Newton, the geometer (Q664619)

In the 1680s Newton became critical of Cartesian geometry. In this paper the authors discuss Newton's work in geometry and the different points of view of Descartes and Newton. Newton felt that the geometrical approach yielded more insight. He rejected Descartes' pointwise constructions based on an algebraic approach and accepted in geometry the curves that Descartes called mechanical and rejected. The authors discuss Newton's elegant geometric solution of Pappus' problem by means of the ``organic construction'' and his work on cubics in which he anticipated projective geometry. They also show the beauty of some of Newton's geometrical results in the Principia.