculum remotà candelà statim desijt, recidentibus ad phialę fundum atomis, quæ caloris vi in aere detinebantur, vt quotidie radiorum solarium beneficio festucis pulueriq; contingit; & vnaquæq; quem in rosa nondum dissoluta locum occupauerat, eundem in huiuscemodi artificiosa restitutione obtinebat; non secus ac subtilissimus huius seculi philosophus Cabeus post Gilber. 1. 1. c. 18. in philosophia magnetica

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On Atoms. Disput. II. of the Chymists, which you may see in Daniel Sennert in Hypomneumata 3. c. 2. where he treats of atoms in that one chapter, which I leave untouched for you to see in the source. A more curious experiment I have, and one closer to a natural miracle, from Jacobus Gafarellus in his Unheard-of Curiosities. I set it forth briefly, because in it, as in a mirror, the whole mystery of Democritean philosophy shines forth. He relates—and he calls as eyewitnesses by name—grave men, and well known in his own house, who in a Polish medicinemusco saw several phials, in the bottoms of which powders prepared by art preserved the souls of flowers in ashes, and lived as it were in their own substance. When that most learned chymist wished to offer his guests a pleasing spectacle, he places a lighted candle beneath the phial held in the air, at a certain distance, in which the prepared rose ashes were preserved; hardly had the heat insinuated itself into the glass, when lo, the little bodies and the crowds of powder begin to move, the ash to be gently stirred, until at length after nearly an hour’s interval the whole powder, with the heat gathered up, suspended in the middle region of the phial, began afterward to be stirred everywhere by various and confused motions: just as when bees, changing their hives, are driven together in the middle of the air into a cloud, and with confused flight fly here and there through their camp. At last, by various agitations, as if the atoms were seeking union with one another, little by little those corpuscles coalesced into a most perfect rose, in which there seemed to be lacking neither order in the petals, nor color, nor the saffron-colored center. But the spectacle ceased immediately when the candle was removed, the atoms falling back to the bottom of the phial, which were held in the air by the force of the heat, as happens daily to chaff and dust by the benefit of the sun’s rays; and each one occupied the place which it had held in the not-yet-dissolved rose, and retained the same in this kind of artificial restoration; no otherwise than the most subtle philosopher of this age, Cabeus, after Gilber. 1. 1. c. 18. in magnetic philosophy

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C. 2. Omnia componi ex atomis. III gnetica refert, quod si auelleretur à suo loco terrę globus, non modo in eundem recideret, verùm etiam, pars septentrioni respondens se se ad illum conuerteret, seruarentq; cæteræ partes, eosdem quos habent cum Sole aspectus, ità, & minimum v nù quod meditullium in rosario efformabat, in phiala suum repetit locum, neq; foliorum texturam subit, & omnem motus ratione experiundo sua in fede co[n]sistit, vt ait Lucret. l. 1. Omne genus motus, & cætus experiundo Tandem deuemunt in tales disposituras. Scio Fretagium in noctibus medicis hanc de rosa fabulam appellare, verùm Quercetanus magni nominis Gallorum Regis Consiliarius, & medicus, eam à se visam refert in defens. contra Anonymum c. 23. adducitq; alios testes oculatos idem Gafarellus, Democritus aute chymiæ mysterijs, & Ægyptiorum doctrina eo argumento astruebat mortuorum resurrectionem ex Plin. l. 7. c. 55. vtq; naturę magis faueret conseruari suum in melle corpus iussit, Lacedemoniorum consuetudine quibus ità in vsu fuisse positum ait Cornelius Nepos, & Xenophon. Illudq; institutum à Democrito manasse testis est Varro apud Nonium Marcellum, quare Heraclides Ponticus plus sapit, qui præcepit vt comburerent (corpora) quam Democritus, qui vt in melle seruarent, quem si vulgus secutus esset, peream, si centum denarijs calicem mulsi emere possemus. Confirmatur autoritate Plini[us] l. 7. c. 3. qui ait visum à se Hippo-centaurum in melle. Columella l. 12. c. 45. Cum enim mortuorum resurrectionem ab Ægyptijs didicisset videretq; balsamo condiri, & asseruari in Ægypto cadauera antiquissimo more vt patet ex Genesis c. 5. v. 2. deficiente in Thracia balsamo mel adhiberi iussit. Hoc autem reformationis rosæ exemplum Democriti sensum in totius mundi ortu sub oculos ponit, quę fusiùs explicabimus proposit. 32.

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C. 2. All things are composed of atoms. III gnetica relates, that if the globe of the earth were removed from its place, not only would it fall back into the same, but also the part corresponding to the north would turn itself toward it, and the other parts would preserve the same aspects which they have toward the Sun, so too the smallest particle, which formed the middle point in the rosary, in the vessel returns to its proper place, nor does it undergo the texture of the leaves, and by experiencing every kind of motion it rests in its own position, as Lucretius says, l. 1. Every kind of motion, and the whole company, by experience At last they descend into such arrangements. I know Fretagius in the medical nights calls this tale about the rose a fable; nevertheless Quercetanus, counselor and physician to the King of France, of great name, reports that he himself saw it in the defens. against the Anonymous, c. 23, and Gafarellus likewise adduces other eyewitnesses. Democritus, however, the man of the mysteries of chemistry, and of Egyptian doctrine, by that argument established the resurrection of the dead, from Pliny l. 7. c. 55. and, as though more favorable to nature, he ordered his own body to be preserved in honey, according to the custom of the Spartans, among whom Cornelius Nepos says this practice was in use, and Xenophon. Varro, as cited by Nonius Marcellus, testifies that this institution came down from Democritus; wherefore Heraclides Ponticus is more sensible, who instructed that they should burn the bodies than Democritus, who wanted them preserved in honey, and if the common people had followed him, I am lost if we could buy a cup of mulsum for a hundred denarii. This is confirmed by the authority of Pliny l. 7. c. 3, who says that a hippopotamus-centaur was seen by him in honey. Columella l. 12. c. 45. For when he had learned the resurrection of the dead from the Egyptians, and saw that bodies were embalmed with balsam, and preserved in Egypt according to an ancient custom, as is clear from Genesis c. 5. v. 2, since balsam failed in Thrace, he ordered honey to be used. Now this example of the reformation of the rose sets before our eyes Democritus’ meaning in the origin of the whole world, which we shall explain more fully in proposition 32.

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De Atomis. Disput. II. VII. Fundamentum sumitur à Lucretio qui ità argu- mentatur l. 1. Præterea nisi erit minimum, paruissima quæque Corpora constabunt ex partibus infinitis, Quippe vbi dimidiæ partis, pars semper habebit Dimidiam partem nec res præfiniet vlla Quod absurdissimu[m] est; & si processus in infinitu[m] passim dam- nant, quare in continuo admittunt? probat insuper itidem l. 1. Lucret. dari minima corpora quæ sint inuisibilia, indu- ctione venti, odorum, dispersi humoris, attritionis, & con- sumptionis annulorum, marmorum, metallorum &c. cum au- tem omne mixtum resoluatur in sua principia, sequitur omnia corpora ex minutissimis, & indiuisibilibus corpusculis co[n]stare. VIII. Fundamentum. Experientiæ, & rationi subuenit autoritas preclarissimorum philosophorum, & facilitas omnia explicandi. Indiuisibilia itaq[ue] agnouit Empedocles cuius in- genim Lucretius tanti facit; Secutus est Leucippus, Zeno, Anaxagoras, Epicurus, Protagoras, Plato, Hippocrates vt pa- ret in l. de carnibus si tamen apogryphus non est, subscripsit inter latinos Lucretius, Hidorus, Sennertus, & alij; inter Ara- bes, Auicenna, & Mesue, & innumeris alij quos recensere mi- noris vtilitatis est quam laboris, suffragia enim ponderamus, non numeramus. Quàm autem facilè omnia explicentur ad- missis atomis aliorum esto iudicium. Ego quidem arbitror re diù perpensa, nullius vnquam scientiam naturalè fore absolu- tam, quin Empedoclem, Democritum, Aristotelem, Platone[m], & Anaxagoram iungat recentionibus, & ab vno quoq[ue] quod verum est reiectis falsis eligat: his enim principibus peculiari ratione celeste lumen affulsit, & quamuis corporis imbecillita- te multa corruperint, plurima tamen quæ fidei lumine discerni- mus scripsere verissima. Pro-

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On Atoms. Disputation II. VII. The basis is taken from Lucretius, who argues thus in book 1: Moreover, unless there is a smallest thing, each and every body will consist of infinite parts; for where there is a half of a part, that part will always have a half-part, nor will any limit be fixed to the thing, which is most absurd; and if they everywhere condemn a process to infinity, why do they admit it in continuous things? Lucretius likewise proves in book 1 that there are smallest bodies which are invisible, by induction from wind, odors, diffused moisture, the wearing away and consumption of rings, marbles, metals, etc. But since every mixture is resolved into its principles, it follows that all bodies consist of tiniest and indivisible corpuscles. VIII. The basis. The authority of the most eminent philosophers, together with the evidence of experience and reason, and the ease of explaining everything, come to our aid. Thus Empedocles acknowledged indivisibles, whose genius Lucretius values so highly; Leucippus, Zeno, Anaxagoras, Epicurus, Protagoras, Plato, Hippocrates followed, as appears in the book De Carnibus, if indeed it is not apocryphal; among the Latins Lucretius, Hidorus, Sennertus, and others subscribed to it; among the Arabs, Avicenna and Mesue, and countless others, whom to list is of less use than labor, for we weigh votes, we do not count them. How easily, moreover, everything is explained when atoms are admitted, let that be the judgment of others. For my part, after mature reflection, I judge that no one’s knowledge will ever be fully complete in natural science unless he joins Empedocles, Democritus, Aristotle, Plato, and Anaxagoras with more recent writers, and from each selects what is true while rejecting what is false; for to these leaders celestial light shone in a special way, and although by the weakness of the body they corrupted many things, nevertheless they wrote very many things most true, which we discern by the light of faith. Pro-

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C.2. Omnia ex atomis componi. Probauimus ergo octo rationibus omnia ex atomis constare quod erat designationis nostræ. PROPOSITIO XX. Atomi definitionem dare. Obseruo primò dari Entia quædam quæ nullo modo nequidem per intellectum diuidi possunt, vt punctum mathematicum, si tamen inter possibilia recenseri debet. Obseruo secundò dari Entia quædam intrinsecè indiuisibilia, extrinsecè verò penes designationem, vel commensurationem quam habent ad aliquid aliud esse diuisibilia, sic Angelus qui commensuratur spatio diuisibili, anima quæ adæquatur corpori, Dei aternitas cui tempus correspondent, quæ quidem diuisibilitas vocatur à me mathematica, ad distinctione[m] physicæ quæ partium vnionem reipsa soluit. Obseruo tertio rationem materialitatis non esse sitam in ipsa diuisibilitate ita vt omne indiuisibile censeatur esse spirituale; quod nouum videri non debet cum multi philosophi existimarint brutorum perfectorum animas esse indiuisibiles totasq[ue]; si nul perire, & ipse Vasquez censuit materiam primam sine quantitate esse totam in toto, & totam in qualibet parte, sufficit igitur ad conceptum materialitatis vt dicat vel dependentiam a subiecto, vel ordinem ad quantitatem, vel etiam appetentiam vnionis cum alijs erusdem secum naturæ quorum interuentu possit fieri totius ab illis compositi diuisio physica, his positis. Atomus definiri potest, Materialis physicæq[ue] extensionis radix, & initium. Vt enim quantitatis discretae vnitas est radix lineæ mathematicæ principium est punctum, sic etiam physicæ, & sensibilis continuitatis origo est atomus, dixi materialis extensionis, vt definitio atomis omnibus conueniret tum sub- stantia-

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C.2. Everything is composed from atoms. We have therefore proved by eight arguments that everything consists of atoms, which was our intended point. PROPOSITION XX. To give a definition of atoms. First, I observe that there are certain beings which in no way, not even by the intellect, can be divided, such as a mathematical point, if, however, it must be counted among possible things. Second, I observe that there are certain beings intrinsically indivisible, but externally divisible by way of designation, or by the commensuration they have in relation to something else, as is the case with an angel, which is commensurate with divisible space, a soul which is matched to the body, God’s eternity to which times correspond; and this kind of divisibility is called by me mathematical, in distinction from physical divisibility, which actually dissolves the union of parts. Third, I observe that the reason for materiality does not lie in divisibility itself, so that everything indivisible should be judged spiritual; this should not seem novel, since many philosophers have thought the souls of perfect animals to be indivisible and entire; if they do not perish, and Vasquez himself judged prime matter without quantity to be whole in the whole, and whole in each part, it is therefore sufficient for the concept of materiality that it signify either dependence on a subject, or relation to quantity, or even an appetite for union with other things of the same nature, by means of which the physical division of the whole composed of them may come about. With these things laid down: An atom can be defined as the root and beginning of material and physical extension. For just as unity is the root of discrete quantity, and a point is the principle of the mathematical line, so too the origin of physical and sensible continuity is the atom; I said material extension, so that the definition would apply to all atoms, both sub-

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114 De Atomis. Disp. II. tentialibus, tùm accidentalibus; cum enim ex principio 7. Quidquid recipitur per modum recipientis recipiatur, sequitur ex vna atomo ignis, educi vnam atomum quantitatis, & aliorum, accidentia enim tum in intensione tum in extensione atomis constant, dixi physicæ, quia atomus vna, etsi habeat suas dimensiones non tamen facit continuum physicum sed tantùm mathematicum, neq[ue] enim sub sensum cadit. Verùm vt meliùs hæc doctrina percipiatur subdo atomorum categoriam vt singulas specificè definiamus. Atomus diuiditur in substantialem, & accidentalem. Sub accidentali sunt absolutæ, & modales. Sub titulo substantialium repono elementares, non elementares. Sub illis pono igneas, aqueas, terreas, & sub istis aereas, neq[ue] enim mixta corpuscula sunt atomi, quamuis de illis sub atomorum nomine egerit Sennertus loco citato. Atomus itaq[ue] substantialis est Entitas corporea substantialis simplex, & purissimè homogenea indiuisibilis ex natura sua per se primò exigitiua quantitatis cuius beneficio fit impetrabilis, & ad continuum physicum componendu[m] ordinata. Atomus ignea est entitas corporea substantialis simplex, & purè homogenea indiuisibilis ex natura sua, calida, & lucida secundùm quid, ordinata à natura ad mixtum cum alijs elementorum atomis faciendum: dixi lucida secundùm quid, nam atomi igneæ non lucent nisi certis conditionibus de quibus suo loco cap. vltimo disp. 3. Atomus aqua est entitas corporea substantialis purè homogenea indiuisibilis ex natura sua, humida, & diaphana, ordinata à natura ad mixtum cum alijs elementorum atomis faciendum. Atomus terrea est entitas corporea substantialis simplex, & purè homogenea indiuisibilis ex natura sua, frigida, & adiaphana secundùm quid, ordinata à natura ad mixtum cum alijs elementorum atomis

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114 On Atoms. Disp. II. potential, and likewise accidental; for since from principle 7, "Whatever is received is received according to the mode of the receiver," it follows that from one atom of fire, one atom of quantity is brought forth, and of the others also; for accidents both in intensity and in extension consist of atoms. I said physical, because one atom, although it has its dimensions, nevertheless makes not a physical continuum but only a mathematical one; for it does not fall under the senses. But that this doctrine may be better understood, I set down the category of atoms in order that we may define the several kinds specifically. An atom is divided into substantial and accidental. Under the accidental are the absolute and the modal. Under the title of substantial I place elemental and non-elemental. Under the former I place fiery, watery, and earthly; and under the latter airy; for mixed little bodies are not atoms, although Sennertus treated of them under the name of atoms in the passage cited. Therefore a substantial atom is a simple corporeal substantial entity, and purely homogeneous, indivisible by its nature, of itself in the first place exigent of quantity, by whose benefit it becomes capable of being received, and ordered toward the composition of a physical continuum. A fiery atom is a simple corporeal substantial entity, and purely homogeneous, indivisible by its nature, hot and bright in a certain respect, ordered by nature for making a mixture with the other atoms of the elements: I said bright in a certain respect, for fiery atoms do not shine except under certain conditions, about which in their place, ch. last, disp. 3. A water atom is a purely homogeneous corporeal substantial entity, indivisible by its nature, moist and diaphanous, ordered by nature for making a mixture with the other atoms of the elements. An earthy atom is a simple corporeal substantial entity, and purely homogeneous, indivisible by its nature, cold and non-diaphanous in a certain respect, ordered by nature for making a mixture with the other atoms of the elements

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C. 2. Omnia ex atomis componi. elementorum atomis faciendum. Dixi adiaphanam secundum quid, quia certis conditionibus positis fiunt diaphanæ, illis sublatis sunt terminatæ, de quib[us] disp. 3. cap. vlt. Atomus aerea est entitas corporea substantialis simplex, & purè homogenea, indiuisibilis ex natura sua, nullis qualitatis bus primis secundisve sensibilibus prædita, omnium tamen fere capax, ordinata à natura vt agentium actiuitatem sinceram, & puram ad passum transmitterat, poros subeat vapores diluat, vacuum impediat, &c. Atomi viuentium vel mixtorum quas multò melius minima naturalia vocaremus, sunt exiguæ quædam particulæ heterogeneæ indiuisibiles secundùm quid, hoc est, eâ conditione vt eadem forma in ipsis maneat, diuisibiles verò in atomos simplices, sed de his sermo non est cum propriè loquendo huiusmodi sint mixta. Vnum annoto. In viuentibus v[er]g[ilicet] in homine est quædam minima extensio sub qua potest esse anima humana cum organis sibi necessarijs ad operandum, & huiuscemodi extensio dici debet terminus paruitatis humanę, at verò in textura partium, compositę sunt particulę ex atomis simplicibus, & alibi maiores, alibi sunt minores prout textura subtilis est, vel prout elaboratam partem exigit forma, & istæ sunt atomi secundarię quas Democritus infinitas potuisset appellare, hoc est indeterminatas in numero, figura & magnitudine, aliter enim se habere credo particulas leonis, & elephanti, aliter leporis, & gemmę. Atq[ue] ex istis corpusculorum elaborationibus plurima erui possunt mysteria medicinę, & physicis explicationibus valde apposita, sic enim specierum miracula, ingeniorum varietates, nascentium ex putri causas, spirituum naturam scrutari possemus. Istis pariter corpusculis fiunt exhalationes, profluuiaq[ue] corporum quorum meminit Antotote- les

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C. 2. Everything is composed from atoms. It must be made from the atoms of the elements. I said diaphanous secundum quid, because, certain conditions being posited, they become diaphanous; these being removed, they are bounded, concerning which see disp. 3, cap. ult. An atom of air is a substantial corporeal entity, simple and purely homogeneous, indivisible by its nature, endowed with none of the first or second sensible qualities, yet capable of almost everything, ordered by nature so that it may transmit the sincere and pure activity of agents to the patient, enter pores, disperse vapors, prevent a vacuum, etc. The atoms of living things, or of mixed bodies, which we would much better call natural minima, are certain tiny heterogeneous particles, indivisible secundum quid, that is, under the condition that the same form remains in them; but they are divisible into simple atoms. However, there is no discussion here, since strictly speaking such things are mixed bodies. One note. In living beings, namely in man, there is a certain minimum extension below which the human soul can exist with the organs necessary for its operation, and such an extension ought to be called the limit of human smallness; but in the structure of the parts, the particles are composed of simple atoms, and elsewhere they are larger, elsewhere smaller, according as the texture is subtle, or according as the form requires a more elaborate part; and these are secondary atoms, which Democritus could have called infinite, that is, undetermined in number, figure, and magnitude. For otherwise, I believe, the particles of a lion and an elephant are different; otherwise those of a hare and a gem. And from such elaborations of corpuscles many mysteries of medicine may be drawn out, and explanations very suitable to physics; for thus we could investigate the marvels of species, the varieties of talents, the causes arising from corruption, and the nature of spirits. By these same corpuscles likewise are formed exhalations and the outflows of bodies of which Aristotle makes mention.

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De Atomis. Disp. II. Leslib. 2. de plantisc. 1. & in lib. de historia animalium. Ille aurem atomi vt superius monui sunt verè mixta sed ob paruitatem, & quod sint texturæ viuentis veluti origines, & rudimenta, ideò nomine atomorum donatæ sunt etiam ab antesignano nostro Abderita: diuidunturq[ue] subinde per vltimam disgregationem in atomos puras, simplices, homogeneas, & vsquequaq[ue] indiuisibiles. Quæ omnia difficultate omni carent, meâ quidem sententià, definitiones quidem supra allatæ quia omnes constant proprio genere, & propria differentia; Annotatio verò quia id ex poris deprehendimus, qui illam viuentium textura[m] oculis sensuiq[ue] subijciunt: definiuimus itaq[ue] atomum quod nobis erat præscriptum. CAPVT TERTIVM. De atomorum proprietatibus. Tomorum proprietates aliæ sunt communes omnibus atomis aliæ verò particulares, & propriæ quarto modo. Communes omnibus sunt tres mobilitas, sympathia, quantitas. Aereis insita est vnionis fuga: Igneis, alijsq[ue] communis est amor sacitumq[ue]; à natura foedus, singulis deinde sua est qualitas figura, & ordo qui spectat ad intétionem, quæ omnia sigillatim explicabimus, & probare conabimur. PROPOSITIO XXI. Omnibus atomis convenit triplex mobilitas prima ratione Vniuersi, secunda ratione Vacui, tertia ratione mixti. Explicatur, & probatur propositio, triplex est atomorum consideratio, primo pro ea quam habent, respectu to- cius,

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On Atoms. Disputation II. L. 2. on plants, 1. and in the book On the History of Animals. Those atoms, as I noted above, are truly mixed, but because of their smallness, and because they are, as it were, the origins and rudiments of living texture, they were also given the name of atoms by our leader from Abdera: and they are subsequently divided by the final disgregation into pure, simple, homogeneous, and everywhere indivisible atoms. All these things, in my opinion, are free of every difficulty, the definitions set out above, because they all consist of a proper genus and a proper difference; the annotation, however, because we detect this from the pores, which subject that living texture to the eyes and the senses: thus we have defined the atom as was prescribed for us. CHAPTER THREE. On the properties of atoms. The properties of atoms are some common to all atoms, others particular and proper in the fourth mode. Common to all are three: mobility, sympathy, quantity. In air there is inborn flight from union: in fire, and the rest, common is love and quiet; a pact from nature. Then to each its own quality, figure, and order, which pertains to intention, all of which we shall explain individually, and endeavor to prove. PROPOSITION XXI. A triple mobility belongs to all atoms: first by reason of the Universe, second by reason of the Void, third by reason of the mixture. The proposition is explained and proved. There is a threefold consideration of atoms, first with respect to that which they have in relation to the whole,

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C. 3. De atomorum proprietatibus 117 rius, habitudine, quo fit vt alièc centrum alièc circumferentiâ querant, deinde cum sit adeò sancta & illibata corporum continuitas, & series vacui abhorrens, fit vt singulis atomis repledi locum, & impediendi vacuum ardor sit insitus: ea nempè est mundi conditio, vt nihil penetrabilitatis capax habeat vnde cùm plenus sit, motâ vnâ parte a liquas alias moueri necesse est cùm singulis suus sit locus, neq[ue] vlla cum alia in eodem loco esse possit. Tertiò cù intrinsecum ordinem dicant ad mixtionem, quæ sine motu locali fieri non potest, sequitur etiam atomis concedendam huiuscemodi facultatem motricem in gratiam formę introducendæ: feruntur autem per omnes lationes in mixtione deorsum, sursum, in transuersum, circulariter, & motu mixto, vt videre est in mixtionibus artificialibus patebitq[ue] inferius. In his naturæ rudimentis mirum quâ perfectè seruetur hæc politicorum regula, publicis priuara cedant, & publica priuatis anteponunto. Prima enim mobilitas respectu loci in vniuerso cedit illi, qua ad mixtionem feruntur, prius est enim concurrere ad mixtionem quam centrum petere: sed tamen prius est fauere toti naturæ impedito vacuo quàm facta mixtione. Primæ mobilitati satisfaciunt atomi per motum perpendicularem siue sit realis ex Aristotele, siue apparens ex Aristarcho, siue insensibiliter deflexus ex Lucretio. Tertiæ mobilitati admixtione necessaria est latio omnis t[ame]n vt atomi atomis concurrere, tum vt suà sede acquisità in illa tandem sub formæ auspicijs conquiescant. Moueri autem in inani atomos fulminis velocitate canit Lucretius l. 1. r. Probarur tota hæc doctrina ex princip. 7. qui dat esse dat etiam consequentia ad esse, sed hæc tria consequuntur naturam atomorum, alioqui fini, & intentioni naturæ satisfacere nô possét, ergo he tres mobilitates ipsis insit[us] s[un]t, quod erat demonstrandum. H 4 PRO-

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C. 3. On the properties of atoms 117 by position, by which it comes about that some seek the center, others the circumference; then, since the continuity of bodies is so sacred and inviolate, and the series of the void is abhorrent, it follows that in each atom there is implanted the desire to fill a place and to prevent the void: that is, the condition of the world is such that nothing capable of penetrability has a place from which, when it is full, if one part is moved, the others must be moved; since each has its own place, and none can be with another in the same place. Thirdly, since they speak of an intrinsic order for mixture, which cannot take place without local motion, it also follows that atoms must be granted this sort of moving power for the sake of the form to be introduced: and they are carried in every kind of motion in mixture, downward, upward, crosswise, circularly, and with mixed motion, as can be seen in artificial mixtures and will be shown below. In these rudiments of nature, how admirably is this rule of statesmanship observed: let private interests yield to public, and let public interests be preferred to private ones. For the first mobility, with respect to place in the universe, yields to that by which they are carried toward mixture; for it is better first to come together for mixture than to seek the center: but still it is better to favor the whole of nature, hindered by the void, than, once mixture has been made. The atoms satisfy the first mobility by a perpendicular motion, whether it be real according to Aristotle, or apparent according to Aristarchus, or imperceptibly deflected according to Lucretius. For the third mobility, admixture is necessary: every kind of motion, however, is such that atoms may meet atoms, and then, having acquired their own seat in it, at last rest there under the auspices of form. But that atoms move in the void with the speed of lightning is sung by Lucretius, book 1, line ... This whole doctrine is proved from principle 7: he who gives being also gives the consequences of being; but these three follow from the nature of atoms; otherwise nature could not satisfy its end and intention. Therefore these three mobilities are in them by nature, which was to be demonstrated. H 4 PRO-

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118 De Atomis Disp. II. PROPOSITIO XXII. Datur Symphathia inter atomos. Sympathia nihil est aliud quam amicitia quæda, & consensus inter aliqua ob mutuam naturæ concordiam, & conuenientem dispositionem, vt explicat Plutarchus; sex autem illius species agnosco. Prima ratio sympathiæ est secundum phases motus localis, ità vt corpus vnum eosdem cum alio patiatur motus: quæ sympathia non conuenit magneti, quia magnes non mouetur ad motum ferri. Illustre verò ipsius sympathiæ exemplum dedit Famianus Strada in prolusionibus academicis, quod fabulosum est Cabæo, illiusq[ue]; mentionem facit doctissimus Kircherus in lib. artis magneticæ; horum alter si moueretur eadem alter ferebatur latione, ità vt etiam alphabeticos orbes stilo pererrarent, vnde & instituta in Indijs, & Lusitatia colloquia, tanto terrarum mariumq[ue]; interuallo. Qui lapides si darentur omni pretio maiores essent: naturæ profectò vim no[n] superat, neq[ue]; naturæ maiestatem contemplanti quidquam ex his mihi videtur fide maius. Hæc autem sympathia primi generis cum sit ad fugam vnionis potius quam ad concordiam, & vnitionem atomis non conuenit. Secunda sympathia sumitur à tarantula, vnguêto armario, & chirurgiacurtorum, de qua doctissimè egit Gaspar Talliac otius Bononiensis professor opere singulari, anno 1597. Tarantula coæuum sibi venenum fundit, & easdem mutationes in ægro facit quas in tarantula commotę veneni reliquie habent. Reparatus verò serui carne Domini nasus coaluit, sed mancipio vita functo computruit recutitus nasus libertate omnimodâ mortem sanciête, nullus enim post mortem seruus aut fideiussor. Oritur hæc sympathia à crasi, & temperamento vtrobiq[ue];

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118 On Atoms, Disputation II. PROPOSITION XXII. There is sympathy among atoms. Sympathy is nothing other than a certain friendship and agreement among things, arising from mutual harmony of nature and a fitting disposition, as Plutarch explains; and I recognize six kinds of it. The first kind of sympathy is according to the phases of local motion, so that one body undergoes the same motions as another: such sympathy does not apply to the magnet, because a magnet does not move with the motion of iron. A notable example of this sympathy was given by Famianus Strada in the Academic Prolusions, though Cabæus calls it fabulous, and the very learned Kircher mentions it in the book on magnetic art; if one of them were moved, the other was carried along by the same motion, so that even the alphabetical spheres would wander about with a stylus, whence also arose conversations established in India and Lusitania, despite so great a distance of lands and seas. If such stones were given, they would be worth more than any price: surely they do not surpass the power of nature, nor does anything seem to me greater in trust than these things when contemplating the majesty of nature. But this sympathy of the first kind, since it is directed more toward the fleeing of union than toward concord and union, does not suit atoms. The second sympathy is taken from the tarantula, the ointment cabinet, and surgical wounds, on which Gaspar Talliacotius, professor at Bologna, treated most learnedly in a singular work in the year 1597. The tarantula pours out poison appropriate to its own age, and produces in the sick person the same changes that the remains of the poisoned wound have in the tarantula when disturbed. But the nose of the servant of the Lord was restored and healed, yet after the servant had died the mutilated nose decayed, as death having utterly freed him there was no longer any slave or guarantor after death. This sympathy arises from the mixture and temperament in both cases;

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C. 3. De atomorum proprietatibus. 119 proportionatis, nasus quidem quamuis esset agglutinatus, & veluti appendix resecti nasi, quia tamen primarium suum hu- midum, radicalis, & primigenia substantia nulla arte valet im- mutari, factu est vt quamuis alia forma, anima nempe Domini viueret nasus, nihilominus tamen suam periodum humido in- sito determinatam absoluit perinde ac si in proprio fundo, seruili scilicet brachio, esset implantatus. Huius medicinæ co- plemeti primus autor fuit Braca Siculus, vt patet epistolâ Ca- lentij ad Orpianum, sed historiam de seruili naso refert autor thesauri rerum admirandarum, eamq; prætermisit Talliacoti- us, quinimol. 1. c. 19. etsi Brancæ, Orpianiq; ex Gourmelio faciat mentionem de illa historia silet, & Ib. cap. 18. vbi ex professo disputat an ex alieno corpore, an verò ex proprio tradux eligendus sit, cum ostendisset ex proprio corpore esse eligendum, ità concludit, difficillimum, et fere impossibile de pro- pagine iudicium, atq; singularem illum induidui charactarem om- nino dissuadere, quo minus in alieno corpore hoc opus aggrediamur. historiam verò illius nasi prætermittit, quam nisi senio seruus defecisse dicatur difficilem esse arduæq; philosophiæ censeo, debetq; referri ad Tertiam rationem sympathiæ quam Gafarellus explicat in suis curiositatibus inauditis, oritur. n. à similitudine reru[m], & consensu partiu[m] cu[m] suo toto, subductis ijsdem in totu[m] & partes astroru[m] formæq; influxibus: ide[m] de vnguento armario iudica. Quarta ratio sympathiæ reperitur inter animalia imagina- tione prædita, cuius instrumentum est species externa habitâ ratione proportionis quam cum phantasia habet, ità ignotus placebit mihi qui Socrati erit exosus; quod fit à morum, san- guinis spirituumq; similitudine, & proportione quæ iudicium nostrum præ occupat, & ab blandienti habitudine irrepit. Quinta ratio sympathiæ est omnium vniuersalissima, & quæ paucio-

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C. 3. On the properties of atoms. 119 proportioned, indeed the nose, although it had been glued on, and as it were an appendix of the cut-off nose, yet because its primary moisture, its radical and primordial substance, cannot in any way be changed by art, it came to pass that although it had another form, namely the soul of the Lord lived in the nose, nevertheless it completed its period determined by the moisture implanted in it, just as if it had been implanted in its own ground, that is, in a servile arm. The first author of this medical addition was Braca the Sicilian, as appears from the letter of Calentius to Orpianus; but the story of the servile nose is related by the author of the treasury of wondrous things, and Talliacotius passed it over, although in book 1, chapter 19, even if he mentions Branca and Orpianus from Gormelius, he is silent about that story; and in book 18, where he expressly discusses whether the graft should be chosen from another body or rather from one's own, after showing that it ought to be taken from one's own body, he thus concludes: the judgment of the offspring is most difficult, indeed almost impossible, and that singular mark of the individual altogether forbids us from undertaking this work in another body. As for the history of that nose, which unless it is said that the servant failed from old age, I judge to be difficult and of a rather hard philosophy, it ought to be referred to The third reason for sympathy, which Gafarellus explains in his Unheard-of Curiosities, arises from the similarity of things and the agreement of parts with their whole, after the same influences of the stars and of forms have been removed from the whole and the parts. Judge the same of the pomander. The fourth reason for sympathy is found among animals endowed with imagination, whose instrument is the external species, taken with regard to the proportion it has with the phantasy; thus the person unknown to me who is hateful to Socrates will please me. This happens from similarity and proportion of morals, blood, and spirits, which forestall our judgment and creep in through a flattering disposition. The fifth reason for sympathy is the most universal of all, and that which a little...

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De Atomis. Disp. II. paucioribuserratis subiacet, oriturq; ab occulta proportione quæ est interagens, & passum; ita magnes ferrum trahit ere omisso, heliotropium solem sequitur neglectâ lunâ, de qui- bus vide Atahanasium Kircherum in doctissimis libris artis magnetice. Sexta ratio sympathiæ oritur à dominio siderum, & naturæ ocultioribus ad quandam designationem stimulis, consistitq; vt celesti imperio inferiora cieantur ad explendos vniuersitatis fines generationum varietate, & indiuiduorum perpetuitate successiuà, ita mares feminis consentiunt, & stupendis mira- culis minutissima animalcula se se inuicem ad generationem quæritant. Alias sympathiæ rationes facilè reduces ad hæc capita, vel certè quod habeant apertas causas, & primario nilu inuestigabiles ex sympathiarum censu expunges, quales refert Theophrast. l. 2. de causis plant. c. 24. 25. 26. Is omnes amicitias, & inimicitias plantarum refert ad vtilitatem aut damnum, vtilitatis tres modos ponit, materiam alimenti, nociui repusionem, & adminiculum: damnu[m] facit strangulationem, alimēti furtum, opacationem, odoris grauedinem, & alimenti de- prauationem. Prima ratio sympathiæ vocetur consensio impetus, quia impressus vni mobile eandem in alio facit lationem. I I. dica- tur cōsensus durationis quod ista sympathica sint coæua. III. sit sympathia configurationis quod à similitudine corporum, & figura celi ortum habeat. IV. Est sympathia ciuilis. V. appelletur sympathia Aristotelica. VI. verò est sympathia Democritica, atq; vt aliæ puris atomis non conueniunt, sic ista ijs propria est: quod patet ex Laertio quiait ex Democriti placitis, cuncta secundum necessitatem fieri, est autem necessitas cæli vertigo generationum omnium causa. Prima-

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On Atoms. Disp. II. is subject to fewer errors, and arises from the hidden proportion which exists between the agent and the patient; thus the magnet draws iron while leaving gold aside, the heliotrope follows the sun, neglecting the moon, of which see Athanasius Kircher in the most learned books of the art of magnetism. The sixth reason for sympathy arises from the dominion of the stars, and from the more hidden powers of nature with certain guiding impulses; and it consists in this, that by celestial command the lower things are stirred to fulfill the ends of the universe through the variety of generations, and the perpetual succession of individuals; thus males agree with females, and by wondrous miracles the tiniest animals seek one another for generation. Other reasons for sympathy, easily reducible to these heads, or certainly such as have clear causes and cannot be investigated from the first principles, you will remove from the roll of sympathies, such as Theophrastus relates in book 2, On the Causes of Plants , ch. 24, 25, 26. He refers all the friendships and enmities of plants to utility or harm; he posits three modes of utility: the substance of nourishment, the repulsion of what is harmful, and support; of harm he makes strangling, theft of nourishment, shading, the heaviness of odor, and the corruption of nourishment. Let the first reason for sympathy be called consent of impulse, because what is impressed upon one movable thing produces the same motion in another. II. It may be called consent of duration, because the sympathetic things are of the same age. III. There is sympathy of configuration, because it arises from the similarity of bodies and from the figure of the heavens. IV. There is civic sympathy. V. It may be called Aristotelian sympathy. VI. But there is Democritean sympathy; and just as other things do not agree with pure atoms, so this is proper to them: which is clear from Diogenes Laertius, because, according to the doctrines of Democritus, all things happen according to necessity, and the necessity of the heavens is the rotation, the cause of all generations. First-

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C. 3. De atomorum proprietatibus. 121 Primaria impulsio atomorum, seu ratio cur moueantur est motus coeli, inquit Democritus; quia scilicet ex quo coalu- runt è floribus elementoru[m] sphæræ cælestes motuq[ue]; vertigino- so ciericeperunt, succedentibus idemtidem nouis influxibus syderum propter alias aliasq[ue]; coniunctiones, oppositiones, ortus, occasusq[ue]; fit vt inferioris mundi atomi, huiuscemodi irradiationibus creantur ad motum, tùm quod cum superiori- bus consentiant, tùm quia natura nouis formis fæta illas par- turire gestit, vnde & variè fusæ atomi sibi ea proportione con- iunguntur, quæ maximè apta est introductioni formæ; verum enim-verò non simplices tantum primariasq[ue]; elementorum atomos mouet ad generationem celi vertigo, verum etia[m] mul- to magis secundarias, & quæ minima naturalia ab alijs vocan- tur, cum habeant iam rationem mixtorum quæ ad vlteriorem compositionem venire debeant, fit vt ob multiplicitatem, & heterogeneitatem sibi insitam influxibus sint magis obsequ- entes, quia scilicet alterari, & mutari facilius possunt. Sym- pathia itaq[ue]; Democritica supponit atomos complures eodem influxu siderum moueri, iungi, & ad naturæ generationes in- vnam venire compositi fabricam. Sicuti si daretur dispensa- tus tanta arte impetus qui secundùm architecti Idæam, lapi- des, calcem, & ligna moueret, ità vt singula suis locis repo- nerentur explerentq[ue]; illud exemplar palatij quod in capite suo peritus ille architectus impressum habet, haberemus na- turæ, & generationis ex atomis perfectam similitudinem. Natura enim rei faciendæ idæam seminis aut succi analogi beneficio habet, cæloq[ue]; tanquam ministro ad consilia sua exe- quenda vtitur, cælum influxibus suis ita singulas compositi particulas mouet vt non modó locum occupent sibi conuenié- tem, faciantq[ue]; aptum formæ domicilium, verùm etiam non- tam habet rationem proportionis extrinsecæ, quam tamen in palmarijs

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C. 3. On the properties of atoms. 121 The primary impulse of atoms, or the reason why they are moved, is the motion of the heavens, says Democritus; because, namely, from the time when the celestial spheres were brought together from the flowers of the elements and, with a whirling motion, began to stir, with ever-new influxes succeeding one another from the stars on account of their various and varied conjunctions, oppositions, risings, and settings, it comes about that the atoms of the lower world are created for motion by such irradiations, both because they agree with the higher ones, and because nature, fertile with new forms, longs to bring them forth; whence also the atoms, spread in various ways, are joined to one another in that proportion which is most suitable for the introduction of form. But in truth, not only simple and primary atoms of the elements are moved by the whirling of the heavens toward generation, but also much more so the secondary ones, and those which are called the smallest natural bodies by others, since they already have the character of mixtures which ought to come to further composition; thus, because of the multiplicity and heterogeneity inherent in them, they are more obedient to influxes, since, namely, they can be altered and changed more easily. Sympathy, therefore, in Democritean doctrine supposes that many atoms are moved by the same influx of the stars, joined, and brought together into the fabric of a composite for the generation of natures. Just as if there were a force, dispensed with such art, which according to the architect’s Idea would move stones, lime, and wood, so that each were placed in its proper location and filled out that model of a palace which that skilled architect has impressed in his mind, we would have a perfect likeness of nature and of generation from atoms. For nature has the idea of the thing to be made by means of the benefit of a seed or analogous juice, and uses the heavens as if it were a minister for carrying out its plans; the heavens, by its influxes, moves each part of the composite in such a way that they not only occupy the place suitable to themselves, and make a dwelling fitting for form, but also has not so much the character of extrinsic proportion, which nevertheless in

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De Atomis. disp. II. 122 palmarijs suis operibus non negligit, quin potiùs qualitatum gradus pro ratione requisita sapientissimè dispensat. Existimabam ante exactius de sympathia Democritica examen totum illius mysterium in figurarum ratione consistere. Scilicet cum sint diuersi ordinis, variæ positionis, multiplicisq; figuræ, fieri suspicabar vt aliæ alijs similes, aliæ contrariæ quadamtenus essent, sic sphæricam omnibus esse antipathicam dum sphærica permanet, quia cum singulis refugit vnionem nisi inueniretur quædam concaua quæ illam conuexitatem sinu apposito exciperet, refugit enim vnionem cum alijs superficiebus sphæra, quia omnes in puncto tantùm tangit ac proinde non potest dari vnio; in puncto enim mathematico non potest sustentari actio physica aut modus. Cubus pyramidi non consentiet quia cum illa non potest replere locum, potentiores figuræ infirmioribus sunt tyranni, potentior autem figura est, quæ magis est dissolutiua minùs vnitium, qualis est quæ à cubo maximè recedit cuius facies alijs suæ speciei iuncta locum non replet. Sed figuræ contrarium nihil est neq[ue] ità obstinatè vnam seruant atomi figurâ quin eam quadamtenus mutare possint vt dicemus inferius. Itaq[ue] à ratione cæli, & maximè à ratione ordinis intrinseci quæ ad mixtione, & generatione dicunt, petenda est earum sympathiæ ratio: quâ dari nullo modo negari potest: sympathia .n. sexti generis est mutuus ad vnum consensus, atqui atomi elementares habent mutuum ad vnum, & eundè fine consensus nempe ad generationes, & mixtiones, ergo habent sympathiam: quod erat propositum. PROPOSITIO XXIII. De atomorum paritate aliquid coniecturà assequi. Certum est primò nullam atomum cadere posse sub sensum, vnde nec tangi vna singulariter potest, quamuis plurimè simul

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On Atoms. Disputation II. 122 He does not neglect his own handy works, but rather dispenses the degrees of qualities in accordance with the required ratio most wisely. I had thought, before a more exact examination of Democritean sympathy, that the whole mystery of it consisted in the relation of figures. For since there are figures of different order, various position, and of manifold kind, I suspected that some would in some measure be similar to others, others contrary; thus the spherical would be antipathic to all while it remains spherical, because it shuns union with each; unless there were found some concave body that might receive that convexity in its fitting hollow. For the sphere refuses union with other surfaces, because it touches them all only at a point, and therefore no union can arise; for in a mathematical point physical action or mode cannot be sustained. A cube will not agree with a pyramid, because with it it cannot fill the place; stronger figures are tyrants to weaker ones. But the stronger figure is that which is more dissolutive, less unifying, such as that which departs most from the cube, whose faces, when joined to others of its own kind, do not fill the place. Yet there is no contrary of figures, nor do atoms preserve one figure so obstinately that they cannot in some measure change it, as we shall say below. Therefore the reason of the heavens, and especially the reason of the intrinsic order which they ascribe to mixture and generation, must be sought as the source of their sympathy: which can in no way be denied. For sympathy is, of the sixth kind, a mutual agreement toward one thing; but elemental atoms have a mutual agreement toward one and the same end, namely toward generations and mixtures; therefore they have sympathy: which was the point to be proved. PROPOSITION XXIII. To infer something by conjecture concerning the parity of atoms. First, it is certain that no atom can come under the senses, and therefore neither can one singularly be touched, although very many together

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C. 3. De atomorum proprietatibus. 123 simul positæ sint sensibiles; quapropter nulla est atomus quæ habeat extensionem quæ sit æqualis vlli quæ sensu percipitur. Certum est secundò atomis suam inesse figuram, ac pro- inde extensionem quam appello mathematicam, primò quod non sit diuisibilis physicè sed tantùm per designationem, se- cundò quia illam imaginari solùm, & lineis imaginarijs, id est, mathematicis dimetiri possumus, non verò physicis. Certum est tertiò quantumuis statuantur paruæ atomi ea- rum tamen numerum iniri posse, & finitas esse finite determinata ad mundi totius vniuersitatem constituendam. Archimedes in libro de arenæ numero reprehendit Samium Aristarchum illius quâ Copernicus innouauit astrologiè prin- cipem, quod orbitæ terrestris nullam esse proportionem cum firmamento dixerit, siue circulu[m] quem terra in Pythagoræoru[m] systemate percurrit esse instar puncti ad stelliferum. Loqueba- tur aute[m] Aristarchus de proportione sensibili, sicuti eo in sensu apud Astrologos certu[m] est terrâ esse instar puncti ad firmamé- tu[m]. Archimedes verò demonstrat dari proportione[m] etia[m] inter granum papaueris, & totum mundum, cuius rationis securus hanc audacem fecit propositionem ille ingeniorum Phoenix, Datum pondus data potentia mouere, rectèq[ue] demonstrauit pro- positum imo inter vnicam atomum totamq[ue] rerum vniuersitatem dari proportionem necesse est, licet enim conijcere quot sint in vniuerso atomi. Nunc autem videamus quantæ sint paruitatis. Plinius l. 11. c. 1 & 2. misquam alibi, ait, naturæ rerum arti- ficium spectabilius est, quam in insectis: In magnis siquidem cor- poribus aut certè maioribus facilis officina sequaci materia fuit. In his verò tam paruis atq[ue] tam nullis quæ ratio, aut quanta vis, tam- que inextricabilis perfectio? Vbi tot sensus collocauit in culice? sunt alia dictu minora. Sed, vbi visum in ea prætendit? Vbi gu- statum

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C. 3. On the properties of atoms. 123 if they are placed together, they are perceptible; wherefore there is no atom which has an extension equal to any that is perceived by sense. Secondly, it is certain that atoms have their own figure, and there- fore a extension which I call mathematical, first because it is not divisible physically, but only by designation, se- condly because we can only imagine it, and measure it by imaginary lines, that is, mathematical ones, not physical ones. Thirdly, it is certain that however small atoms may be posited, their number can nevertheless be reckoned, and that they are finite and finitely determined for constituting the whole universe. Archimedes, in the book On the Number of the Sand, rebukes the Samian Aristarchus, that prince of astronomy whom Copernicus renewed, for saying that the orbit of the earth has no proportion to the firmament, or that the circle which the earth in the Pythagorean system traverses is as a point in relation to the starry heavens. But Aristarchus was speaking of a sensible proportion, since in that sense among astronomers it is certainly held that the earth is as a point in relation to the firmament. Archimedes, however, demonstrates that there is also proportion between a grain of poppy seed and the whole world; secure in this ratio, that bold proposition was made by that phoenix of genius, “Given a weight, given a power to move,” and he rightly demonstrated the proposition. Indeed, between a single atom and the whole universe of things there must be a proportion; for although one may conjecture how many atoms there are in the universe. But now let us see how small they are. Pliny, book 11, ch. 1 & 2: Nowhere else, he says, is the workmanship of nature more remarkable than in insects: for in large bodies, or certainly larger ones, the workshop was easy for pliant matter. In these, however, so small and so negligible, what reasoning, or what force, and what inextricable perfection is there? Where did he place so many senses in a gnat? There are other things smaller still to mention. But where did he set sight in it? Where taste?

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124 De Atomis. Disp. II. statum applicauit? Vbi odoratum inseruit? Vbi truculentam illam, & portione maximam vocem ingenerauit? Quà subtilitate pennas adnexuit, prælongauit pedum crura, disposuit ieum â causeam vti aluiu[m], auidam sanguinis, & potissum humani sitim accendit? Telum verò perfodiendo tergori quo spiculauit ingenio? atq[ue] cum exilitate pene non videatur, ità reciprocâ generauit arte, vt fodiendo acuminatum pariter sorbendoq[ue] fistulosum esset? Aspice vnicum culicis caput tot sensuum officinam, ibi oculos humoribus, tunicis, nervisq[ue]; distinctos, spiritibus animalibus plenos miraberis: quanta auté tenuitas est horum? in pede sunt membranæ, ossa, medulla, nerui, tendines, musculi, vasa deferentia animalculo nutriendo humorem, multiplexq[ue]; partium compages. At cum spiritus vnicus vel vitalis vel animalis vnius eironis multis atomorum millibus constet, paucæ enim non possunt facere mixtionem neq[ue]; præparare formæ alicui præsertim viuenti domicilium, quot in ipso animalculo atomos esse conijcies? Aduerti non semel granum thuris combustum fumo ità disperti vt locum repleuerit septingentis, & amplius millionibus se maiorem. Ille enim locus grana huiuscemodi facilè cepisset Secundum altitudinem 720. Secundum latitudinem 900. In longitudine 1200. In superficie 648000. In area 7776000000. Cum ergo nulla aeris sensibilis portio esset quæ odoros non haberet halitus, granumq[ue]; thuris æquaret cicerem qui sine igne in partes sensibiles saltem mille diuidi posset, sequitur particulas odoras sensibiles fuisse istius num. 77760000000. Atqui singulæ illæ particulæ mixtæ erant, nullamq[ue]; fuisse probabile est cui vns ad minimum elementalium atomorum millio

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124. On Atoms. Disputation II. In what manner did it give it its posture? Where did it insert its sense of smell? Where did it implant that fierce, and proportionally greatest, voice? With what subtlety did it attach the wings, lengthen the legs, arrange the jaw so as to serve as the belly, inflamed with a thirst for blood, and especially human blood? By what ingenuity did it sharpen the weapon for piercing the back? And although it scarcely seems visible because of its minuteness, by what reciprocal art did it make it such that, in piercing, it was pointed and at the same time hollow for sucking? Consider the single head of the gnat, a workshop of so many senses: there you will marvel at the eyes, distinguished by humors, membranes, and nerves, and filled with animal spirits. But how great is the minuteness of these things? In the foot there are membranes, bones, marrow, nerves, tendons, muscles, vessels conveying nourishment to the little creature, and a manifold structure of parts. But since a single spirit, whether vital or animal, of one atom consists of many thousands of atoms—for a few cannot make a mixture or prepare a dwelling for any form, especially for a living thing—how many atoms do you suppose to be in the little animal itself? I have noticed more than once a grain of incense, when burned, dispersed in such a way by smoke that it filled a space larger by seven hundred million and more. For that place would easily have contained grains of this kind: According to height, 720. According to width, 900. In length, 1200. In surface, 648000. In area, 7776000000. Since therefore there was no perceptible portion of air that did not have fragrant exhalations, and since a grain of incense equals a chickpea, which without fire can at least be divided into a thousand perceptible parts, it follows that the fragrant perceptible particles were of this number: 77760000000. And yet each of those particles was mixed, and it is probable that there was none which had not at the least one million atoms of the elementary bodies.

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C. 3. De atomorum proprietatibus. 125 millio inesset, vnde secundum hanc regulam fuissent in hoc thuris grano pisi magnitudinem non superante atomi ele- mentales adminimum 77760000000000000. Ex quibus patet quantę sit paruitatis atomus vna, conijciq[ue] potest quantus sit atomorum numerus in toto vniuerso. Claui- us in cap. 1. Sphæræ, computat quot arenę grana possent imple- re orbem ex suppositione quod 10000. æquarent vnum mi- lij granum, inuenitq[ue]; totum illum numerum comprehendi vnitate, & chiffris quinquaginta. Sed multo plures atomos dari conuincunt superius adducta animalculorum exempla. At in his nihil aliud quam conijcere possumus quis enim nouit an atomi igneę maiores minoresue sint aqueis, & terreis? quis dignoscit aerearum paruitatem, cælorum profunditates om- nes, & extimam illam Beatorum sedem? Furor est mensuram or- bis animo agitare atq[ue]; prodere ausos? quasi verò mensuram ullius rei possit agere, qui sui nesciat. Plin. l. 2. c. 1. PROPOSITIO XXIV. Atomis aeris insitum est, et proprium cum alijs vniri nunquam. N Olui diutiùs in superiori propositione immorari, ne in- nos iaci posset illud Aristophanis comici dicterium quo Chærephontis curiositatem perstrinxit, et Chærephon qui puli- cum cognouit vestigia. Nunc atomoru[m] proprietates non euiden- ti quidem ratiocinatione apertas, sed tamen probabiles exe- quamur. Cum supra dixerimus aerem non ingredi mixtionem, sed dare tantum veluti transitum alijs, sequitur eius atomos nul- lis adhærere, sed suæ semper esse libertatis: si enim, adhære- rent motum præpedirent, retardarent aut accelerarent, at supra videmus experientijs repertitis hoc non fieri, ergo non adhærent alijs. Deinde cum aer careat qualitatibus primis secun-

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C. 3. On the properties of atoms. 125 if there were contained in it 1 million, then according to this rule there would be in this grain of frankincense, not exceeding the size of a pea, at the very least 77,760,000,000,000,000 elemental atoms. From these things it is clear how small one atom is, and it can be inferred how great is the number of atoms in the whole universe. Clavius, in chapter 1 of the Sphere, computes how many grains of sand could fill the globe, on the supposition that 10,000 would equal one grain of a thousand, and he finds that the whole number is contained within one unit and fifty digits. But the above-cited examples of little animals prove that far more atoms exist. Yet in these matters we can do nothing other than conjecture; for who knows whether fiery atoms are larger or smaller than watery and earthy ones? who discerns the smallness of aerial atoms, the depths of the heavens, and that outermost dwelling of the Blessed? It is madness to take the measure of the world in the mind and then to publish it abroad? as though he who does not know his own measure could measure anything else. Plin. l. 2. c. 1. PROPOSITION XXIV. It is inherent in atoms of air, and proper to them, never to unite with others. I did not wish to linger longer in the previous proposition, lest there be thrown at us that jest of the comic Aristophanes by which he mocked the curiosity of Chaerephon, and Chaerephon who knew the tracks of fleas. Now let us set forth the properties of atoms, not indeed made clear by evident reasoning, but nevertheless probable. Since above we said that air does not enter into mixture, but merely gives passage to others, it follows that its atoms adhere to none, but are always free; for if they adhered, they would hinder motion, or retard it or accelerate it; but above we see from repeated experiments that this does not happen, therefore they do not adhere to others. Next, since air lacks the primary qualities, secon-

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126 De Atomis. Disput. II. secundum quas fit ad mixtionem, & vnionem dispositio, con- sequens est ipsum vnioni esse ineptum. Adde quod si vnire- tur, non tam facilè transpiraretur, neq[ue] posset ità poris egredi vel illos subire. Quæres an atomi aereæ alijs aereis sint iunctæ? Respon- deo mihi esse dubium: in eam tamen partem propédeo vt sint tantu[m] contiguæ: ratio quæ me mouet hæc est. Quia quæuis mobilia æquè citò, & æquè velociter descendunt, & diuidunt aerem, ergo signum est nullam omnino esse resistentiam, si enim esset resistentia ratione vnionis quæ solui debet, cur oui crusta inanis, æquè velociter ferretur, ac plumbum ouale pa- ris magnitudinis sed ducentupli ponderis? Superficies corpo- ris ambientis vtriusq[ue]; æqualis est, ergo par est in sustinendo vtrobiq[ue]; aeris quantitas: sed maior est virtus deorsum motrix in plumbo, & maior est vis diuidendi aerem, vtrumq[ue]; tamen mobile paribus motus incrementis ad terræ centrum fertur, ergo signum est nullam esse resistentiam in aere, ac proinde nullam vnionem soluendam; vnde tota aeris extensio, & mo- les est atomorum omni vnione solutaru[m] cumulus, & fortasse neq[ue]; inter se neq[ue]; cum alijs vnibilium, cum à posteriori videa- tur id sequi, & satis superq[ue]; intelligatur aer suo fungi officio etiam si non vnibilis intelligatur. Ergo atomis aereis insitum est alijs non vniri, quod erat probandum. PRPOSITIO XXV. Quomodo se habeant atomi ignea, aqueæ, & terreæ ad Vnionem determinare. E Picurus Democriti affecla in epistola ad Herodotum, Cor- pora alia quidem (ait) concretiones sunt, alia verò ex quibus con- cretiones factæ sunt, at ista indiuidua sunt, & immutabilia nisi omnia in id quod non est interitura sunt, hoc est, alia sunt corpora quæ ex pri-

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126 On Atoms. Disput. II. According to which there is a disposition toward mixture and union, it follows that it is itself unfit for union. Add that if it were united, it would not pass off so easily by transpiration, nor could it thus issue through the pores or enter them. You ask whether the aerial atoms are joined to other aerial atoms? I reply that this is doubtful to me; yet I incline to the view that they are only contiguous. The reason that moves me is this: because any movable bodies descend equally quickly and equally swiftly, and divide the air, therefore it is a sign that there is no resistance at all; for if there were resistance by reason of a union that must be dissolved, why would an empty eggshell be carried downward as swiftly as an oval piece of lead of equal size but two hundred times the weight? The surface of the surrounding body is equal in both cases, therefore the quantity of air is equal in supporting each; but the downward-moving force in the lead is greater, and the force for dividing the air is greater, yet both movable bodies are carried toward the center of the earth with equal increments of motion. Therefore it is a sign that there is no resistance in the air, and consequently no union to be dissolved; whence the whole extension and mass of the air is a heap of atoms freed from every union, and perhaps neither among themselves nor with other things capable of union, since from the a posteriori it seems that this follows, and it is sufficiently and more than sufficiently understood that air performs its office even if it is understood not to be capable of union. Therefore it is inherent in aerial atoms not to be joined to others, which was to be proved. PROPOSITION XXV. To determine how the igneous, aqueous, and earthy atoms are disposed with respect to Union. Epicurus, a follower of Democritus, in the letter to Herodotus says: “Bodies, indeed, are compounds; others are those from which compounds are made, but these are indivisible and immutable, unless all things are to be in that which is not perishable; that is, some bodies are those which are from pri-”

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C. 3. De atomorum proprietatibus. 127 ex primis coaluerunt, alia verò sunt corpora prima, id est atomi indiuisibiles, & immutabiles nisi annihilentur. Quanam autem ratione concrescant non aliter explicat idem Epicurus quam per desiderium quoddam mutum quod habent ad inuicem: quapropter vnionis inter se sunt amantes atomi igneæ, aqueæ, terreæ. Prob. primò materia prima appetit formam ergo, & ea quæ sunt necessaria ad eam assequendam, & retinendam, nam qui dat esse dat etiam consequentia ad esse, & qui vult finem, etiam, media appetit ad illum necessaria ex p. 9. Sed vnio atomorum inter se est necessaria ad formam, ergo atomi vnionis illius sunt appetentes: eamq; non soluunt nisi irritatæ ab extrinseco: cùm itaq; triplicis speciei atomi sint materia, prima, sequitur ipsis esse insitam vnionis cupidinem ratione finis intrinseci quem habent admixtum, & generationem substantialem. Prob. secundò à posteriori omnis resolutio, & corporum corruptio est naturæ violenta secundum quid, sed corruptio fit per dissolutionem vnionis atomorum siue illarum dispersionem, & segregationem, ergo sequitur huiusmodi segregationem, & dissolutionem esse violentam secundum quid, ac proinde à cõtrario vnio atomis est cõnaturalis, & expetira. Prob. tertiò nunquam quiescunt atomi nisi sint coniunctæ inter se quo fit vt corruptio vnius sit generatio alterius, ergo cum illa quies mediante vnione obrineatur, consequens est vnionematomis esse acceptissimam, & reuerà perpetuo agitari dicit Democritus vsquequò ad naturæ instituta, cæliq; vertiginis imperium coaluerint. Quæres an atomi terreæ terreis vniantur, aqueæ aqueis, igneæ igneis? Respondeo videri atomos terreas terreis vniri, ea tamen I lege,

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C. 3. On the properties of atoms. 127 those things which have been formed from first principles are one class; but others are first bodies, that is, indivisible and unchangeable atoms unless they are annihilated. But in what manner they cohere Epicurus explains no otherwise than by a certain mute desire which they have for one another: wherefore the fiery, watery, and earthy atoms are lovers of union among themselves. Proof. First, prime matter desires form, therefore also those things which are necessary for obtaining and retaining it; for whoever gives being gives also the consequences of being, and whoever wills the end also desires the means necessary for it, from p. 9. But the union of atoms among themselves is necessary for form; therefore atoms are desirous of that union, and they do not dissolve it unless irritated from outside. Since, therefore, atoms are matter of three kinds, it follows that there is in them an innate desire for union by reason of the intrinsic end which they have mingled with them, and for substantial generation. Proof. Secondly, a posteriori, every dissolution and corruption of bodies is in a certain respect violent by nature; but corruption occurs through the dissolution of the union of atoms, or their dispersion and separation; therefore it follows that such separation and dissolution is violent in a certain respect, and consequently, on the contrary, union of atoms is natural and desirable. Proof. Thirdly, atoms never rest unless they are joined together with one another, by which it comes about that the corruption of one is the generation of another; therefore, since that rest is attained by means of union, it follows that union is most acceptable to atoms, and indeed Democritus says that they are perpetually agitated until, according to the ordinances of nature, they have coalesced under the rule of the turning of the heavens. You ask whether earthy atoms unite with earthy, watery with watery, fiery with fiery? I answer that the earthy seem to be united with earthy atoms, under this condition however,

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De Atomis. Disp. II. 128 lege, vt alterius vnionis amor præualeat sic vt facilius terrea atomus cum ignea vel aquea, quam cum alia terrea vnienda sit, ratio à priori petitur ab intrinseco fine quem dicunt ad mixta, & videtur colligi à posteriori quod refula terræ aqua, continuo ità immisceatur vt fiat limus, cuius in minimas par- tes diuisionis argumentum est, quod nihil ad tactum mollius sit, nihii minùs asperum. De aqueis atomis idem esto iudi- cium: quæquidem terræ, & igni potiùs quam suæ speciei ato- mis coniungentur, aeri autem nullo modo quod inde patet, quia si aeri facilè vnirentur, non ita conseruaretur aqua in sphærulas collecta si quando mensæ roratim affundatur dein- de quomodo ex vaporibus coalesceret iterum in pluuias? fie- ret enim ex aqua, & aere, aliquid medium mixtum inperfe- ctum quale limus inter aquam, & terram. Quod si aque id proprium est, multo magisterræ. At an igneæ atomi igneis, vniri possint, dubium mihi est, primò quia igneæ atomi extra mixta sunt sphæricæ figuræ vt probabitur inferius, quare non se tangent nisi in puncto mathematico quod vnionis capax non est: cum enim sit mo- dus physicus certam requirit extensionem. Secundò quia ra- tione suæ perfectionis quâ sunt instar animæ in vniuerso vi- dentur potius cupidæ communicandi sui quam vnionis inter se, vnde ad illius appetitus stimulos sunt maximè dispersi lo- cis, & ad naturæ arbitrium huc, & illuc feruntur quo maxi- mè generationes coelum, & causæ particulares moliuntur: ter- tiò quia si vnirentur, tantùm abest vt mixtioni fauerent quin potiùs omnia dissoluerent, earumq; effectus, & vis satis patet in ipso actu dissolutionis mixtorum, in flamma scilicet, quam- uis vaporibus sua actiuitas non parum hebetetur: quid ergo contingeret si vnitæ simul agerent, & in sua perfectione inten- sioneq; naturali politæ? Rectè ergo cautum fuisse suo operi à Deo

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On Atoms. Disp. II. 128 the law, that the love of one union should prevail, so that a terrestrial atom may more readily be united with a fiery or watery one than with another terrestrial one. The reason is taken a priori from the intrinsic end which they say pertains to mixed bodies, and it seems to be gathered a posteriori from the fact that when earth is moistened with water it is so continuously mingled that mud is formed, of which the proof that it is divided into very small parts is that nothing is softer to the touch, nothing less rough. The same judgment is to be made about watery atoms: they will indeed be joined with atoms of earth and fire rather than with atoms of their own species, but with air in no way; and this is evident from the fact that if they were easily united with air, water would not be preserved so well when gathered into droplets if it is sprinkled on a table; then how would it coalesce again from vapors into rain? For something intermediate, an imperfect mixture, would be made from water and air, such as mud between water and earth. If this is proper to water, it is much more so to earth. But whether fiery atoms can be united with fiery ones I doubt, first because fiery atoms outside of mixtures are of a spherical figure, as will be proved below, and therefore do not touch one another except at a mathematical point, which is incapable of union; for since union is a physical mode, it requires a definite extension. Secondly, because by reason of their perfection, by which they are like the soul in the universe, they seem rather eager to communicate themselves than to be united among themselves, and hence, at the impulses of that appetite, they are most widely dispersed through places and are carried hither and thither at the discretion of nature wherever generations and the sky, and particular causes, chiefly strive. Thirdly, because if they were united, they would be so far from favoring mixture that they would rather dissolve everything, and their effect and power is sufficiently clear in the very act of dissolving mixed bodies, namely in flame, although their activity is not a little dulled by vapors. What then would happen if they acted united together and were sharpened in their natural perfection and intensity? Rightly, therefore, God had taken care for his work

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C. 3. De atomorum proprietatibus. 129 Deo Opt. Max. videtur, dum actiuitatis tantę elementum in minimas particulas dispersum reddidit infirmius, magisq; obsequens formis: virtus enim vnit fortior, dispersa debilior, & quod ad naturę totius vtilitatem magis æstimabilem facit non debet in contrarias partes, & nocumenta traduci. Fauet huic meę suspicioni (quę fortassis causam dabit cur ignem seruare nequamus) experientia, videmus enim cęteris elementis certà mole suum stare, & perennare cumulum, igni autem, si alimentum subtraxeris, abire, & disparere necesse est quòd in atomos dispersus indiuisibilis fiat, nulla enim atomus seorsim videri potest: agilitate verò sua fit vt non sint diu contiguę sed semper ferantur etiam ad nubes vsq; vbi generationes moliuntur, dum celesti beneficio formę cuiusdam allicijs in corporis compositionem veniant; mirum cęteroquin est cur nullus ignis apud nos perennet, cùm tamen, & aerem, & mare, & terras habeamus. Diximus itaq; quomodo se habeant atomi ad vnnione inter diuersæ, & eiusde ipecici atomos. Quod nobis erat præscriptu[m]. PROPOSITIO XXVI. Atomis sua inest figura. Hæc propositio clarissima est, cum enim atomi sint corpuscula, differantq; à punctis mathematicis sequitur quod suas habebunt dimensiones, & terminos ac proinde superficie, & latitudine, longitudine profunditatemq; ex post. itaq; 3. habebunt figurâ quâ definiumus ex Eucl. l. I. def. 14. at nô planâ modo verum etiam solidam de qua Idem Eucl. l. I I. def. I. Solidum est quod longitudinem, latitudinem, & erastitudinem habet. Atomis itaq; tua inesse debet figura, quod erat probandum. Sed enim cum quatuor posuerimus atomoru[m] genera, igneas aereas,

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C. 3. On the properties of atoms. 129 To God, the Best and Greatest, it seems that, while He made the element of such great activity, dispersed into the smallest particles, weaker and more compliant to forms; for a force is stronger when united, weaker when dispersed; and what makes for the greater usefulness of the whole nature ought not to be turned to contrary parts and harms. My suspicion is supported by experience, which perhaps will provide a reason why we cannot preserve fire: for we see that the other elements, with a definite mass, maintain their own heap and endure, but fire, if you withdraw its nourishment, must depart and disappear, because, dispersed into atoms, it becomes indivisible; for no atom can be seen separately. Yet because of its swiftness it is such that they are not long contiguous, but are always carried onward even to the clouds, where generations are brought about, while by heavenly favor they come, enticed by some form, into the composition of bodies; and what is more remarkable, no fire endures among us, although we have air, sea, and land. Thus we have said how atoms stand in relation to one another, both among different kinds and among atoms of the same kind. This was what had been prescribed for us. PROPOSITION XXVI. Atoms have their own figure. This proposition is most clear, since atoms are little bodies and differ from mathematical points; it follows that they will have their own dimensions and limits, and therefore surface, breadth, length, and also depth. Thus they will have a figure, as we define it from Euclid, Book I, Definition 14. Not only a plane figure, but also a solid one, of which the same Euclid, Book II, Definition 1, says: A solid is that which has length, breadth, and thickness. Therefore atoms must have figure, which was to be proved. But since we have posited four kinds of atoms, fiery, airy,

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De Atomis. Disp. II. aereas, aqueas, & terreas quid de singulis dicendum sit deter- minandum videtur, quod cum in sequentibus propositioni- bus exactè fieri debeat præmittenda est Platonici dogmatis de elementorum figuris explicatio. Examen doctrinæ Platonicæ de elementorum figuris. Apuleius libro de dogmate Platonis ita loquitur ex diuini illius philosophi mente. I. Initium omnium corporum materiam, esse memorauit: hanc signari impressione formarum: hinc prima ele- menta esse progenita, ignem, & aquam, terram, & aera. Quæ si elementa sunt, simplicia esse debent, neq[ue] ad instar syllabarum nexu mutuo copulari. Hoc est, elementis non adeit vlla heteroge- neitas qualis est in syllabis quæ consonantibus, & vocalibus constant. Quod illis euenit, quorum substantia multimodà potesta- te, coitione conficitur. Qualia sunt mixta quæ coalescentibus inuicem elementistanquam vocalibus, & consonantibus in vnum coalescunt compositum. II. Quæ cum inordinata permixtaq[ue] essent, ab illo ædificatore mundi Deo ad ordinem numeris, & mensuris in ambitum deducta sunt. Hæc è plurimis elementis ad vnum redacta esse. His Apulei verbis explicandis opus est Oedipus. Prima, quidem sententia videtur à biblijs sumpta vbi legitur quod Deus fecit omnia in pondere, numero, & mensura, at quid sibi se- cunda vult propositio cum dicit, hæc è plurimis elementis ad vnum redacta esse? Existimo Platonem censuisse materiam primam atomis constare, quæ deinde formis substantialibus sigillatæ, illæ quidem ignis, illæ verò terra, aqua, aerue fierent, pro ideæ informantis natura, atq[ue] ità clarus erit sensus Apulei, quasi diceret, Architectus rerum omnium Deus numeris mensurisq[ue] instructus elementa in ambitum deduxit, dispersasq[ue] particulas homogeneas quæ eiusdem sunt elementa corporis sive principia, in vnum congregauit, aqueas atomos jungens aques,

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On Atoms. Disp. II. What is to be said of the aereal, aqueous, and earthy kinds seems to require determination; and since this must be done exactly in the following propositions, an explanation of the Platonic doctrine concerning the figures of the elements must be set forth in advance. Examination of the Platonic doctrine concerning the figures of the elements. Apuleius, in the book On the Doctrine of Plato, speaks thus according to the mind of that divine philosopher. I. He stated that the material of all bodies is the beginning of all things; that this is stamped by the impression of forms; whence the first elements are generated, fire, water, earth, and air. If these are elements, they ought to be simple, and not joined together by mutual connection like syllables. That is, in the elements there is no heterogeneity such as there is in syllables, which consist of consonants and vowels. This belongs to those things whose substance is composed by a manifold power and conjunction. Such are mixtures, which, as elements coalescing together, like vowels and consonants, unite into one composite whole. II. Since these were in an unordered and mixed state, by that builder of the world, God, they were brought into order by numbers and measures within the circumference. These things are said to have been reduced from many elements to one. An Oedipus is needed to explain these words of Apuleius. The first statement indeed seems to have been taken from the Bible, where it is read that God made all things in weight, number, and measure; but what does the second proposition mean, when it says that these things were reduced from many elements to one? I think Plato judged that prime matter consists of atoms, which then, being stamped with substantial forms, became indeed fire, or earth, water, or air, according to the nature of the informing idea; and thus the sense of Apuleius will be clear, as if he were saying: the Architect of all things, God, furnished with numbers and measures, led the elements into order, and gathered together the scattered homogeneous particles, which are the elements or principles of the same body, into one, joining aqueous atoms with aqueous ones,

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C. 3. De atomorum proprietatibus. aqueis, terreas terreis, igneasq; igneis, vnde, & à plurimis huiusmodi elementalibus particulis vnum coaluit elementum quod in ambitum propriâ regione deduxit. III. Et ignem quidem & aera, & aquam habere originem atq; principium ex trigono qui sit angulis rectis non paribus. Prima mensura quâ Deum instruit, primusq; numerus hic est expressus radices enim exordia, & origines ignis, siue pri- ma ignis elementa constant, & gignuntur, ex triangulo sca- leno cuius basis sit dimidium laterum, & latus secundum per- pendiculare ad basim, tertium autem latus obliquo ductu vtramq; lineam iungat, sic vtangulus ad basim sit minus acu- tus quam angulus ad verticem, atq; huiuscemodi triangulum duplicatu facit triangulum æquiangulum. Sit. n. triangulu[m] æquiangulum A B C per prop. 1. Eucl. l. 1. 1. diuidatur bifariam per li- neam C B ex prop. 9. eiusdem, habebis duoscalena B A D. B C D. cuiusmodi vnum est prima mensura quam Plato dat summo re- rum architecto, & principium figu- re quam habent atomi igne[us], aere[us], & aque[us] iuxta Platonem, primus autem numerus est ternarius omni- um imparium primus. Quod aute[m] de scaleno intelligendus sit Apuleius, inducor vltra explica- tionem aliâ lectione quæ sic habet, principium ex triangulo quod fit anguli recti non paribus angulis, ita enim in triangulo D B C, est vnum latus rectum B D C, & duo acuti inequales, nam major est D C B quia minorem subtendit lineam per prop. 18. primi Eucl. & per 19. eiusdem, minor autem est angulus D B C, cæteroquistante primâ lectione cum nullum possit esse

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C. 3. On the properties of atoms. watery things, earthy things from earth, and fiery things from fire; whence, from many such elemental particles, one element has coalesced, which it led into its proper region in the circuit. III. And fire indeed, and air, and water have their origin and principle from a triangle that is right-angled and not equilateral. The first measure by which he instructs God, and the first number, is here expressed; for the roots, beginnings, and origins of fire, or the first elements of fire, are constituted and generated from a scalene triangle whose base is half the sides, and the second side is perpendicular to the base, but the third side by an oblique course joins both lines, so that the angle at the base is less acute than the angle at the vertex; and a triangle of this kind, doubled, makes an equiangular triangle. Let there be, then, an equiangular triangle A B C, by prop. 1. Eucl. l. 1. divided in half by the line C B according to prop. 9 of the same, you will have two scalene triangles B A D. B C D. One such is the first measure which Plato gives to the supreme architect of things, and the principle of the figure which the atoms have, fiery, airy, and watery, according to Plato; and the first number is the number three, the first of all odd numbers. But that Apuleius is to be understood of the scalene triangle, I am led, beyond the explanation, by another reading which is as follows: principle from a triangle which has right angles not equal in the angles; for thus in the triangle D B C, there is one right side B D C, and two acute unequal angles, for the greater is D C B because it subtends the lesser line by prop. 18 of the first book of Euclid, and by prop. 19 of the same; but the smaller is the angle D B C, whereas otherwise the first reading stands, since there can be no

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De Atomis. Disp. II. esse triangulum quod non habeat tres angulos, cumq[ue] per 32. primi Eucl[is] illi tres auguli sint æquales duobus rectis, se- quitur quod ex meris rectis non potest fieri triangulum, adde quod omnes recti auguli sunt aquales inter se ex princip. 10. primi Eucl[is] ergo non potest stare prima lectio à me adducta, sed secundæ est insistendum. IV. Terram verò directis quidem angulis, trigonis, & vestigijs paribus esse. Atomiterreæ sunt directis ad se inuicem angulis, trigonis solidis, & faciebus quæ vestigium in inani faciunt imaginarium æqualibus, hoc est anguli constituentes terræ rudimenta prima sunt omnes recti, trianguli autem ex tribus lineis sibi inuicem perpendiculariter insistentibus, quæ faciunt tres angulos, & tres illius corporis dimensiones, facies autem omnes sunt æquales, quæ lineæ nisi in cubo esse non possunt, ergo particulæ terrex sunt cubicæ; Atq[ue] hoc est secundum instrumentum secundusq[ue]; numerus, quæ summo Architecto dedit Plato, angulum scilicet rectum solidum, & primum numerum parem, dualitatem. V. Et prioris quidem formæ tres Species existere pyramidem, octangulam, & vigintiangulam. Ab huiusmodi prima mensura seu angulo scaleno, & imparium numerorum primo tres generantur figuræ, pyramis, octangula, & vigesies angula: quo fit vt nullo modo sit concedendum, prioris conclusionis verba, anguli recti non paribus angulis, intelligenda esse de iso-scele quod duo latera æqualia habet, primò quia si rectus ei insit angulus nunquam ex eo coalescet perfecta pyramis, deinde quod videatur Apuleius tres angulos indicare, rectu vnu[m], & duos alios impares vti explicuimus. Pyramis autem constat quatuor tantum triangulis equiangulis cum perfecta est: Pyramis verò irregularis leges non habet, cum Euclides l. 11. def. 12. pyramidem in genere definiat

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On Atoms. Disputation II. that there is a triangle which does not have three angles, since by 32 of the first book of Euclid its three angles are equal to two right angles, it follows that a triangle cannot be made from mere right angles; add that all right angles are equal to one another, according to principle 10 of the first book of Euclid; therefore the first reading proposed by me cannot stand, but the second must be adhered to. IV. But the earth is said to be with direct angles, triangles, and equal footprints. The atoms of earth are with angles directed toward one another, solid triangles, and faces which make an imaginary footprint in the void, equal; that is, the angles constituting the first rudiments of earth are all right angles, and the triangles, moreover, consist of three lines standing to one another perpendicularly, which make three angles and the three dimensions of that body, while the faces are all equal, which lines can be in no other figure than a cube; therefore the particles of earth are cubic. And this is the second instrument and the second number, which Plato gave to the supreme Architect, namely the right solid angle, and the first even number, duality. V. And of the former form there are indeed three species: the pyramid, the eight-sided, and the twenty-sided. From such a first measure or scalene angle, and the first of the odd numbers, three figures are generated: pyramid, octagonal, and twenty-sided; so that by no means is it to be granted that the words of the former conclusion, “not right angles with non-equal angles,” are to be understood of the isosceles, which has two equal sides, first because if a right angle were present in it a perfect pyramid would never coalesce from it; then because Apuleius seems to indicate three angles, one right one, and two other unequal ones, as we have explained. But a pyramid, when perfect, consists of only four equal triangles. An irregular pyramid, however, has no law, since Euclid in book 11, definition 12, defines a pyramid in general.

