# Eudoxus of Cnidus (c. 400–c. 347 BC)

Eudoxus was a Greek mathematician, astronomer, and physician who devised a scheme of the heavens in which the Sun, Moon, and planets traveled around Earth on 27 geocentric spheres, rotating at different speeds and inclinations. This concept of planetary motion, refined by Callipus and ultimately by Ptolemy, provided the standard model of the cosmos for 2,000 years.

Eudoxus's work on ratios formed the basis for Book V of Euclid's *Elements* and anticipated some aspects of algebra, such as cross
multiplying, which is otherwise absent from ancient Greek mathematics. Eudoxus
constructed many geometric proofs, found formulas for measuring pyramids,
cones, and cylinders, and developed the **method of exhaustion**,
a forerunner of integration, later extended
by Archimedes. He also studied the kampyle
curve, often known as the kampyle
of Eudoxus, in connection with the classical problem of duplicating
the cube.