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Tiloyapanṇatti. The question of pramāņa versus utsedha angula does not seem to be involved here.
Similarly, the ancient canonical values of the areas of the various regions of the Jambu Island can be obtained by a proper and intelligent use of the rule
A = √10 (ch/42)
Where c is the chord (jīvā) and h is the heights of the segment (isu) of a circle. The above rule implies the formula
А= лch/4
for the area of a segment of a circle. Had Mahāvīrācārya used this typical traditional formula in his treatment of an ellipse as a double segment, he would have hit upon the true-modern formula a ab for the area of an ellipse (where a and b are the semi-axes).
One of the most original contributions of the Jaina School of Mathematics is the concept of getting vargita-samṁvargita of any quantity to various orders. It leads to formation of very quickly increasing sequences. The (first) vargita-samvargita of x is defined by xx and is denoted by x]
x=xxy, say.
The vargita-samṁvargita of the first vargita-samvargita of x is called the second vargita-samvargita of x. That is, the vargita-samvargita of y will be the second vargita-samvargita of x. It is denoted by xP. Therefore,
Thus
xP = yy = (xx) (xx)
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Similarly, the vargita-samvargita of y will be called the third vargita-samvargita of x. And so on. For example, with x = 2 we have the following
= z say.
27=22 = 4
22 = 44 = 256
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