Coping with the Tiny: Measures, Computations, and Reasoning with Small Amounts in Jean des Murs's Quadrivial Works

This paper aims at complementing the cross-disciplinary intellectual portrait of Jean des Murs presented in this special issue from the particular perspective of his arithmetical and geometrical works. If looked at from this angle, the general question immediately implies new ones: what are the connections between Jean's arithmetical or geometrical works and those in the other fields of the quadrivium? What is their importance in the global intellectual picture of Jean des Murs as a quadrivial author of the fourteenth century? In order to explore these different issues, I have chosen to focus on a specific question: to what extent do Jean des Murs's mathematical works reflect a persistent effort throughout his career to address the various issues related to small amounts? Focusing on this particularly significant problem will give me the opportunity to cover a representative sample of Jean des Murs's quadrivial works from a specific perspective. Music and astronomy address small amounts in different contexts and with different mathematical tools. However, some deeper similarities appear. They concern mainly the question of measure and incommensurability as well as the relation between mathematical and physical reasoning. Overall, they reflect the intellectual coherence between quadrivial sciences as attested by Jean des Murs's works.