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174 of Ptolemy. He was therefore able to produce a complete new system of astronomy, the first since the days of the Alexandrian school, and the first of all which gave the means of determining the relative distances of the planets. And it was in this way that he showed himself as the great master, and was valued as such by Tycho Brahe, who was better able than any one else to appreciate Copernicus, since his own activity left no part of astronomy untouched. But unfortunately the edifice which Copernicus had constructed was not very far from being as artificial and unnatural as that of Ptolemy. The expedient of letting the earth move in a circular orbit round the sun could explain those irregularities in the planetary motions (stations and retrogradations) of which the synodic revolution was the period (the second inequalities, as the ancients had called them), because they were caused by the observer being carried round by the moving earth. But this could not account for the variable distance and velocity (the first inequality) of which the orbital revolution was the period, and of which Kepler gave the explanation when he found that the planets move in ellipses, and detected the law which regulates the velocities in these. Until Kepler had discovered the laws which bear his name, there was no way of accounting for these variations, except by having recourse to the same epicycles and excentrics which Ptolemy had used so liberally; and the planetary theory of Copernicus was therefore nothing but an adaptation of the Ptolemean system to the heliocentric idea. And the motions were not referred to the real place of the sun, but to the middle sun, i.e., to the centre of the earth's orbit, while the orbit of Mercury required a combination of seven circles, Venus of