सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

138 of the Mandaphala from the Āgama without pointing out how it was formulated and (2) he assumed the period of a Kalpa and that at the beginning of the Kalpa the planets were all in conjunction at the first point of Aries. Similarly in the Upapatti adduced by Bhāskara with respect to the Mandocchas of the planets, he assumed the formulation of Sīghra-phala on the basis of Āgama without proving how the concept of Sīghra-phala was arrived at by the founders of Astronomy and how the difference between the observed apparent positions and the computed mean positions, was resolved into two equations the Mandaphala and the Sīghra- phala. In the proof adduced with respect to the Sīghroccha of Mercury and Venus also Bhāskara did not mention anything as to how their heliocentric sidereal periods could be obtained but simply assumed the formulation of the Mandaphala and Sīghra-phala as already being there on the basis of Āgama. We shall now proceed to describe the method of formu- lation of the Sīghra-phala with respect to the five Tāra- grahas, star planets namely Mercury, Venus and Mars, Jupiter, Saturn and show how so different a set of geomet- ries of the ancients and the moderns the one geocentric and the other heliocentric could give identical formulation with respect to Sīghra-phala. Let us consider the case of Mercury and Venus in the first instance. Having taken the mean Sun to play the part of the ‘Graha’ in the case of Mercury and Venus and having formed a concept of Sīghroccha as mentioned before, whose geocentric period of revolution was determined, without suspecting it to be the heliocentric sidereal period of the planet the ancient Hindu astronomers assumed by analogy from the case of Mandaphala with respect to the Sun and Moon, that the centre of the circle in which these planets revolve does not coincide with the centre of the Earth. In other words, they continued eccentric circle theory here also so that without suspecting heliocentric revolution