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

416 The periphery of the Moon’s orbit was arrived at as follows. “If 790′-35″ of the Moon’s angular motion corresponds to 11858¾ Yojanas to what periphery must 360 × 60′ correspond ?” The answer is (11858¾ × 360 × 60) / (790′-35″) = 324000 Yojanas. Reverting to the subject of parallax on hand, the Drik-lambana or the parallax along the vertical has the formula (4 H sin z) / R I nādīs in Hindu Astronomy where 4 nādīs is the maximum parallax obtained when H sin z = R. From fig. 92, C☉² = CD² + D☉² ie. Drik-lambana² = Nati² + Sphuṭalambana² II CD = ☉C sin CÔD = (4 H sin z / R) × sin CÔD = 4 sin z sin VÔZ = 4 sin ☉Z sin VÔZ = 4 sin ZV = (4 H sin ZV) / R = VB III Thus, the parallax in latitude at any point of the Ecliptic is that at the Vitribha which is conveyed by Bhāskara in the words “कक्षयोरन्तरं यत् स्यात् वित्रीभे सर्वतोऽपि तत्”. Also ☉D = C☉ cos CÔD = 4 sin ☉Z cos Z☉V = 4 cos ZV sin V☉ = (4 H cos ZV H sin V☉) / R² IV = Maximum parallax × Vitribha-Sanku × H sine of the arc V☉. In the above working we proceeded in a modern way. It is worth-hearing Bhāskara as to how these results were arrived at elegantly and ingeneously from first principles.