Euclid (ca. 330–ca. 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 (including prime numbers, perfect numbers and more), and other topics.
More copies have been made of the Elements than of any other work, with the exception of the Bible. It was the world's primary geometry textbook for two millennia, until the 20th century. Clearly, it was a very important work. While Euclid worked out few of the theorems of Euclidean geometry himself, his Elements is very valuable in that it preserves the work of many Greek mathematicians that otherwise would have been lost.
For someone who had such an important influence on geometry, surprisingly little is known about Euclid. The best information we have is provided by Proclus, who wrote around 750 years after Euclid. Proclus writes that Euclid worked in Alexandria during the reign of Ptolemy I, but he had no direct knowledge; an anecdote exists involving him and a certain Ptolemy (which is the source of the quote at the top of the page), and he must have worked before the time of Archimedes (287–212 B.C.) because Archimedes cites Euclid, so the time frame that fits best for Euclid's work is during the reign of Ptolemy I (306–283 B.C.). The dates of Euclid's birth and death are entirely unknown.
Euclid began the Elements by defining various terms, and then stating five postulates. These form the basis of all his theorems. These well-known postulates are:
Following the five postulates, Euclid also stated five "common notions", or axioms. The common notions are:
Euclid, like many other Greek mathematicians (Pythagoras being a particularly good example) would likely have 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.