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

456 formula cos ω = sin (90-δ) cos v or in the Hindu form H cos v = (R H cos ω) / (H cos δ) . In this case β' = (β H cos ω) / (H cos δ) . Or again noting that M K̂ P = 90-λ where λ is the longitude of R, we could use 'Inner side Inner angle formula' with respect to the triangle KMP, which gives 0 = sin 90 cot δ - sin (90 -λ) cot v or cot v = cot ω / cos λ or tan v = cos λ tan ω. But this formula implies the tangent functions which were not used by the Hindu astronomers. Similarly using the elements 90-λ, 90°, v, and 90-δ of the same triangle KMP, another formula could be got for v. Or again noting that K P̂ M = 90+α, we could yet get more formulae where α is the Right ascention of M. Note (4) Thus far we have used modern formulae. Let us now see as to how Bhāskara derives his formula. He takes the triangle MKP' (fig. 107) wherein MK = 90°, KP' = v and P̂' = 90. From fig. 108, the Hsine of MK is Fig. 108 KO equal to R where 'O' is the centre of the sphere and the Hsine of KP is KN so that it is the Āyanavalanajyā, Hence