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No. II]
MATHEMATICS OF NEMICANDRA.
dz=(1+2° +23)a,
dn = (1+ 22 +28+ ... +2" )a=(2n+1 -3)a. So Nemicandra writes :
"Multiply as many twos as equal to the number (of regions) decreased and also increased by unity; then multiply the results by 100000. Subtract from the products zero and 300000 (respectively). The results will be the breadth and diameter (respectively) of the outer region." 1.
He has further stated that the diameter of the outer edge of the nth region=46, – 3a, that of its inner edge = 26,- 3a and mean diameter =36n - 3a. 2
“The two values of the cir Jumference of the Jambudvīpa being multiplied by the diameter of any desired land or sea and divided by the diameter of the Jambudvīpa, will give the two values of the circumference of that land or sea." 3
“Multiply the sum of the outer and inner edges of an annulus by half its breath and set down the results at two places. Multiply it (at one place) by 3 and (at another place, by v1o. The products will be (respectively) the gross and neat values of the area of the annulus.”'4
That is to say, if C1, C, be the inner and outer circumferences of a ciroular annulus of breadth 6 and dj, d, be the corresponding diameters, we shall have
Cy: Cy=d, :d, Gross area of the annulus = (di+d216,
Neat area of the annulus=VTO(d+d2)6. Segment of a Circle. For the mensuration of a segment of a circle, Nemicandra gives the following rules : 5 1. Ibid, Gātbā 309. It should perhaps be noted that the breadth of an annulus
(6) is called val iya-vyäsa and the diameter of its edge (d) the sūci-vyāsa. 2 Ibid, Gātha 310. 3 Ibid, Gatha 314. 4 Ibid, Gātbā 315. 5 Trilokasära, Gāthās 760—766,
