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Inverse ratio
(gcide) | 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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Inverse ratio
(gcide) | 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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