"Prov'd" is just a contraction of "proved". It was common at that time. This might have a familiar ring...

  If this be error, and upon me prov'd,
  I never writ, nor no man ever lov'd.

(It's from Shakespeare's famous sonnet that begins "Let me not to the marriage of true minds / admit impediments".)

Beyond that, "prove", "proof", "proven", etc are all from the latin provare - to try, or test.