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. — : o : — Reference P.C. Sengupta : The Khaṇḍakhādyaka, 1934.