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

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found in 7 × 7 ways = 49 ways. From R, H sin φ could be
found in seven ways by using similarity with the other
seven latitudinal triangles except the second. Also
obtaining H cos φ in seven ways and using the formula
H sin φ = √(R² — H cos² φ) we have seven more ways.
Thus in all there are 7 × 7 + 7 + 7 = 63 ways. Similarly
H cos φ could be found in 63 ways. Extending this to
Agrajyā etc. which could be in as many or more ways
themselves finding H sin therefrom means again finding
it in 69 × 69 ways and so on. Since there is no end in
counting all these ways, it is said that there are infinite
ways to find it. The word 'infinite' here connotes only a
very large number of ways not exactly what we mean by
the word 'infinity'.
Verse 30. To find what is known as Koṇa-Śaṅku.
As a first approximation take
Koṇa-Śaṅku = √(R² — 2A²) where A = Agrajyā and Koṇa-
Śaṅku means H cos z when the azimuth is equal to 45°.
Then take Agrajyā ± the above Koṇa-Śaṅku × s/12 = Śaṅku-
bhuja = b (say) then again Koṇa-Śaṅku = √(R² — 2b²).
Then again take Agrajyā ± the above Koṇa-Śaṅku × s/12
as the new bhuja and proceeding thus by the method of
successive approximations, we arrive at a constant value
which gives the Koṇa-Śaṅku.
Comm. Bhāskara gives later the method of obtaining
H cos z ie. the Śaṅku pertaining to any zenith-distance.
So, he need not have given a separate treatment for this
Koṇa-Śaṅku. But in as much as Brahmagupta and other
previous writers gave it he has also given the same. He
gives here the method of finding the Koṇa-Śaṅku by the
method of successive approximations as given by Śrīpati.
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