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