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

407 In the second example cited by Bhāskara the Ecliptic coincides with the horizon, the pole of the Ecliptic being in the zenith. Then in a Solar Eclipse the Moon eclipses the Sun from the south showing that H sin V = R. That H sin V = R is also evident from the fact that the Ecliptic makes 90° with the prime-vertical, having coincided with the horizon. But here according to Lallāchārya’s formula, H sin ξ = Hvers 90° = R and Āyana Valanajyā is Hvers δ, where δ is the declination of a point whose longitude is 90° more than ☉. If ☉ = 30°, 60° H sin θ = R/2 sin ω/R or (√3/2) (R sin ω)/R ie. (sin ω)/2 or √3/2 sin ω. Evidently the sum of the two Valanas Āyana and Ākṣa cannot be 90° as is also vouchsafed from geometry. So, here also, the flaw is evident. Note 1. Śrīpatyāchārya also followed Lallāchārya vide verses 18, 19, 20 Chandragrahaṇādhyāya, Siddhānta Śekhara. It will be noted that the commentator of Siddhānta Śekhara, while reiterating Bhāskara’s stand as the correct one, himself commits a mistake in saying “सममण्डलीय नतांशज्यास्थाने नतकाकोत्क्रमज्या गृहीता” In fact sin ξ = (sin ϕ sin h) / cos μ = (sin ϕ sin z) / cos δ as proved by us before. The commentator cited above overlooked that sin ξ could be also equal to (sin ϕ sin h) / cos μ , wherein natakāla also is implied. Note 2. It will be noted that even Pṛthūdakāchārya, while commenting on Brahmasphuṭa Siddhānta, ignored Brahmagupta and followed Lallāchārya blindly. Note 3. The formula given by Lallāchārya and followed by Pṛthūdaka as well as by Śrīpati is very rough besides containing the flaw cited, in as much as both μ and δ are taken to be zero, which are not so,