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.
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            Loyal demonstrations toward the prince. --Prescott.
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   3. (Anat.) The exhibition and explanation of a dissection or
      other anatomical preparation.
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   4. (Mil.) a decisive exhibition of force, or a movement
      indicating an attack.
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   5. (Logic) The act of proving by the syllogistic process, or
      the proof itself.
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   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.
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   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):

reductio ad absurdum
    n 1: (reduction to the absurd) a disproof by showing that the
         consequences of the proposition are absurd; or a proof of a
         proposition by showing that its negation leads to a
         contradiction [syn: reductio ad absurdum, reductio]