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).