He was a pupil in mathematics of Archytas in Athens. In mathematical astronomy his fame is due to the introduction of the astronomical globe[?], and his early contributions to understanding the movement of the planets.
His work on proportions shows tremendous insight into numbers. He invented the method of exhaustion[?], which was used masterfully by Archimedes. The work of Eudoxus and Archimedes as precursors of calculus was only exceeded in mathematical sophistication and rigour by Newton himself.
An algebraic curve (the Kampyle of Eudoxus) is named after him
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