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C. 3. De atomorum proprietatibus 133 niat figuram solidam quæ planis continetur, ab vno plano ad vnum punctum collectis; Certum autem est de pyramidæ re- gulari seu tetraedro audiendum Platonem vt probabitur mox autoritate Laertij. Octangula quam Apuleius appellat non est alia figura quâ octaedrum, quod definitur ab Euclide l. 1. 1. def. 27. figura soli- da quæ octo triangulis æqualibus, æquilateris continetur. Malè autem octaedrum, octangulam vertit Apuleius in mathema- ticis parum, vt licet concicere, versatus, cum octaedrum octo quidem superficies, sed angulos solidos sex tantum habeat: reuera octaedrum greca est, vox quæ figuram significat quæ octo faciebus possit consistere siue cui sint octo plana, idem de vigesies angula quam Eicosaedrum esse non dubitamus. Eicosaedrum autem ex eodem Eucl. l. 1 1. def. 29. Est fi- gura solida quæ viginti triangulis æquangulis, æquilateris conti- netur, tantum verò abest vt Eicosaedrum viginti angulos ha- beat vt sint, ei duodecim solùm: dicitur autem eicosaedrum quod viginti planis possit consistere. Confirmatur hæc expositio luculento testimonio Diogenis Laertij qui l 3. de vita philosophorum Platonis opiniones re- ferens ita loquitur: Ex elementis mundum ipsum, æ quæ in eo sunt nasci, solam terram esse immutabilem, causam esse putans figu- rarum ipsius ex quibus constet differentiam, aliorum quippe figuras euusdem generis dicit, compositas nimirum omnes ex vno oblongo ri- angulo, terræ verò propriam esse figuram. Ignis enim elementum, esse pyramidem, aeris quod octaedrum vocat, a quæ eicosaedrum, terræ autem cubum, quocirca neq; terram in ista mutari, neq; in terram conuerti, & corpora hæc quatuor cum sphæra, sunt cor- pora quinq; regularia Platonis de quibus Euclides, & doctis- simus Clauius libro vndecimo, Cælius aljiq; VI. Sphæram, æ pyramidem figuram ignis in se habere. Quiel obscu-

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C. 3. On the properties of atoms 133 in the form of a solid enclosed by planes, gathered from one plane to one point; but it is certain that Plato is to be understood as speaking of the regular pyramid, or tetrahedron, as will soon be proved by the authority of Laertius. The octangular figure which Apuleius calls by that name is no other figure than the octahedron, which Euclid defines in Book 1, Def. 27 as a solid figure contained by eight equal, equilateral triangles. But Apuleius wrongly translates octahedron as octangula, being little versed, as may be gathered, in mathematics, since the octahedron indeed has eight surfaces, but only six solid angles: in truth octaedrum is a Greek word, signifying a figure that can stand with eight faces, or that has eight planes; the same applies to the twenty-angled figure, which we do not doubt is the icosahedron. The icosahedron, moreover, according to the same Euclid, Book 11, Def. 29, is a solid figure contained by twenty equal, equilateral triangles; yet far from having twenty angles, it has only twelve: it is called an icosahedron because it can stand upon twenty planes. This explanation is confirmed by the clear testimony of Diogenes Laertius, who in Book 3, in relating Plato’s opinions on the life of the philosophers, speaks thus: From the elements he thought the world itself and the things in it arise, holding that only earth is immutable, and that the reason for the difference of the figures by which it is constituted is this: he says that the figures of the others are of the same kind, namely all composed from one oblong triangle, but that earth has its own proper figure. For the element of fire is a pyramid, that of air what he calls an octahedron, that of water an icosahedron, and that of earth a cube; wherefore neither can earth be changed into those, nor they into earth, and these four bodies together with the sphere are the five regular bodies of Plato, concerning which Euclid, and the most learned Clavius in the eleventh book, and Caelius and others. VI. That the sphere and the pyramid contain within themselves the figure of fire. Nevertheless obscu-

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De Atomis. disp. II. 134 obscurius? An ignis est in potentia ad sphæram, & pyramidé in figuratione? at cur non etiam ad cubum, magis enim distat sphæra, & tetraedrum quâ sphæra & cubus, quod pauciores angulos habeat tetraedrum, vnde, & ex scientia figuraru[m] isoperimetrarum magis recedit à sphærę natura: Si autem ab extremo ad extremu[m] in figuratione transit ignis, quare no[n] etia[m] per figuras intermedias? an ignis est sphæra, & pyramidé esse. Restat vt dicamus Platonem intellexisse quod dùm ignis sui ex iuris, & liberè pergit ad sphæram tunc sphæricis atomis facit cuneiformem diuidendo aeri figuram, si autem dissolutionem, aut generationem moliatur tunc atomorum ignearum figura ad faciliorem penetrationem fit tetraedica: atq[ue] ex hac configuratione oritur ingens ignis vis, quia cuneus ex Guido Vbaldo reducitur ad duos vectes secundi generis quæst. 17. mechanicarum Aristotel. vide Blancanum ibidem: in locis Aristotelis mathematicis eleganti libro explicatis. VII. Octangulam verò aëris: angulatam vigesies sphæram aquæ dicatam esse, hoc est, aer octaedricę est figurę, aqua ei cosaedricæ; vocat autem sphæram angulatam vicies quod viginti triangulis constet hoc corpus, & parum distet à forma sphærica, ob multiplices angulos. VIII. Æquipedum verò trigonu[m] efficere ex se se quadratum, quadratu[m] verò cubum quæ terræ sit propria, figura. Id est, Isosceles triangulum quod habeat pedes, siue latera vtrimq[ue]; recto angulo insistentia, si per seipsum multiplicetur, efficiet quadratum, nam triangulum A B D. est Isosceles, & illud multiplicatum per se ipsum facit quadratum A B D C. quod est duplum trianguli A B D. quadratum autem multiplicatum per suum Isosceles facit cubum qui terræ fi- gura

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On Atoms, disp. II. 134 more obscurely? Is fire potentially a sphere, and in its shape a pyramid? But why not also a cube, since a sphere and a tetrahedron are more different than a sphere and a cube, because the tetrahedron has fewer angles; whence, also, by the science of isoperimetric figures, it departs more from the nature of the sphere. But if fire passes in shape from one extreme to the other, why not also through intermediate figures? Is fire a sphere, and to be a pyramid? It remains for us to say that Plato understood that when fire, by its own nature, proceeds freely toward the sphere, then he makes with spherical atoms a wedge-shaped figure by dividing the air; but if he is engaged in dissolution or generation, then the figure of the fiery atoms, for easier penetration, becomes tetrahedral. And from this configuration there arises the great force of fire, because the wedge, according to Guido Ubaldo, is reduced to two levers of the second kind, question 17 of the Mechanical Questions of Aristotle; see Blancanus there, in the places of Aristotle explained in a mathematical and elegant book. VII. The octagonal figure of air; and the one called the twenty-angled sphere of water, that is, air is of the octahedral figure, water of the icosahedral; but it is called the twenty-angled sphere because this body consists of twenty triangles, and differs little from the spherical form, because of its many angles. VIII. An equilateral triangle makes from itself a square, and a square a cube, which is the proper figure of earth. That is, the isosceles triangle, which has feet, that is, sides on either side resting upon the right angle, if multiplied by itself, will produce a square; for triangle A B D is isosceles, and when multiplied by itself makes the square A B D C, which is double the triangle A B D. But the square, multiplied by its isosceles, makes a cube, which is the figure of earth.

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C. 3. De atomorum proprietatibus. 135 A B gura est, quod itidem numeris exprimititur, cum enim secunda mensura quam Deo adscribit sit angulus rectus ex num. 4. huius pariter & numerus inter pares primus, nam 2. per 2. faciunt 4. at 2. per 4. reddit 8. primumq[ue] numerum radicem, secudum numerum planum, tertium cubum vocant C D 2. 4. 8. Cubus itaq[ue] conficitur ex duodecim Isoscelibus, & sex quadratis qui numeri sunt proportionales inter radicem, planum, & cubum vt patet 2. 4. 6. 8. 12. Octaedrum constat sexdecim scalenis quorum singula per se revoluta faciunr octo triangula æquilatera. Eicosaedrum ex quadraginta scalenis quæ complicata faciunt viginti triangula æquilatera, harum autem figurarum nulla est radix, ideòq[ue] imparium numerorum primo instruxit Deum Plato. IX. Quapropter mobilem pyramidis formam igni dedit, quod eius celeritas agitationi videatur esse consimilis. Secundæ velocitatis octangula sphæra est, bancaeridetulit, qui leuitate, & pernicitate post ignem secundus est, & Vicenalis sphæra est locotertio huius forma fluida, & volubilis, & aquæ similior est visa. Restat tesserarum figura quæ cum sit immobilis terræ substantiam non absurde sortita est. Et alia initiareperiri forsitam posse quæ aut Deo nota sunt, vel ei qui Dijs sit amicus. In hoc contextu conatur infeliciter Apuleius reddere doctrinæ Platonicæ rationem, primò enim errat cum dicit mobilissimam figurarum omnium esse pyramidem, difficilius enim mouetur quam sphæra, imo quam octaedrum, nam in octaedro eiusdem [left margin] areæ cum pyramidæ, linea directionis minus distat ab angulo, quàm in tetraedro:

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C. 3. On the properties of atoms. 135 A and B the figure is likewise expressed by numbers; for when the second measure which he ascribes to God is the right angle, from number 4. this likewise, and the number among the even ones is first; for 2 by 2 makes 4, but 2 by 4 gives 8; and they call the first number the root, the second the plane, the third the cube. C D 2. 4. 8. The cube therefore is made up of twelve isosceles triangles, and six squares, which numbers are proportional between root, plane, and cube, as is clear from 2. 4. 6. 8. 12. The octahedron consists of sixteen scalene triangles, each of which, when turned over by itself, makes eight equilateral triangles. The icosahedron is made from forty scalene triangles, which, when joined together, make twenty equilateral triangles. But of these figures none has a root; therefore Plato first assigned God to the odd numbers. IX. For this reason he gave the mobile form of the pyramid to fire, because its swiftness seems similar to agitation. The second in velocity is the eight-sided sphere; Bancaeridetulit, who, by reason of lightness and speed, is second after fire. And the twentieth sphere is in the third place; this form is fluid and rolling, and seems more like water. There remains the figure of the dice, which, since it is immobile, not without reason received the substance of earth. And perhaps other beginnings may also be found, which are known either to God, or to him who is a friend to the gods. In this context Apuleius tries unsuccessfully to render the doctrine of Plato; first indeed he errs when he says that the most mobile of all figures is the pyramid, for it is moved with more difficulty than the sphere, indeed than the octahedron, for in the octahedron, of the same [left margin] area as the pyramid, the line of direction is less distant from the angle than in the tetrahedron:

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136 De Atomis. Disp. II. dro: leuissima verò ratio est ignis formam esse pyramidalem quòd flamma in acumen definat, primò quia vt sic est potius conoidea siuè in meteformam, nisi ab alimento determinetur, secundò quia est ignis impurus fumo exhalationibusq[ue] immersus, ergo ab illa agitatione cuspidis malè colligit Plato ignem esse pyramidalem. Sin autem velocitatis motus in elementis habenda esset ratio, cum omnibus par sit videre tur eadem tribuenda figura, nam æquè velociter terra fertur deorsum ac ignis sursum, ratione verò densitatis fluiditatisq[ue] tribuenda esset è quinq[ue] corporibus Platonicis sphærica figura igni, cubica terræ, eicosaedrica aeri, octaedrica aquæ. At enim ad refutandum Platonis literalem sensum, cum elementa debeant replere locum quannam amabo ratione id facient si terra sit cubica aqua ei cosaedrica, aer octaedrus, ignis autem sphæricus vel pyramidalis? nam meri quidé cubi locum replent, tetraedri autem id nequeunt vel cubis iuncti aut per se, octaedri vel eicosaedri multò minus, de sphæra manifestissimu[m] est; Quæ clarissimè demonstrari possunt quia ad id vt locus repleatur, figuræ debent ità inter se coalescere vt angulos faciant quatuor rectis æquales, si enim deficiant se tangent quidem, sed relinquent in medio hiatum; frautem superent nunquam angulum explebunt cuius: propositionis demonstrationem videre potes apud Euclidem Clausj l. 4. elem. Quo spectans Aristoteles argumentatus contra Platone[m] tertio cæli t. 66. ità pronuntiat. Omnino autem eniti simplicibus corporibus figuras tribuere irrationabile est, primò quidem quia accedit non repleri totum; nam in planis tres figuræ videntur implere locum, triangulus, quadratum, & sex angulus, in solidis verò duæ solùm pyramis, & cubus. Quò in loco nota Aristotelis crassissimum lapsum dùm ait pyramides, siue tetraedra (de illis enim ex assumptis à Platone loquitur) replere locum; ex figuris. solidis

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136 On Atoms. Disp. II. dro: indeed, the very weak reason for saying that fire’s form is pyramidal is that flame ends in a point; first, because in this state it is rather cone-shaped, or of the form of a cone, unless determined by its fuel; secondly, because it is impure fire, immersed in smoke and exhalations; therefore, from that motion of the tip, Plato infers badly that fire is pyramidal. But if the speed of motion among the elements were to be taken into account, since all are equally seen to move, the same figure ought to be assigned to them all; for earth is borne downward just as swiftly as fire upward. But by reason of density and fluidity, from the five Platonic bodies the spherical figure should be assigned to fire, the cubic to earth, the icosahedral to air, the octahedral to water. But to refute Plato’s literal meaning: since the elements ought to fill space, by what possible reasoning, I ask, would they do so if earth were cubic, water icosahedral, air octahedral, and fire spherical or pyramidal? For only pure cubes fill space; tetrahedra cannot do this, either joined with cubes or by themselves; octahedra or icosahedra even less so, and in the case of a sphere it is most evident. This can be most clearly demonstrated, because in order for a space to be filled, the figures must cohere with one another so as to make angles equal to four right angles; for if they fall short, they will indeed touch one another, but they will leave a gap in the middle; if they exceed it, they will never fill the angle in question. You can see the proof of this proposition in Euclid, Clavius, book 4 of the Elements. Looking to this, Aristotle, arguing against Plato in Book 3 of On the Heavens, text 66, states as follows: “Altogether, however, it is irrational to assign figures to simple bodies, first indeed because it follows that the whole is not filled; for in planes three figures seem to fill space, the triangle, the square, and the hexagon, but in solids only two, the pyramid and the cube.” Here note Aristotle’s very gross slip when he says that pyramids, or tetrahedra (for of these he is speaking from the figures assumed by Plato), fill space; from the solid figures

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C.2. Omnia ex atomis componi. 137 solidis regularibus soli cubi replent locum solidum per se sumpti, octaedra verò compacta tetraedris idem præstant, vt demonstrat Maurolycus libro de figuris planis solidisq[ue]; locum replentibus. De cubis quidem non est difficultas cum enim octo suis angulis cubi quatuor concurrant qui ex vtraq[ue] superficies æquales sunt quatuor rectis, sequitur quod replent locu[m] solidum. At verò tetraedra per se locum non replent, quia vel confla-rent vnum ex corporibus regularibus vel aliud quod piam; non aliud, neq[ue]; enim datur ex scholio 13. element. neq[ue]; vllum ex illis quia diameter huiusmodi corporis esset dupla lateris eiusdem, cum enim pyramides ad cetrû[m] sphærê concurrant sequitur quod ex duobus lateribus diameter con- stat, ergo diameter illius corporis, & sphæræ inscriptæ esset in dupla proportione quæ proportio in corporibus regularibus non reperitur ex 13. elem. Eucl. ergo tetraedra vacuum non implent. At octaedra compacta tetraedris locum repleat faciuntq[ue]; corpus irregulare. Errauit itaq[ue]; Aristoteles in hoc textu: quod erat demonstrandum. Platonem verò existimant nonnulli primò locutum de singulorum elementorum masla, ità terræ mole cubicam, aliasq[ue]; mundi regiones suis figuris insignitas; Alij mysticè commentatum aiunt, plures Pythagoræ arithmeticam voluisse coniungere geometrię ægyptiacę, alij alia pro studio, & eruditio- ne comminiscuntur. Tu vide Clauij sphæram cap. 1. Marsilium Ficinum, Eugubinum de perenni philosophia &c. Con-cludo autem Platonem existimasse elementa constare ex atomis vt patet ex consequentia quam elicit Aristoteles 1. 3. de cælo

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C.2. That all things are composed of atoms. 137 Among regular solids, only cubes, taken by themselves, fill solid space; but octahedra compacted with tetrahedra do the same, as Maurolycus demonstrates in the book De figuris planis solidisque locum replentibus . As for cubes, there is indeed no difficulty, since four of their angles meet at each of the cube’s eight corners, and these are equal on both surfaces to four right angles; it follows that they fill solid space. But tetrahedra by themselves do not fill space, because either they would form one of the regular bodies or some other kind of body; not another, for none is given, as appears from Scholium 13 of the Elements; nor any of those, because the diameter of such a body would be double its side. For since pyramids meet at the center of the sphere, it follows that the diameter consists of two sides; therefore the diameter of that body, and of the inscribed sphere, would be in a double proportion, a proportion not found among regular bodies, as appears from Euclid, Elements 13. Therefore tetrahedra do not fill the void. But compact octahedra with tetrahedra make space full and produce an irregular body. Thus Aristotle erred in this text: which was to be demonstrated. Some think that Plato first spoke of the mass of the individual elements, namely the cubic mass of earth and the other regions of the world distinguished by their figures. Others say he commented mystically; more say that Pythagoras wished to join arithmetic with Egyptian geometry; others invent other things out of zeal and learning. See Clavius, Sphaera , ch. 1; Marsilio Ficino; Eugubinus, De perenni philosophia , etc. I conclude, however, that Plato thought the elements consist of atoms, as is clear from the consequence which Aristotle draws in De caelo 1, 3.

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138 De Atomis. Disput. II. cælo t. 65. vbi sic ait. Necesse est autem eos qui figuram faciunt vniuscuiusq[ue] elementoru[m], et hæc determinant substantias ipsoru[m] face- re ipsa indivisibilia, sphæra .n. diuisa sphæra non est .c. Attamen comodissimè ex Democrito singulis elemétoru[m] atomis figuras dabimus neq[ue]; vllu[m] sequi videbis aut in loci repletione aut in mixtione inconueniens. Tu verò hanc abstrusioris philoso- phię digressionem Platoni, & Apuleio condonabis: Cum .n. arduissimam aggressuri simus de elementorum figuris primi- genijs disquisitione[m] visus mihi est Plato qui audiretur dignus, licet ipsi nulla tenus subscribam nisi quantum ille Democrito. PROPOSITIO XXVII. Atomis igneis figuram assignare ex Democrito. SCio Epicurum in epistola ad Herodotum, & Pythoclem apud Laertium existimare atomos nullam qualitatem sensibi- lem admittere præter figuram, grauitatem, magnitudinem, qualitas enim omnis mutatur atomi verò nihil mutantur. Democritus au- tealiter censuit, & quamuis nullam qualitatem quæ sensu per- cipi posset in atomo concederet primas tamen, quas intueretur més, admisit, easq[ue] immutabiles posuit, vtsupra diximus, dissol- uitur autem mixtum turbata oeconomia, & atomis ad noua molienda conuolutis ab extrinsecos agente, cuius vis alliciendis ijs potétior sit quam formæ potentia, coercendis: excutiuntq[ue] iugum plerumq[ue]; primæ omnium igneæ atomi, quæ suæ primi- geniæ figuræ restituuntur atq[ue]; ità per aerem, (quem inane, & vacuum appellabat Democritus vt supra diximus confirma- turq[ue]; ex Galeno aduers. empir. Isag. 36.) vagantur nouæ ge- nerationis appetentes. Determinauit autem atomis igneis figuram sphæricam De- mocritus vt ostendimus in synopsi huius libri pag. 24. nume- ro 9. & pag. 26. num. 8. quæ doctrina probatur. Primo

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138 On Atoms. Disputation II. in the heavens, t. 65, where he says thus: “It is necessary that those who make the figure of each of the elements, and who determine these as their substances, should make them themselves indivisible; for a divided sphere is no sphere.” Yet most fittingly, from Democritus, we shall assign shapes to the atoms of each element, and you will see that none follows either in the filling of place or in mixture that is inconsistent. But you will pardon this digression into the more obscure philosophy, to Plato and Apuleius. For since we are about to undertake a very difficult inquiry into the primordial figures of the elements, Plato seemed to me worthy of hearing, though I by no means subscribe to him except insofar as he does to Democritus. PROPOSITION XXVII. To assign a figure to fiery atoms, according to Democritus. I know that Epicurus, in the letter to Herodotus and to Pythocles cited by Laertius, thought that atoms admit no sensible quality except figure, weight, and magnitude; for every quality changes, but atoms do not change at all. Democritus, however, held otherwise; and although he allowed in the atom no quality that could be perceived by sense, he nevertheless admitted the primary qualities that the mind contemplates, and set them as immutable, as we said above. But the mixed body is dissolved when its economy is disturbed, and the atoms, being turned aside to new motions by an external agent whose power in attracting them is stronger than the power of form in restraining them, shake off their yoke, and most often the fiery atoms are the first of all to do so; these are restored to their original figure, and thus wander through the air, which Democritus called the void and empty space, as was confirmed above from Galen against the Empirics, Isag. 36, seeking new generation. Democritus, as we showed in the synopsis of this book, page 24, number 9, and page 26, number 8, assigned a spherical figure to fiery atoms; and this doctrine is proved. First

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C. 3. De atomorum proprietatibus 139 Primò. Amobilitate figuræ sphæricæ quæ quod tangat in puncto, vt demonstrauit Theodosius 1. sphæric. prop. 3. se- quitur quod linea directionis eius motus nullo negotio mutari possit, ignis autem mobilissimus esse debet, & veluti genera- tionum omnium choragus. Secundò. Cû sphæra angulis omnibus careat nihil hamati aut retinentis offendet, facilè permeabit, & quoquo versus ad naturæ penetrabit instituta, diuidet, instar cunei, & quod nulli alteri figuræ contingit contactu puncti labefaciens planum statim amplosinu sibi viam facit, cum nihil habeat angu- losi quo possit detineri, quod eius actiuitati necessarium fuit. Tertiò. Cum ignis nobilissimum sit totius naturę agens ei conuenit figura omnium nobilissima, que sphærica est, cuius viginti proprietates admirabiles, igniq; affines annotaui. I. Proprietas. Figura est simplicissima, cuius generatio fit à semicirculo circa suam diametrum circumuoluto: circuli au- tem origo est duplex, prima ex semidiametro circa extremitatem suam immobilem circumductâ, alia verò est à sectione paralella basi coni atq; vt sic circulus easdem habet fere pro- prietates quas ellipsis, vt annotat Leautaudus in suo de sectione nibus conicistractatu que geometricis problematibus inseru- it. Videtur autem valdè congruum vt hæc figura igni con- ueniat non tantùm tanquam corpori simplici, verùm etiam quod globorum progredientium instar voluntentur, quasi se illo motu pe petuò circinarent: Isq; volutationis motus in globorum tormentariorum eiaculatione probabitur à me suo loco, & in sole manifestus est quod igne constet, ex Scheinero in rosa Vrsina. II. Fortissima figurarum est sphærica, cum non sit ratio cur vnum potius cedat quam aliud, ex quo iuuatur ignis ac- tiuitas. III. Inę-

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C. 3. On the properties of atoms 139 First. From the mobility of the spherical figure, which touches at a point, as Theodosius demonstrated, 1. Sphæric. prop. 3, it follows that the line of direction of its motion can in no way be changed; but fire ought to be most mobile, and as it were the leader of all generations. Second. Since the sphere lacks all angles, nothing hooked or retentive will impede it; it will easily pass through, and in every direction penetrate the dispositions of nature; it divides, like a wedge, and, unlike any other figure, by the contact of a point, breaking up the plane, immediately makes for itself a wide passage, since it has nothing angular by which it can be detained, which was necessary for its activity. Third. Since fire is the noblest agent in all nature, there belongs to it the noblest of all figures, which is the spherical one, whose twenty admirable properties, akin to fire, I have noted. I. Property. It is the simplest figure, whose generation is made from a semicircle revolved around its diameter; but the origin of the circle is twofold: the first, from a semidiameter drawn around its immobile extremity; the other is from a section parallel to the base of a cone, and thus the circle has nearly the same properties as the ellipse, as Leautaudus notes in his treatise On Conic Sections, which he inserted into geometrical problems. It seems, however, very fitting that this figure should belong to fire, not only as to a simple body, but also because, like advancing globes, they are turned about, as though they were continually circling themselves by that motion. And this motion of rolling will be proved by me in its proper place in the launching of cannonballs, and in the sun it is manifest, since it consists of fire, according to Scheiner in the Rose of Ursinus. II. The strongest of figures is the spherical, since there is no reason why one should give way rather than another, from which the activity of fire is aided. III. In-

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140 De Atomis. Disput. II. III. Inæqualiter virtualitates suas omnes seu partes mathematicas situatas habet, nâ in sphærę superficie nulla est imaginabilis quæ ex æquo alteri adiaceat, alioqui curua nô esset. IV. Sphæra habet hoc proprium vt sub exiguis terminis multum comprehendat areæ, est enim figurarum omnium sibi isoperimetrarum capacissima, vnde ex illa collectione, & adunatione maiori, atomo nullo modo dispersa per locum expansum, augetur eius actiuitas. V. partes omnes sphæræ sunt similiter positæ, & superficii puncta omnia pari inflexione, & ordine coronantur. VI. Nulla figura regularis potest moueri circa suum centrum quin locum mutet saltem secundum quid exceptâ sphærâ, quæ moueri potest, & girari loco nulla ratione mutato. Dixi regularis, nam conus, ellipsis solida, cylindrus, parabola, & hyperbola solida sic etiam moueri possunt. Hæc autem mobilitas seu giratio concessa videtur atomis igneis, à natura vt magis vegeti sint caloris, actiuitasq[ue] sua eo motu propagetur. VII. Nulla figura mouetur facilius sphæricà, siue naturaliter, siue violenter. Naturaliter in motu deorsum per aqua (nam per vacuum aut inane, qui est aer, æqualis omnibus figuris est mobilitas) citius descendunt lapidei globi quam plani aut lati lapides. Violenter autem, in motu volutationis id patet, quia difficiliùs sistitur impetus adeò vt linea directionis ad centrum mundi sit in axi globi, tria enim sunt puncta, per quæ debet transire linea recta imaginaria in qua sola qui escere potest globus: primum est centrum mundi, alterum centrum grauitatis globi, tertium punctum contactus, si alterutrum istorum sit extra lineam quietis nunquam firmabitur, sed eo vsq[ue] mouebitur globus dum huiusmodi tria puncta sint in linea directionis, quàm autem facilè sit globum impellere

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140 On Atoms. Disputation II. III. It has all its virtualities, or mathematical parts, situated unequally; for on the surface of a sphere there is no imaginable point which lies equally adjacent to another; otherwise it would not be curved. IV. A sphere has this property, that within small bounds it contains much area; for among all figures that are isoperimetric with it, it is the most capacious, wherefore from that greater collection and union, not dispersed in any way by the atom through extended space, its activity is increased. V. All the parts of a sphere are similarly placed, and all the points of the surface are crowned with equal inflection and order. VI. No regular figure can move about its center without changing its place at least in some respect, except the sphere, which can be moved and turned in place without any change. I said regular, for a cone, a solid ellipsis, a cylinder, a parabola, and a solid hyperbola can also be moved in this way. This mobility or rotation seems to be granted to fiery atoms, so that by nature they may be more active in heat, and their activity may be propagated by that motion. VII. No figure moves more easily than the spherical, whether naturally or violently. Naturally, in downward motion through water (for through a vacuum or empty space, which is air, mobility is equal for all figures), stone globes descend more quickly than flat or broad stones. Violently, in the motion of rolling, this is clear, because the impulse is more difficult to stop, so much so that the line of direction to the center of the world is in the axis of the globe; for there are three points through which the imaginary straight line in which the globe alone can move must pass: the first is the center of the world, the second the center of gravity of the globe, the third the point of contact. If either of these is outside the line of rest, it will never be stabilized, but the globe will keep moving until such time as these three points are on the line of direction; how easy it is, however, to impel a globe

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C. 3. De atomorum proprietatibus. 141 pellere, patet inde quod si sit in plano perfecto illud in puncto tanget ac proinde vno tantum puncto innititur, debiliq[ue]; illo fundamento eijcitur facilè. Contrariâ ratione se se habent figure planè. Deindem meliùs impetum concipit sphéra, diutiùs retinet, violentiùs vrget, æqualiùs dispensat ex quibus ignea mobilitas augetur. Videbis Theoricam nostram mili- tarem Theor. 4. & 5. lib. primi. VIII. Vnum tantum habet punctum coelo vicinius quo- cunq[ue]; in situ ponatur, vnoq[ue]; tantum propius accedit ad cen- trum mundi. IX. Omnium figurarum solidarum est regula præsertim regularium, quæ tales sunt cum earum latera segmentis vndiquaq[ue]; æqualibus sphæram detruncant. Præterea omnes figu- ræ sphærica inscribuntur, & circumscribuntur, proprietatis igneæ symbolum, ignem enim motibus, & figurationibus præsidere voluit Plato. X. Circulus vna linea, sphæra vna superficie finitur quod istis figuris est singulare, ellipsi solida exceptâ quæ ideo sphéroides dici posset, reliquæ enim figuræ vel plures lineas aut plures habent superficies. XI. Oppositæ partes omnes æqualiter à se distant. XII. Longitudo latitudo, & profunditas sphæræ sunt æquales, nempe tres diametri. XIII. Initio, & fine caret sphéra vt etiam circulus. XIV. Sphêræ superficies est incommensurabilis cum su- perficie plana. XV. Sphéra est commensurabilis potentiâ non antem lon- gitudine cum alijs sphêris maioribus vel minoribus. XVI. Sphéra circa suum centrum volutata simul & se- mel sursum deorsum, & in transuersum mouetur, quod egre- giè, & ingeniosè demonstrat Aristoteles in mechanicis agens de motu circulari in principio. XVII.

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C. 3. On the properties of atoms. 141 it is clear from this that if it be on a perfect plane it touches at that point, and therefore rests on only one point, and is easily cast off from that weak foundation. In the contrary way, plane figures behave. Next, a sphere conceives motion more easily, retains it longer, presses more violently, distributes it more evenly, from which its fiery mobility is increased. See our military Theory, Theor. 4 & 5 of the first book. VIII. It has only one point nearer to the heaven, in whatever position it is placed, and only by one point does it approach the center of the world more closely. IX. This is the rule for all solid figures, especially regular ones, which are such when their sides cut the sphere with segments equal on every side. Moreover, all figures are inscribed in and circumscribed about the sphere, a symbol of fiery property, for Plato wished fire to preside over motions and formations. X. A circle is bounded by one line, a sphere by one surface, which is singular to these figures, except for the solid ellipse, which on that account could be called a spheroid; for the remaining figures have either more lines or more surfaces. XI. All opposite parts are equally distant from one another. XII. The length, breadth, and depth of a sphere are equal, namely three diameters. XIII. The sphere, like the circle, lacks beginning and end. XIV. The surface of a sphere is incommensurable with a plane surface. XV. A sphere is commensurable in power, but not in length, with other spheres, whether larger or smaller. XVI. When a sphere is rolled around its center, at the same time and all at once it moves upward, downward, and across, which Aristotle demonstrates excellently and ingeniously in the Mechanics, speaking of circular motion at the beginning. XVII.

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142 De Atomis. Disp. II. XVII. Sphæra non habet vllam secum proportionem, tantùm abest vt sit ei aliqua cum alijs figuris ratio, nam superficiei ad suam diametrum hactenus non potuit reperiri vlla, proportio geometrica. XVIII. Sphæra est prima, & vltima figurarum solidarum, omnes enim ab illa oriuntur, & omnes in eam desinunt: planarum prima est circulus, planarum vltinga circulus, ortus enim trianguli æquianguli est à circulorum æqualium intersectione mutuâ per centrum ex Euclid. I 1. pro. 1. omnes pariter figuræ planæ desinunt in circulum, & cum eo conponuntur vt patet ex lib. 4. element. Euclidis figuræ autem solidæ ad sphæram reducuntur, & quo pluribus angulis sunt præditæ eo magis ad illam accedunt quamuis sphæra sit figura solida omnis anguli expers, quæ autem pauciores habent angulos magis distant à sphæræ perfectione: & quamuis figurarum numerus sit infinitus in hoc tamen infinito datur primum, & vltimum, cum prima figurarum planaru[m] sit circulus idemq[ue]; sit vltima: solidarum verò prima, & vltima sphæra est. XIX. Perfectissima est figurarum eademq[ue]; facillimæ constructionis, quo fit vt Deum rotundæ figuræ somniauerit Anaximenes, & pretiosa facilia esse inuentu, & praxi Diogenes Cymicus pronuntiauerit. Natura verò cui perfectio, & facilitas acceprissima sunt, pleraq[ue]; sua rotundę figurę facit, fructu[m] pleriq[ue]; sunt sphærici aut ad illam figuram accedunt, circulares certè sunt trunci arborum, radices, rami aliaq[ue]; facta videntur ad tornum, quia scilicet faciliùs illis terminis plura continentur, & speciosiori apparatu mundum exornant. XX. Quidquid tangit, exceptà concauitate eiusdem cum sua conuexitate rationis, tangit tantu[m] in puncto vt demonstrauit Theodosius, & ratio est quia curua nulla linea potest adequaretur autem si tangeret in pluribus punctis quam in vno. Hanc

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142 On Atoms. Disp. II. XVII. The sphere has no proportion with itself; so far is it from having any relation with the other figures, for up to now no geometric proportion has been found between its surface and its diameter. XVIII. The sphere is the first and the last of solid figures, for all arise from it, and all end in it: of plane figures the first is the circle, the last of plane figures likewise the circle; for the origin of the equilateral triangle is from the mutual intersection of equal circles through the center, from Euclid I.1, prop. 1. In like manner all plane figures end in the circle, and are composed with it, as is evident from book 4 of Euclid’s Elements. Solid figures, however, are reduced to the sphere, and the more angles they have, the more they approach it; although the sphere is a solid figure without any angle, those which have fewer angles are farther removed from the perfection of the sphere. And although the number of figures is infinite, in this infinite there is nevertheless a first and a last, since the first of plane figures is the circle, and the same is the last; of solids, however, the sphere is both the first and the last. XIX. It is the most perfect of figures, and likewise the easiest to construct, which is why Anaximenes imagined the gods as round figures, and Diogenes the Cynic declared that precious things are easy to discover and to practice. Nature, however, to which perfection and ease are most pleasing, makes most of her things in round form; most fruits are spherical or approach that figure, and certainly the trunks of trees, roots, branches, and other things appear to have been made for the lathe, because more can more easily be contained within those bounds, and they adorn the world with a more pleasing appearance. XX. Whatever touches, except the concavity of the same ratio as its convexity, touches only at a point, as Theodosius demonstrated, and the reason is that no curved line can be made equal to it if it touched at more points than one. This

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C. 3. De atomorum proprietatibus. 143 Hanc sanè originalé esse atomoru ignearu figurâ non diffi- cilè persuadeor, ob potissimas sphærę proprietates que igni conueniunt, nihilominus tamen illam figuram in quamlibet aliam commutari posse duobus indicijs adducor, vt ità cesea. Primò quia cum ignis sit liquidus ex Democrito, & Virgi- lio Eclogà Sileni Et liquidi simul ignis, sequitur eum facilè co- erceri alienis terminis difficile suis, ergo facile mutat figurâ. Secundò quia mutatio illa figure necessaria est ad vnio- nem cum alijs atomis faciendam, neq; enim in puncto mathe- maticè indiuisibili potest vnio, modus nempe physicus, con- sistere, ergo illam relinquit vt commodiorem habeat: adde quod formarum inclinationi, & materiæ organizationi de- bent subseruire: Vnde, & Democritus infinitas esse atomo- rum figuras censuit, hoc est indeterminatas quoad aptitudi- nem eademq; atomus quæ in pluma erit cylindrica, in carne erit parallelepipeda, in osse pyramidalis. Cæterum atomi in libertatem assertæ, & ab vnione segregatæ ad natiuam figu- ram se se continuò reducunt quæ igneis est sphærica. Ignea- rum ergo figuram, & qualitatem atomorum determinauimus ex Democrito, quod erat nobis faciendum. PROPOSITIO XXVIII. Atomorum terrearum figuram ex Democrito determinare. E A est ignem inter, & terram differentia, vt ille diuisus in particulas pluribus locis sit immixtus, suâq; agilitate abusus per omnia loca vagetur, neq; vllum in vniuerso locum occupet determinatum, cum ea, quæ de ignis sphæra somnia- runt veteres, ne minimam quidem veritatis vmbrâ contra re- centiorum astrologorum animaduersiones obtineant. Terra verò suis conglobata nutibus atq; in vnum globum compacta centrum mundi obsidet, quo etiam singulæ, tum aquæ, tum K terræ

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C. 3. On the properties of atoms. 143 I am certainly not with difficulty persuaded that this is the original figure of the fiery atoms, because of the chief properties of the sphere which agree with fire; nevertheless I am led by two indications to think that that figure can be changed into any other, so that it may be said thus. First, because since fire is liquid, according to Democritus, and Virgil in the Eclogue of Silenus, “and at the same time liquid fire,” it follows that it is easily restrained by foreign bounds, but with difficulty by its own; therefore it easily changes figure. Second, because that change of figure is necessary for the union to be made with other atoms, for in a mathematically indivisible point no union, namely the physical mode, can consist; therefore it leaves that and has a more convenient one. Add that they must serve the inclination of forms and the organization of matter. Hence Democritus judged that there are infinite figures of atoms, that is, indeterminate as to aptitude; and the same atom, which will be cylindrical in a feather, will be parallelepipedal in flesh, and pyramidal in bone. Moreover, atoms, when set at liberty and separated from union, continually return to their native figure, which in fiery atoms is spherical. We have therefore determined the figure and quality of fiery atoms from Democritus, which was what we had to do. PROPOSITION XXVIII. To determine, from Democritus, the figure of earthy atoms. The difference between fire and earth is such that the former, divided into particles, is intermingled in many places, and, abusing its own agility, wanders through all places, and occupies no determinate place in the universe, whereas those who dreamed of the sphere of fire hardly have even a shadow of truth against the observations of more recent astronomers. But earth, gathered together by its own impulses and compacted into one globe, occupies the center of the world, where also each of the waters and of the earths ... K terræ

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De Atomis. Disp. II. terræ particulæ perpendiculari via feruntur, quare de atomis igneis aliter quam de terreis nobis philosophandum fuit. Primò itaq[ue] cum sibi inuicem terree particulæ cohæreant debet ipsis conuenire ea figura quà locum repleant, alioqui inter atomos, & atomos vacuum daretur, vt si sphericæ essent, hiatus inter puncta contactuum inanes remanerent sed quæ locum repleant figuræ simul iunctæ sunt tantum tres, triangulum, quadratum, & hexagonum, ex quibus fiunt figuræ solidæ pyramis, cubus, & hexagonum solidum duobus hexagonis oppositis, & sex circumquaq[ue] parallelogrammis terminatum. Verùm vt melius figuram terrearum atomorum inuestigemus. Obseruo primò ex Corollario 15. 1. Eucl[ides] duas rectas se mutuò intersecantes efficere ad punctum sectionis 4. angulos 4. rectis æquales, imo quotcunq[ue] fuerint anguli circa vnum punctum, rectos quatuor non excedent simul sumpti, vt circa punctum A sunt quatuor anguli B A E C, C A D, D A E, E A B, quatuor rectis æquales. Obseruo secundò ex eodem Euclid. 1. 1. in schol. p. 32. omnes angulos figuræ B A rectilineæ cuiusuis æquales esse bis tot rectis angulis quota ipsa est inter figuras rectilineas, prima autem figura est triangulus cuius omnes anguli simul sumpti sunt æquales bis vni recto angulo, id est duobus rectis, anguli figuræ 2. seu quadrati sunt æquales bis duobus rectis id est quatuor. Anguli tertiiæ figuræ seu pentagoni sunt æquales ter duobus rectis id est sex rectis, & sic de alijs: horum autem omitto demonstrationes cum geometriæ tyrocinio sint propriæ, & cuiuis apud Euclidis interpretes obuiæ his præsuppositis. Demon-

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On Atoms. Disputation II. Earthy particles are carried in a perpendicular course; therefore we had to philosophize differently about fiery atoms than about earthy ones. First, then, since the earthly particles cohere with one another, the figure that suits them must be one by which they fill up space; otherwise there would be a vacuum between atoms and atoms. For if they were spherical, empty gaps would remain between the points of contact; but the figures that, when joined together, fill space are only three: the triangle, the square, and the hexagon, from which are formed solid figures, namely the pyramid, the cube, and the solid hexagon, bounded by two opposite hexagons and six parallelograms all around. But that we may better investigate the figure of the earthy atoms, I observe first, from Corollary 15 of Book I of Euclid, that two straight lines intersecting one another produce, at the point of intersection, four angles equal to four right angles; indeed, however many angles there may be around one point, taken together they do not exceed four right angles, as around point A there are four angles, B A E, C A D, D A E, E A B, equal to four right angles. I observe second, from the same Euclid, Book I, in the scholium on p. 32, that all the angles of any rectilinear figure are equal to twice as many right angles as the figure itself has sides. Now the first figure is a triangle, all of whose angles taken together are equal to twice one right angle, that is, two right angles; the angles of the second figure, or square, are equal to twice two right angles, that is, four. The angles of the third figure, or pentagon, are equal to three times two right angles, that is, six right angles, and so on for the others. But I omit the demonstrations of these, since they properly belong to beginners in geometry and are found readily enough in the commentators on Euclid. On these things being presupposed. Demon-

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C. 3. De atomorum proprietatibus. 145 Demonstro quod superius tanquam pro minore mei argu- menti posui, sed ex omnibus figuris quæ simul iunctæ locum repleant sunt tantum tres triangulum, quadratum, hexago- num ità vt inter ipsas deinceps positas nihil intercedat vacui. Cum enim sex triangulorum anguli, & quatuor quadrato- rum, & tres hexagonoru[m] sint [con]quales quatuor rectis, quod spa- tium vnicuiq[ue]; puncto circumfunditur, sequitur his figuris locum repleri posse, alios verò nequaquam: pentagoni enim v.g. anguli tres sunt [con]quales rectis 3. 3/5 tantum ergo deficiunt à loco replendo; quatuor verò anguli [con]quales sunt rectis an- gulis 4. 4/5 ergo excedunt, idem de alijs figuris dictum esto. Egi tantum de figuris regularibus, neq[ue] enim dubium est quin terrearum atomorum figura sit simplex, & regularis, vi- detur enim hoc corporis simplicis conditionem sequi: neq[ue]; vlla est ratio cur aliter, & aliter se habeant anguli ad suum cen trum mathematicum: quare eam ob causam reijcio figuram hexagonoru[m] solidam quæ sit 6. parallelo grammis, & 2. hexa- gonis quamq[ue]; alueanbus suis apiculę adstruunt, reijcio pari- ter cuboides ex rhombis sex, & parallelepipedum. Super- sunt ergo duę tantum figurę de quibus potest institui con- trouersia. Prima est pyramis vel tetraedrum pro qua militant ratio- nes duę primò quod sit in ordine figurarum solidarum prima; secunda quod simplicior sit. Sed duabus deficit conditionibus necessarijs videlicet, vt possit locum replere, quod nequaquam potest, vt supra demonstraui, & vnam lineam physicam facere. Radix enim corporis physicæ est superficies radix superfici- ei, linea, & radix lineæ phyncę, est atomus, addebat sine fundamento Pytagoras ex Alexandro in successionibus philo- sophorum principium quidem omnium esse vnitatem, porro ex vni- tate indefinitam dualitatem, veluti materiam autori vnitate subie- esse. K 2

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Ch. 3. On the properties of atoms. 145 I demonstrate what I set above as the minor premise of my argument, namely, that among all figures which, joined together, fill a space, there are only three: the triangle, the square, and the hexagon, so that among them, when placed successively, nothing empty intervenes. For since the six angles of triangles, and the four of squares, and the three of hexagons are equal to four right angles, the space which is enclosed around each point follows, so that by these figures a place can be filled, but by others not at all: for in the pentagon, for example, three angles are equal to three right angles and 3/5 only; therefore they fall short of filling the space; but four angles are equal to four and 4/5 right angles, therefore they exceed it; the same must be said of the other figures. I have dealt only with regular figures, and indeed there is no doubt that the figure of earthy atoms is simple and regular; for this seems to follow from the condition of a simple body, and there is no reason why the angles should be situated otherwise and otherwise in relation to their mathematical center. For that reason I reject the solid figure of hexagons which is of 6 parallelograms and 2 hexagons, as the beehives construct it with their points; I likewise reject the cuboid of six rhombs and the parallelepiped. There remain, therefore, only two figures concerning which a controversy can be instituted. The first is the pyramid, or tetrahedron, for which there are two arguments: first, that it is the first in the order of solid figures; second, that it is the simplest. But it lacks the two necessary conditions, namely, that it be able to fill space, which it certainly cannot do, as I have shown above, and to make one physical line. For the root of a physical body is a surface; the root of a surface, a line; and the root of a physical line is an atom. Pythagoras, through Alexander, in the Successions of the Philosophers, added without foundation that the principle of all things is unity, and further, that from unity there is indefinite duality, as if matter were subject to the author of unity. K 2

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cisse. Ex monade verò ac indeterminata dualitate numeros gigni, ex numeris puncta ex punctis lineas ex quibus planæ figuræ con- stent. Vide plura apud Laertium lib. 8. At non potest componi linea physica ex tetraedris, quia ex quatuor faciebus tetraedri vna tantum aliud deinceps tetraedrum excipiet, ac proinde prominenti[us] sinusq[ue]; ineqvales in illa erunt linea, & tantum abest vt equam oculi dimensionem per radium patiatur vt etiam veluti serratim serpet quod line[us] perfectioni neutiquam conducit. Ergo atomi terre[us] sunt figur[us] cubic[us], quod hoc argumento probaui. Atomi terreæ simul iunctæ debent eius esse figur[us] quæ lineam faciat, & locum repleat, sed sunt tantum duæ regulares quæ locum repleant ex quibus reiecimus hexagonum solidum, restat ergo solus cubus, qui sine vlla imperfectione lineam potest physicam facere, plures enim cubi simul iuncti lineam physicam facient quæ erit parallelepipedum mathe- maticum. Quæ quidem linea suas atomos ex equo interiacet, vnde, & vera radix line[us] physic[us] erit cubus, & ex huiusce- modi lineis perfecta superficies fiet, quæ ex equo suas lineas di- spositas habebit, vnde & pari ratione corpus solidu[m] perfectum compingetur. Confirmatur hæc ratio quia sicut prima radix numerorum est 2. ex qua conficitur primus cubus (vnitas enim seipsam no[n] multiplicat) qui quidem primus cubus 8. est vnitatum, & octo- narius solidorum numerorum est primus, ita etiam radix cor- porum atomus terrea ex quadratis erit cubica, in ordine figu- rarum secunda, octo angulis constans. Confirmatur, secundò quia cubi proprietates, terræ conue- niunt, illæ autem sunt octo precipuè. Prima, inter omnes figuras solidus cubus omnium difficilli- mè mouetur: immobilitatis terr[us] argumentum, ratio est quia centrum grauitatis est faciliùs in linea directionis, aut certè in ea parte

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... from the monad and from indeterminate duality numbers are generated, from numbers points, from points lines, from which plane figures are made. See more in Laertius, book 8. But a physical line cannot be composed of tetrahedra, because from the four faces of a tetrahedron only one other tetrahedron in succession will be received, and therefore the projections and indentations in it will be unequal; and it is so far from allowing the eye's equal measurement through a ray that it would even creep along, as it were, in a saw-like fashion, which is in no way conducive to lineal perfection. Therefore the atoms of earth are of a cubic figure, which I have proved by this argument. The atoms of earth, when joined together, must be of that figure which makes a line and fills a place; but there are only two regular figures that fill space, of which we have rejected the solid hexagon, so there remains therefore only the cube, which without any imperfection can make a physical line. For several cubes joined together will make a physical line, which will be a mathematical parallelepiped. This line indeed interposes its atoms equally, whence the true root of the physical line will also be a cube, and from lines of this kind a perfect surface will be made, which will have its lines disposed equally; whence also, by the same reasoning, a perfect solid body will be constructed. This reasoning is confirmed because, just as the first root of numbers is 2, from which the first cube is formed (for unity does not multiply itself), which first cube is 8 units, and the number of solid numbers beginning with eight is first, so also the root of bodies, the earthly atom, from squares will be cubic, second in the order of figures, consisting of eight angles. It is confirmed, secondly, because the properties of cubes agree with those of the earth, and these are especially eight. The first: among all figures, the solid cube is moved with the greatest difficulty of all, an argument for the earth's immobility; the reason is that the center of gravity is more easily in the line of direction, or certainly in that part

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C. 3. De atomorum proprietatibus. 147 ea parte quâ corpus innititur. Non argumentor nunc de to- ta vniuersę telluris immobilitate quam vertigine celi indeter- minatam ad iter versus cælum dixere nonnulli, alij innatare aquis, nonnulli radicibus infinitis suffultam esse, Barbariq[ue] philosophi Peguani quatuor innixam columnis quas elephan- ti quatuor sustinerent: sed tantum similitudine quadam, & analogicè probo difficiliùs totum illud moueri cuius singulę partes difficilè mouentur, certè cubi non ità facilè voluntantur, quia vt dixi amplior est lineę directionis basis quę vtrobiq[ue]; ad superiores partes collibratur, quod alijs figuris non contingit. I I. Sequitur ex hac prima, quacunq[ue]; enim sui facie planum tanget habebit lineâ directionis in ea parte quâ planum erit, hinc facillimè quiescit. I I I. Eius tres dimensiones sunt sibi mutuò perpendicula- res, & singulæ magnitudinis eiusdem, cubus enim ex Euclid. est figura solida quę sex quadratis equalibus continetur, in quadrato autem lineę, & anguli æquales sunt ex def. 30. 1. & demonstrat. lib. I I. p. 24. IV. Eius diameter est incomparabilis cum lateribus, vt demonstrat Euclides lib. 10 prop. I I 6. Propositum nobis esto demonstrare in figuris quadratis diametrum esse longitudine incom- mensurabilem ipsi lateri, colligiturq[ue]; ex prop. 9. 10. & ex lib. I. prop 47. V. Cum habeat superficies omnino patentes, & apertas magis est aptus vnioni, nullo enim flexu, nullàue irregularita- te illam refugit, & secundum totam suam latitudine admittit. VI. locum cum alijs cubis perfectissimè replet vtsupra demonstrauimus. VII. Omnes partes coeli sex suis faciebus respicit, duabus quidem oppositis polos duos, alijs verò 4. circumpositis qua- tuor cardines celi: ex quibus nonnulla de magnetica telluris virtute possent colligi. K 3 VIII.

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C. 3. On the properties of atoms. 147 in that part on which the body rests. I am not now arguing about the immobility of the whole earth, which some have said is uncertain because of the motion of the heavens, others that it swims upon the waters, some that it is supported by infinite roots, and the barbarous Peguan philosophers that it rests on four columns sustained by four elephants: but only by a certain similarity and analogically I prove that it is more difficult for that whole to be moved whose individual parts are difficult to move; certainly cubes are not so easily rolled, because, as I said, the base of the line of direction is greater, which on both sides is balanced toward the upper parts, which does not happen in other figures. II. It follows from this first point that whatever face it touches will have the line of direction in that part where the plane is, and therefore it rests most easily. III. Its three dimensions are mutually perpendicular to one another, and each is of the same magnitude; for the cube, from Euclid, is a solid figure enclosed by six equal squares, and in a square the lines and angles are equal, by definition 30 of Book I and demonstrated in Book II, prop. 24. IV. Its diameter is incommensurable with its sides, as Euclid demonstrates in Book 10, prop. 116. Let it be our proposition to demonstrate in square figures that the diameter is incommensurable in length with the side itself, and it is gathered from prop. 9 of Book 10 and from Book I, prop. 47. V. Since it has surfaces completely open and exposed, it is more suited to union; for it avoids it by no bending or irregularity, and admits it along its whole breadth. VI. It fills space with other cubes most perfectly, as we have shown above. VII. With all its parts it faces the heaven’s six faces: with two opposite ones the two poles, and with the other four surrounding ones the four cardinal points of heaven; from which some things about the magnetic virtue of the earth could be inferred. K 3 VIII.

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148 De Atomis. Disput. II. VIII. Vltima coelorum regio scilicet empyreum cubicè est figurę, nam est Ciuitas in quadro posita, & intima vniuersi atomus terrea scilicet cubica est, sic primis vltima conueniunt, & ità videtur cubus prima regula normalis, primumq; operis mundani rudimentum, vltimumq; complementum. Quod autem iuxta Democritum hæc ita se se habeant satis superq; patet ex ijs quę supra de igneis atomis adduximus, tû etiam in synopsi ex authoritatibus Aristotelis initio diductis. Confirmaturq; testimonio insignis, & sua ætate facilè princi- pis philosophi Epicuri, cuius conditum voluptate nomen por- cinam videtur in moralia sectam induxisse, cum tamen ipse ex priscorum authoritatibus anachoretarum seueriora instituta sit secutus, ille inquam eximius naturæ lynx Epicurus non solum de atomis scripserat commentaria quæ glorię ingluuies Stagirita posteris inuidit verùm etiam de angulo atomi librum fecerat singularem, ergo certum est Democriti fuisse placitu atomos quasdam angulis insignire, cęteroqui frustra illud lem ma suo operi Epicurus prefixisset: Quid autem potissimùm in eo libro disputarit certò scire non possumus, sed cum libri titulus sit veluti propylęum quod totius architecture specimen dat, sitq; tanquam gratum quoddam operis vniuersi compen- dium; duo in hoc libro ab Epicuro disputata fuisse suspicor; primò quidem quomodo darentur anguli indiuisibiles, & con- tra huiuscemodi opinionem egit Aristoteles libro de lineis in- secabilibus; secundò quanam ratione angulosa conuenirent cum nô angulosis, id est, cum sphericis, quapropter geometri- cis ratiocinationibus in hac opinione atomorum magnus est locus, & si Platoni placuit hunc scholę suę titulum apponere, nullus ingrediatur sine geometria, sanè Democriticę philoso- phię apprimè necessaria est illa inscriptio. Sed ex occasione istius Epicurei quæsiti scire vis an figuram mutet

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148 On Atoms. Disputation II. VIII. The last region of the heavens, namely the empyrean, is cubic in shape; for it is a city placed in a square, and the innermost atom of the universe, namely the earthly one, is cubic. Thus the first and the last agree, and so the cube seems to be the first normal rule, and both the first rudiment and the last completion of the work of the world. That this is indeed the case according to Democritus is sufficiently clear from the things we have adduced above concerning fiery atoms, as well as in the synopsis drawn at the beginning from the authorities of Aristotle. It is also confirmed by the testimony of the distinguished philosopher Epicurus, who in his age was easily the prince of philosophers, whose name, associated with pleasure, seems to have introduced a swinish sect into morals; yet he himself followed the stricter institutions of the ancient anchorites according to the authorities of the ancients. That outstanding lynx of nature, Epicurus, I say, had not only written commentaries on atoms, which the gluttony of glory begrudged to later generations from the Stagirite, but had also made a separate book on the angle of the atom. Therefore it is certain that it was Democritus’s opinion to mark certain atoms with angles; otherwise Epicurus would have prefixed that title to his work in vain. But what he chiefly discussed in that book we cannot know for certain; yet since the title of the book is like a propylaeum giving a specimen of the whole architecture, and like a certain pleasing summary of the entire work, I suspect that two things were discussed in this book by Epicurus: first, how indivisible angles might be given, and Aristotle dealt against this sort of opinion in the book On Inseparable Lines; second, by what reasoning angular things might agree with non-angular things, that is, with spherical things. Wherefore in this opinion of atoms there is great room for geometrical reasoning, and if it pleased Plato to place this inscription on the entrance to his school, “Let no one enter without geometry,” certainly that inscription is especially necessary for Democritean philosophy. But on the occasion of this Epicurean question, you wish to know whether it changes its shape

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C. 3. De atomorum proprietatibus. 149 mutet terræ atomus, an scilicet circuli quadratura, mutatio sphæræ in cubum, & cubi in sphæram quam tot hactenus fru- stra inuestigarunt naturaliter ad praxim reducatur? Respon- deo mihi probabilius esse non mutari: ratio est quia potissima ratio cur alias atomos figuram mutare concedam, est quod alienis terminis faciliùs quam suis coerceantur, at terra con- trario modo se habet, cum alienos terminos respuat neq[ue]; quid- quam fortiùs sit aut durum magis quod eius angulos possit re- tundere: deinde ad corporum firmitatem conducere videtur, vt sint aliqua immutabilia alia verò mutationis capacia, sic in artefactis v.g. in pariete lapides suam formâ tenent, calx cedit. PROPOSITIO XXIX. Atomorum aquearum figuram determinare. A Rchimedes initio libri de his quæ vehuntur in aqua acu- tissimè demonstrat omnem humorem liquoremue sphæ- ricum esse, ratione habitâ centri grauium, probaturq[ue]; ab Ari- stotele 2. cæli t. 31. cuius dilucidam argumentationem appo- sità figurà convenienti quæq[ue]; desiderabatur, illustrat Blanca- nus Inlocis mathem. Arist. explicatis distinct. 107. At verò quamuis satis apertum sit aquæ superficiem esse sphæricam, de illius tamen elementi particulis indiuisibilibus res manet indecisa: vt itaq[ue]; illis suam demus figuram pauca de humidi liquidiq[ue]; natura dicenda sunt. Obseruo primò liquidum humidumq[ue]; plurimùm differre, metalla enim sicca sunt, & liquida fiunt, Mercurius liquidus est de eius autem humiditate nô satis constat. Humida quæ- dam igne durantur vt mel quod itidem frigore concrescit in grumos, eodem extremo parem pene reddente consistenti- am, igne Vesuviano inuenta sunt anno 1632. mella plane fa- xea, de melle petram fundente Vesuvio vt ait elegantissimus K 4 Recupi-

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C. 3. On the properties of atoms. 149 whether the atom of earth changes; namely, whether the quadrature of the circle, the change of a sphere into a cube, and of a cube into a sphere, which so many have hitherto sought in vain, can be brought into practice naturally? I answer that it is more probable to me that it does not change: the reason is that the chief reason why I allow other atoms to change shape is that they are more easily restrained by alien boundaries than by their own; but earth on the contrary behaves in the opposite way, since it rejects alien boundaries and there is nothing harder or more solid that could blunt its angles: then it also seems to contribute to the firmness of bodies that some things should be immutable, while others are capable of change, as in artifacts, e.g. in a wall the stones retain their shape, the lime yields. PROPOSITION XXIX. To determine the figure of watery atoms. Archimedes, at the beginning of the book On Things That Are Carried in Water, most acutely demonstrates that every liquid and fluid is spherical, with regard to the center of gravity; and this is proved by Aristotle in the 2nd book of the Heaven, text 31, whose clear argument, together with a fitting figure added in the place where it was needed, Blancanus illustrates in In locis mathematicis Aristotelis explicatis, distinction 107. But although it is sufficiently clear that the surface of water is spherical, nevertheless the matter remains undecided concerning the indivisible particles of that element: therefore, in order that we may assign them their figure, a few things must be said about the nature of the moist and the liquid. I observe first that liquid and moist differ greatly; for metals are dry, and become liquid, whereas mercury is liquid, but as to its moisture this is not sufficiently certain. Some moist substances are hardened by fire, as honey, which likewise by cold congeals into lumps, the same extreme rendering consistency nearly equal in both cases; and at the Vesuvian fire found in the year 1632, there were found entirely stony honeys, concerning the honey pouring forth stone at Vesuvius, as says the most elegant K 4 Recupi-

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150 De Atomis. disp. II. Recupitus in suo Nuntio; frigore violentiori indurantur aliquid quando in saxeam firmitatem in Nortuegia. Multa actu humida sunt quæ liquida non sentiuntur vt grande, nix, pruina; Quædam absq[ue] humiditate fluida, & liquida vt ignis, cælum, aer, exhalationes, metalla fusa &c. Obseruo secundò aquam de cuius humiditate, & liquiditate hic sermo est tres habere status, alterum quo in glaciem concrescit, alterum quo in vapores soluitur, tertium quo sua natiuà consistentià gaudet vt in fontibus fluuijsq[ue]; Glaciata aqua leuior est fluidà, imo licet tanta sit differentia in pondere aquæ dulcis, & salsæ, salsa tamen glaciata innatat dulci ob rariorem partium situm, & aerem poris frequentibus constrectum: vnde non satis pollum mirari philosophorum turmas nullà habità experientiarum ratione has sententias pro oraculis colere. I. frigus condensat, & grauius reddit. II. Corpus concretum minus occupat loci quam fluidum quæ licet in aliquibus vera sint in plurimis tamen inductio deficit, Status autem aquæ in vapores dissolutæ explicabitur disp. 3. c. 2. Cum verò suo in situ connaturali manet aqua habet eam proprietate ab humiditate inlita vt facilè adhæreat, à fluiditate autem vt alienis terminis facilè, difficile suis coerceatur. Quare cum ea sit liquidi corporis conditio vt in sui diffusione nullà parte eminere debeat cum sit primum postularum Ptolom. I. de ponderibus corporum, Nullum corpus in seipso graue esse vt aquæ in aquam, oleum in oleum, aerem in aerem, nulliusq[ue] esse quantuatis, quare vniuersa aqua se se ità collibrat vt sphæricam superficiem habeat quo melius vndiquaq[ue]; paribus momentis accedat ad mundi centrum, vnde ad decluiora fit defluxus dum tandem omnia æquali altitudine consultant, hinc illud hydraulicorum axioma: Non altiùs ascendit in cursum naturali fons quam sit sua origo. Et si sursum eat hac vtuntur regula,

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150 On Atoms. disp. II. Received in his report; they are somewhat hardened by a more violent cold when into stony firmness in Norway. Many things are actually moist which are not felt as liquid, as snow, hoarfrost; some things without moisture are fluid and liquid, as fire, the sky, air, exhalations, molten metals, etc. I observe secondly that water, of whose moisture and liquidity this discourse is concerned, has three states: one in which it coagulates into ice, another in which it is resolved into vapors, a third in which it enjoys its native consistency, as in springs and rivers; iced water is lighter than fluid water; indeed, although there is so great a difference in the weight of fresh water and salt water, yet salt water when frozen floats on fresh water because of the more rare arrangement of its parts, and the air being confined in frequent pores: whence I cannot sufficiently wonder that crowds of philosophers, with no regard paid to experience, should cherish these opinions as oracles: I. Cold condenses and makes heavier. II. A solid body occupies less space than a fluid, which, although true in some cases, fails by induction in many others; but the state of water resolved into vapors will be explained in disp. 3, c. 2. But when water remains in its connatural state, it has that property, impressed by its moisture, that it easily adheres, and by its fluidity that it is easily, though with difficulty, restrained by foreign boundaries, not by its own. Wherefore, since it is the condition of a liquid body that in its diffusion it ought not in any part to stand out, as is the first postulate of Ptolemy I. on the weights of bodies: No body is heavy in itself, as water in water, oil in oil, air in air, nor is any body of quantity; therefore the whole of water so balances itself that it has a spherical surface, by which it may more fittingly on every side, with equal moments, approach the center of the world; whence there is a flow down toward lower places until at last all settle to an equal level; hence that axiom of the hydraulicians: A spring does not rise in its natural course higher than its source. And if it goes upward, they use this rule,

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C.3. De atomorum proprietatibus. 151 gula, Par est resistentia aquæ ad motum sursum atq[ue] inclinatio ad motum deorsum: quod si se ita non haberet, motum per syphones perpetuum inuenissemus. Atq[ue] hæc ratione flui- di, aquæ conueniunt: humiditatis verò beneficio partes parti- bus nullonegotio vniuntur idq[ue] in triplici humidorum gene- re, viscoso, pingui, & rorido. Viscosum hamatis, & veluti concatenatis constat particulis ità vt dilaceratione opus sit vixq[ue]; certà auferas mensurà ob adhæsionem. Pingue in oleis butyro, adipe depræhenditur. Purum in aquis, & antiquo- rum balsamo, quod nullo maculæ periculo vestes fragrantia suà aspergebat: at sicuti omne humidum facilè est vnibile ità solum purum, & roridum facilè diuisibile est. Atq[ue] ideò quod aqua superficie sphæricâ semper circumam- biat terram, quod scilicet reperiat in fundo terminos, & ad la- tera, apertum verò aerem in suprema sui parte quæ imbecil- liori corpori non cedit, debet necessariò aliquibus terminis diffiniri. Sphæricam autem induit superficiem quia natura quàm breuissimis vtitur vijs, & nihil facit frustra, breuissimi autem termini habitâ ratione grauitatis corporis, & centri grauium est sphærica, quæ à centro mundi per puncta termi- nantia aquæ limbos duceretur, ad eam ergo se se reducit. Vn- de instituta sunt iucunda quædam problemata quibus pro- batur cyatho plus aque contineri in valle, quam in montis iugo, quod facili negotio demonstratur ex coroll. prop. 33. 1. 6. Euclid. Cum enim aqua, vt diximus se se colligat in sphæ- ram cuius centrum est centrum grauium siue mundi, sit circu- lus AC pro aqua in valle, circulus DB pro aqua in monte, quoniam ergo ex scholio 33. 1. 6. Eucl. æquales rectę lineę ex circulis inequalibus auferunt arcus inequales, maiusq[ue] est segmentum minoris circuli quam, vt sit simile segmento cir- culi maioris, erit ergo cyathi in valle, siue in circulo CA sphe- rica

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C.3. On the properties of atoms. 151 gula, There is equal resistance of water to upward motion and an inclination to downward motion: if this were not so, we would have found a perpetual motion through siphons. And in this way the properties of a fluid agree with water; moreover, by the benefit of moisture its parts are easily united with one another, and this in the three kinds of moist things, viscous, fatty, and dewy. Viscous matter consists of hooked and, as it were, linked particles, so that it hardly yields even to tearing; you can scarcely remove a certain measure because of adhesion. Fatty matter is found in oils, butter, and fat. Pure moisture is found in waters, and in the ancient balsam, which sprinkled garments with its fragrance without any danger of stain; but just as every moist thing is easily capable of union, so only the pure and dewy is easily divisible. And therefore, because water always surrounds the earth with a spherical surface, since, namely, it finds bounds at the bottom and at the sides, but open air above in its upper part, which does not give way to the weaker body, it must necessarily be defined by certain limits. Yet it assumes a spherical surface because nature makes use of the shortest paths and does nothing in vain; and the shortest limits, with regard had to the heaviness of the body and the center of heavy things, are spherical, which would be drawn from the center of the world through the points terminating the edges of the water; therefore it is reduced to that shape. Hence there were devised certain pleasant problems by which it is proved that more water is contained in a goblet in a valley than on a mountain ridge, which is easily demonstrated from corollary 33 to proposition 1.6 of Euclid. For since, as we said, water gathers itself into a sphere whose center is the center of heavy things, that is, of the world, let AC be the circle for the water in the valley, DB the circle for the water on the mountain; since, therefore, from the scholium to 33, 1.6 of Euclid, equal straight lines taken from unequal circles cut off unequal arcs, and the segment of the smaller circle is greater than, so that it may be like the segment of the larger circle, it will therefore be the goblet in the valley, or in the spherical circle CA

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152 De Atomis. Disp. II. rica aque superficies in segmento maiori quâ in circulo mon- tis DB. quod erat demonstrandum, his ità prelibatis. Dico primigeniam ato- morum aquearum figuram esse spheri- cam, cæteroqui fluxa illa est, & versatilis incertisq[ue]; terminis tinita vel in mixto aut in ipsius aque congregatione. Probat. primò quod sit spherica. Si daretur atomus aqua in inani ab omnibus alijs separata, illa se se in spheram collige- ret, ergo spherica figura illis atomis est primigenia, probatur antecedentis sequela à priori, frustra sit per plura quod potest fieri per pauciora, sed hæc atomus debet suis terminis conti- neri ergo paucissimos, & angustissimos admittet, at spheræ fines sunt huiusmodi, nam ex scientia figurarum Isoperime- traru[m] ea figura maioris est areæ quæ plura habet latera quæq[ue] est regularis, sed spherica est in potentia lateribus infinitis, est que regularissima, ergo omnium tibi isoperimetrarum capa- cissima est. Probatur secundò. Illa figura est fluxa, & versatilis quæ alienis terminis est obsequens, at aqueæ atomi ob humiditate[m], & fluiditatem sunt huiusmodi, ergo sunt figuræ inconstantis, & mutabilis; si autem considerentur absq[ue]; alienorum termi- norum adminiculo sphericæ sunt, in mixto verò eam habent figuram quam situs, violentia vicina, exigentia formæ, cæliq[ue] influxus imprimit. Confirmatur hæc ratiocinatio principio 10. Eadem est ratio torius homogenei, & omniu[m] eius partium, quare cum certum, sit totam aquarum conglomerationem sphericam esse, & aque guttas, quæ quod non satis sint in copia vt diffuant, spherarum figuras induere, & Mercurium seu argentum vi- uum si diuidatur, in globulos perfectissimos colligi, atomis certè

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152 On Atoms. Disputation II. the surface in the greater segment than in the circle of the mountain DB, which was to be demonstrated; these things being thus briefly set forth, I say that the primitive figure of the watery atoms is spherical. Otherwise, it is fluid and versatile, and bounded by uncertain limits, either in mixture or in the aggregation of the water itself. Proof, first, that it is spherical. If a water atom were given in the void, separated from all others, it would gather itself into a sphere; therefore the spherical figure is primitive to those atoms. The sequence of the antecedent is proved a priori: what can be done by fewer means is done in vain by more, but this atom must be contained within its own bounds, and therefore will admit the fewest and narrowest. Now the boundaries of a sphere are of this kind; for from the science of isoperimetric figures, that figure has the greater area which has more sides and is regular, but the spherical is potentially of infinite sides, and is most regular; therefore it is the most capacious of all isoperimetric figures. It is proved secondarily. That figure is fluid and versatile which is obedient to foreign limits; but watery atoms, by reason of their moisture and fluidity, are of this kind; therefore they are of an unstable and mutable figure. But if they are considered apart from the assistance of foreign bounds, they are spherical; in mixture, however, they take that figure which position, nearby pressure, the demand of form, and the influx of the heavens impress upon them. This reasoning is confirmed by principle 10: the same reason applies to the whole homogeneous body and to all its parts. Wherefore, since it is certain that the whole aggregation of waters is spherical, and that drops of water, because they are not in sufficient quantity to spread out, assume the figures of spheres, and that mercury, or quicksilver, if divided, gathers into the most perfect globules, certainly the atoms ...

