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Revisiting the mathematical synthesis of the laws of Kepler and Galileo leading to Newton's law of universal gravitation

Newton's deduction of the inverse square law from Kepler's ellipse and area laws together with his "superb theorem" on the gravitation attraction of spherically symmetric bodies, are the major steps leading to the discovery of the law of universal gravitation (Principia, 1687). The goal of this article is to revisit some "well-known" events in the history of science, and moreover, to provide elementary and clean-cut proofs, still in the spirit of Newton, of these major advances. Being accessible to first year university students, the educational aspect of such a coherent presentation should not be overlooked.