Basic Mathematics

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

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bic - T'abET = TEM (3) If = e, then
oti - --#
and so on.
(e) Analytical Methods :
Eight analytical methods71 were basically applied by Virasena to sets' knowledge apart from various other methods. They were pramāņa (measure), kāraṇa (reason), nirukti (explanation), vikalpa (abstraction or extra-creation), khandita (cut), bhājita (division), viralana (spread) and apahsta (removal).
The method of vikalpa72 shows that the author was conversant with the laws of indices and exponentiation for finite and transfinite sets. For example, the set of souls in hell, having mythic outlook is illustrated through a lower vikalpa of a dyadic sequence :
A
• (F)314
L(F)*/4=L. (L)/2. (L)". Similarly,
{1ogn (6) }
T2 :n
The method of Kāraṇa73, has been given as a geometrical representation of an algebraic equation, similar in style to the Greek's method of application of areas :
71. Cf. Jain, L. C., On the Jaina School of Mathematics, C. L. Smriti
Granth, Calcutta, 1967, pp. 265-292. 72. Cf. ibid. 73. Cf. ibid.
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