  Newton's "superb theorem" for the gravitational inverse-square-law force
states that a spherically symmetric mass distribution attracts a body outside
as if the entire mass were concentrated at the center. This theorem is crucial
for Newton's comparison of the Moon's orbit with terrestrial gravity (the fall
of an apple), which is evidence for the inverse-square-law. Newton's geometric
proof in the Principia "must have left its readers in helpless wonder"
according to S. Chandrasekhar and J.E. Littlewood. In this paper we give an
elementary geometric proof, which is much simpler than Newton's geometric proof
and more elementary than proofs using calculus.
