________________
22 = = (%) = (2) Therefore, in the verse it is said as "added by the square of half the diameter of the face (Tearstefarfym)".
If the square of half the face is added, we get
142 + (%)* -8(2) + (*)
146 = d - (%) + (2)
or
When the area of one part of the drum (eka muraja khanda) is 146 square yojanas, then what will be the area of the two parts (i.e. of the complete drum)? Here the multiplicand is 2. That means, "multiply by 2 (faqUIT)" is stated in the verse. If we multiply by 2, we get
142.2 = 2 [0 - +(2) 292 = 2 [-*+ (2) *1
or
The thickness of the FD is 5/4, the thickness of the Fig. 20 is 5/4 and the thickness of the Fig. 19b is also 5/4. Looking at the equality of the thickness, in the end of the verse it is said as "multiply by thickness (at 661)".
If we divide 292 by the denominator of the thickness (v = 5/4), we get 73 and if we multiply 73 by the numerator of the thickness, we get 365 cubic yojanas.
In this way, the volume of the (or a) conch comes out to be
365 cubic yojanas (or [d2 -+ (2)*1).
The main item of interest in the above rationale, from the point of view of History of Mathematics is that it has been assumed that a body with curved boundaries can be deformed into another with plane boundaries in such a way that its volume remains unchanged. 9. DISCUSSION
[A] Mādhavacandra's rationale speaks, through the Fig. 9, that
CD = rm, AB = 1 (0+ m) and AB = 2 CD Therefore, we have
od+m = 2. am
48
Arhat Vacana, 14(1), 2002
Jain Education International
For Private & Personal Use Only
www.jainelibrary.org
