Extraction de la racine carree d'un entier naturel chez al-Baghdadi

Abstract

Between the ninth and fifteenth centuries, several Arab mathematicians studied numerical algorithms on integers. The extraction of the square root of an integer is based on an algorithm known at least since al-Khwarizmi (died around 850) which presents it in the framework of the decimal system of position theory, in his work the Indian calculus (al hisab al-hindi). Although this algorithm is less democratized than the four usual operations of arithmetic, it has experienced the same posterity, since it is still implemented today in our calculators and computers. We have chosen to expose the work of Al-Baghdadi, on the extraction of the square root of integers. His approach is purely numerical, it is more complete and more detailed than the works of its predecessors. We will highlight the interest of al-Baghdadi's text.