How is the work of rene descartes related to that of sir isaac newton? . they both made their most famous discoveries while working for the king of england.. newton and descartes revolutionized navigation with their research, which led to increased colonization of the americas.. descartes's developments in analytical geometry were used by newton in his development of calculus and research into optics.. descartes was inspired to create a system of analytical geometry to describe newton's theory of gravity.