reciprocal ratio

Inverse \In*verse"\, a. [L. inversus, p. p. of invertere: cf. F.
   inverse. See {Invert}.]
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   1. Opposite in order, relation, or effect; reversed;
      inverted; reciprocal; -- opposed to {direct}.
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   2. (Bot.) Inverted; having a position or mode of attachment
      the reverse of that which is usual.
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   3. (Math.) Opposite in nature and effect; -- said with
      reference to any two operations, which, when both are
      performed in succession upon any quantity, reproduce that
      quantity; as, multiplication is the inverse operation to
      division. The symbol of an inverse operation is the symbol
      of the direct operation with -1 as an index. Thus sin-1 x
      means the arc or angle whose sine is x.
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   {Inverse figures} (Geom.), two figures, such that each point
      of either figure is inverse to a corresponding point in
      the order figure.

   {Inverse points} (Geom.), two points lying on a line drawn
      from the center of a fixed circle or sphere, and so
      related that the product of their distances from the
      center of the circle or sphere is equal to the square of
      the radius.

   {Inverse ratio}, or {Reciprocal ratio} (Math.), the ratio of
      the reciprocals of two quantities.

   {Inverse proportion}, or {Reciprocal proportion}, an equality
      between a direct ratio and a reciprocal ratio; thus, 4 : 2
      : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
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Reciprocal \Re*cip"ro*cal\ (r[-e]*s[i^]p"r[-o]*kal), a. [L.
   reciprocus; of unknown origin.]
   1. Recurring in vicissitude; alternate.
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   2. Done by each to the other; interchanging or interchanged;
      given and received; due from each to each; mutual; as,
      reciprocal love; reciprocal duties.
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            Let our reciprocal vows be remembered. --Shak.
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   3. Mutually interchangeable.
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            These two rules will render a definition reciprocal
            with the thing defined.               --I. Watts.
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   4. (Gram.) Reflexive; -- applied to pronouns and verbs, but
      sometimes limited to such pronouns as express mutual
      action.
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   5. (Math.) Used to denote different kinds of mutual relation;
      often with reference to the substitution of reciprocals
      for given quantities. See the Phrases below.
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   {Reciprocal equation} (Math.), one which remains unchanged in
      form when the reciprocal of the unknown quantity is
      substituted for that quantity.

   {Reciprocal figures} (Geom.), two figures of the same kind
      (as triangles, parallelograms, prisms, etc.), so related
      that two sides of the one form the extremes of a
      proportion of which the means are the two corresponding
      sides of the other; in general, two figures so related
      that the first corresponds in some special way to the
      second, and the second corresponds in the same way to the
      first.

   {Reciprocal proportion} (Math.), a proportion such that, of
      four terms taken in order, the first has to the second the
      same ratio which the fourth has to the third, or the first
      has to the second the same ratio which the reciprocal of
      the third has to the reciprocal of the fourth. Thus, 2:5:
      :20:8 form a reciprocal proportion, because 2:5:
      :1/20:1/8.

   {Reciprocal quantities} (Math.), any two quantities which
      produce unity when multiplied together.

   {Reciprocal ratio} (Math.), the ratio between the reciprocals
      of two quantities; as, the reciprocal ratio of 4 to 9 is
      that of 1/4 to [frac19].

   {Reciprocal terms} (Logic), those terms which have the same
      signification, and, consequently, are convertible, and may
      be used for each other.
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   Syn: Mutual; alternate.

   Usage: {Reciprocal}, {Mutual}. The distinctive idea of mutual
          is, that the parties unite by interchange in the same
          act; as, a mutual covenant; mutual affection, etc. The
          distinctive idea of reciprocal is, that one party acts
          by way of return or response to something previously
          done by the other party; as, a reciprocal kindness;
          reciprocal reproaches, etc. Love is reciprocal when
          the previous affection of one party has drawn forth
          the attachment of the other. To make it mutual in the
          strictest sense, the two parties should have fallen in
          love at the same time; but as the result is the same,
          the two words are here used interchangeably. The
          ebbing and flowing of the tide is a case where the
          action is reciprocal, but not mutual.
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