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Mathematical Expositions of Vīrasena in Dhayalā Commentary: (204)
Law of Indices (Vol. 3, p. 253)
The law of indices has been utilized to calculate many large numbers under many topics of Dhavalā. For example, number of wrong-faithed beings has been stated to lie between (10%) and (10) which have been expressed as 22 and 2?'. These expressions seem to be more complex than the direct power on 10. The author has also given a division on the basis of law of indices, i.e.
22'122° = 220 While expressing the material with indices, following formulae have been utilized:
xo.x.x = xa+b (x"/x) = xat
Table 2: Denominational Units of Number Minimum
Current Maximum Current Value
Value Time Samaya
Palyopama/ 4.13 x1036-50 yrs
Sāgaropama Length Practical
- 10-13 cm Yojana 8 miles Paramäņu
Rajju
-102 miles Volume Trasareņu
Vāha
2.5 Quintal Mass General :
5.8 g Bhāra
99.44 kg Ardhakarsa Gold 0.121 g Svarna 9.68 g
etc. : Gunjā The pre-decimal-age methods of duplation and mediation are also traceable in Dhavalā, which seem to have formed the basis of logarithmic system on different basis. Singh has indicated that the theory of indices in Dhavalā is somewhat different from other works and seems to be primitive and earlier than 500 CE. Fundamental Operations
Dhavalā indicates nearly all the fundamental arithmetical operations of (1) addition (2) subtraction, (3) multiplication, (4) division, (5) square and square roots, (6) cube and cube-roots, (7) successive squares and successive cubes and their roots and (8) raising number to its own power (i.e. vargita-samvargita etc.). We need not illustrate these processes from the text, as they were already
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