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JAINA BIBLIOGRAPHY
1853
Since a negative number by its own nature is not a square, it has no square-root (Gss. i, 52).
P. 35. Classification of equations-earliest reference in Sthānānga sūtra (sūtra 747) a canonical work of circa 300 B.C. (see Datta : Jaina Math., Bulletin of the Calcutta Mathematical society, xxi, Pp. 119 ff.
P. 36. Linear equations in one unknown-early solutions : reference in the Sthānanga sutra to a linear equation by its name (ravat-tāvat), suggests the method of solution followed at that time (Datta, Jain Math, B.C.M.S. xxi, p. 122).
P. 38. Rule of false position : very limited applications of it are found in the arithmetical treatises of Mahāvira (850); finding out the unknown (Gss. iii-107108).
Pp. 44-46. Rule of Concurrence (Sankramana); Gss. vi, 2 Linear Equations; Gss. vi, 139, 1401, 142, 268, 91, 270-21.
Pp. 49-53. Linear equations--solution by false position; Mahāvíra Gss. vi. 159, 160-2, 251-2521-2531.
P. 56. Certain interest problems treated by Mahāvira lead to simple simultaneous equations involving several unknowns. In these problems certain capital amounts are stated to have been lent out at the same rate of interest for different periods of time-Gss. vi, 37, 39, 42.
P. 60. Quadratic equations : Geometrical solution of quadratic equation is found in the early canonical works of the Jainas (500-300 B.C.) and also in the Tattvārthadhigama sutra (c 150 B.C.) Datta : Geometry in the faina Cosmography, Quellen und studien zur Ges. d. Math., Ab-B, Bd 1 (1931). pp. 245-54.
Pp. 66-67. Mahāvira--The only work of Mahāvira (850) which is available now, is the Ganita-sāra-samgraha. As it is admittedly devoted to arithmetic, we cannot expect to find in it a rule for solving the quadratic. But there are in it several problems whose solutions presuppose a knowledge of the roots of the quadraticproblem and its solution cited-Gss. iv, 34, 44.
Pp. 73-74, Two roots of the quadratic-known to Mahāvira-rules and illustrations--Gss. iv, 57, 59,61,62-4, 35-52, vi 29 ff.
Pp. 77-81. Equations of Higher Degrees-Mahāvira considered certain simple equations of higher degrees in connection with the treatment of the geometric series-types given--Gss. ii, 97, 101, 102, iv, 51, 52, 54-55, 56.
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