________________
Approximate Volumes of Irregular Solids
The volume of the fields occupied by various fluas living outside Svayamprabha mountain and having two to five sense organs, are given an approximate calculation. The 'depth (ogahana) or the height of each creature is stipulated in the following verse, and the other sizes are given by Virasena in his calculation of each volume."
34
35
samkho puna bäraha jovanani gomhi bhava tikosam tul Bhamaro joyanam egami maccho puna joyanasahassoll (1) A bee (bhamara): Approximation by a semi-cylinder If the length of the field of a bee height circumference
a = 1 yojana
= h = 1/2 yojana c/2 = 1/2 yojana
and
then the formula for calculating the field of a bee, given by Virasena is -
3
c/2 V = xhxa 2
8
where a = 1, h = 1/2, c/2 = л x 1/2 3/2 (with л= 3).
It is interesting that for the circumference and the area of a circle, the value of л is taken as 3.
V = abh
where 'n' is a countable number."
Arhat Vacana, 14(2-3), 2002
Jain Education International
Semi-cylindrical field occupied by a bee
36
(2) A centipede (gomhi): Approximation by a rectangular solid.
When the length 'a' of a centipede is three forth of an utsedha yojana, the width 'b', one-eight of 'a' and the thickness 'h', half of the width, all these are multiplied mutually, a countable number 'nth' part of a cubic utsedha-yojana is obtained.
27
8192
37
h
3 3 3
4
32 64
1
"
=
utsedha yojana3.
n
c/2
a
utsedha-yojana".
For Private & Personal Use Only
87
www.jainelibrary.org
