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

162 Comm. Ref. verse 45, Spaṣṭādhikāra, Śiṣya Dhī- vṛddhida तद्रहिताऽऽशुभुक्तिः, त्रिज्ज्याहता स्वचलकर्णहताऽऽशुचापभोग्य ज्यया विगुणिता विहृताऽऽद्यमौर्व्या, लब्धं त्यजेत्, स्वचलतुङ्गगतेः सदैव शेषं स्फुटा भवति च ग्रहभुक्तिरेवम्" i.e. ( शीघ्रगति-मन्दस्फुटगति ) × R Śīghraphala Bhōgyakanda --------------------------- × ----------------------- K 225 = Sīghragatiphala. Here the quantity within the brackets is δm. What Lallācharya had in his mind is as follows. ‘If for the Ādya Khanda 225 we have H cos E = R, what shall we have for the Bhōgya Khanda of the Sīghraphala ?’ The result would be [ H sin (E + 225) - H sin E ] × R / 225 = ( H sin E H cos 225 + H cos E H sin 225 / R - H sin E ) × R / 225 Taking H cos 225 = R and H sin 225 = 225 it would be H cos E × 225 / R × R / 225 = H cos E. So Lallācharya’s formula would become (δm / K) × H cos E as given by Bhās- kara. The charge levelled at Lallācharya is due to the fact that by the word ‘Āsu-chāpa’ by which Lallācharya meant ‘आशुफलचाप’ Bhāskara meant ‘आशुकेन्द्रचाप’. When the Kendra = 90 or 270, the Bhōgyakhanda being Zero, the Sīghragatiphala would be Zero. Also where it ought to be zero namely (90 + H sin⁻¹r) & (270 - H sin⁻¹r) it would not be zero. If Lallācharya had really meant what Bhāskara allributed to him, the formula would be (H cos mδm / K) and it is very unlikely that Lallācharya would have meant this wrong formula, for, even if K were taken by him to be steady, δ (r H sin m / K) = (r H cos mδm / K) and Lallāchar- ya’s formula does not contain ‘r’. The only non-rigorous part in Lallācharya’s formula is at the point where he took