inverse. See {Invert}.]

1. Opposite in order, relation, or effect; reversed;

inverted; reciprocal; -- opposed to {direct}.

2. (Bot.) Inverted; having a position or mode of attachment

the reverse of that which is usual.

3. (Math.) Opposite in nature and effect; -- said with

reference to any two operations, which, when both are

performed in succession upon any quantity, reproduce that

quantity; as, multiplication is the inverse operation to

division. The symbol of an inverse operation is the symbol

of the direct operation with -1 as an index. Thus sin-1 x

means the arc whose sine is x.

{Inverse figures} (Geom.), two figures, such that each point

of either figure is inverse to a corresponding point in

the order figure.

{Inverse points} (Geom.), two points lying on a line drawn

from the center of a fixed circle or sphere, and so

related that the product of their distances from the

center of the circle or sphere is equal to the square of

the radius.

{Inverse}, or {Reciprocal}, {ratio} (Math.), the ratio of the

reciprocals of two quantities.

{Inverse}, or {Reciprocal, {proportion}, an equality between

a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3

: 1/6, or 4 : 2 : : 3 : 6, inversely.

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 3/4 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.

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.

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 3/4 to 1/9.

{Reciprocal terms} (Logic), those terms which have the same

signification, and, consequently, are convertible, and may

be used for each other.

Usage: {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.

adj : concerning each of two or more persons or things; especially

given or done in return; "reciprocal aid"; "reciprocal

trade"; "reciprocal respect"; "reciprocal privileges at

other clubs" [ant: {nonreciprocal}]

n : (math) one of a pair of numbers whose product is 1: the

reciprocal of 2/3 is 3/2; the inverse of 7 is 1/7 [syn: {inverse}]

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