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