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

328
Agrā / s = S. S. / 12 = Taddhṛti / k = (Agrā + S. S. + Taddhṛti) / (s + 12 + k)
(1) (2) (3)
= 1800 / (9 + 12 + 15) = 1800 / 36 = 50 II
(4)
Equating (1) and (4) Agrā = 9 × 50 = 450
Equating (2) and (4) S. S. = 12 × 50 = 600
Thirdly Taddhṛti = 15 × 50 = 750
Again Equating (1) and (6) of I
Agrā / Krāntijyā = 5 / 4 = 450 / Krāntijyā ∴ H sin δ = (450 × 4) / 5
= 360 from which λ could be computed.
Verse 98. The chara at a place where s = 9, is equal
to 3 nādis. If you could compute the longitude of the
Sun, then certainly you are a leader among astronomers,
Oh ! Scholar !
Verse 99. Answer to the problem above.
12 Carajyā / √((12 × Carajyā / R)² + s²) = H sin δ where from λ the
longitude of the Sun could be computed.
Comm. Let H sin δ = x; then from the third lati-
tudinal triangle Kujyā / Krāntijyā = s / 12 = 9 / 12 = 3 / 4
∴ Kujyā = 3 x / 4 since Krāntijyā means H sin δ
∴ Carajyā = 3 x / 4 × R / (H cos δ) = 3 R x / (4 √(R² - x²))
= H sin (3 × 6) = H sin 18° ∴ Squaring
9 R² x² = 16 (R² - x²) H sin² 18 = 16 Carajyā² (R² - x²)