*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

This section contains 652 words(approx. 3 pages at 300 words per page) |

## Euclidean and Non-Euclidean Geometry

In 300 B.C.E., Euclid of Alexandria put forward a logical construction of a geometry, which has come to be known as Euclidean geometry. Until the middle of the nineteenth century mathematicians believed that Euclid's geometry was the only type of geometry possible. Euclidean geometry is based on a number of fundamental statements called postulates, or axioms.

In his book *Elements,* Euclid based his geometry on five axioms. The fifth axiom, also known as the parallel axiom, states the following: Given a line *m* and a point *P* not on *m*, there is only one line through *P* which is parallel to *m*.

In mathematics, a set of axioms has to fulfill two conditions: consistency and independence. A set of axioms is consistent if its use does not produce an absurd result that contradicts a statement derived from the axioms. A set of axioms...

This section contains 652 words(approx. 3 pages at 300 words per page) |