Basic Mathematics

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

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Regarding the development of the place value system of notation, Datta86 finds, "We can not say what were the forms of the numerals used by the early Jainas. That they had some numeral characters, we have no doubt. For as early as the fourth or fifth century before the Christian era, we find in a list enumerating the different written characters (lipi) known about that time, the mention of ankalipi and ganita-lipi.2 That list has been reproduced in the Prajñapana-sutra3 of Syâmârya who died in 376 A. V. (= 92 or 151 B.C.). There two names suggest further that the forms of numerals used for different purposes were different. The former refers to the numerals used in engraving and the latter to those used in ordinary writing. In the Jaina literature, as also in the Vedic literature we ordinarily find that a distinction is made between form of alphabets used in engravings, (called by the Jainas Kaşṭakarma or "wood work") and in manuscripts, (called pustaka-karma or "book work").4 This reference is very important in as much as it shows how one-sided and partial are the views of those writers who consider the origin and development of the Hindu numerals on the palaeographic evidence only."
In the Viseṣāvaśyakabhāṣya (v. 704) of Jinabhadra Gaņi, a verse of Bhadrabāhus Avaśyakaniryukti is quoted as
"Thibugāgāra jahanno vaṭṭo ukkosamayao kiñci".
Hemcandra Suri opines that thibuga signifies "bindu". Datta asked Kapadia87 whether "Is it then the 'zero' of the decimal place-value notation? If so, it will have to be admitted that the modern place-value notation was known in India in the 4th century before the Christian era". Kapadia88 further advances the following points in this regard,
86.
87.
88.
(1) In the 142nd sutra of Anuyogadvāra there is a reference to sthāna (thāṇehim) or places of decimal notation.
(2) A denominational name like koţa koţi (koḍa koḍi) is mentioned in this sūtra as indicating its connection with places of numeration.
Cf. The Jaina School of Mathematics, op. cit.
Cf. Ganita Tilaka by Sripati, op. cit., p. xxi, intro.
Cf. ibid., p. xxii.
In the Tiloyapaṇṇaṭṭi, acalātma denoting (84)31 (10) 90 years has been expressed as 84|31|90. Here 31 stands for the product of 84 to be effected 31 times into itself, and 90 stands for 90 zeros to be placed after the term as place values. (Cf. T.P., I. v. 4. 308, p. 178).
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