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

152 EPICYCLIC THEORY OF ANCIENT INDIANS
a mean inferior planet or the mean Sun. EA the direction of the
apogee of apsis and ES that of the
śīghra. The inequality of the apsis takes
the mean geocentric planet from M to
M₁, such that MM₁ is parallel to EA.
Let EM₁ be joined cutting the con-
centric at M₂ ; M₂ is taken as the
centre of the śīghra epicycle or the
real circular orbit in which the appa-
rent planet moves.
Fig. 18
With M₂ as the centre and the radius of the inferior pla-
nents' śīghra epicycle as radius, describe the circle NVU which
is here the śīghra epicycle or the real circular orbit. In it draw
the radius M₂V parallel to ES; then EV is the geocentric position
of the inferior planet.
Here the first displacement MM₁ is due to the inequality
of apsis and is for finding the position of M₂ the centre of the
real circular orbit. The idea was that the apparent planet moved
in a circular orbit of which the centre was very near the mean
position of the Sun, the first operation in this construction was
calculated to determine the centre of this so-called circular orbit
of an inferior planet.
The śīghra of an inferior planet moves round the Earth at
the same mean rate in which the inferior planet moves round the
Sun; hence the line ES in this figure is always parallel to the line
joining the Sun to the mean heliocentric inferior planet, and in
our construction, it is parallel to M₂V.
This in brief is an outline of the Indian idea of planetary
motion as taught by Āryabhaṭa I, Brahmagupta and Bhāskara II.
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Reference
P.C. Sengupta : The Khaṇḍakhādyaka, 1934.