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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 Jain Education International For Private & Personal Use Only www.jainelibrary.org
SR No.006597
Book TitleNandanvana
Original Sutra AuthorN/A
AuthorN L Jain
PublisherParshwanath Vidyapith
Publication Year2005
Total Pages592
LanguageEnglish
ClassificationBook_English
File Size25 MB
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