Final answer:
Descartes' contributions to analytical geometry were essential mathematical tools for Newton's development of calculus and his work in optics.
Step-by-step explanation:
The work of Rene Descartes is related to that of Sir Isaac Newton in that Descartes' developments in analytical geometry were foundational and used by Newton in his advancement of calculus and research into optics. Newton did not work for the king of England during his most famous discoveries, and Descartes did not create his system of analytical geometry to describe Newton's Theory of Gravity, since Descartes lived before Newton. Therefore, Descartes' work in geometry provided the mathematical tools that Newton later utilized to develop his own theories.