Diagram from Section 8 of The Principia: Mathematical Principles of Natural Philosophy by Isaac Newton, illustrating the motions of bodies, specifically the orbits of bodies moving under arbitrary centripetal forces. Prop. 41: "Supposing a centripetal force of any kind, and granting the quadrature of curvilinear figures, it is required to find the trajectories in which bodies will move, and also the times of their motions in the trajectories so found." Newton (1642-1727) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian. His monograph Philosophae Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton describes universal gravitation and the three laws of motion.