An Unknown Medieval Hebrew Anonymous Treatise on Arithmetic

An anonymous Hebrew arithmetical treatise, apparently from the late twelfth or early thirteenth century, represents a tradition of teaching arithmetic that is quite different from that found in most medieval Hebrew arithmetic textbooks currently known. Whereas the standard format for teaching arithmetic in medieval Hebrew textbooks is based primarily on methods of written computation, occasionally accompanied by mental computations, this treatise is based solely on the latter methods. The structure of the text is also uncommon, inasmuch as each chapter is devoted to a specific arithmetical operation and deals both with integers and with fractions. In other examples of medieval Hebrew arithmetic texts, fractions are usually treated separately. This anonymous treatise is clearly connected to the work of two of the most important early medieval Jewish mathematicians, Abraham bar Ḥiyya (ca. 1065–1136/1145) and Abraham Ibn Ezra (1092–1167). The text also seems to share some features with a Latin miscellany, assembled apparently in the third quarter of the twelfth century in Toledo, which has recently been designated The Toledan Regule (Liber Alchorismi, part II).

The anonymous treatise is described in brief and its mathematical content examined in detail. It is compared to the Toledan Regule and to the works of Bar Ḥiyya and Ibn Ezra. It is suggested that this anonymous text may indicate a link between the Hebrew arithmetical works of the two Abrahams and the Latin miscellany.