Just looked up "proof" and found a few fun facts. The 200 proof = 100% alcohol is a legislative concept, not a chemistry one.

The original "proof" came from the idea that gunpowder wet with a spirit would fail to burn if the spirit had too little alcohol in it. In order to "prove" that rum wasn't over-watered, they would actually douse gunpowder in the stuff and light it.

That mixture is actually 3:4 water:alcohol. This is an interesting ratio, because it means that in your typical 1750ml bottle of 100 proof alcohol (chemical proof, not legislative proof), exactly 1000ml of it is pure alcohol. I wonder if that was what was intended before the legislators took over.