2. (Bot.) Inverted; having a position or mode of attachment
the reverse of that which is usual.
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 whose sine is x.
{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}, or {Reciprocal}, {ratio} (Math.), the ratio of the
reciprocals of two quantities.
{Inverse}, 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.
Corruption is a reciprocal to generation. --Bacon.
2. (Arith. & Alg.) The quotient arising from dividing unity
by any quantity; thus 3/4 is the reciprocal of 4; 1/(a +
b) is the reciprocal of a + b. The reciprocal of a
fraction is the fraction inverted, or the denominator
divided by the numerator.
2. Done by each to the other; interchanging or interchanged;
given and received; due from each to each; mutual; as,
reciprocal love; reciprocal duties.
Let our reciprocal vows be remembered. --Shak.
These two rules will render a definition reciprocal
with the thing defined. --I. Watts.
4. (Gram.) Reflexive; -- applied to pronouns and verbs, but
sometimes limited to such pronouns as express mutual
action.
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.
{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 3/4 to 1/9.
{Reciprocal terms} (Logic), those terms which have the same
signification, and, consequently, are convertible, and may
be used for each other.
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.