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

249 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. 32