Inverse 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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Ratio \Ra"ti*o\ (r[=a]"sh[i^]*[-o] or r[=a]"sh[-o]), n. [L., fr.
   reri, ratus, to reckon, believe, think, judge. See {Reason}.]
   1. (Math.) The relation which one quantity or magnitude has
      to another of the same kind. It is expressed by the
      quotient of the division of the first by the second; thus,
      the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b
      by a/b; or (less commonly) the second term is made the
      dividend; as, a:b = b/a.
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   Note: Some writers consider ratio as the quotient itself,
         making ratio equivalent to a number.
         [1913 Webster] The term ratio is also sometimes applied
         to the difference of two quantities as well as to their
         quotient, in which case the former is called
         arithmetical ratio, the latter, geometrical ratio. The
         name ratio is sometimes given to the rule of three in
         arithmetic. See under {Rule}.
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   2. Hence, fixed relation of number, quantity, or degree;
      rate; proportion; as, the ratio of representation in
      Congress.
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   {Compound ratio}, {Duplicate ratio}, {Inverse ratio}, etc.
      See under {Compound}, {Duplicate}, etc.

   {Ratio of a geometrical progression}, the constant quantity
      by which each term is multiplied to produce the succeeding
      one.
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