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

191 Comm. This is clear from fig. 24. If S be the end of Vṛiṣabha, S' in the figure denotes the end of Karkaṭa them from the right-angled triangle SAP, ^ sin S'A = sin SA = sin APS × sin PS = sin A'K × cos SK sin S'A ∴ sin A'K = ————— . But sin S'A = cos S'♈ cos SK and cos SK = cos δ where δ is the declination at S. A'K converted into time gives the rising time of AS' ie. Karkaṭa. cos S' ∴ the rising time of Karkaṭa = ———— cos δ In tbe Hindu form, it will be Karkaṭa-anta-Koṭijyā Karkaṭa-Rāsi-Udayakāla = ————————————— × R Karkaṭa-anta-Dyujyā as stated. cos ♈S In modern terms sin A'K = cos ♈K = ———— cos δ from the formula cos λ = cos α cos δ. Thus, virtually the formula is a statement of the formula cos λ = cos α ^ cos δ. Aslo the formula sin AS' = sin P sin PS is parallel to the formula sin δ = sin λ sin ω which we proved already from Hindu methods. Verse 57. Still an alternative method. The H sines of Meṣa etc. being multiplied by H cos ω divided by their respective H cos δ's and the arcs thereof being subtracted as before the preceding from the succeeding we have the rising times of Meṣa etc. Comm. From figure 24, ^ SN SN = SL cos LSN and ————— = perpendicular from cos SK K on ♈