Page:A short history of astronomy(1898).djvu/116

72 equant to represent an irregular motion, if he had found that the motion was thereby represented with accuracy. The criticism appears to me in fact to be an anachronism. The earlier Greeks, whose astronomy was speculative rather than scientific, and again many astronomers of the Middle Ages, felt that it was on a priori grounds necessary to represent the "perfection" of the heavenly motions by the most "perfect" or regular of geometrical schemes; so that it is highly probable that Pythagoras or Plato, or even Aristotle, would have objected, and certain that the astronomers of the 14th and 15th centuries ought to have objected (as some of them actually did), to this innovation of Ptolemy's. But there seems no good reason for attributing this a priori attitude to the later scientific Greek astronomers (cf. also §§ 38, 47).

It will be noticed that nothing has been said as to the actual distances of the planets, and in fact the apparent motions are unaffected by any alteration in the scale on which deferent and epicycle are constructed, provided that both are altered proportionally. Ptolemy expressly states that he had no means of estimating numerically the distances of the planets, or even of knowing the order of the distance of the several planets. He followed tradition in accepting conjecturally rapidity of motion as a test of nearness, and placed Mars, Jupiter, Saturn (which perform the circuit of the celestial sphere in about 2, 12, and 29 years respectively) beyond the sun in that order. As Venus and