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.