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

161 Taking H cos δ M = R and H sin δm = δm P₂c = (H cos E δm) / R This is at the end of E₁ P₂ i.e. at the end of K; so to get the corresponding chord in the deferent we do Karnānupāta so that the result is (H cos E δm) / R × R / K = (H cos E δm) / K as given by Bhāskara. We have cut short Bhāskara’s method of Bhōgyakhanda Sphutīkaraṇa to make it clear to a modern student. Since P₂c is small, passing on from the H sine to the arc is not necessary, for, the H sine of a small arc is equal to the arc itself. Bhāskara’s argument, however, is as follows:— “If for 225, we have Bhōgya Khanda, what for δm?” The result is (B × δm) / 225; Then B is rectified as follows:— “When the H cosine E is equal to the radius, i.e. initially in the H sine table, the Bhōgyakhanda is 225, then what is it for H cos E?” The result is (H cos E × 225) / R which we have to substitute for B. Then if this be at the end of K what is it at the end of R?” The result is (H cos E × 225) / R × δm / 225 × R / K = (H cos E × δm) / K as given. Before we proceed to explain ‘शेषं च वक्रा विपरीतशुद्धौ’, we shall explain what Bhāskara pointed out as a mistake in Lallācharya. Verse 40. Let Mathematicians understand that what formula was given by Lallācharya for Sīghragatiphala is not correct. When the anomaly is 90° or 270°, the gati- phala vanishes and there will be gatiphala at the points where it ought to be Zero according to his formula. 21