Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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common ratio, whereas their energy-levels increase by unity. Similar phenomena happen to be in Yoga station structures in forms of varga, vargaņā, spardhaka, gunahāni etc.102 If a varga is denoted by v, energylevel by s, d as the common difference, vargaņā by W, then the first spardhaka of the first geometric regression or gunahāni is given by W + w$+1 + ws+2 + “v-d + Wy-20 + ........... + w 2s-1
"v-(s-1)d with the help of the superscripts and subscripts.
V
The first spardhaka of the second gunahāni may be written in the following form
(n+1) WV
(n+1)s+ s-1 W V
i d
+
(n+1)s + 1 W V d 22
+ ............ +
2
Ž - (S-1).
Thus it appears that the study of complicated forms of sequences and progressions were the first requisits of the Jaina Karmic philosophy and theory of cosmological structures, round the advent of Christian era.102A
(e) Mensuration
The geometry of a circle and a straight line is a geometry of the Jambū island and its symmetric mountains. Moreover the conics are the outcome of various sections of the cone subtended at the eye of an observer by the paths of various heavenly bodies in all of their aspects.
Thus the relations between various parts for the unknowns became a subject of intensive study since the philosophy in India took a turn, some centuries before Christ. The new philosophy was required to explain the effect of action in all its phases, and alongwith the past knowledge, a scientific quest was initiated in order to unravel the secrets of nature, observed and unobserved. Mathematics was called upon to satisfy the queries of how why, when, where, and what and the schools carried on an exhaustive
102. Cf. ibid., v., 233. Cf. also, Jaina, L. C., Mathematical foundation of
Jaina Karma System, op. cit.
102-A. The works on Karma theory, like the Kasāya Pāhuda and the
Satkhandāgama were composed in the c. 1st or 2nd century A. D. Naturally, the works appear to have been founded long before them, and they needed mathematical manoeuvre.
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