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

262
dala in figure 44, (H cos z) / 12 = R / K = (Unmandala Śaṅku) / 12 (c)
Eliminating Krāntijyā and Unmandala Śaṅku from
(a), (b) and (c) (Unmandala Śaṅku) / (H sin λ H nis ω/R) = s / k
∴ (12R / K) / (H sin λ H sin ω / R) = s / k ie. 12R² / (KH sin λ H sin ω) = s / k
∴ K = (12R² × k) / (s H sin λ H sin ω). Here 12R² / (H sin ω) = (12 × 3438²) / 1397
= 101531 ; but Bhāskara has taken 101530 taking a
more correct value of R. Then 101530 / (H sin λ) is symbolized as
para so that para × k / s = K = Unmandala Karṇa. Regard-
ing the Samavṛttakarṇa, in the place of (b) above we have
(Sama-Śaṅku) / Krāntijyā = k / s (b') by the similarity between the
first and the fifth latitudinal triangles. Equation (c)
holds good with respect to any H cos z and the corres-
ponding K since 12 R = K × Śaṅku and 12 R is a cons-
tant. Noting therefore R / K' = (Sama-Śaṅku) / 12 (c')
eliminating Krāntijyā and Sama-Śaṅku among (a), (b'),
(c'), we shall have
K = (12 R² s) / (k H sin λ H sin ω) = para × s / k as stated.
Second half of Verse 42. To obtain the Dinārdha-
karṇa from the Unmandalakarṇa.
(Un-mandalakarṇa × Charajyā) / Antyā = Dinārdhakarṇa.
Comm. We have equation (c) above stating
12 R = K × Śaṅku. (c) But