The Collaborative International Dictionary of English v.0.48:

Demonstration \Dem`on*stra"tion\, n. [L. demonstratio: cf. F.
   d['e]monstration.]
   1. The act of demonstrating; an exhibition; proof;
      especially, proof beyond the possibility of doubt;
      indubitable evidence, to the senses or reason.
      [1913 Webster]

            Those intervening ideas which serve to show the
            agreement of any two others are called "proofs;" and
            where agreement or disagreement is by this means
            plainly and clearly perceived, it is called
            demonstration.                        --Locke.
      [1913 Webster]

   2. An expression, as of the feelings, by outward signs; a
      manifestation; a show. See also sense 7 for a more
      specific related meaning.
      [1913 Webster +PJC]

            Did your letters pierce the queen to any
            demonstration of grief?               --Shak.
      [1913 Webster]

            Loyal demonstrations toward the prince. --Prescott.
      [1913 Webster]

   3. (Anat.) The exhibition and explanation of a dissection or
      other anatomical preparation.
      [1913 Webster]

   4. (Mil.) a decisive exhibition of force, or a movement
      indicating an attack.
      [1913 Webster]

   5. (Logic) The act of proving by the syllogistic process, or
      the proof itself.
      [1913 Webster]

   6. (Math.) A course of reasoning showing that a certain
      result is a necessary consequence of assumed premises; --
      these premises being definitions, axioms, and previously
      established propositions.
      [1913 Webster]

   7. a public gathering of people to express some sentiment or
      feelings by explicit means, such as picketing, parading,
      carrying signs or shouting, usually in favor of or opposed
      to some action of government or of a business.
      [PJC]

   8. the act of showing how a certain device, machine or
      product operates, or how a procedure is performed; --
      usually done for the purpose of inducing prospective
      customers to buy a product; as, a demonstration of the
      simple operation of a microwave oven.
      [PJC]

   Direct demonstration, or Positive demonstration, (Logic &
      Math.), one in which the correct conclusion is the
      immediate sequence of reasoning from axiomatic or
      established premises; -- opposed to

   Indirect demonstration, or Negative demonstration (called
      also reductio ad absurdum), in which the correct
      conclusion is an inference from the demonstration that any
      other hypothesis must be incorrect.
      [1913 Webster]

WordNet (r) 3.0 (2006):

demonstration
    n 1: a show or display; the act of presenting something to sight
         or view; "the presentation of new data"; "he gave the
         customer a demonstration" [syn: presentation,
         presentment, demonstration]
    2: a show of military force or preparedness; "he confused the
       enemy with feints and demonstrations"
    3: a public display of group feelings (usually of a political
       nature); "there were violent demonstrations against the war"
       [syn: demonstration, manifestation]
    4: proof by a process of argument or a series of proposition
       proving an asserted conclusion [syn: demonstration,
       monstrance]
    5: a visual presentation showing how something works; "the
       lecture was accompanied by dramatic demonstrations"; "the
       lecturer shot off a pistol as a demonstration of the startle
       response" [syn: demonstration, demo]

Moby Thesaurus II by Grady Ward, 1.0:

211 Moby Thesaurus words for "demonstration":
   absolute indication, allegorization, alphabet, art, beef, bitch,
   blazon, blueprint, boycott, bravura, brilliancy, burden of proof,
   case, case in point, challenge, charactering, characterization,
   chart, choreography, citation, clarification, complaint,
   compunction, conclusive evidence, confirmation,
   conventional representation, cracking, cross reference,
   damning evidence, dance notation, daring, dash, decipherment,
   decoding, deduction, deductive reasoning, delineation, demo, demur,
   demurrer, demythologization, depiction, depictment, description,
   determination, diagram, discourse, discourse of reason,
   discursive reason, display, drama, dramatics, drawing, eclat,
   editing, elucidation, emblem, emendation, enactment, enlightenment,
   establishment, etalage, euhemerism, evidence, example, exception,
   exegesis, exemplar, exemplification, exhibit, exhibition,
   exhibitionism, explanation, explication, exponent, exposition,
   expostulation, exposure, expounding, false front, fanfaronade,
   figuration, figure, flair, flaunt, flaunting, flourish, grievance,
   grievance committee, hieroglyphic, histrionics, howl, iconography,
   ideogram, illumination, illustration, imagery, imaging,
   incontrovertible evidence, indication, indignation meeting,
   indisputable evidence, induction, inductive reasoning, instance,
   ironclad proof, item, kick, letter, light, limning,
   logical thought, logogram, logograph, manifestation, map, march,
   musical notation, nonviolent protest, notation, object lesson,
   objection, onus, onus probandi, opening, ostentation, pageant,
   pageantry, parade, particular, performance, philosophy, picketing,
   pictogram, picturization, plan, portraiture, portrayal,
   prefigurement, presentation, presentment, printing, production,
   projection, proof, protest, protest demonstration, protestation,
   qualm, quotation, rally, ratiocination, rationale, rationalism,
   rationality, rationalization, rationalizing, realization, reason,
   reasonableness, reasoning, reference, relevant instance,
   remonstrance, remonstration, rendering, rendition, representation,
   representative, retrospective, schema, score, script, scruple,
   settlement, sham, show, showing, showing-off, simplification,
   sit-in, solution, sophistry, specious reasoning, spectacle, splash,
   splurge, squawk, staginess, strike, substantiation, sure sign,
   sweet reason, syllabary, symbol, tablature, teach-in, testimony,
   theatrics, type, typical example, unfolding, unfoldment, unlocking,
   unmistakable sign, unveiling, varnishing day, vaunt, verification,
   vernissage, writing



Bouvier's Law Dictionary, Revised 6th Ed (1856):

DEMONSTRATION. Whatever is said or written to designate a thing or person.
For example, a gift of so much money, with a fund particularly referred to
for its payment, so that if the fund be not the testator's property at his
death, the legacy will fail; this is called a demonstrative legacy. 4 Ves.
751; Lownd. Leg. 85; Swinb. 485.
     2. A legacy given to James, who married my cousin, is demonstrative;
these expressions present the idea of a demonstration; there are many James,
but only one who married my cousin. Vide Ayl. Pand. 130; Dig. 12, 1, 6; Id.
35, 1, 34 Inst. 2, 20, 30.
     3. By demonstration is also understood that proof which excludes all
possibility of error; for example, mathematical deductions.