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JAINA BIBLIOGRAPHY
P. 80. Siddhasena Gani (6th century) used zero in calculation. (Footnote). SMITH and KARPINSKI (Hindu-Arabic Numerals p. 53) state, the Ganita-sarasangraha of Mahaviracharya (c. 830 A.D.), while it does not use the numerals with. place-value, has a similar discussion with zero'. The first part of the statement is incorrect, because Mahavira has always used numerals with place-value. In fact, no trace of numerals without place-value is to be foundin the Ganita-sara-sangrahaJ. TROPFKE's statement (Geschichte d. Elementar-Mathematics, Bd.II, 1926, p. 56) that zero was not regarded as a number before the seventeenth century A.D., is incorrect B. DATTA, Early literary evidence of the use of the zero in India', American Math. Monthly, XXXVIII, 1931, p. 569.
1841
Pp. 83-84. The place-value Notation in Hindu Literature. Jaina canonical works. The earliest literary evidence of the use of the word 'notational place' is furnished by the Anuyogadvara-stra, a work written before the Christian era; the total number of human beings in the world is given by a 'number which when expressed in terms of the denominations, kofi-koti, etc. occupies twenty-nine (29) places (sthana). Reference to the places of numeration is found also in a contemporary work, the Vyavahara-sutra (ch. i; of B. DATTA, Scientia, July, 1931; p. 8).
P. 125. The only works available which deal exclusively with patigaṇita (science of calculation) are; the Bakhshäli manuscript (c. 200), the Trisatika (c. 750), the Ganita-sara-samgraha (c. 850) and three other works.
P. 145. Cross Multiplication Method (tastha-gunana). This method has been. mentioned by Mahavira also.
P. 150. Division-a method of division by removing common factors seems to have been employed in India before the invention of the modern plan. This removal of common factors is mentioned in early Jaina works (Tatvarthägamasutra) Bhasya of Umäsväti (c. 160). It has been mentioned by Mahavira who knew the modern method.
P. 151. The method of long division-according to Mahavira.
P. 155. Square-The Sanskrit term for square is varga or Krti. Definition and method: "The product of two equal numbers is varga' p. 12).
(Mahavira Gss.
Minor methods of squaring-Mahavira (Gss. p. 13,
Pp. 162-68. Cube ie. Ghana: the continued product of three equal numbers is ghana (Gss. Pp. 14-15); Minor methods (Gss. p. 15, Gss. ii, 44, 45).
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