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

378 than ω, the obliquity of the ecliptic, KM̂N will be equal to ξ - θ and θ - ξ respectively. The formula given in the present verse is ξ = H sin⁻¹ (H sin 90h / (D/2) × H sin ϕ / H cos δ) or H sin ξ = H sin (90h / (D/2)) × H sin ϕ / H cos δ where h and D/2 are measured in nādīs, h being the hour angle of the Moon and D/2 half-the duration of the Moon's stay above the horizon. Evidently the formula is intended as an approximate one, for all practical purposes considered equivalent to formula II given above namely sin ξ = sin ϕ sin z / cos δ or H sin ξ = H sin ϕ H sin z / H cos δ . Thus in the place of z we are given 90h / (D/2) which means " when z = 90°, D/2 is the hour angle measured in nādīs, what is z when the hour angle is h?". The answer is h × 90 / (D/2) . This formula is approximate because h and z are not strictly in proportion though h increases or decreases along with z. Nonetheless, the formula serves for practical purposes very approximately and the beauty lies in the concept of Sama-Vritta-Natāṁśa, which means measuring hour- angle in terms of the arc of the prime-vertical instead of an arc of the celestial equator. The error, it will be noted will not be much in low latitudes. So far with respect to the commentary on the present verse. Now we shall see how Bhāskara tackles the pro- blem rigorously in Golādhyāya under the caption Valana Vāsanā' ie. 'concept of Valana'.