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

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∴ (Taddhṛti × 12 s) / k² = sin δ. Thus assuming H sine
of the given Unnatakāla to be Taddhṛti and multiplying
it. by 12 s and dividing by k² we have the value of H sin δ.
But this is approximate because the given Unnatakāla is
not exactly Taddhṛti but only an approximate value.
From this H sin δ, compute H cos δ, Charajyā, Kujyā
and through the process indicated in verse 54 namely
“Subtract the Characāpa from the Unnatakāla. The
H sine of the result is called Sūtra. Multiply the Sūtra
by H cos δ and divide by R; then we have Kalā. Add
Kujyā to Kalā; we get Iṣṭa-Hṛti”, we obtain a more
correct value of Taddhṛti. Then here we may cut short
the process as follows namely ‘ If by the assumed Taddhṛti
we had the previous H sin δ, what shall we have for this
more approximate Taddhṛti ’? The result will be a more
approximate value of H sin δ. Again form the Taddhṛti
with this H sin δ and so repeating the process till we have
a stationary value, we have the correct value of H sin δ.
Note. This is a beautiful example of the method of
successive approximations which is a modern technique
but which was so much in vogue and favourite with the
Hindu astronomers. (It will be noted how to cut short the
method).
Verses 84, 85. Answer to the second question.
Obtain 12² R²/(R² − H sin² h) s² + 1 and divide R² by
this and take the square root which gives H sin δ. Then
(R × H sin δ) / (H sin ω) gives H sin λ whose Cāpa gives the longitude
of the Sun.
Comm. The H sine of the given Natakāla is H sin h
and R² − H sin² h = H cos² h. Let H sin δ be x, which
is required to be found. Then R² − x² = H cos² δ;
H cos h = Sūtra and