ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

34 ASTRONOMY IN ANCIENT NATIONS passages of which he shows his dissatisfaction with the Ptolemaic system. In the chapter on the Moon (to which we have already alluded ) he counts up the various anomalies, among which he mentions the anomaly of illumination, that is, the spots on the Moon, which he believes to be caused by other bodies moving in the lunar epicycle and unequally exposed to the Moon's light. He then says that we should expect in a simple theory to find the centre of the epicycle in equal times describing equal arcs on the deferent, and the diameter of the epicycle joining the pericentre and the apocentre pointing to the centre of the deferent. But neither of these conditions is fulfilled. In the theories of the planets he makes the same objections, which it must be said are very just, since the introduction of the equant was a very unna- tural arrangement. But this is nothing to the artificial machinery designed by Ptolemy to account for the motion in latitude of the five planets, especially of Mercury and Venus. Nasir ed-din des- cribes the marvellously complicated movements of the deferents and epicycles of these planets, and remarks that "these motions require the introduction of a system of guiding spheres, about which the ancients have not said anything". He next proceeds in the following chapter to explain a system of his own which allows us to discard these combinations. First he proves that if there are, two circles in one plane, one touching the other internally and of a diameter equal to half that of the other, and if the greater one rotates, and a point moves along the circumference of the smaller one in the opposite direction with twice the velocity and starting from the point of contact, then that point will move along a diameter of the greater circle.¹ These two circles may now be assumed to be the equators of two spheres, and for the point we may substitute a sphere representing the Moon's epicycle (1 in the figure), Nasir ed-din assumes another sphere (2) surrounding the epicycle and destined to keep the diameter from apogee to perigee in its place always coinciding with the diameter of the sphere (4) "let us give it a suitable thickness, but not too great, so as not to take up too much space." He next assumes two more spheres, one (3) which corresponds to the smaller sphere in the distance of the centre of the deferent in the Ptolemaic system from the

1. Compare Copernicus, De revolutionibus, III. 4 (Secular ed. 1873, p. 166).