On Straight Lines Intersecting One Another: A Construction by Statics

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Original title: De lineis rectis se invicem secantibus statica constructio A Latin geometrical treatise printed at Milan by Lodovico Monza (Ludovicus Montia) as a quarto of [8], 83, [1] pages with ten folded plates, dedicated to Ferdinando Carlo Gonzaga, duke of Mantua and Montferrat. After a dedicatory epistle presenting geometry as a neglected queen in need of patrons, and a proem recounting the author's fruitless labours on the quadrature of the circle and hyperbola, the work sets out a 'static construction': configurations of mutually intersecting straight lines are resolved by treating points as centres of gravity and segments as balances, placing weights in the stead of lines. Book I derives from static axioms (notably the uniqueness of the centre of gravity) five foundational propositions called 'elements', including the triangle-concurrence result and a treatment of Menelaus's transversal, with worked problems enumerated by cases and a geometrical verification appended from another mathematician; it extends to pyramids and three-dimensional configurations. Book II applies the method to polygons circumscribed about circles and ellipses, tangents of the parabola, and a surveying instrument measuring distances along visual rays without a known baseline, closing with a claim that all such configurations resolve into the elements. A geometrical appendix gathers results from the abandoned quadrature work on lunes, cylindrical segments, hyperbolic solids and centres of gravity, including Torricelli's infinite solid, and ends with a scholium judging Cavalieri's method of indivisibles ingenious but uncertain for the surfaces of round solids. 👉 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.

• Read our introductory primer, full report, and finding guide here
• View the original source file

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Early European Books, CopyRight 2011 ProQuest LLC. Images reproduced by courtesy of the Biblioteca Nazionale Centrale di Firenze. CFMAGL 1.7.137