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

406
Comm. Lallāchārya gave the Valana in terms of the
following verses “स्पर्शादिकालजनितोत्क्रमशिञ्जिनीभिः, क्षुण्णाक्षभा
पलभवश्रवणेन भक्ता, चापानि पूर्वनतपश्चिमयोः फलानि, सौम्येतराणि
समवेहि पृथक् क्रमेण; ग्राह्यात् सराशित्रितयाद् भुजज्या व्यस्ता ततः प्राग्वदप-
क्रमज्या...” Verses 23, 25 Chandragrahaṇādhikāra, wherein
he formulated the Valana in terms of Hversine in the
place of Hsine. The reason for his slip, we have already
explained. Now Bhāskara gives two glaring examples to
substantiate his formula and to show up the flaw in
Lallāchārya's formulation.
In the first example, where the Ecliptic takes the form
of a Vertical, the Sun being in the zenith, the Spaṣṭa
Valana which is the angle between the Ecliptic and the
prime-vertical is the same as the arc between the East
point and the intersection of the Ecliptic with the horizon
known as Lagna. Since the Sun is then in the zenith,
the longitude of the Lagna is (90 + ☉) so that the said
arc is the Agra of the point whose longitude is 90 + ☉ as
stated. Hence Spaṣṭa Valanajyā = sin A = sin δ/cos ϕ
where A is the agrā (using Napier's rule from triangle
PNL where L is the Lagna N the north-point and P the
celestial pole). In the Hindu form, this is given by
H sin V = H sin A = (R H sin δ) / (H cos ϕ) where δ is the declination
of a point of the Ecliptic whose longitude is (90 + ☉). But
Lallāchārya's formula gives the Valanajyā as Hvers δ,
δ being the declination of a point of the Ecliptic whose
longitude is (90 + λ), λ being the longitude of the Eclipsed
body ignoring the latitude. In other words, in the case of the
lunar Eclipse when the Moon is in the zenith his Valanajyā
= Hvers δ (δ having the above value) the Ākṣa Valanajyā
here being zero. Since (R H sin δ) / (H cos ϕ) ≮ Hvers δ, the mistake
committed by Lallāchārya is evident even supposing
H cos ϕ = R when we ignore the latitude ie. take ϕ to
be zero.