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

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[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)