Book 1: Chapter 24, Early Greek Mathematics and Astronomy Summary and Analysis

The Greek noted their preeminence mostly in mathematics and astronomy. They derived their theories from Egypt and Babylonia although they originated mathematical demonstration.

Mathematical investigations were mostly initiated through practical problems, such as the demand to find the height of the pyramid, where Thales fulfilled the request of the king and measured the height of the pyramid by measuring its shadow when it was equal to its height. The laws of perspectives were studied first by Agatharcus, a geometer, who was to paint the background of Aeschylus's plays. The Greeks discovered the square root of two and Pythagoras made geometry a liberal education.

From the theory of irrationals Eudoxus devised the geometrical theory of proportion. This theory claims that the ratio of a to b is the same as...