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

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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'.