Commentary

This explanation of the two operations that give the treatise its title is widely cited and reflects the procedural character of al-Khwarizmi's algebra. Al-jabr, the restoration or completion of a term, and al-muqabala, the balancing of like terms on opposite sides of an equation, are presented as the two basic moves by which a problem is brought to a standard form. Roshdi Rashed has argued that these terms were chosen to describe concrete manipulations familiar from commercial and legal calculation, and that their adoption as the name of the discipline reflects this grounding in practice. Victor Katz observes that al-Khwarizmi's reduction of equations to six canonical types, with worked numerical examples, was an innovation in the systematic presentation of mathematical method, though he cautions that the treatment remains entirely rhetorical rather than symbolic. Muhsin Mahdi, in his work on Arabic intellectual history, has noted the continuity between such technical vocabulary and the wider Arabic tradition of legal reasoning. The wording here is a paraphrase drawn from secondary descriptions and should not be attributed as a direct quotation. Rashed's critical edition and translation provide the authoritative basis for the terms and their Arabic usage.