  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.
