 Perhaps the most significant impact of Kepler’s two laws can be found by considering their cosmological consequences. The first law abolishes the old axiom of the circular orbits of the planets, an axiom which was still valid not only for pre-Copernican astronomy and cosmology but also for Copernicus himself, and for Tycho and Galileo. The second law breaks with another axiom of traditional astronomy, according to which the motion of the planets is uniform in swiftness. The Ptolemaic tradition in astronomy was, of course, aware of this difficulty and applied a particularly effective device for saving the “appearance” of acceleration: the equant. Copernicus, for his own part, insisted on the necessity of the axiom of uniform circular motion. Ptolemy’s equant was understood by Copernicus as a technical device based on the violation of this axiom. Kepler, on the contrary, affirms the reality of changes in the velocities of the planetary motions and provides a physical account for them. After struggling strenuously with established ideas which were located not only in the tradition before him but also in his own thinking, Kepler abandoned the circular path of planetary motion and in this way initiated a more empirical approach to cosmology (though see Brackenridge 1982).