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 ¼ to . -- Reciprocal terms (Logic), those terms which
have the same signification, and, consequently, are convertible, and
may be used for each other.
Syn. -- Mutual; alternate. -- 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.
Re*cip"ro*cal, n. 1. That which is reciprocal to another thing.
Corruption is a reciprocal to generation.
Bacon.
2. (Arith. & Alg.) The quotient arising from dividing unity by any
quantity; thus, ¼ 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.
Re*cip`ro*cal"i*ty (-kl"*t), n. The quality or condition of being
reciprocal; reciprocalness. [R.]
Re*cip"ro*cal*ly (r*sp"r*kal*l), adv. 1. In a reciprocal manner; so
that each affects the other, and is equally affected by it;
interchangeably; mutually.
These two particles do reciprocally affect each other with the same
force.
Bentley.