**Re*cip"ro*cal** (?), a. [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.

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 1/4 to 1/9. -- Reciprocal terms Logic, those terms which have the same signification, and, consequently, are convertible, and may be used for each other.

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*.

© Webster 1913.

**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 1/4 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.

© Webster 1913.