Euclid's Elements
The Elements is a geometrical treatise that is the basis of Euclidean geometry and was compiled by Euclid in the time of ancient Greece. It is divided into thirteen volumes, each containing many axioms and theorems.
History
Euclid wrote The Elements circa 300 BC, as a conglomerate of others' work and his own. It was possibly translated into Latin during the reign of the Roman Empire, but this is doubtful. The Arabs acquired copies of The Elements circa 750 AD, and it was translated into Arabic circa 800 AD. The first printed edition was printed in 1482.
Original Greek manuscripts still exist in the Bodleian Library at Oxford University, and at the library of Vatican City.
Contents
Euclid's work is split into thirteen volumes. It covers not only geometry, but number theory and some algebra throughout various volumes.
Each volume has "common notions" (axioms), postulates, and "propositions" (theorems). Each proposition would be derived from the axioms and the previous propositions. Additionally, the first volume defines the terms used.
Volumes 1, 3, 4, 6, 11, 12, and 13 deal with geometry; volume one notably contains the Pythagorean Theorem. The other volumes deal with a combination of algebra and number theory, though arguably volume 10 in fact lays the foundation for integral calculus.
