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

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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.