The paper focusses on the spread of Hindu-Arabic arithmetic among European practitioners. The analysis is based on an original database recording detailed information on over 1200 practical arithmetic manuals, both manuscript and printed. This database provides the most detailed reconstruction available of the European tradition of practical arithmetic from the late 13th to the end of the 16th century. The paper argues that studying this spread makes it possible to open a perspective on a progressive transmission of ‘useful knowledge’ from the ‘commercial revolution’ to the ‘little divergence’. Focussing on the transmission of practical arithmetic allows to stress the role of skills and human capital in pre-modern European economic development. Moreover, it allows to reconstruct a progressive transmission, from the Mediterranean to the Atlantic, of a ‘practical knowledge’ which eventually contributed to major developments in European ‘theoretical knowledge’.
Together with introducing a set of key innovations in commercial practices, the merchant-bankers of the commercial revolution of the 13th century were also the first European economic agents to adopt Hindu-Arabic numerals. As practical arithmetic provided the mathematical foundation for commercial innovations, studying its European spread provides a particularly suitable angle to study the diffusion of practical knowledge in the pre-modern period. Italy was the early adopter of these techniques, while in England these practices became widespread at the onset of the little divergence. In this paper, I discuss in comparative perspective the social diffusion of this knowledge in Italy and England, and its wider impact. On the one hand, this analysis makes it possible to show a number of parallels between the trajectories followed by these societies. On the other hand, it allows to observe the complex interactions between practical knowledge and wider economic, institutional, and social changes.
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