Indirect demonstration

Indirect \In`di*rect"\, a. [Pref. in- not + direct: cf. F.
   indirect.]
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   1. Not direct; not straight or rectilinear; deviating from a
      direct line or course; circuitous; as, an indirect road.
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   2. Not tending to an aim, purpose, or result by the plainest
      course, or by obvious means, but obliquely or
      consequentially; by remote means; as, an indirect
      accusation, attack, answer, or proposal.
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            By what bypaths and indirect, crooked ways
            I met this crown.                     --Shak.
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   3. Not straightforward or upright; unfair; dishonest; tending
      to mislead or deceive.
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            Indirect dealing will be discovered one time or
            other.                                --Tillotson.
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   4. Not resulting directly from an act or cause, but more or
      less remotely connected with or growing out of it; as,
      indirect results, damages, or claims.
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   5. (Logic & Math.) Not reaching the end aimed at by the most
      plain and direct method; as, an indirect proof,
      demonstration, etc.
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   {Indirect claims}, claims for remote or consequential damage.
      Such claims were presented to and thrown out by the
      commissioners who arbitrated the damage inflicted on the
      United States by the Confederate States cruisers built and
      supplied by Great Britain.

   {Indirect demonstration}, a mode of demonstration in which
      proof is given by showing that any other supposition
      involves an absurdity (reductio ad absurdum), or an
      impossibility; thus, one quantity may be proved equal to
      another by showing that it can be neither greater nor
      less.

   {Indirect discourse}. (Gram.) See {Direct discourse}, under
      {Direct}.

   {Indirect evidence}, evidence or testimony which is
      circumstantial or inferential, but without witness; --
      opposed to {direct evidence}.

   {Indirect tax}, a tax, such as customs, excises, etc.,
      exacted directly from the merchant, but paid indirectly by
      the consumer in the higher price demanded for the articles
      of merchandise.
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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.
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            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.
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   2. An expression, as of the feelings, by outward signs; a
      manifestation; a show. See also sense 7 for a more
      specific related meaning.
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            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.
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   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.
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   {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.
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