Euclid's Elements

Euclid of Alexandria is often called "the father of geometry" because his text The Elements was used as the standard geometry text for about 2000 years. It was an excellent compilation of the mathematics known at the time (about 350 BC), and it set an important standard for the logical organization and presentation of mathematics. However, it is so often associated with geometry that many people forget three of the thirteen books of the Elements are about number theory (books VII, VIII, and IX). In these three books he defines prime numbers, develops many properties of divisibility, presents the Euclidean algorithm for finding the greatest common divisor of two integers, shows how to find an even perfect number from (what is now called) a Mersenne prime, proves that there are infinitely many primes, and states a version of the fundamental theorem of arithmetic.

Euclid's elements is one of the most widely circulated books in history. More than one thousand editions have appeared since the first printed version in 1482, and even before that it was the standard mathematical text in the west. The quality of definitions and the axiomatic development of arithmetic have greatly improved since Euclid's day, but the foundational value of Euclid's texts is difficult to overstate.

See Also: Euclid

Related pages (outside of this work)

• An excellent on-line version of Euclid's Elements