Mathematics in the Accademia del Cimento : from a Language of Nature to a Language of Reason

This paper examines the works on pure mathematics (geometry and algebra) published by Giovanni Alfonso Borelli, Carlo Rinaldini, and Vincenzo Viviani during or shortly after the period of activity of the Accademia del Cimento. By examining the content and motivations of these treatises, as well as their authors' epistemological conceptions concerning the nature of mathematical knowledge and its relation to natural philosophy, I aim to show that, although mathematics played a minimal role within the Cimento's scientific programme, it was not a minor parallel topic of research for the Academicians. Beside contributing to the political image of the founders of the Cimento as promoters of science, mathematics played a role in defining the intellectual processes that govern the production of scientific knowledge in both mathematics and the new science of nature, and in maintaining the Galilean assertion of the ontological and epistemic connection between mathematics and nature. [Publisher's text]