________________
by the breadth (vyasa) 13. Here the area of a lune (bälendu cresent moon
or young moon) is half of that area.
B1
L. C. Jain
36
B2
1
2
1
a
2 2
where P1, P2 & P, are the circumferences of the circles C1, C2 and C, respectively.
15
Jain Education International
•
4. YATIVRSABHA
In his Prakrit work titled Tioloyapannatti. Yativṛṣabha quotes the following rule, in Sanskrit, for finding the area (A) of a (plane) conch.
A =
a
.
2
(TP, v. 321, p. 208)
The diameter (uyasa) 'd', multiplied by itself, diminished by half the face (vadana). added by the square of half the face (mukha) 'm', multiplied by two (dvi), and divided by four, is, they say, the mathematics of this (figure) having a focus (nābhi).
(P1 + P2)
2
(P2 + P3)
2
व्यासं तावत् कृत्वा, वदन दलोनं मुखार्धवर्ग- युतम् ।
द्विगुणं चदुर्विभक्तं सनाभिकेऽस्मिन् गणितमाहुः ।।
This may imply that
π
4
In the JSOIM 14, A = 73 square yojanas is calculated when d = 12 yojanas and m = 4 yojanas (cf. also Table B).
[1958] obtained the above result through the following way.
л (radius)2 A = 2
2·0·01
d2
-
-73.28 square yojanas.
=
+ 48
d-m
2
A =
+ d.m.
[21]
2
This may be a possible reason behind his proposal of a figure (Fig. 4) to the conch-like plane one although he categorically stated that the figure by Yatiurṣabha might be different. 16
[2h]
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