Euclid among the Arabs

An Approach to the Arabic Reading of The Elements

Abstract

It is common to hear that the Western world owes the Arabs the discovery of algebra. Nevertheless, the development of this discipline can be interpreted as a melting pot of different scientific traditions that was possible thanks to the classification, translation, and criticism of both the classics and the works that the Arabs obtained from the peoples they conquered. Among these works were The Elements of Euclid. 

The Elements were carefully translated during the Caliphate of Al-Ma'mÅ«n by the mathematician Mohammed ibn-Musa Al-KhwÄrizmÄ«, author of Al-jabr wa'l muqÄbalah, who laid the foundations for the discipline that would later become known as algebra and who, in the first part of his work, provides us with three methods to solve three types of equations that he calls “combined equations”. Throughout this paper I offer arguments to claim that the methods for solving these equations constitute a reinterpretation, in the algebraic field, of theorems 6, 7 and 8 of the second book of Euclid's Elements. My objective is to answer the following question: What reading of Euclid’s Elements made possible the emergence of algebra in the Arab world? To answer this question, it is necessary to explore the approach that the Arabs had with Book II of The Elements, in order to propose an interpretation of the possible factors that led them to formulate algebra. The latter is found in the first part of Al-KhwÄrizmÄ«'s work.