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

386 λ = 0 Hversin (90 — λ) = R — H cos (90 — λ) = R — H sin λ = R — H sin 0° = R — 0 = R. Hence Lallācharya took by mistake that the Āyana Valana varies as Hvers (90 — λ) instead of H sin (90 — λ) since both Hversine and H sine of 90 — λ̄ are zero at the Ayanas and maximum at r and ♎. The same mistake was committed by Lallācharya in the context of the Moon’s phase also as criticised by Bhāskara as we shall see later. In fact, this latter criticism is not so justified as the former, as will be shown in that context. Note 5. If instead of taking the Āyana Valana to vary as H sin (90 — λ) we happen to take according to Lallācharya that it varies as Hversine, then in places (Ref. verses 38, 39 Valana Vāsanā, Golādhyāya) removed by 90° from the points of intersection of the Ecliptic and the prime-vertical, where there should be no Sphuta- Valana, we do get that there is some Sphuta Valana there, since the value of Hversine differs from Hsine, though these two functions happen to be zero simultaneously and maximum simultaneously. Bhāskara continues in verses 66-68 (Ibid) “ I shall now depict Ākṣa Valana by means of the hour-angle. Take the sum or difference of S'anku-Agrā and S'anku-tala according as they are of the same direction or not ; compute √(R² — B²) where B is the result ; then H sin ϕ H sin h ─────────────── is equal to H sin ξ where ξ is the Ākṣa Valana ”. √(R² — B²) Comm. We saw before in the Tripraśnādhyāya that A = S + B where A = S'anku-Agrā, S = S'anku-tala, and B = S'anku-bhuja = H sin µ where µ is represented in fig. 79. Hence √(R² — B²) = H cos µ so that the above formula gives H sin ϕ × H sin h H sin ξ = ───────────────────── which is the same as got by H cos µ the modern formula in Equation II.