His first postulate, that the universe is spherical, is supported by vague and inconclusive reasons similar to those given by Ptolemy and others; for the spherical form of the earth he gives several of the usual valid arguments, one of his proofs for its curvature from east to west being the fact that eclipses visible at one place are not visible at another. A third postulate, that the motions of the celestial bodies are uniform circular motions or are compounded of such motions, is, as might be expected, supported only by reasons of the most unsatisfactory character. He argues, for example, that any want of uniformity in motion “must arise either from irregularity in the moving power, whether this be within the body or foreign to it, or from some inequality of the body in revolution.... Both of which things the intellect shrinks from with horror, it being unworthy to hold such a view about bodies which are constituted in the most perfect order.” 77. The discussion of the possibility that the earth may move, and may even have more than one motion, then follows, and is more satisfactory though by no means conclusive. Coppernicus has a firm grasp of the principle, which Aristotle had also enunciated, sometimes known as that of relative motion, which he states somewhat as follows:— “For all change in position which is seen is due to a motion either of the observer or of the thing looked at, or to changes in the position of both, provided that these are different. For when things are moved equally relatively to the same things, no motion is perceived, as between the object seen and the observer.”[49] Coppernicus gives no proof of this principle, regarding it probably as sufficiently obvious, when once stated, to the mathematicians and astronomers for whom he was writing. It is, however, so fundamental that it may be worth while to discuss it a little more fully. [Illustration: FIG. 37.—Relative motion.] Let, for example, the observer be at A and an object at B, then whether the object move from B to B′, the observer remaining at rest, or the observer move an _equal_ distance in the _opposite_ direction, from A to A′, the object remaining at rest, the effect is to the eye exactly the same, since in either case the distance between the observer and object and the direction in which the object is seen, represented in the first case by A B′ and in the second by A′ B, are the same.