Editing Nicolo Tartaglia (section)

==Translations==
Archimedes' works began to be studied outside the universities in Tartaglia's day as exemplary of the notion that mathematics is the key to understanding physics, [[Federigo Commandino]] reflecting this notion when saying in 1558 that "with respect to geometry no one of sound mind could deny that Archimedes was some god".<ref>Clagett, Marshall, "William of Moerbeke: Translator of Archimedes", pp. 356-366.</ref> Tartaglia published a 71-page Latin edition of Archimedes in 1543, [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/V3WUN5FQ/index.meta&start=1&pn=1 ''Opera Archimedis Syracusani philosophi et mathematici ingeniosissimi''], containing Archimedes' works on the parabola, the circle, centres of gravity, and floating bodies. Guarico had published Latin editions of the first two in 1503, but the works on centres of gravity and floating bodies had not been published before. Tartaglia published Italian versions of some Archimedean texts later in life, his executor continuing to publish his translations after his death. Galileo probably learned of Archimedes' work through these widely disseminated editions.<ref>Henninger-Voss, Mary J., "'New Science' of Cannons", p. 392.</ref>

Tartaglia's Italian edition of [[Euclid]] in 1543, [https://books.google.com/books?id=ymWnEXab_7UC&pg=PA1 ''Euclide Megarense philosopho''], was especially significant as the first translation of the ''[[Euclid's Elements|Elements]]'' into any modern European language. For two centuries Euclid had been taught from two [[Latin]] translations taken from an Arabic source; these contained errors in Book V, the [[Eudoxus of Cnidus|Eudoxian]] theory of proportion, which rendered it unusable. Tartaglia's edition was based on [[Zamberti]]'s Latin translation of an uncorrupted Greek text, and rendered Book V correctly. He also wrote the first modern and useful commentary on the theory.<ref>See Malet, Antoni, "Euclid’s Swan Song: Euclid’s Elements in Early Modern Europe", where Tartaglia's work on Euclid is described as "mathematically cogent, innovative, and influential" (p. 207).</ref> This work went through many editions in the sixteenth century and helped diffuse knowledge of mathematics to a non-academic but increasingly well-informed literate and numerate public in Italy. The theory became an essential tool for [[Galileo]], as it had been for [[Archimedes]].