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

248 Comm. The first statement is based on the similarity between the third triangle and the others and the second statement is evident. Second half of verse 27. Other elements could be derived from what is already known and from what has been obtained. Also by alternando and invertendo we could pass from one element to the other and vice- versa. Verse 28. Karṇa = √(Bhuja² + Koti²) Bhuja = √(Karṇa² − Koti²) Koti = √(Karṇa² − Bhuja²) Thus the third could be had from the other two in all the triangles. Verse. There are sixty-three ways of obtaining H sin ϕ and H sin ϕ. On account of hundreds of ways of obtaining Agrajyā etc., there are an infinite number of ways of obtaining H cos ϕ etc. Comm. Under verse 23 Bhāskara says that there are 98 ways of obtaining Taddhṛti. Taking the third latitude triangle, H sin δ could be obtained in seven ways, from this H sin δ, Kujyā could be obtained in seven ways; hence, according to the principle of association namely that when one thing could be done in m ways and another in n ways, both the operations could be together performed in mn ways, so Kujyā could be obtained in 7 × 7 = 49 ways; similarly the upper segment of Taddhṛti could be had in 49 ways; so that adding the two Taddhṛti could be obtained in 98 ways. Similarly suppose we have to find H sin δ. H cos ϕ could be found in seven ways and from H cos ϕ, H sin δ could be found in seven ways. Thus H sin ϕ could be