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Reciprocal

Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. 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.

Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. 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.

Reciprocal

Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. 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.

Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. 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.

Reciprocal

Reciprocal 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 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.

Reciprocal 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 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.

Reciprocal

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.

- of reciprocal functions Reciprocal spiral: a plane curve Reciprocal averaging, a statistical technique for aggregating categorical data Reciprocal aircraft...

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

- 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 evolutionary biology, reciprocal altruism is a behaviour whereby an organism acts in a manner that temporarily reduces its fitness while increasing...

- A reciprocal construction (abbreviated RECP) is a grammatical pattern in which each of the parti****nts occupies both the role of agent and patient with...

- Reciprocal liking, also known as reciprocity of attraction, is the act of a person feeling an attraction to someone only upon learning or becoming aware...

- Reciprocal determinism is the theory set forth by psychologist Albert Bandura which states that a person's behavior both influences and is influenced by...

- Reciprocal teaching is an instructional activity that takes the form of a dialogue between teachers and students regarding segments of text for the purpose...

- A reciprocal pronoun is a type of pronoun which is used for one of the parti****nts of a reciprocal construction, i.e. a clause in which two parti****nts...

- In algebra, the reciprocal polynomial, or reflected polynomial p∗ or pR, of a polynomial p of degree n with coefficients from an arbitrary field, such...

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

- 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 evolutionary biology, reciprocal altruism is a behaviour whereby an organism acts in a manner that temporarily reduces its fitness while increasing...

- A reciprocal construction (abbreviated RECP) is a grammatical pattern in which each of the parti****nts occupies both the role of agent and patient with...

- Reciprocal liking, also known as reciprocity of attraction, is the act of a person feeling an attraction to someone only upon learning or becoming aware...

- Reciprocal determinism is the theory set forth by psychologist Albert Bandura which states that a person's behavior both influences and is influenced by...

- Reciprocal teaching is an instructional activity that takes the form of a dialogue between teachers and students regarding segments of text for the purpose...

- A reciprocal pronoun is a type of pronoun which is used for one of the parti****nts of a reciprocal construction, i.e. a clause in which two parti****nts...

- In algebra, the reciprocal polynomial, or reflected polynomial p∗ or pR, of a polynomial p of degree n with coefficients from an arbitrary field, such...

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