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 7 - Place-value system of decimal notation

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It appears that India has been the birth-place of various numerical notations. Out of them, the one in which there are used only ten symbols, is of considerable importance. In this notation nine symbols represent numbers one to nine, and the tenth, zero. The former nine symbols are designated as anka2 and the latter viz., the zero-symbol as sunya. This notation with a decimal scale goes by the name of "place-value system of decimal notation" or "the decimal place-value system", and is adopted throughout the civilized world, since the application of the principle of this place-value is both sufficient and efficient to enable one not only to write any number whatsoever but to write it in the simplest way possible. That this place-value system of decimal notation was known in India several centuries before the dawn of Christianity can be deduced from the following particulars:-

2-3 These literally mean "a mark" and "empty" respectively. 4 In Jinabhadra Gani's Visesavasyakabhasya (v. 704), a gatha of the Avasyakaniryukti of Bhadrabahu is quoted as under:- " sibugagara jahanno vatto ukkosamayao kimci " What is the true radical significance of the word thibuga and in what sense has it been employed in the above passage? The commentator Hemacandra Suri is of opinion that it signifies "bindu". Dr. Datta asks me a question: "Is it then the 'zero' of the decimal numeral notation? If so, it will have to be admitted that the modern decimal place-value notation was known in India in the 4 th century before the Christian era." 4 gani o

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(1) In the 142 nd sutra of Anuyogadvara there is a reference to sthana (thanehim) or places of decimal notation. (2) A denominational name like kotakoti (kodakodi) is mentioned in this sutra as indicating its connection with places of numerations. (3) A very big number extending to 29 places i. e. to say a number consisting of 29 digits is here referred to as we shall shortly notice. (4) Vyavaharasutra (uddesaka I) furnishes us with a term gananasthana for place of calculation. So says Dr. Datta.

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