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34
JAINA ANTIQUARY.
Mensuration Formulae
Circle.
Nemicandra says:
"The circumference of a circle is grossly equal to three ti es its diameter; and neatly it is the square-root of ten times the square of the diameter. The quarter of the diameter multiplied by the circumference gives the accurate area."1
If C denote the circumference of a circle, d its diameter and A the area then
C (gross)=3d, C (neat) =√10d2, 4=1Cd.
Whence we shall have
For calculating the neat value (sukṣmaphala) of the circumference and of the area of the Jambudvipa the second formula has been employed. It has been stated that if r be the radius of a circle equivalent to a square of side a, then3
d1 =a, ds=(1+22)a,
r =
9
-a 16
16 2
*= (-10).
7=
[ Vol. I
1
b1= 100000 yojana=a, say
b2 =2a, b,=22a,..., bn =2"-1 a;
and
Circular Annulus. In the Jaina cosmography, the earth is supposed to be a flat plane divided into successive regions of land and water by a system of concentric circles. The innermost region is one of land, called Jambudvipa. Its diameter is 100000 yojana. Breadths of the successive annular regions are stated to be increasing by multiples of 2. Now if b1, b2, bз, ... denote the breadths and di, da, ds,... the corresponding diameters of outer edges, then we shall have
1. Trilokasara, Gatha, 311. See also Gathas 17, 96.
2. Ibid, Gathas 312-13.
3. Ibid, Gatha 18,
