section_path: History/Momentum conservation and the third law
section_name: Momentum conservation and the third law
paragraph_text: Momentum conservation and the third law
  
  Johannes Kepler suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite. In his Principles of Philosophy (1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a plenum, that is, filled with matter, so all motion required a body to displace a medium as it moved.
  
  During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum. Christopher Wren would later deduce the same rules for elastic collisions that Huygens had, and John Wallis would apply momentum conservation to study inelastic collisions. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.
  
  Newton arrived at his set of three laws incrementally. In a 1684 manuscript written to Huygens, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called Galilean invariance, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the Principia, with three primary laws and then other statements reduced to corollaries, during 1685.