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

188 [चित्र: Fig. 15] Fig. 15 True motion of the planets = δ (A'EV) or δ (A'EJ) But δ (A'EV) = δ (A'EV'–n̂) and δ (A'EJ) = δ (A'ES–n̂) In the case of the Inferior planet δ (A'EV') = δ (ASV) = Sīghrōcchagati and δn is Sphutakendragati where n is called Sphutakendra, m being called Madhyakendra. In the case of the Superior planet δ (A'ES) = S'īghrōcchagati because the Sun plays the part of S'īghrōccha in the case of a Superior planet and δn = Sphutakendragati as before. Hence in both the cases, Sphutagati = S'īghragati – Sphuta- kendragati. We have now to find Sphutakendragati to obtain Sphutagati, as Bhāskara remarks rightly “महामति- द्भिः केन्द्रगतिरेव स्पष्टीकृता”. In other words we have to find δn. From the figures K cosn – R cos m = r (i) Differentia- ting this we have – K sin n δn + cos n δK + R sin m δm = 0 (ii). But K² = R² + r² + 2Rr cos m so that 2δK × K = – 2Rr sin mδ m (3) Eliminating δK between (2) and (3) – K sin nδ n – (Rr sin mδ m × cos n) / K + R sin mδm = 0 i.e. K sin nδn = R sin mδm ( 1 – r / K cos n ) = (R sin mδm / K) (K – r cos n)