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C. 3. De atomorum proprietatibus. 153 certè aqueis idem omnino conuenire par est. Neq; de terreis eadem est ratio, terra enim primò non est perfectè, & exacte sphérica, quiescens autem aqua, loquendo geometricè glo- bosa est; prætereà liquiditate omni terra caret quapropter de atomis terreis longè diuersa pronuntiauimus. Præterquam quod hæc dicendi ratio satisfacit exigentię particulari atomorum, exigentię totius elementi quod vnio- ne sua delectatur, exigentię mixtorum in quibus atomi aqueę formis facilè obsequuntur, exigentię fluiditatis, & humidi- tatis, repletioni loci, & cuiuis deniq; aquarum officio, qua- propter ex atomis aqueis infinita fiunt figurarum genera pro- ut agentibus externis placet. Ex hac philosophia deduci fa- cilè posset ratio figurarum quas in grandine niuisq; floccis na- tura exprimit: niuem certè adeò perfecte in stellulas efforma- tam vidimus anno 1644. Ticini, quod doctissimis viris ad- stantibus ostendi, vt portentum artis non fortuitum naturę opus legitimà admiratione diceretur. Determinauimus itaq; figuram atomis aqueis iuxta Demo criti placita quod nobismetipsis præscripseramus faciendum. PROPOSITIO XXX. De atomorum aerearum figura iuxta Democritum pronuntiare. A Tomi aereę omnium subtilissimę sunt, versatiles, poly- formę, ipsisq; est incomparabilis promptitudo cogendi se sub alijs alijsq; terminis ferme in instanti, si ità corporibus alijs, naturęq; totius continuitati quę sarta tecta foueri de- bet, sit opus. Hæc verò agilitas summa, duabus de causis concessa est aeri, primò vt quiduis vacui impediat, & locum repleat commodiùs, secundò vt meliùs pororum angustias su- beat, extrudentiq; se cuiuis alteri cedat. Habent hoc prætereà atomi aereę vt nunqua[m] vel inter se vel cu[m] alijs vniantur sed sint tantum contiguę vt supra ostendimus. Vnum

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C. 3. On the properties of atoms. 153 certainly the same is rightly held to apply to watery ones. Nor is the case of earthy ones the same; for earth, first, is not perfectly and exactly spherical, whereas still water, speaking geometrically, is glo- bose; moreover, earth lacks all liquidity, for which reason we have pronounced very differently concerning earthly atoms. Besides, this manner of speaking satisfies the particular requirement of atoms, the requirement of the whole element, which delights in its union, the requirement of mixed bodies in which watery atoms easily accommodate themselves to forms, the requirement of fluidity and humidity, the filling of place, and finally any office of waters what- soever; wherefore from watery atoms there are made infinite kinds of figures, as external agents please. From this philosophy the reason for the figures which nature expresses in hail and in snowflakes could easily be deduced: indeed we saw snow so perfectly formed into little stars in the year 1644 at Pavia, which I showed in the presence of very learned men, so that it was said with due admiration to be a prodigy, not the accidental work of art but the legitimate work of nature. We have therefore determined the figure of watery atoms according to Democritus, as we had set out for ourselves to do. PROPOSITION XXX. To pronounce on the figure of airy atoms according to Democritus. Airy atoms are the most subtle of all, versatile, multi- formed, and they possess incomparable readiness for gathering themselves under one boundary or another almost in an instant, if it is required by other bodies and by the continuity of the whole of nature, which must be kept whole and sound. This highest agility, however, has been granted to air for two reasons: first, that it may prevent any void and fill place more fittingly; second, that it may better pass through the narrowness of pores and give way to any other body forcing its way out. Airy atoms have this further property: that they are never joined either among themselves or with others, but are only contiguous, as we have shown above. One

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De Atomis. Disp. II. Vnum subiungo quod si aeris atomus vnica in spatio imaginario vel in aquis poneretur, se se continuo in sphericam colligeret; in spatio quidem imaginario quia breuissimis terminis vellet comprehendi vt supra de igneis aqueisue demonstrauimus ex scientia figurarum isoperimetrum, & principio physicę quod natura semper breuiorem viam sequatur. In aqua verò pariter sphericę essent, quia quam minimam diuisionem inter aquam, & aquam facerent; & reuerà vt hoc obiter annotem non in aqua tantum quod ex bullis, & aere per aquas extruso pater, verùm etia in oleo, melle, sanguine alijsq; liquoribus idem fit, in quibus spuma constat globulis, aut certè spherarum portionibus, in oleo verò ubi nulla est spuma, aer etiam se in spherâ colligit, ut corpus illud crassum penetret: quod non benè aduertens Cardanus censuit lampadem suam quâ in lib. primo de subtilitate proponit ideò semper ardere succedereq; oleum oleo, quia quod superest olei rare fit semper, atq; ità plena manet lampas, sed neutiquam ità se res habet, in uitreis enim huiuscemodi lampadibus aduerti post singula ferè minuta subire globulum aeris, & rectà utà summum lampadis fastigium per olei continuitatem petere, ut illic uacuum impedire: ità ut cum huiuscemodi lampas esset cylindrica succederet per foramen aer, qui collectus in spheram quàm breuissimà lineà emergebat in summa cylindri axe, & nunquam à centro huiuscemodi aberrabat. Sunt itaq; atomi igneę originaliter sphericę illiusq; figurę amantes, per accidens autem quamlibet aliam induunt in gratiam formarum substantialium, & naturę commoda. Atomi terreę sunt originaliter cubicæ neq; figuram mutant, quia nihil est illis solidius firmiusue, & reuera si metus uacui sit in terra, diuiditur, violenterq; laceratur ut fluxa corpora succedant. Atomi

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On Atoms. Disputation II. I add one point: if a single atom of air were placed in an imaginary space or in water, it would immediately gather itself into a spherical shape; in imaginary space indeed because it would wish to be enclosed by the shortest boundaries, as we have shown above in the case of fiery and watery things from the science of isoperimetric figures, and from the physical principle that nature always follows the shorter way. In water, likewise, they would be spherical, because they would make the least possible division between water and water; and in truth, as I note this by the way, this happens not only in water, which is evident from bubbles and from air forced out through waters, but also in oil, honey, blood, and other liquids, in which foam consists of little globules, or certainly portions of spheres; but in oil, where there is no foam, the air also gathers itself into a sphere, so that it may penetrate that thick body: which Cardano, not observing this well, judged that his lamp, which he describes in the first book On Subtlety, burns continuously and oil succeeds oil, because what remains of the oil is always made rare, and thus the lamp remains full; but the matter is by no means so. For in glass lamps of this kind I observed that after nearly every minute a bubble of air rises, and goes straightway to the very top of the lamp through the continuity of the oil, so as to prevent a vacuum there; so that when a lamp of this kind was cylindrical, the air would pass in through the opening, and, gathered into a sphere, would emerge by the shortest line at the top on the axis of the cylinder, and never would it stray from the center of this kind. Therefore the atoms of fire are originally spherical and lovers of that figure; but by accident they assume any other in favor of substantial forms, and for the convenience of nature. The atoms of earth are originally cubic and do not change shape, because nothing is firmer or more solid than they are; and indeed if there is fear of a vacuum in the earth, it is divided, and violently torn apart so that fluid bodies may succeed. Atoms

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C. 3. De atomorum proprietatibus. 155 Atomi aqueæ cuiusuis figuræ sunt capaces, separatis verò conuenit sphærica. Atomi aereæ sunt originaliter indifferentes ad quamuis fi- guram per accidens tamen, & aliorum ratione in sphæram col- liguntur. Atomis itaq[ue] figuras determinauimus quod erat postulatum. Ex quibus vides rectè censuisse Aristotelem 3. cælit. 66. Elementis non posse inesse diuersas figuras singulas singulis, sed vnum tantum modo figurari posse, reliquis informibus, ego verò non informia dico sed vertibilis figuræ tria constituo, quæ originarijs tamen terminis sint sphærica, vnam terram immu- tabili esse figura opinatus. PROPOSITIO XXXI. Motus atomorum ad figuram seu atomorum figuratio potest explicari analogicè. CVM atomi igneæ, aqueæ, & aereæ figuram mutent vt diximus ex mente Democriti, nunc est videndum quæ nam sit illa virtus intrinseca secundum quam ipsis conuenit il- le motus ad figuram. Figuratio est actus entis in potentia prout in potentia in ordin ad figuram: Quæ in rebus diuisibilibus est triplex, per additionem per detractionem, per transpositionem solam partium, sic sic ceræ ceram addas figura mutabitur, si detrahas itidem. Detractione constat ars statuaria, additione plastica: transpositio verò partium mathæmaticis adeò vsurpata, phy- sicè loquendo fieri potest vel per compressionem, vel per ad- iunctionem à separatione præsuppositâ consequentem, vel si aliquid ab intrinseco eius est virtutis, vt alium aliumq[ue]; situm possit obtinere figuramq[ue]; suam variare; vt species visibiles quæ in puncto confusionis seu decussationis obscure sunt, & vix

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Chapter 3. On the properties of atoms. 155 Water atoms are capable of any shape; taken separately, however, they agree with the spherical. Air atoms are originally indifferent to any shape, but accidentally, and by reason of others, they are gathered into a sphere. Thus we have determined the figures of atoms, which was what had been required. From these things you see that Aristotle judged rightly, De Caelo 3, 66, that diverse figures cannot belong to the elements, each to each, but only one can be figured, the rest being formless; but I, indeed, do not say formless, but I establish three changeable figures, which, however, in their original bounds are spherical, since I have thought that earth alone has an immutable figure. PROPOSITION XXXI. The motion of atoms toward figure, or the shaping of atoms, can be explained analogically. Since the fiery, watery, and airy atoms change figure, as we have said, according to the mind of Democritus, now it must be seen what that intrinsic power may be, according to which that motion toward figure belongs to them. Shaping is the act of a being in potency insofar as it is in potency, in relation to figure: in divisible things this is threefold, by addition, by subtraction, by the mere transposition of parts; thus if you add wax to wax, the figure will be changed, and likewise if you subtract. Sculpture consists in subtraction, plastic art in addition; transposition of parts, however, so much used by mathematicians, speaking physically, can occur either by compression, or by an adjoining that follows upon a presupposed separation, or if there is something in it from within of such power that it can obtain another and another position and vary its own figure; as visible species, which at the point of confusion or intersection are obscure, and scarcely

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156 De Atomis. Disp. II. vix vlla figurà certà præditę, ab illo verò puncto progressę dilatantur, & figuram suam prototypo corespondentem obtinent; Compressio fit dum partes diffunduntur ad latera ob corpus vicinum cogens, & coarctans, hę sunt tres transpositionis rationes quas etia in artefactis deprehendimus, vel certè ars ipsa naturę mysterijs abutitur ad illa reflectenda quo lubet, vt dum species per refractiones crystallorum ex inuersis fiunt rectę, & unius crystalli beneficio, imagines diffire, & aliud omninooculo puro representantes, collectę per refractione nouam imaginem pingunt. Oblatę sunt CARDINALI INFANTI tres in vno octangulo Cardinalium effigies, qui in administrandis rebus excelluerunt, Albornoz, Granuellani, Ximenes. Contuentiq[ue] per polygonam crystallum ingeniosâ refractione disparentibus illis, vnus apparebat in tabula INFANS, vt quorum absorberet species visibiles, etiam haberet prudentiam in se cumulatam. Omnes autem hę mutationes sine motu locali concipi non possunt. Ex prima, & secunda ratione figurationum nihil in rem nostram venire potest, cum atomo nihil vel addi vel demi possit, quapropter eas immutabiles appellabat Epicurus in sua Epitome naturali ad Herodotum. Tertia verò aliquid lucis præfert quâ præeunte nonnihil verosimile reperiemus. Atomus quidem est substantia simplicissima absq[ue] compositione, sine vlla vnione, virtualitates tamen habet intrinsecas, & extrinsecas, secundu[m] quas eàdem omnino mole, & quantitate permanente potest occupare modo maiorem, modo minorem locum extrinsecum, minorem cum erit sub sphærica figura aut alijs regularibus polygonis, maiorem cum sub irregularibus deliteicet: quod non facit vt totum elementum crescat in extensione minuaturue, sed toto elemento immoto manente commotis solummodo quibusdam atomis, atomus A maiori-

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156 On Atoms. Disputation II. hardly endowed with any certain figure, from that very point they are advanced and spread out, and they obtain a shape corresponding to their prototype; Compression occurs when the parts are dispersed to the sides by the neighboring body forcing and narrowing them; these are the three ways of transposition which we also detect in artifacts, or certainly art itself makes use of nature’s mysteries to reflect them wherever it wishes, as when, by refractions of crystal, species from inverted forms become straight, and by the aid of a single crystal, images differing and showing something altogether different to the pure eye, collected through refraction paint a new image. There were offered to the CARDINAL-INFANT three portraits of Cardinals in one octagon, who excelled in the administration of affairs: Albornoz, Granvellanus, Ximenes. When he looked through a polygonal crystal, those figures disappearing by ingenious refraction, one appeared in the picture, the INFANT, as if it had absorbed their visible forms, and also had prudence gathered up within itself. But all these changes cannot be conceived without local motion. From the first and second reason of the shapes nothing can come to our purpose, since nothing can be either added to or taken away from an atom; for this reason Epicurus called them immutable in his Natural Epitome to Herodotus. The third, however, presents some light, by which leading the way we shall find something probable. For an atom is a most simple substance without composition, without any union; nevertheless it has intrinsic and extrinsic virtualities, according to which, the very same mass and quantity remaining constant, it can occupy now a larger, now a smaller external place, smaller when it is under a spherical figure or other regular polygons, larger when it lies hidden under irregular ones: which does not make the whole element grow in extension or diminish, but with the whole element remaining unmoved while only certain atoms are moved, atom A greater-

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C. 3. De atomorum proprietatibus 157 maioribus modò, modò breuioribus terminis compræhendetur. Neq[ue] verò inflata illa puncta, Neotericorum ad rarefactionis soluendas difficultates figmentum admitto, sed tota hæc mea doctrina in isoperimetrarum figurarum propositionibus innititur, maiorem enim locum cera occupat extensa in parallelepipedum, quàm collecta in sphæram, nihilominus tamen inflata non est, maioribus similiter terminis gaudebit atomus A cum erit in conum exporrecta, quàm si in cylindrum, cuius basis eadem esset atq[ue] coni. Et sicuti figura pondus non auget, ita neq[ue] quantitatem vel molem, sed terminos tantùm mathematicos: eadem est manus in volam expansa, & contracta in pugnum, sic eadem atomus tetraedrica, & cubica erit, neq[ue] mole cum terminis augetur, hæc inquam geometriæ initiatis manifestissima sunt ex tractatu figurarum isoperimetrarum, quem à Clauio in geometria practica poteris repetere. In cera quidem rectè id concipimus quia mutatio figuræ fit per aliâ partium situationem, & vnionem, at verò in atomo nullæ sunt huiuscemodi diuisiones, & situationes, cum partibus careat secundu[m] quas situ[m] mutare posset. Nihilominus tamen cum non possimus in rebus abditis meliorem inuestigandi modum habere, quàm analogismum, inuenio quatuor entia, quæ nobis similitudine quâdam in his obscuritatibus aliquid lucis afferunt, figuratio ceræ supra allata, figuratio specierum visibilium, & earum imaginum quæ in obscuris cubiculis per exiguum foramen in cartam allapsæ conspiciuntur, figuratio Angeli, & motus animæ in corpore humano se se extendentis, & colligentis ad corporis incrementum vel decrementum. Angelus potest se se porrigere in cylindrum, & colligere se in globum, isq[ue] est entitas simplex purè spiritualis, indiuisibilis, itaq[ue] figuræ mutation non continuò infert diuisibilitatem, si enim

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C. 3. On the properties of atoms 157 will be contained now by greater, now by shorter bounds. Nor do I admit that swollen points, the Neoterics’ invention for resolving the difficulties of rarefaction, but rather the whole of this doctrine of mine rests on the propositions of isoperimetric figures; for wax occupies a greater place when spread out into a parallelepiped than when gathered into a sphere, yet nevertheless it is not swollen; similarly the atom A will enjoy greater bounds when extended into a cone than if it were in a cylinder, whose base would be the same as that of the cone. And just as a figure does not increase weight, so neither quantity nor bulk, but only the mathematical bounds: the hand is the same when spread into the palm and when contracted into a fist; thus the same atom will be tetrahedral and cubic, nor does it increase in bulk with its boundaries; these things, I say, are most evident to those initiated in geometry from the treatise on isoperimetric figures, which you may consult again in Clavius’s Practical Geometry. In wax indeed we rightly conceive this, because the change of figure occurs through another arrangement and union of the parts; but in the atom there are no such divisions and arrangements, since it lacks parts according to which it could change its position. Nevertheless, since in hidden things we cannot have a better means of investigation than analogy, I find four entities which by a certain likeness bring us some light in these obscurities: the shaping of wax mentioned above, the shaping of visible species, and of those images which, in dark rooms, having slipped through a tiny opening onto paper, are seen, the shaping of an angel, and the motion of the soul in the human body extending itself and contracting itself for the increase or decrease of the body. An angel can stretch itself out into a cylinder and gather itself into a globe, and it is a simple, purely spiritual entity, indivisible; and so a change of figure does not at once bring about divisibility, for if

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158 De Atomis. Disp. II. si enim Angelus se ponat in cylindro, deinde eiusdem areæ globum occupet, quamuis diuersa sit vtrobiq[ue] peripheria, certum est neq[ue]; auctum neq[ue]; diminutum, ac proinde nullam virtualem reproductionem inibi somniandam. Animus prætereà humanus corpori diuisibili, cùm sit indiuisibilis aptatur, figuramq[ue]; ad corporis modum mutat. Finge tibi animo ceram esse adæquatè indiuisibilem, diuisibilem autem secundum quid, siue stante partium cum toto adhæsione, optimè percipies mutari figuram sine diuisibilitate adæquata & totali, sed cum atomi sint simpliciter, & absolutè indiuisibiles, videndum porro est quidnam de illis aptiùs dici possit, sentio enim rei spiritualis cum materiali comparationem reijciendam, neque verò idem habent virtutis atomi, ac proinde neque eundem agendi modum, modus enim operandi sequitur essentiæ rationes, siue vt vulgò aiunt, modus operandi sequitur modum essendi. Species itaque visibiles quas primus adinuenit Democritus quasque corpora appellabat, non physica quidem, sed mathematica, constant enim suis dimensionibus figuræque sunt solidæ, nobis aliquid singularius dabunt. Obseruo primò, nonnumquam in flexu, & viæ longioris decursu mutari specierum figuram, nam omnia è longinquo sphærica apparent, vt si sol v[.] g[.] cubicæ esset figuræ, nihilonùs tamen globosus à nobis conspiceretur, cum adeò distet vt 9482202000000000. minor, quam sit, appareat, quod incredibile foret, nisi astronomicæ obseruationes geometricis, & arithmeticis ratiocinationibus fulcirentur. Si itaq[ue] datur aliqua stella alterius figuræ, quàm sphæricæ, verbi gratiâ eicosaedri, illa emittit species sui secundum pyramidem, quæ tot facies habet, quot sût quas complectitur sectio, quæ sic ab oculi positione ductis adeius circumferentiam rectis, & tamen in de-

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158 On Atoms. Disp. II. for if an Angel place itself in a cylinder, then occupy a globe of the same area, although the perimeter is different in each case, it is certain that it is neither increased nor diminished, and therefore no virtual reproduction is to be imagined there. The human mind, moreover, being indivisible, is fitted to a divisible body, and it changes its form according to the body’s mode. Imagine in your mind that wax is adequately indivisible, but divisible in a qualified sense, that is, with the adhesion of the parts to the whole remaining, you will very well perceive the form to change without adequate and total divisibility; but since atoms are simply and absolutely indivisible, it must further be considered what can more fittingly be said about them. For I think the comparison of a spiritual thing with a material one must be rejected, nor indeed do atoms have the same power, and therefore neither the same mode of acting, for the mode of operating follows the conditions of the essence, or, as people commonly say, the mode of operating follows the mode of being. Thus the visible species which Democritus first invented and which he called bodies, not indeed physical, but mathematical, for they consist in their dimensions and are solid in form, will give us something a little more singular. I observe first that sometimes, in bending and in the course of a longer path, the shape of the species changes, for all things appear spherical from afar, as if the sun were of a cubic shape, nevertheless it would be seen by us as globular, since it is so far distant that it appears 9482202000000000 times smaller than it is, which would be incredible unless astronomical observations were supported by geometric and arithmetic reasonings. If therefore there is any star of a shape other than spherical, for example an icosahedron, it emits its species according to a pyramid which has as many faces as there are which the section contains, and this thus, by lines drawn from the position of the eye to its circumference, yet in de-

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C. 3. De atomorum proprietatibus. 159 in decursu anguli omnes ità retunduntur vt perfectæ spheræ imago oculis excipiatur. At cum ibi sit imminutio, aliud afferro exemplum, sit triangularis species A B per vitra, & crystallos refracta, fiat quadrangularis eà ratione vt quadra- tum siue cubus sit equalis tetraedro: mutauit figuram sine ad- ditione vel diminutione aut detractione. Obseruo secundò, sic esse visibiles species, vt sit earum cen- trum tanquam cardo circa quem versantur, atq[ue] cum pyrami- daliter diffundantur ab obiecto tanquam à basi, ad oculum tanquam ad verticem pyramidis, sequitur ipsis suam inesse axim, quæ non est alia nisi linea imaginaria vel potiùs poten- tior radius, qui ad oculu[m] perpendiculariter cadit, & circa eius axis punctum decussans vertuntur, inuertuntur, fusdeq[ue] ap- parent determinatæ à foraminibus, crystallis, lentibus con- cauis, speculis ali, sq[ue], quæ vel sors vel ars obijcit, mutant itaq[ue]; circa illud punctum suam primigeniam figuram, videturq[ue]; ini- bi vim præcipuam specierum esse reposita. Nunc itaq[ue]; hoc illustri analogismo vtamur ad atomorum figurationem inuestigandam. Possunt ad huiuscemodi mo- tum determinari atomi, primò ob aliorum fortiorum vim quâ comprimuntur, vel ad formæ exigentiam secundum quam eo, & eo modo ad mixtionem venire debent, vel tandem vt se suis terminis coerceant, quacunq[ue]; autem lege id contingat, à centro sui mathematico tanquam à machine puncto princi- pali virtuales partes quibus atomi sunt præditæ diffunduntur, vt est opus, neq[ue]; verò vlla sequitur diuilibilitas neq[ue]; reprodu- ctio, sed tantum adductio, & retractio virtualium atomi par- tium, sic autem figuram atomi mutant vt in omnibus par sit area, neq[ue]; vnquam vel augeatur vel minui possit, omnis au- tem figuræ centrum datur, vnum nempè punctum quod dia- metris duabus se se intersecantibus signatur. Atq[ue] hæc de ato- morum

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C. 3. On the properties of atoms. 159 in the course of the angle all are thus rounded off, so that the image of a perfect sphere is received by the eyes. But since there is there a diminution, I cite another example: let the triangular appearance A B, refracted through glass and crystals, become quadrangular, in such a way that a square or cube is equal to a tetrahedron; the figure has been changed without addition or diminution or subtraction. Secondly, I observe that visible appearances are such that their center is like a hinge around which they turn, and since they spread out pyramidally from the object as from a base to the eye as to the apex of the pyramid, it follows that they have their own axis, which is nothing other than an imaginary line, or rather a stronger ray, falling perpendicularly to the eye, and around the point of this axis they cross and turn, are inverted, and likewise appear as determined by holes, crystals, concave lenses, mirrors, and the like, which either chance or art presents; and thus they change their original figure around that point, and it seems that the chief power of appearances is deposited there. Now therefore let us use this illustrious analogy to investigate the shaping of atoms. Atoms can be determined to such motion, first by the force of other stronger things by which they are compressed, or according to the requirement of form, according to which they ought to come into mixture in this way and that way, or finally so that they are restrained within their own limits; however this may happen, from the mathematical center of themselves, as from the principal point of the machine, the virtual parts with which atoms are endowed spread out as needed, and no divisibility or reproduction follows, but only an extension and contraction of the virtual parts of the atom; and thus they change the figure of the atom so that in all respects the area is equal, nor can it ever be increased or diminished; moreover, a center is given for every figure, namely one point marked by two intersecting diameters. And these things concerning the atoms

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CAPVT QVARTVM. De mixtione, & dissolutione atomorum. Vinq[ue] propositionibus caput istud expediam. I. Qua- nam ratione mundus ex atomis coaluisse potuerit. II. Quomodo atomi alterentur. III. Quomodo misceantur. IV. De poris, & mixtionum gradibus. V. Quo- modo dissoluatur mixtum. Subdam paradigmaphilosophâ- di ex atomorum doctrina. PROPOSITIO XXXII. Mundi genesim explicare per atomos iuxta Democritum. N[on] Vlli dubium est quin Democritus in crassis gentilium te- nebris errauerit dum fortuito atomorum concursu mun- dos coaluisse innumeros pronuntiauit, quos interire redireq[ue] ad concretionem alià formà alijsq[ue] ornatibus non dubitabat. Sed tamen opinio quæ atomos admitrit Deum creantem nul- lo modo respuit, quin imo Mundum Dei opus appellabat De- mocritus, Cleanthes l. de atomis censuit Verbu Deu omnia face- re, hunc quippe sempiternum per ipsam materiam omnem singula creare. Ponit autem hoc decretum Zeno Citticus in libro de essentia, Cleanthes l. de atomis, & Chrysippus in primò phys. in fine: Arche- demus quoq[ue] in libro de elementis, & Possidonius in secundo natura- lis rationis. Hæc ad verbum ex Diogene l. 7. de vita philos. in Zenone Cittico. Mundi autem ex atomorum congregatio- ne in inanisluce acre generationem ex Democriti placitis des- cribunt

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CHAPTER FOUR. On the mixture and dissolution of atoms. I will treat this chapter in five propositions. I. By what means the world could have come together from atoms. II. How atoms are altered. III. How they are mixed. IV. On pores and the degrees of mixtures. V. How a mixed body is dissolved. I shall add a philosophical paradigm drawn from the doctrine of atoms. PROPOSITION XXXII. To explain the origin of the world through atoms according to Democritus. There is no doubt for anyone that Democritus erred amid the dense darkness of the Gentiles when he declared that countless worlds had come together by the chance collision of atoms, which he did not doubt would perish and return to a congealed state in another form and with different ornaments. Yet the opinion which admits atoms does not in any way reject a creating God; indeed, Democritus called the world the work of God. Cleanthes, in his book On Atoms, judged that the Word of God does all things, namely that he eternally creates everything individually through matter itself. Now this decree is stated by Zeno of Citium in his book On Essence, Cleanthes in his book On Atoms, and Chrysippus in the first book of Physics at the end; Archedemus also in his book On Elements, and Posidonius in the second book of Natural Reason. These are his very words from Diogenes, book 7, On the Life of Philosophers, concerning Zeno of Citium. But the formation of the world from the congregation of atoms and the generation of things in empty space and light are described according to the doctrines of Democritus

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C.4. De mixtione atomorum. 161 cribunt Lucretius l.2. Hipp. l. de Carnibus, Leucippus apud Laertium. Sic itaq[ue] canit subtilissimus T. Carus. Contemplator enim cum solis lumina cunq[ue]; Insertim fundunt radios per opaca domorum, Multa minuta modis multis per inane videbis Corpora misceri radiorum lumine in ipso, Et velut æterno certamine prælia, pugnasq[ue]; Edere turmatim certantia nec dare pausam, Concilijs, & dissidijs exercita crebris: Conijcere vt possis ex hoc primordia rerum, Quale sit in magno iactari semper inani. Explicat diuersitatem generationum ex atomis varià trans- politione sicuti ijsdem litteris scribimus flumina, fulmina, & comædia tragædiaq[ue] eisdem characteribus exprimitur. Sic ipsis in rebus item iam materiai Interualla, viæ, connexus, pondera, plagæ, Concursus, motus, ordo, positura, figuræ Cum permutantur mutari res quoq[ue] debent. Deinde sub libri finem vbi probare tentat mundorum plura- litatem ità canit. Cum præsertim hic sit naturâ factus, & ipsa Sponte sua forte offensando semina rerum Multimodis temerè incassum, iactataq[ue] frustra Tandem coierunt ea quæ coniectarepente Magnarum rerum fierent ex ordia semper Terræ, maris, & cæli generisq[ue] animantum. At licet aliquatenus sententiam Democriti ista illustrent non tamen sinceram referunt, cùm Empedoclis placitum exponat Lucretius, qui volebat dari infinita principia non multitudine tantùm quod admittebat Democritus, verùm etiam specie. Leucippus apud Diogenem Laertium l.9. commodiùs scribit. L 2 Multa

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C.4. On the mixture of atoms. 161 write Lucretius, book 2, Hippocrates, book On the Flesh, Leucippus apud Laertium. Thus, then, the most subtle T. Carus sings. Contemplate, for when the lights of the sun and all such things pour out their rays in close array through the dark spaces of houses, you will see many tiny bodies, in many ways, mixed through the void in the very light of the rays, and as though in an eternal contest, battles and fights issuing forth in troops, contending and giving no pause, exercised by frequent councils and dissensions: so that you may infer from this the first principles of things, what it is like to be always tossed about in the great void. He explains the diversity of generations from atoms by various trans- position, just as with the same letters we write flumina, fulmina, and comædia and tragædia are expressed by the same characters. So too in the things themselves, likewise, now the intervals, ways, connexions, weights, strokes, meetings, motions, order, position, figures when they are changed, things also must be changed. Then, near the end of the book, where he tries to prove the plurality of worlds, he sings thus. Especially since this world has been made by nature, and of itself of its own accord, perhaps striking against the seeds of things in many ways, rashly, in vain, and thrown about uselessly, at last those things came together which might suddenly be conceived as the origins of great things, always of earth, sea, and sky, and of the race of living creatures. But although these things in some measure illuminate the opinion of Democritus, nevertheless they do not give a pure account, since Lucretius sets forth the view of Empedocles, who wished that there be infinite first principles not only in number, as Democritus admitted, but also in kind. Leucippus apud Diogenes Laertius, book 9, writes more fittingly. L 2 Many

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De Atomis. disp. II. Multa corpora figuris omnigena in magnum vacuum ferri, eaq[ue] in vnumcoacta, vnam vertiginem efficere, secundum quam offende- re ac circumuolui modis omnibus, atque ita discerni vt scorsum simi- lia quæ sunt sui similia petant. Cæterum æquilibra cum ob multitu- dinem iam minimè circumferri possint, exilia quidem ad exterius va- cuum concurrere sic ordinante natura, cætera subsidere, & innexa atq[ue] in se implicata inuicem concurrere atq[ue] ea concursione priùs qua- dam concretionem efficere rotundam. Hanc autem veluti membra- nam subsistere, continentem in se omni gena corpora, quæ dum secun- dum medij reluctationem circumuoluuntur tenuem per gyrum men- branulam fieri iuxta vertiginis tractum, corporibus perpetuis semper confluentibus, atq[ue] it à fieriterram, manentibus quæ semel in mediu[m] iniecta erant ipsumq[ue], rursus continentem me[n]branæ instar augeri iux- ta externorum influentiam corporum, & cum vertigine fertur quæ- cumq[ue]; attigerit ea acquirere. Ex his quædam complicata concretio- nem facere, primò quidem humidam ac luteam, exsiccata, & circum- acta cum totius vertigine, deinde incensa, & ignita siderum effic- ere naturam: esseq[ue] solis circulum extimum, lunæ proximum terris, cæ- teris in medio positis. Hæc Leucippus: quæ recidunt in illud antiquorum chaos, quod admiserunt Orpheus, Homerus, Pla- to, & alij pleriq[ue], tum philosophorum, tum Poetarum. Hip- pocrates vel autor libri de carnibus num. primo, ait elementa in circumuolutione turbata fecisse generationes. At cum isti ex proprijs locuti fuerint principijs, aut certè re obscurâ bre- uitate sint complexi oper[um] pretium est recensere, & per capita distribuere quonam modo existimarit Democritus mundum fuisse creatum. 1. In generationibus omnibus externa primùm, tùm verò interna componi voluit Democritus, vsus exemplo bombycu[m], qui virtutis instar formatricis in suo ovo laborant, quòd aurem ita censuerit probatur testimonio Aristotelis 1. 2. de genera- tione

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On the Atomists. Disputation II. Many bodies of every kind of shape are carried into the great void, and being gathered together there, they produce a single vortex, according to which they strike against one another and are whirled about in every way, and thus are separated so that things akin go off to their like. Moreover, since by reason of their multitude the balanced bodies can no longer be carried around, the light ones indeed run together to the outer void, nature so ordering it; the rest settle down, and, being entwined and involved in one another, run together and by that collision first produce a certain round concretion. This then stands as it were as a membrane, containing within itself bodies of every kind, which, while they are whirled around according to the resistance of the middle, a thin little membrane is formed along the path of the vortex, as perpetual bodies always flow together, and so the earth came to be; those things which had once been cast into the middle remained, and that very middle, like a membrane, increased again in proportion to the influx of external bodies, and whatever the vortex carries along acquires whatever it may touch. From these some produce a compound concretion, first indeed moist and clay-like, dried and then carried around with the whole vortex, then ignited and inflamed to produce the nature of the stars; and the circle of the sun is the outermost, the moon next to the earth, the others placed in the middle. These are Leucippus’ views, which fall back into that ancient chaos, admitted by Orpheus, Homer, Plato, and many others, both philosophers and poets. Hippocrates, or the author of the book On Flesh, in the first section, says that the elements, being disturbed in their circular motion, made generations. But since these men have spoken from their own principles, or at least have compressed the matter obscurely and briefly, it is worth while to review and set out point by point how Democritus thought the world was created. 1. In all generations Democritus wished the external parts first, and then the internal, to be formed, using the example of silkworms, who work in their egg with the power, as it were, of a formative force; that he judged this to be so is proved by the testimony of Aristotle, 1, 2, On Generation

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tione animal c. 4. Quamobrem qui ità vt Democritus aiunt, exte- riora primu[m] animalis discerni, tu[m] interiora, quasi lapideum aut ligneu[m] animal condant, non rectè dicunt. Auxtà hanc Democriti metho- dum philosophandi, primu[m] quod in inanis immensitate coaluit ex atomis est exterior mudi pars, inuolucrumq[ue] omniu[m], nempè cælum extimum, quod in prima sui origine tenerum appel- lat elegantissimus Virgilius; Et ipse tener mundi concreuerit orbis. I I. Hâc primà concretione factà, cui præsideret principiu[m] illud sempiternum ab Democrito vocatum indemonstrabile, 1. 2. de generat. an. c. 4. cęperunt in aere concludę atomi va- rijs cieri motibus, tùm localibus tùm etia[m] ad figuram, cumq[ue] includeantur vastissimo illo carcere, seq; mutuò quæritarent ad generationes, in centro mundi euitatà circumferentiæ va- stitate sibi inuicem consenserunt, & primò quidem nobilissi- mum coaluit corpus sol scilicet, qui è delitijs elementorum co- pactus ingenti concretione maximam ignis portionem cum haberet, in orbis centro tornatus adepta suà co[n]sistentià gyro- sis an fractibus motuq[ue]; volutationis se se perpetuò circinans fursum ad suam sedem, vnde nunc lucet, violentissimà rapidi- tate delatus, tribus in illa ascensione factis circa terram spiris, horis septuaginta duabus, tantum spatij est emensus, quantum hinc ad solem numerant Astronomi. III. Hoc principe adminiculo influente, vertigo ipsa cæli solidior, tanquam excoquente calore, facta, cęteri planetę effor- mati primùm, à cétro mundi ad suas iuere sphæras, turbinatim Spiroso meatu Venus, & Mercurius delati solem ideò circum- ambiunt; Post stellas autem fixas, quæ itidem sunt in orbis centro circinatæ, & motu mixto ex perpendiculari, & circu- lari stelliferum adiere, omnium stellarum vltima compacta est luna, absumptà a theris purioris parte, quantu[m] superfuit, aquis contemperatum in se se recepit, & tardo motu petijt eam par- tem L 3

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tione animal c. 4. Wherefore those who, as Democritus says, first distinguish the external parts of the animal, then the internal, as though they were constructing a stony or wooden animal, speak incorrectly. According to this method of philosophizing of Democritus, the first thing that was compacted out of atoms in the immensity of the void is the outer part of the world and the covering of all things, namely the outermost heaven, which the most elegant Virgil in the first origin of the world called tender; And the tender orb of the world itself grew firm. II. After this first compaction had been made, over which presided that eternal principle, called by Democritus indemonstrable, 1. 2. de generat. an. c. 4, the atoms began to be confined in the air and to move in various ways, both locally and also with respect to figure; and since they were enclosed in that vast prison, they sought one another for generations, and in the center of the world, having avoided the vastness of the circumference, they agreed among themselves, and first indeed the most noble body was compacted, namely the sun, which, formed from the delights of the elements with a great condensation, having the greatest portion of fire, was turned in the center of the orb; and having gained its consistency by whirling, with its revolutions and motions, ever circling itself upward toward its own seat, from which it now shines, carried along with most violent rapidity, after making three spirals about the earth in that ascent, in seventy-two hours it traversed as much distance as astronomers reckon from here to the sun. III. By this chief instrument acting, the very vortex of the heaven, being more solid, as though by a consuming heat, being formed, the remaining planets first came into being and departed from the center of the world to their spheres, carried in a whirling, spiraling course; Venus and Mercury therefore circle the sun. After the fixed stars, which likewise are whirled in the center of the orb and by a mixed motion, from perpendicular and circular, came to the star-bearing heaven, the last of all the stars compacted was the moon; the purer portion of the ether having been consumed, as much as remained, tempered with waters, it received into itself, and by a slow motion sought that part L 3

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164 De Atomis. Disp. II. rem cæli quę centro vicinior quam maximè à sole distaret, ne violentiori igne aquosa sua teneritudo dissiparetur, lentèq[ue] tandem, veluti carbonibus ad mensuram datis induruit, ità vt post diem à sua natiuitate decimum quartum ardores ecclipsis innoxiè pateretur. IV. Factis sideribus veluti vniuerso mundi seminario cætera atomorum multitudo crassà Mineruà inuicem permixta est & in centro orbis remansit vt generationibus animalium subseruiret, hinc terrę globus aqua, & terra coaluit. Natura perinde ac prudens pater familias nihil amittere solet ex quo facere aliquid commodi possit, dispensatur autem in cura rei familiaris vt primò, & optimè liberis, deinde socijs, postea seruis prouideatur. Arist. 2. gen. an. c. 4. Ità, & in ortu rerum contigit, vt facto prius concretionis termino sine quo nihil in immenso fieri posset, distractis perpetuò per infinitas regiones corpusculis, nobilissimis corporibus prouideatur, quęq[ue] posteà cæteris præsideant, hinc omnium primus sol, postea pro varia dignitate coaluerunt sidera. Solis autem compactio ità fuit vt concretione exteriori primùm ex omnium elementorum figuratis aptè corpusculis, tanquam membranâ coalescente remaneret inclusæ ætheris ignisue purioris copia maxima, quæ cùm omnis non posset concrescere ob terrę, & aque minorem copiam in solis meditullio tanqua in quodam inani remanerunt atomi ignis copiosissimę, quę perpetuo agitâtur motu, neq[ue] inter se immediatè vnibiles sunt, vti supra diximus, hinc soli contingit voluntari circa proprium sui globi centrum, & agitatione istâ atomorum per cęli liquiditatem deferri, sicuti ignium nitratorum artificiosâ compagine contingere videmus: Luna verò quod maiorem aquarum copiam includat, quam, vt vniuersa igni posset exiguo contemperari concretione illâ exteriori compacta mansit aque in vacuo Lunæ meditullio quantitas, quæ ibi viginti

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164 On Atoms. Disputation II. the part of the heaven nearer the center, rather than being farther from the sun, so that its watery tenderness should not be dissipated by a more violent fire; and thus it gradually hardened, as it were like charcoal laid down in due measure, so that after the fourteenth day from its birth it could harmlessly endure the heat of an eclipse. IV. When the stars had been made, as it were the whole seedbed of the universe, the remaining multitude of atoms, mixed together by coarse Minerva, remained in the center of the orb so as to serve the generations of animals; hence the globe of the earth was formed by water and earth together. Nature, like a prudent head of a household, is accustomed to lose nothing from which it can make some advantage; but in managing domestic affairs care is so distributed that first and best provision is made for the children, then for companions, afterward for servants. Arist. 2 gen. an. c. 4. So too, at the birth of things it happened that, after first the boundary of condensation had been established—without which nothing could be made in the vast expanse—while the particles were continually dispersed through infinite regions, provision was made for the noblest bodies, and for those that afterward would preside over the rest; thus first of all the sun, then the stars, according to their varying dignity, came together. But the formation of the sun was such that, by the outer condensation, there first remained enclosed from the well-shaped particles of all the elements, as if a membrane had been formed, a very great store of purer ether or fire; and since not all of it could condense, because of the smaller amount of earth and water, in the middle of the sun, as in a certain void, there remained a great number of fire-atoms, which are continuously stirred by motion and are not immediately capable of uniting with one another, as we said above. Hence it happens that the sun moves of its own accord around the center of its own globe, and is carried by this agitation of atoms through the fluidity of heaven, just as we see to happen in the artificial structure of fired nitre. But the moon, because it includes a greater quantity of waters than could, with its very small amount of fire, be tempered into a single whole by that outer condensation, there remained in the empty middle of the moon a quantity of water, which there twenty

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C.4. De mixtione atomorum. 165 viginti quatuor horarum interuallo circumuoluta supparé luna facit faciei phasim, ità vt & luna vno die naturali semel circa proprium centrum circumgiretur. Reliquorum sideru[m] ignotior est ob exiguitatem, & distantiam concretio singula- risq[ue] motionis character. Hæc omnia ex mente Democriti qui cum irrequietas cen- suerit in inani atomos, sequitur quod bi ille reperientur, mo- tum facient, qui licet non sit semper conspicuus, & sensibilis vt ait Lucretius, ratione tamen sureq[ue] sequele debet admitti. Alcinous c.13. doct. Plat. dodecaedro ad vniuersi constru- ctionem vsum fuisse Deum ait. Illustrari potest hæc doctrina eleganti cogitatione Anastæ- tij Sinaitæ in 4 Exameron. vbi ait stellas omnes in terra fuisse compactas, ità vt Deus optimus naturæ maiestate suam adum- braturus potentiam, in aeris diffusione informes quasdam elementorum massas congesserit, à quibus tanquam Figulus ab aceruo luti accepit quantum ad cælos stellasq[ue] cōcinnandas esset opus, atq[ue] ità cælum factum est ex elementorum delicijs, virgineq[ue] natura, cuius flos in palmarium huiuscemodi opus diffusus est. Deinde accepit diuinus idem Figulus quo solem reliquasq[ue] stellarum concinnaret, quas omnes in mundi centro veluti in rota circinauit, & perfecta illa corpora sibimetipsis reliquit vt congruum naturæ suæ, totiq[ue] vniuerso vtilem locu[m] peterent, vnde, & velocissimo motu probante opus suum Deo à centro ad circumferentiæ destinatas plagas venerunt. Ex- pletis hisce officijs corporibusq[ue] in natura principibus effor- matis, quod supererat elementorum imperfectè atq[ue] adeò sine feueritate immiscuit, sic vt aquarum maxima portio sine terra, terra verò alicubi sine aqua esset, vtrumq[ue] tamen vncio globo complexum in centro orbis veluti in officina libraretur, atque ex magis apparentibus elementis globum vocamus terrá & L 4 aqua

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C.4. On the mixture of atoms. 165 turning at the interval of twenty-four hours, the waning moon makes a phase of the face, so that the moon in one natural day once revolves around its own center. The arrangement of the other stars is less known because of their smallness and distance, and the character of their particular motion. All these things are according to the mind of Democritus, who, when he thought that atoms are restless in the void, it follows that wherever they are found they will make motion, which, although it is not always conspicuous and perceptible, as Lucretius says, must nevertheless be admitted by reason and by its consequence. Alcinous, c. 13 of the doctrine of Plato, says that God used the dodecahedron for the construction of the universe. This doctrine can be illustrated by an elegant thought of Anastasius of Sinai in the 4th Exameron, where he says that all the stars were compacted in the earth, so that God, best in majesty of nature, wishing to shadow forth his power, gathered in the diffusion of the air certain shapeless masses of the elements, from which, as a potter from a heap of clay, he took whatever was needed for fashioning the heavens and the stars; and thus heaven was made from the delights of the elements, and from virgin nature, whose flower was diffused into the chief work of this kind. Then the same divine Potter took what was needed to fashion the sun and the rest of the stars, all of which he arranged in the center of the world as if on a wheel, and left those perfect bodies to themselves, that they might seek a place fitting to their nature and useful to the whole universe; whence, proving his work by a most rapid motion, they came from the center to the destined regions of the circumference. When these tasks had been completed and the principal bodies formed in nature, what remained of the elements he mixed in an imperfect manner and, indeed, without distinction, so that the greatest part of the waters should be without earth, and the earth in some places without water; yet both, joined together in one globe, were balanced in the center of the sphere as if in a workshop, and from the more conspicuous elements we call the globe earth & water

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166 De Atomis. Disp. II. aquà compactum. Plura elegantissimus Anastasius Sinaita in 4. Examen: quæ deinde cælestibus imbuuntur sensibus sacrorum more, quę, & mentem eleuant, & omnia ad mores commodissimè deriuant. Quod si aliam rationem placeret comminisci, quid impedit quo minùs ex atomis primigenijs compactæ sint atomi secundæ, seu minima naturalia, quæ amicitiæ, & inimicitiæ stimulis se sequeritantia in medio aere veluti commisso prælio solaria corpuscula solaribus, lunaria lunaribus conuenerunt, aliæq[ue] deinceps stellæ sunt formatæ? residuæ? verò illorum superiorum corporum particulæ ijs aliquâ vim adeptis sursumq[ue]; delatis manserunt in informi terrarum globi massa inclusæ, hinc superiorum cum inferioribus consensio, & occulta illa arcanamotuum qui philosophos hactenus vexarunt. Verum quidem est hâc etiam ratione quę accedit ad Anaxagoræ OMOMOROIAN de qua Lucretius l. 1. mundum ab Omnipotenti Deo potuisse creari, quanam autem ratione sit factus conijcere potiùs quam nosse concessum est. At istas Democriti sententias volui deducere quia vt ait Aristotel. 2. cælit. 60. Veneratione quam temeritate digna est promptitudo illa, si quis propter philosophiæ sitim, etiam in ijs paruas sufficientias amat, de quibus maximas habemus dubitationes. De mundi autem fabrica exactiùs disputare huius loci non est. PROPOSITIO XXXIII. Modus agendi atomorum est triplex: Primus per intrusionem sui in poros: Secundus per propagationem qualitatis in spatio libero: Tertius per inhibitionem qualitatis contrariæ. CVM, vt supra diximus, mixtio sit miscibilium alteratorum vnio, videndum est, quânam ratione miscibilia hoc est atomi alterentur, quod sine explicatione modi quo agunt intelligi nequit. Dico

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166 On Atoms. Disp. II. compacted by water. The most elegant Anastasius Sinaita in 4. Examen: things which thereafter are imbued with heavenly senses by the sacred mode, and raise the mind, and most suitably direct everything to morals. But if it should please one to devise another explanation, what prevents the second atoms, or minima naturalia, from being compacted out of the primary atoms, which, following the stimuli of friendship and enmity, as if in a battle fought in the middle air, gathered themselves together, so that the solar little bodies with solar ones, the lunar with lunar ones, and then other stars were formed? But perhaps the remaining particles of those higher bodies, having somehow gained force and been carried upward, remained enclosed in the shapeless mass of the terrestrial globe; hence the agreement of the higher with the lower, and that hidden harmony of movements which has so far troubled philosophers. Yet it is true that by this reasoning too, which approaches Anaxagoras’s OMOMOROIAN, concerning which Lucretius, book 1, says that the world could have been created by the Omnipotent God, but by what process it was made we are granted to conjecture rather than to know. But I wanted to set out these opinions of Democritus because, as Aristotle says, 2. cælit. 60., that eagerness is worthy of reverence rather than rashness, if anyone, because of a thirst for philosophy, also loves small certainties in matters about which we have the greatest doubts. But to discuss the structure of the world more exactly is not the business of this place. PROPOSITION XXXIII. The mode of action of atoms is threefold: First, by intrusion of themselves into pores; second, by the propagation of a quality in free space; third, by the inhibition of a contrary quality. SINCE, as we said above, mixture is the union of alterable things capable of being mixed, it must be seen by what manner the things capable of mixture, that is, the atoms, are altered, which cannot be understood without an explanation of the mode by which they act. I say

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Cap. 4. De mixtione atomorum. 167 Dico itaq[ue]; primò dari actionem in natura à diffusione spiri- tuum seu corpusculorum per poros subeuntium, quæ proposi- tio tanti est momenti vt enucleatè probari debeat. Probatur itaq[ue]; primò authoritate Hipp. l. de aere, aquis, & locis, in libris epidemiorum. Galeni disertis verbis l. 1. de element. c. 6. l. 1. de sem. c. 16. Auicennæ l. 4. Fen. 6. t. 3. c. 22. ad 57. Senecæ l. 6. q. nat. c. 28. Plinius l. 2. c. 93. ita Vi- dus Vidius, Fernelius, Cardanus, Septalius, Sanctorius, Ferne- lius, Augenius, Leuinus Lemnius, Vallesius, Langius, Fortu- nius Licetus, Iulius Cæsar Scaliger, Amatus Lusitanus, Mer- catus, & alij tùm veteres, tùm recentiores Medici potiores. Probatur secundò ratione. Omnia corpora naturalia præ- sertim viuentia sunt in perpetuo fluxu, alia verò exeduntur, & imminuuntur, sed nihil perit in natura, quia non datur an- nihilatio, ergo superest vt huiuscemodi corpuscula huc illucq[ue] vagentur, & vicinorum corporum poros subeant. Prima propositio certissima est experientiâ quotidianâ patetq[ue] ex Sanctorij aphorismis staticæ medicæ, secunda autem propositio dependet ex primo princip. disp. 1. sequitur ergo hinc & inde effluere, dariq[ue]; hanc spirituum propagationem, quam Græci vocant APORROIAN. Probatur tertio inductione multiplici: primò ex notione manifesta atmosphæræ seu vapidæ circa terram regionis quæ refractionum cælestium causa est. Secundò ex aquæ vapori- bus, & humiditate aeris fluuijs, & paludibus incubant. Ter- tiò infinitis pene venenatoru[m] halituum historijs quas referunt D. Augustinus l. 3. de Ciuit. Dei c. 3 1. Diodorus Siculus l. 1 2. Amatus Lusitanus cent. 3. curat. 8 3 Mercurialis de venenis c. 1 3. Vidius p. 2. f. 2. l. 1. c. 1 1. Iulius Capitolinus in Verò ait in Babylonia apertam veterem arcam èqua, tàm exitiosa pe- stis exhalauit vt ad Parthos ulq[ue] grassaretur. Guaiinerius de peste

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Chapter 4. On the mixing of atoms. 167 I say, therefore, first, that there is action in nature from the diffusion of spirits, or of corpuscles passing through pores, a proposition of such great importance that it ought to be proved in detail. It is proved, therefore, first by authority: Hippocrates, in On Airs, Waters, and Places , in the books of the Epidemics ; Galen in express words, book 1, On Elements , chapter 6; book 1, On Semen , chapter 16; Avicenna, book 4, Fen. 6, tract 3, chapter 22, ad 57; Seneca, book 6, Natural Questions , chapter 28; Pliny, book 2, chapter 93; likewise Vidus Vidius, Fernelius, Cardanus, Septalius, Sanctorius, Fernelius, Augenius, Levinus Lemnius, Vallesius, Langius, Fortunius Licetus, Julius Caesar Scaliger, Amatus Lusitanus, Mercatus, and others, both the older and the more recent and eminent physicians. It is proved secondly by reason. All natural bodies, especially living bodies, are in continual flux; some are moreover eaten away and diminished; but nothing perishes in nature, because annihilation is not given. Therefore it remains that such corpuscles wander here and there, and enter the pores of neighboring bodies. The first proposition is most certain and is evident from daily experience and from Sanctorius’s aphorisms of statical medicine; the second proposition depends on the first principle, dispute 1. It follows, therefore, on both sides, that there flows out and that there is this propagation of spirits, which the Greeks call aporroia . It is proved thirdly by multiple induction: first, from the manifest notion of the atmosphere, or the vaporous region around the earth, which is the cause of celestial refractions. Secondly, from the vapors of water and the moisture of the air resting over rivers and marshes. Thirdly, from the almost infinite histories of poisonous exhalations, which are related by St. Augustine, book 3 of The City of God , chapter 31; Diodorus Siculus, book 12; Amatus Lusitanus, century 3, case 83; Mercurialis, On Poisons , chapter 13; Vidius, part 2, fol. 2, book 1, chapter 11; Julius Capitolinus in Verus , where he says that in Babylonia, when an ancient opened chest was brought forth, so deadly a pestilence was exhaled that it spread even to the Parthians. Guainerius, On the Plague

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De Atomis. Disput. II. peste c. 1. Barclaius in Icone animorum c. 9. Philippus Ingrassia, Informatione del pestifero, et contagioso morbo di Palerma nell'anno 1575. et 1576. parte prima capo secondo Pareus l. 10. c. 13. Sabellicus Enneade 5. l. 9. & Enneade 7. l. 7. Cardanus l. 2. de uenenis c. 9. Fallopius de bubone pestilenti c. 2. Andreas Gallus Tridentinus fasciculo 2. de peste. Et illi spiritus cum respiratione subeunt, uel per poros cutis intrant, aut per arteriarum meatus, & uenarum oscula penetrant. Imo ipso oculorum intuitu id effluuij accidit unde (Ouidius,) Dum spectant læsos oculi læduntur, et ipsi Multaq[ue] corporibus transitione nocent. Hanc autem minimorum corpusculorum diffusionem probatam uidebis apud Sennertum in Hypon. 3. c. 2. sed cum hæc in mixtis à nemine quod sciam negentur corporum effluua, & clarè explicentur ab Aquilonio Optic. l. 5 p. 2. Scaligero exercit. 12. s. 3. Faloppio t. de lue Gallica c. 89. in ipsis etiam elementis admisit disertis uerbis Galenus iuxta Hipp. doctrina Ego enim (inquit) non difficile dico eum qui ad ignem vt cale fiat accedit introducere ignem in suum corpus et c. l. 1. de elem. c. 6. Dico 2. Actio atomorum perpendi debet penes locum ubi agunt, nam uel considerantur in mixto, uel in aeris libera sphæra, uel quatenus patiens aliquod aggrediuntur. Hocq[ue] ultimo modo per intrusionem, penetrationem in poros, insinuationemq[ue]; uariam potiùs agunt, quàm propagatà qualitate. Sic aquam calefieri crediderim quod illam spiritus ignei peruadant, probaturq[ue] quia si patinam aquâ purâ plenam igni superposueris uidebis e fundo plurimas bullas exiguas emergere, quod explicari non potest, nisi dicamus id contingere ob crumpentes igneos spiritus, qui suppetijs aduentitijs sociorumq[ue]; auxiliaribus copijs deinde ebullitionem concitant. Neque solum id igni proprium est, uerùm etiam glaciei, si quidem uinum

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On Atoms. Disput. II. on plague c. 1. Barclaius in Icone animorum c. 9. Philippus Ingrassia, Informatione del pestifero, et contagioso morbo di Palerma nell'anno 1575 . and 1576. part one chapter two. Pareus l. 10. c. 13. Sabellicus Ennead 5. l. 9. & Ennead 7. l. 7. Cardanus l. 2. de uenenis c. 9. Fallopius de bubone pestilenti c. 2. Andreas Gallus Tridentinus fascicle 2. de peste . And these spirits, along with respiration, rise, or enter through the pores of the skin, or penetrate through the passages of the arteries and the openings of the veins. Indeed, by the very gaze of the eyes this effluence occurs, whence (Ovid) While the eyes look on the wounded, they themselves are wounded, And many things harm bodies by transmission. Now you will see this diffusion of the smallest corpuscles proved in Sennertus in Hypon. 3. c. 2. But since, as far as I know, no one denies these effluvia of bodies in mixed things, and they are clearly explained by Aquilonius Optic. l. 5 p. 2. Scaliger exercit. 12. s. 3. Faloppius, on the French disease c. 89. Galen also expressly admitted them in the elements themselves according to Hippocrates' doctrine: For I myself (he says) do not find it difficult to say that he who approaches the fire to become warm brings fire into his own body; and c. l. 1. de elem. c. 6. I say secondly: the action of atoms must be considered according to the place where they act, for either they are regarded in a mixture, or in the free sphere of the air, or insofar as they attack some patient body. And in this last way they act more by intrusion, penetration into pores, and various insinuation, than by a propagated quality. Thus I would believe that water is heated because fiery spirits pass through it, and this is proved because if you place a pan full of pure water over fire, you will see many tiny bubbles rising from the bottom, which cannot be explained except by saying that this happens because fiery spirits burst forth, who, with the help of newly arrived allies and their auxiliary troops, then stir up the boiling. Nor is this proper only to fire, but also to ice, if indeed wine

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C.4. De mixtione atomorum. 169 uinum in glacire frigigeratum contrahit nescio quam duritié, & grauitatem, quam ab intrusis frigidissimis atomis viri dubium non est, nociuàq[ue]; magis est stomacho debili frigiditas huiusmodi quam si ex fonteuel puteo frigefieret. Actio atomorum in aere sit etiam per propagationem suæ qualitatis, cum enim aer sit indifferens ad omnes omnino qua- litates, eas etiam facilè poterit sustinere, propagata uerò hu- iuscemodi qualitas, si ad mixtum aliquod perueniat, illud qui- dem afficiet, & alterabit, sed eà ratione ut cognatis sibi ato- mis societur, alijs uerò noceat quidem, sed ijs non subiectetur. In mixtis enim non agunt propriè in se inuicem atomi, ità ut atomus ignea frigida fiat, atomus uerò aquea sicca uel ca- lida reddatur, sed uirtute sibi insità mutuam retundunt acti- uitatem, atomus enim ignea præpediet aqueam, eiusq[ue] ex- porrectam sphæram restringet, & cohibebit, atomus uerò terrea uicinitate suâ faciet, ne atomus ignea tantum expro- mat uirium. Quare prout uigent atomi nonnullæ aliarum debilitate actiuitatem suam exerere deprehenduntur, nul- lamq[ue]; aliam in mixtis alterationem admisit Democritus, quàm istam, quam inhibitiuam, retundentem uoco, Ioubertus au- tem in paradoxis refringentem maluit appellare: à nobis est Fernelius qui in 1.3. physiol. elementa alterari negat. Ex triplici itaq[ue]; medio uel passo modus agendi atomorum est triplex quod erat exponendum. PROPOSITIO XXXIV. Modum quo atomi miscentur explicare. Tria necessariò ad mixtionem, quam generatio substan- tialis sequitur, concurrunt, materia scilicet tanquam su- biectum, instrumenta pro inducendis dispositionibus, & for- ma ultimum operis complementum. Sicuti ad statuam ex- sculpen-

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C.4. On the Mixture of Atoms. 169 Wine cooled in ice acquires, I know not what, hardness and heaviness, which, because of the intrusion of the very cold atoms, there is no doubt is harmful; and such cold is more injurious to a weak stomach than if it were cooled from a spring or well. The action of atoms in air also takes place through the propagation of their quality; for since air is indifferent to all qualities whatsoever, it can easily sustain them. But when a quality of this kind has been propagated and reaches some mixed body, it will indeed affect and alter it, but in such a way that it is joined with atoms akin to itself, while it does harm to others, though it is not subjected to them. For in mixed bodies atoms do not act properly upon one another, so that a fiery atom becomes cold, or a watery atom is made dry or hot; rather, by an innate power they blunt one another’s activity. For a fiery atom will impede a watery one and restrict and curb its extended sphere, while a earthy atom by its nearness will cause the fiery atom not to bring forth so much strength. Therefore, just as some atoms are vigorous, they are found to exert their activity through the weakness of others. And Democritus admitted no other alteration in mixed bodies than this, which I call inhibitive or blunting; Joubert, however, preferred in his Paradoxes to call it refractive. Fernelius, on our side, denies in book 1, chapter 3 of the Elements of Physiology that elements are altered. From a threefold medium, therefore, or subject, the mode of action of atoms is threefold, which had to be explained. PROPOSITION XXXIV. To explain the manner in which atoms are mixed. Three things necessarily concur in mixture, which is followed by substantial generation: matter, namely as the subject; instruments for inducing dispositions; and form, the final completion of the work. Just as for carving a statue...

