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

150 EPICYCLIC THEORY OF ANCIENT INDIANS
wards the apogee, then CS is a constant length and C is a fixed
point. Hence the locus of S is an equal circle with the centre at
C. Thus both the eccentric, and the epicycle and the concentric
combined, led to the same position.
It was thus usual to explain the planetary motion under
both the assumed constructions; and both gave the position for a
planet. The eccentric circle construction appears to be the earlier
in the history of astronomy and the latter was later. If the
former construction can be traced to Apollonius of Perga who did
so much to develop the "conic sections" as science, the reason why
he preferred the eccentric circle to the ellipse, appears to be that
either that this planetary construction was always deep-rooted in
the minds of men or that he was carried by the idea that "the
circle was the most perfect curve." We are inclined to the view
that the eccentric circle idea was transmitted from Babylonia to
Greece. We now pass on to consider the Indian construction for
the possition of superior and inferior planets.
Superior Planets
With regard to the five planets, Mercury, Venus, Mars,
Jupiter and Saturn, the Indian astronomers give only one constru-
ction for finding the apparent geocentric position. Each of
these "star planets" is conceived as having twofold planetary
inequalities : (i) the inequality of apsis, (ii) the inequality of the
śīghra. With regard to the superior planets, the śīghra apogee or
the śīghrocca coincided with the mean position of the Sun. As
Varāhamihira observed, of the other planets beginning with Mars,
the Sun is the so-called śīghra. (PSi. XVII. 1)
Let AMSP be the concentric of which the centre E is the
same as that of the earth(Fig.17);
A'M₁P' the eccentric circle of
apsis of a superior planet, of
which the centre is C;A,M,S,P be
respectively the apogee, the Mars
.planet, the direction of the
śīghra and the perigee of the
concentric; A',M₁,P' be the
apogee, the planet as corrected
by the equation of apsis, P' the
perigee in the eccentric. The arc
Fig. 17