Basic Mathematics

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

Page 60

Progressions have also been detailed in the Tiloy pannatti98 as well as Gommaţasara, Trilokasāra and earlier texts. They are either arithmetical progressions or geometrical series. The general terminology of the arithmetic progression is as follows:
First term: Adi, Mukha, Vadana, Prabhava,
Common Difference: Caya, Uttara,
Number of terms: Gaccha, Pada,
Sum: Sankalita, Dhana.
The general formula99 for the sum, transformed in various forms is Gaccha
Sum =
2 first term +(Gaccha-1) common difference
2
For the geometrical progression, 100 common ratio is called guņakāra, and its general formula has been given as Gaccha
Sum
(common ratio) - 1 Common ratio - 1
Saraswathi remarks, "Arithmetical progressions find full treatment with separate formulae for finding the first term (a), the common difference (d), the period (n) and the sum (s). The series which occasions these rules, is a rather complex one of 49 terms with 7 groups within it, which themselves are separate progressions whose periods again form another arithmetical series. The expression
S = n
n-1 2
for the sum of any group within the series is a distinct contributions of the TP to series Mathematics. The treatment of geometrical progressions is comparatively meagre. "100-A
2
n
[a+()'d
2
+
first term
-
43
The same type of series appear in the description of three operational activities in Jaina philosophy working at various control stations affecting Karmic output as well as state existence.101 The gunahānis (geometric regressions) are such that their elements in particles decrease in
d
98. Cf. T. P. G., pp. 41-48.
99.
Cf. ibid., p. 43.
100. Cf. ibid., p. 48.
100-A. Cf. The Mathematics in the first...... Trilokaprajñapti, op. cit., p. 51. 101. Cf. Gommaṭasara, Jivakāṇḍa.
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