A Medieval Mystery: Nicole Oresme's Concept of Curvitas

摘要

In 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 fourteenth-century 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.