The religious and legal aspect of al-Khwarizmi's algebra and its status in the hierarchy of sciences of al-Farabi

The paper deals with a genuine Islamic scientific discipline, the science of the calculation of inheritance shares (‘Ilm al-Fara’id), and the applications of arithmetic and algebra to the problems of the distribution of inheritance according to the rules developed in this discipline. The main treatises considered in this regard are the relevant chapters of “The Compendious Book on Calculation by Completion and Balancing” by al-Khwarizmi, in which algebraic methods have been applied to the computation of the legal shares of legacy, the treatise on the law of inheritance “Sirajiyya” of al-Sajawandi, as well as the “Enumeration of Sciences” of al-Farabi, who provides a philosophical understanding of the status and nature of algebra.