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

390 Then the next argument is 'If for H sin λ equal to R we have the declination equal to H sin ω, what shall we have for the above Dorjyāntara. The result is (H sin ω / R) × (H cos λ × b / R). Since this is in modern terms sin ω cos λ × b and b = Δλ, we perceive that this expres- sion is Δ (H sin δ) where δ stands for LM of fig. 84, ie. the difference of the declinations of the points S and L of the disc of fig. 84. The next argument advanced by Bhāskara, namely that on account of declination, the disc is slanted and LM gets thereby enlarged into L'M of fig. 84 and adduces proportionality from fig. 86. But this argument seems to be faulty. In fact, the magnitude of LM is got for the diurnal circle of radius H cos δ. To get its value for radius R, the result would be [(H sin ω H cos λ × b) / R²] × [R / (H cos δ)] = (b. H sin ω H cos λ) / (R. H cos δ) . Then the argument is 'If in the disc of radius b, we have Δδ equal to the above what will it be for radius R? The result would be (H sin ω H cos λ) / (H cos δ) . Note. Our argument is based on the idea that lines of the small circle namely the diurnal circle get enlarged for a circle of radius R in the porportion R: H cos δ. Bhāskara's concept of enlargement on account of slanting does not seem to be plausible because, on account of decli- nation, the disc may occupy an overhead position when the Equator is itself inclined. Thus slanting does not arise out of declination. The question might be asked as to how Bhāskara got the right answer by such an argument. He got the answer up his sleeves through the other methods he gave and he adduced this argument to get at that answer.