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170 De Atomis. Disp. II. sculpendam requiritur marmor pro materia, celte, malleus, scalpraq; pro instrumentis, & idça artificis secundum quam instrumenta diriguntur, cuiq; si manus non fefellit, respon- det resultans in marmore effigies. Pro mixtione naturali ha- bemus materiam atomos aqueas, terreas, igneas; pro instru- mentis erunt qualitates primæ atomorum, & siderum influ- xus, quem uertiginis nomine distinguebat Democritus; (de simplicissima mixtione nunc loquor, ad alias enim perfectissi- mas longè maior requiritur accidentium, & instrumentorum apparatus ut patet in generatione uiuentium.) & tandem est ipsius formæ nondum existentis afflatus intentionalis, idçalis, directiuisq; operis, Ista itaq; atomi sic inuicem coniunguntur, ut antea motus localis multiplex inter ipsas fieri debeat: sicut enim in mixtio- nibus, coctionibus artificialibus contingit omnia susdeq; uer- ti, diuq; circumagi antequam in unius consistentiç rationem uenire possint; pariter in mixtione naturali inter atomos id fieri necesse est: quia tantæ tamq; mirabiles mixtionum uarie- tates fortuito ordine fieri non possunt, multę enim erunt ali- quando simul quę alijs debent attemperari: ad unionem de- inde figura non rarò mutari debet, prætereà interclusus aer ejiciendus, nonnunquam exigit id mixti ratio ut intercipiatur: quę sine motu locali fieri non possunt. Influxus in super coe- lettis est ueluti stimulus, calcar, & incentium atomis mouen- dis efficacissimum, eoq; influxu in rebus præsertim inanimatis figillatur materia, nam pro exigentia mixti dispensat atomos, quapropter si ad calidum mixtum influentia dirigatur, fiet ut igneę atomi numero terreas superent, atq; id diuersis neq; fa- cilè explorabilibus proportionibus, unde uaria tempera[m]éra resultabunt. Et sicuti in uino uidemus uim concoctricem ità efficaciter omnia digerere ut impuritates per spumam eijciat, craf-

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170. On Atoms. Disputation II. For carving, marble is required as the material, along with a chisel, hammer, and sculptor’s tools; and the artist’s idea, according to which the tools are directed, to which, if the hand has not failed, the resulting image in marble responds. For natural mixture we have as material watery, earthy, and fiery atoms; for instruments there will be the primary qualities of the atoms and the influence of the stars, which Democritus distinguished under the name of whirl; (I am now speaking of the most simple mixture, for in other, more perfect mixtures a far greater apparatus of accidents and instruments is required, as is evident in the generation of living things.) and finally there is the intentional, ideal, and directive breath of the form itself, not yet existing, of the work. Thus, then, these atoms are joined together in such a way that beforehand a multiple local motion among them must take place: for just as in mixtures, in artificial cookings, it happens that all things must be turned now this way, now that, and circulated round and round before they can come to the condition of a single consistency, so likewise in natural mixture among atoms the same must necessarily occur: because so many and so wonderful varieties of mixtures cannot come about by chance order; for many things will at one time be together which must be accommodated to others: then, for their union, the figure must often be changed; moreover, the air shut in must be expelled; sometimes the nature of the mixture requires that it be intercepted: these things cannot happen without local motion. The influence in the supercelestial realm is like a stimulus, a spur, and a most effective incitement for moving atoms, and by that influence matter is impressed, especially in inanimate things; for according to the requirement of the mixture it distributes the atoms, wherefore if the influence is directed to a hot mixture, it will come about that the fiery atoms in number surpass the earthy, and that by various proportions not easily to be explored, whence various temperaments will result. And just as in wine we see the digestive power so effectively to digest everything that it casts out impurities by foam, craf-

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C.4. De mixtione atomorum. 171 crassiores uerò partes in fæces subsidant, eaq[ue] est disgregatio, ut quamuis impure sint uue[n] nihilominus tamen moru natiuo uinum redditur purissimum, pariter etiam influxus celestis sic attemperabitur, ut in mixto quod molietur, uarias atomos figat uarias autem eijciat. Contingit autem rarò, quod optimè anima duertit Sennertus ut in eleméta pura dissolutio fiat, sed potiùs in minima physica plerumq[ue] eam contingere innumeris chymicorum experientijs comprobatur. In istis verò naturæ operibus oportet semper recordari versissimi illius pronuntiati, opus naturæ opus intelligentiæ. p.9. Ex his causam afferre licet cur nonnulla alijs sunt calidiora quod scilicet suum temperamentum à mixtione, quam plures atomi igneæ ingrediuntur, resultet: Nihilominus tamen calidissima naturæ mixta ad tactum frigida sunt vt piper, sulphur, rosmarinus, quia sunt occultæ qualitates quæ vim earu[m] modificant, quæq[ue] à formæ penetratibus exortæ dominantur in elementales, & illis nouâ quâdam singulisq[ue] formis aptâ ratione abutuntur. Quare eius sum mentis primas qualitates habere aliquid potentialitatis, cùm in mixtis constitutæ viuaciùs non rarò agant, quam si puro essent elemento coniunctæ, & vbiq[ue] fere diuerso modo, sic frigus cicut[ur] à frigore papaueris differt, non solum in intensione quam vtrobiq[ue] fere æqualem medicorum principes sentiunt, verùm potiùs in modo agendi. Vnde etiam sic vt ignis alio modo in pipere alio in cinnamomo, alio verò in melle agat, & idem in diuersis ventriculis aliter aliterq[ue] alterabit, & alterabitur. Forma enim directrix est & applicatiua suarum qualitatum, & pro varia earum moderatione idem instrumentum non semper vniformi modo operatur ob diuersam figuram. Nunc vt reconditum hoc mysterium in lucem ponam rationemq[ue] modificationis qualitatum occultum adeò arcanum explicem. Obseruo

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C.4. On the mixture of atoms. 171 the coarser parts settle into the lees, and that is a separation, so that although they are impure, nevertheless by natural course the wine is made most pure; likewise also the celestial influx will be so tempered that, in the mixed body which it is to work upon, it will strike various atoms and drive out others. Yet it happens rarely, as Sennert rightly observes, that in pure elements a dissolution takes place; but rather, in physical minima it commonly occurs, as is proved by innumerable chemical experiments. In these works of nature one must always remember that most elegant saying: the work of nature is the work of intelligence. p. 9. From this it is possible to give the reason why some things are hotter than others, namely because their temperament, arising from mixture, in which more fiery atoms enter, results thus. Nevertheless, the hottest mixtures in nature are cold to the touch, such as pepper, sulphur, rosemary, because there are hidden qualities which modify their power, and which, arising from the penetrations of form, prevail in elemental things, and use them in a new manner suited to each particular form. Therefore, its meaning is that the primary qualities have something of potentiality, since in mixed things they are constituted and often act more vigorously, than if they were joined to a pure element, and almost everywhere in a different way; thus the cold of hemlock differs from the cold of poppy, not only in intensity, which the leading physicians judge to be almost equal in both, but rather in the mode of acting. Whence also fire acts in one way in pepper, in another in cinnamon, and in yet another in honey, and the same thing in different stomachs will alter and be altered in different ways. For form is the directing and applying principle of its qualities, and according to the varying moderation of these qualities the same instrument does not always operate in a uniform manner because of a different figure. Now, to bring this hidden mystery into the light and explain the reason for the modification of qualities, so hidden an arcane thing, I observe

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172 De Atomis. Disp. II. Obseruo primò non parum intendi vel minui vim qualita- tum à densitate, & raritate subiecti, sic ignis aquæ vitæ impu- ne tractatur, velocissimè verò comburit ferrum candens. Obseruo secùdò eundé solis radiu[m], quamuis vbiq[ue]; sit idem, nihilominus tamen, vehementer alicubi ardere, alibi verò re- missiùs, & pro varia reflectione, refractione, oppositione dire- ctione, obliquitate, aspectuq[ue]; minuitur vel augetur solis calor. Idem de internis corporum mixtorum ignibus dicere pos- sumus, qui cum varijs itidem medijs excipiatur, cumq[ue]; alibi rarior sit textura, densior alibi, sit vt etiam diuersimodè appli- catus diuersimodè agat, præterè non dubito vim etiam mul- tarum ignis atomorum paucis aqueis infringi posse, & eludi, si videlicet ità earum vis actiua excipiatur vt à concauo in co- nexum desinat, fiet enim quod in tubis opticis contingit vt di- spergantur, tùm lucis, tùm caloris radij, atq[ue] ità vis dispersa debilissima fiet. Deinde si ars varià ignis applicatione, tàm diuersa miracula patrat, quidni directrice formà idem analogi- cè fieri poterit? Atq[ue] quod de calore insinuaui de frigore & c[on] dictum esto. Igitur in gratiam formæ natura cælestisq[ue] influ- xus ità mouet atomos, & mixtionem dispensat, ut modo sibi connaturali qualitatibus vti possit, & pro modo essendi habe- at operandi modum. Diximus itaq[ue]; qua ratione atomi in mi- xtione dispensentur, quade re instituti nostri erat differere. PROPOSITIO XXXV. Plures sunt mixtionum gradus, una ordinatur ad perfectiorem, mixta simpliciora perfectiorum sunt materia, mixtisq[ue]; plurimi insunt pori qui ab atomorum seriatim positarum connexione ortum habent. NON est omnino Rhetoris ea cogitatio, quà dicitur na- tura in violis, rosarum, & tulipparum rudimenta pone- re, nam

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172. On Atoms. Disputation II. First, I observe that the power of qualities is increased or diminished not a little by the density and rarity of the subject; thus fire is handled with impunity in aqua vitae, but it very quickly burns hot iron. Secondly, I observe that the same ray of the sun, although it is everywhere the same, nevertheless burns very fiercely in one place, but more mildly in another; and according to the various reflection, refraction, opposition, direction, obliquity, and aspect, the heat of the sun is diminished or increased. The same may be said of the internal fires of mixed bodies, which are received through various mediums as well, and since the texture is rarer in one place and denser in another, being also applied in diverse ways, they act in diverse ways. Moreover, I do not doubt that the power of many fire-atoms can also be weakened and evaded by a few watery ones, if indeed their active force is received in such a way that it passes from a concave into a continuous form; for then what happens in optical tubes will occur, namely that the rays of both light and heat are dispersed, and thus the dispersed force will become very weak. Then, if art by a varied application of fire performs such different marvels, why could the same not be done analogically by a directing form? And what I have suggested about heat should also be understood concerning cold. Therefore, for the sake of form and the heavenly influx, it moves atoms and arranges the mixture in such a way that it may use qualities in a way natural to itself, and may have its mode of operation according to its mode of being. Thus we have said in what manner atoms are distributed in a mixture, which was the matter of our discussion. PROPOSITION XXXV. There are several degrees of mixtures; one is ordered toward a more perfect one; the simpler mixed bodies are the matter of the more perfect; and in mixed bodies there are very many pores, which arise from the connection of atoms placed in sequence. This is not at all the sort of thought of a rhetorician, when it is said that nature places the rudiments of violets, roses, and tulips, for

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C.4. De mixtione atomorum. 173 re, nam sensim perficit se, & imperfectionibus ad perfectiona vtitur. I. Gradus mixtionis is est quo atomi elementares miscen- tur elementaribus atq; in hunc primùm gradum frequenter dissoluuntur perfectiona mixta, rarò enim contingit vt in ele- mentum purum resolutio fiat atq; huius mixtionis minima vo- cari possunt prima in ordine mixtionis. II. Gradus mixtionis fit à mixtione primorum minimoru[m], quæ elaboratius aliquanto mixtum faciunt, quia scilicet formæ perfectioni subijci debent, atq; huius mixtionis minima, se- cundaria dici possent. III. Gradus mixtionis est quo secunda minima inuicem permiscentur, faciuntq; ad vegetantium texturam, aut ad id quod in vegetantibus perfectius est mixtionem, cuius deinde minima sunt magis composita, & tertij ordinis dicuntur. IV. Gradus mixtionis oritur à commixtione minimorum tertij ordinis fitq; mixtum cuius minima sunt quarti ordinis. V. Pariter ex istis compactis minima fiunt elaboratiora quæ quinti ordinis nominentur, & sic de alijs mixtionum gradibus, & perfectionibus. Vnde patet quod atomi elemen- tales sunt radices omnium, & minimorum maximum compo- situm illud est quod perfectioni formæ subijcitur. Sed ne gratis ista dici videantur prob. tota hæc doctrina ex- perientiâ, nam plantæ succu[m] quendam trahunt ex elementis in- ter se compactis, deinde in planta sunt partes magis minusve elaboratæ, pro belluis non ità requiritur exquisita partium temperies, vt pro homine cuius anima immortalis, & intelle- ctiua eo perfectius operatur quo perfectionibus organis est pre- dita: ergo ista mixtionum diuersitas oritur à varijs minimis, & reuerà si res ità se non habet, cur vix quidquam ad victum as- sumimus quod vitæ fuerit expers? panis, vinum, carnes, her- bæ tran-

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C.4. On the mixture of atoms. 173 by this means, for it gradually brings itself to completion, and uses imperfections toward perfection. I. The first degree of mixture is that in which elemental atoms are mixed with elemental atoms; and often perfect mixtures are dissolved back into this first degree, for rarely does a resolution into a pure element occur; and the minima of this mixture may be called the first in the order of mixture. II. The second degree of mixture is made from the mixture of the first minima, which make the mixed thing somewhat more elaborately, since, namely, the forms must be subjected to perfection; and the minima of this mixture could be called secondary. III. The third degree of mixture is that in which the secondary minima are mixed with one another, and they make the mixture that belongs to the texture of living things, or to that which is more perfect in living things; and of this mixture the minima are then more composite and are called of the third order. IV. The fourth degree of mixture arises from the intermingling of the minima of the third order, and there results a mixed thing whose minima are of the fourth order. V. Likewise from these more compact things there come more elaborated minima, which are named of the fifth order, and so on with the other degrees and perfections of mixtures. Whence it is clear that elemental atoms are the roots of all things, and that the greatest composite of minima is that which is subjected to the perfection of form. But lest these things seem to be said without proof, this whole doctrine is demonstrated by experience: for plants draw a certain juice from the elements compacted among themselves; then in the plant there are parts more or less elaborated. For beasts, such an exact tempering of the parts is not required as for man, whose immortal and intellectual soul acts the more perfectly the more the organs are furnished with perfections. Therefore this diversity of mixtures arises from various minima; and indeed, if the matter were not so, why do we scarcely take anything as food that has been without life? bread, wine, meats, herbs—

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De Atomis. Disp. II. bar transeunt in nostri substantiam quia ex his minimis magis elaboratis humana faciliùs, virtute concoctrice coalescunt, nullum animal elemento nutriri potest, atq[ue] inter dispensaticis naturæ munera illud obseruatu dignum est, quod nulla planta plantis viuat, quamuis agnus tartaricus portento similis plantas sibi circumpositas exsiccet, brutorum quædam alij vescuntur, sed homini in omnia ius est à Deo sancitum, minus tamen herbæ nutriunt quâ carnes quod magis in ijs sit elaborandu[m] vt ex suis minimis alia fiant homini nutriendo apposita. Sic optimè seruatur ea subordinatio quam in formis imperfectionibus ad perfectiores fieri contendit elegantissimus Fernelius lib. 1. de abditis rerum caulis c. 4. Singularum partium formas quosdam veluti gradus esse quibus ad supremam illam totius formam promoueatur, nec alia de causa illas in subiectum impressas, nisi vt istà præparatione ad hanc introducendam via præsterneretur, & quam subordinatione demonstrat in formis Fernelius eandem in materijs agnouit Democriti amicus, & admirator Diuinus Senex noster, cum ait mixta imperfectiora, perfectioru[m] esse materiam. Consentiuntq[ue] physicorum principia duo, primùm quod nullum animal elemento puro viuere possit, imò si mel, & manna excipias, quæ libro singulari probaui esse meteora, nullà re omnino vitam protrahimus quæ à viuentibus non sit excepta, melle sanè aliquamdiu vixit Democritus vtsupra innui, & Israelitarum exercitus manna: hic excipio ventriculoru[m] monstra, virtutisq[ue] concoctricis portenta hoc etiam sæculo visa, na[m] Lazarus quipiam vitriuorax ab effectu dictus est, & alius Lugduni summà auiditate patinas saxulis plenas deuorabat: sed anijs vescerentus non parum dubito. Secundùm quo perfectior est forma eo plures, & elaboratiores admittit dispositiones quæ in tres classes referuntur, ad tem- periem,

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On Atoms. Disp. II. they pass into our substance because, from these smallest and more elaborated particles, human beings more easily coalesce by the power of digestion. No animal can be nourished by an element; and among the dispensations of nature it is worthy of note that no plant lives on plants, although the Tartar lamb, a creature like a prodigy, dries up the plants placed around it; some of the brute creatures feed on others, but for man a right over all things has been sanctioned by God. Yet herbs nourish less than flesh does, because in the latter there is more to be elaborated so that from their smallest parts other things may be made fit for nourishing man. Thus is best preserved that subordination which, in the forms of imperfections, strives to advance to the more perfect, as the most elegant Fernelius teaches, lib. 1. de abditis rerum causis c. 4. The forms of individual parts are as it were certain stages by which it is promoted to that supreme form of the whole, nor for any other reason are those forms impressed upon the subject, except that by such preparation a way might be opened for introducing this one; and what Fernelius shows by subordination in forms, the friend of Democritus and our divine old man, admirer of him, likewise acknowledged in matters, when he said that the more imperfect mixtures are the matter of the more perfect. And the principles of the physicists agree in two points: first, that no animal can live on a pure element; indeed, if you except honey and manna, which I have proved in a separate book to be meteors, we prolong life by nothing at all that has not been excepted from living things. Truly Democritus lived for some time on honey, as I noted above, and the army of the Israelites on manna. Here I except monsters of the stomach and prodigies of the digestive faculty, seen even in this century; for one Lazarus, called vitreovorous from the effect, and another at Lyon devoured dishes full of pebbles with the greatest avidity: but whether they fed on eggs I greatly doubt. Second, the more perfect a form is, the more numerous and more elaborate are the dispositions it admits, which are referred to three classes, as to temperament,

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C.4. De mixtione atomorum. 175 periem, synthesin, spiritum calidum, & humidum radicale. Pro temperie est is quem explicui minimorum ordo, pro syn- thesi sunt ossa, nerui, caro, venæ, tendines, parenchymata singula sua sede reposita. Spiritus verò insitus, & humidum radicale quod vltimam dispositionem ponit, oritur à totius na- turæ nixu, cum ad illum concurrat parentum semen, influxus cæli, & partium temperies: atq; vt formę ignobiliores nobilio- ribus substernuntur, pariter & materia rudis, ad elaboratioré est apposita. Ex his explicari plurima possunt in Theorica medicinæ dif- ficillima degeneratione rerum toto genere differentium, in nostro corpore quales sunt lapides, vermes, lumbrici, & solui quæstio illa quæ ad ranam, vt dicunt, vagam, non paucos phi- losophos neque ignobiles, tanquam ad bonum hospitium de- duxit, cum degeneratione animalium insectorum quæque ex putri materia fiunt disputarent: quo de argumento omnibus palmam eripuit Doctissimus huius ætatis philosophus Fortu- nus Licetus primarius Bononia professor in libris despontaneo viuentium ortu. Sunt enim huiuscemodi vermium, & lumbricorum minima tertij verbi gratia ordinis, quæ cum alimentis assumpta vim concoctricem subterfugerunt, atq; quod debilior esset, non ità potuerunt edomari, quin seruarent seminales spiritus for- mamq; partialem, vnde ex aliqua horum copia, quæ tanto fa- ciliùs cumulantur quo sympathia ea ad se inuicem trahit, & iungit, fit vt excitati spiritus qui in minimis diutissimè conser- uantur, se paulatim perficiant, & abducto ad se alimento cre- scant. Calculi verò fiunt ex renum qualitate Lithopoijticà, id est, petrificà, quæ aliunde non prouenit nisi quod excisum à pa- rentibus semen illi parti efformandæ destinatum quidpiam. minus elaborati habuit quod huiuscemodi lapidum insentibi- les

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C.4. On the mixture of atoms. 175 life, synthesis, the hot spirit, and radical moisture. For temperament there is that order of the smallest parts which I have explained; for synthesis there are bones, nerves, flesh, veins, tendons, and parenchymas, each placed in its own seat. But the innate spirit, and the radical moisture which establishes the final disposition, arise from the striving of the whole of nature, since to this concur the seed of the parents, the influence of the heavens, and the temperament of the parts: and just as more noble forms are set beneath the less noble, so too the crude matter is placed in order to be more elaborately worked up. From these things may be explained many matters very difficult in the theory of medicine: the degeneration of things differing in the whole genus, such as in our body are stones, worms, roundworms, and the solution of that question which, as they say, concerning the wandering frog led not a few philosophers, and not ignoble ones, as to a good lodging, when they were disputing about the degeneration of insects and whatever things are made from putrid matter. On this subject the most learned philosopher of this age, Fortunus Licetus, professor at Bologna, won the palm over all in the books On the Spontaneous Origin of Living Things . For the smallest of this kind of worms and roundworms, for example of the third order, which, taken up with food, escaped the digestive power, and because it was weaker could not be so subdued that it would not preserve the seminal spirits and the partial form; whence, from some abundance of these, which are gathered all the more easily the more sympathy draws and joins them to one another, it comes about that the spirits, once stirred, which are preserved longest in the smallest parts, gradually perfect themselves, and, drawing nourishment to themselves, grow. But stones are produced from the lithopoietic, that is, petrifying, quality of the kidneys, which arises from no other source than that the seed cut off from the parents had in it something destined for the forming of that part, less elaborated, from which such stones of insensible

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176 De Atomis. Disput. II. les particulas semimaceratas, ac veluti colliquatas tantum de- ueheret, vnde & paremchyma de illa qualitate participat, & viscosa arenosaq; magis trahit sibiq; natiuo quodam visco ag- glutinat, vt ex princ. 12. facilè est subducere; sequitur quod tandem coalescet calculus, & ex pluribus insensibilibus parti- culis, vnum valde sensible, & summè dolorificum exurget: adde quod ipse lapidum particulæ ob virtutis expultricis debi- les conatus, & humoris circum fusi glutinum adhærent alijs, & paulatim agglomerantur complura; videturq; hæc philolo- phandi ratio ipso calculorum aspectu non parum habere pro- babilitatis, cum ex granulis compacti esse percipiantur, præ- sertim si nondum recocti friabiles sint. Sapienter ergo diætetica nephriticis alimenta in arenosis nata prohibet, quod omnia è solo vbi oriuntur participent ex Theophrasto l. 1. & 2. de causis plant. c. 5. 6. vt patet in vinis, frumentis, ciceribus quorum aliqui ratione soli vix arte vllâ macerari vnquam possunt, quapropter alimenta grumis lapi- diformibus prædita vt pira cidonia &c. nephritici ne at- tingant cautum est medicis legibus. Nam cum succo attr- ærunt arenulas aliaq; insensibilia, quæ non satisedomita, in- corpore humano non parum pariunt incommodi, ex visco la- pides fiunt, & ex insensibilibus particulis calculi, sex & am- plius nunciarum. De illa autem attractione succi varij qui aliam naturam quam viuentis induat dubium esse non potest. Narrat Godignus in vita Syluerię, esse longissimum in Mono- motapa terrarum tractum aurifodinis ditissimum, in quo non rarò arborum trunci auri ramentis insignes deprehenduntur, attracto scilicet eo succo qui in aurum transire debuit, ibi enim ob soli siccitatem arbores sunt famelicæ, vnde obuijs quibus- uis se se explent; at enim succi illius qualitates indomabiles proprio indulgentes genio in ipso trunco aurum fiunt. Ita sci- licet

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176 On Atoms. Disputation II. the semi-digested particles, as it were only melted down, it would carry away from there, whence the parenchyma also shares in that quality, and it draws to itself the viscous and sandy matter more strongly and agglutinates it with some native viscid substance, as from princ. 12 it is easy to infer; it follows that the calculus will at length coalesce, and from many insensible particles one very perceptible, and exceedingly painful, body will arise: add to this that the very particles of the stones, by the weak efforts of the expulsive faculty and the glue of the surrounding humor, adhere to others, and gradually many are agglomerated; and this reason for philosophizing seems to have no small probability from the very appearance of stones, since they are perceived to be compacted of grains, especially if they are not yet baked and brittle. Therefore the dietetic treatment wisely forbids nephritic sufferers foods born in sandy soils, since all things partake of the earth from which they arise, as Theophrastus says, l. 1 and 2, De causis plant. c. 5, 6, as is clear in wines, grains, chickpeas, some of which, by reason of the soil, can scarcely ever be softened by any art; wherefore foods endowed with stony kernels, such as pears, quinces, and the like, are, by medical laws, forbidden to nephritic patients to touch. For when they attract with the juice little grains of sand and other insensible particles, which, not sufficiently subdued, cause not a little trouble in the human body, stones are made from viscid matter, and calculi from insensible particles, of six and more ounces. But concerning that attraction of juices, various writers say there can be no doubt that they assume a nature other than that of the living body. Godignus relates in the life of Syluerię that there is in Monomotapa a very long tract of land rich in gold mines, in which the trunks of trees are often found marked with gold filings, namely because they have attracted that juice which ought to have passed into gold; for there, because of the dryness of the soil, the trees are hungry, and therefore fill themselves with whatever comes to hand; but the qualities of that juice, ungovernable and indulging their own nature, become gold in the very trunk. Thus indeed

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C.4. De mixtione atomorum. 177 licet insitum est formis ad natium statum reducere se se exp.8. si quando dispositionibus adhuc vigentibus, neq; alijs poten- tioribus superinductis, id moliri possint. Hæc & infinita alia ex Democriti principijs licet deducere, vnde claro testimonio nobiliq; laude Aristoteles loco supra citato, videtur (inquit) Democritus omnia præuidisse, & principia supposuisse, quibus omnia possent explicari. Quoad poros, elementa pura ijs carent, mixta imperfe- cta paucos habent, quia crassior illis temperies est, neq; exi- gunt tanta profluua spiritum, vel transpirationem, quæ non- nisi per poros fieri possunt, quare vitrum, lateres coctiles, vas marmoreum, aliaq; huiusmodi odorata spirituosaq; seruant melius, essentiasq; chymicorum quàm pixides eburneæ, buxæ aliaq; lignea osseaue. Ista enim transudant manifestè, in alijs autem sensim fiunt effluia: Nemo de poris in ligno dubitabit qui hederaceum viderit poculum, quod à Plinio, & alijs ob- seruatum est aquam capere non posse, vino verò fidelem esse custodem, cuius rei non semel feci experimentum. Ratio dari posset quod atomia queæ illis poris proportionatæ sunt vt pote figure magis conuenientis minorisq; magnitudinis, vini verò minima non item; nô tamen inficianda est occulta hederæ dos qualitasq; recondita oriens à propria partiù contemplatione. Humani pori sub sensum cadunt, & substantia viuentium tota est peruia, sicuti domus vndiquaq; columnis tantum suffulta, vel cui plurimę per ambitum sunt fenestrę, portę plures, aliæq; excipiendo aeri apertę vię, neq; vllum est cubiculum cui por- ta sua fenestraue desit, ita vt ab vno ad aliud sit via, textura, insuper multiformi, variè se se pori habent ità vt optimè com- paretur textura viuentium tibialibus sericis quæ ità sunt con- fecta vt facilè dilatentur, & constringantur, quia annulatim se se connectumt fila, & foramina nunc grandiora, nunc patentia minus

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C.4. On the mixture of atoms. 177 although it is inherent in forms to reduce themselves to their natural state if ever, while their dispositions are still active, and no stronger ones have been superinduced, they can bring this about. These and countless other things may be deduced from Democritus’s principles; whence, by clear testimony and worthy praise, Aristotle in the passage cited above seems to have said: Democritus, he says, foresaw everything, and laid down principles by which everything could be explained. As for pores, pure elements lack them; mixed imperfect bodies have few, because their constitution is denser, and they do not require such abundant exhalation of spirit, or transpiration, which can occur only through pores. For this reason glass, baked bricks, marble vessels, and other such fragrant and spirituous things preserve odours and the essences of the chemists better than ivory boxes, boxwood, and other wooden or osseous ones. For these visibly transpire, whereas in the others the effluvia are gradual. No one will doubt the presence of pores in wood who has seen the ivy cup, which, as Pliny and others have observed, cannot hold water, but is a faithful keeper of wine; I have not once made trial of this. A reason might be given, namely that the atoms proportioned to those pores are of a more fitting shape and smaller size, whereas those of wine are not the smallest; yet the hidden virtue and secret quality of ivy, arising from a proper contemplation of its parts, must not be denied. The pores of human beings fall under the senses, and the substance of living things is wholly permeable, just like a house supported only by columns on every side, or one that has very many windows around its circumference, several gates, and other open passages for admitting air; nor is there any chamber lacking its own door or window, so that there is a way from one to another. Likewise, with a manifold texture, the pores of living things are variously disposed, so that they may be compared most aptly to silk stockings, which are made in such a way that they may easily expand and contract, because the threads are joined together in rings, and the holes are now larger, now less open.

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De Atomis. Disp. II. 178 minus pro pedis modo habent. Orpheus sanè vt retis implexum animal constitui suis in carminibus cecinit ex Arist. 1. 2. de gen. anim. c. 1. Quod si subtilitatis pororum quispiam habere velit argumenta, consideret culicis tenuitatem, qui cum vitæ sit particeps, alimentum exsugit, porosq; habet quibus illud distribuit. Quo perfectiora sunt mixta eo plures habent poros, nam varietati partium, organisq; compingendis plura sunt necessaria, atq; ex hac mixtureis explicatione, viuentiumq; textura, intelligitur quomodo fiat nutritio augmentatioq; quid sit transpiratio, effluuium, halitus insensibilis, sudor, attractio ambientis &c. Plures itaq; sunt mixtionum gradus &c. quod erat ostendendum. PROPOSITIO XXXVI. Explicatur dissolutio mixti ex Democriti principijs. Generatio, & corruptio sunt veluti choragi duo naturæ, formarum admissionales, & subductores: Quæ licet adeò contraria sint tamen manu se tenent, vt altera aliam statim sequatur sicuti dolorem voluptas, & voluptatem dolor; quare Aristoteles generatio vnius est corruptio alterius, et corruptio vnius, est alterius genesis. Breuiter in Superioribus explicui mixtionis gradus, hoc est generationum mysteria, quòd hìc doctrinæ potiùs fundamenta indicem, quam vt atomorum diffusam vniuersalemq; tractationem, cubitale opus, mihi scribendam proposuerim. Ex principio 8. supposuimus omnia reuocare se ad natium statum, quantum quidem possunt, quare si illum deperdunt, vi extrinsecus adhibitæ tribuendum est: acqui status ille naturalis atomorum non modo qualitatum est primarum verum etia[m] figuram complectitur: quare statim ac extrinsecum quidpiam, verbi

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On Atoms. Disp. II. 178 less than the measure of a foot. Truly Orpheus sang in his songs that an animal is formed entangled like a net, from Aristotle, De generatione animalium 1.2, c. 1. And if anyone should wish to have proofs of the fineness of pores, let him consider the delicacy of the mosquito, which, though it partakes of life, sucks out nourishment, and has pores through which it distributes it. The more perfect the mixtures are, the more pores they have; for the variety of parts and the organs to be joined together require more things, and from this explanation of mixture, and the structure of living things, it is understood how nourishment and growth take place, what transpiration is, effluence, insensible vapour, sweat, the attraction of surrounding things, etc. There are therefore more degrees of mixtures, etc., which was to be shown. PROPOSITION XXXVI. The dissolution of the mixture is explained from the principles of Democritus. Generation and corruption are, as it were, the two leaders of nature, admitting and dismissing forms: although they are so contrary, yet they hold each other by the hand, so that one immediately follows the other, just as pleasure follows pain and pain pleasure; wherefore Aristotle says that the generation of one thing is the corruption of another, and the corruption of one thing is the genesis of another. Briefly, I have explained above the degrees of mixture, that is, the mysteries of generations; here I indicate rather the foundations of the doctrine than propose to myself the labor of writing a diffuse and universal treatment of atoms, a task fit for a couch. From principle 8 we supposed that all things return to their natural state, as far as they can; therefore if they lose it, this must be attributed to force applied from outside. But that natural state of atoms includes not only the primary qualities but also figure: wherefore as soon as something external, for example

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C. 4. De mixtione atomorum. 179 verbi gratià ignis, atomos igneas in mixti penetralibus refusas, & ad formæ partiumq[ue]; sibi vnitarum exigentiam figuratas proritat, atomi auxiliaribus illis copijs motæ, contempto formæ imperio, natiuæ primæq[ue]; libertatis cupidæ, figuram recuperant primum, quæ cum sit sphærica, & vt sic, vnionis, vt diximus, cum cubo incapax, statim exiliunt, & cum sint valde mobiles erumpunt à vinculis, vnde dissolutionem continua- tis huiuscemodifectionibus consequi necessarium est. Formæ enim illud exercent in qualitates elementales impe- rium vt quamdiu vegeta est, istæ maneant sibi obsequentes, & subditæ, at verò si debili quodam agente proritentur facili ne- gotio administris formæ qualitatibus quæ ab ipsa promanant immediatè coercentur, cogunturq[ue]; ijs gradibus exerere suam vim quæ principi formæ magis est apposita. Verùm vt est vir- tus formæ certis limitibus coercita, eo nonunqua[m] excrescunt elementorum vires, vt spretis eius imperijs sibi potiùs studeat, languorum, & tandem corruptionis causæ: hoc autem domi- nium formæ necessarium fuit, vt aliquandiu mixta consiste- rent; facili enim negotio separantur elementa cum nullum a- gnoscunt huiuscemodi principatum, vt in mixtis imperfectis animaduertimus. Ignis qui maximè dissoluit mixta eò velocius agit, quò mi- nùs compactæ sunt compositi particulæ; In aliquibus enim tenaciter sibi omnia adhærent, in alijs vno laxior facillimè ce- dit: videntur aute[m] tenacioribus vinculis ea contineri in quibus certà proportione terra prædominatur vt in saxis, & metallis. Corrumpit verò ignis, vel cum flamma, vel sine flamma, vt in carbonibus contingit. In corruptione quam flamma comita- tur consideranda, præter ipsum mixtum, corpus flammeum, deinde fumus. Flamma ergo definiri potest mixtum imperfectum è mixto perfecto

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C. 4. On the mixture of atoms. 179 for example, fire, atomos igneas, in the innermost parts of the mixture scattered abroad, and shaped according to the form and needs of the parts united to it, the atoms, moved by those auxiliary forces, despising the rule of form, and eager for their native and original liberty, first recover their shape, which, since it is spherical, and thus, as we said, incapable of union with the cube, they at once leap out, and since they are very mobile, break free from their bonds; whence it is necessary that dissolution follow from such continued changes. For form exercises that power over elemental qualities so that, so long as it is vigorous, they remain obedient to it and subject to it; but if they are stirred by some weak agent, they are easily governed by the attendant qualities of form, which proceed from it immediately, and are compelled to exert their strength in those degrees that are more suitable to the principle of form. But since the power of form is restrained by certain limits, sometimes the forces of the elements grow so far that, despising its commands, they seek rather their own good: then come weakness and, at last, the causes of corruption. Yet this dominion of form was necessary, so that the mixture might remain together for some time; for the elements are easily separated when they recognize no such principate, as we observe in imperfect mixtures. Fire, which dissolves mixtures most, acts the more quickly the less compact the particles of the compound are; for in some things all parts adhere to one another tenaciously, while in others, with a looser bond, they yield very easily. It seems, however, that those things are held by stronger bonds in which earth predominates in a certain proportion, as in rocks and metals. Fire corrupts either with flame or without flame, as happens in charcoal. In corruption accompanied by flame, besides the mixture itself, the flaming body, and then smoke, are to be considered. Therefore flame may be defined as an imperfect mixture from a perfect mixture

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180 De Atomis. Disp. II. perfecto tendente ad corruptionem vi ignis in humido pingui prædominantis, dicitur mixtum imperfectum, quia tunc tem- poris non insunt mixti conditiones saltem perfectæ, etenim flamma est veluti via ad perfectam resolutionem: Ignis autem resoluendi vim habet, neque flammam emittit nisi pinguis alimentibeneficio, quo deficiente lucore omnicaret; In flamma itaque est pinguedo, exhalatio, vapor, halitus, spiritus ignei, qui ob suam raritatem, & viuacitatem totum corpus pro varia refractione variè tingunt, & tandem non desunt quædam pertinaciores magisq; inclytæ mixti qualitates, quod ab odore colligitur. Concatenantur autem atomi atq; sicuti catenæ contingeret quæ annulis quibusdam idemtidem, & alternatim priuaretur hoc mixto euenire est intelligendum, sed antequam integra fiat dissolutio trahunt se se quæ firmiùs hærent, & in flamma reliquias suæ vnionis dissoluunt, quo sit ut flamma in metæ formam, siuè conoidem figuram terminetur; cùm enim aliæ particulę nondum sint solutæ, alię adhuc humido pingui inio- rentur sit vt paulatim, modo scilicet agentibus naturalibus proprio, soluantur, & per cuspidis extrema auolent in fumum, vbi in secunda veluti probatione depurantur magis, secretioq; elimatior humido pingui absumpto consequitur. Ex quibus facili negotio rationem reddes cur in eadem candela depressior modò, modò elatior sit flamma, & cur quæda[m] ligna flammam diutius foueant, quàm alia. Ex flamma sit fumus qui ità est cum flamma compactus, ut coni duo videantur oppositi ità tamen vt pars dextra dextrę; sinistra uerò sinistre repondeat, sitq; axis intermedius utriq; cono communis nulla tamen decullatione intermediâ quam- uis aliqua contingat confusio partium. Fumus uerò definiri potest, aggregatum per accidens ex uapore,

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180. On Atoms. Disp. II. perfect tending toward corruption by the force of fire in the predominating fatty moisture, it is called an imperfect mixture, because at that time the conditions of a mixture are not present, at least in full perfection; indeed, flame is as it were the way to a perfect dissolution. Fire, however, has the power to dissolve, and emits flame only by the benefit of fatty nourishment, which being lacking, it would be entirely without brightness; in flame there is therefore fatness, exhalation, vapor, breath, fiery spirit, which, because of their rarity and vitality, stain the whole body in various ways by different refraction, and at last certain more tenacious and more illustrious qualities of the mixture are not lacking, which is inferred from the odor. Moreover, the atoms are linked together, and as if it would happen to chains which would be deprived of certain links here and there, and alternately, so must it be understood to happen to this mixture; but before the complete dissolution is achieved, those parts draw themselves together which cling more firmly, and in the flame they dissolve the remains of their union, so that the flame is terminated in the form of a cone, or rather a conoid; for since the other particles are not yet dissolved, some are still joined to the fatty moisture, so that gradually, by the proper action of natural agents, they are dissolved, and through the tip’s extremities they fly off into smoke, where, in a second sort of testing, they are purified more, and a more refined separation follows when the fatty moisture has been consumed. From these things you will easily give the reason why in the same candle the flame is now lower, now higher, and why certain woods sustain the flame for a longer time than others. From flame comes smoke, which is so compacted with the flame that two cones seem to be opposed, yet in such a way that the right part corresponds to the right, the left indeed to the left, and there is an intermediate axis common to each cone, without any intermediate falling away, though some confusion of the parts occurs. Smoke, moreover, can be defined as an accidental aggregate from vapor,

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Cap. 4. De mixtione atomorum. 181 uapore, exhalatione, spiritu igneo aerisq[ue]; particulis compactu[m], residuisq[ue]; mixti qualitatibus quibusdam uirtute ignis dissoluti. Sed ne longiùs abeamus experientijs duabus affero dissolutionis mixti paradigmata. Quotidie uidemus cineres è ligno fieri qui manifestè ostendunt ex minimis particulis omnia constare, difflatis enim intermedijs minimis quibus illæ partes terree uniebantur, remanent dissolutæ. Et uiolentiori calore liquatum sæpius plumbum, exhaustis aque ignisq[ue]; uinculis mutatur in subrufum quendam puluerem, qui deinde arte magis comminutus pictorum usui cedit. Cæteras corruptiones facili negotio poteris explicare, si imminutum formæ imperium, elementales qualitates ui externâ proritatas, natiui status, ac ueluti libertatis appetitum, definitionemq[ue]; Democriti qui dissolutione atomorum, siuè disgregatione corruptiones definiebat, attentè perpéderis: his enim principijs quatuor, ueluti rotis tota hæc doctrina circumferrur: neq[ue]; est quod diutiùs in hoc immorer uel in carbonum resolutione, uel in cadauerum putredine aut in ijs que in aquis corrumpuntur explicandis. Moneo tantùm ex occasione flammæ nullo modo secundu[m] sphæram ignem agere, hoc est, ut in ipso igne sumatur centru[m] è quo ad circumferentiam æquales lineæ ductæ paribus omnino caloris gradibus sint affectæ; de lumine secus pronuntio, si enim liberum detur illi spatium undiquaq[ue]; diffunditur æqualiter tamq[ue]; prodigiosâ latitudine ut expertus sim sphæram illuminatam ab lampadis unius ordinariæ flammâ, habuisse diametrum 140. passuum, quare locum occupabat lumen uiginti millionibus millionum maiore, cùm ipsa flamma dimidij tantum digiti esset. At uerò calor, ut ex hoc Democriti etiam placitum stabiliam, qui spiritibus igneis potius quam diffusioni qualitatis actionem tribuebat, adeò inæqualiter diffunditur, ut in M 4

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Chap. 4. On the mixture of atoms. 181 vapor, exhalation, fiery spirit, and air; with compact particles, and the remnants of mixed bodies, by certain qualities dissolved by the power of fire. But lest we go further astray, I present two examples of the dissolution of a mixture. Every day we see ashes made from wood, which clearly show that all things consist of the smallest particles; for when the smallest intermediate parts by which those earthy parts were joined together are dispersed, the parts remain dissolved. And lead, which has often been melted by a more violent heat, when the bonds of water and fire have been exhausted, is changed into a certain reddish powder, which is then more finely crushed by art and used by painters. You will be able to explain the other corruptions with little trouble, if you carefully consider the diminished power of form, the elemental qualities stirred up by external force, the natural condition, and as it were the appetite for freedom, and the definition of Democritus, who defined corruptions by the dissolution of atoms, or disintegration; for upon these four principles, as it were upon wheels, this whole doctrine turns. Nor is there any reason for me to linger longer over explaining either the reduction of charcoal, or the putrefaction of corpses, or those things that are corrupted in waters. I merely warn, by way of occasion, that flame in no way acts according to the sphere on fire, that is, that in the fire itself a center is assumed from which equal lines are drawn to the circumference, all equally affected by equal degrees of heat; I speak differently of light: for if free space is granted to it on every side, it spreads equally and with such prodigious extent that I have found a sphere illuminated by the flame of a single ordinary lamp to have had a diameter of 140 paces, wherefore the light occupied a space twenty million times greater, though the flame itself was only half a finger’s breadth. But heat, in order that I may also establish this view of Democritus, who attributed action rather to fiery spirits than to the diffusion of a quality, is diffused so unevenly, that in M 4

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182 De Atomis. Disp. II. in distantia cubiti plus agat secundum flammæ axem quam ad latera ad quatuor tantum digitorum distantiam. Ibi enim nempè in cuspide, ut pote lineâ perpendiculari, uia spirituum, & genuino atomorum ignearum decursu potentissima actione[m] exerit, sunt enim frequentiores ibi spiritus ignei, & suapte natura illac delatæ magno impetu corporibus obuijs insinuant se se. Quod aduerti primùm cum Italum qui solâ lampadis flammâ durissima quæuis metalla, imò etiam uitrum colliquabat uidissem, is enim propulsâ per tubum flammâ ità ad mouebat flammę lateribus digitos ut tantùm non tangeret, idq[ue] impunè, cùm tamen vitro metallisq[ue] in cuspide liquatis ut placebat abuteretur ad omnem figuram. Olla igni imposita citiùs aliquanto bulliet quam quę lateribus applicabis. Fumi autem actiuitas pari ratione propagatur ut secundùm axem potentior sit, quo magis ab eâ lineâ remouetur eo minori uirtute est præditus; Neq[ue] sit ulla inter flammam, & fumum decussatio quod initio specierum visibilium exemplo persuasus suspicabar, sed composità candelà quę alterà quidem parte uiridem, alterà uerò communem lucis colorem habebat, deprehendi eâ parte fumi quę uiridi flammę è directo imminebat easdem uigere qualitates quas in ipsa flamma cernebam, unde admitto confusionem quidem in conorum cuspidibus aliquâ, sed sine decussatione quam satis impedit spirituum impetus, & motus sursum. Prætereà flammâ circumuelliri subtiliori corpore uidemus, quę in basi angustior eo dilatatur magis, quo altiùs prouehitur, dum tandem fumo suis angustijs initium det, constituatq[ue] finito cono angustam quandam uian: quà quidquid enucleatè dissoluitur ad libertatem medij pergit. Licet autem plerumq[ue] contingat quod Aristoteles ait l.2. de gen. animal. c.4. Euenit nanq[ue] omnibus vt quod Vltimum fit, id primùs deficiat, & quod primùm id Vltimum: quasi natura de cursionem re- ducem

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182 On Atoms. Disp. II. at a distance of a cubit it acts more along the axis of the flame than to the sides, at a distance of only four fingers. For there indeed, namely at the point, as by a perpendicular line, the way of the spirits, and the genuine course of the fiery atoms, it exerts its most powerful action; for there are more fiery spirits there, and by their own nature, being carried thither, they insinuate themselves with great force into bodies that come in their way. I first noticed this when I had seen an Italian man who, with the flame of a lamp alone, melted the hardest metals, and indeed even glass; for, driving the flame through a tube, he moved his fingers so close to the sides of the flame that they almost touched it, and did so without harm, although with glass and metals liquefied at the point, as he pleased, he made use of them for every shape. A pot placed on the fire will boil somewhat sooner than one applied to the sides. The activity of smoke is propagated in the same manner, so that it is more powerful along the axis; the farther it is removed from that line, the less virtue it is endowed with. Nor is there any crossing between flame and smoke, as at first, persuaded by the example of visible species, I suspected; but in a composite candle, which on one side had a green flame, while on the other it had the common color of light, I found in that part of the smoke which directly overhung the green flame the same qualities to be active as I observed in the flame itself; whence I admit indeed some confusion at the tips of the cones, but without a crossing, which the impetus of the spirits and their upward motion sufficiently prevent. Moreover, we see the flame surrounded by a subtler body, which, being narrower at the base, expands the more the higher it is carried, until at last the smoke, starting from its narrowness, forms a certain narrow path with its finished cone, by which whatever is thoroughly dissolved proceeds to the freedom of the medium. But although it often happens what Aristotle says in Book 2 of Generation of Animals, ch. 4: for it happens to all things that what is made last is destroyed first, and what is first, last: as if nature were a reverse course of running

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Cap. 4. De mixtione atomorum. 183 ducem agat, et à meta ad carceres, vnde proruit, redeat. Id tamen in uiolentis corruptionibus non semper accidit, cùm, & à fundamentis, & à tecto possit ruina incipere. Explicuimus ergo mixtorum dissolutionem quod erat intentionis nostræ. DEMOCRITVS DOCENS Siue paradigmæ explicandi arduæ quæuis per corpusculorum doctrinam. THEMA PHILOSOPHICVM. O Laus Magnus in historia septemtrionali narrat Gothis fuisse familiare ex balænarum ossibus extruere tuguria in maris littore, vbi deinde gens potus auida sese ingurgitarent; Contingebat autem omnibus sub hoc ossium tecto dormientibus quasi sub vmbra mortis, tetris vexari insomnijs tempestatum, naufragiorum, iactationum in mari: & si quæ vel diuersa in sua inconstantia oceanus, aut scæua in procellis, aut horrenda in gurgitibus haberet. STATVS QVÆSTIONIS. Quæritur causa horum insomniorum, quæ quod constanter omnibus qui somniabant, & sæpius accidebant diuersis eadem, debet esse statu, & determinata: fortuita enim non habent statos fixosque recursus. INVESTIGATIO GENERALIS. Nullus penè in natura assignabilis est effectus ad quem plures causæ non concurrant, arduumq; est singulis suam effectus portionem assignare. In nostro autem casu concurrunt, balænarum ossa, somnius, imaginatio, ebrietas, cæreuisia, homo mari assuetus, quæ se habent ex parte causæ materialis, & efficientis; causæ autem formalis, & finalis hîc non videntur inuestigandæ. PRÆ-

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Cap. 4. On the mixture of atoms. 183 let it guide, and return from the goal to the starting-gates, from which it rushed out. Yet this does not always happen in violent corruptions, since ruin can begin both from the foundations and from the roof. We have therefore explained the dissolution of compounds, which was the aim of our intention. DEMOCRITUS TEACHING Or paradigms for explaining anything difficult through the doctrine of corpuscles. PHILOSOPHICAL THEME. O Laus Magnus in the northern history narrates that it was familiar to the Goths to build huts from whale bones on the seashore, where afterward that people, eager for drink, would gorge themselves; but it happened that all sleeping under this roof of bones, as it were under the shadow of death, were tormented by grim dreams of storms, shipwrecks, tossing on the sea: and whatever else the ocean might have, either different in its inconstancy, or savage in its storms, or dreadful in its whirlpools. STATE OF THE QUESTION. The cause of these sleepless dreams is asked for, and since they constantly happened to all who dreamed, and more often the same things to different people, it must be fixed and determinate: for chance occurrences do not have fixed and regular returns. GENERAL INVESTIGATION. In nature there is scarcely any effect assignable to which more than one cause does not contribute, and it is difficult to assign to each its share in the effect. But in our case whale bones, sleep, imagination, drunkenness, beer, and a man accustomed to the sea all concur; these belong on the side of the material and efficient cause, while the formal and final causes do not here seem to be inquired into. PRE-

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184 De Atomis. Disp. II. PRÆNOTIONES. I. Omnia corpora sunt in perpetuo fluxu vt probauimus prop. 33 & à singulis corporibus emanant corpusculorum effluua, quæ cum sint mixtorum halitus, eorum etiam qualitates aliquamdiù retinent. II. Res naturales conantur redire ad statum sibi connaturalem ex principio 8. disp. 2. eôfirmauimusque prop. 19. fund. 6. Illa autem rerum omnium restitutione fit quinque modis, primô generando aliquid sibi simile si adsint seminales spiritus, ita tartarum vini surculum dedit, & arbor vegetabilis chymicoru[m] succrescit. Secundò tentant sui restitutionem expulsis contrarijs, ita succi depurantur, fæces sublidunt, & singula sui similibus iunguntur ex princip. 12. disp. 2. Tertiò impetum sequuntur à natura impressum. Quartò proprietatibus suis quamdiù possunt vtuntur quia agunt necessariò, & in illarum vsu perfectionem videntur adipisci Quintò omnes suas partes quantum fieri potest in situ connaturali adaptant, ita vt infime cum supremis no[n] confundantur quod exemplo rosæ probauimus prop. 19 fund. 6. hinc nubium signaturæ, spectorum plurimorum ab halitibus cadauerum velpertine apparitiones, & in medicina pronuntiatum Hipp. 2. prophet. t. 1. Stquippiâ in vrina sublime petierit, occultato coxæ dolore delirium portendit, & Galen. 3. epid. com. 3. ægrot. 2. 1. 83. qui etiam in alijs ægris cum dixerit, suspensiones elatæ, statim subiecit, delirauit. Cuius reratio à solo flatu adæquata non est, sed quia contenta in vrina restituunt se ad statum quem habituri essent in corpore, vnde quæ sursum ibant, sursum in vrina eleuantur. III. Quæ non agunt per electionem determinari debent ab extrinseco ad modum actionis, ita arbores ab alime[n]to, pecudes ab obiectis extrinsecis mouentur, & imaginatio nostra ab aliquibus aduentitijs excitatur. IV. Dor-

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184 On Atoms. Disp. II. PRELIMINARIES. I. All bodies are in perpetual flux, as we proved in proposition 33, and from individual bodies there emanate exhalations of particles which, since they are the vapors of mixtures, retain their qualities for some time as well. II. Natural things strive to return to their natural state, from principle 8 of disp. 2. we also confirmed this in prop. 19, fund. 6. This restoration of all things, however, takes place in five ways: first, by generating something like itself if seminal spirits are present, as tartar gives rise to a vine shoot, and the vegetable tree of the chemists grows. Second, they attempt their restoration by driving out contraries; thus juices are purified, dregs settle, and each thing joins itself to what is similar to it, from principle 12 of disp. 2. Third, they follow the impulse impressed by nature. Fourth, they use their own properties as long as they can, because they act necessarily, and in their use they seem to attain perfection. Fifth, they adapt all their parts, as far as possible, to their natural position, so that the lowest are not confused with the highest, as we proved by the example of the rose, prop. 19, fund. 6. Hence the signs of clouds, the many apparitions of specters from the vapors of corpses or blood, and in medicine the statement of Hippocrates, 2. prophet. t. 1.: if something in the urine rises upward, while pain in the hip is concealed, it portends delirium; and Galen, 3. epid. com. 3. aegrot. 2. 1. 83, who also said in other illnesses, “suspensions raised,” immediately added, “he raved.” The reason for this is not to be explained by wind alone, but because the contents in the urine restore themselves to the state they would have in the body; thus what was going upward is elevated upward in the urine. III. Those things which do not act by choice must be determined from outside according to the mode of action; thus trees are moved by nourishment, cattle by external objects, and our imagination is stirred by certain adventitious things. IV. Dor-

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C.4. De mixtione atomorum. 185 IV. Dormiens, ebriusque sui iuris non est neque cogitationibus imaginationiue imperat cum sit interregnum rationis, vnde tunc temporis imaginatio vaporibus debilitata redit ad eas actiones quæ cum obiectis familiarissimis sunt annexæ, cu[m] auté somnus sit mortis imago, dormientibus ex pura assuetudine actiones adscribêdę, vt mortuis facit Vigilius 1.6. Æneid. Stant terræ defixæ hastæ, passimq[ue] soluti Per campos pascuntur æqui, quæ gratia currum Armorumq[ue] fuit viuis, quæ cura nitentes Pascere equos, eadem sequitur tellure repostos. V. In ebrietate plurimi sursum ad caput vapores feruntur: colligiturq[ue]; ex Aristotele 1.3. probl. contingere ebrietatem à capitis repletione, & eius quod replet motu, hinc ebrijs omnia videntur circumferri probl. 9. & probl. 10. Res vna plures repræsentat, ob velociorem motum fumi, & spirituum; Nihil autem interest conspectus moueatur an res conspectui obvia fit enim ratione vtralibet vt id quod dixi videatur: Idem imaginationi quod oculis contingit, plura de ebrietate, & somnis videbis in libro de tabaco Exercit. 5. S. & Exercit. 6. S. 3. 4. 5. 6. 7. & Exercit. 10. S. 4. COLOR SIVE ADAPTATIO. Balænæ ossa præsertim recentia magnum habent corpusculorum effluuium, & plurimas fundunt sui particulas ex prænot. I. Illc inimuant se in apertos hominum poros qui habent corpus transpirabile ex prop. 35. & 36. illi spiritus, siuè minima retinent de balenę qualitatibus, & conantur se se ad pristinum statum reuocare exerendo eas actiones quas in belluę membris moliebantur ex prænot. II. Nauta autem ex prænotione III. Debet determinari ad agendum ab extrinseco cum dormiat, & cùm ebrius sit, exeret actiones ab obiectis sibi familiarissimis ex prænot. IV. Vaporibus autem, & hali-

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C.4. Of the mixture of atoms. 185 IV. A sleeping man, and a drunk one, is not master of himself, nor does he direct his thoughts or imagination, since there is an interregnum of reason, whence at that time the imagination, weakened by vapors, returns to those actions which are connected with the most familiar objects, for since sleep is the image of death, actions are attributed to sleepers from pure habit, as Virgil does to the dead in Aeneid 1.6. Stant terrae defixae hastae, passimque soluti Per campos pascuntur equi, quae gratia currum Armorumque fuit vivis, quae cura nitentes Pascere equos, eadem sequitur tellure repostos. V. In drunkenness very many vapors are carried upward toward the head: and it is gathered from Aristotle, Probl. 1.3, that drunkenness arises from the repletion of the head, and from the motion of that which fills it; hence in drunk men everything seems to whirl around, Probl. 9 and Probl. 10. One thing represents many, because of the swifter motion of smoke and spirits; but it makes no difference whether the sight itself is moved or whether the thing comes into view before the sight, for in either way it happens that what I said seems to be so: The same thing happens to the imagination as to the eyes; you will see more about drunkenness and dreams in the book On Tobacco, Exercise 5, Sect. 3, and Exercise 6, Sects. 3, 4, 5, 6, 7, and Exercise 10, Sect. 4. COLOR OR ADAPTATION. Whale bones, especially fresh ones, have a great effluence of tiny particles, and they give off very many of their own particles from the aforementioned principle I. There they insinuate themselves into the open pores of men who have a body capable of transpiration, from propositions 35 and 36; those spirits, or minima, retain something of the qualities of the whale, and try to return themselves to their former state by carrying out those actions which they were attempting in the limbs of the beast, from the aforementioned principle II. But the sailor, from the aforementioned principle III, must be determined to act from something external when he sleeps, and when he is drunk, he will perform actions derived from the objects most familiar to him, from the aforementioned principle IV. But by vapors, and hali-

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186 De Atomis. disp. II. halitibus balænæ habet caput agitatum speciesq[ue]; internas illo atomorum siue minimorum motu agitatas, nam perpetuò ex se se iaculatur in viuêtes circumfusos corpuscula sceletus cæti. Agitantur omnia in ebrij capite ex p. 5. RESOLVITIO QVÆSTIONIS. Ob istas igitur causas à priori assignatas, vel huiuscemodi homo nihil somniabit, vel determinatâ imaginatione ab cor- pusculis balænæ ossium, familiaritate oceani, nauigationisq[ue]; frequentia, de mari somniabit, at cùm habeat agitatum caput ob cereuisiæ delatos sursum vaporosas atomos, concurrence balænarum afflatu, de mari agitato habebit insomnia cùm au- tem statuosa sit cereuisia ventos, ob specierum circumgirationem vortices, ob humiditatem naufragia tempestatesq[ue]; sibi repræsentabit, nam ob refractionem internam specierum motumq[ue]; multiplicem exigui motus videntur in somno magni: vt ait Aristoteles l. de diuinatione per somnum c. 1. ANNOTATIONES. I. Corpora humido suo exinanita non habent amplius effluuiorum copiam sed per attritionem consumuntur, & cum sicca sint attrahent potius externas impressiones vt ijs imbibâ- tur quam vt suas effundant: hinc seminum post triennium ef- fetæ vires, & medicam[m]etorum statæ est virtutis ætas, post quam inutilia sunt, & carie consumûtur, quod patet in radice China quæ ob vetustaté cum ad has partes venit vix alicuius est acti- uitatis, quare & ossa balænæ post aliquot æstates modica cor- puscula eiaculabuntur, hinc minùs ad insomnia concurrent. II. In somnijs plurimum affert modificationis temperies corporis, curæ solitæ, ætas, anni tempus, & alia huiusmodi, co- piaq[ue]; aliméti, nam cùm abundantissimè caput undiquaque re- plet, somnium non contingit, vt in pueris ex Arist. c. 3. de in- somnijs. Ebrijs verò contingere fere semper horrenda somnia notauit

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186 On Atoms. disp. II. from the vapors of the whale has a stirred head and appearances; within it, stirred by the motion of atoms or smallest things, for it is continually shooting forth from itself little bodies into the living beings around it, the skeleton of the herd. All things are stirred in a drunkard’s head, from p. 5. SOLUTION OF THE QUESTION. Therefore, for those causes assigned a priori, either such a man will dream nothing at all, or, with a determined imagination, from the little bodies of the whale’s bones, through familiarity with the ocean and frequent navigation, he will dream of the sea; but when he has a stirred head because of the vaporous atoms of beer carried upward, by the concurrence of whale exhalations, he will have sleepless dreams of the sea being agitated; but since beer is windy and subject to disturbances, because of the circling of appearances and vortices, because of moisture, shipwrecks and storms he will represent these to himself, for because of the internal refraction and the multiple motion of appearances, small motions seem great in sleep, as Aristotle says, book On Divination through Sleep, ch. 1. NOTES. I. Bodies deprived of their own moisture no longer have an abundance of effluvia, but are consumed by friction, and since they are dry they will rather attract external impressions so that they may be imbibed by them rather than that they may emit their own: hence the spent powers of seeds after three years, and the fixed term of the virtue of medicines, after which they are useless and are consumed by decay; this is evident in China root, which, because of its age, when it comes to these parts is scarcely of any activity; wherefore the bones of the whale after a few seasons will emit only small bodies, and thus contribute less to dreams. II. In dreams the temperament of the body, ordinary cares, age, the season of the year, and other such things, and abundance of food, contribute much to the modification; for when it fills the head most abundantly on every side, sleep does not occur, as in children, according to Aristotle, ch. 3 On Sleeplessness. But in drunkards horrid dreams almost always occur, he noted

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C.4. De mixtione atomorum. 187 notauit Doctissimus Asinus aureus l.1. metam. Ne meritò me- dici fidi cibo, & crapulà distentos scæua, & gravia somniare autumāt. III. In conatu quo corpuscula, tùm balenç, tùm cereuisiç tentant redire ad suum statum connaturalem, fit pugna inter spiritus hominis, & illos hospites siuè aduentitios hostes, qui cum sint à forma principali remoti ersi in ventriculo, & cere- bro tanquam in inani diu multumq; agitentur, vincuntur ta- men à calore humano vel dissipantur, vel resoluuntur, vel im- mut antur figurâ, ordine, connexu, ità vt in hominis partes transeant. REFLEXIO. Hanc exercitationem Democriti docentis volui interere vt modum in hac via philosophandi non præceptis modo ve- rùm etiam exemplo aperirem. Posuimus ergo primò prin- cip. 1 5. d. 2. experientiam. Deinde statum quæstionis aperui- mus ne videlicet ad alia vagaremur. Tertiò indicauimus cau- sarum capita quæ è narrationis visceribus debent depromi, quare circumstantiç in experimentis omittendę sunt nullę. Quartò cum omnis scientia discursiua omnisq; doctrina ex an- tecedenti fieri debeat quæstione, vt ait Aristoteles l.1 poste- riorum c.1. t.1. prenotiones afferre debuimus. Quintò cum omnis prænotio ex eodem Aristoteles sit vniuersalis, debuit co- lorem accipere restricta ad particularis quæstionis nostræ statu[m], ex quibus Sextò quæstionem difficilem clarè soluimus. At cum semper supersint aliquè difficultates, ideò in annotationibus nonnullas attigimus. Ex quibus vides methodum, & methodirationem. CAPVT

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C.4. On the mixture of atoms. 187 noted by the most learned author of Asinus aureus , l. 1. Metam. No wonder that doctors think those who are devoted to food and gorged with excess have unpleasant and heavy dreams. III. In the effort by which the little bodies, both of balen and of beer, try to return to their natural state, a struggle arises between the spirits of man and those foreign, or adventitious, enemies; and since they are removed from the chief form, even though they are in the stomach and brain, as in an empty place they are for a long time greatly agitated, yet they are overcome by human heat, and are either dispersed, or dissolved, or changed in shape, order, and connection, so that they pass into the parts of the human being. REFLECTION. I wished to insert this exercise of Democritus the teacher, so that I might show the method in this way of philosophizing not only by precepts but also by example. We therefore first set down principle 1 5. d. 2. experience. Then we opened the state of the question, lest we should wander off to other matters. Third, we indicated the chief points of the causes which ought to be drawn from the very bowels of the narrative, for which reason no circumstances in experiments are to be omitted. Fourth, since all discursive science and all doctrine ought to arise from a preceding question, as Aristotle says, Posterior Analytics 1.1, t.1, we ought to bring forward preliminaries. Fifth, since every preliminary notion, according to the same Aristotle, is universal, it ought to receive a color restricted to the particular state of our question; from which, sixth, we clearly solve the difficult question. But since there always remain some difficulties, therefore in the annotations we touched on certain of them. From these you can see the method, and the reflection on method. CHAPTER

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CAPVT QVINTVM. Difficultatum in quæstione continui solutio ex proprijs atomorum principis. D Iximus c. 2. prop. 19. disp. 2. num. 8. maximam esse omnes difficultates explicandi in doctrina atomorum facilitatem, nunc vt fidem meam liberem, Obseruo omnes obiectiones quæ in disputatione de continuo fiunt re- duci ad tres classes, aliæ enim sunt obiectiones mathematicæ, aliæ physicæ, aliæ de vtraq[ue]; participant scientia, ideòq[ue]; phy- sicomathematicas appello, Deinde cum quælibet opinio suas habeat difficultates peculiares, ideò persoluto vniuersali de- bito ad proprias atomisobligationes deueniam cap. sequen- ti. Verùm cum infinita aduersariorum pro ingeniorum va- rietate proposita sint communioribus, & difficilioribus ex- plicatis, cætera philosophus in Democriti sensis exercitatus ex eo quod præmitto seminario responsonu[m] facili negotio soluet. SEMINARIVM Responsonum ad argumenta mathematica. LEMMA I. Mathematica abstrabit ab omni materia, et subiecto reale. Formale mathematicarum, geometriæ præsertim, obiectum est terminatio extensionis, totale autem, & adæquatum est ipsa extésio quatenus terminata est ex ea enim varię figurę varijq[ue]; oriuntur numeri. Atque hæc extensio, siuè quantitas est subiectum, siuè materia intelligibilis mathematicarum quę distinguitur à physica quod hæc actu sit, mathematica autem sola

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CHAPTER FIFTH. Solution of the difficulties in the question of the continuum from the proper principles of atoms. We said in c. 2. prop. 19. disp. 2. num. 8. that there is greatest ease in explaining all difficulties in the doctrine of atoms; now, in order to free my promise, I observe that all objections made in the dispute about the continuum are reduced to three classes: for some are mathematical objections, others physical, others partake of both sciences, and therefore I call them physico-mathematical. Then, since every opinion has its own particular difficulties, therefore, the universal debt having been settled, I shall come in the next chapter to the special obligations of atoms. But since, according to the variety of minds, infinite objections have been proposed against them; after the more common and more difficult ones have been explained, the rest, a philosopher trained in the sense of Democritus, will easily solve from what I now set forth in the seedbed of responses. SEMINARY Responses to the mathematical arguments. LEMMA I. Mathematics abstracts from all matter and from the real subject. The formal object of mathematics, especially of geometry, is the termination of extension; but its total and adequate object is extension itself insofar as it is terminated, for from it various figures and various numbers arise. And this extension, or quantity, is the subject, or intelligible matter, of mathematics, which is distinguished from physics in that the latter is actual, but mathematics only

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C. 5. Obiectiones contra atomos. 189 solà intellectus formalitate subsistat. Id ex naturâ linearum mathematicarum quæ ex punctis fiunt, & ex postulato 4. lib. 1. Eucl. manifestum est: sic enim ille, quacunq[ue] magnitudine da- tà potest dari maior vel minor. Ergo si mathematicus non ab- strahit ab quolibet subiecto reali non potest dari linea maior quàm axis mundana, ac proinde postulatum illud Euclidis ad- mittendum non est. Instrumentis tanquam causis per acci- dens vti, dummodo nihil assumant sibi in consequentis, omnibus conceditur: Sunt autem h[oc] e[st] linee[m], & superficies tan- quam instrumenta mathematicorum, & vt loquitur Blan- canus additamenta de natura mathematicarum, omnes figuræ sunt exactissimi idearum diuinaru[m] humanaturu[m]q[ue]; characteres, quorum typos Deus, & artifex in mente habet: concluditq[ue]; idem elegans mathematicus. Quapropter dicendum est entia hæc geometrica omnibus numeris absoluta, esse entia per se, & ve- ra: figuræ verò, tùm naturales, tùm artificiales quæ in rebus exi- stunt esse entia per accidens, imperfecta, & falsa, vt triangulum in carta verum non est, sed verum est illud quod in idæa diuina est, vnde, & dixit Plato Deum geometrizare. Consentit his Aristo- teles 1. 13. metaphys. Summa 1. c. 2. Et reuera vti sunt ma- thematicorum numeri ità & lineæ, sed numeri abstrahunt à materia quauis, ergo etiam lineæ. Itaq[ue] mathematica suppo- nit tantùm extensionem quamlibet terminatam abstrahentem ab reali existentia quod erat assumptum. LEMMA II. Diuisibilitas extrinseca non infert diuisibilitatem intrinsecam. M Vlta sunt essentialiter, & ab intrinseco indiuisibilia quæ tamen designatiuè, mathematicè, extrinsecè, per con- ceptum diuisibilia sunt, sic Angelus collectus in spherâ potest extrinsecè, & per intellectum diuidi per diametrum, segmen- ta, &

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Only by the formality of the intellect does it subsist. This is manifest from the nature of mathematical lines, which are made from points, and from Postulate 4 of Book 1 of Euclid: for thus, whatever magnitude is given, a greater or smaller one can be given. Therefore, if the mathematician does not abstract from every real subject, a line greater than the axis of the world cannot be given, and consequently that postulate of Euclid must not be admitted. To use instruments as accidental causes, provided they assume nothing for themselves in the consequence, is granted to all. But lines and surfaces are, as it were, instruments of mathematicians, and, as Blancanus says, additions belonging to the nature of mathematical things; all figures are the most exact characters of divine and human ideas, whose models God and the craftsman have in the mind; and the same elegant mathematician concludes this. Wherefore it must be said that these geometrical beings, complete in every respect, are beings in themselves and true; but figures, both natural and artificial, which exist in things, are beings by accident, imperfect, and false, as a triangle on paper is not true, but true is that which is in the divine idea, whence Plato also said that God geometrizes. Aristotle agrees with this, Metaphysics 1.13. Summa 1, ch. 2. And indeed, just as the numbers of mathematicians are, so also are lines; but numbers abstract from any matter, therefore lines also. Thus mathematics supposes only any bounded extension abstracting from real existence, which was the assumption. LEMMA II. Extrinsic divisibility does not imply intrinsic divisibility. There are many things which are essentially, and intrinsically, indivisible, yet designatively, mathematically, and extrinsically, by concept, they are divisible; thus an angel, enclosed in a sphere, can extrinsically and in thought be divided by a diameter, into segments, and

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ta, & sphericas curuasq; lineas (cùm enim habeat extensione finitam subiacet figurationi) omnis aute figura diuidi potest. Deinde Angelus dici potest diuisibilis extrinsecè quatenus correspondet spatio diuisibili, vt Æternitas Dei virtualiter diuisibilis est, quia correspondet tempori, Anima humana indiuisibiliter corpori diuisibili counensuratur. Duo itaq; in atomo quauis concipienda sunt, primò eius atomi substantia physica, quę vt sic est indiuisibilis, secundò eius respectus extrinsecus, siuè figura, & spatium extensione mathematica penes quam atomus quæuis diuisibilis est in infinitum, suas enim dimensiones habet; vnde diximus in synopsi pag. 26. num. 9. Atomos indiuisibiles esse modo communi, & non proprio ex Auerroe 1. phys. comment. 35. quorum terminorum explicationem v. Ibid. LEMMA III. Non sunt expendendæ actiones physicæ regulis geometricis. HOC lemmata fuit iam assumptu pro axiomate 13. huius disp. verùm cum non sit prima notio, & apud vulgares philoso phos vix vsurpetur, ob illius necessariam in hac disputatione applicationem videtur declarandum, & confirmandum acuratiùs. Geometre in suis demonstrationibus lineis vtuntur imaginarijs que ab hypothesi falsa sequuntur, neq[ue] ideò mathematicis quidquam derogatur quin imò multum accedit authoritatis, alioqui materiè imbecillitati immerse[n] nihil admirandi demonstrarent, facto autem suo linearum immutabilium instrumento abstrahentes à materia, plurima adinueniunt exponuntq[ue]; supra praxim, quia ad actum deduci nihil potest nisi corporum beneficio que variabilia sunt, & multis casibus obnoxia, adde quod quæ physicè sunt emanationes lineis physicis propagantur, que aliquam necessariò habent cum

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thus, and spherical and curved lines (for since it has finite extension, it is subject to configuration), every other figure can be divided. Next, an Angel can be said to be extrinsically divisible insofar as it corresponds to divisible space, just as the eternity of God is virtually divisible because it corresponds to time; the human soul is measured with the divisible body in an indivisible way. Therefore, two things must be conceived in every atom: first, its physical substance, which as such is indivisible; second, its extrinsic respect, that is, its figure and the mathematical space of extension, according to which any atom whatever is divisible to infinity, for it has its own dimensions. Hence we said in the synopsis, page 26, no. 9, that atoms are indivisible in the common, and not the proper, sense, from Averroes, Physics 1, commentary 35; see there for the explanation of these terms. LEMMA III. Physical actions are not to be judged by geometric rules. This lemma had already been assumed as axiom 13 of this disputation; however, since it is not a primary notion, and is hardly used among common philosophers, and because of its necessary application in this discussion, it seems it should be declared and more accurately confirmed. Geometers in their demonstrations use imaginary lines, which follow from a false hypothesis, yet this does not detract from mathematics; rather, much authority is added to it. Otherwise, immersed in the weakness of matter, they would demonstrate nothing admirable. But by their method, using the instrument of immutable lines and abstracting from matter, they discover and set forth many things beyond practice, because nothing can be brought to act except by means of bodies, which are variable and exposed to many cases. Add also that what are physical emanations are propagated by physical lines, which necessarily have some relation with

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C. 5. Obiectiones contra atomos. 191 cum longitudine crassitiem, & latitudinem, nam ad omnem physicam actionem certa requiritur extensio. Adde quod in- tensio accidentium non est purè proportionata vt numeris ex- primi possit, vti neq[ue] actiuitatis sphæra exacta est, cum illa ratione medij, passi, aliarumq[ue] circumstantiarum fiat diuersæ figurationis. Egregiè verò ad hæc intuens Aristoteles l. 2. moral Eudem. c. 7. Immobilia autem, vt in mathematicis, non per se quidem sed similitudine quadam principia appellantur. Hic enim ipso principio labefactato, labefieri omnes, quæ ab illo prin- cipio fluxere, demonstrationes oportet: cum ipsæ inter se demonstra- tiones altera alteram non euertat, nisi quantum communis illa supposi- tio, vndelucem istæ habent, non euertitur. Et Plato 7. de Repub. ait Mathematicos circa quantitatem quodammodo somniare. Itaq[ue] cum demonstrationes geometricæ procedant ab hypothesi quam probare non est mathematici, sed alterius facultatis, quæ eâ refellit, ideò lineis mathematicis regulisq[ue] strictè geometri- cis actiones philicæ no[n] sunt expendendæ, quod erat assumptu[m]. OBIECTIONES MATHEMATICÆ. Ex his tribus Assumptis omnia mathematicorum argumenta quæ vulgò in doctrina de continuo adducuntur facili negotio per propria atomorum principia diluo. OBIECTIO I. De triangulo. Si continuum constat ex atomis non potest construi triangulum, Con- struatur enim triangulum ABC. sit linea AC basis duarum atomorum, BC, BA trium, ducantur à singu- larum atomorum finibus lineæ basis pa rallelæ DE, FG. Cum ergo FG fit

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C. 5. Objections against atoms. 191 with length, thickness, and breadth, for every physical action a definite extension is required. Add that the intensity of accidents is not purely proportionate, so that it can be ex- pressed by numbers, nor is the sphere of activity exact, since that varies in form according to the relation of the medium, the subject, and other circumstances. And Aristotle, looking excellently to these things, in l. 2. Moral. Eudem. c. 7. says: “But immovable things, as in mathematics, are called principles, not indeed in themselves, but by a certain likeness.” For here, when the principle itself has been shaken, all those things that have flowed from that principle must necessarily be shaken too: since the demonstrations themselves do not overthrow one another, except insofar as that common supposi- tion, from which these have their light, is not overthrown. And Plato in book 7 of the Republic says that mathematicians in a certain sense dream about quantity. Therefore since geometric demonstrations proceed from a hypothesis which it is not the task of a mathematician to prove, but of another faculty, which refutes it, therefore physical actions are not to be measured by mathematical lines and strictly geometri- cal rules, which was assumed. MATHEMATICAL OBJECTIONS. From these three assumptions I easily dissolve all the arguments of mathematicians which are commonly brought forward in the doctrine on the continuous by means of the proper principles of atoms. OBJECTION I. On the triangle. If the continuum consists of atoms, a triangle cannot be constructed. For let triangle ABC be constructed. Let line AC be the base of two atoms, BC and BA of three; let parallel lines DE, FG be drawn from the ends of the individual atoms of the base. Since therefore FG is

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192 De Atomis. Disp. II. sit maior quam DE, vt demonstratur in scholio 29.1. excessus eius erit vnius saltem atomi, nihil enim dari potest minus, ergo etia[m] si DE sit vnic[us] atomus, FG duaru[m] erit: erut ergo æquales lineæ FG, AC, quod implicat, est que contra pro pos. 16. primi, & axioma 13. primi. Non itaq[ue] potest triangulum construi admissis atomis. Respondeo ab Assumpro 3. fieri transitum à lineis mathematicis ad physicas quæ atomis constant: dico autem triangulum lineis mathematicis esse mensurandum, vel certè à physicis physicis radijs regularibus; Et quidem concedo lineam AC esse duarum atomorum, AB, BC trium, DE vnius, FG duarum, nego autem à multitudine atomorum sequi longitudinem, aut breuitatem linearum, vt manifestum erit ex propos. 45. disput. tertiæ; transit autem aduersarius à constitutione physica ad geometricam, contra lemmatertium. OBIECTIO II. De quadrato. CVM ad primam obiectionem responsum sit atomos potuisse irregulariter configurari, accipio nunc atomos quatuor terreas quæ cubum suum non mutant, sint autem illæ in superficie quadrata ABCD, sequitur lineam AB æqualé esse diametro AC, vtraq[ue] enim duabus atomis similiter configuratis constat, atqui hoc implicat, cum enim angulus ABC sit rectus per constructionem, sequitur ex prop. 32. primi esse maiorem angulo BAC, & angulo BCA seorsim sumptis, ijs aute[m] simul sumptis ex eadem prop. æqualem, ergo angulus ABC ex 19. primi maiori lateri sub- tendi-

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192 On Atoms. Disp. II. let it be greater than DE, as is shown in scholium 29.1; its excess will be of at least one atom, for nothing less can be given; therefore even if DE is a single atom, FG will be of two: therefore the lines FG and AC will be equal, which is contradictory, and is against proposition 16 of the first book and axiom 13 of the first. Therefore a triangle cannot be constructed with atoms admitted. I reply that, from Assumption 3, a transition is made from mathematical lines to physical ones, which consist of atoms: but I say that a triangle must be measured by mathematical lines, or certainly by physical rays that are regular; and indeed I grant that line AC is of two atoms, AB and BC of three, DE of one, FG of two; but I deny that from the multitude of atoms the length or shortness of lines follows, as will be manifest from proposition 45 of the third disputation; moreover the adversary passes from physical constitution to geometrical, against lemma three. OBJECTION II. On the square. Since in answer to the first objection it has been said that atoms could be arranged irregularly, I now take four earthly atoms, which do not change their own cube; let them be on the square surface ABCD: it follows that line AB is equal to diagonal AC, for both are composed of two similarly arranged atoms; but this involves a contradiction, since the angle ABC is right by construction, it follows from proposition 32 of the first book that it is greater than angle BAC and angle BCA taken separately, but if these are taken together, by the same proposition it is equal; therefore angle ABC, from proposition 19 of the first, to the greater side sub-

