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DOCTRINE
42
or THE JAINAS allowed to judge by the favourite ideas he presumably cherished. Nor is the astronomy of the Jains, as, above all, it is offered to us by the Surapannatti, a creation of his own, but it rather reflects the thinking of generations. This becomes cqually clear by the usage of "we" instead of "I"and by the absence of polemics1. As to the aspect of the world, however, it bears Mahavira's stamping by his doubling the widths of geographical units, a geometrical line with the quotient 2 (§ 122). This, perhaps, accounts for the contention that there are two suns and moons over Jambuddiva, which then leads up to the doubling of further stars (§ 128). The arithmetical line is applied in Mahavira's teaching to the sums. Of a sum (jumma or rāsi or rāsi-jumma)" continuously diminished by 4 there remains 4 (o1 0), 3, 2 or 1, and it is called accordingly by the terms used at dice-playing kada-jumma, teoya, dāvara or kali-oya (Viy. 744b)3, and even khuddāga may be paced at the head of these names of khudda-jumma (Viy. 948b). They are called small "sums" as against the "large" ones, mahā-j. (Viy. 964b). They are sums expressing by their name not only the final remainder but also the number of the factors, the latter always preceding in the bipartite names of kada-jumma-kaḍajumma, k.-teopa, etc.1. These calculations -to be found in the last passages of the Viy-are applied in the most different connexions", though even Abhayadeva I We here give the different kinds of arithemetics as known from Than 263a, 496a parikamma, the clements, and vavahara, the application, are followed by rajj uü, geometry, and räsi, addition, kala-savanna, fractions, jāvam-tāvai, multiplication, and vagga, ghana, vagga-vagga, involution to the square, the cube and the fourth power Comp also Bibhutibhushan DATTA, Origin and History of the Hindu Names for Geometry Quellen u Studien z Gesch d Math 1, 113-119 The SAME, The Jaina School of Mathematics, Bull of the Calcutta Mathematical Soc 21, 115-145, D M ROY, The Culture of Mathematics among the Jains of S India in the Ninth Century in ABHORI 8
2 Even the totality of things characterized by either the presence or absence of soul (jiva) is called rasi (Samav 7b 133a)
3 Thus jumma denotes the even and oya the odd sums (Viy 860a; Vy 745b) 4 Examples 16 is kada-jumma (ie the lowest possible), since it is divisible by 4 with o remaining The division is done 4 times, and 4 is in itself kada-j Accordingly 16 is called kadajumma-kadajumma lowest possible), since it is divisible by 4 with 3 remaining 19 1s teoya (1 e the The division is Hence 19 is called kadajumma-teoya -6 1s davara, since it's divisible by 4 with 2 remaining The division is done once, and i is kali-oya Hence 6 is called kaltoya-davara
done as above
5. Comp. also Thân, 237 a
