Ganita-Sara-Sangraha of Mahaviracarya

This rare treatise on ancient Indian mathematics, by Hahaviracharya, highlights the great strides that were made in development of Indian algebra. All that is known about Mahavira’s life is that he was a Jain and that he wrote Ganitasarasangraha (“Compendium of the Essence of Mathematics”) during the reign of Amoghavarsha (c. 814–878) of the Rashtrakuta dynasty. The work comprises more than 1,130 versified rules and examples divided in nine chapters: the first chapter for “terminology” and the rest for “mathematical procedures” such as basic operations, reductions of fractions, miscellaneous problems involving a linear or quadratic equation with one unknown, the rule of three (involving proportionality), mixture problems, geometric computations with plane figures, ditches (solids), and shadows (similar right-angled triangles). Mahavira introduced modifications, improvements or generalizations upon the works of his predecessors particularly Brahmagupta. His work on rational triangles and quadrilaterals deserve special mention as some of the problems discussed by him are not found in the work of any anterior mathematician. Mahavira’s contributions stimulated the growth of mathematics in India and have a special position in the history of Indian Mathematics.