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Mathematical Expositions of Virasena in Dhavalā Commentary:
(197)
16
It is clear that many of the contents of JZSS are involved in the Vyavahāra (applied mathematics) section of the Jainas. The relative numeration and sequences do not seem to be included in the ten-fold mathematics, but as per L.C. Jain, they could be taken as part of Rasi1. Vīrasena must have the knowledge of this canonical system. He has used1 them without describing them in his commentary as they must be quite popular. Table 1 also indicates some topics in Th. as little more varied and advanced than the JZSS text. However, the Vīrasena mathematics could also be taken as super worldly maths too because of numerical counting of realities and others. In fact, the super worldly term should mean those numerical values, which are uncountable with respect to general applied mathematics. These may include the ultimate particle, space point, larger, numerable, innumerable, and infinite numbers. Thus, the space-point-based numbers should belong to super worldly category while the divisionbased numbers should belong to the worldly numeration. However, there could be exceptions too.
Table 1: Chapters of Mathematics in Jaina and Chinese Books S.N. JZSS
1.
Field measurement (plane geometry, surveying) Serials (percentage, proportion) Ratio and proportion (series, rule of 3)
Width (Roots)
2.
3.
4.
5.
6.
7.
8.
9.
Excess and deficiency (1 degree eqn.)
Rectangular assays (determinants)
Sides of triangle (Pythagorean geometry)
S.N. Sthānanga
3
Construction Consultation (solid 4 geometry)
Fair Tax (Labour, motion problem)
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2
1
7
6.
11.
5.
8
9.
10.
Plane geometry (Rajju)
Vyavahära (applied maths) Fundamental operations
Squares/square roots, quadratic equations
Răsi (solid geometry, sequences).
Simple equations (Yavat tavat)
Excess/deficiency (alpabahutva)
Fractions
Second degree equation, cubic equation
Squared squares, Bi-quadratic equations
Permutation and combination
(Vikalpa)
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