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Cap. 5. Obiectiones contra atomos 193 tenditur, erit ergo maior linea AC quam CB vel BA demonstrariq[ue]; idem posset per 47. primi, 8. secundi, 12. sexti, 9. decimi Euclidis nô ergo costrui potest ex atomis quadraru[m] q[ui]d erat, p[ro]ba[n]du[m] ergo nec datur atomi, neq[ue]; si datur vlla cubica est. Respondeo ex lemmate tertio fieri transitum à lineis physicis ad mathematicas, dico autem lineam AC maiorem esse quam linea AB, quia linea AC ducitur per diametros atomorum, linea verò AB per latera, est autem in vna atomo cubica diameter imaginaria, & mathematica maior latere, quare licet atomi quatuor A, B, C, D, sint similiter figurat[ur], non sunt tamen respectu linearum AB, AC, similiter constitutæ, debet autem situs attendi, & linearum imaginariarum per indiuisibile spatium deductio. OBJECTION III. De circulis concentricis. SInt circuli duo concentrici exterior quidem maiorq[ue]; ACF interior & minor E. Dico supposita atomorum doctrinà eos esse æquales. Sit enim circuli ACF peripha- riè portio CA e- tomorum septé, cû ex primo po- stulato primi Eu clidis liceat à pú- cto ad punctum lineam ducere poterunt ab illa peripheriè portione ad centrum D duci lineę septem quę circulum interiorem E secabunt, erunt ergo pariter in cir- culo N 2

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Chapter 5. Objections against atoms 193 is drawn, therefore line AC will be greater than CB or BA, which can be demonstrated; the same could be done by Euclid I.47, II.8, VI.12, X.9. Therefore it cannot be constructed from atoms as a square; but this was to be proved. Therefore atoms are not given, nor, if there is one, is there a cubic atom. I reply that from the third lemma there is a passage from physical lines to mathematical ones. I say, moreover, that line AC is greater than line AB, because line AC is drawn through the diameters of the atoms, whereas line AB is drawn through their sides. But in a single cubic atom the diameter is imaginary and mathematical, greater than the side; therefore, although the four atoms A, B, C, D are similarly figured, they are not, with respect to the lines AB and AC, similarly constituted. One must attend to the position and to the drawing of imaginary lines through indivisible space. OBJECTION III. On concentric circles. Let there be two concentric circles, the outer indeed larger, ACF, and the inner and smaller, E. I say, on the supposition of the doctrine of atoms, that they are equal. For let the portion CA of the circumference of circle ACF be seven atoms. Since by the first postulate of Euclid I it is permitted to draw a line from point to point, seven lines can be drawn from that portion of the circumference to the center D, which will cut the inner circle E; therefore they will be equally in the circle N 2

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194 De Atomis. Disput. II. culo E tot atomi quot in FA, ergo erunt æquales quod implicate non itaq[ue] potest constare continuum ex atomis. Respondeo ex lemmate tertio fieri transitum à lineis mathematicis ad physicas, nego enim à peripheria CA septe[m] atomorum, ad punctum D posse septem lineas physicas duci adequatè inter se distinctas, ac proinde argumentum nihil conuincit, cum sint quatuor termini, & contra lemmam secundum confundat extensionem realem, & materiam sensibilem cum imaginaria, & mathematica. OBJECTION IV. De circuli tetragonismo. I Mpossibilis est circuli quadratura, esset autem possibilis si continuum atomis constaret. Probatur prima propositio; tetragonismus non potest institui quin inueniatur proportio diametri ad peripheriam, & comparetur linea recta cum curua siuè longitudine, siuè potentiâ, nulla autem datur huiuscemodi proportio, imò neq[ue] circulu circulo nisi mediante quadrato potest comparari vt patet ex lib. 12. Eucl. prop. 2. Neque diameter comparari potest cum sua peripheria, multò minus cum superficie, quæ tamen ad tetragonismum necessaria sunt, non ergo possibilis est, dato enim medio impossibili eoq[ue] vnico impossibilis est finis. Quæ demonstrari facilè possent ex 20. 6. per 2. lib. 12. Eucl. & per 1 1. prop 1. 5. Pappi Alexandrini, & c. circuli autem impossibilem quadraturam agnoscens Aristotel. c. 3. de prædicamentis ait, circuli quadratura, si est scibilis, scientia quidem eius nondum est, vbi illa additio conditionata, si est scibilis, ostendit satis quid de ea philosophus existimarit. Quod autem positis atomis hæc omnia sunt falsa patet, primò quia datur commensurabilitas, & longitudine, & potentià inter diametrum, & peripheriam se habent enim in- ter

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194 On Atoms. Disputation II. there are as many atoms as there are in FA, therefore they will be equal, which is impossible; therefore a continuum cannot consist of atoms. I reply that, from the third lemma, a transition is made from mathematical lines to physical ones; for I deny that from the circumference CA of seven atoms, to the point D, seven physical lines can be drawn adequately distinct from one another, and therefore the argument proves nothing, since there are four terms, and it confounds, contrary to the second lemma, real extension and sensible matter with imaginary and mathematical extension. OBJECTION IV. On the quadrature of the circle. The quadrature of the circle is impossible; but it would be possible if the continuum were composed of atoms. The first proposition is proved: tetragonism cannot be established unless a proportion is found between the diameter and the circumference, and a straight line is compared with a curved one, either in length or in power; but no such proportion is given, indeed neither circle with circle can be compared except by means of a square, as is clear from book 12, Euclid, prop. 2. Nor can the diameter be compared with its circumference, much less with the surface, which nevertheless are necessary for tetragonism; therefore it is not possible, for if the means are impossible, and that the only one, the end is impossible. These things could easily be demonstrated from 20.6, through 2, book 12 of Euclid, and through proposition 11.1.5 of Pappus of Alexandria, etc. Now Aristotle, acknowledging the impossible quadrature of the circle, in chapter 3 of the Predicaments says: the quadrature of the circle, if it is knowable, has not yet had its science; where that conditional addition, if it is knowable, sufficiently shows what the philosopher thought about it. But that, if atoms are posited, all these things are false is clear, first because there is commensurability both in length and in power between the diameter and the circumference; for they stand in- between

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C. 5. Obiectiones contra atomos. 195 ter se pro ratione compositionis, sit ergo diameter 10. atomorum, peripheria 31. se habent vt numerus ad numerum, datâ autem proportione longitudinis sequitur proportio potentię, ergo circuli quadratura datis atomis contra demonstrata à mathematicis per comparabilitate poterit reperiri, quod implicat: ergo continuum atomis non constat. Respondeo ex lemmate tertio, non debere fieri transitum à lineis mathematicis ad physicas, sumitur autem comparabiltas, & incomparabilitas linearum, & figurarum à spatio mathematico non verò reali. Et quidem in terminis mathematicis nego circuli quadraturam esse impossibilem, aut id satis conuinci ab adductis probationibus, neq[ue] verò vnicum mediû est comparabilitas immediata, sed fortasse circulo, & quadrato reperiri potest mensura communis quam hactenus inuestigarunt tot eximij mathematici, vt Orontius, Claius, & iam pridem ingeniorum apex Archimedes, & septem ab ipso seculis Nicomedes, & alij plures, qui si quadraturam inuestigarunt non existimauere impossibilem, cognito enim non esse comparabilem diametrum quadrati cum suo latere, nullus in ea re inuestiganda laborauit; At hactenus latuisse mathematicos tetragonismum, difficilem inuentu, non autem impossibilem videtur inferri. Multùm Dei prouidentiæ in abstrusis debemus, ad ea enim inuestiganda dùm se se accingunt viri insignes etsi punctum non ferant pulcherrima tamen reperiunt Imò multi inuentam à se quadraturam putauere, vt Hippocrates Chius abductionis author in nobili illo paralogismo quem affert Aristoteles 2. priorum c. 26. qui licet adeò sit notus tamen quia admirandum est inuentum quodq[ue] possibilem circuli quadraturam esse ostendit ideo illud subdo omisis Hippocratis erroribus. N 3 PRO-

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C. 5. Objections against atoms. 195 whether they stand in ratio to one another according to the manner of composition; let the diameter therefore be 10 atoms, the circumference 31; they stand to one another as number to number. But a proportion of length being given, a proportion of power follows; therefore the squaring of the circle, being demonstrated by mathematicians from given atoms by comparison, may be discovered, which implies: therefore the continuum does not consist of atoms. I answer, from the third lemma, that there ought not to be a transition from mathematical lines to physical ones; but the comparability and incomparability of lines and figures is taken from mathematical space, not real space. And indeed, in mathematical terms I deny that the squaring of the circle is impossible, or that it is sufficiently proved by the arguments brought forward; nor is immediate comparability the only means, but perhaps for the circle and the square a common measure may be found, which so many outstanding mathematicians have hitherto investigated, such as Orontius, Clavius, and long before them the pinnacle of intellect, Archimedes, and seven centuries after him Nicomedes, and many others, who, if they investigated the quadrature, did not consider it impossible. For once it was known that the diameter of the square and its side were not comparable, no one labored in investigating that matter. But that the tetragonism has so far escaped mathematicians, being difficult to discover, does not seem to imply that it is impossible. We owe much to the providence of God in hidden matters, for while distinguished men set themselves to investigate these things, even if they do not hit the mark, they nevertheless discover very beautiful results. Indeed many thought that they had found the squaring of the circle, as Hippocrates of Chios, the author of the reduction, in that famous paralogism which Aristotle presents in the second book of the Prior Analytics, chapter 26; which, although so well known, nevertheless because it is a remarkable discovery and one that shows the squaring of the circle to be possible, I therefore add it, omitting Hippocrates’ errors. N 3 PRO-

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196 De Atomis. Disp. II. PROPOSITIO XXXVII. Problema. Meniscum, siuè lunulam quadrare. SIT circulus ABH vtcumq[ue]; ductà diametro AH & se- midiametro ad illam perpendiculari BC, & subtenden- te BA, fiat circulus FACB, diametro AB, erit circu- lus in diametro AH duplus circuli in subtendente AB de- scripti per 2. 12. Circuli enim eam inter se rationem habent quam descripta à diametris quadrata, sed quadratum line[um] AH duplum est quadrati lineæ AB per 47. primi, est enim diameter eius quadrati quod per lineam AB construitur, ergo circulus etia[m] ABH duplus est potentià circulo AFBC, erit ergo segmè- tum in subtendente AB duplum segmenti AKC in subtendente AC, sunt enim similes figure, & si- militer descriptæ per 3 I. 6. duo itaq[ue]; segmenta mi- nora lineis BC, AC co- prehensa si sumantur simul æqualia sunt maiori segmento AEB, quarta itaq[ue]; circuli maioris pars æqualis est semicirculo minoris ex 2. 12. cum itaq[ue]; eiusde[m] circuli semicirculi sint æquales, & si ab æqualibus æqua- lia demas que remanent sunt æqualia, sublato segmento AEB manebit meniscus, siuè lunula AEBF, similiter ab altero semicirculo, ACB tolle segmenta B1C, CKA ma- nebit residuum triangulum ACB æquale lunulæ AEBF quod erat inueniendum. Verùm cætera non potuit excui Hipp. & paralogismo vsus reliquum tentat tetragonismi, vt videbis

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196 On Atoms. Disputation II. PROPOSITION XXXVII. Problem. To square a meniscus, or little lune. LET the circle ABH be any one whatever; having drawn the diameter AH and from it the perpendicular semidiameter BC, and the subtending BA, let the circle FACB be made, with diameter AB; the circle on diameter AH will be double the circle described on the subtending AB by 2. 12. For circles have to one another the same ratio as the squares described from the diameters, but the square of line AH is double the square of line AB by 47 of the first, for it is the diameter of that square which is constructed by line AB; therefore the circle ABH also is double in power to the circle AFBC. Therefore the segment on the subtending AB is double the segment AKC on the subtending AC, for the figures are similar and similarly described, by 3 I. 6. So then the two smaller segments enclosed by the lines BC, AC, if taken together, are equal to the larger segment AEB; therefore the fourth part of the larger circle is equal to the semicircle of the smaller, by 2. 12. Since therefore the semicircles of these circles are equal, and if from equal things equal things be taken away the remainders are equal, when the segment AEB is removed there will remain the meniscus, or lune AEBF; likewise, from the other semicircle, remove the segments B1C, CKA, and there will remain the triangle ACB, equal to the lune AEBF, which was to be found. But the rest Hipp. could not excise, and using a paralogism he attempts the remaining tetragonism, as you will see.

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C. 5. Obiectiones contra atomos. 197 videbis apud Arist. loco cit. Antipho. apud eundem in primo Elenchoru[m] c. 10. & Bryslo quadraturâ diuersis vijs tentarunt. Hæc autem Hippocratis demonstratio insistit rei inuestigâ- de scilicet problemati constituendo ad tetragonismum, Theo- rema enim inuentum est ab Archimede, 1. de dimensione cir- culi prop. 1. & 1. de lineis spiralibus prop. 18. inuenit rectam lineam [con]qualem circumferenti[us] primi circuli spiralis lineæ, & prop. 19. aliam recta [con]qualem circumferenti[us] secundi circuli, idemq[ue] quadrauit parabolam. Vide Pappum in collect. 1. 4. Ioannem Buteonem in lib. quadraturarum omniu[m] vetru[m], & re- centiorum, ex quibus conijcies an problema demonstratiuè construens aream quadrata [con]qualem areæ circulari sit impos- sibile, si enim naturaliter sit quare demonstrari non poterit? Detinentur autem hactenus mathematici in probatione mino- ris syllogismi Hippocratis qui ita se habet. Omnis figura re- ctilinea quadratur, sed circulus ad rectilineam deduci potest ergo quadrabitur. In probatione minoris facta est APAGO- GE, seu abductio, dùm quisq[ue] medium quæreret quo circu- lus ad rectilineam figuram deduceretur, hinc Hipp. minorem abduxit ad lunulę inuestionem, alij ad quadraticem, vt fecit Pappus, & Clauius l. 6. elemen. & alij ad alias vias sunt deflexi, in quibus hactenus frustrà viri extra omnem doctrinæ ingenijq[ue] aleam positi insudarunt OBJECTION V. De linea conchili. EX linea conchili Nicomedis arguitur manifestè continuu[m] omne diuisibile esse in infinitum, ide[m] etia[m] ex lineis asymp- totis pro quarum explicatione sit. N 4 PRO-

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C. 5. Objections against atoms. 197 you will see in Aristotle, in the cited passage, Antipho. apud eundem in the first Elenchorum c. 10. and Bryslo attempted quadrature by different ways. But this demonstration of Hippocrates insists on investigating the thing— namely, on establishing the problem for tetragonism; for the theorem was discovered by Archimedes, 1. de dimensione cir- culi prop. 1. and 1. de lineis spiralibus prop. 18. he found a straight line equal to the circumference of the first spiral circle, and prop. 19. another straight line equal to the circumference of the second circle, and he also squared the parabola. See Pappus in collect. 1. 4. Ioannes Buteon in lib. quadraturarum omnium vetru[m], & recentiorum, from which you may infer whether the problem of demonstratively constructing an area square equal to a circular area is impossible; for if it is natural, why can it not be demonstrated? Mathematicians are thus so far held up in the proof of the minor premise of Hippocrates’ syllogism, which runs as follows. Every rectilinear figure can be squared, but a circle can be reduced to a rectilinear figure; therefore it can be squared. In proving the minor premise there was made an APAGOGE, or abductive proof, while each sought the middle term by which the circle could be reduced to a rectilinear figure; hence Hippocrates diverted the minor proposition to the question of the lunula, others to the quadrature, as Pappus did, and Clavius l. 6. elemen. and others were turned aside to other ways, in which hitherto they have labored in vain, men placed outside all chance of doctrine and ingenuity. OBJECTION V. On the shell line. From Nicomedes’ shell line it is plainly argued that every continuous thing is divisible into infinity; the same also from asymptotic lines, for the explanation of which let there be. N 4 PRO-

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198 De Atomis. Disp. II. PROPOSITIO XXXVIII. Dantur lineæ quæ productæ in infinitum semper magis, ac magis accedunt, nunquam tamen vel inter secant se, vel se tangunt, quamuis aliunde distent magis, magis in infinitum, nunquam tamen ultra certam distantiam à se inuicem abesse possunt. D Vc lineas AB, CD parallelas in infinitum, à puncto E vt libet extra lineas assumpto duc lineam perpendiculare EFG, deinde à puncto E duc infinitas rectas secates obliquè lineam AB quales sunt EH, EK, EM, eâ tamen lege vt lineę pars quę lineam AB superabit sit æqualis lineæ FG segmento, qualia sunt HI, KL, MN, æqualia ipsi FG, nunc verò puncta G, I, L, N, aliaq[ue] intermedia pari ratione inuenta connecte ductà lineà G, I, L, N, & habebis lineam conchilem quam Nicomedes inclytus inter geometras est imaginatus: apud quem punctum E vocatur polus, quòd circa illud tanquam circa cardinem voluntur lineę, & sui segmento designent lineam conchilem: lineam AB vocat

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198 On Atoms. Disp. II. PROPOSITION XXXVIII. There are lines which, being produced to infinity, come ever nearer and nearer, yet never either intersect or touch one another, although, in another respect, they are farther and farther apart to infinity, yet can never be farther from one another than a certain distance. Thus let the parallel lines AB, CD be extended to infinity; from the point E, taken arbitrarily outside the lines, draw the perpendicular line EFG; then from the point E draw infinitely many straight lines cutting the line AB obliquely, such as EH, EK, EM, under this condition, that the part of the line which lies beyond line AB shall be equal to the segment FG of the line, as HI, KL, MN are equal to FG itself; now connect the points G, I, L, N, and the other intermediate points found in the same way, by drawing the line G, I, L, N, and you will have a shell-like line which the renowned Nicomedes among geometers imagined: with him the point E is called the pole, because the lines revolve about it as about a hinge, and by their segment designate the shell-like line; he calls line AB

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C. 5. Obiectiones contra atomos. 199 vocat normalem, quòd sit linea dirigens lineas ortas à puncto E, lineam verò EG axem dicit, & lineam FG sagittam directam, alias verò HI, KL, sagittas obliquas appellat. Iam verò appello etiam illos qui Euclide non sunt initiati, nonne patet quò longius prouehitur linea GILN eo magis accedere ad lineam AB & magis distare à linea CD. nunquam tamen vel cum AB coibit, & semper minus distabit à CD quam sit mensura FG. Ratio huius rei satis clara est à lineę generatione, cum enim tota oriatur à lineis ductis à pun- do E intersecantibus lineam AB sequitur angulum, qualis est NMB, semper intercessurum inter conchilem, & lineam AB. alioqui ducta linea EM fieret parallela lineæ AB, quam tamen intersecat, & sic duæ rectæ haberent vnum, & idem segmentum commune contra axioma 10. lib. 1. Eucl. Neq[ue] solum id in linea conchili particulare est, verùm etiam Apollonius Pergæus in suis asymptotis eandem proprietatem demonstrat in hyperbole, & rectâ coni diametro correspon- dente huiusmodi sectioni. Pretereà Leautaudus meliori die dignus mathematicus peculiari subtilissimaq[ue] demonstratione eandem asymptoton proprietatem ab omni dubitatione exi- mit: nouamq[ue] in sua quadratrice reperit asymptoton idem probl. 57. Plura de linea conchili habet Clauius in geometria practica. Ex hac doctrina sic argumentor: Vbi excessus sunt infiniti in materia, ibi est diuisibilitas in infinitu[m], sed excessus perpen- dicularium quæ excitantur à puctis sagittarum extremis ad normalem AB sunt infiniti, ergo aderunt infinitæ diuisibili- tates ac proinde atomi innumeræ; cæteroqui tot essent exces- sus quot atomi, quod implicat. Respondeo ex lemmate 2. omne continuum ex Democrito esse infinitum mathematicè, extrinsecè, & designatiue, intrin- secè

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C. 5. Objections against atoms. 199 he calls normal, because it is the line directing the lines drawn from point E; but he calls the line EG the axis, and the line FG a direct arrow, while other lines, HI, KL, he calls oblique arrows. Now I also ask those who are not initiated into Euclid: does it not appear that the farther the line GILN is extended, the more it approaches the line AB and the more it recedes from the line CD; yet it will never join AB, and it will always be less distant from CD than the measure FG. The reason for this is sufficiently clear from the generation of the line; for since the whole arises from lines drawn from point E intersecting the line AB, it follows that an angle such as NMB will always intervene between the conchilic line and the line AB. Otherwise, if the line EM were drawn, it would become parallel to line AB, which nevertheless it intersects; and thus two straight lines would have one and the same common segment, contrary to axiom 10 of book 1 of Euclid. Nor is this property peculiar only to the conchilic line; rather, Apollonius of Perga also demonstrates the same property in his asymptotes, and the corresponding straight line of the cone’s diameter for this kind of section. Moreover, Leautaudus, a mathematician worthy of a better day, by a special and most subtle demonstration removes the same property of the asymptote from all doubt; and he discovered a new asymptote in his quadratrix, problem 57. Clavius has more on the conchilic line in practical geometry. From this doctrine I argue thus: where there are infinite excesses in matter, there is divisibility to infinity; but the excesses of the perpendiculars which are raised from the extreme points of the arrows to the normal AB are infinite; therefore there will be infinite divisibilities and consequently countless atoms; otherwise there would be as many excesses as atoms, which implies a contradiction. I reply, from lemma 2, that every continuum according to Democritus is infinite mathematically, extrinsically, and by designation, intrinsically

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De Atomis. Disp. II. 200 secè verò, & physicè finitum, tum penes indiuiduas atomos, tum penes diuisibilitatem realem, argumentum ergo peccat contra lemmam 3. fit enim transitus à lineis mathematicis ad physicas, & à spatio imaginario ad reale contra lemmam primum. Vetùm vt hæc responsio cui totus Democritus innititur, facilius admittatur. Obseruo triplicem esse proportionalitatem quarum naturâ complecti omne, non est pronû, pauca ad rem meam delib[us]. Arithmeticaproportionalitas augetur in infinitu[m], sed in infinitu[m] non decrescit. Ita natura continui realis ex atomis in infinitum crescere potest, infra atomi extensionem non potest decrescere, Harmonica proportionalitas decrescit in infinitum sed in infinitum augeri non potest. Ita linea[m] asymptoti, & conchilis in infinitum decrescunt ratione approximationis, & tamen non augentur in infinitum in ratione distantiæ ab alia à qua magis ac magis recedunt. Geometrica proportionalitas, & augetur, & decrescit in infinitum sicuti spatium mathematicum, cui cum adæquentur atomi, etiam illo mediante extrinsecam, & imaginariam diuisibilitatem habent. Ex quibus quidquid contra nos à linea conchili dici potest satis refutatur. Vide Campanum, Proclum, Clauium in definit. lib. 5. Eucl[is] si plura de proportionibus cupis. SCHOLIVM. Vulgò in scholis ad probandum infinitum in magnitudine implicare adducitur hic syllogismus. Lineæ decussatæ quo longius producuntur, eo magis distant, Sed producuntur in infinitum, Ergo distant infinitè. Maior fundatur ratiocinatione geometrica, & maximè p. 29. 1. vbi demonstratur principium 13. Euclidis Clauiani: atq[ue] adeò in illo principio physicorum è proportionis natura petito, vt se habet simpliciter, ad simpliciter ut à magis ad magis. Illud tamen

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On Atoms. Disp. II. 200 but strictly speaking, and physically finite, both with respect to individual atoms and with respect to real divisibility, therefore the argument sins against lemma 3; for there is a transition from mathematical lines to physical ones, and from imaginary space to real space, contrary to the first lemma. Yet so that this response on which the whole of Democritus rests may be more readily admitted, I observe that there are three proportionalities, the nature of which it is not easy to comprehend all at once; a few things pertinent to my purpose I shall note here. Arithmetic proportionality increases to infinity, but does not decrease to infinity. Thus the nature of real continuum from atoms can increase to infinity, but it cannot decrease below the extension of the atom. Harmonic proportionality decreases to infinity, but it cannot increase to infinity. Thus the line of the asymptote and of the conchoid decrease to infinity in respect of approximation, and yet they are not increased to infinity in respect of distance from another line from which they recede more and more. Geometric proportionality both increases and decreases to infinity, just as mathematical space does; and when atoms are equated with it, they also, by means of it, have extrinsic and imaginary divisibility. From these things whatever can be said against us from the line of the conchoid is sufficiently refuted. See Campanus, Proclus, Clavius in the definition of Book 5 of Euclid, if you desire more on proportions. SCHOLIUM. In the schools, the following syllogism is commonly adduced to prove that the infinite in magnitude is involved. Intersecting lines, the farther they are extended, the more they are separated; but they are extended to infinity; therefore they are separated infinitely. The major premise is founded on geometric reasoning, and especially on p. 29, 1, where the 13th principle of Euclid as explained by Clavius is demonstrated; and indeed in that principle, drawn from the nature of proportion, as it is simply so, to simply so, as from more to more. Yet that

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C. 5. Obiectiones contra atomos. 201 tamen argumentum meo iudicio sophisticum est, cuius defectum etsi ostendere nequeam vel in materia vel in forma vt aiunt logici, tamen analogiâ ostendo esse sophisma, quia ex ijsdem premissis elicio consequentiam falsam vt hic videre est. Lineæ decussatæ quo magis propagantur eo magis distant, sed ex sup- positione propagantur in infinitum conchilis GILNN, & linea DC quæ se decussant in G, ergo distant infinitè. Primus syllogismus videtur in Barbara, secundus in Darij, cuius minor cu[m] sit particularis assumpta sub vniuersali minoris primi syllogismi, concedi debet ab aduersario, & tamen consequentia falsa est, neq[ue] enim vnquam distabit linea conchilis ab linea DC per lineam GF, ergo primùm argumentum sophisticum est. Hanc digressionem mihi condonabit Vrbanus lector si præsertim sciat interesse Democriti infinitum in magnitudine propugnare. Ille enim infinitum admisit aerem quem inane, & vacuum appellabat, neq[ue] multum repugnauit Aristoteles c[uius] l. 2. de anima t. 68. perpetuum corpus quod sursum est nominet. OBJECTION VI. De contactu globi, & plani. Globus perfectè sphericus tangit planum in puncto mathemathico, ergo continuum ex ijs constat, non autem ex atomis, probatur antecedens à Theodosio l. 1. sphericoru[m] prop. 3. & sequitur manifestè à propos. 2. & 16. l. 3. Eucl. conuinciturq[ue]; hac ratione quam mathematicarum expertes meliùs capient, linea curua potest tangere rectam, ergo cum non possit adæquari recte eam tantùm in puncto mathematico tanget. Respondeo in atomo esse puncta mathematica virtualiter non autem formaliter, vnde atomus sphæræ, tangit atomum plani non adæquatè sed secundum aliquam sui virtualitatem quæ puncto respondet, illiq[ue] æquiualet. Ad

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C. 5. Objections against atoms. 201 however, the argument is sophistical in my judgment, whose defect, although I cannot show it either in matter or in form, as the logicians say, nevertheless I show by analogy that it is a sophism, because from the same premises I draw a false conclusion, as may be seen here. Crossed lines, the more they are extended, the more they are distant; but by sup- position they are extended to infinity in the shell GILNN, and the line DC, which cross each other at G, therefore they are infinitely distant. The first syllogism seems to be in Barbara, the second in Darij, whose minor, since it is particular, assumed under the universal of the minor of the first syllogism, must be granted by the opponent, and yet the conclusion is false; for the line of the shell will never be separated from the line DC by the line GF, therefore the first argument is sophistical. Urbanus the reader will pardon me for this digression, especially if he knows that Democritus’s infinite in magnitude is at stake. For he admitted an infinite air, which he called the void and empty space, and Aristotle did not greatly oppose it, who in his l. 2 of De Anima, t. 68, names the perpetual body that is above. OBJECTION VI. On the contact of the sphere and the plane. A perfectly spherical globe touches a plane at a mathematical point; therefore the continuum consists of these, and not of atoms. The antecedent is proved by Theodosius, l. 1, of the Spherics, prop. 3, and follows manifestly from propositions 2 and 16 of l. 3 of Euclid, and is also proved by this reasoning, which those inexperienced in mathematics will better understand: a curved line can touch a straight line; therefore, since it cannot be made equal to the straight line, it will touch it only at a mathematical point. I پاسخ: in an atom there are mathematical points virtually, but not formally; whence the atom of the sphere touches the atom of the plane not adequately but according to some virtual aspect of itself which corresponds to a point, and is equivalent to it. To

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Ad idem recidit argumentum à figurarum perfectione petitum, tetraedrum, pyramis, conus, cubus, & aliæ figuræ angulares in puctu desinere debent vt pronuntiauit Euclides. Respondeo enim sufficere vt sit punctu virtualiter, & equi- valenter, negando autem debere adesse puncta mathema- tica formaliter. OBJECTIO VII. De lineis insecabilibus. Contra atomos est integer Aristotelis libellus de insecabili- bus lineis cuius argumenta facili negotio eademq[ue] distin- ctione diuisibilitatis physicæ, & mathematicæ diluuntur. Vnum validissimum de multis accipe. Si datur linea insecabilis, (qualem in vna atomi dimensione admittere necessarium est) omnes lineæ erunt commensurabi- les, nam omnes ab indiuiduis lineis dimetientur quæq[ue] longitudine quæq[ue] potentia sunt commensurabiles: indiuiduæ autem lineæ sibi ipsis commensurabiles sunt longitudine cum inter se sint æquales: quæ- re potentia quoq[ue]; quod si hoc est, diuiduum erit quadratum. Ecce obscurum Aristotelis telum quod clariùs ità in formam syllogisticam contorqueo. Illæ lineæ sunt commensurabiles quibus datur mensura communis, sed datur omnibus lineis mensura communis, nempè linea insecabilis, quæ cùm sit vltima, & minima quæ dari possit, omnes alias componit ac proinde etiam metitur, licet enim dicere quoties in quauis contineatur, ergo omnes lineæ sunt commensurabiles, ergo diameter, & costa quadrati sunt comensurabiles, nô potentiâ modò verum etiam logitudine quod implicat vt patet ex pro- positione sequenti. PRO.

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That same argument is repeated, drawn from the perfection of figures: a tetrahedron, pyramid, cone, cube, and other angular figures must end in a point, as Euclid stated. For I reply that it is enough for there to be a point virtually and equivalently, while denying that mathematical points must be present formally. OBJECTIO VII. On indivisible lines. Against the atoms there is the whole little book of Aristotle on indivisible lines, whose arguments are easily refuted by the same distinction between physical and mathematical divisibility. Take one of the strongest among many. If an indivisible line is granted, such as must be admitted in one dimension of an atom, then all lines will be commensurable; for all will be measured by indivisible lines, and any lines that are commensurable in length are also commensurable in power: but indivisible lines are commensurable with one another in length, since they are equal to one another; therefore also in power. And if this is so, the square will be divisible. See here Aristotle’s obscure weapon, which I turn more clearly into syllogistic form in this way. Those lines are commensurable to which a common measure is given; but a common measure is given to all lines, namely the indivisible line, which, since it is the ultimate and smallest that can be given, composes all the others and therefore also measures them; for it may be said how many times it is contained in any given line. Therefore all lines are commensurable; therefore the diameter and the side of a square are commensurable, not only in power but also in length, which follows, as is evident from the next proposition. PRO.

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C. 5. Obiectiones contra atomos. 203 PROPOSITIO XXXVIII. Latus quadrati est incommensurabile longitudine cum diametro sua. CVM enim ex 47. 1. quadratum diametri duplum sit qua- drati ex latere descripti habebit quadratum ex diametro ad quadratum ex latere proportionem 2. ad 1. vel 4. ad 2. vel 8. ad 4. sed sumptis in proportione dupla quotcunq[ue]; numeris ab vnitate 1. 2. 4. 8. 16. &c. solu[m] tertius ab vnitate nempe 4. quadratus est per decimam noni, & reliqui numeri vnum in- ter se omittentes, nam primus ab vnitate nempe 2. quadratus non est, erunt ergo tantum hi numeri quadrati 4. 16. 64. re- liqui verò 2. 8. 32. non quadrati, quare cum 4. sit quadratus, & 2. non sit quadratus, non habebit 4. ad 2. proportionem quam quadratus ad quadratum, ergo nec quadratum ex dia- metro ad quadratum costę, ergo sunt incommensurabiles costa & diameter, deinde cum inter numeros proportionales dupla[m] proportione habentes ex octaua octaui nullus cadat propor- tionalis, sequitur diametrum, & costam esse incommensura- biles, nam ex nona decimi, quadrata inter se proportionem non habentia quam quadratus numerus ad quadratum nume- rum, neq[ue] latera habebunt commensurabilia; Verùm non arithmeticè modo sed etiam geometricè nostram propositione[m] ex professo demonstrat Euclides propos. vltimà lib. 10. Vis itaq[ue] argumenti Aristotelis qui callebat satis mathema- ticas in eo sita est, vt probet à nostris lineis insecabilibus istud impossibile, costam, & diametrum esse commensurabiles, sicut enim vnitas omnes numeros metitur, ità, & linea insecabilis omnes alias lineas dimetietur. Respondeo itaq[ue] costam, & diametrum esse incommen- surabiles mathematicè, nostrasq[ue] lineas essequidem physicè insecabiles sed non mathematicè, à mathematicis verò lineis non

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C. 5. Objections against atoms. 203 PROPOSITION XXXVIII. The side of a square is incommensurable in length with its diagonal. FOR since from 47. 1. the square of the diagonal is double the square described from the side, the square from the diagonal will have to the square from the side the proportion of 2 to 1, or 4 to 2, or 8 to 4. But if, in a double proportion, any numbers whatever are taken from unity, 1, 2, 4, 8, 16, &c., only the third from unity, namely 4, is a square, by the tenth of the ninth; and the remaining numbers, omitting one another in turn, for the first from unity, namely 2, is not a square, there will therefore be only these square numbers, 4, 16, 64; the rest, 2, 8, 32, are not square. Therefore, since 4 is square and 2 is not square, 4 will not have the proportion to 2 that square has to square; therefore neither will the square of the diagonal have to the square of the side that proportion. Therefore the side and the diagonal are incommensurable. Then, since among proportional numbers having a double proportion, by the eighth of the eighth no proportional number occurs, it follows that the diagonal and the side are incommensurable; for from the ninth of the tenth, squares not having among themselves the proportion that square number has to square number, neither will the sides have a commensurable relation. But Euclid proves our proposition not only arithmetically, but also geometrically, in the last proposition of Book 10, expressly. Therefore the force of Aristotle’s argument, who understood mathematics well enough, lies in this, that he wishes to prove as impossible, from our indivisible lines, that the side and the diagonal are commensurable; for just as unity measures all numbers, so an indivisible line will measure all other lines. I reply, therefore, that the side and the diagonal are incommensurable mathematically, and that our lines are indeed physically indivisible, but not mathematically; but from mathematical lines not

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De Atomis. Disp. II. non autem à physicis sumenda est ratio commensurabilitatis, & incommensurabilitatis: neq[ue] ideo quod detur linea physicè insecabilis ea propter debebit assumi tanquam communis mé- sura, cum vt supra diximus mensuræ proprietas sit esse vna, & inuariabilis, atqui istæ lineæ pro varia figuratione atomorum variantur, ergo non possunt assumi tamqua[m] cæteraru[m] mensura. Cætera argumenta Aristotelis nil moror, cùm hâc vnicâ so- lutione ruant, & adducto sint aliquanto inbecilliora: omniaq[ue] contra lemmata tertium, & primum procedant. OBJECTION VIII. De angulo contactus, & angulo acuto. NON tantùm atomus diuisibilis est in infinitum verùm etiam partes habet determinabiles maiores vna[m] quapiam determinatà. PROPOSITIO XXXIX. In atomo ABC potest designari pars B quâ maiores, & maiores in infinitum in eadem atomo ABC possumus assignare. Demonstratur ex Eucl. prop. 16. l. 3. Quæ ab extremitate diametri cuivsq[ue] circuli ad angulos rectos linea ducitur, extrà circulum cadet, & in locum inter ipsam rectam lineam, & peripheriâ conprehensum altera recta non cadet, & semicirculi angulus quouis acuto rectilineo maior est, reliquus autem minor, hæc propositio qua- tuor habet partes quarum prima, & secunda ità clarè de- monstrantur ab Orontio Finæo, tertia verò, & quarta à Clauio in Euclidem vt dubitationis omnis aleam vel suspicionem collant quamuis Peletarius erroris Euclidem hic pene damnare sit conatus, neq[ue] hic eas demonstrationes transcribere de- beo cum omni plagiatu abstinere decreuerim. Euclidi consentiunt Proclus lib. 3. ad prop. 4. lib. 1. Eucl. Apol-

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On Atoms. Disp. II. but the ratio of commensurability and incommensurability is not to be taken from physical things; nor for that reason, because there is given a physically indivisible line, ought it therefore to be assumed as the common mea- sure, since, as we said above, the property of a measure is to be one and invariable; but these lines vary according to the varying configuration of the atoms, therefore they cannot be taken as the measure of the others. As for the rest of Aristotle's arguments, I care nothing for them, since with this single so- lution they fall, and by what has been adduced they are somewhat weaker; and all of them proceed against the third and first lemmas. OBJECTION VIII. On the angle of contact, and the acute angle. NOT only is the atom divisible into infinity, but also it has determinable parts greater than any one determinate part. PROPOSITION XXXIX. In the atom ABC a part B may be designated, and greater and greater parts to infinity may be assigned in the same atom ABC. This is demonstrated from Euclid, prop. 16, bk. 3: Whatever line is drawn from the extremity of the diameter of any circle at right angles, it will fall outside the circle, and no other straight line will fall into the space enclosed between it and the circumference; and the angle of a semicircle is greater than any acute rectilinear angle, but the remaining one is less. This proposition has four parts, of which the first and second are so clearly demonstrated by Orontius Finaeus, but the third and fourth by Clavius in his Euclid, that they remove every occasion of doubt or suspicion, although Peletarius has here attempted almost to condemn Euclid for error. Nor ought I here transcribe those demonstrations, since I have resolved to abstain from all plagiarism. Proclus agrees with Euclid, lib. 3, ad prop. 4, lib. 1 of Euclid. Apol-

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C. 5. Obiectiones contra atomos. 205 Apollonius Pergæus lib. 1. prop. 32. Proclus; addiscemus, inquit, quod cornicularis angulus semper est inæqualis acuto, id est minor, ratio est quia cornicularis angulus potest semper esse pars an- guli contactus, ac proinde cùm torum illud cuius potest esse pars sic semper minus quous angulo acuto quantumuis par- uo, necessariò dicendum est angulum cornicularem multò mi- norem esse, neq; dicas vocem illam inæqualem intelligi debere de incommensurabilitate, vel de omnimoda incomparabilita- te, nam ipsemet Proclus demonstrat huiuscemodi angulos cor- niculare, & acutum esse commensurabiles potentiam quod vi- de is apud Clauij Euclidem lib. 5. def. 5. Apollonius verò Pergæus lib. 1. prop. 32. In locum qui inter coni sectionem, rectam lineam interijcitur altera recta non cadit, atq; adeò angulus ille contactus minor est quous acuto rectilino, reliquus angulus si perpendicularis excitetur omni acuto rectilino ma- ior, quod in parabola hyperbola, & ellipsi demonstrat. Et qui theoricè practicam iunxit ingeniosissimus machiarum arti- sex Archimedes idem innuit libro abstrusæ scientiæ de sphæra, & cylindro, neq; vllus est qui clarissimis illarum positionum demonstrationibus possit obsistere. His ità constitutis sic argumentor: In quauis atomo potest designari angulus contactus, & angulus acutus, sed angulus acutus potest in alios acutos diuidi in infinitum, qui quantum- uis paruisint, quous angulo contactus sunt maiores, ergo datà vna parte determinatà in atomo, possunt dari aliæ determina- te maiores in infinitum, infiniti nempè anguli acuti angulo contactus maiores, quod erat ostendendum, quare pro corol- lario huius propositionis merito Cardanus; potest, inquit, vna quantitas infinitè augeri, & alia infinitè minui, & tamen augmen- tum illius quantumcumq; sit semper erit minus decremento istius. Augeatur enim in infinitum angulus contactus, minuaturq; in in-

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C. 5. Objections against atoms. 205 Apollonius of Perga, book 1, prop. 32. Proclus says, “we shall learn that the cornicular angle is always unequal to the acute angle, that is, smaller;” the reason is that the cornicular angle can always be a part of the angle of contact, and therefore, since that whole of which it can be a part is always less than any acute angle, however small, it must necessarily be said that the cornicular angle is much smaller; nor should you say that that word “unequal” must be understood of incommensurability, or of complete incomparability, for Proclus himself shows that angles of this sort, the cornicular and the acute, are commensurable in power, as you may see in Clavius’ Euclid, book 5, def. 5. Apollonius of Perga, however, book 1, prop. 32. In the place which is inserted between a conic section and a straight line, no second straight line falls in; and therefore that angle of contact is smaller than any acute rectilinear angle; the remaining angle, if a perpendicular is raised, is greater than every acute rectilinear angle, as he demonstrates in the parabola, hyperbola, and ellipse. And that most ingenious artificer of machines, Archimedes, who joined theory with practice, indicates the same in the book On the Sphere and Cylinder, a work of abstruse science; and there is no one who can resist the most evident demonstrations of those propositions. Since these things are thus established, I argue as follows: in any atom there can be designated an angle of contact and an acute angle, but an acute angle can be divided into other acute angles to infinity, which, however small they are, are greater than the angle of contact; therefore, given one determinate part in an atom, other determinate parts greater to infinity can be given, namely infinitely many acute angles greater than the angle of contact, which was to be shown. Therefore, as a corollary of this proposition, Cardano rightly says: one quantity can be increased infinitely, and another diminished infinitely, and yet the increase of the former, however great it may be, will always be less than the decrease of the latter. For let the angle of contact be increased to infinity, and let it be diminished in-

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206 De Atomis. Disp. II. in infinitum angulus acutus semper tamen hic maior erit illo: quia scilicet quiuis angulus acutus applicatus perpendiculaxiter diametro circuli intra circulum cadit, angulus verò contactus cadit extra circulu[m], ergo angulus contactus cuiuscumq[ue] sit magnitudinis semper se habet ad angulum acutum vt pars ad totum. Dices primò vel inter circulum, & lineam contingentem intermediat spatium vel non, si primùm poterit in eo duci recta linea, quia quolibet spatio dato quælibet construi potest figura, si secundum, hoc est, si non inrermediat spatium, sequitur quod recta contingens non cadit extra circulum. Respond. intermediare spatiu[m] sed asymmetron cum linea[m] recta, proportionatum verò circularibus, & inflexis per quas angulus ille diuisibilis est in infinitum: ad probationem, quolibet spatio dato quælibet construi potest figura, distinguo, de spatio complectente aream concedo, de spatio siue area indeterminata qualis est inter angulorum lineas, nego. Dices secundò latitudo anguli contactus potest diuidi per lineam recta[m], ergo, & ipse angulus, nam propagatio linearum non mutat naturam anguli cuius natura sita est in inclinatione alterius ad alteram quæ productis lineis non variatur. Respondeo negando propagationem linearum curuarum non mutare naturam anguli, quamuis de rectis lineis id concedam, ratio est quia lineæ mixtæ, & circulares irregulariter duci possunt, at recta vnico fluxu, & vnicâ viâ ducitur, rectæ enim duæ non possunt habere vnum, & idem segmentum commune, hoc est vt vna pars rectæ sit pars alterius, vt patet axiomate 10. 1. curuæ autem id possunt vt patet in ellipsi, & lineis mixtis. Dices tertiò contingit tranire à maiori ad minus, & per omnia media ergo etiam per æqualę, circumducatur diamet- ter

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206 On Atoms. Disp. II. in infinitum an acute angle will nevertheless always be greater than this than that: for, namely, any acute angle applied perpendicularly to the diameter of a circle falls within the circle, but the angle of contact falls outside the circle; therefore the angle of contact, of whatever magnitude it be, is always related to the acute angle as part to whole. You will say first: either between the circle and the tangent line there intervenes space, or not; if the first, a straight line can be drawn in it, because in any given space any figure can be constructed; if the second, that is, if no space intervenes, it follows that the tangent straight line does not fall outside the circle. Reply: space does intervene, but asymmetrically with the straight line, yet proportioned to circular and curved lines through which that angle is divisible to infinity: to the proof, in any given space any figure can be constructed, I distinguish: of space including area, I grant; of space or indeterminate area such as is between the lines of an angle, I deny. You will say secondly: the breadth of the angle of contact can be divided by a straight line, therefore the angle itself too; for the extension of lines does not alter the nature of an angle, whose nature lies in the inclination of one to another, which is not varied by lines being produced. I answer by denying that the extension of curved lines does not change the nature of an angle, although of straight lines I grant this; the reason is that mixed and circular lines can be drawn irregularly, but a straight line in one single flow and by one single path is drawn; for two straight lines cannot have one and the same common segment, that is, so that one part of one straight line is a part of the other, as is clear from axiom 10. 1. But curved lines can do this, as is clear in the ellipse and mixed lines. You will say thirdly: it is possible to pass from greater to lesser, and through all the intermediates, therefore also through the equal; let the diamet-

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C. 5. Obiectiones contra atomos. 207 ter incumbet tandem, & coincidet cum linea co[n]tingenti ergo transiuit à maiori ad minus, & per omnia media & consequen ter per æquale, ergo datur angulus acutus æqualis angulo contactus. Resp[ondeo] distinguendo, si detur illud æquale concedo, si no[n] de- tur nego, & affero duplicem instantiam, prima est de propor- tione diametri circuli ad circumferentiam, quæ non est vt 7. ad 22 exactè loquendo, siue non seruat rationem proportionis tri plæ sesquiseptimæ, excedit vero proportionem 7. ad 21. dein- de daretur angulus acutus æqualis angulo semicirculi, nam circumducta linea contingens vsq[ue]; dum coincidat in diametrum transibit à maiori ad minus, & per omnia media, non tamen per æquale, nullum enim datur. Dices 4. Euclides lib. 10. prop. 1. Si, inquit, Duabus magnitudinibus inæqualibus propositis, de maiore detrabatur plus dimidio, iterumq[ue]; de residuo detrabatur plus dimidio, idq[ue]; semper fiat, relinquetur quædam magnitudo minor alterà minore ex duabus propositis. ergo angulus acutus ita per dimidia frequêter imminutus tandem fiet minor angulo contactus. Resp[ondeo] propositionem illam libri decimi intelligendam de quantitatibus cuiuscunq[ue]; generis dummodo vtraus multiplicata alteram excedere possit, sed multiplicatus angulus contactus non potest excedere angulum acutum, ergo de huiusce-modi magnitudinibus non agit hæc propos[itionis] ex quibus ita argumentor. Non potest intelligi hæc partis determinatio sine diuisibilitate ergo atomus est diuisibilis. Resp[ondeo] demonstrationem Euclidis esse optimam, sicut, & Pappi, Apollonij, Cardani, Procli, & aliorum, sed dico in sequela argumenti duplex erratum committi, & primus quidem paralogismus est contra lemmæ 1. materiam enim physicam, siue atomos mathematicis principijs imbuit: Secundus quod O vocet

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C. 5. Objections against atoms. 207 then at last it will lie against, and coincide with the tangent line; therefore it has passed from the greater to the less, and through all the intermediates, and consequently through the equal; therefore an acute angle equal to the angle of contact is given. I answer, distinguishing: if that equal be given, I grant it; if it be not given, I deny it, and I offer a twofold instance. The first is from the proportion of the diameter of a circle to the circumference, which is not exactly, strictly speaking, as 7 to 22, that is, it does not preserve the ratio of the triple sesquiseptimal proportion; rather, it exceeds the proportion of 7 to 21. Next, an acute angle equal to a semicircle would be given, for when the tangent line is drawn around until it coincides with the diameter, it will pass from the greater to the less, and through all the intermediates, yet not through the equal, since none is given. You say 4. Euclid, book 10, prop. 1. If, he says, from two unequal magnitudes proposed, more than half be taken away from the greater, and again more than half be taken away from the remainder, and this be done always, there will remain a magnitude smaller than the other smaller of the two proposed. Therefore an acute angle, thus frequently diminished by halves, will at last become smaller than the angle of contact. I answer: that proposition of the tenth book is to be understood of quantities of whatever kind, provided one, when multiplied, can exceed the other; but a multiplied angle of contact cannot exceed an acute angle; therefore this proposition does not treat of magnitudes of this kind. From which I thus argue. This determination of the part cannot be understood without divisibility; therefore the atom is divisible. I answer: Euclid’s demonstration is excellent, as are those of Pappus, Apollonius, Cardan, Proclus, and others; but I say that in the sequel of the argument a double error is committed, and the first paralogism is indeed against the matter of the lemma, for he imbues physical matter, or atoms, with mathematical principles. The second is that O calls

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208 De Atomis. Disput. II. vocet angulum contactus partem determinatam, cum tamen aream non claudat sitq[ue]; inassignabile illud spatium quod latitudine anguli facit, quod si assignabile esset diuideretur vtiq[ue]; per rectam, quare cum angulus contactus spatium non comprehendat, sicuti neq[ue] angulus acutus ex principio 12. primi, duæ enim rectæ spatium non comprehendunt. Sequitur neutrum esse partem determinatam, vnde apparet illud argumentum etiam habitâ ratione spatij mathematici esse sophisticum. OBIECTIONES PHYSICOMATHEMATICÆ. Harum obiectionum conclusiones sunt plerumq[ue]; vitiosæ vel certè non conuincentes, oblemmata superius adducta, conclusio enim deteriorem sequitur partem, quare si premissa habeat aliquid defectus vel ex mathesi vel ex philosophia, eo sequela inficitur. OBIECTIO IX. De motu rotæ. Si continuum co[m]ponitur ex atomis, sequitur debe re frangi totam in motu, sit enim rota ACBF maior, rota autem minor HEQ, angulus ab axe O ad circumferentiam ductus A OG, arcus exterior AG duarum atomorum, arcus interior EH, vnius atomi, moueatur circa eundem axem O ab A in C, & ab E in H, sequitur quod dum atomus

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208. On Atoms. Dispute II. calls the angle of contact a determinate part, when nevertheless it does not enclose a space and is an inassignable space which the width of the angle makes; for if it were assignable, it would surely be divided by a straight line. Therefore, since the angle of contact does not comprehend space, just as neither does an acute angle from the beginning of the 12th proposition of the First Book, for two straight lines do not comprehend space. It follows that neither is a determinate part; whence it appears that this argument, even with regard to mathematical space, is sophistical. OBJECTIONS FROM PHYSICO-MATHEMATICS. The conclusions of these objections are for the most part faulty, or certainly not convincing, because of the objections stated above; for the conclusion follows the worse part, and therefore if the premise has some defect, either from mathematics or from philosophy, the consequence is tainted by it. OBJECTION IX. On the motion of a wheel. If the continuous is composed of atoms, it follows that the whole must be broken in motion. Let the wheel ACBF be larger, and the wheel HEQ smaller; let the angle drawn from the axis O to the circumference AOG, the outer arc AG of two atoms, the inner arc EH of one atom, move about the same axis O from A to C, and from E to H; it follows that while the atom

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C. 5. Obiectiones contra atomos 209 atomus AL reperitur in LG tota atomus EH pertran- sierit, ergo atomus AL non ipsi amplius adhæret, quod si non mutauit locum atomus EH, fuit immobilis contra hy- pothesim, si mutauit locum, minor rota tantumdem conficit spatij atq[ue] maior in pari velocitatis gradu, vt patet ex lineis 1H, ML perpendicularibus, & dissoluta est totæ compa- ges, quæ absurdissima sunt. Respondeo ego ex lemmate 2. Atomo inesse mathematicam ex- tensionem secundùm quam potest locum mutare inadæquatè secundùm aliquam sui virtualitatem, dum ergo atomus exte- rior totum locum mutat, interior pro rata parte mutat locum secundùm quid, non autem absolutè, ita dum atomus AL mu- tauit locum in LG atomus EH secundùm mediam sui ex- tensionem delata est vltra punctum H, & sic de cæteris, inte- rior autem vicinaq[ue]; centro atomus cum habeat similiter innumeras virtualitates extensionis mathematicæ, ideò secundùm quid sui locum mutare potest. OBJECTION X. De comparatione maioris, et minoris extensionis. TOT essent partes mathematicæ in vna atomo quot in to- to cælo, sequela absurda est, nam etiam mathematicè loquendo totum maius est sua parte, probatur antecedens, sint circuli duo concentrici interior vnius atomi, exterior verò linea Ecliptica, dico tot esse partes in vna atomo quod in toto cælo, nam ab singulis cæli punctis ad interioris sphæræ centrû[m] lineas diduces, ergo vtrobiq[ue]; par est partium etiam mathe- maticarum numerus, quod est absurdum. O 2 Respon-

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C. 5. Objections against atoms 209 An atom AL is found in LG when the whole atom EH has passed through; therefore atom AL no longer adheres to it. But if atom EH has not changed place, it was motionless, contrary to the hypothesis; if it has changed place, the smaller wheel covers just as much space as the larger one at the same degree of speed, as is clear from the perpendicular lines 1H, ML, and the whole structure is dissolved, which is most absurd. I answer from Lemma 2. In an atom there is mathematical extension, according to which it can change place inadequately according to some of its virtuality. Therefore, while the outer atom changes the whole place, the inner atom changes place in proportion, secundum quid, but not absolutely. Thus, when atom AL changed place in LG, atom EH, according to the middle of its extension, has been carried beyond point H, and so on in the other cases. But the inner atom, and the part near the center, since it likewise has countless virtualities of mathematical extension, can therefore change its place in a qualified sense. OBJECTION X. On the comparison of greater and lesser extension. There would be as many mathematical parts in one atom as in the whole sky; the consequence is absurd, for even speaking mathematically the whole is greater than its part. The antecedent is proved thus: let there be two concentric circles, the inner one of an atom, the outer one the ecliptic line. I say that there are as many parts in one atom as in the whole sky, for from each point of the sky to the center of the inner sphere lines can be drawn; therefore in both cases the number of mathematical parts is equal, which is absurd. O 2 Respon-

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De atomis. Disput. II. Respondent aliqui domi suæ nobiles philosophi non posse dici tot, & quot, puerile responsum. Alius negabat posse comparari circulum cum circulo in ratione partium. Respondeo sensum propositionis hunc esse, tot posse fingi distinctiones, lineas, figuras. delignationes in spatio vnius atomi quot in cælo transeat, neq[ue] verò id absurdum est cum vtrobiq[ue] sarium sit infinitum extrinsecè, & per imaginationem, vt aiebat Democritus, quod autem ab intellectu fingente rei inest, absurdum in natura dici non potest: sicuti autem rerum imagines vastissimas lumen exiguis terminis coercet, quid impedit quominùs imaginatio idem præstet, designetq[ue] in vnius atomi angustijs omnes firmamenti constellationes? lineæ non possunt duci distinctè, & separatim a singulis firmamenti atomis ad orbis centrum, argumentum itaque procedit contra lemma 2. & 1. OBJECTION XI. De luminis propagatione, & figuratione. CVM superiùs responsum sit fieri transitum àlienis mathematicis ad physicas, nunc argumentum ex meris radijs siue lineis physicis affero, & primum suppono illud perspectiuæ principium, A quousis corporis lucidi puncto ad quodlibet medij punctum, lumen quoquo versus emicat, ita vt à quousis puncto lucidi tanquam à centro circumquaq[ue] effusum in modum sphæræ diffundatur. Deinde prepono experientiam quotidianam figurationis lucis de qua egit Aristoteles, s. 15. probl. 5. quando ità quærit, Cur sol per quadrilatera profluens, non rectis lineis figuram describit, sed circulum format vt in cratibus patet? & quidem ex prima suppositione ita argumentor, si sol, verbi causà, atomis constet, cum vndiquaque lineas lucis effundat, tot erunt à sole lucis lineæ quot eius superficies atomis componitur, quia ab vna atomo

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On atoms. Disputation II. Some noble philosophers at home respond that it cannot be said “so many” and “as many,” a childish answer. Another denied that a circle could be compared with a circle in respect of the parts. I answer that the sense of the proposition is this: as many distinctions, lines, figures, and markings can be imagined in the space of one atom as pass through the heavens; nor is this absurd, since in both cases the infinite is external, and, through imagination, as Democritus said. But what is in the thing itself as fashioned by the intellect cannot be called absurd in nature: just as light confines the vast images of things within narrow bounds, what prevents imagination from doing the same, and from indicating in the narrow limits of one atom all the constellations of the firmament? Lines cannot be drawn distinctly and separately from each individual atom of the firmament to the center of the world; therefore the argument proceeds against lemma 2 and 1. OBJECTION XI. On the propagation and shaping of light. SINCE above it has been answered that there is a passage from mathematical to physical arguments, now I bring forward an argument from mere rays or physical lines, and first I assume this principle of perspective: from any point of a luminous body to any point of the medium, light flashes forth in every direction, so that from any point of the luminous body, as from a center, it is spread round about in the manner of a sphere. Next I set before you the everyday experience of the shaping of light, of which Aristotle treated in Problem 15, question 5, when he asks: Why does the sun, flowing through quadrilateral openings, not describe its figure by straight lines, but forms a circle, as is evident in grates? And indeed, from the first supposition I argue thus: if the sun, for example, consists of atoms, then since it emits lines of light on every side, there will be as many lines of light from the sun as there are atoms composing its surface, because from one atom

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C. 5. Obiectiones contra atomos. 211 atomo non possunt duæ lineæ physicæ promanare, cùm autem illæ lineæ se se simul tangant in superficie solis, sequitur quod pro ratione elongationis distabunt magis, ergo inter se maxi- ma tenebrarum spatia relinquent, contrarium autem sensu patet, aer enim vniformiter illuminatur ergo, corpora nô con- stant ex atomis. Ex secunda suppositione ita argui potest, sit conus lucis subiens perforamen quadratum, quomodo resti- tuet se post decussationem in formam rotundam si dentur ato- mi? an peribunt aliquè, an verò de subiecto in subiectum pos- sunt transire illud dici non potest, cùm lumen sit accidens vt probauit Aristoteles 2. de an primùm autem gratis asseritur: Ergo admissis atomis figuratio, & propagatio luminis fieri nequit. Respondeo ad primùm, negando à singulis atomis lineas physicas lucis effundi, sed illud perspectiuorum principium intelligendum esse de puncto sensibili: atomus autem sub sen- sum non cadit. Deinde omne totum agit per modum totius, singulę autem partes secundum se sumptę non agunt nisi con- comitanter cum toto: nisi enim res ità se haberet eslet breuis- sima omnium agentium sphæra actiuitatis. Adde quod nego ab vna atomo vnam tantùm diffundi posse lineam, cum inten- sio lucis, & caloris exigat multas atomos in eadem subiecti par- te. Ad secundam difficultatem de lucis figuratione. Respō- deo atomos illas quæ in angulis quadrilateræ fissuræ reperiun- tur sensum deficere, ob violentam figuram quæ obiecto contra- ria est. Natura autem vt diximus principio 8. huius disput. Semper connaturali sibi statui se se restituere conatur. De illa autem lucis figuratione vide Vitellionem nu. 39 l. 2. Aristote- lem, & Septalium loc. cit. Maurolycum in suis posthumis pho- tismis, Kappletum in paralipomenis ad Vitellionem. Aquilo- nium l. 1. opt. Blancanum in loc. Arist. numero 345. Aliolq- tum O 3

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C. 5. Objections against atoms. 211 from an atom two physical lines cannot proceed; but when these lines touch one another together on the surface of the sun, it follows that, in proportion to the elongation, they will be farther apart, therefore they will leave the greatest spaces of darkness between themselves; but the contrary is evident to sense, for the air is uniformly illuminated; therefore bodies do not consist of atoms. From the second supposition the argument can be made thus: let a cone of light passing through a square opening be given; how will it restore itself after the crossing into a round form if atoms are given? Will some perish, or rather can they pass from subject to subject? this cannot be said, since light is an accident, as Aristotle proved in 2 De Anima; but at first this is asserted without reason. Therefore, if atoms are admitted, the shaping and propagation of light cannot take place. I answer the first point by denying that physical lines of light are emitted from individual atoms, but that principle of perspective must be understood of a sensible point: an atom, however, does not fall under sense. Next, every whole acts by the mode of the whole, whereas the individual parts taken in themselves do not act except concomitantly with the whole; for if things were not so, the sphere of activity of all agents would be the briefest possible. Add that I deny that from one atom only one line can be diffused, since the intensity of light and heat requires many atoms in the same part of the subject. To the second difficulty, concerning the shaping of light, I answer that those atoms which are found in the corners of the quadrilateral opening fail the sense, because of the violent shape which is contrary to the object. Nature, however, as we said in principle 8 of this disputation, always tries to restore itself to its connatural state. For that shaping of light, see Vitellio no. 39, book 2; Aristotle; and Septalius, in the place cited; Maurolycus in his posthumous Photisms; Kappletus in the Paralipomena to Vitellio; Aquilonio, book 1, Opt.; Blancanus, in the place of Aristotle, number 345; and someone else. O 3

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212 De Atomis. Disp. II. tum mathematicos tum philosophos in lib. de anima vbi de specierum natura disputant. OBIECTIO XII. De illuminatione globi. Sol applicatur nostro horizonti continuè successivè ergo pa- riter illuminat continuè successivè, & consequenter eius lumen diuisibile est in infinitum, deinde si hoc non admittatur erit falsum istud theorem opticis omnibus astrologisq[ue] certissimum: Sphera luminosa illuminat semissem sphæræ opacæ æqualis, plus autem semisse, sphæræ opacæ minoris, minùs de- niq[ue]; semisse sphæræ opacæ maioris, quare etiam inde colligi- tur plusquam mediam terræ partem a sole illuminari: Vitellio enim Alhazenus prop. 10. pag. 59. 180. gradus cum minutis 27. & secundis 52. ponit: Clauius verò 180. gr. min. 26. cę- terum clarissimè hoc Theorema demo[n]stratur ab Aquilonio in opticis, à Clauio lib. de crepusculis, à Vitellione loco citato, & ab alijs passim. Sit itaq[ue] opacus globus quatuor atomoru[m], dispo- natur eo modo ad luminosu[m] globu[m] vt lineæ contingentes inci- dant in medias atomos, sequitur vel mediam atomum obscuram fore, aliam illuminatam, ac proinde sequetur luminis diuisibilitas, vel hoc Theorema esse falsum, contra demonstrationes virorum in mathematicis principum. Respondeo ad hoc argumentum, solis motum, & eius illu- minationem differre, nam licet applicetur continuè successivè eo sensu quo inferius explicabimus, tamen illuminatio non se- quitur seuerè leges motus, ratio est, quia motus connotat ex- trinsecum spatium, illuminatio verò etiam subiectum exigit in quo recipiatur, ac proinde debet illud extensum esse, minima autem extensio est vnius atomi, vnde vnam totam simul il- luminat, & vna tota simul lumen perdit: vnde in forma, transe- at antecedens nego consequentiam. Ad in-

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212 On Atoms. Disputation II. both the mathematicians and the philosophers in the book On the Soul, where they dispute about the nature of species. OBJECTION XII. On the illumination of a globe. The sun is applied to our horizon continuously and successively; therefore it likewise illuminates continuously and successively, and consequently its light is divisible into infinity. Moreover, if this is not granted, then the following theorem, most certain to all opticians and astronomers, will be false: A luminous sphere illuminates half of an opaque sphere of equal size, more than half of a smaller opaque sphere, and less than half of a larger opaque sphere; whence it is also gathered that more than half of the earth is illuminated by the sun. For Vitellio, following Alhazen, in proposition 10, page 59, sets it at 180 degrees, 27 minutes, and 52 seconds; but Clavius gives 180 degrees, 26 minutes. However, this theorem is most clearly demonstrated by Aquilonius in his Optics, by Clavius in his book On Crepuscles, by Vitellio in the cited passage, and by others everywhere. Let there then be an opaque globe of four atoms, arranged with respect to the luminous globe in such a way that tangent lines fall upon the middle atoms; it follows either that the middle atom will be dark and another illuminated, and therefore the divisibility of light will follow, or that this theorem is false, contrary to the demonstrations of the foremost men in mathematics. I reply to this argument that the motion of the sun and its illumination differ, for although it is applied continuously and successively in the sense explained below, nevertheless illumination does not strictly follow the laws of motion. The reason is that motion implies external space, whereas illumination also requires a subject in which it is received; and therefore that subject must be extended, but the smallest extension is that of a single atom, wherefore it illuminates one whole atom at once, and one whole atom loses the light at once. Hence, in form: let the antecedent pass; I deny the consequence. To the in-

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C.5. Obiections contra atomos. 213 Ad instantiam deductam à theoremate opticorum respôdeo. In mathematicis duas esse scientiarum species, aliæ sunt purè mathematicæ vt geometria speculatiua, & arithmece Theori- ca, aliæ verò physicomathematicæ vt optica, astrologia, me- chanica quam physicæ, & mathematicarum horizontem vocat Aristoteles. Harum scientiarum propositiones veræ sunt si nudè, & ad sensum sumantur, sin verò examinentur in rigore geometrico sunt falsæ, sic qui radium visualem existimaret li- neam esse mathematicam erraret toto cælo, opus enim est cer- tâ quâdam extensione ad agendum; pariter non quæuis quan- titas ponderis bilances mouet vt pulueris granulum, quia cer- ta ponderis ratio requiritur. Geometricè itaq[ue] loquendo hæc propositio quæ sciothericorum horologiorum fundamentum est, falsitatis conuincitur, terra puncti instar obtinet ad firmamen- tum, datur enim proportio terræ cum firmamento vt demon- strat Archimedes lib. de arenæ numero, & hanc pariter assero falsam, vmbræ matutinæ sunt æquales vespertinis, & hanc crepu- sculum matutinum æquale est vespertino, pariter etiam quæ de globoru[m] illuminatione adducta est ab aduersario in mediu[m] geo metricè, & strictè loquendo vera non est, quamuis ad sensum hæ omnes extra dubium sint positæ. Ratio à priori est quia conclusio sequitur deteriorem partem, ergo in opticorum syl- logismis aliorumq[ue] qui naturalem scientiam cum mathemati- ca miscent, maior propositio erit geometrica, minor physica, conclusio ergo debebit esse physica hoc est deterior, & minus exacta, neq[ue] verò sunt examinandæ actiones physicæ regulis geometricis ex lemmate 3. OBIECTIONES PHYSICÆ. Quanto obscurior est naturæ maiestas altioribusq[ue] penetra- libus velata manet, tanto difficiliores sunt rationes ab ipsa derivatæ: quatuor aut quinq[ue] t[um] vitâde[m], pliætatis causa afferet. O 4 OBI-

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C.5. Objections against atoms. 213 I reply to the objection drawn from the theorem of optics. In mathematics there are two kinds of sciences: some are purely mathematical, such as speculative geometry and theoretical arithme- tic; others are physicomathematical, such as optics, astrology, me- chanics, which Aristotle calls the horizon of physics and mathematics. The propositions of these sciences are true if taken simply and in accordance with the senses; but if examined with geometric rigor they are false. Thus he who should think that the visual ray is a mathematical line would be utterly mistaken, for a certain extension is required for action; likewise not every quantity of weight moves a balance like a grain of dust, because a certain ratio of weight is required. Therefore, speaking geometrically, this proposition, which is the foundation of sundials, is proved false: the earth has the status of a point with respect to the firmament; for there is indeed a proportion of the earth to the firmament, as Archimedes shows in book On the Sand-Reckoning, and I likewise assert this to be false: morning shadows are equal to evening shadows, and this one: the morning twilight is equal to the evening twilight; likewise also what the adversary has adduced concerning the illumination of globes is not, speaking geo- metrically and strictly, true, although in every sense these things are beyond doubt. The reason a priori is that the conclusion follows the worse part; therefore in syllogisms of optics and others which mix natural science with mathe- matics, the major proposition will be geometric, the minor physical, and therefore the conclusion must be physical, that is, worse and less exact. Nor indeed are physical actions to be examined by geometric rules, according to lemma 3. PHYSICAL OBJECTIONS. The more obscure the majesty of nature is, and the more it remains hidden in deeper recesses, the more difficult are the reasons derived from it: he will set forth four or five, for the sake of the time, as well as the pliætas.

