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.