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2 definitions found
 for Reciprocal proportion
From The Collaborative International Dictionary of English v.0.48 :

  Inverse \In*verse"\, a. [L. inversus, p. p. of invertere: cf. F.
     inverse. See Invert.]
     [1913 Webster]
     1. Opposite in order, relation, or effect; reversed;
        inverted; reciprocal; -- opposed to direct.
        [1913 Webster]
     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.
        [1913 Webster]
     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.
        [1913 Webster]

From The Collaborative International Dictionary of English v.0.48 :

  Reciprocal \Re*cip"ro*cal\ (r[-e]*s[i^]p"r[-o]*kal), a. [L.
     reciprocus; of unknown origin.]
     1. Recurring in vicissitude; alternate.
        [1913 Webster]
     2. Done by each to the other; interchanging or interchanged;
        given and received; due from each to each; mutual; as,
        reciprocal love; reciprocal duties.
        [1913 Webster]
              Let our reciprocal vows be remembered. --Shak.
        [1913 Webster]
     3. Mutually interchangeable.
        [1913 Webster]
              These two rules will render a definition reciprocal
              with the thing defined.               --I. Watts.
        [1913 Webster]
     4. (Gram.) Reflexive; -- applied to pronouns and verbs, but
        sometimes limited to such pronouns as express mutual
        [1913 Webster]
     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.
        [1913 Webster]
     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
     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:
     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.
        [1913 Webster]
     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.
            [1913 Webster]

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