## Euclid (325BC - 265BC)

We’re unsure where or when he was born and died and some people even wonder if the person Euclid existed.

But what we do have is a book called The Elements, which was produced in Alexandria, Egypt and is the most influential mathematics book ever written.

The Elements, which is made up of thirteen separate books, has exerted the influence that it has because it gathered together the mathematical knowledge of the day and presented it in a clear and concise form.

Just how influential can be judged from the fact that most textbooks on geometry up to about 1950 followed the form of the Elements.

What gives the book its mathematical power are its proofs but perhaps more important than the proofs in the book is the way the book was presented.

Euclid started with basic ideas and built systematically on them - vast structure built logically on firm but small foundations.

The 13 books of The Elements open with a series of postulates and definitions followed by proofs building on these.

This way of organising information is known as the axiomatic method - setting arguments upon a foundation of proofs.

Euclid helped to standardise mathematics and set the standard for the rigor and logical structure of mathematics to come. His book, first printed in 1482 has gone through over 1000 editions.

Euclid was attacked by contemporaries as being too self-evident, but more recently he has been attacked for not being thorough enough. His god-like status began to crumble in the 19th century when non-Euclidean geometry was developed.

But the core principles set down in The Elements are still at the heart of basic geometry and number theory taught today and his way of compiling information set the standard for all mathematicians to come. His Proposition V1 was their Theorem 6; his proof was in essence their proof. The Elements also dealt with the theory of numbers.

We give two of his results and their proofs - one in geometry, and one concerning prime numbers. The proofs below are in the style of Euclid, but neither is the proof that he gave for this result.