An Approximation for Square Roots known in India prior to Alexander's Conquest

TL;DR

This paper discusses an ancient Indian method for approximating square roots, predating Alexander the Great's conquest, suggesting that such mathematical techniques were known in India long before Newton's method was formalized.

Contribution

It provides historical evidence that an approximation method for square roots was known in India prior to Alexander's conquest, predating Newton's method.

Findings

Ancient Indian mathematicians used a method similar to Newton's for square root approximation.

The technique was documented in a 19th-century publication based on older Indian sources.

This challenges the notion that such methods originated solely in Europe.

Abstract

This paper was published in French under the title \textit{Sur une m\'ethode d'approximation des racines carr\'ees dans l'Inde ant\'erieurement \`a la conqu\^ete d'Alexandre}, in the Bulletin de la S. M. F., volume 7 (1879), p. 98-102. It argues that the process of approximating the irrational square root of an integer, now commonly known as Newton's method, was known in India since very ancient times.