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

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But K — r cos n = R cos E.
∴ δn = (R sin mδm × R cos E) / (K² sin n) But R sin m = K sin n
Cancelling δn = (R cos Eδm) / K = (H cos E δm) / K as given by
Bhāskara. In the formula H sin E = (r H sin m) / K, Bhāskara
perceived the variability of both H sin m and K on
the right hand side and he exclaims “ न हि केन्द्रगतिजमेव
फलयोरन्तरं स्यात्, किन्त्वन्यथाऽपि अद्यतनभुजफलश्वस्तनभुजफलान्तरे
त्रिज्यागुणे अद्यतनकर्णहृते यादृशं फलं न तादृशं श्वस्तनकर्णहृते, स्वल्पा-
न्तरेऽपि कर्णे भाज्यस्य बहुत्वात् बह्वन्तरं स्यादित्येतदानयनं हित्वा अन्यत्
महामतिमद्भिः कल्पितम्, तद्यथा केन्द्रगतिरेव स्पष्टीकृता ” i.e. “ The
variation in the Sīghraphala is not entirely constituted
by the variation in m but also by that in K......So
leaving the method of seeking δE through the formula
H sin E = (r H sin m) / K the great intelligent astronomers
used the formula.
Sphutabhukti = Sīghra Bhukti — Sphuta Kendra-
bhukti (Bhukti means gati) wherein it was'sought to obtain
the variation in Sphutakendra i.e. n̂ in the figures.
We have given a proof of Bhāskara’s formula, which
circumvented finding Sīghragatiphala but which sought
directly Sphutabhukti, by using the modern heliocentric
figures. We shall now see how Bhāskara could deal with
such a tough problem. Refer fig 16. Let P₁, P₂ be two
positions of the planet on two consecutive days relative to
the Sīghra A₂, so that P₁E₁P₂ is the Sphuta Kendragati
spoken of. It will be noted that it is not Sphutagati be-
cause P₁, P₂ are positions of the planet relative to A, which
is itself moving (as rightly remarked by Bhāskara). It is
Sphuta Kendragati because A₂E₁P₁ and A₂E₁P₂ are the