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

286 Comm. Since U.S. is the projected segment of Charajyā on a vertical plane and since the diahedral angle between the planes is φ the latitude U.S. / Charajyā = Cos φ and so Śara × cos φ = (Śara × H cos φ) / R = Ūrdhwa. From fig. 54, Dinārdha-Śanku — Ūrdhwa = o'q — βr (fig. 54) = o'β' = yX = Iṣṭa-Śanku. In modern times, this means, Śara = H. vers (h) = (R — cos h) = 1 — cos h in modern terms phala = (Śara × H cos δ) / R = (1 — cos h) × cos δ ,, ,, phala × (H cos φ) / R = Ūrdhwa = (1 — cos h) cos δ × cos φ ,, ,, Dinārdha Śanku — Ūrdhwa = Iṣṭa Śanku H cos z = cos z (in modern terms) = H cos (φ — δ) (taking northern declination and following Hindu convention with respect to signs) = Dinārdha·Śanku = cos (φ — δ) in modern terms. ∴ cos (φ — δ) — (1 — cos h) cos φ cos δ = cos z ie. cos φ cos δ + sin φ sin δ — cos φ cos δ + cos φ cos δ cos h = cos z ie. cos z = sin φ sin δ + cos φ cos δ cos h as before. Verse 61. Computation of H cos z (Mahā Śanku) through Antyā and Hṛti. Let the Dinārdha Śanku (D.S.) be computed through Iṣṭāntyā and Iṣṭa Hṛti and therefrom Iṣṭa Śanku. From the Śanku, Drik·jyā ie. H sin z and the shadow (KH sin z) / R could be computed —H sin z should not be computed from Hṛti.