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De Atomis. Disp. II. OBIECTIO XIII. De continuo, & tempore. TOT sunt partes in continuo quot in tempore, sed in tem- pore sunt infinitæ realiter inter se distinctæ, ergo & in co- tinuo. Maior fundatur in principio 17. huius, minor patet quia instans quod nunc fluit differt à fluxo, & fluxuro, ergo diuiduntur realiter, sunt autem infinita instantia, ergo, & to- tidem diuisiones, & distinctiones. Respondeo concedendo maiorem, & distinguendo mino- rem, sed in tempore sunt infinitæ realiter penes connotatum concedo, absolutè nego: continuo, motui, & tempori respon- dent tria quæ diuisibilitatem patiuntur infinitam, continuo quidem spatium mathematicum de quo supra, motui conno- tatio loci, & tempori duratio cum fluxu. Sed hæc solutio per- cipietur tantum cap. 1. disput. 3. OBIECTIO XIV. De quantitatis ratione. QVantitas est realiter diuisibilis in infinitum cum eius gra- tia materia diuisibilis fiat, sed atomus A est quanta ergo est diuisibilis, quod si dicas atomi substantiam non esse diuisi- bilem, sed tantum quantitatem, redibunt omnes difficultates quibus alij obruuntur. Respondeo hanc obiectionem à me fuisse præuisam in totius operis huius fundamento, cum hoc axiomate vsus sum, quid- quid recipitur per modum recipientis recipitur, sed atomi ele- mentales, vt probauimus sunt indiuisibiles ergo, & educta ab ipsis accidentia: quare ad argumentum Nego maiorem, nam quantitatis essentia non est sita in diuisibilitate, sed in im- penetrabilitate actuali. Ratio à priori est quia intelliguntur atomi

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On Atoms. Disp. II. OBJECTION XIII. On the continuous and time. There are as many parts in the continuous as in time, but in time there are infinitely many parts really distinct from one another; therefore also in the continuous. The major premise is based on principle 17 of this work; the minor is clear because the instant that now flows differs from what has flowed and what will flow, therefore they are divided really; but there are infinite instants, therefore also as many divisions and distinctions. I reply by granting the major premise, and distinguishing the minor: in time there are infinitely many things really, as to the connoted aspect, I grant it; absolutely, I deny it. To the continuous, motion, and time correspond three things which suffer infinite divisibility: to the continuous, namely, mathematical space, of which above; to motion, the connotation of place; and to time, duration with flux. But this solution will be understood only in chap. 1, disput. 3. OBJECTION XIV. On the nature of quantity. Quantity is really divisible to infinity, since matter by its nature becomes divisible; but atom A is a quantity, therefore it is divisible. But if you say that the substance of the atom is not divisible, but only its quantity, then all the difficulties by which others are burdened will return. I reply that this objection was foreseen by me in the foundation of this entire work, when I used this axiom: whatever is received is received according to the mode of the receiver. But elementary atoms, as we have proved, are indivisible; therefore also the accidents derived from them. Wherefore, as to the argument, I deny the major premise, for the essence of quantity does not lie in divisibility, but in actual impenetrability. The a priori reason is because atoms are understood

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C. 5. Obiectiones contra atomos. 215 atomi antequam sint quantæ, & quidquid tibi materiæ finxeris non accipiet indiuiduorum multiplicationem ab accidente, accidentibus enim non multiplicantur substantiæ. Instabis si corpus non esset quantum non posset diuidi, ergo habet à quantitate diuisibilatem. Respondeo corpus sine quantitate futurum penetrabile ac proinde physicè corporeis instrumentis non diuidetur. Vt autem animo tibi fingas corpus quantitate destitutum, reuoca in mente poeticas apparitiones quæ oculos explent sed tactum non sustunt, ità Æneas Anchisem in elysijs videns. Ter conatus ibi collo dare brachia circum, Ter frustra compensa manus effugit imago, Par leuibus ventis volucriq[ue] simillima somno. Neq[ue] verò aufugit Anchises qui filium comitabatur sed quod non esset impenetrabilis, ideò Æneæ manus sunt elusæ: & inspectri militisq[ue] monomachia. Nil gladios remorata cutis, nihil ossa ruentis Impetuum, & immani per fossum vulnere pectus. Occuluit vulnus subitò tenuitq[ue] cruorem. Anchisem non poterat tenere Æneas vt pote penetrabilem, & militis gladius videbatur spectrum fodere sed quod abesset quantitas ideò in eodem loco reperiebatur, & nihil hiatus relinquebat. Accipe speculum parabolicum exquisitum egredi videbis è speculo imaginem tuam, & in aeris medio extra speculum subsistere, illamq[ue] impunè fodies, & tenere frustra quæres: ex quibus vides triplicem esse diuisibilitate, altera est crassa, & popularis, altera metaphysica quæ indiuidua ab indiuiduis distinguit, tertia mathematica penes spatium imaginariu[m], diuidetur autem corpus quantitate, destitutum separatis ab inuicem atomis, siue indiuiduis. OBIE-

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C. 5. Objections against atoms. 215 atoms before they are quantities, and whatever matter you may imagine, it does not receive the multiplication of individuals from accident, for substances are not multiplied by accidents. You will insist: if a body were not a quantity it could not be divided; therefore it has divisibility from quantity. I reply that a body without quantity would be penetrable and therefore would not be divided physically by corporeal instruments. But that you may picture to yourself a body deprived of quantity, call to mind poetical apparitions which fill the eyes but do not support the touch, as when Aeneas seeing Anchises in Elysium: Ter conatus ibi collo dare brachia circum, Ter frustra compensa manus effugit imago, Par leuibus ventis volucriq[ue] simillima somno. Nor indeed did Anchises flee, who accompanied his son, but because he was not impenetrable, therefore Aeneas’ hands were deceived; and in the combat of the spectator and the soldier: Nil gladios remorata cutis, nihil ossa ruentis Impetuum, & immani per fossum vulnere pectus. Occuluit vulnus subitò tenuitq[ue] cruorem. Aeneas could not hold Anchises, since he was penetrable, and the soldier’s sword seemed to pierce a phantom, but because quantity was absent it was therefore found in the same place and left no gap. Take an exquisite parabolic mirror: you will see your image emerging from the mirror and standing in the middle of the air outside the mirror, and you may pierce it with impunity, and you will seek in vain to hold it. From these things you see that divisibility is threefold: one is coarse and common, another metaphysical, which distinguishes individuals from individuals, the third mathematical, with respect to imaginary space. A body is divided, however, by quantity, when the atoms, or individuals, separated from one another, are deprived of it. OBIE-

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De Atomis. Disp. II. OBJECTION XV. De indiuisilibus simul iunctis. Indiuisibile iunctum indiuisibili non facit maius, quia tangit secundum se totum, sed atomus est indiuisibilis, ergo atomus iuncta atomo non facit maius. Respondeo maiorem de punctis mathematicis esse euidentem non autem de alijs indiuisilibus quæ suas habent dimensiones secundum quas jungi vniriq[ue]; cum extensionis incremente possunt. OBJECTION XVI. Argumentum Zenonis. Motus non potest fieri per spatium quoduis nisi prius mobile pertranseat minus quam maius, sed quancunq[ue] assignes partem alia est minor, & alia minor in infinitum, ergo non potest fieri motus, numquam enim incipiet. Respondeo huic argumento satisfieri non posse nisi admissis in continuo indiuisilibus, & id contendebat Zeno deducendo ad absurdum, neq[ue] enim motum negabat. Respondeo itaq[ue] aliam esse minorem mathematicè concedo, realiter nego, motus autem consideratur ab aduersario penes realem rerum existentiam. Respondebat Empedocles puncta mathematica transiri tota simul, & quietibus interpolatis motuum velocitatem, & tarditatem distingui. Cæteræ quæ à motu petuntur aut rarefactione obiectiones non possunt dilui nisi disput. 3. OBIE-

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On Atoms. Disp. II. OBJECTION XV. On indivisibles joined together. An indivisible joined to an indivisible does not make something greater, because it touches according to itself as a whole; but an atom is indivisible, therefore an atom joined to an atom does not make something greater. I reply that the major premise is evident in the case of mathematical points, but not in the case of other indivisibles, which have their own dimensions, according to which they can be joined and united, and can be increased by extension. OBJECTION XVI. Zeno’s argument. Motion cannot take place through any space unless the moving body first passes through less than the greater, but whatever part you assign, there is another smaller, and another smaller to infinity; therefore motion cannot take place, for it will never begin. I reply that this argument cannot be answered unless indivisibles are admitted in the continuum, and that is what Zeno was maintaining by reducing to absurdity; for he was not denying motion. I reply, then, that in one sense there is another smaller thing mathematically, I grant; really, I deny it. But motion is considered by the opponent with respect to the real existence of things. Empedocles replied that mathematical points are traversed all at once, and that the speed and slowness of motions are distinguished by the interposed pauses. Other objections derived from motion or from rarefaction can only be dissolved in disputation 3. OBIE-

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C.5. Obiectiones contra atomos. 217 OBJECTION XVII. Contra indiuisibilitatem atomorum. QVod est materiale existit modo materiali, hoc est, habet par tes extra partes, quod autem partes habet extra partes diuisibile est, sed atomus existit modo materiali, ergo est diuisibilis. Respondeo conceptum materialitatis dicere duo, primùm exigentiam impenetrabilitatis per quantitatem, secundò ordinem essentialem ad aliquid aliud quod erit tanquam sui perfectiuum in ratione entis completi aut subiectiuum, quę duo atomis conueniunt, ordo ad quantitatem, & ad mixti formâ: quare nego existere modo materiali esse habere partes extra partes. Hæc autem obiectio soluenda est Vasquez qui materiam primam absq[ue] quantitate ait esse totam in toto, & Thomistarum nonnullis qui animas brutorum dicunt esse indiuisibiles, negant tamen esse spirituales. Dices pars orientalis atomi A non est realiter occidentalis B ergo possunt separari. Respondeo partem occidentalem, & orientalem esse realiter idem, connotatiuè verò differre. CAPVT SEXTVM. Responsa ad Obiectiones singularem atomorum doctrinam impugnantes. Mnes attingere difficultates non vacat neq[ue]; cui vacat potest, paucas ergo è potissimis quæ mihi occurrerunt delib[us]. Obiectio

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C.5. Objections against atoms. 217 OBJECTION XVII. Against the indivisibility of atoms. What is material exists in a material mode, that is, it has parts outside parts; but what has parts outside parts is divisible; therefore an atom exists in a material mode, and thus is divisible. I answer that the concept of materiality signifies two things: first, the demand of impenetrability through quantity; secondly, an essential order to something else, which will be as it were its perfective in the notion of a complete being or as its substrate; these two belong to atoms, namely the order to quantity and to the form of a mixture: therefore I deny that to exist in a material mode is to have parts outside parts. This objection must also be answered against Vasquez, who says that prime matter without quantity is wholly in the whole, and against some Thomists who say that the souls of brute animals are indivisible, yet deny that they are spiritual. You will say: the eastern part of atom A is not really the western part of B; therefore they can be separated. I answer that the western part and the eastern part are really the same, but differ conceptually. CHAPTER SIXTH. Responses to objections attacking the distinctive doctrine of atoms. It is not possible, nor is there time, to address all the difficulties; and he who has time may do so. Therefore I shall set out a few from among the principal ones that have occurred to me. Objection

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218 De Atomis. Disp. II. OBJECTIO I. Pro Aristotelis textu 66. 3. de cælo contra id quod diximus proposit. 26. tetraedra non posse replere locum. ME diu sequens ratiocinatio in errore cum Aristotele detinuit. Illę figurę replent locum quorum anguli simul iuncti faciunt angulos æquales quatuor rectis, arqui anguli tetraedrorum iuncti faciunt angulos sex quatuor rectis æquales, ergo replent locum. Probatur minor, sint sex triangula æquiangula, & æquilatera ABI, BIC, CID, DIE EIF, FIA, circa punctum I dico angulos sexilli puncto circumfusos esse æquales quatuor rectis, cum enim ex Eucl. l. 1. p. 32. Anguli tres cuiuslibet trianguli sint æquales duobus rectis, triangula autem AFI, ABI, BIC, & alia sunt æquian-gula per prop. 8. primi, quoniam per constructionem sunt æqui- latera, sequitur quod tres eorum anguli quomodolibet sumpti sunt æquales duobus rectis, ergo FIA, ALB, BIC, sunt æquales duobus rectis; Idem de alijs tribus FIE, EID, DIC, dictum esto; Ergo anguli sex circa punctum I cir- cum-

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218. On Atoms. Disp. II. OBJECTION I. Against Aristotle’s text 66. 3, On the Heavens, contrary to what we said in the proposed thesis. 26. That tetrahedra cannot fill space. This reasoning has long kept me, together with Aristotle, in error. Those figures fill space whose angles joined together make angles equal to four right angles; but the angles of tetrahedra joined together make angles of six right angles, which are equal to four right angles; therefore they fill space. The minor premise is proved thus: let there be six equiangular and equilateral triangles ABI, BIC, CID, DIE, EIF, FIA, around the point I. I say that the six angles surrounding that point are equal to four right angles, for since, from Euclid, Book I, Prop. 32, the three angles of any triangle are equal to two right angles, but the triangles AFI, ABI, BIC, and the others are equiangular by Prop. 8 of the first book, because by construction they are equilateral, it follows that any three of their angles taken together are equal to two right angles; therefore FIA, ALB, BIC are equal to two right angles. The same must be said of the other three, FIE, EID, DIC; therefore the six angles around the point I sur-

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C.6. Obiectiones contra atomos. 219 cum fusi sunt æquales quatuor rectis, ergo implent locum quod erat demonstrandum. Excitentur itaq[ue] in illis basibus tetraedra sex, replebunt locum, & si hiatus adsint, cum oriantur à tetraedris, alijs similiter positis tetraedris implebuntur, fietq[ue] figura ex tetraedris solida, quod erat pro Aristotele de- monstrandum. Et confirmatur à constructione Octaedri, sienim delinees octo triangula æquiangula & æquilatera, deinde complices & vniæ habebis confectum octaedrum regulare: ergo optimè censuit Aristoteles tetraedris locum repleri. Respondeo ad hoc argumentum cuius fallacia me aliquam diù fascinauit, concedendo triangula sex circa punctum 1 es- se æqualia quatuor rectis, & replere locum planum quod ma- nifestè demonstrauit Aduersarius; at nego superpositis in illis triangulis tanquam in sua basi tetraedris sex, ijs repleri locum solidum de quo hic sermo est, sit enim. PROPOSITIO XL. Tetraedra non replent locum solidum. Excitentur enim tetraedra in illis planis: Dico primò eorum verticem futuram in punctis sublimibus G.H.L.M.N. O. quoniam enim æqui, distant anguli basis ab angulo verticis sequitur quod in basis ad horizontem constitutæ centrum oculo in axe posito debet proijci vertex, axis enim est linea recta, ergo eius extrema obumbrant media, debet itaq[ue] tota axis in puncto H colligi: quod cum sit in diametrorum AQ, BP. RI, intersectione sequitur esse centrum basis, confirmaturq[ue] ex propos. 4. 1. 4. Euclidis. Dico secundò inter tetraedra excitata super planis illis sex futuros hiatus seu vacuum cuius mensura sunt lineæ GH, HL, LM, MN, NO, OG, quos hiatus alijs tetrae- dris

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C.6. Objections against atoms. 219 when they are melted down, they are equal to four right angles, therefore they fill space, which was to be demonstrated. Let six tetrahedra therefore be raised on those bases; they will fill the space, and if gaps are present, since they arise from the tetrahedra, they will likewise be filled by other tetrahedra similarly placed, and thus a solid figure will be made from tetrahedra, which was to be demonstrated on Aristotle’s behalf. And this is confirmed by the construction of the octahedron: for if you draw eight equiangular and equilateral triangles, then fold them together and join them, you will have completed a regular octahedron. Therefore Aristotle judged very well that space is filled by tetrahedra. I answer this argument, the fallacy of which had long fascinated me, by conceding that six triangles around point 1 are equal to four right angles and fill the plane, as my opponent clearly demonstrated; but I deny that when tetrahedra are placed upon those triangles as upon their base, six in number, they fill the solid space of which we are here speaking. Let it be so. PROPOSITION XL. Tetrahedra do not fill solid space. For let tetrahedra be raised on those planes: I say first that their vertex will be in the elevated points G, H, L, M, N, O. For since the angles of the base are equally distant from the angle of the vertex, it follows that, the base being set horizontal, the vertex must be projected into the center, with the axis placed in the eye; for the axis is a straight line, therefore its ends shade its middle, so the whole axis must be gathered into point H: and since this lies at the intersection of the diameters AQ, BP, RI, it follows that it is the center of the base, and this is confirmed from proposition 4 of book 4 of Euclid. I say secondly that between the tetrahedra raised upon those six planes there will be gaps or voids, whose measure is the lines GH, HL, LM, MN, NO, OG, which gaps by other tetrahedra

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De Atomis. Disp. II. 220 dris impleri posse nego. Cum enim punctu H in vertice axis distet à puncto H in basi per totam rectam IR, quæ triangulum AIB bifariam secat per 9.1. sitq[ue] recta IR perpendicularis, & vera mensura profunditatis vacui, quod inter tetraedra dehiscit ex coroll. 19.1. sequitur, quod in tetraedris quæ vacuum illud replebunt, linea IR profunditas vacui, minor erit quam linea GH latus tetraedri. In triangulo enim æquilatero latus est maius sua diametro per prop. 1. & 9. primi: atqui hoc fallum est. Dico enim tertiò lineam IR maiorem esse quam linea HG. cum enim linea HG & HI sint eiusdem circuli semidiametri per 15. quart. sequitur per definit. 15. primi esse æquales vt pote ab eodem centro H ductæ, erit ergo excessus lineæ IR supra lineam HG, segmentum HR, ac proinde linea IR maior est quam linea HG: quod erat demonstrandum. Dico autem quartò hos hiatus consequenter repleri non posse tetraedris, quia cum profunditas sit maior quâ latitudo, & logitudo, sequitur nullo modo posse constitui tetraedru sed debebit

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On Atoms. Dis. II. 220 I deny that they can be filled by rectangles. For since the point H in the vertex of the axis is distant from the point H in the base by the whole straight line IR, which cuts the triangle AIB in half according to 9.1, and the line IR is perpendicular, and the true measure of the depth of the void, which opens between the tetrahedra, follows from corollary 19.1, it follows that in the tetrahedra which will fill that void, the line IR, the depth of the void, will be less than the line GH, the side of the tetrahedron. For in an equilateral triangle the side is greater than its diameter by proposition 1 and 9 of the first book: but this is false. For I say thirdly that the line IR is greater than the line HG. For since the lines HG and HI are semidiameters of the same circle, by 15.4, it follows by definition 15 of the first book that they are equal, as drawn from the same center H; therefore the excess of the line IR over the line HG is the segment HR, and consequently the line IR is greater than the line HG: which was to be demonstrated. I say moreover fourthly that these gaps cannot consequently be filled by tetrahedra, because since the depth is greater than the width and length, it follows that in no way can a tetrahedron be formed, but it will have to

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Cap. 6. Obiectiones contra atomos 221 debebit impleri hoc vacuum pyramidæ irregulari cuius duæ facies erunt triangula æquilatera, & æquiangula, aliæ autem duæ extra figuram visendæ erunt Isosceles. Ergo benè notauimus Aristotelem tetraedris locum solidum repleri non posse, quod autem ipsum se fellit est omissa tetraedrorum inclinatio ad se inuicem, quâ angustius sursum spatium faciunt, na[m] angulum exteriorem inter se relinquunt 60. gradibus minorem, ergo te- traedro non potest repleri, quod vides delineatum circulo HGONML, & tamen deberet idem circulus sex capere tetraedra sex hiatibus replendis, quod fieri nequit, cum profun- ditas sit maior latitudine. Ad Confirmationem, Respondeo, Eam sapere crassam in mathesi ignorantiam. octaedri enim centrum est in superficie quadrati, ergo pyramides octaedri non sunt tetraedra, sed fa- ciunt in centro angulos quatuor rectos, angulus autem tetrae- dri quilibet deficit mediâ sui parte à recto. Vide sis Euclidem lib. 12. 13. 14. & 15. vbi agit de corporibus solidis. Ad- duximus autem ex his libris aliam demonstrationem pag. 137. sed quod ea non iret obuiam difficultati sed thesim tantum probaret placuit hanc faciliorem, & ex rudioribus principijs mathematicis construere. Ex quibus mirari satis no[n] possum Alcinoum eò impesisse vt diceret ex quinque corporibus solidis Platonis omne vacuum repleri ita vt nihil inanis esset in natura. sic enim ille c. 13. Isa- goges ad doctrinam Platonis, His cum ab ipso Deo figuris (cu- bo, octaedro, icosaedro, tetraedro, dodecaedro) esset mate- ries formata, primò quidem rudibus vestigijs absq[ue]; ordine moueba- tur, donec in ordinem reducta est ab eo, singulaq[ue]; inter se apta con- iuncta sunt proportione, & composita. Neque tamen hæc loco discreta manent sed, & ipsa in motu sunt perpetuo, eundemq[ue], materiæ affe- runt, ab ambitu enim mundi constricta pelluntur, atq[ue] alternis ipsa pulsibus

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Cap. 6. Objections against atoms 221 it ought to be filled, this void, by an irregular pyramid whose two faces will be equilateral triangles, and equiangular, but the other two will be seen outside the figure as isosceles. Therefore we have rightly noted that Aristotle could not think that the solid place is filled by tetrahedra, which indeed deceives him is that the inclination of the tetrahedra toward each other is omitted, by which they make the space narrower above, for they leave a[n] outer angle between themselves 60 degrees smaller; therefore it cannot be filled by a tetrahedron, which you see drawn by the circle HGONML, and yet that same circle ought to hold six tetrahedra for filling six gaps, which cannot happen, since the depth is greater than the breadth. In confirmation, I reply that it savors of gross ignorance in mathematics. For the center of the octahedron is in the surface of the square, therefore the pyramids of the octahedron are not tetrahedra, but make at the center four right angles; but any angle of the tetrahedron falls short by half of itself from a right angle. See, please, Euclid, books 12, 13, 14, and 15, where he treats of solid bodies. We have also brought from these books another demonstration on page 137, but since it did not meet the difficulty, but only proved the thesis, it seemed good to construct this one more easily, and from more elementary mathematical principles. From which things I cannot sufficiently wonder that Alcinous pressed so far as to say that from the five solid bodies of Plato every void is filled, so that nothing empty would be in nature. For thus he says in ch. 13 of the Isagoge to the doctrine of Plato: These figures having been formed by God himself (cube, octahedron, icosahedron, tetrahedron, dodecahedron), matter was at first moved without order, with rough traces, until it was brought back into order by him, and the individual parts were fitted together with proportion, and composed. Nor do these remain separated in place, but are themselves in perpetual motion, and bring the same thing to matter; for being constrained by the circumference of the world they are driven out, and by turns they themselves with blows

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De Atomis. Disp. II. pulsibus agitata feruntur, tenua semper in regione solidorum. Quæ de causa nihil omnino inane relinquitur, nihil corporis vacuum, atq[ue] in illis inæqualitas permanens concussionem affert. Ab ijs enim mate- ria, ista vicissim à materia agitantur. Equidem terra quam cubum facit locum replebit, at tetraedra iuncta cubis locum non replent, nec cubi iuncti octaedris, nec tetraedra iuncta tetraedris, nec icosaedris, aut dodecaedris sed ex omnibus istis figuris locum replent cubi quidem per se, octaedra verò iuncta tetraedris, reliquæ figuræ vacuum relinquunt, ergo malè infert Alcinous ex istis figuris nihil vacui in mundo relinqui. Apuleius verò de quo superius propos. 26. nihil de dodecaedro di- xit: quâ tamen figurâ plurimùm vsum fuisse Deum recenset Alcinous. Dodecaedron autem ad vniuersi constitutionem adhibuit Deus: vnde animalium formæ duodecim in Zodiaco conspicuntur quorum quodlibet in partes triginta secatur. Similiter in dodecaedro quod pentagonis duodecim constat, si in triangulos quinq[ue]; quidlibet eor- um diuiseris sex insunt singulis trianguli (id est in vnoquoq[ue] trian- gulo sex scalena inuenies) atq[ue] in tota dodecaedro trecenti sexaginta reperiuntur trianguli quot in Zodiaco sectiones sunt. At libra certè animal non est, illa autem reflectio Alcinoi pro circuli Zodiaci diuisione est ingeniosa, & acurata nam suut Pentagona 12. quæ diuisa in 5. triangulos, faciunt 60. triangulos, quorum quilibet diuisus in 6. exprimit numerum 360. vt patet ex hac multiplicatione numerorum. Cætera Alcinoi sensa ex plicuimus loco citato, nisi quod ipse subdit pyramida lem figuram igni conuenire quod melius diuidat, & sit rarior vt pote minoris areæ. De sphærica autem figurâ non meminit. Rectè itaq[ue] Platonem, Aristotelemq[ue] in figuris locum replentibus reiecimus, & obiectionem diluimus quod erat faciendum. Obiectio

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On Atoms. Disputation II. driven by impulses, they are carried on, always in the region of solids. For this reason nothing altogether empty is left, nothing void of body, and in those things a permanent inequality brings about concussion. For by these matter is agitated, and in turn these are agitated by matter. Indeed earth, insofar as it makes a cube, will fill a place, but tetrahedra joined to cubes do not fill a place, nor cubes joined to octahedra, nor tetrahedra joined to tetrahedra, nor icosahedra or dodecahedra; but of all these figures, cubes indeed by themselves fill a place, octahedra joined to tetrahedra, however, the rest of the figures leave a void. Therefore Alcinous wrongly infers from these figures that nothing of the void is left in the world. Apuleius, however, about whom above, proposition 26, said nothing of the dodecahedron; yet Alcinous notes that God made abundant use of that figure. But God employed the dodecahedron for the constitution of the universe: hence the twelve forms of animals are seen in the Zodiac, each of which is divided into thirty parts. Similarly in the dodecahedron, which consists of twelve pentagons, if you divide any one of them into five triangles, there are six in each triangle, that is, in every triangle you will find six scalene triangles; and throughout the whole dodecahedron there are found three hundred and sixty triangles, as many as there are divisions in the Zodiac. But a balance surely is not an animal; that reflection of Alcinous for the division of the Zodiacal circle is ingenious and accurate, for there are twelve pentagons, which divided into five triangles make sixty triangles, each of which divided into six expresses the number 360, as is clear from this multiplication of numbers. We have explained the rest of Alcinous’ views in the cited place, except that he adds that the pyramidal figure is suited to fire because it divides better and is rarer, as being of smaller area. But he makes no mention of the spherical figure. Therefore we rightly rejected Plato and Aristotle in the figures that fill a place, and resolved the objection, which was the thing that had to be done. Objection

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C.6. Obiectiones contra atomos. 223 OBJECTION II. De Atomis, & vacuo Democriti. Obijcies Democritum admisisse vacuum cum atomis, vnde dicebat apud Gal. I. de elem. nihil esse absolutum nisi atomos, & vacuum. Respondeo atomos à nobis admitti itemq; vacuum, siue inane quod Democrito nihil aliud fuit quam aer, duplicis aute[m] generis vacuum ipse appellabat, alterum quod nobis est imaginarium spatium, alterum verò inane siue aerem, vbi tanquam in medio indifferenti omnes qualitates se se manifestarent, quapropter Aristoteles libro 2. de anima textus 74. Non enim benè hoc dicit Democritus, opinatus si fieret vacuum quod medium est, perspici vtiq[ue] exquisitè etiam si formica in cælo esset; ergo duplex fuit vacuum Democriti, alterum extra mundum, quo distarent mundi à se inuicem, alteru[m] quod in singulis mundis esset, & primum quidem vacuum imaginarium, secundum reale appellauit, vnde dicebat atomum dari, & vacuum, per vacuum intelligens medium in quo atomi mouerentur. Confirmatur hæc doctrina pag. 25. vbi distinctio fit de magno, & paruo inani ex Virgilio, item Claudiano qui vacuum, & inane distinguit ibid. deinde pag. 23. authoritate Galeni ibi adductâ, præterea totà proposit. 13 disp. 1. conneniunt enim aeri ea quæ vacuo adscribit Democritus, par omnium in aere motus naturalis, omnium qualitatum primarum, & secundarum carentia, & alia quæ de aere diximus. OBJECTION III. De mixtionis imperfectione. SI atomis suas habent dimensiones non miscentur perfectè, sed omnia sunt aggregatum per accidens, nam atomorum medulla manet illibata. P Re-

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C.6. Objections against atoms. 223 OBJECTION II. On Democritus’s atoms and void. You will object that Democritus admitted a vacuum together with atoms, whence he said in Gal. I. de elem. that nothing is absolute except atoms and vacuum. I answer that atoms are admitted by us, and likewise vacuum, or the void, which for Democritus was nothing other than air. Yet he called vacuum of two kinds: one, what for us is imaginary space; the other, truly void, or air, where, as in an indifferent medium, all qualities would manifest themselves; for which reason Aristotle, book 2. de anima, text 74, says: “For Democritus does not say this well, thinking that if the medium were made void, one would certainly see even an ant in the sky exactly.” Therefore Democritus’s vacuum was twofold: one outside the world, by which the worlds would be separated from one another, and the other in the individual worlds themselves; and the first he called imaginary vacuum, the second real vacuum. Hence he said that an atom exists, and vacuum, by vacuum understanding the medium in which atoms moved. This doctrine is confirmed on page 25, where a distinction is made between the great and the small void from Virgil, likewise Claudian, who distinguishes vacuum and void there; then on page 23, with the authority of Galen cited there; moreover, throughout proposition 13 of disp. 1. For the things which Democritus attributes to vacuum agree with air: equal natural motion of all things in air, absence of all primary and secondary qualities, and other things which we have said about air. OBJECTION III. On the imperfection of mixture. If the atoms have their own dimensions, they do not mix perfectly, but everything is an accidental aggregate, for the core of the atoms remains untouched. P Re-

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De Atomis. Disp. II. Respondeo ex definitione temperamenti adducta secundum Auicennam l. 1. Fen 1. doct. 3 c. 1. sufficere ad mixtionem perfectam vt elementa sint diuisa in minima siuè atomos, ità vt si de quibusdam multùm capias de alijs plurimum habere necesse sit, & reuerà mixtionis definitio pro nobis est, mixtio enim est miscibilium alteratorum vnio, miscibilia sunt atomi quæ alterantur, & vniuntur. OBJECTIO IV. De motu, tempore, rarefactione condensatione, intensione, et remissione. M Vltra difficillima explicatu contingunt in motu admissis semel atomis, tùm in causis, tùm in temporum commé- suratione, proportionibus motuum, & alijs quæ ità non pos- sunt exponi sicuti admissa continui diuisibilitate, motus enim est ens successium, ac proinde diuisibile in infinitum, at motus & spatium tempusq[ue] sunt analoga. Deinde quomodo poterit fieri rarefactio vel condensatio cum atomi, nec crescant, nec minuantur? Tùm quot in alijs tractatibus philosophicis dif- ficultates occurrent? faciliùs itaq[ue] omnia per partium diuisi- bilitatem intelliguntur. Respondeo his difficultatibus tanquam consequentijs à me fuisse dicatam disput. sequentem, in qua omnia facilè, & con- sequenter juxta Democritum exponere sum conatus. DISPV.

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On Atoms. Disp. II. I reply that from the definition of temperament brought forward according to Avicenna, l. 1, Fen. 1, doct. 3, c. 1, it is sufficient for a perfect mixture that the elements be divided into the smallest parts, or atoms, so that if from certain things you take much, from others it is necessary to have most; and indeed the definition of mixture is for us the mixture itself, for mixture is the union of the altered things that are mixable; the mixable things are the atoms which are altered and united. OBJECTIO IV. On motion, time, rarefaction, condensation, intensification, and remission. M. Far more difficult things occur to explain in motion once atoms have been admitted, both in causes and in the measurement of times, the proportions of motions, and other matters which cannot be explained in that way as when the divisibility of the continuum is admitted; for motion is a being of succession, and therefore divisible to infinity, but motion and space and time are analogous. Then how can rarefaction or condensation take place when atoms neither grow nor diminish? And how many difficulties will occur in other philosophical treatises? Therefore everything is more easily understood through the divisibility of parts. I reply that these difficulties, as consequences, were dealt with by me in the following disputation, in which I have tried to explain everything easily and consequently according to Democritus. DISPV.

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Consequentiæ DISPVTATIO III. De consequentijs præcipuis ex Democriti philosophia deductis. Vmea quæ de rerum coagmentatione instituitur quæstionullo modo possit enucleari quin de motu locali tractetur deq[ue] rarefactione, & alteratio- ne, has tres difficultates paucis enodare iuxta De- mocritum volo, & tandem quarto ingeniosam eius de coloribus sententiam ex atomorum mixtione elicitam aperire probareq[ue] tentabo. DEFINITIONS. I. Motus localis est actus entis in potentia prout in poten- tia in ordine ad locum, vel spatium. II. Rarefactio est acquisitio maioris extensionis, veloc cu- patio maioris loci intrinseci, vt si palmus solidus extendatur in duos palmos solidos. III. Condensatio est restrictio corporis ad minorem locu[m], vt si palmus solidus restringatur in semipalimum solidum. IV. Figura regularis est ea quæ lateribus æqualibus con- stat, vel cuius omnes partes æqualiter distant à centro vt in cir- culo contingit. V. Figura irregularis est ea cuius latera sunt inæqualia vel cuius partes inæqualiter distant à centro. VI. Grauitas est virtus motrix deorsum tantùm, leuitas est virtus motrix sursum tantùm, hæc autem particula tamùm diligenter notanda. VII. Rarefactio impropriè dicta est occupatio maioris loci P 2 ob im-

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Consequences DISPUTATION III. On the chief consequences drawn from the philosophy of Democritus. My present inquiry into the composition of things cannot in any way be fully explained unless one also treats of local motion and of rarefaction and alteration; therefore I wish briefly to unravel these three difficulties according to Democritus, and finally I shall attempt to explain and prove his ingenious opinion about colors, derived from the mixture of atoms. DEFINITIONS. I. Local motion is the act of a being in potency, as it is in potency, in relation to place, or space. II. Rarefaction is the acquisition of greater extension, or the desire for a greater inner space, as when one solid palm is extended into two solid palms. III. Condensation is the restriction of a body to a smaller place, as when one solid palm is reduced to half a solid palm. IV. A regular figure is one which consists of equal sides, or one all of whose parts are equally distant from the center, as happens in a circle. V. An irregular figure is one whose sides are unequal, or whose parts are unequally distant from the center. VI. Gravity is a moving power downward only; lightness is a moving power upward only; but this point must be carefully noted. VII. Rarefaction, improperly so called, is the occupation of a greater place P 2 ob im-

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De Atomis. Disp. III. ob immixtionem alterius corporis vel partium disperionem, vt palmus aquæ addito palmo aeris occupabit duos palmos, & puluis dispersus totum cubiculum implet, collectus verò pugno coercetur. VIII. Densum illud est quod paucissimos habet poros, vel quod nullos, vel quod habet paucos eosq; angustissimos. Rarum è contra quod multos, eosq; latos, & patentes. IX. Lux, & lumen idem sunt apud me: quæ vocabula magnà religione ab alijs distingui authoribus notum est. PRINCIPIA. I. Omne agens debet continere effectum suum vel formaliter vel eminenter hoc: est, debet habere vel eam qualitatem quam producit, vel aliquam quæ sit præstantiæ cuiusdam ordinisq; vniuersalioris sed fecundi. II. Grauitas, & leuitas sunt contraria. III. Motus, locus, tempus sunt analoga, hoc est, proportionalia nulla enim est pars motus cui pars spatij temporisque non respondeat. IV. Mobilia quæ naturaliter mouëtur, ad locu que appetut illuc tédût quâ fieri potest breuissimè, & facillimè, natura eni compendiosa est suaq; per lineas breuissimas omnia mouet. V. Non datur vacuum in natura. VI. Non datur penetratio naturalis, hoc est, vt duo corpora in eodem loco esse possint. VII. Natura si non interturbetur in suis operibus ordinis est obseruantissima: opus enim naturæ opus intelligentiæ, princeps verò intelligentiæ scopus est ordo. VIII. Non dantur motus, in instanti metaphysico, siue in illo quod respondet puto mathematico, atq; hoc principiu[m] non modo de motu locali, verum etiam de alteratione propriè dicta, vbi præsertim datur reactio, est intelligendum. IX.

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On Atoms. Disp. III. from the admixture of another body or the scattering of its parts, as a palm of water with a palm of air added will occupy two palms, and dust scattered fills the whole room, but when collected it is held together by the fist. VIII. That is dense which has very few pores, or none, or which has few and very narrow ones. Rare, on the contrary, is that which has many, and those broad and open. IX. Light and lumen are the same thing for me: which words it is known are distinguished by other authors with great scruple. PRINCIPLES. I. Every agent ought to contain its effect either formally or eminently; that is, it ought to have either that quality which it produces, or some one that is of a more excellent and more universal yet fruitful order. II. Gravity and levity are contraries. III. Motion, place, time are analogous, that is, proportional; for there is no part of motion to which some part of space and time does not correspond. IV. Bodies which are moved naturally, in that place to which they tend, go there as briefly and as easily as possible, for nature is thriftily compendious and moves all things by the shortest lines. V. There is no vacuum in nature. VI. There is no natural penetration, that is, that two bodies should be able to be in the same place. VII. If nature is not disturbed in its operations, it is most observant of order: for the work of nature is the work of intelligence, and the chief aim of intelligence is order. VIII. There are no motions in a metaphysical instant, or in that which corresponds to the mathematical point, and this principle must be understood not only of local motion, but also of alteration properly so called, where especially reaction is present. IX.

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Consequentia. 227 IX. Inclinatio ad locum deorsum æqualis est resistentiæ ad morum sursum. X. Si aliquibus delatis differat aliquod non delatum, non delatum in contrarium ferri putabitur. Est propositio 54. perspectiuæ Euclidis. XI. Æqua magnitudine corpora sunt quæ loca replent æqua. Est primùm principium tractatus Euclidis de leui, & ponderoso cuius fragmentum vidi ab Io: Heruagio editum anno 1546. Basileæ. XII. Motus communes non sunt sensibiles. XIII. Agens necessarium omnibus ad agendum prærequisitis necessariò agit. XIV. Totum hoc vniuersum à Deo creatum est plenu[m], eaq[ue] instructum quantitate quę toti singulisq[ue] corporibus sufficeret. XV. Corpora pro varia suarum partium contemplatione exigunt diuersimodè esse in loco vt patet in metallis fusis & solidis, in luto & terra sicca, in glacie & aqua fluente actu. XVI. Si non datur condensatio neq[ue]; etiam dabitur rarefactio, & si non datur rarefactio neq[ue]; etiam condensatio, & vno horum ad misso aliud sequi necesse est. XVII. Res omnes visibiles sub angulis tantùm percipiuntur, quos emissis à se radijs constituunt in oculo, & quo ampliores sunt anguli eo maius videtur obiectum, quo minores minus &c. Euclides in opticis ità pronuntiauit, nisi quod ab oculo emissiones fieri non autem ab obiecto fabulabatur. POSTVLA TA. I. Statuimus quolibet motu dato posse dari velociorem. II. Supponimus quod experiètià manifestu[m] et dari impetu[m]. III. Qualibet datâ lineâ potest dari maior, & qualibet datâ figurà potest dari maior. IV. Concedatur dari colores reales non autem apparentes tantùm. P 3 CAPVT

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Consequences. 227 IX. The inclination toward the place downward is equal to the resistance to motion upward. X. If, among things carried away, one thing differs from one not carried away, the not carried away thing shall be thought to be carried in the opposite direction. This is proposition 54 of Euclid’s perspective. XI. Bodies of equal size are those which fill equal places. This is the first principle of Euclid’s treatise On the Light and Heavy, a fragment of which I saw published by Io: Heruagius at Basel in the year 1546. XII. Common motions are not perceptible. XIII. A necessary agent, all things prerequisite for acting being present, necessarily acts. XIV. The whole of this universe was created by God full, and furnished with such quantity as would suffice for all bodies individually and collectively. XV. Bodies, according to the varying consideration of their parts, require to be in place in different ways, as is evident in fused and solid metals, in mud and dry earth, in ice and flowing water actually. XVI. If condensation is not given, rarefaction will not be given either; and if rarefaction is not given, condensation will not be given either; and with one of these omitted, the other must follow. XVII. All visible things are perceived only under angles, which the rays emitted from them make in the eye, and the greater the angles, the larger the object appears; the smaller, the smaller, etc. Euclid stated this in the Optics, except that he claimed the emissions come from the eye and not from the object. POSTULATES. I. We establish that, for any given motion, a faster one can be given. II. We suppose, as experience makes manifest, that there is impulse. III. For any given line, a greater one can be given, and for any given figure, a greater one can be given. IV. Let it be granted that real colors are given, not merely apparent ones. P 3 CHAPTER

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CAPVT PRIMVM. De motu locali atomorum. HIC quantum sat est ad Democriti doctrinam percipi- endam breuissimè me expedio, consistit autem difficul- tas quod in atomorum opinione successio perfecta negari de- bet alioqui motus erit diuisibilis in infinitum, ac proinde stabi- litis in continuo atomis, ijsdem difficultatibus iactabimur quæ peripateticos absorbent, neque quidquam à nobis erit factum cum spatium, & motus sint analoga ex princ. 3. PROPOSITIO XLII. Quamuis admitti debeat grauitas, & leuitas popularis, nihilominus tamen non datur grauitas neque leuitas strictè, & philosophicè dicta. Contendebat superius Abderites noster aerem neque leuem neque grauem esse, quæ ipsi etiam in esset indifferentia quamuis alia corpora grauia forent vel leuia, nunc omnibus naturæ corporibus eadem immunitas à grauitate, & leuitate propriè dicta concedenda est, & Probatur primò, grauitas est virtus motrix deorsum tâtùm, leuitas virtus motrix sursum tantùm, sed nullu[m] est corpus quod naturaliter non habeat alias lationes ergo nullum corpus gra- ue est vel leue propriè loquendo, maior à nemine negatur cum sit definitio legitima, probatur minor Primò, in pyrobolis rotatis, ignis nullo impetu sibi exterius impresso mouetur circulariter à se ipso, sed motus circularis est compositus ex omnibus lationibus, parsenim circuli quædam ascendit, alia descendit, ferunturq[ue]; in transuerium aliæ, ergo ignis

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CHAPTER ONE. On the local motion of atoms. Here I shall briefly set myself free, as far as is enough, for understanding Democritus’ doctrine; but the difficulty lies in this, that in the opinion of atoms perfect succession must be denied, otherwise motion will be divisible to infinity, and thus, if rest is established in continuous atoms, we shall be entangled in the same difficulties that overwhelm the Peripatetics, nor will anything have been done by us, since space and motion are analogous, from principle 3. PROPOSITION XLII. Although popular gravity and lightness must be admitted, nevertheless there is no gravity nor lightness strictly and philosophically speaking. Our Abderite above contended that air is neither light nor heavy, that there was in it even an indifference, although other bodies were heavy or light; now the same immunity from gravity and lightness, properly so called, must be granted to all bodies of nature, and First it is proved: gravity is a moving power downward only, lightness a moving power upward only; but there is no body that does not naturally have other motions; therefore no body is heavy or light in the proper sense. The major premise is not denied by anyone, since it is a legitimate definition; the minor is proved First, in rotating pyroboles, fire is moved circularly by itself with no external impulse impressed upon it; but circular motion is composed of all motions, for one part of the circle ascends, another descends, and they are carried sideways as well, therefore fire

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C. 1. De motu locali atomorum. 229 ignis habet vim se se mouendi per omnes lationes, vnde neque grauis est neque leuis est simpliciter. Respondit primæ notæ philosophus, hunc motum esse di- rectum ab arte, neque de natura rerum ab artificialibus dedu- cenda argumenta, cum ars naturæ proprietatibus cæcisq[ue] im- petibus abutatur, vt nautæ qui obliquè ventum sibi contra- rium excipiunt illoq[ue]; ad institutam nauigationem promouen- dam vti norunt. Sed contra. Ars dirigit naturam tantùm, ergo nihil naturæ addit, tem- perat enim moderaturq[ue]; eius vires, neque vnquam nautica contrario vento vti potest, sed tantùm lateralibus, & obliquis: & quamuis medicus arte maximà medicamentum calidum componat illo sanè refrigerabit nunquam: hic autem ignis à figura tantùm extrinseca determinatus circulariter fertur, de- terminatio autem est conditio extrinseca quæ supponit virtu- tem in subiecto, vt calcar vim currendi in equo. Probatur secundò ex p. 1. Causa principalis debet cōtinere effectum suum vel formaliter, vel eminenter, sed ignis est cau- sa huius lationis ergo debet illam continere vel formaliter vel eminenter, vnde leuis non est simpliciter quia leuitas est virtus motrix sursum tantùm. Probatur tertiò. Omne corpus naturale est productium impetus, ergo nullum corpus naturale est graue vel leue; Pro- bat antecedens inductione: terra enim vel saxum aut lignum de orsum cadens colligit impetum secundum quem auget mo- tum; hinc variè subiecta ligna atteruntur pro distantia casus, & quod deest in pondere reparatur impetu, qui pondere equi- ualet. Si enim corpus graue cadens è spatio cubitorum sex frangit asserem qui habet resistentiam vt tria, illud idem deci- dens ex alto in distantia cubitorum viginti franget asserem qui habebit resistentiam vt nouem circiter, hac vero de repelsunt exactæ P 4

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C. 1. On the local motion of atoms. 229 Fire has the power of moving itself through all motions, whence it is neither heavy nor light simply. The philosopher of the first note replied that this motion is directed by art, and that arguments about the nature of things are not to be drawn from artificial things, since art makes use of the properties of nature and of blind impulses, as sailors do, who receive a wind blowing obliquely against them and know how to use it to advance the intended voyage. But on the contrary. Art directs nature only; therefore it adds nothing to nature, for it tempers and moderates its powers, nor can nautical art ever make use of a contrary wind, but only of lateral and oblique ones; and although the physician, by great skill, compounds a hot medicine, that medicine will surely never cool him. But here fire, determined only by an extrinsic figure, is carried circularly; yet determination is an extrinsic condition which presupposes a virtue in the subject, as the spur presupposes the power of running in the horse. It is proved secondly from p. 1. The principal cause ought to contain its effect either formally or eminently; but fire is the cause of this motion, therefore it ought to contain it either formally or eminently, whence it is not simply light, because lightness is a motive power only upward. It is proved thirdly. Every natural body is productive of impetus; therefore no natural body is heavy or light. He proves the antecedent by induction: for earth, or stone, or wood falling downward gathers impetus, according to which it increases its motion; hence woods placed in various ways are worn away according to the distance of the fall, and what is lacking in weight is restored by impetus, which is equivalent to weight. For if a heavy body falling from a space of six cubits breaks a plank that has a resistance of three, that same body falling from a height of twenty cubits will break a plank that has a resistance of about nine; by this reply, however, the exact P 4

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exactè institui regule, quia licet corpora differenter expro- mant impulsionem in subjectam materiam, tamen æqualibus momentis per aerem tanquam per inane ferunrur: hinc Galilæus 1. de motu hanc habet propos. quâ momenta impetus quê mobile colligit explicat. Si aliquod mobile descendat, à puto quietis suæ, spatia in temporibus æqualibus peracta, eam inter se retinent rationem quam habent numeri impares ab unitate consequentes. Sint quatuor temporis partes notatè in linea AB quibus mobile O descendit per lineam CD, primè parti temporis respondet spatiu[m] 1. secundè parti téporis spatium 3. tertiæ parti temporis spatium 5. atq[ue] ità secundum istam motus accretione[m] mobile suum motum accelerat. Hæc tamen an ità se se habeant videbimus in Theorica militari lib. 1. sed enim certissimum est velociorem esse motu in fine quam in principio pro mobile descendentibus; quod medio impellenti assignare in crementum mihi pene ridiculum videtur cum aeris imbecillitas, & ad diuisionem indifferentia id abunde refellat: superest igitur vt dicantur mobilia impetum colligere. De aqua pariter aere, & igne dubium non est quin non impetum colligant modò, verùm etiam in alijs producant. Vt patet in tormento bellico alijsq[ue] infinitis, tùm naturæ, tùm artis experimentis. Omneitaq[ue] corpus naturale est productium impetus, quod erat antecedens probandum. Ad consequentiam accedo, ergo nullum corpus naturale est graue vel leue in rigore loquendo, probatur, quia impetus est

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exactly establish the rule, because although bodies differently impress the impulse upon the subject matter, nevertheless with equal moments they are carried through the air as through a void: hence Galileo in book 1 on motion has this proposition, by which he explains the moments of impetus which the moving body gathers. If any moving body descends from, I suppose, a state of rest, the spaces covered in equal times retain among themselves the same ratio that odd numbers following unity bear to one another. Let four parts of time be marked on line AB, in which the body O descends through line CD; to the first part of time corresponds a space of 1, to the second part of time a space of 3, to the third part of time a space of 5, and thus according to this increase of motion the moving body accelerates its motion. Whether these things are really so we shall see in the Theorica militaris, book 1; but it is most certain that the motion is faster at the end than at the beginning for descending bodies; which to assign to the impelling medium as an increase seems to me almost ridiculous, since the weakness of the air and its indifference to division sufficiently refute this: it remains therefore that moving bodies are said to gather impetus. Concerning water, likewise air, and fire, there is no doubt that they not only gather impetus, but also produce it in others. As is evident in artillery and in countless other experiments, both of nature and of art. Therefore every natural body is productive of impetus, which was the antecedent thing to be proved. I proceed to the consequence; therefore no natural body is heavy or light in the strict sense of the word, it is proved, because impetus is

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C. I. De motu locali atomorum. 231 est qualitas motrix in omnem locum, & per omnem lationem prout determinatur ab extrinseco, ergo omne id quod illam qualitatem poterit producere neq[ue]; graue erit neq[ue]; leue: nam capax esset virtutis motricis amplioris ac proinde leuitas aut grauitas essent frustrà, deinde sibi esset contrarium producendo id quod sue[us] qualitati connaturali vim afferret, ergo produciuum impetus neq[ue]; graue est neq[ue]; leue formaliter ex princ. 1. Confirmatur propositio: sublato vno contrariorum tollitur etiam illud metaphysicè loquendo, sed non datur leuitas ergo neq[ue]; grauitas eius contrarium ex p. 2. prbatur minor, si leuitas esset in aliquo, esset tantum ratione elementi prædominantis, mixta enim vt ait Aristoteles mouentur ad motum elementi prædominantis: sed nullum mixtum mouetur sursum, quamuis in multis prædominetur ignis, ergo ignis non est leuis, ac proinde neq[ue]; vllum mixtum: piper, & euphorbium habent ignem prædominantem, cur ergo deorsum pari velocitate feruntur ac plumbum, nec pariter carbones accensi volant? Cur canis venenati morsus rabidus à spuma ignea sit, quæ tamen deorsum cadit? cùm ergo nullum corpus naturaliter sursum feratur, sequitur nullum esse leue simpliciter, ergo neq[ue]; graue. Dice vapores ascendere, & ignem. Resp. ascésum vaporum ideo fieri quia aqua vt sic dilatata rarefactaq[ue]; exigit ampliori loco diffundi, vnde latitudinem medij quærit, tamdiu ergo in altum abit, quamdiu reflectione, radiorum solis fauetur eius cursui, vt autem maxima sit hæc reflectio 52. nilliaria non excedit vt demonstrant ij qui de atmosphæra, refractionibus cælestibus, crepusculisq[ue]; disputarunt. Ignis autem necessariò ex ratione dissolutionis, debet cuspidem pyramidalem efformare, quia punctum perfectæ dissolutionis debet distare ab vltima superficie perfecti mixti, est autem mixtum perfectum candela, flamma verò est

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C. I. On the local motion of atoms. 231 It is a motive quality toward every place, and through every motion, insofar as it is determined from outside; therefore whatever can produce that quality is neither heavy nor light: for it would be capable of a greater motive power, and therefore lightness or heaviness would be useless; then it would be contrary to itself by producing that which would bring force against its connatural quality. Therefore the producer of impulse is formally neither heavy nor light, from principle 1. The proposition is confirmed: when one of opposites is removed, the other is also removed, metaphysically speaking; but lightness is not given, therefore neither is heaviness, its contrary, from p. 2. The minor is proved: if lightness were in anything, it would be only by reason of the predominating element. For mixed bodies, as Aristotle says, are moved according to the motion of the predominating element. But no mixed body is moved upward, although in many the fire predominates; therefore fire is not light, and consequently no mixed body is either: pepper and euphorbium have fire predominating, so why are they carried downward with the same speed as lead, and why do burning coals not fly upward in the same way? Why is the rabid foam of a venomous dog bite fiery, yet falls downward? Since therefore no body is naturally carried upward, it follows that there is nothing light simply speaking, and therefore nothing heavy either. You may say that vapors ascend, and fire as well. Reply: the ascent of vapors takes place because water, thus expanded and rarefied, seeks to be diffused in a larger space, whence it seeks the width of the medium; therefore it rises as long as the reflection of the sun’s rays favors its course. But for this reflection to be greatest, it does not exceed 52 miles, as those who have discussed the atmosphere, celestial refractions, and the twilight show. Fire, however, necessarily, from the nature of dissolution, must form a pointed pyramid, because the point of perfect dissolution must be distant from the outer surface of the perfect mixed body; but the perfect mixed body is a candle, whereas the flame is

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De Atomis. Disput. III. 232 est mixtum imperfectum à mixto ortu vi ignis, tendens ad dissolutionem, quæ fit cum in cuspide flammæ se se explicant, & expediunt ab alijs ignei spiritus, quæ vindicatio cum sensim fiat, ideo necesse est flammam ita efformari, vt ostendi pag. 179. vnde nullâ ratione probat hoc exemplum ignem esse leuem philosophicè, & strictè loquendo. Dices, curigitur sunt quædam corpora quæ perpetuò deorsum feruntur? Respondeo determinari ab extrinseco ad illum motum deorsum, a naturali scilicet mundi constitutione quæ exigit vt ea quæ partium suarum dispersione gaudent amplumq[ue]; spatium amant ferantur ad circumferentiam orbis, locum nempe capacissimum, quæ verò stringi angi[us]; cupiunt neq[ue]; suas partes ità dispergi patiuntur, angustias medij sibi deposcunt, vbi collectior locus suę inclinationi fauet; quo verò collectiores strictioresq[ue]; sunt mixti vel elementi partes eo magis ad centrum fori appetit; quem appetitum vulgus grauitatem, pondusq[ue]; vocat à quâ appellatione non recedam, dummodò de re confiter, scilicet non dari in illis corporibus virtutem motricem deorsum tantùm, sed dari virtutem in omnem locum, & per omnes lineas motricem, prout ab extrinseco determinabitur. Determinant autem quinque. Primò mundi constitutio ordoque, qui cum nil aliud sit quam natura quædam vniuersalis, sit vt leges naturæ in agendo seruet, quare motus à naturà precisi sè determinati sunt simplices, & ex princip. 4. breuissimi, hoc est perpendiculares, vel circulares vt in coelis. Secundò mouens aliquod per directionem cursus, vt in sclopis, & telis quæ manu iaciuntur. Tertiò spatium intermedium per retusione[m] stupefactionem, & refractionem de quibus in Theorica militari lib. 1. Theor. 7. Quartò corpus occurrens, & transitum in pediens, sitit sudum, solidum, vnitumq[ue]; per reflectionem, de

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On Atoms. Disput. III. 232 is an imperfect mixture arising from the force of fire, tending toward dissolution, which takes place when, at the tip of the flame, they unfold themselves, and release from the other parts the fiery spirits; and since this release takes place little by little, it is therefore necessary that the flame be so formed, as was shown on p. 179. Whence by no means does this example prove fire to be light philosophically, and strictly speaking. You will say, then, why are there certain bodies which are perpetually carried downward? I answer that they are determined from without to that downward motion, namely by the natural constitution of the world, which requires that those which delight in the dispersion of their parts and love ample space be carried to the circumference of the orbit, that is, to the most capacious place; but those which desire to be compressed and narrowed, and do not allow their parts to be dispersed in that way, seek the narrowness of the middle, where a more collected place favors their inclination; and the more collected and stricter the parts of a mixture or element are, the more they desire to move to the center; this desire the common people call heaviness, weight, from which name I shall not depart, provided the thing be acknowledged, namely that there is not in those bodies a moving power downward only, but that there is a power moving toward every place, and through all lines, insofar as it is determined from without. Now there are five determinants. First, the constitution and order of the world, which, since it is nothing other than a certain universal nature, is such that in acting it preserves the laws of nature; wherefore motions precisely determined by nature are simple, and, from principle 4, the shortest, that is, perpendicular, or circular, as in the heavens. Second, some mover by the direction of a course, as in guns and missiles that are thrown by hand. Third, the intermediate space by repulsion, stupification, and refraction, of which in the Military Theory, book 1, Theory 7. Fourth, a body encountered, and impeding the passage, if it be dry, solid, and united, by reflection, de

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C.1. De motu locali atomorum. de qua Ibid. Theor. 5. arena enim verbi gratia reflectendi globum capax non est, sed potius retundendi. Quintò mobilis ipsius compaginatio, figura, & pondus per receptionem, & implantationem impetus pertinaciorem: sunt enim quædam corpora impetui minus apta, sic carta non æquè proijci potest, ac lapis: figura verò determinat etiam impetu vt patet in proiectis volutatis, si enim circularem lapidem per planum directà volutatione proijcias in fine cursus efformabit lineam turbinatam. De implantatione, & concentratione impetus egi Theor. 3. lib. 1. atque hæc quinque, mundi ordo, mobilis status, corpus occurrens, spatium, & mouens impetum determinant. Vnde est maxima inter motus animalium, & inanimatorum differentia, animal enim determinatur ab intrinseco ad motum, ab extrinseco autem alia mixta. Ex quibus probabile fecimus quod quamuis detur grauitas, & leuitas ad vulgi sensum, nihilominus tamen non datur in rigore philosophico quod Democriti placitum erat asserendu[m]. PROPOSITIO XLIII. Motus localis est entitas permanens, tota simul in natura, & successiua in connotatione, cuius causa productrix est solus impetus. HIC potius anno to opiniones atomorum doctrinam consequentes quam vt eas fusè persequi velim: pro hac propositionis prima parte, quæ necessario admitti debet ab his qui atomis patrocinantur. Obseruo quatuor esse quæ abstrahunt ab omni reali extrinseco, numerum, dimensionem, motum, & durationem; numeri sunt merum opus intellectus omnes enim intelligimus in Dei infinitate, quà tamen nihil est simplicius aut magis numeri expers. Dimensiones mathematicæ abstrahunt ab omni spatio reali, intellectus enim in spatijs imaginarijs dimetietur, & deli-

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C.1. On the local motion of atoms. of which, see likewise Theor. 5. for sand, for example, is not capable of reflecting a ball, but rather of deadening it. Fifthly, the moving thing’s own composition, figure, and weight make it more tenacious by the reception and implantation of impulse; for there are certain bodies less suited to impulse, thus paper cannot be thrown as well as a stone: moreover, figure also determines the impulse, as is clear in spun projectiles; for if you throw a circular stone across a plane by direct rolling motion, at the end of its course it will form a spiraling line. I have spoken, Theor. 3, book 1, concerning the implantation and concentration of impulse; and these five things, the order of the world, the state of the moving thing, the body encountered, space, and the mover, determine impulse. Hence there is the greatest difference between the motions of animals and of inanimate things, for an animal is determined to motion from within, but from without, by other mixed things. From these considerations we made probable that although gravity and lightness are granted according to common usage, nevertheless in strict philosophy nothing is granted, as Democritus’ opinion claimed. PROPOSITION XLIII. Local motion is a permanent entity, all at once in nature, and successive in notation, whose productive cause is impulse alone. HERE rather than pursuing to a point the opinions following upon the doctrine of atoms, I wish not to treat them at length: for the first part of this proposition, which must necessarily be admitted by those who defend atoms. I observe that there are four things abstracted from every real extrinsic thing: number, dimension, motion, and duration; numbers are a mere work of the intellect, for we all understand them in God’s infinity, though nothing is simpler there, or more devoid of number. Mathematical dimensions abstract from all real space, for the intellect will measure in imaginary spaces, and deli-

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De Atomis. Disp. II. 234 delineabit Archimedis, Pappiq; inuenta. Tempus autem realiter sumptum nihil est aliud quam ipse motus quatenus habet partes priores, & posteriores; formaliter verò duratio abstrahit ab omni motu, cum etiam si quiescant celi, & omnis motus, anima immortalis perdurabit: Motus pariter ab omni spatio abstrahit etiamsi enim fieret in vacuo esset successiuus. Ex quibus patet quanta sit analogia inter ista vt diximus princip. 3 spatium est diuisibile in infinitum extrinsecè, & mathematicè vt supra diximus non autem physicè, pariter etiam tempus, & motus. His positis prima pars propositionis Probatur primò vt se habet spatium reale, ità & motus realis ex princ. 3. sed in spatio reali sunt atomi, ergo & in motu erunt atomi, sed atomi motus non possunt fingi animo quin intelligantur totæ simul, ergo datur motus totus simul, qui tamen erit successiuus in connotatione, seu extrinsecè penes satiu[m] mathematicu[m]. Sit, exempli gratià, atomus motus A—B. atomus spatij C—D virtus illa AB est tota simul, sed defert tamen mobile per spatium CD successiuè sicuti quipiam orator habet integrum conceptum totum simul, illum tamen successiuè tantum promit, atq; ità illi atomo motus A—B respondebit præcisè spatium C—D atomus integra, quà elapsà si impetus magis vigeat pro vna atomo restituet duas aut tres, deinde pro tribus, quatuor vel quinque, dùm tandem fatiscens impetus foecunditatis erit minoris, fit autem illa multiplicatio atomorum aut intensio motus per ordinationem atomorum in eadem parte, vt explicabimus cum de alteratione erit sermo. Probatur secundò illud non potest existere cuius nulla pars existit, sed motus successivi intrinsecè nulla pars existit, omnes enim sunt priores, & posteroses, & nulla est præsens, ergo motus successiuus intrinsecè est impossibilis. Scio responderi ab ad-

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On Atoms. Disp. II. 234 will delineate Archimedes’ and Pappus’ inventions. But time, taken in the real sense, is nothing else than motion itself, insofar as it has earlier and later parts; formally, however, duration abstracts from all motion, since even if the heavens and every motion should cease, the immortal soul will still endure: likewise motion abstracts from every space, for even if it were to occur in a vacuum it would still be successive. From these things it is clear how great is the analogy among these things, as we said in principle 3: space is divisible into infinity extrinsically and mathematically, as we said above, but not physically; likewise also time and motion. These points being laid down, the first part of the proposition is proved first thus: as real space is, so also real motion, from principle 3. But in real space there are atoms; therefore also in motion there will be atoms. Yet atoms of motion cannot be conceived in the mind unless they are understood all together, therefore there is given a motion all at once, which nevertheless will be successive in connotation, or extrinsically with respect to the mathematical subject. Let there be, for example, the atom of motion A—B. The atom of space C—D: that force AB is all at once, but it nevertheless carries the mobile through the space CD successively, just as some orator has a complete concept all at once, yet delivers it only successively; and thus to that atom of motion A—B will correspond exactly the space C—D, an entire atom, which once it has elapsed, if the impetus be more vigorous, for one atom it will restore two or three, then for three, four or five, until finally, when the impetus is exhausted, the power of fecundity will be less. But that multiplication of atoms, or intensification of motion, is brought about by the ordering of atoms in the same part, as we shall explain when the discussion turns to alteration. Secondly, it is proved thus: that cannot exist of which no part exists; but in successive motion intrinsically no part exists, for all are earlier and later, and none is present; therefore successive motion intrinsically is impossible. I know it will be answered by ad-

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C. I De motu locali atomorum. 235 ab aduersarijs fluenter, sed qui potest capere capiat, pauci enim intelligunt hunc fluxum existentem. Probat. tertio: si motus est diuisibilis physicè in infinitum tot erunt partes motus tardi quot velocis; ac duæ partes velocis coexistunt vni motus tardi, ergo vel ista erit permanens cu[m] existat in duobus temporibus, vel omnes motus sunt æquales aut in velocitate, & tarditate contra experientiam. Resp[ondeo]dèt primò, esse partes motus tardi permanentes fluêter; quasi dicerem canem esse rationabilem irrationabiliter, mustum esse humidum sicco modo. Resp[ondeo] secundò alij, omnes motus esse æquales in velocitate, differre autem quod in tardis idemtidem mobile quiescat, in- uelocibus verò pauciores sint pausæ minusq[ue]; diuturne[m]: Con- trà, eo enim puncto quo quiescit mobile vel id facit defectu virtutis vel spatij, sed spatiu[m] est vniforme, virtus autem adest, ergo non quiescit, agens enim necessarium omnibus ad agendum requisitis necessariò agit ex p. 13. Confirmatur tandem propositio Democriti, facilè enim explicantur omnes proprietates motus; primò successio in connotatione ad spatiu[m] mathematicum diuisibile in infinitum extrinsecè, ità & motus penes connotatum est diuisibilis in infinitum; secundò velocitas explicatur quod plures atomi impetus sint simul in eadem atomo mobilis, vel quod fortior vna adsit aliqua, vtroq[ue]; enim modo dici posset, sed multiplicatio atomorum mihi videtur Democrito potiùs adscribenda, quam specieru[m] tanta varietas in atomis 3. tarditas, quod pauciores sint atomi vel maior medij resistentia: regularitas, & irregularitas sumitur ab extrinseco dirigente, & determinante: comparabilitas à spatio mathematico, contrarietas, & subcontrarietas à termino ad quem &c. Plures sane luc difficultates tollendę essent, vt I. de genera- tione

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C. I. On the local motion of atoms. 235 from opponents fluently, but whoever can receive it, let him receive it, for few understand this existing flux. He proves it thirdly: if motion is physically divisible to infinity, there will be as many parts of slow motion as of fast; and two parts of fast motion coexist with one motion of slow motion, therefore either this will be permanent since it exists in two times, or all motions are equal either in speed and slowness, contrary to experience. I answer first, that the parts of slow motion are permanent in a flowing way; as if I were to say that a dog is rational in an irrational way, must is moist in a dry manner. I answer secondly, according to others, that all motions are equal in speed, but differ in this, that in slow motions the mobile now and then rests, while in swift motions there are fewer pauses and a shorter duration. Against this: for at the very point at which the mobile rests, it does so either from defect of power or of space, but space is uniform, and power is present; therefore it does not rest, for an agent that is necessary, with all things required for acting present, necessarily acts, from p. 13. Finally, the proposition of Democritus is confirmed, for all the properties of motion are easily explained: first, succession in relation to mathematical space, which is externally divisible into infinity, and thus motion, with respect to the correlated thing, is divisible into infinity; secondly, speed is explained by the fact that there are more atomic impulses at once in the same moving atom, or that one stronger one is present in some atom; indeed either way it could be said, but the multiplication of atoms seems to me to be more properly ascribed to Democritus than such great variety of species in atoms; thirdly, slowness, that there are fewer atoms or greater resistance of the medium; regularity and irregularity are taken from an external director and determiner; comparability from mathematical space; contrariety and subcontrariety from the term toward which, etc. Truly many other difficulties would have to be removed, such as I. on genera-

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tione atomorum. 2. de secu[n]ditate, & multiplicatione ipsarum. 3. an dentur diuersæ speciei? 4. an possit dari atomus inefficax hoc est quæ non moueat? 5. an possit dari motus vniformiter differmis? 6. an detur quies inter mouendum? 7. de interitu atomorum &c. R. ad primum generari atomos ab impetu, impetum autem à forma substantiali, quæ est principium motus. R. ad secundum foecunditatem sequi numerorum naturam, & multiplicari vt hydræ Herculis capita quando intenditur motus, imò omnis generis multiplicationem sequitur hæc foecunditas ità vt non modo per impares numeros, verùm etiam per quadratos, & cubos sæpe multiplicetur. R. ad tertium esse problema, inclinat ad negatiuam Democritus vt pote inutilem illam specierum multiplicationem censens. R. ad quartum non posse dari, sed impetum efficacem distingui ab inefficaci quod impetus efficax producat atomos motus, inefficax verò sit sterilis. R. ad tertium ad sensum dari posse motum vniformiter difformem non autem strictè loquendo, quia est semper aliquod spatium per quod motus est æqualis, & vniformis idq[ue] necessariò atomorum naturam sequitur. R. ad sextum non dari quietes in motu ob rationem supraallatam. R. ad septimum interire atomos quod scilicet cursu suo peracto, vel præpedito, detentoq[ue]; statim fatiscant, neque vlteriorum vim à causa productrice obtinuerunt. Essent etiam aliæ plurimæ grauissimæ quæstiones quas fusiùs prosequi nolo nec vacat. Secunda pars propositionis impetum esse vnicam vim motricem, probatur, quia eâ positâ reliquæ sunt inutiles, Impetu enim

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1. the generation of atoms. 2. their secularity and multiplication. 3. whether different species are given? 4. whether there can be an inefficacious atom, that is, one which does not move? 5. whether there can be uniformly dissimilar motion? 6. whether rest is given in the midst of motion? 7. concerning the destruction of atoms, etc. R. to the first: atoms are generated from impulse, and impulse from substantial form, which is the principle of motion. R. to the second: fecundity follows the nature of numbers, and is multiplied like the heads of the Hydra of Hercules when motion is intensified; indeed this fecundity follows every kind of multiplication, so that it is often multiplied not only by odd numbers, but also by squares and cubes. R. to the third: it is a problem; Democritus leans to the negative, judging that multiplication of species is useless. R. to the fourth: it cannot be given; rather, an efficacious impulse must be distinguished from an inefficacious one, because an efficacious impulse produces atoms of motion, whereas an inefficacious one is sterile. R. to the third: in a sense, uniformly dissimilar motion can be said to be given, but not strictly speaking, because there is always some span through which motion is equal and uniform, and this necessarily follows the nature of atoms. R. to the sixth: rests in motion are not given, for the reason stated above. R. to the seventh: atoms perish, namely, once their course has been completed, or impeded and detained; they at once fail, and they have not obtained their further force from the producing cause. There would also be many other very serious questions, which I do not wish to pursue more fully, nor have I time to do so. The second part of the proposition, that impulse is the single moving force, is proved because, once that is posited, the rest are useless. For by impulse...

