Algebraic symbolism in medieval Arabic algebra

Medieval Arabic books read more or less like transcriptions of lectures, a fact that stems from the fundamentally oral nature of medieval Islamic civilization. Books covering algebra are no exception. There we find algebraic solutions to problems written all out in words, with no notation even for numbers. But problems were not solved rhetorically. Algebraists would work out a problem in some kind of notation on a dust board or other ephemeral surface, and to record it in a book a rhetorical version of the calculations would be composed. From early texts it appears that only the coefficients of polynomials were written in Hindi notation. But in the Maghreb in the twelfth century a notation specific to algebra developed in which the power was indicated also. This symbolic notation is not presented as a scientific development in the manuscripts, but is instead shown in textbooks to instruct students in its use. In this article we explain the notation, its context, and how it differs from modern notation.