|Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction
of being the world’s oldest continuously used mathematical textbook. Little is known about the author, beyond the fact that he lived in Alexandria around 300 BCE. The main subjects of the work are geometry, proportion, and number theory.
Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of
earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from five simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously
discovered theorems: e.g., Theorem 48 in Book 1.