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

159 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