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C.1. De motu locali atomorum. 237 sit quidquid per grauitatem, leuitaté, vim magneticâ alijsq[ue] vocabulis explicat Lycæum, & Academia: frustra enim sit per plura quod potest fieri per pauciora, natura autem nihil facit frustra. Motus ergo est entitas permanens &c. cuius causa productiua est impetus, quod nobis erat propositu[m] co[m]probare. OBICTIONES. Contra doctrinam Democriti de motu locali. OBIECTIO I. De motu tardissimo, et velocissimo. Si motus constat atomis, sequitur posse dari motum quo tardior dari no[n] possit, sit enim vnica atomus, cu[m] nihil minus dari possit sequitur motum fore tardissimum, quamuis adeò velox assignari non possit quin velocior in infinitum detur; sed huiuscemodi tarditatis extremitas videtur absurda cùm ex postulato 1. no[n] detur velocissimus, ergo, & opinio vnde sequitur. Respondeo hoc argumentum potuisse fieri contra atomos ipsas elementares, illis enim non potest dari corpus minus quamuis in infinitam pene molem possint excrescere ipsa elementa. Sicut arithmetica proportionalitas augetur in infinitum, sed in infinitum non decrescit. Itaq[ue] dico primò non esse absurdum concedere vltimam motus tarditatem in spatio determinato. Dico secundò idem spatium etiam determinatum posse tardiùs, ac tardiùs in infinitum transmitti, suffocatis scilicet atomis motus, antequam sint multum progressæ, & interpolatâ quiete antequam gignatur alia. Sit, verbi gratiâ spatium A B C D quod vna atomus transmittit, quando erit in B suffocabitur fietq[ue]; quies, & morâ postea fiet alia, quæ pariter opprimetur in C, ac proinde non est difficultas quin hac ratione tarditas possit conciliari, sed cum quies non sit motus,

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C.1. On the local motion of atoms. 237 whatever Lycæum and Academia explain by gravity, lightness, magnetic force, and other terms, is in vain; for in vain is that done by many means which can be done by fewer, but nature does nothing in vain. Motion, therefore, is a permanent entity, etc., whose productive cause is impetus, which was what we set out to prove. OBJECTIONS. Against Democritus’s doctrine on local motion. OBJECTION I. On the very slow and the very fast motion. If motion consists of atoms, it follows that there can be motion of such slowness that no slower motion can exist; for let there be a single atom, since nothing smaller can be given, it follows that the motion will be the slowest, although so fast a one cannot be assigned that a faster one may not be given ad infinitum; but the extreme of such slowness seems absurd, since from postulate 1 no fastest motion is given; therefore, the opinion follows from it as well. I answer that this argument could be directed against the elemental atoms themselves; for of them a smaller body cannot be given, although the elements themselves can increase into an almost infinite bulk. Just as proportional arithmetic increases to infinity, but does not decrease to infinity. Therefore I say, first, that it is not absurd to admit the ultimate slowness of motion in a determinate space. Secondly, I say that the same space, even if determinate, can be traversed more and more slowly to infinity, namely by suffocating the atoms of motion before they have made much progress, and by inserting a pause before another is generated. Let, for example, there be the space A B C D, which one atom traverses; when it is in B it will be suffocated and there will be a pause, and after delay another will be made, which likewise will be crushed in C, and therefore there is no difficulty in conciliating slowness in this way; but since rest is not motion,

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238 De atomis. Disput. III. sit motus, dico posse dari motum tardissimum, vt datur minima quantitas, minimus numerus, & minima proportionalitas arithmetica. OBJECTIO II. De quietibus, et saltibus, siuè transmissione Spatiorum non transeundo per medium. SEquitur dari actu quietes, & morulas in motibus velocissimis, imò etiam saltus ità vt ab extremitate lineę ad aliam extremitatem feratur mobile non transiens per mediû; Prob. major quia cum primæ atomi interierunt, impetus saltem vno instanti eget ad alias substituendas, sicuti cum rana nata vno quidem tractu per 2. palmos feretur, deinde recolligit se impetuq; nouo per alios 2. deuehitur, & sic suum natatum veluti internodijs distinguit; & opus est illam quiescere, quia ea quiete meliùs veluti innixu se propellit. Quod autem dentur saltus manifestè probatur hoc modo: sit quadratu AB, quod complectatur aliud minus quale est CD, producatur BG ad E & DH ad F secundum rectitudinem laterum, sintq; duæ paralleleę DF, BE. Intelligatur quadratum AB circa punctum G tanquam circa polum volui ad conficiendum iter BE, certum est quod A cadet in 1 eritq; GA eo in loco vbi G1. at verò eo motu linea HC incumbet li- neæ

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238 On atoms. Disputation III. Let there be motion, I say that the slowest motion can be given, just as there is a smallest quantity, the smallest number, and the smallest arithmetical proportionality. OBJECTION II. On rests and leaps, or the transmission of spaces without passing through the middle. It follows that actual rests and pauses are given in the swiftest motions, indeed also leaps, so that from one extremity of a line the moving body is carried to another extremity without passing through the middle. Proof: the major premise, because when the first atoms have perished, the impetus at least needs one instant to substitute others, just as when a frog, having leapt in one stretch for 2 palms, is then gathered together again and by a new impetus is carried for another 2, and thus distinguishes its swimming, as it were, by interludes; and it is necessary for it to rest, because in that rest it propels itself better, as if leaning upon it. But that leaps are given is clearly proved in this way: let there be the square AB, which encloses another smaller one such as CD; let BG be produced to E and DH to F according to the straightness of the sides, and let there be the two parallels DF, BE. Let the square AB be understood to turn around point G as around the pole, in order to complete the path BE; it is certain that A will fall in 1 and GA will be in that place where G1 [is]. But by that motion the line HC will lie upon the line

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C. I. De motu locali atomorum. 239 neæ MN. ergo saltu transluiuit spatium sibi vicinum HM. & eo instanti quo quadratum AB circumuolutum per sua quatuor latera incûbet lineę LE secundùm latus BO, tunc latus DP erit in linea QF. translijt ergo spatia HM. NR. SQ. & saltus fecit, alioquin fatendum esset quadratu CD quatuor circumuolutionibus tantundem pene emensum spatij quantum quadratum AB totidem circumuolutionibus, cum ramen latus AG duplum sit lateris CH etiam logitudine, & quadratum CD quatuor suis lateribus deinceps positis faciet tantùm lineam DR paulò plus quam medium lineæ BE quęquatuor quadrati AB lateribus longitudine respondet: ac proinde ex prima ratione constat constitutis atomis sequi quietem, ex secunda verò dari saltus in motu neque motum esse perfectè successium etiam in connotatione, siuè penes spatium. Resp. ad hoc argumentum non esse opus vt virtus motrix habeat aliquid temporis ad atomos intereuntibus substituendas, sed ità prompta est, vt vna aliam sequatur, licuti cum duo ligna aptantur inuicem non opus est vt detur hiatus intermedius: ad exemplum ranę cuius natatus bellè explicat naturam atomorum in motu; Resp. negando paritatem, ratio est quia rana determinatur ab intrinseco fatigatq; organa motus, lapis verò non fatigatur, & ab extrinseco determinatur. Ad secundam partem argumenti quæ intendit probare motum non esse successium etiam penes connotatum, respo[n]debo postquam explicuero naturam motus circularis secundu[m] quem supponit adversarius voluntari quadratum, quod in circumuolutionibus facit circulum, cuius diameter eadem est ac quadrati nempè GO. vt manifestum est cum puncta diametro quadrati respondentia in volutatione faciant arcus, & pariter etia[m] singula lateru[m] puncta circulos describunt, du[m] voluntur supra linea[m] BE vel DF. sit itaq; Q Pro-

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C. I. On the local motion of atoms. 239 and so, by a leap, it traversed the neighboring space HM. And at the instant when the square AB, revolving around its four sides, lies upon the line LE along the side BO, then the side DP will be on the line QF. Therefore it traversed the spaces HM, NR, SQ, and made a leap; otherwise one would have to admit that the square CD, by four revolutions, measured about the same amount of space as the square AB by the same number of revolutions, whereas the side AG is double the side CH even in length, and the square CD, with its four sides successively placed, will make only a line DR a little more than half of the line BE, which corresponds in length to the four sides of the square AB: and therefore from the first reason it is clear that, with atoms arranged, rest follows; from the second, however, leaps are found in motion, and motion is not perfectly successive even in connotation, that is, with respect to space. Reply: to this argument it is not necessary that the moving power have some time in which to substitute atoms as they perish, but it is so prompt that one follows another, just as when two pieces of wood are fitted to each other there is no need for an intermediate gap: as in the example of the frog, whose swimming nicely explains the nature of atoms in motion; reply by denying the parity, the reason is that the frog is determined from within and tires the organs of motion, whereas the stone is not fatigued, and is determined from without. To the second part of the argument, which aims to prove that motion is not successive even with respect to what is connoted, I shall answer after I have explained the nature of circular motion according to which the adversary assumes a square, which in revolutions makes a circle, whose diameter is the same as that of the square, namely GO, as is manifest when the points corresponding to the diameter of the square, in rotation, make arcs, and likewise also the individual points of the sides describe circles, while they are turned over the line BE or DF. Let there be therefore Q Pro-

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De Atomis. Disp. III. PROPOSITIO XLIV. Circularis motus in volutatione tripliciter fertur, motu scilicet pro- gressivo, motu regressivo, & circa centrum, maior autem est retrocessio in maiori circulo quàm in minori. I Vre merito Aristoteles in mechanicarum quæstionum prin- cipio omnium pene artium miracula ab circuli motu oriri pronuntiauit, & revera, inquit, rationi id consentaneum est ex admirabili enim mirandum accidere quidpiam non est absurdum, maximè verò admiratione dignum est simul contraria fieri. Circulus verò ex huiusmodi contrarietatibus genitus est, nam prima eius origo est ab immoto, & commoto simul, nempè lineà quæ circa vnum sui extremum immotum voluatur: at quid quiescente, & moto magis est contrarium? præterea li- nea quæ circulum ambit nullius latitudinis concaua tamen est, & conuexa &c. Contrarietas præterea ista reperitur in circulo quòd ad exteriorem simul, & posteriorem parté feratur. Sit circulus AB qui à puncto C ferri de- beat per lineam CD motu incipiente à puncto C. cum dia- meter B fertur ad partes E tunc C pú- ctum vicinius ipsi D retrocedit versus A. punctu autem E ac- cedit ad D ergo partes quædam circuli retrocedunt, aliè verò progrediuntur; sunt itaq[ue] tres motus in circulo volutato pro- gressiuus ad D, regressiuus ad A & circa centrum O. Secunda

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On Atoms. Disputation III. PROPOSITION XLIV. Circular motion in rolling is carried in three ways, namely, by progressive motion, regressive motion, and around the center; and the retrocession is greater in a larger circle than in a smaller one. I very rightly indeed, says Aristotle at the beginning of the Mechanical Questions, declared that almost all the wonders of the arts arise from the motion of the circle; and truly, he says, this is consistent with reason, for it is not absurd that something marvelous should come from what is marvelous, and it is especially worthy of admiration that contraries should occur at the same time. But the circle is generated from such contrarieties, for its first origin is from something immobile and moved at the same time, namely a line which rolls around one of its fixed ends: but what is more contrary than something at rest and something moved? Moreover, the line which describes the circle is of no width, yet it is concave and convex, etc. This contrariety is also found in the circle in that it is carried toward the exterior side and at the same time toward the rear. Let there be a circle AB which is to be carried from the point C through the line CD, the motion beginning from the point C. As the diameter B is moved toward the parts E, then the point C recedes more closely toward D, back toward A. But the point E approaches D; therefore certain parts of the circle recede, while others advance. Thus there are three motions in the rolling circle: progressive toward D, regressive toward A, and around the center O. Second

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C. I. De motu locali atomorum. 241 Secunda pars propositionis difficilior est quam hæc prima, retrocessionem scilicet in maiori circulo esse maiorem quam in minori; retractio tamen ad centrum maior est in minori circulo quam in maiori. Retrocesso enim in minori circulo nunquam excedit diametrum Q E, in maiori verò, erit per totam diametrum B A punctum enim B regredietur in A & punctum Q in E, excepto illo quod in progressuo motu circuli acquirent lineæ C D, nunc enim comparantur ipse circuli motiones quæ circa centrum sunt, certum enim est quod circulo adunatè considerato punctum B in motu volutationis semper accedet ad D sed respectiuè ad alias partes circuli retrocedit. Magis tamen in motu circa centrum coercet se minor circulus quam maior, punctum enim Q est vicinius quiescenti O quam punctum B. ducatur enim recta O G, & ex puncto H intersectione circulim minoris, & rectæ ductæ excitetur perpendicularis in I & item à puncto H ducatur HL parallela ipsi I A, & à puncto L excitetur item perpendicularis LN fietq[ue] parallelogrammum HILM. iam itaque sic argumentor. A motum in L tantum confecit spatij secundùm naturam quam E motum in H, vtrobiq[ue] enim perpendicularibus equalibus ML, IH, hoc spatium metimur, omnia autem perpendicularibus sunt dimetienda, dùm tamen punctum A motum est in L retractum est ad centru[m] per sinum versum AM; dùm autem E latum est in H retractum est ad centrum per sinum etiam versum EL. atqui EL maior est quam AM. quia ex 33.6. æquales rectæ ex circulis inæqualibus auferunt segmenta inæqualia, maiusq[ue] est segmentum quod à minori circulo quam quod à maiori aufertur. Sed sinus rectus IH est æqualis sinur recto ML, & maior est circulus AB quam EQ ergo minore auert par- Q 2

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C. I. On the local motion of atoms. 241 The second part of the proposition is more difficult than this first one, namely, that the retrocession in the larger circle is greater than in the smaller; yet the retraction toward the center is greater in the smaller circle than in the larger. For in the smaller circle the retrocession never exceeds the diameter Q E; but in the larger it will be through the whole diameter B A, for the point B will go back to A, and the point Q to E, except for that which the lines C D will acquire in the forward motion of the circle; for now the motions of the circles themselves, which are about the center, are being compared. For it is certain that, if the circle is considered as a whole, the point B in the motion of revolution will always approach D, but in relation to the other parts of the circle it retrocedes. Nevertheless, in the motion around the center the smaller circle restrains itself more than the larger; for the point Q is nearer to the resting point O than the point B is. Let the straight line O G be drawn, and from the point H, at the intersection of the smaller circle and the drawn line, let a perpendicular be raised in I; and likewise from point H let H L be drawn parallel to I A, and from point L let another perpendicular L N be raised, and there will be the parallelogram H I L M. Now then I argue thus: A has completed in L as much space according to nature as E has completed in H; for in both cases we measure this space by equal perpendiculars M L and I H; but everything is to be measured by perpendiculars. While, however, point A has moved to L, it has been drawn back to the center through the versed sine A M; but while E has been carried to H, it has been drawn back to the center through the versed sine E L as well. But E L is greater than A M, because from 33.6 equal straight lines taken from unequal circles cut off unequal segments, and the segment taken from the smaller circle is greater than that taken from the larger. But the straight sine I H is equal to the straight sine M L, and the circle A B is greater than E Q; therefore the smaller one removes par- Q 2

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tem LM quam HI. Retractio itaq[ue] ad centrum maior est in minori circulo quam in maiori mensurantur enim per sinus versos AM, EI. Circularis ergo motus in volutatione &c. quod erat demonstrandum. Ex his nunc respondeo difficultati supra positæ de saltibus quadrati minoris, pro quo resumamus si placet schema supra positum quadrata AB, CD, parallelasq[ue] DF, BE, mouentur ista duo conclusa quadracirca polum G non autem solum circa centrum K, quare hic est complicatus motus septem circulorum quorum duo sunt circumscripsi quadratis AB, CD eorumq[ue] semicirculos vides descriptos à centro K: OBG scilicet, & PDH, alij verò quinq[ue] circumnuntur à centro G penes semidiametros GO, GH, GP, GA, GC, cadentes in puncta T, V, Z, à minori quadrato, & IX à maiori, cum ergo A fertur per arcum AI, tunc punctum C fertur per arcum CT motuq[ue] illo naturali subdeficit per lineam TN. cum enim A est in I tunc C reperitur in N. ac proinde deberet sensibiliter etiam lacerari frangiq[ue] quadratum, vel saltum facere, cum adeo sit magna deficientia qualem notat li- neola

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the same as LM than HI. Therefore the return to the center is greater in the smaller circle than in the larger, for they are measured by the versed sines AM, EI. Therefore the circular motion in rolling, etc., which was to be demonstrated. From these things I now answer the difficulty stated above concerning the leaps of the smaller square; for which let us take up again, if you please, the above figure, the squares AB, CD, and the parallels DF, BE. These two, enclosed, are moved quadratically around pole G, not however only around center K; wherefore here there is a composite motion of seven circles, of which two are circumscribed about the squares AB, CD, and you see their semicircles described from center K: namely OBG and PDH. But the other five are revolved around center G along the semidiameters GO, GH, GP, GA, GC, falling into points T, V, Z, from the smaller square, and IX from the larger; when therefore A is carried through arc AI, then point C is carried through arc CT and under that natural motion falls short by line TN. For when A is in I, then C is found in N. And consequently the square should also be sensibly torn and broken, or make a leap, since the deficiency is so great as the little line indicates

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C. I. De motu locali atomorum. 243 neola TN, ac proinde si tantum aduerteretur ad motum maiorum circulorum quæ describuntur à puncto G certè aduersarij argumentum conuinceret, sed manifestus est paralogismus quod omiserit aliorum circulorum considerationem, primò quidem nemo non videt quam ineptè dixerit saltum primum esse HM, etsi enim ibi non quiescat transgreditur tamen totum illud spatium secundum circulares CT, HZ. deficit autem Z à verò puncto quietis M vt punctum T à verò puncto quietis N. Equidem miraculo proximum est quomodo deinde restitui possit, & qua via linea HC deinde occupet locum MN, cùm GA occupat locum GI, quia scilicet in motu secundario quem intelligimus fieri secundum circulos à centro polygonorum K descriptos (iste enim motus est volutationis) punctum G retrocedere intelligitur in B, ac proinde cùm absit magis à directione lineæ GE eiusq; distantia sit perpendicularis Yq. hoc est sinus versus qui duplus est potentia sinui verso F2, per 2. 12. quæ est aberratio puuci H delati circa centrum K, manifestè sequitur quadratum minus duplum sinus versi in progressu per arcus CT super lucrari, vnde æquantur postea in situ secundum suas lineas, quia ob immixtam retractionem circulorum circa K descriptorum plus maior circulus aberrat, vnde & minor compèfat hac occasione defectum in volutatione circa circulos descriptos à centro G. Hæc est demonstratio refellens satis superius argumentum quod ingeniosius est aliquanto quam validum. Aristoteles in mechanicis q. 24. quærit cur maior circulus æqualem minori circumvoluitur lineam quâdo circa idé cætrum fuerint posui, seorsum autem revoluti quemadmodum alterius magnitudo ad magnitudinem se habet alterius, sic & illorum adinuicem sunt lineæ causamq; reddit quia vnicus est vtriusq; motus, sunt enim alligati: sed meo iudicio non satis- Q 3 facit

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C. I. On the local motion of atoms. 243 neola TN, and therefore if attention were paid only to the motion of the larger circles described from point G, the adversary’s argument would certainly be convincing; but the fallacy is evident, because he omitted consideration of the other circles. First, indeed, everyone sees how ineptly he said that the first leap is HM; for although it does not come to rest there, nevertheless it traverses the whole of that space according to the circular motions CT, HZ. But Z falls short of the true point of rest M, as point T does of the true point of rest N. Truly, it is almost a miracle how it can afterwards be restored, and by what route the line HC then takes the place of MN, since GA takes the place of GI, because namely, in the secondary motion which we understand to occur according to the circles described from the center of the polygons K (for this motion is one of rolling), point G is understood to move backward in B; and therefore, since it is farther from the direction of line GE and its distance is perpendicular Yq, that is, the versed sine, which is double in force of the versed sine F2 by 2.12, which is the deviation of point H carried around center K, it clearly follows that the lesser square, double the versed sine, in its progress through the arcs CT gains the upper hand, whence they are afterwards made equal in position according to their lines, because, on account of the intermingled retraction of the circles described around K, the greater circle deviates more, whence also the smaller compensates by this occasion for the defect in the rolling around the circles described from center G. This is a demonstration refuting sufficiently the foregoing argument, which is somewhat more ingenious than sound. Aristotle in the Mechanics, q. 24, asks why the greater circle, when the same center has been posited, rolls through an equal line with the smaller one, but when rotated separately, inasmuch as the magnitude of one relates to the magnitude of the other, so also their lines are related to one another; and he gives the reason because there is one and the same motion of both, for they are bound together: but in my judgment he does not sufficiently satisfy

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De Atomis. Disp. III. facit problemati difficillimo, ad quod explicandum debuisset distinguere motum in circulis duobus quintuplicem, primò est motus raptus quem patitur minor, secundò est motus centrorum aut axis vtrumq[ue]; circulum vincientis, 3. est motus subdeficienti[us], 4. motus retrocessionis in minori, 5. autem motus intercalarium momentorum, qui motus omnes ab admirandis circuli proprietatibus oriuntur. Cæterum breuissimè hanc demonstrationem, vt etiam superiorem constrinxi quia scio paucos abstrusorum mathematicę mÿsteriorum esse intelligentes; nunc ab his linearum circulorumq[ue]; labyrinthis commodum elapsi vnam de multis grauissimam præterea obiectionem diluere tentemus. OBJECTION III. De successione motus. NOn potest negari perfecta successio in motu, quia si datur successio penes connotatum, accipiam cultrum calamarium motuq[ue]; continuato cartam secabo, vnde sic arguo, soluuntur vniones atomorum cõtinuè successiuè, ergo datur perfecta diuisibilitas continuata, ergo & perfecta successio in motu, ac proinde motus est diuisibilis physicè in infinitu[m], eo enim modo diuidetur carta quo modo mouetur culter. Respondeo ad hoc argumentum motum quidem esse successiuum extrinsecè non autem intrinsecè. Ad initantiam Respondeo vnionem duas atomos iungentem solui totam simul, & cultrum deinde per diuisas pergere ad sequentes duas vnitas, quas pariter diuidit totas simul, peritq[ue]; vnio, iterumq[ue]; per vulnus victor culter transit, sicq[ue]; solutis omnibus vnionibus continuè discretè, fit etiam motus continuè successiuus penes connotatum; Ratio cur ità respondeam est quia non potest sub minori paruitate vnio consiltere, vnde labefactato suo spatio, aut

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On Atoms. Disputation III. It leads to a most difficult problem, for the explanation of which one ought to distinguish motion in the two circles as fivefold: first, there is the motion of the lesser one being carried along; second, there is the motion of the centers, or of the axis of each circle binding the other; third, there is the motion of the one falling short; fourth, the motion of retrocession in the lesser one; fifth, however, the motion of the intervening moments, all of which motions arise from the marvelous properties of the circle. But, very briefly, I have compressed this demonstration, as I also did the preceding one, because I know that few understand the hidden mysteries of mathematics; now, having conveniently escaped from these labyrinths of lines and circles, let us try to dissolve one, besides, of the many and most serious objections. OBJECTION III. On the succession of motion. Perfect succession in motion cannot be denied, because if there is succession with respect to what is connoted, I will take a penknife and with continuous motion I shall cut paper; from which I argue thus: the unions of atoms are dissolved continuously and successively; therefore there is perfect continuous divisibility; therefore also perfect succession in motion, and consequently motion is physically divisible into infinity, for in the same way the paper is divided as the knife moves. I reply to this argument that motion is indeed successive extrinsically, but not intrinsically. To the instance I reply that the union joining two atoms is dissolved all at once, and then the knife proceeds through the divided parts to the next two units, which it likewise divides all at once, and the union perishes; and again the victorious knife passes through the wound, and so, with all the unions dissolved continuously and discretely, motion too becomes continuously successive with respect to what is connoted; the reason why I reply thus is that a union cannot subsist under less minuteness, whence, with its space weakened, or

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C.1. De motu locali atomorum. 245 aut vltra modum compresso statim perit. Responderent alij negando vnonem omnem in continuo soluiq; ea diuisione dicerent contigitarem conlocatam, sed ego qui modis exilium non sanciui, primâ responsione difficul- tati satisfacio. Hæc pauca de motu sufficiant, cætera meliori otio reseruantur. CAPVT SECVNDVM: De rarefactione, & condensatione iuxta Democritum. Hic porrò cæcutiunt pene omnes densissimisq; tenebris nuoluuntur qui aliò qua ad Democritum digressi de ra- refactione, & condensatione secudu[m] Stoæ principia disputant. PROPOSITIO XLV. Rerum quotidianus vsus rarefactionis, & condensationis naturam ostendit. QVotiescunque corpora compacta comminuuntur in pul- uerem si illum manu attollas, & per aerem deijcias etiam vnum tantum pugillum, videbis statim pulueris nubeculam, & id quod manu complexus es vlnarum amplexum longè su- perare: recidens tamen huiuscemodi puluis cartà paruulâ ex- cipietur, & quod adeò amplum occupauit spatium in angustos limites cogetur, obtegutur huiuscemodi pulueris nulibus equi- tes, cùm agglomerari per siccas viascurrunt vnde Poeta. It nubes inter sompes, neque fulmina Cæsar Inuidet irato; sola tellure repulsà Agglomerat nubes, quales Neptunia Thetis Excisas Phoebi radijs submittit olympo. Q 4 Reuera

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C.1. On the local motion of atoms. 245 or, being compressed beyond measure, it immediately perishes. Others would answer by denying any union in the continuous and would say that by that division what was placed together is dissolved; but I, who have not enjoined exile by any mode, in my first response satisfy the difficulty. Let these few things suffice concerning motion; the rest are reserved for better leisure. CHAPTER THE SECOND: On rarefaction and condensation according to Democritus. Here, moreover, almost all are blind and are rolled about in the thickest darkness who, having turned aside to something other than Democritus, dispute about rare- faction and condensation according to the principles of the Stoics. PROPOSITION XLV. Daily use of things shows the nature of rarefaction and condensation. Whenever compact bodies are broken up into dust, if you lift it with your hand and scatter it through the air, even if it be only a single handful, you will immediately see a cloud of dust, and what you have enclosed in your hand will far exceed the span of a cubit; yet when it falls back, dust of this sort will be received by a small sheet of paper, and what occupied so great a space will be forced into narrow limits. Such dust will be covered by clouds of horsemen, when they run agglomerated through dry roads, whence the Poet. “It is a cloud among the darkness, nor does Caesar begrudge the thunderbolts to the angry one; the earth alone repelled, it gathers clouds, such as the Neptunian Thetis sends up, torn by Phoebus’ rays, to Olympus.” Q 4 In truth

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De atomis. Disput. III. Reuera nullam hic Poeta differentiam facit inter nubes à puluere petitas, & nubes ab aqua excisas nisi quod istæ sint aqueæ illæ verò terre: quis enim hac imagine nubium quam puluis dispersus facit sibi non facilè persuadeat etiam in minimas particulas dispersam aquam, ità in vapores attolli? Iride apparente nulla dubio procul est pluuia densa, sed solùm nubes est rorida quæ in guttas minores conglomeratur; accipe aquam in ore eamq; ad solis radios cubiculum tuum subeuntes auerso soli tergo disperge flatu violento compressisq; labijs, videbis in aere nubem roridam à te factam, & nullius Deæ commercio genitam Iridem. Cum eleuâtur ab aquis vapores guttulas tenues eleuari par est credere, quæ deinde alijs iunctæ con crescent deciduntq; optimè verò lib 7. philosophatus est Virgilius vnoq; spumaru vocabulo arcanu philosophicu aperuit. fuit intus aquæ vis Fumidus atque altè spumis exuberat amnis, Nec iam se capit vnda, volat vapor ater ad auras. Ecce primùm ad rarefactionem gradum, commotio, quam furore explicat, spumam deinde fumido amni dat; Est autem spuma sinuata in tenué veluti superficiem aqua, quæ aere plena est: quod spumarum vocabulum meo iudicio optimè rem nostram explicat, si quidem inuisibiles spumæ ab sole eleuantur, conglobatæq; aeris atomi ab aqua expansa, calore solis aspirante circumstringutur, & ob eam quam habent affinitatem aeris, & aquæ portiones sursum attolluntur, vsq; dùm in eo suspendantur loco quem perpetuum haberent, nisi facto diuortio aqua ad suum locum recideret calore fatiscéte: quapropter vapores omnes subtilissimas esse spumas existimo quæ ob frigus deinde, complexum destituentes aerem, quòd in alia temperie aliter in loco esse postulent, vt dixi principio 14. adunatæ in guttas stillasq; in rorem pluuiamq; decidût. Hunc primò

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On atoms. Disputation III. Truly the poet here makes no difference between clouds drawn from dust and clouds cut off from water, except that these are watery, those earthy. For who would not easily persuade himself, from this image of clouds which scattered dust makes, that water, dispersed even into the smallest particles, is also borne upward into vapors? When a rainbow appears, there is without doubt a dense rain; but there is only a dewy cloud which gathers into smaller drops. Take water in your mouth, and, with your back turned to the sun, as his rays enter your chamber, scatter it with a violent breath and compressed lips; you will see in the air a dewy cloud made by you, and an iris born without any commerce of a goddess. When vapors are raised from the waters, it is right to believe that tiny droplets are raised, which then, joined with others, grow together and fall back. Virgil, however, in book 7, philosophized excellently, and with a single word, spumae, opened the secret of philosophy. within was the force of the water the river, smoky and rising high with foam, overflows; now the wave can no longer contain itself, a black vapor flies up to the skies. See first the step toward rarefaction, the stirring, which he expresses by fury, then he gives foam to the smoky river. Now foam is water bent into a thin kind of surface, as it were, which is full of air. In my judgment the word spuma best explains our matter, since invisible foams are raised by the sun, and the atoms of the air, gathered together from the expanded water, are compressed as the heat of the sun breathes upon them; and because of that affinity which they have, the portions of air and water are lifted upward, until they are suspended in that place which they would hold permanently, unless, the separation having been made, the water should fall back to its own place as the heat grows weak. Therefore I hold all vapors to be the subtlest foams, which afterward, owing to cold, leaving the air without its embrace, because in another temperature they require to be in another place, as I said at the beginning of section 14, are united into drops and tiny distillations and fall as dew and rain. This first

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C. I. De motu locali atomorum. 247 primò hausi conceptum cum præcipites torrentium per alpiu[m] prærupta saltus admiratus essem, vidissemq[ue]; quà vectigal ab equitibus exigitur in Sangothardicis alpibus ad solem matutinum, & meridianum, his enim temporibus illac tertiò iter face re contigit, perpetuam apparere Iridem quod ab aquæ lapsu dispersa aqua in guttulas effusamq[ue]; spumâ vndiquaq[ue]; cieretur De fumi etiam natura nô aliter philosophandum esse duxi dissoluuntur enim atomi, & in huiscemodi halitus diffunduntur separationem integram à se inuicem tot deuiationibus per aera querentes, mixtus enim aeri aquæ, & terræ ignis neque satis commixtus habet vim dispersiuam, vnde si pugillus pulueris, cinerumq[ue]; vncia commota, totum cubiculum opplet, si aquæ ciathus vaporibus ingentes cados obscurat, quis dubitabit idem igni disperso contingere? pulueris itaq[ue]; spumarum, nubiumq[ue]; roridarum exemplis optimè ad rarefactionis naturæ notitiam deu eniri potest, quod erat ostendendum. PROPOSITIO XLVI. Vnica atomus sine rarefactione, sine inflatione aut reproductione potest naturaliter occupare maiore[m], & maiore[m] locum in infinitum. A Tomus est omnis figuræ capax, ergo occupare potest maiorem, & maiorem locum in infinitum: cum enim figure regulares in isoperimetris sint magis collectæ minoremq[ue]; locu[m] occupent, sequitur quod quo irregularior erit figura eo maiore[m] occupabit locum, at non potest dari, ita irregularis, quin magis irregularis esse possit, ergo etia[m] maioris loci capax. Ducatur enim duæ parallelae AF, CG in infinitum, construaturq[ue]; quadratum AD, & ductis à punctis C, & D parallelis CE, DF constructu[m] erit parallelogrammu[m] C E F D. Intelligitur autem quadratum AD esse atomum, cum ergo parallelogramma super eadem basi, & in eisdem parallelis co- stituta

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C. I. On the local motion of atoms. 247 I first conceived the idea when I admired and saw the rushing torrents among the steep passes of the Alps, and when, where the toll is collected from horsemen in the Sangothardic Alps, toward the morning sun and toward noon; for on these occasions, as it happened that I was making the journey there a third time, a perpetual rainbow appeared, because the water, dispersed by the fall of the water, was spread into droplets and foam was stirred on every side. On the nature of smoke also I judged that no different philosophy should be pursued; for atoms are dissolved, and are diffused into vapors of this kind, seeking a complete separation from one another through so many deviations through the air. For a mixture of air, water, earth, and fire, not yet sufficiently mixed, has a dispersive force; whence, if a handful of dust or ash, when stirred, fills the whole room, if a cup of water obscures great jars with vapors, who will doubt that the same happens with fire when dispersed? Therefore, from the examples of dust, foam, clouds, and dewy mists, the knowledge of the nature of rarefaction can be most excellently attained, which was to be shown. PROPOSITION XLVI. A single atom, without rarefaction, without inflation, or reproduction, can naturally occupy a greater and greater place to infinity. An atom is capable of every shape; therefore it can occupy a greater and greater place to infinity: for since regular figures in isoperimeters are more compact and occupy less space, it follows that the more irregular a figure is, the greater a space it will occupy. But there cannot be given such an irregular figure that it could not be made still more irregular; therefore it is also capable of a greater space. Let two parallels AF, CG be drawn to infinity, and let the square AD be constructed; and, lines CE and DF being drawn from the points C and D parallel to them, the parallelogram C E F D will be constructed. Now the square AD is understood to be the atom; since therefore parallelograms constructed on the same base and between the same parallels are...

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stituta sint æqualia ex 35. 1. sequitur quod parallelogrammum CHEFD æquale est parallelogrammo AB DC. quod ità clarum est, vt quivis mathema- ticaru ignarushanc de- môstrationem palpare possit: triangulum enim AEC æquale est triangulo BDF per 4. 1. est enim laterum æqualium, dempto ergo communi vtriq; triangulo BHE remanent trapezia ACHB, & HDFE æqualia, ex æqualibus enim æqualia si demas quæ re- manent sunt æqualia, vtriq; autem trapezio additur commune triangulum CDH: ergo parallelogramma AD, CF sunt æqualia. Sed maior est extensio CF quam AD, & quo longius ducentur parallele CG, AF seruatis ijsdem basibus AB, CD semper eo magis extendetur parallelogrammum, nam EF est æqualis AB, at EC quinquies, & sexies fe- rè superat latus BD, ac proinde vna atomus cubica minus spatij occupabit quam eadem in parallelepipedum expansa, solidas enim figuras per planas dimetiuntur mathematici, quod aute[m] maior sit locus occupatus à parallelogrammo CF, quamab AD manifestum est, locus enim est superficies cor- poris

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...are made equal from 35.1. It follows that the parallelogram CHEFD is equal to the parallelogram ABDC, which is so clear that even someone ignorant of mathematics can grasp this demonstration: for triangle AEC is equal to triangle BDF by 4.1, since they have equal sides; therefore, removing the common triangle BHE from each, the trapezia ACHB and HDFE remain equal. For from equal things, if equal things are taken away, the remainders are equal; and to each trapezium there is added the common triangle CDH: therefore the parallelograms AD and CF are equal. But the extension of CF is greater than that of AD, and the farther the parallels CG and AF are drawn, while the same bases AB and CD are preserved, the more the parallelogram will be extended; for EF is equal to AB, but EC exceeds BD by nearly five or six times, and consequently one cubic atom will occupy less space than the same atom expanded into a parallelepiped, for mathematicians measure solid figures by planes. And that the space occupied by parallelogram CF is greater than that by AD is evident, for place is the surface of a body.

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C.2. De rarefact. & condens. 249 poris ambientis, atqui maior est ambitus parallelogrammi CF quam AD ergo, & maior locus, quod vt videas ad oculum affero sequens schema: Æqualis est peripheria figurę parallelogrammę AC, atq[ue] figurę quadratę EF, quamuis EF quatuor constet partibus ex his quarum BD habet tantum tres, ex quo ingeniosâ nequitâ quispiam vicino suo imposuit, cui erat ager quadratus qualis EF, ipse verò habebat qualis est BD, persuasusq[ue]; antiquæ simplicitatis vir vt commutaret agrum ratus æqualis esse areæ quod æqualis vtriusq[ue]; esset peripheria, inuenit in experimento minus foecundum BD quam esset suus primus EF, & sterilitatem imaginariam in terræ angustias nunquam reiecit, neq[ue]; enim figurę rationes nouerat, quod si hoc ità se habet quanto maioris peripherię esset BD si diuideretur per rectam intermediam à puncto I ad punctum G, & ità applicarentur in longum duo parallelogramma IA, IB. excederet tunc figura DB in sua peripheria quadratu EF quod tamen maius est in area. At in his nulla est rarefactio, nulla reproductio, vel admixtio alieni corporis, ergo vnica atomus sine rarefactione &c. potest occupare maiorem, & maiorem locum in infinitum quod erat demonstrandum. Dices ergo definitio rarefactionis non est bona cum sine rarefactione maior acquiratur extensio, aut occupatio maioris loci. Respondeo no[n] acquiri adęquate maiorem extensionem secundùm omnes dimensiones, debet enim huiuscemodi incrementum lineis perpendicularibus censeri, quæ in parallelogrammo AD sunt AC, AB at verò in parallelogrammo CF quâ exigue sunt, tùm quæ excitabitur in basi CD vt DH, tùm quę in linea DF à puncto verbigratia G. vnde cum oblique lineę cum perpendicularium detrimento crescant, non est quod ità censeatur adęquata extensio quæ in corpo-

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C.2. Of rarefaction & condensation. 249 in the surrounding spaces; yet the circumference of the parallelogram CF is greater than that of AD, and therefore the place is greater, which, that you may see with the eye, I present the following diagram: The perimeter of the parallelogram figure AC is equal to that of the square figure EF, although EF consists of four parts, while BD has only three of these, from which a certain man, by ingenious deceit, imposed upon his neighbor, to whom there was a square field such as EF, while he himself had one such as BD; and, persuaded by the man of ancient simplicity to exchange the field, thinking the area to be equal because the perimeter of each was equal, he found by experiment BD to be less fruitful than his first EF, and never referred the imagined sterility to the narrowness of the land; for he did not know the proportions of figures. But if this is so, how much greater a perimeter would BD have if it were divided by the intermediate straight line from point I to point G, and thus the two parallelograms IA, IB were applied lengthwise. Then the figure DB would exceed the square EF in its perimeter, though the latter is greater in area. But in these there is no rarefaction, no reproduction, or admixture of a foreign body; therefore a single atom, without rarefaction, etc., can occupy a greater and greater place ad infinitum, which was to be demonstrated. You will say then that the definition of rarefaction is not good, since without rarefaction a greater extension, or occupation of a greater place, is acquired. I answer that a greater extension is not acquired adequately according to all dimensions; for an increase of this kind must be reckoned by perpendicular lines, which in the parallelogram AD are AC, AB, but in the parallelogram CF they are quite small, both those raised on the base CD, such as DH, and those on the line DF from the point, for example, G. Hence, since oblique lines grow at the expense of the perpendiculars, there is no reason why that should be reckoned an adequate extension which in body-

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250 De Atomis. Disput. III. corporibus solidis, cuiusmodi sunt ea quæ rarefiunt, debet su- mi penes tres dimensiones longitudinem, latitudinem, & pro- funditatem: præterea est occupatio maioris loci extrinseci non auté intrinseci, vtrobiq[ue]; enim par est area sub inæqualibus ter- minis atq[ue]; ita intelligendu[m] est 1 1. principium ab Euclidis tra- ctatu de leui, & ponderoso acceptum. PROPOSITIO XLVII. Quamuis admitti debeat aliqua in natura rarefactio impropriè dicta, nulla tamen datur propria, & legitima: siuè omnis rarefactio fit per intrusionem atomorum, condensatio per extrusionem. SVppositis his principijs non dari vacuum, non dari penetra- tionem corporum etiam inadequatam, non dari reprodu- ctionem annihilationemq[ue]; Naturæ viribus, & præterea quæ adhanc materiam spectant adducta disp. initio principia: Sed potissimùm propositione 44. quæ exemplis confirmat, quod hîc ratione sumus stabilituri Certum est primò dari aliquam rarefactionem in natura cu[m] fumus, vapores, nubes, ebullitio cacabi, aliaq[ue]; innumera eam adstruant: sed quomodo fiat non consentio cum peripateticis, eamq[ue]; fieri dico per admixtionem alieni corporis vt explicui definit. 7. Certum est secundò rarefactionem propriè dictam esse eam quâ corpus nullo alio sibi admixto maiorem locum occupat vnicâ sui substantiâ, & quantitate, sic cubus palmaris ceræ fiet bipalmaris cubus ceræ puræ, & hoc fieri non posse conten- do in mea propositione quæ Probatur primò quidquid existit determinatos habet exte- sionis limites vltra quos non potest porrigi, infra quos non potest adigi, ergo non datur rarefactio neque condensatio pro- priè dicta conseq[ue] est certa, maior sequitur ex hoc principio modus existendi sequitur modum essendi. Pro-

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250. On Atoms. Disputation III. In solid bodies, such as those which become rarefied, it must be taken with respect to the three dimensions: length, breadth, and depth; moreover, there is occupation of a greater external place, not an internal one; for in both cases the area is the same beneath unequal boundaries. And thus is to be understood the 1st principle taken from Euclid’s treatise on the light and the heavy. PROPOSITION XLVII. Although some rarefaction, improperly so called, must be admitted in nature, nevertheless no proper and legitimate rarefaction is given; that is, all rarefaction occurs by the intrusion of atoms, condensation by extrusion. These principles being supposed, that there is no vacuum, that there is no penetration of bodies even inadequately, that there is no reproduction and annihilation by the powers of Nature, and besides the principles brought forward at the beginning of the disputation concerning this matter, but especially Proposition 44, which confirms by examples what here we are about to establish by reason, it is certain, first, that some rarefaction exists in nature, since smoke, vapors, clouds, the boiling of a kettle, and countless other things attest it; but I do not agree with the Peripatetics as to how it takes place, and I say that it occurs by the admixture of foreign body, as I explained in Definition 7. It is certain, second, that properly so called rarefaction is that by which a body, with nothing else mixed into it, occupies a larger place by its own single substance and quantity; thus a one-span cube of wax will become a two-span cube of pure wax, and I contend that this cannot happen, in accordance with my proposition, which is proved first: whatever exists has determinate limits of extension, beyond which it cannot be extended, and within which it cannot be compressed; therefore proper rarefaction and condensation are not given. The consequence is certain; the major premise follows from this principle: the mode of existing follows the mode of being. Pro-

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C.2. De rarefact. & condens. 251 Probatur secundò: vel inter primam atomum, & secundam intermediat aliquid vel nihil, si nihil, ergo datur vacuum in rarefactione, si intermediat aliquid, ergo erit corpus exoticum, siue minimum illac illapsum; quod si rarefactæ duæ atomi A, B, dicantur se se tangere mutuo neque quidquam interme- diare, sed cum essent ambæ vnius grani occupant nunc locum duorum granorum sic argumentabor; non potest dilatari ma- teria ab accidente, ergo nullus calor poterit, atomum dilatare. Probatur Primò antecedens, accidens educitur è subiecto, ergo supponit subiectum in suo esse etia[m] extenso, nam ad subie- cta[m]dam actionem requiritur extenso; si itaq[ue]; calor sequitur ne- cessariò rationem existédi atomorum quo modo potest atomos dilatare? in illo enim priori existétię intelligitur atomus cui su- perueniunt varij caloris gradus, aut ordines atomoru[m] acciden- taliu[m], ergo cum quidquid recipitur per modum recipientis re- cipiatur, sequitur quod isti omnes gradus sequantur modum existendi atomi quem habebat ante illorum receptionem, at- qui vt sic non erat rarefacta, ergo neque postmodum rare fiet propriè loquendo; facient autem intrusa inter atomos aeris ignisue coopuscula, vt dispergantur ac proinde maiorem locu[m] videantur occupare. Hæ duæ rationes sunt apriori. Probatur tertio à posteriori experientijs scilicet, quibus ad- ducor vt ità argumenter. Nulla datur códensatio, ergo neque rarefactio consequens est ex princ. 16. Probatur primò antece- dens experimentis. Primò si peluim aqua plenam aeri hiemali objicias glaciabitur aqua, eâ tamen lege vt quamuis ad limbos peluisq[ue]; oras depressior glacies, quam aqua fuerat, videatur, tamen in medio videbis assurgere, & quasi gibbam, ergo re- parat eâ mole dispendia depressionis in littoribus, ac proinde condensata non est, cum tantumdem spatij occupet quam- uis in situ diuerso; ratio autem huius cōglomerationis est quia con-

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C.2. On rarefaction and condensation, 251 Secondly, it is proved thus: either between the first atom and the second something intervenes, or nothing does; if nothing, then a vacuum is granted in rarefaction; if something intervenes, then it will be an alien body, that is, a minimum body slipped in there. But if two rarefied atoms, A and B, are said to touch one another mutually and nothing to intervene between them, yet when both were of one grain they now occupy the place of two grains, I shall argue thus: matter cannot be dilated by an accident; therefore no heat will be able to dilate an atom. The antecedent is proved first: an accident is drawn out of a subject; therefore it presupposes a subject extended in its being, for for subjecting action extension is required. If, then, heat necessarily follows the nature of existing atoms, how can it dilate atoms? For in that prior existence is understood the atom upon which various degrees of heat, or orders of accidental atoms, supervene. Therefore, since whatever is received is received according to the mode of the receiver, it follows that all these degrees follow the mode of being of the atom which it had before their reception; but as such it was not rarefied, therefore neither afterwards will it become rarefied, properly speaking; rather, inserted little bodies of air or fire will cause the atoms to be dispersed and thus seem to occupy more space. These two reasons are a priori. Thirdly, it is proved a posteriori from experiences, namely, from which I am led to argue thus. No condensation is granted; therefore neither is rarefaction consequent from principle 16. The antecedent is first proved by experiments. First, if you expose a basin full of water to winter air, the water will freeze, yet on the condition that, although near the rims and edges of the basin the ice may appear lower than the water had been, nevertheless in the middle you will see it rise up and almost become convex; therefore it makes up, by that mass, for the loss caused by the lowering at the sides, and consequently it is not condensed, since it occupies the same amount of space, although in a different position. Now the reason for this clustering is that...

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De atomis. Disput. III. 252 conuoluta in globum aqua plus resistit, est enim profundior, ac proinde vt se ab externa virtueatur ità recolligit se se, vt etiam leges æquijacentiæ sibi adeo natiuas violet, alia deinde coniecturà adducor, vt negem aquam glaciatam esse densiorem fluidà, quia scilicet glacies supernatat, atqui videretur ex ratione frigoris constipata magis debere fundum petere, nô itaq[ue] condensatura aqua; sed supernatat quia subtilior aqua subside[n]tibus in fundo terreis partibus quę multum plerumq[ue]; afferunt ponderis, & aere in transfugarum locum accito, fit, vt minus ponderet glacies, quod autem in glacie includatur aer videbis si luci oppositam intuearis, tota enim est ampullis distincta. Nix præterea quæ aqua est congelata ampliorem locum occupat quam liquata, quia scilicet immixtæ sunt plurimæ aeris atomi quæ ità delicatam, & veluti concameratam niuis structuram implent, degradine idem esto iudicium. Tertiò colliquata metalla non plus occupant loci, quam solida concretaue, quod patet in arte fusoria, exprimûtur enim minutissimi in fabulo pili, quod fieri non posset si condensatio daretur, peri- rent enim minutæ lineæ, neque illas metallum referret concretum: at liquefactio rarefactioni est affinis, concretio condensationi, cum itaq[ue] neutrum contingat signum est neutram dari. Equidem aduersarij non possunt tueri se, aut argumentis satisfacere, vel aliquid intelligibile proferre, quin in absurda incidant, concedantq[ue]; vel vacuum, vel penetrationem partiûm, aut aliquid aliud monstruosius, Democritus verò rarefactionem per intrusionem copusculorum, codensationem verò per extrusionem fieri pronuntiat, quæ rarefactio est impropriè dicta, & mille quotidianis exemplis patet. Sed enim peripateticorum nunc fundamenta videamus, quæ eo fortiora vulgò existimantur quod experientijs constent. Obiectio

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On atoms. Disputation III. 252 When water, gathered into a globe, offers greater resistance, it is because it is deeper and therefore, in order to ward off external force, it draws itself together; so much so that it even violates the laws so native to itself of being on an even level. From another consideration I am led to deny that frozen water is denser than fluid water, because, namely, ice floats on the surface. Yet from the force of cold it would seem that, being more compressed, it ought rather to seek the bottom. It is not therefore because the water is condensed; but it floats because the subtler water, while the earthy parts settle to the bottom—parts which for the most part contribute much weight—and air is drawn in to take the place of the escaping matter, it comes about that ice weighs less. That air is enclosed in ice you will see if you look at it against the light; for it is entirely marked off by little bubbles. Snow, moreover, which is frozen water, occupies a larger space than water in liquid form, because very many atoms of air are mixed in, which fill out that delicate and, as it were, vaulted structure of snow. The same judgment should be made about hail. Thirdly, melted metals do not occupy more space than solid or compact metals, as is clear in the art of casting; for the finest hairs are pressed out into the sand, which could not happen if condensation were taking place, for the tiny lines would disappear, nor would the solidified metal restore them. But liquefaction is akin to rarefaction, and solidification to condensation; since therefore neither of these occurs, it is a sign that neither is present. Indeed, the opponents cannot defend themselves, or satisfy the arguments, or produce anything intelligible, without falling into absurdities and conceding either a vacuum, or the penetration of parts, or something else even more monstrous. Democritus, however, declares that rarefaction occurs by the intrusion of tiny bodies, and condensation by their extrusion; but this so-called rarefaction is improperly named, and is refuted by a thousand everyday examples. But now let us examine the foundations of the Peripatetics, which are commonly thought all the stronger because they agree with experience. Objection

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C.2. De rarefact. & condens. OBIECTIO De multiplici experientia quâ videtur concludi rarefactio, & condensatio. Prima. Cucurbitulę medice quibus aër inclusus igne extin- cto ad minorem locum coactus attrahit carnem spiritusq; hominis, cum tamen si non daretur vera condensatio faciliùs esset existentes in cucurbitula partes detinere, quonam enim abeunt illa corpuscola, quæ cucurbitulam replebant? Secunda. Vaporum, fumi, flammæq; adeo visibilis acoreti o est, vt etiam granum pulueris tormentarij in sphæram adeò sui multiplicem porrigatur, vt dictum est cap. 3. disput. 1. Tertia. Vasa obsignata igni applicata franguntur, non obsi- gnata verò perdurant quia scilicet ob rarefactionem, quæ ca- lorem sequitur his claustris coerceri non potest, vel aer, vel a- qua, at verò amoto operculo euaporatur. Quarta est condensatio aeris in pilam lusoriam vi intrusi, quod autem densus reddatur aer probatur facili negotio quia quo plus ingeritur, vtrisco est grauior: deinde accepi inquit Galilæus G. lagenam vitream satis amplam, cui os obtura- ui diligenter præterquam quod inferni digitale coriaceum cui iuncta erat strictissimè vtris lusorij animula, quâ deinde, instru- mento ad id apto maximam aeris quantitatem intrusi, & quia facilè condensatur, duæ aut tres aeris lagenæ intrudentur, præter eum aerem quo primum plena erat. Hoc vtitur experimento ad inuestigâdam aeris grauitatem ità enim congestus aer ponderosiorem fatit lagenam, & aper- to aditu subleuatur pondus: sed enim sicuti à se factum, ait, pro aeris pondere experimentum illud pro condensatione ac- cipio, nam indicat experiendi medium vt possimus scire quan- tum etiam aeris intrusum est præter priorem qui inerat. Igitur

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C.2. On Rarefaction & Condensation. OBJECTION From the various experiences by which rarefaction seems to be concluded, and condensation. First. Medical cupping vessels, in which the enclosed air, after the fire is extinguished, being forced into a smaller space, draws in the flesh and spirit of a person; yet if there were no true condensation, it would more easily be possible to keep the parts that are in the cupping vessel from escaping. For where, indeed, do those little bodies go, which were filling the cupping vessel? Second. The visible force of vapors, smoke, and flame is so great that even a grain of gunpowder is expanded into so large a sphere of itself, as was said in chap. 3, disputation 1. Third. Sealed vessels applied to fire burst, while unsealed ones endure, because, namely, through rarefaction, which follows heat, neither air nor water can be restrained within these closures; but when the lid is removed, it evaporates. Fourth is the condensation of air in a football by the force of what is driven in. That the air is made denser is proved easily, because the more is forced in, the heavier the bladder becomes. Then, says Galileo G., I took a sufficiently large glass bottle, whose mouth I carefully stopped, except that to the bottom I fitted a leather finger-cot, to which was most tightly joined the little bladder of a football; and then, with an instrument suited for the purpose, I forced in a very large quantity of air, and because it is easily condensed, two or three bottles of air are forced in, besides that air with which it was first full. He uses this experiment to investigate the weight of air; for thus the congested air makes the bottle heavier, and when the opening is made, the weight is lifted. But, just as he himself did it, he says, I take that experiment for the weight of air as concerning condensation; for it indicates a means of testing, so that we may know how much air has also been forced in, besides the earlier air that was in it. Therefore

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254 De Atomis. Disp. III. Igitur vt ostendat aerem esse condensatum, & vt inuestiget quantum aeris præter solitum adsit, alligat lagenam alteram primæ, quæ in fundo ita aptè perforata sit, vt aditus possit commodè aperiri itaq[ue]; firmè iuncto hoc vase cum superiori, datoq[ue] aeri condensato in subiectam aqua plenam aditu, tantum effluet aquæ, quantum aeris violenter congestum erat, & condensatum, apparebitq[ue]; hâc experientiâ quænam aeris quantitas in lagena præter primum aderat; quantitas enim aquæ expulsa æqualis est moli aeris quæ in lagenam intrusa erat. Quinta experientia condensationis est ista. Præparetur lagena vitrea cum animula vtris, vt superius dictum est, & violenter intrudatur aqua absq[ue]; aeris exitu, qui vt irruenti aquæ locum det necessariò debet comprimi, & sanè poterit etiam plusquam dimidium aquæ in sufflari in lagenam, quod autem maior sit aeris quantitas quam vt liberè medium lagenæ occupet, probatur, quia si exactè ponderetur cum arenæ granulis leuior est, cum locus datus est aeri quàm dum compressus erat ille aer. Hæc sunt p[er]tæcipua experimenta, nam quod de vase obijcitur cineribus pleno, quod tantumdem pene aquæ sit capax quam vacuum, de nummis in scyplum iniectis qui plenum omnino illibatumq[ue]; nullo effuso liquore magna quantitate demissi seruant, ità vt aliquando miserim in exiguum satis ciathum quantum fieri poterat aquâ cumulatissimum, nummos aureos philippicos, quos vulgo duplas vocant 45. nullo effluente liquore, flectitur enim conuexaq[ue]; sit in vitri limbis aqua, quam si vel accicula tangas, facilè per madium, & veluti signatum iter decidet: Quæ inquam, huiusmodi vulgò afferuntur experimenta difficultate carent, ideoq[ue]; operæ pretium non est in ijs immorari. Ad

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254 On Atoms. Disputation III. Therefore, to show that the air is condensed, and to investigate how much air beyond the usual amount is present, he ties another bottle to the first, which in the bottom is so neatly perforated that the passage may be conveniently opened; and so, with this vessel firmly joined to the upper one, and the condensed air given an entrance into the water-filled vessel beneath, so much water will flow out as there was air violently crowded in and condensed. And by this experiment it will appear what quantity of air was in the bottle besides the original amount; for the quantity of water expelled is equal to the volume of air that had been driven into the bottle. The fifth experiment of condensation is this. Let a glass bottle with a little bladder be prepared, as stated above, and let water be violently forced in without any exit for the air, which, in order to make room for the incoming water, must necessarily be compressed; and indeed more than half the bottle can even be blown full of water. But that the quantity of air is greater than would freely occupy half the bottle is proved, because if it is weighed exactly with grains of sand, it is lighter when room has been given to the air than when that air was compressed. These are the principal experiments; for the objection raised about a vessel full of ashes, that it can hold almost as much water as when empty, and about coins thrown into a cup which, without any liquid spilling, preserve it completely full and undisturbed even when a large quantity has been let in, so that at times I have poured into a very small cup as much water as possible, together with 45 gold Philippics, commonly called ducats, with no liquid running out—for the water bends and arches in the rim of the glass, and if you touch it even with a needle, it will readily fall through the middle, as though along a marked path: such things, I say, are common experiments of this sort and are without difficulty, and therefore it is not worth the trouble to linger over them. To

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C.2. Derarefact. et condens. 255 Ad soluendas verò difficultates, suppono primò, corpus humanum summopere esse porosum, experimento est, & con- iecturæ sudor, surfures aliæque transpirationes innumeræ de- quibus libello singulari egit in statica medica Sanctorius à Sæ- ctorio. Suppono secundò inter ea quæ tractamus corpora vix in- ueniri minus porosum quam sit vitrum, ratio est quia frequen- ti fusione ità depuratum est, sicq; partes partibus hærent ob vi- scositatem, vt sint valde constipati contortiq; huiuscemodi pori vnde etiam difficilis est, cuiuis etiam subtilissimo corpori exitus. Suppono tertiò, maximum visibile cætera obruere, & cum plures colores minutim permixti sunt, resultare vnam spe- ciem neutram quæ de vtroq; tamé extremo participat, sic ma- gnum lumen minores luces absorbet, & diuersi coloris arenu- læ mixtæ vnicum intermedium confusumq; repræsentant leu- copheumplerunq; qui de albo nigro, & intermedijs coloribus participat. Suppono quartò quod satis in hac materia inculcari nô po- test principium 15. corpora enim pro varia sui contempera- tione aliter exigunt esse in loco, & quidquid tandem molitio- num sit inter accidentia, illud porrò secundum naturæ præci- puam designationem tendit ad generationem quæ si non con- sequatur datur tamen quædam commotio, quæ illam intendit inchoare. Suppono quintò ità esse immixtum vaporibus, exhalatio- nibus, alijsq; corpusculis aerem, vt ne spirantes quidem possi- mus ab huiuscemodi impurorum attractiones satis cauere, id ponò ad solis radios satis videtur, palpatur nebulis terram ob- ruentibus, & tandem manifestè crepusculorum doctrinà con- uincitur, crepuscula enim ideò fiunt, quod vaporibus alijsque R crassio-

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C.2. Of rarefaction and condensation 255 To solve the difficulties, I assume first that the human body is exceedingly porous, as experience and conjecture show: sweat, surfures, and countless other transpirations, concerning which Sanctorius of Sæctorio treated in a separate little book in his Static Medicine. I assume second that, among the bodies we are dealing with, scarcely anything is found less porous than glass; the reason is that by frequent fusion it has been so purified, and thus the parts cling to one another on account of viscousness, so that its pores are very compact and twisted, whence the passage out is difficult even for the subtlest body. I assume third that the greatest visible thing overwhelms the rest, and that when many colors are minutely mixed there results one neutral species which participates in both extremes; thus great light absorbs lesser lights, and grains of sand of different colors mixed together represent a single intermediate and confused appearance, usually whitish, which participates in white, black, and intermediate colors. I assume fourth, that the principle 15 cannot be sufficiently inculcated in this matter: for bodies, according to their different tempering, require to be in place in different ways, and whatever the motions among accidents may be, that moreover tends according to nature’s chief designation toward generation, which, if it does not follow, there is nevertheless a certain commotion that tends to begin it. I assume fifth that the air is so mixed with vapors, exhalations, and other little bodies, that even we who breathe cannot sufficiently guard against the attractions of such impure things; this is sufficiently apparent with the sun’s rays, is felt by the mists covering the earth, and is finally plainly proved by the doctrine of the crepuscules, for twilight occurs for this reason, because with vapors and other thick-

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De Atomis. Disp. III. crassioribus fumis immixtus aer solis radios refringat, vnde, & sol cùm est sub horizonte, supra conspicitur, sicuti argenteum nummum in pelui repositum sex passuum distantia non videbis adieet à verò in peluim aqua, videbis: idem pariter refractionis arcanum in crepusculis agnoscunt docti omnes. Respondeo ad primam obiectionem negando comprimi aerem in cucurbitulis medicis, si enim condensaretur præcisè aer cur etiam applicatę ligno cucurbitulæ illud non duellum cum naturæ tantus sit vacui horror? causa itaq[ue] huiuscemodi attractionis est quia commoti spiritus ignei qua possunt irruunt, abeuntq[ue]; vnde natura facili negotio succedente carne locum replet: quo fit vt etiam ad illam tractionem humores confluant: neque me de via quâ abeût roges, sunt. n tam lati humani pori, adeo subtiles ignei spiritus, vt ab alijs corporibus secreti quauis facillimè penetrent euadantq[ue]; etiam per poros strictissimos, & multò difficilius est igneos spiritus detinere quam mollissimam carne vellicare quare natura quę semper faciliori vià sua facit, carnem trahit, dimittit spiritus: at si applices cucurbirulam ligno nihil attrahet, quia facilius est detinere spiritus igneos aliquantisper quàm lignum trahere. Ad secunda[m] fumi, vaporis, ignis, grani pulueris tormentarij nihil noui dictum volo quam quod proposit. 44. supposit. 4. & princip. 15. adduxi, ista enim tantum abest vt aduersarium iuuent, quin potius pro me faciunt, præsertim si suppositionem etiam tertiam ab opticorum principijs petitam illis experimentis adaptes, est enim huic experientiarum ordini consecrata. Vide disp. 1. c. 3. Ad tertiam, quod vasa obsignata frangantur applicata igni facilè respondeo ex princip. 15. si quidem id quod inclusum est corpus calore adueniente stimulatur admixtionem, & generationem ambit, vnde, & suas partes vult hinc, & inde ad aliarum

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On Atoms. Disputation III. Air mixed with thicker fumes refracts the rays of the sun, whence, when the sun is below the horizon, it is seen above, just as you would not see a silver coin placed in a basin from a distance of six paces, yet if water is poured into the basin, you will see it: likewise all the learned recognize the hidden secret of refraction in the twilights. I answer the first objection by denying that the air is compressed in medicinal cupping-glasses; for if the air were precisely condensed, why would cupping-glasses applied to wood not also draw it, since the horror of a vacuum is so great in nature? Therefore the cause of this kind of attraction is that the stirred fiery spirits rush in wherever they can, and go away; hence, as nature follows up easily, the flesh yields and the place is filled: and thus it happens that the humors also flow together to that drawing. Do not ask me by what route they depart; the pores of human flesh are so broad, the fiery spirits so subtle, that, when separated from other bodies, they can most easily penetrate and escape through any pores whatever, even the narrowest; and it is much more difficult to detain fiery spirits than to pinch the softest flesh. Therefore nature, which always takes the easier path for its work, draws the flesh and lets the spirits go. But if you apply a cupping-glass to wood, it will attract nothing, because it is easier to hold the fiery spirits for a little while than to draw the wood. As to the second point, concerning smoke, vapor, fire, and a grain of gunpowder, I wish to say nothing new except what I set forth in proposition 44, section 4, and principle 15; for these things are so far from helping the opponent that they rather support me, especially if you also apply the third supposition, taken from the principles of optics, to those experiments, for it is consecrated to this order of experiences. See Disputation 1, chapter 3. As to the third, that sealed vessels are broken when fire is applied, I answer easily from principle 15: namely, because what is enclosed, when heat arrives, is stirred up to admixture and generation, whence it seeks its own parts here and there toward those of the others.

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C.2. De rarefact. & condens. 257 aliarum vnionem quærendam dispergi, eius autem, quod hiante est ore vasis, corpuscula facilè auolant, & suæ libertati relicta stimulos caloris nullo negotio sequuntur. Quarta, & quinta experientia eiusdem omnino sunt generis quibus satisfacio per suppositionem quintam, fit enim vt intrudantur vapores aliaq[ue] corpuscula loco aeris qui insensibiliter difflatur, nequeverò quidquam experimenti à se facti audet depromere aduersarius, sed tantum modum illius explorationis ingeniosum indicat, quod facere sæpius tentaui neque quidquam ex his potui deprehendere, imo, etiam lagenam capacissimam omni ope aere infercij, deinde magna vi aquam immisi, & referato orificio appositoq[ue] tenuissimo filo accenso explorabam num saltem ab erumpente violenter aere fluitaret flamma, sed omnia manserunt æquè imperceptibilia atq[ue] si suo aere primo plenam reliquissem: quod autem ponderosior fiat, id propter corpuscula, & vapores continget. Imo ab his experientijs, & præcipuè ab ea vacui fuga, quæ apud omnes decantata est, cõtendo nullam dari rarefactionem neque condensationem. Si enim datur rarefactio, & condensatio equidem nihil facilius est quam hæc duo, nullo enim negotio ad aliarum rerum exporrectionem, & amplitudinem stringitur aer, nullo negotio dilatatur, ad quid ergo siphonibus tubifq[ue] tractorijs eleuabitur aqua ad vlnas 18. (nam vacui fugà nihil plus in arte factis poret siue angustus siue latus aquæ cylindrus) potest enim aer rarefieri aqua statim cõdenlari vnoq[ue] aeris halitu siphonem subeunte totus oppleri sipho tubusq[ue]; facilius enim est aeri rarefieri quam aquæ ascendere cum tot machinis illud ars moliatur, illud verò ad fumi, vaporum, motuumq[ue] quorumuis arbitrium fiat, si ergo datur fuga vacui sequitur non dari rarefa- ctionem neque condensationem, quam quidem popularem, &

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C.2. On rarefaction and condensation 257 the union of the others being sought, dispersal occurs, and the little particles of that which is at the mouth of the vessel easily fly away, and, left to their own freedom, they readily follow the impulses of heat. The fourth and fifth experiments are entirely of the same kind, which I answer by the fifth supposition; for it happens that vapors and other little corpuscles are introduced in place of the air, which is imperceptibly dispersed, and the adversary dares not produce anything from an experiment made by himself, but only indicates the ingenious manner of testing it. I have often tried to do this and could detect nothing from these things; indeed, even when I filled a very capacious flask, by every means, with imported air, then with great force I poured in water, and, the opening having been reopened and a very fine thread attached and lit, I tested whether at least the flame would flicker from air violently bursting out, but everything remained just as imperceptible as if I had left it full of its own air from the beginning. But that it becomes heavier will happen because of corpuscles and vapors. Indeed, from these experiments, and especially from that flight from the void, which is trumpeted by everyone, I contend that no rarefaction or condensation occurs. For if rarefaction and condensation are granted, then truly nothing is easier than these two things; for the air is, without difficulty, compressed to the expansion and breadth of other things, and without difficulty expanded. Why then, with siphons and drawing tubes, is water lifted up to 18 cubits? (For the flight from the void contributes nothing more in contrivances, whether the column of water be narrow or broad.) For air can be made rarefied, water can immediately be condensed, and with one breath of air entering the siphon, the siphon and tube are filled completely. For it is easier for air to be rarefied than for water to rise, though art contrives the latter with so many machines, whereas the former is subject to the will of smoke, vapors, or any movements whatsoever. Therefore, if the flight from the void is granted, it follows that rarefaction and condensation do not occur, which indeed the common opinion, and

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CAPVT TERTIVM. De alteratione, intensione, & remissione qualitatum iuxta Democritum. Voniam à vadis, & scopulis iam nostra cuasit philosophia facillimus nobis reliquus cursus ostenditur, totum itaq[ue] hoc caput vnicà propositione expedio, modum enim agendi atomorum superius attigi prop. 33. & 34. & est apud Aristotelem lib. 1. degen. 1. 56. 57. apud Danielem sennertum quem superius laudaui. PROPOSITIO XLVIII. Potissima corporum alteratio fit per meatus insensibiles, intensio per ordinem, et positionem multiplicem atomorum, remissio per solutionem ordinis. PRimam propositionis parte probauimus propos. 33. disp. 2. Secunda pars quod intensio per ordinationem atomoru[m] fiat probatur. Omnia constant ex atomis, tùm accidentia corporea, tùm etiam substantiæ, nam de spiritualibus non disputo, atqui intensio fit cum in eadem parte subiecti sunt plures gradus qualitatis, ergo tunc subiectum intensiorem habet qualitatem cu[m] plures subiectat atomos: Sit in atomo aque A atomus vna frigoris, in atomo B frigidiori erunt duæ aut tres huius accidentis atomi indiuisibiles, tùm secundum intensio- nem,

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CAPUT TERTIVM. On alteration, intension, and remission of qualities according to Democritus. Now that our philosophy, having escaped the shallows and rocks, shows the rest of the course to be very easy for us, I shall therefore explain this whole chapter with a single proposition; for the way in which atoms act I touched on above in props. 33 and 34, and it is found in Aristotle, book 1, de gen. 1. 56, 57, and in Daniel Sennert, whom I praised above. PROPOSITION XLVIII. The chief alteration of bodies takes place through insensible passages; intension through the order and manifold position of atoms; remission through the dissolution of order. We proved the first part of the proposition in prop. 33, disp. 2. The second part, namely that intension takes place through the ordering of atoms, is proved as follows. All things consist of atoms, both corporeal accidents and substances too, for I do not dispute about spiritual things; but intension occurs when in the same part of the subject there are several degrees of quality, therefore then the subject has a more intense quality when it subjects more atoms. Let in atom A there be one atom of coldness; in atom B, which is colder, there will be two or three indivisible atoms of this accident; then according to intension,

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C.3. De Alteratione atomorum. 259 nem, tùm secundum extensionem: quàm autem multiplex sit huiuscemodi ordo eâ assequi licet coniecturâ quæ ad paruitatem atomorum suspicandam nos deduxit, si enim aer noster impurus se habet in pondere ad aquam vt 10000 ad vnum, quanta erit proportio igneæ atomi viuidæ cu[m] atomo aerea cui insita erit vnica caloris atomus, ea fortè quæ 1000000 ad 1. Ex hac philosophia facilè explicamus quomodo intendantur propagentur, & finiant sphæræ actiuitatis, dùm eâ proportione decrescunt vt vltima tandem quæ vnica est atomus in extrema sphæræ circumscriptione sit sterilis, aliæ autem quæ multæ sunt in eodem subiecto fæcundæ sint, & parem numerum vnitate exceptà generent in proximo sibi subiecto. Sint enim consequentes atomi substantiales A, B, C, D, E. Sitq; A quinq; atomorum ordinatione calidum, procreabit in B 4. atomos, B autem degenerans educet tres ex C, C auté duas parturiet in D, quæ penultima sphæræ atomus cælibem vnam atomum eamq; infecundam generabit in E, vbi sphæræ actiuitatis nouissimus erit terminus, nô est tamen quod hæc regula exactè seruetur, sed paucis multa complector mysteria, dùm dico sphæræ actiuitatis radios propagari vt angulos pyramidu[m] quarum basis in agente sit, apex in sphæræ termino sicut ergo modò claudu[n]tur angustis spatijs lineæ, modò post grande[m] hiatum breui coeunt vt fit in obtusis angulis, modò latè funduntur vt fit in acutissimis angulis, qui ab exigua sui origine modicaq; basi lineas propagant longissimè, pari etiam proportione sphæram actiuitatis vario ordine, multiplici[us]; dispositione vniformiter difformiter ad sensum produci est existimandu[m]: Refractionibus autem reflectionibusq; varia contingunt quæ ex his possumus etiam explicare, nam Democritus ad omnes omnino difficultates principia ponit, videturq; vt ait Aristoteles, omnia curasse. R 3 Tertia

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C.3. On the Alteration of Atoms. 259 now according to extension: how manifold such an order is may be inferred from that conjecture which led us to suspect the minuteness of atoms; for if our impure air stands in weight to water as 10,000 to 1, what will be the proportion of a fiery living atom to an airy atom in which there is seated a single atom of heat, perhaps 1,000,000 to 1. From this philosophy we easily explain how the spheres of activity are extended, propagated, and brought to an end, while they decrease in such proportion that at last the final one, which is a single atom on the outer boundary of the sphere, is barren, whereas the others, which are many in the same subject, are fertile, and generate in the next subject a like number, apart from unity. Let the successive substantial atoms be A, B, C, D, E. And let A, by an arrangement of five atoms, be warm; it will produce 4 atoms in B, but B, degenerating, will bring forth three from C, C however will bear two in D, and the penultimate atom of the sphere will generate one unmated atom, and an infertile one, in E, where the last limit of the sphere’s activity will be reached. Yet it is not that this rule is to be observed exactly, but I include many mysteries in a few words when I say that the rays of the sphere of activity are propagated like the angles of pyramids whose base is in the agent and whose apex is at the limit of the sphere; just as lines are sometimes confined within narrow spaces, sometimes after a great gap they come together briefly, as happens in obtuse angles, sometimes they are spread widely, as happens in acute angles, which from a small origin and modest base propagate lines very far, so too by an equal proportion the sphere of activity must be thought to be produced perceptibly in a varied order, with manyfold arrangement, uniformly and disuniformly. But with refractions and reflections various things occur, which from these points we can also explain; for Democritus lays down principles for absolutely all difficulties, and, as Aristotle says, seems to have attended to everything. R 3 Third

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De Atomis. Disput. III. 260 Tertia pars sequitur manifestè ex secunda perit enim vna caloris atomus diuersusq[ue], manet ordo, quippe qui totam immutat sphæram actiuitatis: si pereat in eius centro, seu fonte, & in particulari suo subiecto aliam facit dispositionem quæ numeris alijs efferri debet. Vnum superest argumentum Hippocratis lib. de natura humana, quod fusè deducit Galenus lib. 1. de elementis cap. 2. vbi ostendit ex atomorum admissa doctrina sequi impossibilem alterationem dolorem præsertim. Sed concludit tantu[m] ex hypothesi contra eos qui vnicum admittunt elementum, aut atomos vnius tantum rationis, quare (inquit) nequaquam sumus ex vna simplici vniformiq[ue]; substantia constituti: quod concedit Democritus cum elementa dari tria præter aerem existimet, vt patet ex Aristotele citato in synopsi doctrinæ Democriticæ, deinde sensus non fit nisi ex atomis secundarijs, quod dico vt diluam quæ subdit Galenus eodem in loco. Quæres primò cur densitas subiecti iuuet actionem. Resp. quia magis vniuntur atomi sitq[ue]; ordo firmior collectiorq[ue]; neque ità à centro vigoris distant partes, virtus autem vnita fortior: densitas verò non agit, quia non intendit assimilare sibi passum hoc est facere illud densum, verus autem agentium character est assimilatio. Quæres secundo an quatuor atomi caloris in atomo A possint producere totidem in atomo B. Resp. non posse immediatè sed tantùm mediante forma substantiali quam ad vltimum intentionis complementum stimulabunt. Quæres tertio an atomi omnes caloris sint eiusdem speciej? Resp. esse, neque enim vlla ratio cogit hanc inutilem multiplicationem specierum admittere. Quæres quartò an in atomo quæ octo, verbi gratià, caloris gradus

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On Atoms. Disputation III. 260 The third part follows clearly from the second: for one atom of heat perishes and the order remains different, since it wholly changes the sphere of activity; if it perish in its center, or source, and in its particular subject it makes another disposition, which must be expressed by other numbers. One argument remains from Hippocrates, in the book On the Nature of Man, which Galen expounds at length in book 1 of On the Elements, chapter 2, where he shows that from the admitted doctrine of atoms there follows an impossible alteration, especially of pain. But he concludes only from the hypothesis against those who admit a single element, or atoms of only one kind; wherefore (he says) we are by no means constituted of one simple and uniform substance: which Democritus grants, since he thinks that three elements are given besides air, as is clear from Aristotle cited in the synopsis of Democritean doctrine; then sensation does not arise except from secondary atoms, which I say in order to refute what Galen adds in the same place. You ask first why the density of the subject helps action. Answer: because the atoms are more united and the order is firmer and more compact; nor are the parts so far from the center of force, but united power is stronger: density, however, does not act because it does not intend to assimilate the patient to itself, that is, to make it dense; but the true mark of agents is assimilation. You ask secondly whether four atoms of heat in atom A can produce as many in atom B. Answer: not immediately, but only through the substantial form, which they will stimulate up to the final completion of the intention. You ask thirdly whether all atoms of heat are of the same species? Answer: they are, for no reason compels us to admit this useless multiplication of species. You ask fourthly whether in an atom which contains eight, for example, degrees of heat

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C.3. De Alteratione. 261 gradus habet, sit quidam primus ratione aliquà, vt situ, prio- ritate, dignitate &c. Respondeo posse esse primùm aliquem, aliu[m] secundùm ra- tione temporis quo sunt educi, alteratio enim sit successuè. Quæres quintò quomodo intereant illæ atomi, & quor- dine, cum enim nulla sit differentia nisi indiuidualis cur A pe- ribit potius quam B, aut B quam C? Respondeo modum interitus sumi in sphaera actiuitatis à prima instratione minuente angulum, qui deinde hac serie im- minutus eadem manente basi, sed diminuta propagatione re- stat; in atomo autem singulariter si id quæras. Respondebo sequi analogicè hanc spheræ destructionem, & penes centri fluxus angulorumq[ue] mathematicorum dimensiones, figura- tionesq[ue]; varias interitus ordinem sumi. Quæres sextò an sphaera actiuitatis propagetur in instanti? Resp. plurima quidem agentia incredibili velocitate eam propagare vt sol qui ab densitate sibi innata, firmissimaq[ue]; par- tium compaginatione, qua fortasse vnicum orbis est corpus quod poris careat, quodq[ue]; ex elementorum delicijs compa- ctum, tantùm ex solidioribus aqua, terra, & igne hausit vt nihil acris habeat, ideòq[ue]; ob firmissimam, & æquabili tenore dispo- sitam seriem atomorum longissimè, & pene in instanti lumen fundit ad nos, sed imperceptibili successione id fieri necesse est, cum nulla sit ratio cur de calore id potius quam de luce di- camus, videmusq[ue]; in nubibus frequentes lucis fontes, dùm nubes viuaciori radio sol peruadit: cæterum ratio ordinis di- spositionisque Democritice id exigere videtur, cùm pars vic- mior agenti de ipso plus citiusq[ue]; participet quam remota. Quæres septimò quomodo fiat antiperistalis? Respon. fieri quia ambiens contrarium coercet dispersio- nem corpusculorum impeditq[ue]; ne diffluant, quare viuuntur magis, virtus autem vnitæ viuidior. R 4 Quæ

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C.3. On Alteration. 261 has degrees, so that there is some first thing by a certain relation, as by place, priority, dignity, etc. I answer that there can be some first, another second according to the relation of the time in which they are brought forth, for alteration takes place successively. You ask fifthly how those atoms perish, and in what order, since there is no difference except individual, why should A perish rather than B, or B rather than C? I answer that the manner of destruction is taken in the sphere of activity from the first narrowing, diminishing the angle, which then, by this series, having been diminished with the same base remaining, but the spread lessened, remains; but in the atom, if you ask it in particular, I shall answer that this destruction of the sphere follows analogically, and according to the central flow and the mathematical dimensions of angles and shapes, various orders of destruction are to be taken. You ask sixthly whether the sphere of activity is propagated in an instant? I answer: indeed, many agents propagate it with incredible speed, as the sun does, which by the density innate in it, and the very firm compactness of its parts, for perhaps it is the only body of the heavens that is without pores, and which, being compacted out of the delights of the elements, has drawn only from the more solid things—water, earth, and fire—so that it has nothing of air in it, and therefore, because of the firmest series of atoms arranged with equal regularity, it pours forth light to us from a great distance, and almost in an instant; but it must happen by imperceptible succession, since there is no reason why we should say this rather of heat than of light. And we see frequent sources of light in the clouds, while the sun passes through the clouds with a more lively beam. Moreover, the reason of order and arrangement in the Democritean manner seems to require this, since the part nearer to the agent participates more and more quickly in it than the remote part. You ask seventhly how antiperistasis comes about? The answer: it comes about because the surrounding contrary restrains the dispersion of the tiny bodies and prevents them from flowing apart; for that reason they are stirred more, and the united force is more lively.

