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Reciprocal equation

Reciprocal 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 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. Syn: Mutual; alternate. 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.

Reciprocal 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 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. Syn: Mutual; alternate. 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.

- In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics...

- In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice). In normal usage, this first lattice...

- In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium...

- In mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting...

- In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects...

- The Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the...

- In crystallography, the Laue equations relate the incoming waves to the outgoing waves in the process of diffraction by a crystal lattice. They are named...

- In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative...

- In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of...

- This article is a summary of common equations and quantities in thermodynamics (see thermodynamic equations for more elaboration). SI units are used for...

- In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice). In normal usage, this first lattice...

- In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium...

- In mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting...

- In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects...

- The Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the...

- In crystallography, the Laue equations relate the incoming waves to the outgoing waves in the process of diffraction by a crystal lattice. They are named...

- In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative...

- In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of...

- This article is a summary of common equations and quantities in thermodynamics (see thermodynamic equations for more elaboration). SI units are used for...

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