Two Sciences, Two Methods for Handling Fractions: Arithmetic and Inheritance Shares in Nineteenth-Century West Africa

Abstract The objective of this chapter is to contextualize the links between manuals on arithmetic ( ḥisāb ) and manuals dealing with inheritance shares ( farāʾiḍ ) in nineteenth-century West Africa by highlighting some key differences between the two disciplines. To do so, I take the case study of texts written by various authors found in the library of a West Saharan scholar, Shaykh Sīdiyyā al-Kabīr (d. 1868), and the inheritance-share manual that he himself wrote. I show that the way numbers are represented and conceptualized differs significantly across disciplines. Whereas ḥisāb puts emphasis on the representation of numbers using numerals, farāʾiḍ ostensibly has to do with a practical activity of inheritance-share calculation and uses number-words. Whereas ḥisāb considers fractions as mathematical objects that can be summed or multiplied, farāʾiḍ obfuscates manipulations of fractions through a process called tasḥīḥ , which could be translated as “transformation into integers”. I posit that this difference in the conceptualization of fractions in ḥisāb and farāʾiḍ is less due to a strict opposition between the theoretical and the practical and more due to the fact that two traditions regarding fractions, each with their own historical trajectory, were made to coexist.