Al-Samaw'al, al-bīrūnī et Brahmagupta: les méthodes D'interpolation

Abstract

In a manuscript which is being studied here for the first time, al-Samaw'al (12th century) quotes a paragraph from al-Bīrūnī (11th century) which shows that the latter knew not only of Brahmagupta's method of quadratic interpolation, but also of another Indian method (called sankalt). Al-Samaw'al examines these methods, as well as linear interpolation, compares them, and evaluates their respective results. He also tries to improve them. In this article the author shows that al-Bīrūnī had used four methods of interpolation, two of which were of Indian origin; and that al-Samaw'al explicitly introduced a new way of evaluating these different methods. He also throws light on the active movement of research on numerical methods that constitutes the background to al-Bīrūmī's and al-Samaw'al's work, and uses modern means to evaluate the different methods and to justify the mathematicians' choices. The author has edited and translated al-Samaw'al's text in order to make it available to historians of Arabic and Indian mathematics. This allows them to follow the history and the mathematical arguments, and deepens our understanding of the importance to the development of mathematics of certain astronomical work. It also highlights the contribution of Indian mathematicians to the development of Arabic mathematics.