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.