Prove, v. t. [imp. & p. p. Proved; p. pr. & vb. n. Proving.]
Etymology: [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. Thou hast proved mine heart. Ps. xvii. 3.
2. To evince, establish, or ascertain, as truth, reality, or fact, by argument, testimony, or other evidence. They have inferred much from slender premises, and conjectured when they could not prove. J. H. Newman.
3. To ascertain or establish the genuineness or validity of; to verify; as, to prove a will.
4. To gain experience of the good or evil of; to know by trial; to experience; to suffer. Where she, captived long, great woes did prove. Spenser.
5 more senses
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.
6. (Printing)
To take a trial impression of; to take a proof of; as, to prove a page.
Syn. -- To try; verify; justify; confirm; establish; evince; manifest; show; demonstrate.
1 other Webster entry under this spelling
Prove, v. i.
1. To make trial; to essay.
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. So life a winter's morn may prove. Keble.
3. To succeed; to turn out as expected. [Obs.] "The experiment proved not." Bacon.
Shades of meaning
Fernald has no entry of its own for prove; he lists it under confirm, reason.
Where he writes about it:
Demonstrate strictly applies to mathematical or exact reasoning; prove may be used in the same sense, but is often applied to reasoning upon matters of fact by what is called probable evidence, which can give only moral and not absolute or mathematical certainty. — from reason
To demonstrate is to force the mind to a conclusion by irresistible reasoning; to prove is rather to establish a fact by evidence; as, to prove one innocent or guilty. — from reason