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]

Moby Thesaurus II by Grady Ward, 1.0:

230 Moby Thesaurus words for "demonstrate":
   account for, adumbrate, advertise, affect, afford proof of, air,
   allegorize, approve, argue, ascertain, attest, audit, balance,
   balance the books, beef, bespeak, betoken, bitch, blazon forth,
   body forth, boggle, boycott, brandish, breathe, bring forth,
   bring forward, bring home to, bring into view, bring out,
   bring to notice, broaden the mind, call in question, call to mind,
   catechize, challenge, check, check out, cinch, cite,
   cite a particular, civilize, clarify, clear up, clinch, complain,
   connote, crack, cry out against, dangle, decipher,
   demonstrate against, demur, demythologize, denote, describe,
   determine, develop, direct, disclose, display, dispute, divulge,
   document, double-check, dramatize, edify, educate, elucidate,
   emblazon, embody, enact, enlighten, enter a protest, establish,
   euhemerize, evidence, evince, example, exemplify, exhibit, explain,
   explain away, explicate, expose, expose to view, exposit,
   expostulate, expound, express, figure, fix, flash, flaunt,
   flourish, follow, follow from, foreshadow, furnish evidence,
   give a for-instance, give indication of, give instruction,
   give lessons in, give reason for, give sign, give the meaning,
   give token, go to show, ground, guide, have a case, highlight,
   hold good, hold up, hold water, holler, howl, illuminate, illumine,
   illustrate, image, impersonate, imply, incarnate, indicate, inform,
   instance, instruct, inventory, involve, itemize, kick, make clear,
   make good, make out, make plain, manifest, march, mark,
   materialize, mean, mirror, nail down, name, object, open the eyes,
   overhaul, parade, particularize, perform, personate, personify,
   picket, point to, popularize, prefigure, present, press objections,
   pretypify, proclaim, produce, project, protest, prove, prove to be,
   prove true, put forth, put forward, quote, raise a howl, rally,
   rationalize, realize, reeducate, reflect, remonstrate,
   remove all doubt, represent, reveal, roll out, school, scruple,
   set, set at rest, set forth, set right, settle, settle the matter,
   shadow, shadow forth, sharpen the wits, shed light upon, show,
   show forth, show how, show signs of, show the way, signalize,
   signify, simplify, sit in, solve, speak for itself, speak volumes,
   spell out, sport, spotlight, squawk, state a grievance, strike,
   suggest, symptomatize, take stock, teach, teach a lesson, teach in,
   teach the rudiments, tell, tend to show, throw light upon, token,
   trot out, trumpet, trumpet forth, unfold, unlock, unravel, vaunt,
   verify, wave, yell bloody murder