That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.

In his study of the quadrature and duplication-problems, Hippocrates contributed much to the geometry of the circle.

The property of similar triangles, and that contained in Prop. 47, Book I [the ], are most important theorems in Geometry.

A pretty little story is related by Stobæus: "A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, 'What do I get by learning these things?' So Euclid called his slave and said, 'Give him threepence, since he must make gain out of what he learns.