\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.