sentences:  Ptolemy's unique contribution to this theory was the equant—a point about which the center of a planet's epicycle moved with uniform angular velocity, but which was offset from the center of its deferent.This violated one of the fundamental principles of Aristotelian cosmology—namely, that the motions of the planets should be explained in terms of uniform circular motion, and was considered a serious defect by many medieval astronomers.In Copernicus' day, the most up-to-date version of the Ptolemaic system was that of Peurbach (1423–1461) and Regiomontanus (1436–1476).