________________
30 JAINA ANTIQUARY.
[Vol. I "The ardhaccheda of the dividend minus the ardhaccheda of the divisor is always the ardhaccheda of the quotient.” 1
2m = 2n = 2m-n. « The distributed number multiplied by the ardhaccheda of the substituted number will always give the ardhaccheda of the resulting number."9
If the number M be distributed into its units and each unit be then substituted by the number N the resulting number R will be
R=NM Now if N=2", then
R=21M as stated in the rulo.
“The ardhaccheda of the distributed number added with the ardhaccheda of the substituted number is the varga-salākā of the resulting number.”3
(2")" – 2014* Thus Nemicandra knew fully the Law of Indices.
20" x x" = xm+", cm = x1 = xm-n, (.zm)" =wmn
Series Nemicandra distinguishes fourteen kinds of series (dhārā) : * (1) Sarva-dhārā (“ general series” of natural numbers),
1, 2, 3, 4, ..., N, ... (2) Sama-dhārā ("even series "),
2, 4, 6, 8, ..., 2n, ... (3) Disama-dhārā ("odd series "),
1, 3, 5, 7, ..., (2n-1), ...
1 Ibid, Gathā 106. 2 Ibid, Gāthā 107. 3 lbid, Gāthā 108.
4 Triloká sāra, Gāthās 53-66, 77-88,
