Even though Cartesian coordinates offered a new and powerful way of representing equations as shapes on his coordinate system, many of Newton’s contemporaries saw such equations as a property of a given figure, a line or a circle or some more complicated form. But it took Newton just a few months after encountering Descartes to realize, as his biographer, Richard Westfall reports, “The equation is more basic than the curve; the equation defines, or as Newton put it, expresses the nature of the curve.”
