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