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

300 Iṣṭa-Karṇa × I. A. = D. K. × Antyā = U. K. × Carajyā so that I.A. = (D.K. × Antyā) / I.K. – (U.K. × Carajyā) / I.K. I But U.K. = 12 R / U.S. (verse 40) ∴ U.K. × Carajyā = (12R × Carajyā) / U.S. = (12R × Kujyā × R) / (U.S. × H cos δ) since Carajyā = (Kujyā × R) / (H cos δ) But Kujyā and U.S. are the Karṇa and Koṭi of the seventh latitudinal triangle so that Kujyā / U.S. = k / 12 Comparing with the first fundamental latitudinal triangle. ∴ U.K. × Carajyā = (12R² × k) / (H cos δ 12) = kR² / (H cos δ) Hence substituting in I I.A. = (U.K. × Carajyā) / I.K. = kR² / (H cos δ × I.K.) Thus we have proved the first part of the statement. Having obtained I.A., from fig. 52 we have Antyā – I.A. =(FQ–AN)=CQ. The Utkrama Cāpa of CQ = NQ = h and Dinārdha – h = Unnatakāla. Let us see what this procedure means in practice. Since on any day at any place, φ and the declination of the Sun are known we can compute all the magnitudes given in the verse or more easily H cos δ so that from the formula Iṣṭāntyā = 12R² / (H cos δ × I.K.) where K = √(S² + 12), the shadow being observed Iṣṭāntya could be computed in no time. Also the Antyā of the day R+(H tan φ tan δ) can be computed so that the segment CQ can be got. The inverse Hversine of this is h. The arc CQ above was symbolized as Sara.