A Medieval Mystery: Nicole Oresme’s Concept of Curvitas

I n a paper published in 1952, J. L. Coolidge (1873–1954) appreciates that the story of curvature is “unsatisfactory” [2], and he points out that “the first writer to give a hint of the definition of curvature was the fourteenth century writer Nicole Oresme, whose work was called to my attention by Carl Boyer.” Then Coolidge comments: “Oresme conceived the curvature of a circle as inversely proportional to the radius; how did he find this out?” The scholarly conditions of the fourteenth century make this discovery phenomenal and the question as to how it was achieved worth researching. In the present article we describe how a fourteenthcentury scholar (i) gave a correct definition for curvature of circles and attempted to extend it to general curves, (ii) tried to apply curvature to understand the behavior of real-life phenomena, and (iii) produced in his research a statement that anticipates the fundamental theorem of curves in the plane. In various cases Oresme’s work is not cited when the history of curvature is discussed (e.g., [5], [8]), while some authors (e.g., [1], p. 191) make note of his contribution to this concept. Several scholars have even concluded that the medieval sciences contributed very little to the modern scientific revolution. In addressing this perception, Edward