Demonstrate, v. t.
Etymology: [L. demonstratus, p. p. of demonstrare to demonstrate; de- + monstrare to show. See Monster.]
1. To point out; to show; to exhibit; to make evident. Shak.
2. To show, or make evident, by reasoning or proof; to prove by deduction; to establish so as to exclude the possibility of doubt or denial. We can not demonstrate these things so as to show that the contrary often involves a contradiction. Tillotson.
3. (Anat.)
To exhibit and explain (a dissection or other anatomical preparation).
Shades of meaning
Fernald has no entry of its own for demonstrate; he lists it under 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