________________
or
(cf. also DVL-III, p. 253)
(b) and
or
(v.426, p. 356)
the second square root multiplied by the third square root, or the cube of the third square-root; expressly
In particular, the law
56
226
225
296
264 232 = 296
बितियवगमूलं ततियवगमूलपडुप्पण्णं, अहवणं ततियवगमूलघणप्यमाणमेत्ताओ
and if m = 2,
1
The above selected statements are conclusive to show that the Jaina school of Indian mathematics knew the addition law of indices,
a. a" = a+
Archimedes (287 B.C. 212 B.C.) made use of this addition law but without its specific mention.3 (cf. Smith, pp.5 and 518)
الله الله
Jain Education International
[2.1.3] Instances - The instances of the use of the laws of indices are numerous in the Jaina school of Indian mathematics. Here we are interested only to show that the subtraction law :
a" ÷ a" = am-n
was known to the school and therefore we select an interesting and popular instance as follows:
छट्ठदगेण सत्तमवग्गे भागे हिदे छट्टवग्गो आगच्छादि ।
(DVL-III, p. 254)
The seventh square (of 2) divided by the sixth square (of 2) gives the
sixth square (of 2).
Expressly,
am"
a1/4 a1 a3/8
1/8
=
227
a2n
3
= (1/21/20
-
226
÷ am(n-1)
=
can be inferred from the above instance.
÷ a2(n-1)
=
=
226
a(m-1)m(n-1)
=
a2(n-1)
For Private & Personal Use Only
Arhat Vacana, 15 (4), 2003)
www.jainelibrary.org
