Eudoxus

Eudoxus of Cnidos was an ancient Greek mathematician, astronomer, and physician who was a native of Cnidos (now Knidos in Turkey). He was probably born around 408 B.C. and lived to the age of 53. He was widely travelled, making journeys to southern Italy, Sicily, Athens, and Egypt, at which places he was exposed to many different ideas.

In the field of mathematics, Eudoxus discovered the theory of proportion and also described the method of exhaustion for measuring areas and volumes. Eudoxus was a highly original thinker and may have made other significant discoveries; however, all of his works are lost, so we know nothing about his discoveries other than what other authors wrote about him.

The general theory of proportion, as expounded in Book V of Euclid's Elements, is due to Eudoxus. When Pythagoras and/or the Pythagorans discovered the existence of irrational numbers, it caused problems for the theory of proportion in use at the time, which couldn't handle irrationals. Eudoxus' theory of proportion is able to account for these.

Eudoxus also studied the method of exhaustion, which is used to find the area of a shape by inscribing within it a series of polygons. Archimedes would use this method to calculate the value of π.