  In this article, we review the main results of Volume I of Newton's Principia
which relates Kepler's law of planets and universal gravitation. In order to
clarify the reasoning of Newton, elementary and simple proofs are given to
inspire earnest young students. All proofs are based on either the symmetry of
spheres or taking great advantage of Kepler's law of area which also reflects
the symmetry of centripedal forces.
