RECIPROCAL
reciprocal
(adjective) of or relating to the multiplicative inverse of a quantity or function; “the reciprocal ratio of a:b is b:a”
reciprocal, mutual
(adjective) concerning each of two or more persons or things; especially given or done in return; “reciprocal aid”; “reciprocal trade”; “mutual respect”; “reciprocal privileges at other clubs”
reciprocal
(noun) something (a term or expression or concept) that has an inverse relation to something else; “risk is the reciprocal of safety”
Source: WordNet® 3.1
Etymology
Adjective
reciprocal (not comparable)
Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.
Mutually interchangeable.
(grammar) expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive
(math) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.
Done, given, felt, or owed in return
Synonyms
• mutual, two-way
• contrary, opposite, converse, inverse, inverted, cross
• (grammar): reflexive
• See also contrary
Noun
reciprocal (plural reciprocals)
(arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.
(grammar) A construction expressing mutual action.
Synonyms
• (in arithmetic): multiplicative inverse
Source: Wiktionary
Re*cip"ro*cal, a. Etym: [L. reciprocus; of unknown origin.]
1. Recurring in vicissitude; alternate.
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.
3. Mutually interchangeable.
These two rules will render a definition reciprocal with the thing
defined. I. Watts.
4. (Gram.)
Definition: Reflexive; -- applied to pronouns and verbs, but sometimes
limited to such pronouns as express mutual action.
5. (Math.)
Definition: 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 ÂĽ to
1/9.
– 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.)
Definition: The quotient arising from dividing unity by any quantity; thus
ÂĽ 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.
Source: Webster’s Unabridged Dictionary 1913 Edition