Eudoxus of Cnidus (c.408–c.355 B.C.), Greek astronomer and mathematician, a student of Plato. He created a test of the equality of two ratios, invented the method of exhaustion for calculating areas and volumes within curved boundaries, and introduced an astronomical system consisting of homocentric celestial spheres. This system views the visible universe as a set of twenty-seven spheres contained one inside the other and each concentric to the earth. Every celestial body is located on the equator of an ideal sphere that revolves with uniform speed on its axis. The poles are embedded in the surface of another sphere, which also revolves uniformly around an axis inclined at a constant angle to that of the first sphere. In this way enough spheres are introduced to capture the apparent motions of all heavenly bodies. Aristotle adopted the system of homocentric spheres and provided a physical interpretation for it in his cosmology. R.E.B.