Nilakantha's Critique on Aryabhata's Verses on Squaring and Square-roots

By : N. K. Sundareswaran

Page No: 107-124

Abstract
NÁlakaõÇha’s commentary on °ryabhaÇÁya is well known for clarity and simplicity of language and for its expository nature. He goes on clarifying all the possible doubts. The way in which he formulates and interconnects ideas is simply beautiful. At times his commentary on a particular point runs into pages. But it would be a pleasure to read it, for, the language and style of argument are the same as in a polemical text of philosophy. This paper makes a close study of the commentary on the fourth verse of GaõitapÀda, wherein NÁlakaõÇha explains the method for finding the square root of a number, focusing on the development of ideas and the thought process. Here NÁlakaõÇha deals, at length, with many of the rationales and the concepts involved. The explanation given by NÁlakaõÇha for BaudhÀyana’s approximation of is unique. It is a fine specimen of geometrical demonstration of arithmetical ideas, a significant trend of medieval school of Kerala mathematics.