Ganitatilaka (Sanskrit text and English introduction)

by H. R. Kapadia | 1937 | 49,274 words

The Sanskrit text of the Ganitatilaka with an English introduction and Appendices. Besides the critically-edited text, this edition also includes the commentary of Simhatilaka Suri. The Ganitatilaka is an 11th-century Indian mathematical text composed entirely of Sanskrit verses and authored by astronomer-mathematician Shripati. The text itself dea...

Part 10 - The four types of numbers

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Even, in the time of the Vedas, we find the distinction made between odd and even numbers. These are styled as ojas (3) and yugma (c) in Jainism. Furthermore, it is interesting to note that they are associated with krta, dvapara, treta and kali, the well-known names for the four yugas of That he uses contrary moves even while expressing numbers by resorting to Katapayadi system in its second variant is borne out by Gommatasara (Jivakanda, v. 158) and Trilokasara (gatha 98 ).

4 In the following verse of Dasagitika of Aryabhata I (499) varga means "odd" and avarga means "even":- "vargaksarani varge'varge'vargaksarani kat imau yah | khadvivake svara nave varge'varge navantyavarge va || " In later works the words visama and sama stand for "odd" and "even".

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the Vaidika Hindus. To put it plainly, I shall quote from Sthananga:- "cattari jumma pannatta, tam jaha- kadajumme, teoe, davarajumme, kalioe "" Here jumma means a kind of rasi. On a quaternity being deducted from a rasi, it may either end in 4, 3, 2, or I. These are respectively called krtayugma, tryojas, dvaparayugma, and kalyojas. This seems to suggest that the numbers can be classified as 4 m+4, 4 m+3, 4 m+2, and 4 m+1.

1 Sanskrit rendering:- 1 3 catvari yugmani prajnaptani tadyatha - krtayugmam, vyojah, dvaparayugmam, kalyojah . 2 This is how it is explained on p. 238 by Abhayadeva Suri in his commentary to Sthananga.

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