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De Atomis. Disp. III. Queres octauò an Democritus admiserit qualitates diuersas à primis cum Galenus lib. 1. de elementis cap. 2. sic ex mente ipsius loquatur. Lege enim (dicebat Democritus) color est, lege amarum, lege dulce; atomus verò, & vacuum verè est, ipse ET ELS dixit; Credidit enim ille sensiles qualitates ex individuorum illorum corpusculorum conuentu per solam ad nos qui sentimus collationem gigni, ipsa verò naturà nihil esse album aut nigrum, flauum aut rubrum, amarum aut dulce, quippe hoc illi lege, seu NOMO significabat, ex nostra nimirum existimatione non ex ipsa rerum natura: ita etiam illi ETHEH ab ET EON deductum est, quod verum significat: vt vniversi sermonis illius sensus sit: Arbitrantur quidem homines quippiam esse album, vel nigrum, vel dulce, vel amarum, sed re vera omnia sunt vnum, & nihil: nam & ille hoc modo loquitur qui atomos vocat vnum, vacuum autem nihil; hæc Galenus, qui subdit atomos omni qualitate carere sed ex illarum synodo omnes oriri, & agitari atomos per omnem æternitatem, quem integrum Galeni locum etsi satis feliciter verterit Trincauellius, aliqua nihilominus addita alia imminutæ significationis vocabula reperi, cum ad græci exemplaris fidem testimonium pro Democriti doctrina adeò luculétum reuocaui, est enim mihi integer Galenus grecus, quod opus nuspiam reperiri existimât aliqui viri doctissimi, Aldi characteribus editum est ab Andrea Torresano Venetijs anno 1525. Resp. Democritum admisisse has omnes qualitates de quibus hic est sermo, sed nihilominus tamen ità esse voluit in natura vt cuipiam vnu[m] dulce esset, alteri verò amarum, quis enim nescit ceruos serpentibus, capras cicutâ pingueiscere vt ait Lucretius at nobis est venenum. Nonnullis rosæ sunt exose vsq; ad animi deliquium, alijs sunt delicię: coturnices vescuunt helleboro gallinæ araneis: pariter mulierem vidi quæ moschum magis quam foetorem cadaueris horrebat, & sacharo dulci-

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On Atoms. Disp. III. You ask, thirdly, whether Democritus admitted various qualities distinct from the primary ones, since Galen in book 1, On the Elements, chapter 2, speaks thus from his own understanding. For “by law,” said Democritus, “color is, by law bitter, by law sweet; but atom and void are truly”; he himself said ET ELS. For he believed that sensible qualities are produced from the meeting of those tiny bodies, by the mere comparison of them made with us who perceive them, while in nature itself nothing is white or black, yellow or red, bitter or sweet, since for him this signified “by law,” or NOMO, that is, from our own estimation, not from the nature of things itself: thus also ETHEH in that text is derived from ET EON, which signifies “true”; so that the sense of the whole statement is this: men indeed think that something is white, or black, or sweet, or bitter, but in truth all things are one and nothing; for in this way too he speaks who calls atoms “one” and void “nothing.” Thus Galen, who adds that atoms are devoid of all quality, but that all things arise from their conjunction, and that atoms are moved through all eternity. Although Trincavellius translated this whole passage of Galen fairly successfully, I nevertheless found in it some words added, and others diminished in meaning, when I brought back this testimony, so clear in support of Democritus’s doctrine, to the fidelity of the Greek exemplar; for I have the complete Greek Galen, printed in Aldine characters by Andrea Torresano in Venice in the year 1525, a work which some very learned men think cannot be found anywhere. Reply. Democritus admitted all these qualities of which the present discussion is concerned, but nonetheless he wanted it to be so in nature that to one person one thing would be sweet, but to another bitter. For who does not know that deer fatten on serpents, goats on hemlock, as Lucretius says, “but to us it is poison”? To some, roses are so hated as to bring on faintness of spirit; to others they are delights. Quails feed on hellebore, hens on spiders. Likewise I saw a woman who shuddered at musk more than at the stench of a corpse, and at sweet sugar...

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C. 3. de Alteratione atomorum. 263 dulcibusq; vexabatur, hoc itaq; voluit indicare Democritus certâ quadâ lege, & proportione inter agens, & patiens aliud alteri dulce esse quod amaru est alteri; Cirus numquam volu- ptuolius bibit quam aquam turbidam, nomo ergo dulcis erat, æger saccharum ob impuros succos amarum pronuntiat nomo ergo saccharum est amarum &c. Si cui verò id parum probabile videatur legat Maffeum vbi de Iaponum moribus agit, illis nostra musica absurdissima est, insipide sunt epulæ nostro modo apparatæ, Europæana diæta inutilis egrotis quibus pisces exhibent crudos quos sani coctos comedunt, Europæi nullam in Iaponum musica harmoniam, nullum in suis epulis saporem offendunt, hæc omnia ergo no- mo, siuè proportione sunt harmonica, sapida, & sana: nostros odores quibus delicatissimi quiuis in Europa recreantur vt fę- tores quosdam abhorrent, sui verò nobis non arrident, nomo ergo odoratum est moschum, odora ambara, & zibetum: reue- ra cum inter agens, & passum debeat intercedere proportio, si illa desit non sequetur effectus, at primas elementorum qua- litates non eâ voluit proportione probari, neq; dixit Galenus nomo ignem esse calidum &c. De coloribus acturi sumus cap. seq. vacuum autem, & atomum verè dixit esse hoc est vniuersali intellectus acceptatione quia non requiritur ad hæc ea pro- portio quæ in qualitatibus no rarò desideratur, sunt enim fortè quidam odores quos percipit canis quorum homo non est ca- pax ETEON vocabulum est poeticum deriuatum ab EO, sum. CAPVT

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C. 3. On the Alteration of Atoms. 263 and was troubled by sweet things; this, therefore, Democritus wished to indicate: by a certain law and proportion between the agent and the patient, one thing is sweet to one, which is bitter to another; Cyrus never drank more pleasantly than muddy water, therefore to him it was sweet; a sick man pronounces sugar bitter because of impure humors, therefore sugar is bitter, etc. If anyone should think this less probable, let him read Maffei where he discusses the customs of the Japanese: our music is most absurd to them; dishes prepared in our manner are tasteless; European diet is useless to the sick, for they are given raw fish, which healthy people eat cooked; Europeans find no harmony in Japanese music, no savor in their dishes; therefore all these things are not in themselves, but according to proportion, harmonious, tasty, and wholesome: our odors, with which anyone whatever in Europe is refreshed, they abhor as some kind of stench; theirs, however, do not please us; therefore musk, amber, and civet are odoriferous to them. Truly, since a proportion ought to intervene between agent and patient, if that is lacking the effect will not follow; but he did not wish the primary qualities of the elements to be proved by such proportion, nor did Galen say that fire is hot, etc. We shall speak of colors in the next chapter. But he truly said that vacuum and atom are something, that is, in the universal acceptance of the intellect, because for these there is not required that proportion which is not seldom desired in qualities; for perhaps there are certain odors perceived by a dog of which man is incapable. ETEON is a poetic word derived from EON, sum. CHAPTER

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CAPVT QVARTVM. De Colorum generatione iuxta Democritum. Visquis in naturæ adyta familiariùs se se ingessit, nihil penè ab intellectus vi de lumine, coloribusq; videri à se potuisse confessus est, sunt enim quatuor quæstiones, quæ humanum captum videntur superare: de compositione continui, de motu, de specierum intellectualium imaginationisq; oeconomia, & de colorum causis: nihilominus tamen, vt imaginationis vires specierûq; naturam dectissimè probauit Democritus ità etiam de coloribus sanissimè, certè facillimè pronuntiauit. PROPOSITIO XLIX. Color est lumen internum corporum ab atomis igneis diffusum, & per allas atomos refractum. QVis fuerit author libelli de coloribus qui vulgò Aristotelis operibus adnectitur, quamuis & Stagiritæ, & Theophrasti ingenio principijsq; aduersetur, & vtriusq; sublimi mente sit indignus, satis disputatur inter doctos. Sed enim in primo capite primaq; fere linea, hoc absurdum pronuntiat: aer & aquæ per se sunt naturà alba, ignis autem & sol flaui, terra verò naturà alba est, & infra, niger autem color consequitur elementa cum in se invicem mutantur: Sed quam id mereatur audiri quemlibet facio iudicem: cum originales duos colores faciat alb,um & flavum reliquosq; omnes ex his ortos, quam autem ratione fiet niger? tinctura enim nulla est nisi ab elemétis quæ flaua sunt & candida, vnde si eximium albedinis gradum qualem

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CHAPTER FOUR. On the generation of colors according to Democritus. Whoever has more intimately entered the recesses of nature has confessed that he could hardly perceive anything by the power of the intellect concerning light and colors; for there are four questions which seem to surpass human understanding: concerning the composition of the continuous, concerning motion, concerning the economy of intellectual species and of imagination, and concerning the causes of colors. Nevertheless, just as Democritus most acutely demonstrated the powers of imagination and the nature of species, so also he spoke about colors most soundly, certainly most easily. PROPOSITION XLIX. Color is the internal light of bodies diffused from fiery atoms, and refracted by other atoms. Who was the author of the little book On Colors which is commonly attached to the works of Aristotle, although it is opposed both to the genius and to the principles of the Stagirite and of Theophrastus, and is unworthy of the lofty mind of either, is sufficiently discussed among the learned. But in the first chapter and almost the first line it makes this absurd statement: air and water are by nature white in themselves, fire and the sun are yellow, but earth is by nature white; and below, black color follows the elements when they are changed into one another. But I leave anyone as judge of how much this deserves to be heard: since it makes white and yellow the two original colors, and all the rest arising from these, how then will black be produced? For there is no dye except from the elements which are yellow and bright white, whence if the highest degree of whiteness is removed, such as

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C.4. De Colorum natura 265 qualem in niue prima videmus, ad exquisitam flauedinem qua[m] habent genistæ flores, per omnes omnino colorum intermediorum gradus deducas, omnes colores possibiles secundum istam sententiam attingere necesse erit, quamuis nec purpureus, nec caeruleus, nec viridis nec niger eorumq; affines sint libati. Eleganter omnino Costæus l.2. de stirpium natura cap.44. Si color perspicui terminatiq; corporis extremum est quod admittunt omnes, ergo aer, aqua, ignis qui alienis terminis continentur colore carent, cum non sint terminata, terra autem colore carebit cum non sit perspicua, nullo igitur colore pura elementa tingi necessarium est. Sed enim an Claudiano assentiredebemus qui ità ait in Mallij paneg. Sitne color proprius rerum lucisne repulsæ Eludant aciem? an Lucretij sententiæ qui vult colores. progigni luminis ictu? an alijs qui à quatuor primarum qualitatum dominio omnes oriri colores crediderunt? Suppositis aute[m] his principijs elementa carere omni colore cum sunt defecata, & ab omni mixtione immunia; Et existione perspicui, & opaci varios enasci colores (quos apparentes vocant, melius tamen dicerentur transeuntes, alij verò quos veros dicunt, aptius permanentes appellarent) sic explico sententiam Democriti. Ad corporis cuiuscunq; compositionem concurrunt elementales atomi, hoc est terræ, aquæ, ignisq; particulæ, terra, quidem cubos suos confert de quibus egimus initio eosq; perspicuos, & diaphanos secundum quid, hoc est, cum secundum latera lumen excipiunt ignisq; radios per aquæ atomos non habetatos hauriunt; aqua verò versatiles suas atomos omnisq; figuræ capaces, ignisq; tanquam nobilior mixti pars lumine

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C.4. On the nature of colors 265 such as we see in the first snow, to the exquisite yellowness which the flowers of genista have, if you carry it through all the intermediate degrees of colors whatsoever, it will be necessary to reach all possible colors according to this opinion, although neither purple, nor blue, nor green, nor black, nor their affinities are drawn in. Quite elegantly Costæus, l.2. De stirpium natura, chap. 44. If color is the extremity of a bounded and distinct body, which all admit, then air, water, fire, which are contained within foreign limits, lack color, since they are not bounded; earth, however, will lack color since it is not transparent. Therefore it is necessary that the pure elements be touched by no color. But then, should we agree with Claudian who says thus in the panegyric of Mallius: Is there a color proper to things, or do they elude the gaze because of the repulsion of light? or with the opinion of Lucretius, who wants colors to be produced by the blow of light? or with others who believed that all colors arise from the dominion of the four primary qualities? But with these principles assumed, the elements are devoid of all color when they are purified and immune from all mixture; and from the existence of the transparent and the opaque various colors arise (which they call apparent, though they would be better called transient, while others, which they call true, would more suitably be called permanent). Thus I explain the opinion of Democritus. To the composition of any body whatsoever elemental atoms come together, that is, particles of earth, water, and fire. Earth, indeed, contributes its cubes, of which we spoke at the beginning, and these, being transparent and diaphanous in a certain respect, that is, when on their sides they receive light and draw in the rays of fire through the unimpeded atoms of water; water, moreover, with its versatile atoms capable of every shape, and fire as the nobler part of the mixture, with light

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266 De Atomis. Disp. III. mine suo perfusus mixtionem ingreditur, & hoc quidem lumen cum atomi laxitatem non excedat videri seorsim non potest nisi plurimus ignearum particularum cumulus adsit vt in flamma mixtisq[ue]; omnibus contingit, itaq[ue]; aqua absolutè quidem diaphana est, terra verò secundum quid. Quod autem hæc ità se habeant primò quidem lumen inesse igni dubium esse non potest, tum experientiâ tum etiam omnium pene philosophorum authoritate, & rationibus. Videamus enim focum, cædelas, lampadesq[ue]; lucere, & hoc instrumento vicarios soles quotidie astraq[ue]; domestica facimus: at causa aliqua proxima luminis istius est assignanda, quæ nulla fingi potest quam ignis: Ille quidem licet in se ipso sit lucidus nihilominus effectum suum non promit nisi in humido pingui dominetur, ratio est quia humidum pingue videtur compactarum partium, viscosarumq[ue]; esse, difficilius ergo ab his laqueis se se expediunt ignei spiritus, vnde & plures simul cateruatim in flamma morantur, factaq[ue]; multitudine conspicui fiunt, lucentq[ue]; eâ de causâ quæ pinguiora sunt, & viscidiora diutius flammam pascunt, vt cera quæ gluten habet immixtum, vt ait Apum Cælarumq[ue]; Poeta Vigilius collectum hæc ipsa ad numera glutem Et visco, & phrygiæ seruant picefirmius Idæ. Ob lentam etiam viscosamq[ue]; humiditate pinguem diutissimè lampades viuunt, minus sæuum, modico verò tempore lignu[m], minùs viscosa, minùs perdurant, pingua plus flammæ lucentis edunt, vt pinus quæ pinguis est sed visco caret flammam reddit hilarem, sed nullius pene custodiæ, quercus viscidior est, quam pinguior, subtristi ergo est flammà quamuis diuturnâ, & economicæ vtili: fraxinus quod viscida pinguisq[ue]; sit focorum præcipuus est honor. Lumen itaque puro defæcatoq[ue]; ignis elemento inest. Aquam

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266 On Atoms. Disp. III. …being imbued with its own mine, it enters into mixture; and this light, since it does not exceed the looseness of the atoms, cannot be seen apart unless there be present a very large accumulation of fiery particles, as happens in flame and in mixtures of all kinds; thus water is absolutely transparent, but earth only in a qualified sense. That these things are so can first of all admit of no doubt, for light is in fire, both from experience and from the authority and arguments of almost all philosophers. For let us look at hearths, candles, and lamps shining, and by this instrument we make daily our substitutes for suns and our domestic stars: but some proximate cause of that light must be assigned, and none can be imagined except fire. Although fire is bright in itself, nevertheless it does not produce its effect unless it prevails in a moist fat substance; the reason is that a moist fat substance seems to be of compact and viscous parts, and therefore the fiery spirits more difficultly free themselves from these snares, whence also many together remain in a heap in the flame, and, having become numerous, are made conspicuous and shine. For this reason things that are more fatty and more viscid nourish the flame longer, as wax, which has glue mingled with it, as the poet Virgil says of bees and wax: collectum haec ipsa ad numera glutem Et visco, et Phrygiae servant pice firmius Idae. Because of a slow and viscous fatty moisture, lamps also live for a very long time, with less violence; but wood, for a short time, if it is less viscous, endures less. The fattier give forth more shining flame, as pine, which is fatty but lacks glue, produces a cheerful flame, but of scarcely any steadiness; oak is more viscid and therefore more gloomy in flame, though lasting and useful for the household; ash, because it is viscid and fatty, has chief honor among hearth-fuels. Thus light is present in the pure and refined element of fire. Water

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C.4. De Colorum natura. 267 Aquam diaphanam esse dubium non est cùm sit eadem ratio totius homogenei singularumq; eius partium, & istud sanè ele- mentum viderur priscæ primæuæq; suæ puritatis vestigia pul- chra retinere in ijs duabus qualitatibus quas in aqua omni per cipimus perspicuitate, & fluiditate. Cæteras enim ob neces- sarium cum alijs corporibus commercium corrumpit, etiam foedus illud quo lenora debet supernatantia ferre, nam in Pe- ruuia, vt inquit Yncas Garcillasso de la Vega, nobilis Peruanus, qui commentaria Regum Peruanorum edidit, Lacus est Titica- ca 48. vlnis altus circumfusus verò per milliaria plusquam du- centa, qui omne omnino lignum absorbet, neque vel leuissimâ nauculà potest nauigari; cum itaq; aqua omnibus fere quali- tatibus alijs idemtidem varijsq; in locis priuetur, & maneans vbiq; gentium illæ duæ transparentia, & fluiditas quæ frigorit vi tamen præpeditur, fatendum est primigeniam illam anti- quamq; elle aque dorem; Terræ verò atomos perspicuas esse secundum quid colligi- mus à posteriori, quia si nunquam essent lumini inuiæ omnia corpora essent diaphana, & si semper essent adiaphanę nul- lis corporibus mixtis perspicuitas competeret, quam videmus in vitris, crystallo, adamante, smaragdo alijsq; tum solidis tum liquidis corporibus: præterea sal in quo terrę dominium agno- scunt plurimi Diaphanum est crystalli instar in Hispania Tar- raconensi. Annotanda præterea est differentia inter lumen purum, & impurum. Purum illud est quod omni alieno caret definiturq; forma accidentalis, quæ facit actualiter visibile perspicuum, quod alieno colore terminatum in potentia erat tantum visi- bile; hæc est explanatio eius obscuræ definitionis quam Aristo- teles tradidit, actus perspicui vt perspicuui est, l.2. de an. t. 69. Lumen verò impurum est illud quod aliquam à terminante tincturam

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C.4. On the nature of colors. 267 There is no doubt that water is transparent, since the same reason applies to the whole homogeneous body and to each of its parts; and this element certainly seems to preserve the traces of its ancient and primitive purity in those two qualities which we perceive in all water: transparency and fluidity. For the rest, because of its necessary intercourse with other bodies, it is corrupted, even in that quality by which it ought to bear lighter things floating upon it; for in Peru, as Yncas Garcillasso de la Vega, a noble Peruvian who published the Commentaries of the Peruvian Kings, says, there is Lake Titicaca, 48 leagues in breadth and, all around, more than two hundred miles in extent, which absorbs every kind of wood whatsoever, and cannot even be navigated by the lightest little boat. Since, then, water is deprived of almost all other qualities in different places and at different times, and everywhere retains those two, transparency and fluidity, though the latter is hindered by the force of cold, it must be admitted that it preserves its original and ancient nature. As for earth, we gather from experience that its atoms are transparent in a certain respect, because if they were never impervious to light all bodies would be transparent; and if they were always opaque, no mixed body would possess transparency, such as we see in glass, crystal, diamond, emerald, and other bodies, both solid and liquid. Moreover, salt, in which many recognize the dominion of earth, is transparent like crystal in the Tarraconensian Spain. A distinction must also be noted between pure and impure light. Pure light is that which lacks all foreign element and is defined by an accidental form, which actually makes visible that which is transparent; and, being terminated by a foreign color, it was only potentially visible. This is the explanation of that obscure definition which Aristotle gave: the act of the transparent as transparent, bk. 2, De Anima, text 69. But impure light is that which has some tint from the terminating body

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tincturam habet, nihilq[ue]; aliud est quam color quispiam lumen inficiens, vel quod istius radij sint refracti, vel quod in corpus aliquod impingant terminati. Vel vt nitidius ait Aguillonius lib. 1. prop. 38. & 41. suæ opticæ, lumen impurum est lumen incorpore aliquo variè refractum, vel à luminesic refracto pro- pagatum. Lumen uerò purum uideri non posse, facile conuinci potest ratione, & experientia; Ratione quidem quia in omni usione requiritur terminus, actiones enim debent limitari, at- qui lumen purum non potest esse terminatum, ergo non potest uideri; Experientia uerò quotidiana est, quod enim lu- men in pariete illapsum uides, in aere oculum etiam explora- bundum fallit, neque illuminatus aer uidetur nisi ratione cor- porum opacorum, ratio est quia aer nullo modo terminat lu- men, crystallus autem quamuis nullius esse coloris uideatur tamen ob uariatam refractamq[ue]; radiorum admissionem lumen terminat secundum quid. Vnde & ea ratione fit ut defecati spiritus ignei qui per aerem uolitant nullo modo uideâtur quia non est terminatum eorum lumen, & nimis exiguum ab una funditur atomo quam, ut possit species excitare. His præsuppositis accedamus propiùs ad fontem colorum probabiturq[ue]; possea assertio. Cum in mixtionem veniunt ista tria quatuorue ignis, aer, aqua, terra, necessarium est ignis lucem per aerem propagatam in aqua refringi, & in ter- ram impingere modò, modò verò reflecti; modò cum diapha- na est aliam pati refractionem, præterea cum non à luce so- lùm, & corpore obuio petatur ratio refractionis verùm etiam multo magis à figura; crystallus enim sub prismatis forma, aliter lumen refringit quam sub sphæræ cylindriue typo immo mixtam vmbris lucem profundit ex omphaloptra crystallina, eius enim illuminatæ limbi sunt soli illuminati cę- teris

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It has a tint, and is nothing else than some color infusing the light, either because those rays are refracted, or because they strike upon some body and are terminated. Or, as Aguillon says more elegantly, lib. 1, prop. 38 and 41 of his Optics, impure light is light variously refracted in some body, or propagated from refracted light. That pure light cannot be seen can easily be proved by reason and by experience. By reason indeed, because in every vision a termination is required; for actions ought to be bounded. But pure light cannot be terminated, therefore it cannot be seen. By experience also, which is everyday: for that light which you see falling on a wall deceives the eye even when examined in the air, and the illuminated air is not seen except by reason of opaque bodies. The reason is that air in no way terminates light; but crystal, although it seems to be of no color, nevertheless, by the varied and refracted admission of the rays, terminates light in a certain respect. Hence also it comes about that the refined igneous spirits which fly through the air are in no way seen, because their light is not terminated, and is too small, being poured from one atom as it were, to be able to excite an image. With these things presupposed, let us come more closely to the source of colors, and the assertion made above will be proved. When those three or four elements, fire, air, water, and earth, come into mixture, it is necessary that the light of fire, propagated through the air, be refracted in water and strike upon the earth, and then at times be reflected; at times, when it is transparent, undergo another refraction. Moreover, the cause of refraction is sought not only from light and an obstructing body, but much more from shape. For crystal, under the form of a prism, refracts light differently than under the type of a sphere or cylinder; indeed, from a crystalline omphaloptra it pours forth a mixed light with shadows, for its illuminated rims alone are illuminated, the rest being dark.

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C.4. De Colorum natura. 269 teris obscuris, nisi fortasse pro ratione conuexitatis circa cen- trum modica pars illustretur, at mutantur in diuersas figuras aqueæ atomi ergo etiam varias immo, & omnimodas pene facient refractiones; terreæ verò pro situ vario diuersimodè excipient lumen illudq[ue] coercebunt. Ex quibus Probatur primò sententia Democriti qui colorem dixit esse lumen ignis in corporibus mixtis variè refractum; non potest fieri mixtio sine multiplici refractione luminis, & proportio- ne perspicui, opaci, densi, rariue, ergo (etiam ex supposi- tione quod nulla sit alia causa colorum) istà ratione vnicà mul tiplices imo infiniti generabuntur; antecedens est probatum superius confirmaturq[ue]; varijs experimentis vt si diuersi gene- ris immisceas corpuscula diaphana varièq[ue]; lucem applices va- riæ resultabunt refractiones opaci, & illuminati, sic anima- duertit ingeniosè Sanctorius in artem paruam Galeni quæst. 48. sphærulas vitreas aquâ plenas opacare lumen, tenebrasq[ue]; pro luce reddere, at verò si vacuæ fuerint albedinem habebunt quod quidem experimentum sic ipse præscribit, dimitti iubet in purissimæ materiè vitreâ phialam vitreas pariter spherulas complures vacuas, & album oculis exhiberi colorem asserit; si compleantur aquâ, nigrum facient; non ergo poterunt com- plura corpora adhiberi lumini quin varias faciat refractiones, probatut itaq[ue] consequentia. Colores iridis oriuntur, ab opacatione luminis, sed in mi- xtis est opacatio ergo etiam in ijs oriri poterunt colores, nam eadem causa posita cur non eosdem effectus expectabimus? cum ergo illa opacatio variaq[ue]; refractio sit constans in mixtis constantes etia[m] permanentesq[ue]; colores exhibet. Itaq[ue]; etiamsi nulla inuenta esset alia colorum generatio hæc vnicà ratione omnes explicari facilè possent; frustra igitur quascunq[ue]; alias somnabis cum natura hoc ipso quod misceat, coloret. Si

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C.4. On the nature of colors. 269 in dark bodies, unless perhaps, by reason of the conveixity around the center, a moderate part is illuminated; but when the atoms of water are changed into different shapes, they will therefore also produce various, indeed almost all kinds of refractions; earthy particles, however, according to their various positions, will receive that light in different ways and restrain it. From these things First, the opinion of Democritus is proved, who said that color is the light of fire variously refracted in mixed bodies; a mixture cannot be made without a multiple refraction of light, and according to the proportion of the transparent, the opaque, the dense, and the rare; therefore, even on the assumption that there is no other cause of colors, by this single means multiple, indeed infinite, colors will be produced; the premise has been proved above and is confirmed by various experiments, as if you mix together translucent particles of different kinds and apply light in various ways, different refractions of the opaque and the illuminated will result. Thus Sanctorius cleverly observed in the little art of Galen, question 48, that glass spheres filled with water make light opaque and turn darkness into light; but if they are empty they will have whiteness. He prescribes this experiment in the following way: he orders several glass spheres, likewise empty, to be placed in a glass vial made of the purest material, and says that a white color will appear to the eyes; if they are filled with water, they will make black. Therefore several bodies cannot be applied to light without causing various refractions; the consequence is thus proved. The colors of the rainbow arise from the darkening of light; but in mixed bodies there is a darkening, therefore colors can also arise in them, for if the same cause is posited, why should we not expect the same effects? Since then that darkening and various refraction are constant in mixed bodies, they also produce constant and lasting colors. Therefore, even if no other generation of colors had been found, all of them could easily be explained by this single reason; in vain, then, will you dream up any others, when nature by this very act of mixing gives color. If

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De Atomis. Disp. IIII. Si enim refractio transiens facit colores transeuntes refractio permanens debet facere permanentes, sed datur in mixtis refractio luminis permanens, ergo debet in ijs facere colores permanentes. Irim autem reflexos esse in humidis nubibus radios definuit Zeno Citticus, vt ait Possidonius in meteorologica, declaratio seissuræ radiorum solis aut lunæ in nube roscida concaua atq[ue] continua quæ circulo Iridis magni sui orbis circumferentiam ostendit coloratam. Ità Laertius lib. 7. Probatur secundò videmus in nubibus omnes omnino colores lacteum, nigrum, viridem, rubrum aliaq[ue]; innumeras differentias, sed earum causa vnica est lumen refractum, ergo à pari in corporibus mixtis vbi lumen varijs modis refringitur idem contingere debet: & reuera quod in nubibus uideamus à radijs solis fieri id etiam deprehendimus in uarijs flammis: Ignis enim uarios colores dat flammis, sic cartæ crassioris flamma cærulea est, cerei candida, sulphuris cianea, picis nigra obscuraue, subflaua olei, rubicunda in buxo, pallida in foeno; fumus pariter uarius est pro materiæ uarietate, sic lignorum siccorum leucophus est, obscurior est uiridium, fumus mercurij sulphure mixti rubet, albescit stibij tumus, uirescit ortus ab ære fuso uapor, aliaq[ue]; alijs corporibus ob refractione luminis ignis in subiecto raro uel denso, perspicuo uel opaco, profundo uel parum alto, aliter aliterq[ue]; figurato, vnde expressè Democritus nigredinem ab asperitate à læuitate verò albedine oriri voluit; quod licicet multiplici refractione vmbraq[ue]; quæ in asperis sit necessariò maior sit opacitas, & consequenter, nigredo, leuia verò cum vmbram opacumue non faciant, sed æqualiratione lumen excipiant album repræsentant; quod si alios colores singulatim velis à refractionibus opacitateq[ue]; rimari, oportet in Iridis coloribus refractionum momenta perpendere; statuere figuram, densitatem, profunditatem, termi- num,

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On Atoms. Disputation IIII. For if a passing refraction produces passing colors, a permanent refraction ought to produce permanent ones; but in mixed bodies there is found a permanent refraction of light, therefore it ought to produce permanent colors in them. But Zeno of Citium defined the rainbows as reflected rays in moist clouds, as Posidonius says in the Meteorologica: a splitting of the sun’s or moon’s rays in a dewy, hollow, and continuous cloud, which shows the colored circumference of the great circle of the rainbow. So Laertius, book 7. It is proved secondarily: we see in clouds all colors at all events, milky, black, green, red, and others; countless differences, but the single cause of them is refracted light. Therefore, by the same reasoning, in mixed bodies where light is refracted in various ways, the same thing must happen. And in truth, what we see in clouds to be caused by the sun’s rays we also detect in various flames: for fire gives various colors to flames; thus the flame of thicker paper is bluish, that of a candle white, of sulfur cyan-colored, of pitch black and dark, of oil pale yellowish, red in boxwood, pale in hay; smoke likewise is various according to the variety of the material: thus that of dry wood is grayish-white, darker in green wood, the smoke of mercury mixed with sulfur is red, the vapor of fused antimony turns whitish, the vapor arising from molten bronze turns green, and others. In other bodies, because of the refraction of light, in fire the substratum is rare or dense, transparent or opaque, deep or not very deep, differently and differently formed; whence Democritus expressly wished blackness to arise from roughness, but whiteness from smoothness. Although by means of multiple refraction and shadow, which is necessarily greater in rough things, there is greater opacity and consequently blackness; smooth things, however, since they do not make a shadow or an opaque mass, but receive the light with equal proportion, represent whiteness. But if you wish to investigate separately the other colors from refractions and opacity, it is necessary to consider the moments of the refractions in the colors of the rainbow; to establish figure, density, depth, termin-

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C. 4. De colorum natura. 271 num, lumenq; atq; ex his deuenies in multorum notitiam. Si enim refractio 10. graduum virorem facit, refractio vero 25. graduum repræsentet rubedinem fatendum est quod in in- termedijs refractionis radijs intermedij colores poterunt re- periri. Ex Spherulis vt supra dixi vacuis emergere albedinem dixit Sanctorius eiq; fauet experientia spumæ, quæ tota sphærulis vacuis constat, & candida est: Sed necessaria est omnino leui- tas, vt animaduertit Democritus in physicis oculatissimus, quam in suis etiam globulis vult Sanctorius, & reuera ea spu- mæ inest perfectissima: Si autem hæc læuitas desit nequaqua[m] albedo resultabit ob facierum multiplicitatem, quæ varieta- tem nimiam effundenti se se lumini inducet. Atq; ex hac philosophandi ratione problemata, quæ circa colores fiunt facillimè soluentur, tum quæ de multiplicitate, tum quæ de mutatione, aut effusione luminis specierumq; à corporibus disputantur. Hanc de coloribus sententiam adorauit Plato in Timæo, sed cù in omnes ellet implacidus ex Athenæo l. 1 1. c. 22. Democritum non laudauit. Color est flammula quædam fulgorq; corporum à singulis corporibus emicans partes habens visui ad sēsum accomodatas; idemq; Diuinus philosophus authore Laertio lib. 3. sic existi- mabat. Constare mundum ex igne, aqua, acre, & terra. Ex igne quidem vt visibilis sit, ex terra vt solidus, ex aqua & aere vt pro- portione non vacet &c. Et in Timæo Locri alleruit; corpora prop- terignem videri, & propter terram tangi. Conuenit itaque cum Democrito quod Colorem vterq; censeat esse lumen internum corporum, vnde toto cælo abest vterq; ab ea sententia quam mali sequuti sunt veteru[m], à solo lumine extrinseco suum vni- cuiq; corpori affeciri colorem, quamuis enim lux extrinseca adelle debeat ad species à corporibus reflectione, medioq; il- lustrato

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C. 4. On the nature of colors. 271 through this you will come to know many things. For if refraction of 10 degrees produces green, and refraction of 25 degrees represents redness, it must be admitted that in the inter- mediate rays of refraction intermediate colors can be found. From little spheres, as I said above, vacuity gives rise to whiteness, said Sanctorius, and experience supports him in the foam, which consists wholly of hollow spheres, and is white. But lightness is absolutely necessary, as Democritus, most observant in natural philosophy, noted; Sanctorius also wants this in his own globules, and indeed such most perfect lightness is found in foam. If, however, this lightness is lacking, whiteness will by no means result because of the multiplicity of surfaces, which will impose too great a variety on the light as it pours forth. And from this manner of philosophizing the problems that arise concerning colors will be most easily solved, both those that are debated about multiplicity, and those about the change or effusion of light and its species from bodies. This opinion on colors Plato in the Timaeus embraced, but since he was hostile to all, as appears from Athenaeus l. 11 c. 22, he did not praise Democritus. Color is a certain little flame and brightness of bodies, emanating from individual bodies, having parts adapted to vision and sensation; and the divine philosopher, according to Laertius book 3, thought thus. That the world consists of fire, water, air, and earth. Of fire, indeed, so that it may be visible; of earth, so that it may be solid; of water and air, so that it may not lack proportion, etc. And in the Timaeus of Locris he claimed; that bodies are seen because of fire, and touched because of earth. It therefore agrees with Democritus that each considers color to be the internal light of bodies, and thus both are far removed from that opinion which the bad men of old followed, that color is imparted to each body by extrinsic light alone; for although extrinsic light must be added in order for the species from bodies by reflection, and the medium illuminated

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De Atomis. Disput. III. 272 illustrato deuehendas, nihilominus felicibus etiam conatibus exerunt nonnunquam vires suas corpuscula, & ignis sui interni beneficio se se produnt, vt carbunculi, sapphyri crystallo- eidei, aliaq; cuius etiam rei si ad manum habere velis experimentum, accipe purpuram aut viride quidpiam, & eo supra mundam cartam linteumuè inclinato videbis virore nitidissimo, vel purpura delicatissima cartam perfundi quasi ipsa etia[m] vmbra tingeretur. OBIECTIONES. Dices primò si hoc ità se se haberet omnes colores eiusdem essent specieij, nam omnes sunt lumen. Resp. negando sequelam, ad probationem dico non concludere argumentum quia à specie ad genus non valet consequentia, siuè à minus vniuersali ad magis vniuersale: lumen autem internum est genus pro definiendis singulis coloribus, differetia verò sumi debet à ratione refractionis, & opacitatis. Dices secundò si lumen est per se visibile deberent colores sine luce extrinseca videri, sunt enim lumen. Resp. lumen opacatum non posse videri nisi excitentur eius species à lumine non opacato, quia radius, refractus est debilior quam vt possit se se expromere, & imagines ad oculum propagare. Dices tertio si nihil est coloratum nisi ratione ignis sequitur nullam esse sensibilem terræ particulam in qua non sint spiritus ignei, cum nulla sit adeò modica quæ non videatur colorata, sequela est paradoxum ridiculum, deinde queram ex suppositione quod detur aliqua ignis expers an videbitur? Respondeo id non esse incredibile, imò id ità se habere argumento sunt generationes quæ vbiq; fiunt, lucci, alimenta q; herbarum, arborumq; & reuera ad vniuersi commoda permixta sunt isthæc elementa, aqua, terra, ignis; ad suppositione respon-

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Of Atoms. Disput. III. 272 though to be made clear, nevertheless even in fortunate attempts their corpuscles sometimes exert their powers, and by the benefit of their internal fire they reveal themselves, as carbuncles, sapphire crystals, and the like; and if you wish to have an experiment of this matter at hand, take purple or something green, and, inclining it over clean paper or linen, you will see the brightest greenness, or the most delicate purple, spread over the paper, as though its very shadow were being dyed. OBJECTIONS. You will say first, if this were so, all colors would be of the same species, for all are light. Reply: denying the consequence; to the proof I say the argument does not conclude, because there is no valid inference from species to genus, that is, from the less universal to the more universal: but light within is the genus for defining individual colors, and the difference must be taken from the manner of refraction and opacity. You will say secondly, if light is visible of itself, colors ought to be seen without extrinsic light, for they are light. Reply: obscured light cannot be seen unless its species are excited by un-obscured light, because a refracted ray is weaker than to be able to show itself and propagate images to the eye. You will say thirdly, if nothing is colored except by reason of fire, it follows that there is no sensible particle of earth in which there are not fiery spirits, since there is no particle so slight that it does not appear colored; the consequence is a ridiculous paradox. Then I will ask, on the supposition that there be some thing without fire, will it be visible? I reply that this is not incredible; indeed, that it is so are the generations that take place everywhere, the sap, the foods and of herbs and trees; and truly, for the advantages of the universe, these elements are mixed together: water, earth, fire; on the supposition respon-

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C. 4. De colorum natura. 273 respondebo si in eo sit situ vt diaphana non sit, tunc erit visibilis impropriè per lumen scilicet quod terminabit, sicut enim corpus diaphanum visibile est per lumen quod recipit ità corpus opacum, & non coloratum videri potest per lumen quod terminat; Si verò sit diaphanum apparebit vt cætera diaphana quæ colore carent. Dices quartò inauditum esse terram posse esse diaphanam. Respon. magis inauditum esset si quispiam id negaret cum in sale, crystallo, alijsq[ue] infinitis sint terreę portiones, imò & omnia corpora diaphana esse secundum quid rationibus opticis probatur, & experientia, optici enim metallicæ, lignea, saxeaq[ue]; faciunt specula, at necesse est recipi speciem in speculo secundùm aliquam profunditatem vt possit fieri commoda reflectio, ergo necesse est secundum aliquam sui portionem singula esse diaphana; & reuera ità contingit in vsu, lignea enim tæniolæ quales nonnunquam abscindunt qui asseres poliunt lumen non arcent, sicuti neq[ue]; carta quæ certa quadam mixtione peruncta sit trasparens, ità vt manus etiam ab vna facie applicata ab altera appareat non obscurè modo verum etiam colorata; corru opacum est cum plures adsunt superficies, sed duetum in laminas tenues est purissimi luminis capax: atque ita de singulis naturę corporibus poteris philosophari: vnde absudum non est terram certis quibusdam sitibus modo diaphanam modo verò opacam, & terminatam pronuntiare. Dices quintò si à mutatione mixtionis variaq[ue]; atomorum opacitate, & refractione fierent colores sequeretur quod attritu colorum, & infusione olei in marmore præsertim læuissimo deberet fieri eoru[m] aliqua mutatio, contra picturæ comoda. Respondeo ità exigua esse atomos vt nunquam ea attritione deueniatur ad vltimam diuisionem quod 100000 atomoru[m] componitur; nihilominus tamen remtuntur aliquâ- S 2 do in-

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C. 4. On the nature of colors. 273 I will answer that if in that position it is not diaphanous, then it will be visible improperly, namely through the light which will terminate it; for just as a diaphanous body is visible through the light it receives, so a body that is opaque, and not colored, can be seen through the light which terminates it. But if it is diaphanous, it will appear as other diaphanous things which lack color. You will say, fourthly, that it is unheard of for earth to be diaphanous. Reply. It would be more unheard of if anyone denied it, since in salt, crystal, and other countless things there are portions of earth; indeed, it is proved both by optical reasoning and by experience that all bodies are diaphanous in a certain respect. Optical workers make mirrors of metal, wood, and stone; but it is necessary for an image to be received in a mirror to some depth, so that a suitable reflection may occur; therefore each thing must be diaphanous according to some portion of itself; and in fact this happens in practice. For wooden strips, such as those sometimes cut off by people who polish boards, do not keep out the light; likewise paper, if it has been smeared with a certain mixture, becomes transparent, so that a hand applied on one side appears from the other not only plainly, but even colored; a corroded body is opaque when there are many surfaces present, but reduced into thin sheets it is capable of the purest light; and thus you can philosophize about each natural body: whence it is not absurd to say that earth, in certain positions, is now diaphanous, now opaque, and terminated. You will say, fifthly, that if colors were produced from a change of mixture and from the various opacity and refraction of atoms, it would follow that by rubbing colors together, and by pouring oil into marble, especially the very smooth kind, some change in them ought to occur, which is contrary to convenience in painting. I answer that the atoms are so extremely small that by such rubbing one never reaches the ultimate division, though it is composed of 100000 atoms; nevertheless, however, they are sometimes restored in-

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De Atomis. Disput. III. do intendunturq[ue] colores, non nunquam verò in aliam specie[m] transeunt, vnde etiam aliquid artis est in atterendo: si in infusum violarum guttam olei ex tartaro inieceris, fiet viridis color ex puniceo, gallarum, & calchanti diluta seorsim spectata diaphana sunt instar aquæ, si verò misceantur nigerrima fi- ent, quod atomi in ea mixtione figuras mutant, & ex laeubus reddantur asperæ vnde nigredo resultat, Dices 6. duo croci filamenta integrum aquæ cyathum tingent flauo; vt qui potuerunt tot esse ibi spiritus ignei ad totam illam aquæ quantitatem peruadendam? Resp. dissolui huiuscemodi filamenta, & sanè dispersionis atomorum corpusculorumq[ue]; miracula perpendenti istud nullo modorarum videbitur, halitus subtiliores in croci filamentis eos esse qui aquæ phialam tingant, vt vna aquæ vitæ gutta odorem, & aliqué gustu singulis eius particulis dispersa dabit. Dices 7. debere videri atomos igneas cum sint luminosæ at non videntur ergo, ratio maioris est quia nihil est frequentius ijs in aere cum sint in perpetuo fere motu, sintq[ue]; spiritus quem descripsit Virgilius agitantem vniuersa. Spiritus intus alit totamq[ue]; infusa per artus. Mens agitat molem. neq[ue]; dicas non terminari eorum lumen quia toties ipsis alia occurrunt corpuscula eaq[ue]; contingut aut ità vicina sunt vt facilè effusos radios possint excipere, quod cum aduersetur experientiæ signum est lucidos non esse spiritus igneos, quo sublato fundamento tota hæc de coloribus ingeniosa Democriti sententia ruit. Respondeo primò quod iam supradixi, nimis exiles esse radios quam vt eos percipiamus, atomus enim adeo est exigua vt ne mille quidem simul positæ acutissimum sensum feriant quanto magis si de vna procedat argumentum, sed si hæc resposio physica quæ certam proportionem requirit inter agens, & passum

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On Atoms. Disput. III. colors are intended, but sometimes they pass into another species, whence there is also some art in rubbing: if you have injected into a vial of violets a drop of oil from tartar, a green color will be produced from the crimson; gall-nuts and diluted calx, when looked at separately, are transparent like water, but if mixed together they will become blackest, because the atoms in that mixture change their shapes, and from smooth surfaces become rough, whence blackness results, You will say 6. two threads of saffron will dye a whole cup of water yellow; how could there have been so many fiery spirits there as to permeate that whole quantity of water? Reply. that such threads are dissolved, and indeed a dispersion of atoms and little bodies; to one considering marvels this will seem in no way surprising, the subtler vapors in the saffron threads are those which tint the flask of water, just as a single drop of aqua vitae will impart odor, and a pleasant taste, dispersed through each of its parts. You will say 7. atoms ought to be seen as fiery, since they are luminous, but they are not seen; therefore the reason is the greater, because there is nothing more frequent than them in the air, since they are in almost continual motion, and are the spirit which Virgil described as stirring all things. The spirit within nourishes, and poured through all the limbs. Mind moves the mass. Nor should you say that their light is not terminated because so many other little bodies meet them and touch them, or are so near that they can easily receive the emitted rays; which, since it is contrary to experience, is a sign that the fiery spirits are not luminous, and when this foundation is removed, this whole ingenious opinion of Democritus about colors falls. I answer first what I have already said above, that the rays are too subtle for us to perceive them; for an atom is so tiny that not even a thousand placed together would strike the keenest sense, much less if the argument proceeds from one alone. But if this physical response, which requires a definite proportion between agent and patient

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C. 4. De colorum natura. 275 & passum non satisfacit affero responsonem mathematicam deductam ex principio 17. Res enim omnes visibiles ab oculo percipiuntur secundum angulos quos emissis à se radijs in ipso oculo constituunt, vnde quæ sub maioribus angulis videntur, vt aut Euclides in opticis, maioræ apparent, quæ sub minoribus minora quæ sub æqualibus æqualia: nihilque omnino cerni potest nisi sub angulo cuius basis sit in obiecto; ergo obiectum debet esse capax plurium radiorum, (nam à radijs physicis componitur angulus visorius non autem à mathematicis, sunt verò radij lineæ physicæ) vt possit facere non angulum modò, verum potius conum vel pyramidem cuius vertex est in oculo, basis in obiecto; at atomus ignea non sufficit ad id, quia atomus est principium lineæ physicæ ergo si aliquid posset, faceret tantu lineam physicam quæ vt oculum feriat, necessariò est inuisibilis, caret enim latitudine longitudine, & profunditate, cum secundum extremam sui atomum eamq; vnicam oculum feriat; cum itaq; sub nullo angulo physicò, & sub nullis radijs possit comprehendi atomus sequitur eam siue lucida sit siue opaca esse inuisibile. Sicut enim in puncto mathematico non potest statui basis pyramidis mathematicę, ne quidem per aberrantem in chameras intellectum, ita neq; in atomo quæ punctum est physicum potest erigi vel fingi pyramidis aut conus physicus qualis necessariò interuenire debet ad visionem. Omitto plures alias implicitantias huius rei cum hæc redargutio sit demonstratiua. Et statuamus post tot probationes solutosq; difficultatum nodos, Colorem esse lumen internum corporum variè refractum, & opacatum, quod erat nobis pro Demo- crito euincendum. S 3 Com-

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C. 4. On the nature of colors. 275 and the same does not satisfy; I offer a mathematical reply derived from principle 17. For all visible things are perceived by the eye according to the angles which, with the rays sent out from them, they form in the eye itself; whence those seen under greater angles, as Euclid says in the Optics, appear larger; those under smaller angles smaller; those under equal angles equal: and nothing at all can be seen except under an angle whose base is in the object; therefore the object must be capable of many rays, (for the visual angle is composed from physical rays, not from mathematical ones; but the rays are physical lines) so that it may be able to make not merely an angle, but rather a cone or pyramid whose vertex is in the eye and base in the object; but a fiery atom is not sufficient for this, because an atom is the principle of a physical line; therefore if it could do anything, it would make only a physical line which, in order to strike the eye, must necessarily be invisible, for it lacks breadth, length, and depth, since only by its extreme atom, and that one alone, does it strike the eye; since therefore an atom can be comprehended under no physical angle, and under no rays, it follows that it, whether it be luminous or opaque, is invisible. For just as in a mathematical point the base of a mathematical pyramid cannot be established, not even by a mind wandering into chimæras, so neither in an atom, which is a physical point, can a physical pyramid or cone be erected or imagined, such as necessarily must intervene for vision. I omit many other inconsistencies of this matter, since this refutation is demonstrative. And let us establish, after so many proofs and after the knots of difficulties have been untied, that Color is the internal light of bodies variously refracted, and obscured, which was the thing we had to prove against Democritus. S 3 Com-

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CONCLVSIO. HÆC pro Democrito subscriuius speculationibus, & vigilijs quæ mihi somno gratiores sunt, conscripta, si quos habent defectus ingenio per tot occupationes distra- cto concedendi, vbi autem aliquid elimati acuratiq[ue] occurret, Urbanelector, EXCELLENTISSIMI SENATVS MEDIOLANENSIS auspicia venerare: FINIS.

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CONCLUSION. These things, written for Democritus under my speculations and watchings, which are dearer to me than sleep, if they have any defects, allow them to the mind distracted by so many occupations; but where something polished and accurate occurs, courteous reader, reverence the auspices of the MOST EXCELLENT SENATE OF MILAN: END.

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INDEX. Rerum memorabilium quæ in hoc Opere continentur. A A Bductio Hippocratis pag. 196. Æneas in elysijs pag. 215. Æolipylus Vitruuij 79. AER. Aer est inane Democriti 23. 86. ingenerabilis, & incoruptibilis 44. non est elementum 65. caret qualitibus primis à pag. 65. ad 69. aeris infectio 68. Aer non vnitur alijs elementis 69. Aeris grauitas quæ 84. In aere an possit navigari 84. 85. aer caret grauitate, & leuitate 86. 87. aeris extensio 126. figura 134. aeris pondus 254. aeris impuritas 255. Agens instrumentale, & principale in quo differant 83. Alcinoi error in mathesi 221. Analogismus in abditis adhibendus 157. ANGVLVS. Anguli figuræ rectilineæ 144. angulus atomi 148. angulus contactus, & angulus acutus 204. sophisma de angulo contactus 207. Antiperistasis 261. Alterationis modus 258. A Q V A. Aqua incorruptibilis 43. eius dotes 71. aqua non potest calefieri 82. figura 134. aquæ triplex status 150. proprietates Ibid. Regulæ hydraulicoru[m] Ibid. aquæ superficies sphærica 151. aqua quomodo calefiat 168. diaphana est 267. ARISTOTELES. Aristoteles Democriti libros combussit 14. iudicium de Democrito 18. Aristotelis commendatio 29. eius inuenta, & errata 35. error insignis in mathematica 136. 221. ATOMI. Atomis omnia constant à pag. 104. ad 113. atomi elementales 106. atomorum creatio 107. vnio 108. mixtio 110. 111. congregatio Ibid. doctrina atomorum facilis 112. quid sit atomus 113. atomorum categoria 114. proprietates 116. mobilitas triplex 116. sympathia 118. 121. atomorum ratio non est sita in sola figura 122. paruitas 122. numerus 124. vniones variæ 125. 126. atomis sua inest figura 129. figuratio 155. inquietudo 165. atomorum retusio, refractioq; 169. atomi materiales, & indiuisibiles 217. motus 234. ATOMI AEREÆ. Atomiaereæ neque inter se neque cū alijs vniuntur 125. 128. 153. sphericæ sunt, figuræ mutabilis 154. ATOMI AQVEÆ. Sunt sphæricæ 149. 152. figuram mutant 152. ATOMI IGNEÆ. Atomi igneæ igneis vniri nequeunt 129. figura sphærica igneis atomis conuenit 138. figuram mutant 143. sunt lucidæ 274. inuisibiles tamen Ibid. ATOMI QVALITATVM. Earum fæcunditas, intensio, species, ordo 260. interitus 261. ATOMI TERREÆ. Cubicæ sunt 143. non mutant figuram 149. Auri rameta in arboribus reperta 176. C Cal-

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INDEX. Contents of the memorable matters contained in this Work. A A Abduction of Hippocrates, page 196. Æneas in the Elysian Fields, page 215. Æolipylus of Vitruvius, 79. AIR. Air is the void of Democritus, 23, 86; ingenerable and incorruptible, 44; it is not an element, 65; it lacks the primary qualities, from page 65 to 69; corruption of air, 68. Air is not united with the other elements, 69. The heaviness of air, which, 84. Whether one can sail in the air, 84, 85. Air lacks heaviness and lightness, 86, 87. Expansion of air, 126. Figure, 134. Weight of air, 254. Impurity of air, 255. Instrumental and principal agent, wherein they differ, 83. Alcinoüs’ error in mathematics, 221. Analogism to be applied in hidden matters, 157. ANGLE. Angles of a rectilinear figure, 144. Angle of the atom, 148. Angle of contact and acute angle, 204. Sophism concerning the angle of contact, 207. Antiperistasis, 261. Mode of alteration, 258. WATER. Water incorruptible, 43; its qualities, 71; water cannot be heated, 82; figure, 134; the three states of water, 150; properties, ibid.; rules of hydraulics, ibid.; the spherical surface of water, 151; how water is heated, 168; it is transparent, 267. ARISTOTLE. Aristotle burned the books of Democritus, 14. Judgment concerning Democritus, 18. Praise of Aristotle, 29. His inventions and errors, 35. A notable error in mathematics, 136, 221. ATOMS. All things consist of atoms, from page 104 to 113; elemental atoms, 106; creation of atoms, 107; union, 108; mixture, 110, 111; aggregation, ibid.; doctrine of atoms is easy, 112; what an atom is, 113; category of atoms, 114; properties, 116; threefold mobility, 116; sympathy, 118, 121; the explanation of atoms is not based solely on figure, 122; smallness, 122; number, 124; various unions, 125, 126; atoms have their own figure, 129; formation, 155; restlessness, 165; crushing and refraction of atoms, 169; material and indivisible atoms, 217; motion, 234. AERIAL ATOMS. Aerial atoms are united neither among themselves nor with others, 125, 128, 153; they are spherical, of changeable figure, 154. WATERY ATOMS. They are spherical, 149, 152; they change figure, 152. FIERY ATOMS. Fiery atoms cannot unite with fiery things, 129; a spherical figure suits fiery atoms, 138; they change figure, 143; they are luminous, 274, yet invisible, ibid. ATOMS OF QUALITIES. Their fecundity, intensity, species, order, 260; destruction, 261. EARTHY ATOMS. They are cubic, 143; they do not change figure, 149. Sprigs of gold found in trees, 176. C Cal-

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INDEX. C C Alculorum generatio 175. Cardinali Infanti donum Cerebrum 63. CHYMICI. Chymicorum obscuritas in loquendo 51. 52. principia pro elementis Chirurgia curtorum CIRCULVS. Circuli generatio duplex 139. circulares concentrici comparati circuli quadratura non est impossibilis ad 197. circuli miracula in motu Cæloru[m] creatio Contactus globi, & plani COLOR. Coloru[m] confusio 255. quid sit ex Democrito CONTINVVM. Cur ignora continui natura 31. continuitas supponit materiam CORPVS. Corpus naturale quid sit 54. corpora, platonica CORRUPTIO. Corruptionis explicatio per atomos 178. 181. corruptionis ordo Cabi proprietates octo Cucurbitulæ medicæ D Cyathis in valle quam in monte capacior 151. D D Arijluetus 5. DEMOCRITVS. Democriti nobilitas 1. educatio Densitas iuuat actionem Diameter, & costa quadrati sunt incomensurabiles Dignitas rerum expensa regulis quatuor Diuisibilitas triplex Dodecaedron mensura cæli ex Alcinoo E E Brietas 185. EFFLVIA CORPORVM. An detur in elementis 75. in mixtis ELEMENTA. Elementa symbola dissymbola 24. incorruptibilitas elementorum à

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INDEX. C Generation of shells 175. Gift to the Cardinal Infant Brain 63. CHEMISTS. The obscurity of chemists in speaking 51. 52. principles taken as elements Surgery of the deformed CIRCLE. Double generation of circles 139. circles compared concentric The squaring of the circle is not impossible at 197. marvels of circles in motion Creation of the heavens Contact of the sphere and the plane COLOR. Confusion of colors 255. what it is according to Democritus CONTINUUM. Why the nature of the continuum is unknown 31. continuity supposes matter BODY. What a natural body is 54. Platonic bodies CORRUPTION. Explanation of corruption through atoms 178. 181. order of corruption The properties of the die eight Medicinal cupping-glasses D Better in the valley than on the mountain, cups are more capacious 151. D D Arijluetus 5. DEMOCRITUS. The nobility of Democritus 1. education Density aids action The diameter and the side of a square are incommensurable The dignity of things examined by four rules Triple divisibility The dodecahedron, measure of the heavens according to Alcinoüs E Drunkenness 185. EFFLVIA CORPORVM. Whether there are effluvia in the elements 75. in mixed bodies ELEMENTS. Elements, symbols, dissimilar symbols 24. incorruptibility of the elements from

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INDEX. 174. Elementa pura colore carent 265. sunt permixta locis 272. Empedoclis opinio de motu 216. Empyreum est cubicæ figuræ 148. Euclidis methodus ad atomos traducta 32. Excentricos quis inuenit 60. F FIGVRA. Figuræ quæ locu repleant 137.144. 218 pentagona non replent locu nec tetraedra 145. figuratio quid 155. figuræ isoperimetra 248. FLAMMA. Flamma 179.182. flammæ lux vnde 266. colores varij 270. Formarum imperium in mixto 179. Fumus 180. G Galeni opera græca 262. GENERATIO. Generatio difficilior conseruatione[m] 43. incipit ab exterioribus 162. 163. generatio mixti 170. GLACIES. Glacies leuior, & rarior quam aqua 150. glaciei consideratio 251. GLOBVS. Globi, & plani contactus 201. Globi illuminatio 212. Gothorum tuguria ex ossibus balænarum 183. GRANVM. Granum pulueris nitrati accensum eiusq; sphæra 77. GRAVITAS. Grauia omnia æquè cito per aerem de scendût 89. Grauitas, & leuitas no[n] dantur 228. H Hederæ proprietas 177. HIPPOCRATES. Hippocrates amicus Democriti, 5. Hippocratis de Democrito testimonia 15.16.17. Hipp. primus omnium elementa agnouit, & eorum qualitates 61. Horologium orontij 65. HVMDITAS. Humidi, & fluidi differentiæ 149. humor omnis sphæricus liquorq; omnis Ibid, humidi triplex genus 151. I I Aponum sensus differunt à nostris 263. IGNIS. Ignis ingenerabilis est, & incorruptibilis 41.46. eius dotes 41. Cur tata copia videatur 78. lux 79. Ignis fons 79. Ignis non potest frigefieri 82. cur igne seruare nequeamus 129. figura 135. actiuitas 181. Ignis est lucidus 266. IMPETVS. Impetum colligunt corpora in descensu. 230. quibus determinetur. 232. Atomorum impetus generatio, species, efficacia, interitus, 236. Inanimata sterilia sunt 46. Infinitum in magnitudine non implicat. 200. In inani omnia æquè mouentur 86. Insectorum exiguitas 123. Insomnia ebriorum 185. IRIS. Iris perpetua 247. Iridis colores 269. L Lacus in Peruua non nauigabilis 267. Lampas Cardani 154. Lapilli alphabetici Stradæ 118. Lazarus vitriuorax, & lapillorum epulo 174. LINEA.

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INDEX. 174. Pure elements are without color. 265. are mixed in places 272. Empedocles’ opinion on motion 216. The empyrean is of cubic figure 148. Euclid’s method applied to atoms 32. Who discovered eccentrics 60. F FIGURE. Figures that fill a place 137.144. 218 pentagons do not fill a place, nor tetrahedrons 145. What is figuration 155. figures equal in perimeter 248. FLAME. Flame 179.182. the light of flame whence 266. various colors 270. The rule of forms in the mixture 179. Smoke 180. G Galen’s Greek works 262. GENERATION. Generation is more difficult than preservation[m] 43. it begins from external things 162. 163. generation of a mixture 170. ICE. Ice is lighter and more rare than water 150. consideration of ice 251. GLOBE. Contact of globes and planes 201. The illumination of the globe 212. The huts of the Goths made from whale bones 183. GRAIN. A grain of nitre powder ignited and its sphere 77. GRAVITY. All heavy bodies descend equally quickly through the air 89. Gravity and lightness are not given 228. H Properties of ivy 177. HIPPOCRATES. Hippocrates, friend of Democritus, 5. Testimonies of Hippocrates concerning Democritus 15.16.17. Hippocrates first of all men recognized the elements and their qualities 61. The horologium of Orontius 65. HUMIDITY. Differences between the moist and the fluid 149. every moisture is spherical, and every liquid likewise Ibid., the threefold kind of moisture 151. I The senses of the Japanese differ from ours 263. FIRE. Fire is ingenerable and incorruptible 41.46. its qualities 41. Why it seems so abundant 78. light 79. The source of fire 79. Fire cannot be cooled 82. why we cannot preserve fire 129. figure 135. activity 181. Fire is luminous 266. IMPULSE. Bodies gather impulse in descent. 230. by what it is determined. 232. The generation, species, efficacy, and destruction of the impulse of atoms, 236. Inanimate things are sterile 46. The infinite in magnitude does not imply a contradiction. 200. In the void all things move equally 86. The smallness of insects 123. The sleeplessness of drunkards 185. RAINBOW. A perpetual rainbow 247. The colors of the rainbow 269. L A lake in Peru not navigable 267. Cardano’s lamp 154. Alphabetical pebbles of Strada 118. Lazarus, a glass-eater, and a diner on pebbles 174. LINE.

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INDEX. LINEA. Perpendicularis omnium mensura 55. linea phisica 145. sit ex cubis 146. linea insecabilis 148.202. conchilis 198. lineæ asymptoti 199. Lumbricorum generatio 175. Luminis diffusio, & figuratio 210.211. Lumen purum, & impurum 267.268. Luna 163.164. M MATERIA. Materiæ primæ proprietates quatuor 36. Materia prima Aristotelis est chymérica, & inutilis 49. Mathematicarum natura 188.189. 190.191. propositiones quomodo veræ 213. Methodus generalis 32. particularis. 187. MEL. Mel Democrito gratum 7. melle con-dita cadauera 111. mella saxeæ 149.150. MINIMA. Minima elementalia 47.96. minimum quid sit 115. Variæ minimorum elaborationes 173. MIXTIO. Quomodo ex atomis fiat 170.223 mixta calda quæ 171. mixtionum varijs gradus 172. Mixta omnia mo- uentur deorum. 231. MOTVS. Motus perpendicularis tripliciter ac- ceptus 117. motus rotæ 208. motus perfectè successiuus cum atomorum doctrina dari non potest. 228. Mo- tus, duratio, dimensio, numerus ana- loga. 233. motus perfectè successius est imposibilis 234. datur motus tar- dissimus 237. In motu non dantur quietes neque saltus. 238. ad 244. MVNDVS. Mundus incorruptibilis 39. Creatio ex Platone 130. ex Democrito 160. ex Anaxagora 166. N Natura fugit infinitum 105. aco- nomia 164. Natura se se ad statum commodum. restituit 184. Nix stelliformis Ticini 153. niuis na- tura 252. P Pestis 167.168. PHILOSOPHI HODIERNI. Horum sed a triplex, 28. Varia prin- cipia 50.51. PLATO. Plato vult combure libros Demo- criti 14. Platonis doctrina de ele- mentorum figuris. 130. ad 136. Plato fuit in omnes implacidus 271. PORI. Pororum ratio 168.177. Pori huma- ni 255. vitri pori quales 255. PROPORTIO. Proportiones elementorum 92. pro- portionalitatum miracula 200. Punctum mathematicum 98 puncta inflata 157. Q Qvadratorum circumscriptorum motus flupendus pag. 239, & 242. QUALITAS. Qualitates primæ 63. Earum defini- tiones nouæ reiectis Aristotelicis 72.73. earum sphera activitatis, &c agendi modus 75. qualitates primæ habent aliquid potentialitatis 171. qualitatum consideratio accura 2. 172. qualitates sunt tantu[m] respectuè 262. Quantitati comparatio 209. quantitatis essentia. 214. R Rana vaga 175. RA-

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INDEX. LINE. Perpendicular all measure 55. physical line 145. made from cubes 146. indivisible line 148. 202. shells 198. asymptote lines 199. Generation of worms 175. Diffusion and formation of light 210. 211. Pure and impure light 267. 268. Moon 163. 164. M MATTER. Four properties of prime matter 36. Prime matter of Aristotle is chimerical, and useless 49. Nature of the mathematical sciences 188. 189. 190. 191. how propositions are true 213. General method 32. particular. 187. HONEY. Honey pleasing to Democritus 7. bodies preserved in honey 111. honey of stone 149. 150. MINIMA. Elemental minima 47. 96. what a minimum is 115. Various elaborations of minima 173. MIXTURE. How it is made from atoms 170. 223. what hot mixtures are 171. The various degrees of mixtures 172. All mixtures are mo- ved by the gods. 231. MOTION. Perpendicular motion taken in three ways 117. motion of the wheel 208. motion perfectly successive cannot be granted with the doctrine of atoms. 228. Mo- tion, duration, dimension, number are analogous. 233. perfectly successive motion is impossible 234. the slowest motion is granted 237. In motion there are no rests nor leaps. 238. to 244. WORLD. The world incorruptible 39. Creation from Plato 130. from Democritus 160. from Anaxagoras 166. N Nature shuns the infinite 105. economy 164. Nature restores itself to a convenient state. 184. Snow star-shaped at Pavia 153. the nature of snow 252. P Plague 167. 168. MODERN PHILOSOPHERS. Their seat is threefold, 28. Various prin- ciples 50. 51. PLATO. Plato wants Democritus' books to be burned 14. Plato's doctrine about the figures of the elements. 130. to 136. Plato was implacable toward everyone 271. PORES. Nature of pores 168. 177. Human pores 255. what the pores of glass are like 255. PROPORTION. Proportions of the elements 92. miracles of proportionalities 200. Mathematical point 98. inflated points 157. Q The remarkable motion of circumscribed squares, page 239, and 242. QUALITY. Primary qualities 63. Their new definitions, with Aristotelian ones rejected 72. 73. their sphere of activity, etc., and mode of acting 75. primary qualities have something of potentiality 171. accurate consideration of qualities 2. 172. qualities are only in a relative sense 262. Comparison with quantity 209. essence of quantity. 214. R Wandering frog 175. RA-

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INDEX. RAREFACTIO. Rarefectionis, & condensationis verè exempla 245. rarefactio propriè dicta non datur 250. experimenta Galilæi. 253. 254. vana sunt 257. REFRACTIO. In atmosphæra 92. 93. in aqua 256. refractionis gradus 271. Respiratio quare fiat. 91. Rosa polonica 110. S Sapientiæ regio qualis 16. Siccitas, dubium an sit priuatio 53. SOL. Solis descensus 40. paruitas apparens 158. creatio, volutatio 163. compactio 164. solis motus, & illuminatio quomodo differant. 213. Radiorum solis reflectio quanta 231. SPhÆRA. Sphæræ diuersæ 12. sphæra actiuitatis 75. 211. proprietates sphæræ viginti 139. sphæra inter isoperimetras est maioris areæ 152. sphæræ actiuitatis propagatio 159. 261. SPECIES visibiles 158. 159. earu[m] tinctura 272. Speculum parabolicum 115. Spectrum 215. Sou quid; 89. STATICA medica 167. STELLÆ in mundi centro formatæ 165. SVBIECTVM. Subiectum primarium, secundarium, inhæsionis, denominationis quid; 33. Sympathia sex modis sumpta 118. T TERRA. Terræ, & salis rationes 70. terræ ad aquam pondus 70. eius dotes 71. figura 132. 134. immobilitas 197. quantum terræ illuminetur à sole. 212. diaphana est 267. 273. Tetraedra non replent locum 219. TRIANGVLVM. Scalenum 131. æquilaterum ibidem instrumenta Dei creantis ex Platone 131. constructio 191. V VACVVM. Vacuum Democriti 223. 23. 86. Vacui fuga quas habet vires 257. Visio quomodo fiat 275. FINIS.

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INDEX. RAREFACTION. Of rarefaction and condensation, true examples 245. Rarefaction properly so called does not exist 250. Galileo’s experiments 253. 254. are vain 257. REFRACTION. In the atmosphere 92. 93. in water 256. degree of refraction 271. Why respiration takes place 91. Polish rose 110. S What the kingdom of wisdom is like 16. Dryness, whether it is a privation, doubtful 53. SUN. Descent of the sun 40. apparent smallness 158. creation, rolling 163. compacting 164. how the sun’s motion and illumination differ 213. how great is the reflection of the sun’s rays 231. SPHERE. Different spheres 12. sphere of activity 75. 211. properties of the twenty sphere 139. the sphere among isoperimeters is of greater area 152. propagation of the sphere of activity 159. 261. VISIBLE SPECIES 158. 159. their tincture 272. Parabolic mirror 115. Spectrum 215. What sound is; 89. Medical statics 167. STARS formed in the center of the world 165. SUBJECT. Primary, secondary, of inherence, of denomination subject; what; 33. Sympathy taken in six ways 118. T EARTH. Of earth and salt, proportions 70. of earth to water, weight 70. its properties 71. shape 132. 134. immobility 197. how much the earth is illuminated by the sun. 212. it is transparent 267. 273. Tetrahedra do not fill space 219. TRIANGLE. Scalene 131. equilateral, ibid. instruments of God creating according to Plato 131. construction 191. V VOID. The void of Democritus 223. 23. 86. What powers the fear of the void has 257. How vision takes place 275. END.

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Transcription: ATR-1

Quæ in librum irrepserunt errata, Typorum penuriæ, & Autoris occupationibus quæ breue ad correctionem ne- que constans tempus concesserunt adscribi de- bent: potiora anno to, cætera tu ipse corriges, Vrbane lector. Pag. Linea. Errata. Emendatio. 6 19 culloquium colloquium 9 15 idæm idæam 20 4 hæc linea malè disposita est tollendumq; punctum. 21 15 cogestas congestas 27 27 qui dubium quid dubij 29 16 haberit habuerit 44 30 .... tamen ... tatem 46 9 introductiori introductioni 55 4 Io II 61 29 Aristotele Aristoteles 68 2 isinta insita 80 12 al-erat alterat 87 25 grauitas grauitatis 92 32 reddunt redeunt 96 16 quod quot 16. 29 radice radix 100 4 passum passuum 118 11 desunt hæc duo verba. In duobus lapillis. 118 15 Lusitatia Lusitania 134 11 ex est 142 23 Cymicus Cynicus 159 18 reposita repositam 167 26 incubant incubantis 16. 30 Verò Vero 189 12 additamenta addittamento 197 11 vetrum veterum 205 11 potentiam potentia 215 13 compensa compensa 231 10 illud illud

Transcription: Translated (English)

The errors that have crept into the book should be attributed to the scarcity of type, and to the author’s occupations, which allowed neither a brief nor a steady time for correction: the more important ones, O reader, you will correct yourself; the rest in year ten. Page Line Error Correction 6 19 culloquium colloquium 9 15 idæm idæam 20 4 this line is badly set; the point should be removed. 21 15 cogestas congestas 27 27 qui dubium quid dubij 29 16 haberit habuerit 44 30 .... tamen ... tatem 46 9 introductiori introductioni 55 4 Io II 61 29 Aristotele Aristoteles 68 2 isinta insita 80 12 al-erat alterat 87 25 grauitas grauitatis 92 32 reddunt redeunt 96 16 quod quot 16. 29 radice radix 100 4 passum passuum 118 11 the following two words are missing. In duobus lapillis. 118 15 Lusitatia Lusitania 134 11 ex est 142 23 Cymicus Cynicus 159 18 reposita repositam 167 26 incubant incubantis 16. 30 Verò Vero 189 12 additamenta addittamento 197 11 vetrum veterum 205 11 potentiam potentia 215 13 compensa compensa 231 10 illud illud