Euclid

Euclid (330 - 275 B.C.) was the first major scholar at the Library of Alexandria. His most important work was his Elements, a collection of the most important results of the previous three centuries of Greek mathematics. This book was divided into thirteen volumes, the first six of which dealt with plane geometry ("Euclidean geometry"), and the last seven dealing with solid (three-dimensional) geometry, number theory (for example, perfect numbers), and other things.

More copies have been made of the Elements than of any other work, with the exception of the Bible. It had been the primary geometry textbook for two millennia. Clearly, it was a very important work. The work of many Greek mathematicians that otherwise would have been lost has been preserved in the Elements.

Euclid started the book by stating his five (actually there were ten, but only five were geometric) postulates. These form the basis of all his theorems. These well-known postulates are:

1. A straight line can be drawn between any two points.
2. A straight line can be extended indefinitely.
3. A circle can be described by its centre and its radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, if produced indefinitely, meets on that side on which are the angles less than the two right angles.

Euclid, like many other Greek mathematicians (Pythagoras being a particularly good example) held the idea of applying his mathematical theorems to practical use in contempt. Once, when asked how a certain theorem could be applied to practical use, he ordered his slave: "He must profit from learning; give him a penny". Interestingly, the word "geometry" is not to be found in the Elements. This might be because geometry meant "earth measurement" ("geo" = earth + "metria" = measurement) at the time. He likely didn't want people to think that his geometry was for practical use.