RECIPROCALLY
inversely, reciprocally
(adverb) in an inverse or contrary manner; “inversely related”; “wavelength and frequency are, of course, related reciprocally”- F.A.Geldard
mutually, reciprocally
(adverb) in a mutual or shared manner; “the agreement was mutually satisfactory”; “the goals of the negotiators were not reciprocally exclusive”
Source: WordNet® 3.1
Etymology
Adverb
reciprocally (comparative more reciprocally, superlative most reciprocally)
In a reciprocal manner; by way of returning (e.g. a favour, insult, etc).
Source: Wiktionary
Re*cip"ro*cal*ly, adv.
1. In a reciprocal manner; so that each affects the other, and is
equally affected by it; interchangeably; mutually.
These two particles to reciprocally affect each other with the same
force. Bentley.
2. (Math.)
Definition: In the manner of reciprocals. Reciprocally proportional (Arith.
& Alg.), proportional, as two variable quantities, so that the one
shall have a constant ratio to the reciprocal of the other.
RECIPROCAL
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 ¼ 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
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.
Source: Webster’s Unabridged Dictionary 1913 Edition