You can find Newton's comments in his work on Optics. Feynman goes over this in his Physics.

Proofs are shown in Griffiths Introduction to Electrodynamics. Newton's original proof, for gravity, is in the Principia.

@Narasimham: x,x˙ are linearly independent.

@ManRow: just look at the link provided earlier for the conditions. The mathematical proof is in Earnshaw's theorem. If you study the proof carefully, you should be able to see that any such configuration is unstable. The proof is generally done as homework in a junior/senior level field theory class.