Eudoxus of Cnidus
Eudoxus of Cyzicus.
Eudoxus of Cnidus (Greek Eυδοξοσ) (circa 408 BC - circa 347 BC) was a Greek astronomer, mathematician, physician, scholar and friend of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy.
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; it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers. When it was revived by Tartaglia and others in the 1500s, it became the basis for quantitative work in science for a century, until it was replaced by the algebraic methods of Descartes.
Eudoxus invented the method of exhaustion, which was used in a masterly way 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
- a2x4 = b4(x2 + y2).
