Volume 8, Issue 2, Fall 2019
On the Realist Mathematisation of Motion in the Seventeenth Century
This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of diagrammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. Upon the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathematics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist foundation for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion.