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a. [ L. reciprocus; of unknown origin. ] 1. Recurring in vicissitude; alternate. [ 1913 Webster ]

2. Done by each to the other; interchanging or interchanged; given and received; due from each to each; mutual; as, reciprocal love; reciprocal duties. [ 1913 Webster ]

Let our reciprocal vows be remembered. Shak. [ 1913 Webster ]

3. Mutually interchangeable. [ 1913 Webster ]

These two rules will render a definition reciprocal with the thing defined. I. Watts. [ 1913 Webster ]

4. (Gram.) Reflexive; -- applied to pronouns and verbs, but sometimes limited to such pronouns as express mutual action. [ 1913 Webster ]

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. [ 1913 Webster ]

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. [ 1913 Webster ]

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. [ 1913 Webster ]

n. 1. That which is reciprocal to another thing. [ 1913 Webster ]

Corruption is a reciprocal to generation. Bacon. [ 1913 Webster ]

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. [ 1913 Webster ]

n. The quality or condition of being reciprocal; reciprocalness. [ R. ] [ 1913 Webster ]

adv. 1. In a reciprocal manner; so that each affects the other, and is equally affected by it; interchangeably; mutually. [ 1913 Webster ]

These two particles do reciprocally affect each other with the same force. Bentley. [ 1913 Webster ]

2. (Math.) In the manner of reciprocals. [ 1913 Webster ]

Reciprocally proportional (Arith. & Alg.), proportional, as two variable quantities, so that the one shall have a constant ratio to the reciprocal of the other. [ 1913 Webster ]

n. The quality or condition of being reciprocal; mutual return; alternateness. [ 1913 Webster ]

v. t. To give and return mutually; to make return for; to give in return; to interchange; to alternate; as, to reciprocate favors. Cowper. [ 1913 Webster ]

v. i. [ imp. & p. p. Reciprocated p. pr. & vb. n. Reciprocating. ] [ L. reciprocatus, p. p. of reciprocare. See Reciprocal. ] To move forward and backward alternately; to recur in vicissitude; to act interchangeably; to alternate. [ 1913 Webster ]

One brawny smith the puffing bellows plies,
And draws and blows reciprocating air. Dryden. [ 1913 Webster ]

Reciprocating engine, a steam, air, or gas engine, etc., in which the piston moves back and forth; -- in distinction from a rotary engine, in which the piston travels continuously in one direction in a circular path. --
Reciprocating motion (Mech.), motion alternately backward and forward, or up and down, as of a piston rod. [ 1913 Webster ]

n. [ L. reciprocatio: cf. F. réciprocation. ] 1. The act of reciprocating; interchange of acts; a mutual giving and returning; as, the reciprocation of kindness. [ 1913 Webster ]

2. Alternate recurrence or action; as, the reciprocation of the sea in the flow and ebb of tides. Sir T. Browne. [ 1913 Webster ]

n. [ Cf. F. réciprocité. See Reciprocal. ] 1. Mutual action and reaction. [ 1913 Webster ]

2. Reciprocal advantages, obligations, or rights; reciprocation. [ 1913 Webster ]

Reciprocity treaty, or
Treaty of reciprocity, a treaty concluded between two countries, conferring equal privileges as regards customs or charges on imports, or in other respects. [ 1913 Webster ]

Syn. -- Reciprocation; interchange; mutuality. [ 1913 Webster ]

a. [ L. reciprocus returning, reciprocal + cornu horn. ] (Zool.) Having horns turning backward and then forward, like those of a ram. [ R. ] Ash. [ 1913 Webster ]

a. Reciprocal. [ Obs. ] [ 1913 Webster ]

a. [ F. réciproque, L. reciprocus. ] Reciprocal. [ Obs. ] B. Jonson. [ 1913 Webster ]