Contribution of Ancient Jaina Mathematicians

Author(s): B S Jain
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf

Page 14

This shows that the Jainas combined the idea of infinity with that of division, defining infinity in one, two or three and infinite directions.
10. LAWS OF INDICES
In Anuyogadwara-Sutra', one finds certain interesting terms for higher powers, integral as well as fractional, particularly the successive squares (Varga) and square-roots (Varga mula). According to this sutra, for a quantity 'a'
the prathma-varga (first square) of 'a' means a2,
the dvitiya-varga (second square) of 'a' means (a2)2 i.e. a.
the tritya-varga (third square) of 'a' means (a4)2 i.e. a.
In general, the nth varga of 'a' means a 2×2×2× .........n times Again, the prathma-varga-mula (first square-root) of 'a' means the dvitiya-varga-mula (second square root) of 'a' means a the tritya-varga-mula (third square root) of 'a' means
1.
2.
3.
4.
૪૬
In general, the nth varga-mula of 'a' means a
i.e. an
The Anuyogadwara-sutra (about 100 B.C.) gives only in positive or negative powers of 2. But the Uttaradhyana-sutra (300 B.C.) gives the other powers. In the later sutra is used the multiplicative instead of the additive principle. Thus the second power is called varga ("square"), the third power as ghana ("cube"), the fourth power as varga-varga ("square-square"), the sixth power as ghana-varga ("cube-square"), and the twelfth power is called ghana-varga-varga ("cube-square-square").
In Anuyogadwara-sutra3, we come across with statements such as:
33
axx
a2 X a = (a1)3.
2. "the second square-root multiplied by the third square-root, or the cube of the third square-root". Expressed symbolically, this means
See Sutra 142.
1. "the first square-root multiplied by the second square-root, or the cube of the second square-root." Expressed in symbols, this means
According to Anuyogadwara-sutra", the total population of the world is a number which in terms of the denominations koti-koti etc, occupies twenty-nine places (sthana). It is a number which will be obtained on multiplying the sixth square (of two) by the fifth square, or a number which can be divided (by two) ninety
six times.
Chap. XXX 10, 11
Sutra 142.
142.
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i.e. as"
a i.e. a,
ie. a*,
√√√Theat
i. e. a.
............n times
axa* = (a)ສ.
आचार्य रत्न श्री देशभूषण जी महाराज अभिनन्दन पन्थ