Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of mathematics as calculation had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the equation as known in Arabic algebra.

}, isbn = {978-1-4020-8404-1}, url = {http://dx.doi.org/1854/11276}, author = {Heeffer, Albrecht}, editor = {Rahman, Shahid and Street, Tony and Tahiri, Hassan} }