Euclid (c. 330-c. 260 BC)

Greek mathematician who wrote the Stoicheia/Elements in 13 books, of which nine deal with plane and solid geometry and four with number theory. His great achievement lay in the systematic arrangement of previous discoveries, based on axioms, definitions, and theorems. Euclid's works, and the style in which they were presented, formed the basis for all mathematical thought and expression for the next 2,000 years. He used two main styles of presentation: the synthetic (in which one proceeds from the known to the unknown via logical steps) and the analytical (in which one posits the unknown and works towards it from the known, again via logical steps). Euclid went to the recently founded city of Alexandria (now in Egypt) in around 300 BC and set up his own school of mathematics there. His mathematical works survived in almost complete form because they were translated first into Arabic, then into Latin; from both of these they were then translated into other European languages. In Stoicheia/Elements Euclid used the synthetic approach; he used the analytical mode of presentation in his other important mathematical work, Treasury of Analysis.