________________
summation of series, from which the first few terms are omitted, as Vyutkalita®, and he has given all the formulae for geometric progression (G.P.) thus earning for himself a prominent position in this respect.
In keeping with the traditions of those days, many topics on algebra and geometry have been discussed in the GSS. Mahavira's work on 'rational triagnles and quadrilaterals' contains many other problems of similar nature, and a number of illustrative examples are given therein. But it is noteworthy that his investigations in this particular field' have certain remarkable features, and they deserve a special consideration for the following two reasons :
i) He treated certain problems, on rational triangels and quadrilaterals, which are not found in the work of any anterior mathematician e.g. problems on right triangles involving areas and sides, rational triangles and quadrilaterals having a given area or circum-diameter, pair of isosceles triangles etc; (ii) in the treatment of other common problems, Mahavira introduced modifications, improvements or generalisations upon the works of his predecessors, particularly of Brahmagupta (6th cent. A.D.)
It may be remarked here that the credit, which Mahavira rightly deserves for his discovery of certain methods for the solution of rational triangles and quadrilaterals has gone almost unnoticed by historians of ancient mathematics, like: L.E. Dickson".
Mahavira, by his protracted achievements in several branches of Mathematics, has a distinct position and his contributions stimulated the growth of mathematics.
Delhi University
Foot-Notes
Bhagwati Sutra. Sutra 90 Antagada Dasao and Anuttaro. Vavaya Dasao. Eng. Trans by L.D. Bernett. 1907, p.30. Commentary on Surya Prajnapti by Malayagiri. Sutra 11 This work was found by Buhler Sutra 747 Brahma-Sphutta-Siddianta. Chap. XII. p55 Rule 9 GSS. chap. VII. p.31 On Mahavira's solution of rational triangles and quadrilaterals by B.B. Datta. Bull. Calcutta Math. Soc., XX. 1930 History of Theory of Numbers by L.E. Dickson. 3 Vols. 1919-1923
Jain Education International
For Private & Personal Use Only
www.jainelibrary.org
