Reciprocal

a. [Lat. reciprocus, It. & Sp. reciproco, Pr. réciproc, Fr. réciproque.]

1. Recurring in vicissitude; alternate.
2. Done by each to the other; interchanging or interchanged; given and received; 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. Watts. 4. (Gram.) Reflexive: — applied to pronouns and verbs; also, sometimes limited to such as express mutual action. Reciprocal equation, an equation which remains unchanged in form, when the reciprocal of the unknown quantity is substituted for that quantity. Math. Dict.—Reciprocal figures (Geom.), figures of the same kind (as triangles, parallelograms, prisms, &c.) 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.—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.), quantities which, multiplied together, produce unity.—Reciprocal ratio, 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, &c. 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, &c. 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 once; 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. Hence, we may speak of a mutual friendship, because this feeling may pass and repass between two parties, but not so of a mutual friend in the concrete. In this case, we say a common friend.