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=== Newton on Mathematics and Natural Philosophy ===
Newton's two most important works of natural philosophy were the ''Principia'', published in 1687 [[CiteRef::Newton (1687)]], which dealt with his theories of motion and universal gravitation, and ''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions, and Colours of Light'' [[CiteRef::Newton (1704)]] which was published in 1704 and dealt with his theories of light and color. [[CiteRef::Westfall(1999)]] Newton made mathematics much more central to the conduct of natural philosophy than Descartes, by producing a general mathematical theory of the motion of bodies. [[CiteRef::Janiak (2016)]] He posited three mathematical '''laws of motion''', together with a '''law of universal gravitation'''. Changes in the state of motion of objects were caused by '''forces''' acting on them. Quantities of force and amounts of matter were measurable. The laws specified the mathematical relationship between the acceleration experienced by an object, the quantity of matter composing it, and the magnitude of the forces acting on it. [[CiteRef::Smith (2009)]]
In contrast with the Cartesian mechanical philosophy, in Newton’s physics, material objects were not required to be in direct contact in order to influence each other's motion. Forces could act at a distance. To explain both falling bodies and the motions of the moon and planets, Newton posited a '''gravitational force''' that acted as the inverse square of the distance between objects. He claimed to have derived this relationship from Kepler's observational laws of planetary motion. The works of Ptolemy, Copernicus, and Kepler used the mathematical language of geometry in their descriptive accounts of celestial motions. In the ''Principia'' Newton likewise presented his arguments geometrically. Newton sought not simply to describe celestial motions, but to explain these motions in terms of gravitational forces acting between bodies. In order to do this, Newton invented a new branch of mathematics, '''integral and differential calculus'''. Calculus deals with mathematical quantities that are continuously changing, such as the magnitude and direction of gravitational forces acting on an orbiting body. [[CiteRef::Friedman (2002)]][[CiteRef::Smith (2009)]] He developed the basic concept of calculus during 1665-6, while Cambridge University was closed due to a plague. [[CiteRef::Cohen and Smith (Eds.) (2002)|p. 10]]
