The Collaborative International Dictionary of English v.0.48:

Demonstrate \Dem"on*strate\ (?; 277), v. t. [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.
      [1913 Webster]

   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.
      [1913 Webster]

            We can not demonstrate these things so as to show
            that the contrary often involves a contradiction.
                                                  --Tillotson.
      [1913 Webster]

   3. (Anat.) To exhibit and explain (a dissection or other
      anatomical preparation).
      [1913 Webster]

WordNet (r) 3.0 (2006):

demonstrate
    v 1: give an exhibition of to an interested audience; "She shows
         her dogs frequently"; "We will demo the new software in
         Washington" [syn: show, demo, exhibit, present,
         demonstrate]
    2: establish the validity of something, as by an example,
       explanation or experiment; "The experiment demonstrated the
       instability of the compound"; "The mathematician showed the
       validity of the conjecture" [syn: prove, demonstrate,
       establish, show, shew] [ant: confute, disprove]
    3: provide evidence for; stand as proof of; show by one's
       behavior, attitude, or external attributes; "His high fever
       attested to his illness"; "The buildings in Rome manifest a
       high level of architectural sophistication"; "This decision
       demonstrates his sense of fairness" [syn: attest,
       certify, manifest, demonstrate, evidence]
    4: march in protest; take part in a demonstration; "Thousands
       demonstrated against globalization during the meeting of the
       most powerful economic nations in Seattle" [syn:
       demonstrate, march]