Source : Webster's Revised Unabridged Dictionary (1913)

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.

            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.

   2. An expression, as of the feelings, by outward signs; a
      manifestation; a show.

            Did your letters pierce the queen to any
            demonstration of grief?               --Shak.

            Loyal demonstrations toward the prince. --Prescott.

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

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

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

   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.

   {Direct}, 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}, 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.

Source : WordNet®

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