The Collaborative International Dictionary of English v.0.48:

Prove \Prove\, v. i.
   1. To make trial; to essay.
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   2. To be found by experience, trial, or result; to turn out
      to be; as, a medicine proves salutary; the report proves
      false. "The case proves mortal." --Arbuthnot.
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            So life a winter's morn may prove.    --Keble.
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   3. To succeed; to turn out as expected. [Obs.] "The
      experiment proved not." --Bacon.
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The Collaborative International Dictionary of English v.0.48:

Prove \Prove\, v. t. [imp. & p. p. Proved; p. pr. & vb. n.
   Proving.] [OE. prover, F. prouver, fr. L. probare to try,
   approve, prove, fr. probus good, proper. Cf. Probable,
   Proof, Probe.]
   1. To try or to ascertain by an experiment, or by a test or
      standard; to test; as, to prove the strength of gunpowder
      or of ordnance; to prove the contents of a vessel by a
      standard measure.
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            Thou hast proved mine heart.          --Ps. xvii. 3.
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   2. To evince, establish, or ascertain, as truth, reality, or
      fact, by argument, testimony, or other evidence.
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            They have inferred much from slender premises, and
            conjectured when they could not prove. --J. H.
                                                  Newman.
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   3. To ascertain or establish the genuineness or validity of;
      to verify; as, to prove a will.
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   4. To gain experience of the good or evil of; to know by
      trial; to experience; to suffer.
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            Where she, captived long, great woes did prove.
                                                  --Spenser.
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   5. (Arith.) To test, evince, ascertain, or verify, as the
      correctness of any operation or result; thus, in
      subtraction, if the difference between two numbers, added
      to the lesser number, makes a sum equal to the greater,
      the correctness of the subtraction is proved.
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   6. (Printing) To take a trial impression of; to take a proof
      of; as, to prove a page.
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   Syn: To try; verify; justify; confirm; establish; evince;
        manifest; show; demonstrate.
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Moby Thesaurus II by Grady Ward, 1.0:

134 Moby Thesaurus words for "prove":
   affirm, afford proof of, argue, ascertain, assay, attend, attest,
   audit, authenticate, back, back up, balance, balance the books,
   be found, bear out, become of, bespeak, betoken, bolster,
   bring home to, bring out, bring to test, buttress, certify, check,
   check and doublecheck, check out, check over, cinch,
   circumstantiate, clinch, collate, come about, come of, come out,
   confirm, corroborate, cross-check, cut and try, demonstrate,
   determine, develop, document, double-check, end, engrave, ensue,
   essay, establish, eventuate, evince, examine, experiment, fall out,
   fare, fix, follow, follow from, fortify, get out, give a try,
   give a tryout, have a case, have a go, hectograph, hold good,
   hold water, impress, imprint, indicate, inventory, issue,
   make good, make out, mimeograph, multigraph, nail down, overhaul,
   overprint, pan out, play around with, practice upon, print,
   probate, proof, prove to be, prove true, publish, pull,
   pull a proof, put out, put to bed, put to press, put to trial,
   ratify, recheck, reinforce, reissue, remove all doubt, reprint,
   research, result, road-test, run, run a sample, run off, sample,
   set at rest, settle, settle the matter, shake down, show, stamp,
   strengthen, strike, substantiate, support, sustain, take stock,
   taste, terminate, test, triple-check, try, try it on, try out,
   turn out, undergird, unfold, uphold, validate, verify, warrant,
   work out