Basic Mathematics

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

Page 53

7. Varga (square or quadratic equations), 8. Ghana (cube or cubic equations), 9. Varga-varga (square of square or biquadratic equations), 10. Vikalpa (abstraction or permutation and combination).
From the earlier treatment it will be manifest that the above ten topics alongwith alpabahutva (comparability), which has, unfortunately, not been included above, the mathematical philosophy of Karma could well go on. Sequences and comparability could be included in topic of "set" or "rāśi" which is a word used very frequently, specially in the Dhavala commentary, for every quantity or quality there was a number associated with it.
Datta ventured to presume that the term yavat-tāvat was connected with the Rule of False Position, which, in the early stage of algebraic science in every country, was the only method of solving linear equations. 81 He further remarks:"82 “That term enters largely into Hindu Algebra of later times as the symbol for the unknown. It has been suggested that it is connected with the definition of the unknown quantity by the Greek Diophantus (c.75 A.D.) as "containing an indeterminate or undefined multitude of units (pléthos monádon aoriston)". The implication behind that suggestion was to show the Greek influence in the Hindu Algebra. It is now found that yāvat-tāvat has entered into Hindu mathematics more than five centuries before Diophantus. So if that suggestion be at all true, though I doubt it, it will have to be admitted that the balance of evidence is in favour of the Hindus, showing the possibility of the Greek Algebra being influenced by the Hindu Science. This will take aback the author of that suggestion."
(b) Place value notation for subtraction :
The Jaina School is found to use a place value notation for subtraction from factors of numerical or algebraic quantities. This notation83 has been used in the Tiloypaņņafti. It has been used profusely in the commentaries of the Gommațasāra. Todarmala,84 one of the commentators, has exposed the use in the following manner :
81.
2.
The Jaina School of Mathematics, op. cit. Cf. ibid. cf. also G. R. Kaye, Indian Mathematics, Calcutta, 1915, p. 25. Cf. also, Jaina L. C., On the Jaina School of Mathematics, op. cit. Cf. TP, pt. II, p. 609, op. cit. Cf. T Arthasamdrsti of Gommata sāra, Gandhi Haribhai Deokaraņa Granthmala, Calcutta, c. 1919.
83.
36