None of Kepler's contemporaries believed the law of the areas, nor was it accepted until the publication of the "Principia" of Newton. In fact, no one in those times understood the philosophical meaning of Kepler's laws. He himself did not foresee what they must inevitably lead to. His mistakes showed how far he was from perceiving their result. Thus he thought that each planet is the seat of an intelligent principle, and that there is a relation between the magnitudes of the orbits of the five principal planets and the five regular solids of geometry. At first he inclined to believe that the orbit of Mars is oval, nor was it until after a wearisome study that he detected the grand truth, its elliptical form. An idea of the incorruptibility of the celestial objects had led to the adoption of the Aristotelian doctrine of the perfection of circular motions, and to the belief that there were none but circular motions in the heavens. He bitterly complains of this as having been a fatal "thief of his time." His philosophical daring is illustrated in his breaking through this time-honored tradition. In some most important particulars Kepler anticipated Newton. He was the first to give clear ideas respecting gravity. He says every particle of matter will rest until it is disturbed by some other particle--that the earth attracts a stone more than the stone attracts the earth, and that bodies move to each other in proportion to their masses; that the earth would ascend to the moon one-fifty-fourth of the distance, and the moon would move toward the earth the other fifty-three. He affirms that the moon's attraction causes the tides, and that the planets must impress irregularities on the moon's motions. The progress of astronomy is obviously divisible into three periods: 1. The period of observation of the apparent motions of the heavenly bodies. 2. The period of discovery of their real motions, and particularly of the laws of the planetary revolutions; this was signally illustrated by Copernicus and Kepler. 3. The period of the ascertainment of the causes of those laws. It was the epoch of Newton. The passage of the second into the third period depended on the development of the Dynamical branch of mechanics, which had been in a stagnant condition from the time of Archimedes or the Alexandrian School.