Geometry, Time and Force in the Diagrams of Descartes, Galileo, Torricelli and Newton

Abstract
Cartesian method both organizes and impoverishes the domains to which Descartes applies it. It adjusts geometry so that it can be better integrated with algebra, and yet deflects a full-scale investigation of curves. It provides a comprehensive conceptual framework for physics, and yet interferes with the exploitation of its dynamical and temporal aspects. Most significantly, it bars a fuller unification of mathematics and physics, despite Descartes' claims to quantify nature. The work of his contemporaries Galileo and Torricelli, and of his successor Newton, illustrates conceptual possibilities Descartes left aside, due to his attachment to method.
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