Euclidean Geometry

Most principles of geometry upon which mathematicians base their work today—and for the past twenty-three centuries—are related to the theories and methods first recorded around 300 B.C.E. by the Greek writer Euclid. His comprehensive work on mathematical theory, The Elements, was probably heavily based on the work of his predecessor Eudoxus, who had been a student of the philosopher Plato. Euclid refined Eudoxus's theories, along with geometric principles that were the results of generations of mathematicians. His Elements, written in Egyptian Alexandria, has been a central influence for twenty-three centuries, from the Hellenistic world after the conquest of Alexander the Great to the Roman Empire, to the Byzantine Empire, the Islamic Empire, into the medieval world and on to today.

The Elements is a comprehensive treatise that brings together geometry, proportion, and number theory, tying them all into one complete theory for the...