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Tuesday - December 18, 2018

In my view, the Christian religion is the most important and one of the first things in which all children, under a free government ought to be instructed... No truth is more evident to my mind than that the Christian religion must be the basis of any government intended to secure the rights and privileges of a free people.
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1828 Noah Webster Dictionary
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1828.mshaffer.comWord [reciprocal]

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reciprocal

RECIP'ROCAL, a. [L. reciprocus.]

1. Acting in vicissitude or return; alternate.

Corruption is reciprocal to generation.

2. Mutual; done by each to the other; as reciprocal love; reciprocal benefits or favors; reciprocal duties; reciprocal aid.

3. Mutually interchangeable.

These two rules will render a definition reciprocal with the thing defined.

Reciprocal terms, in logic, those terms that have the same signification, and consequently are convertible and may be used for each other.

Reciprocal quantities, in mathematics, are those which, multiplied together, produce unity.

Reciprocal figures, in geometry, are those which have the antecedents and consequents of the same ratio in both figures.

Reciprocal ratio, is the ratio between the reciprocals of two quantities; as, the reciprocal ratio of 4 to 9, is that of 1/4 to 1/9.

RECIP'ROCAL, n. The reciprocal of any quantity, is unity divided by that quantity. Thus the reciprocal of 4 is 1/4.




Evolution (or devolution) of this word [reciprocal]

1828 Webster1844 Webster1913 Webster

RECIP'ROCAL, a. [L. reciprocus.]

1. Acting in vicissitude or return; alternate.

Corruption is reciprocal to generation.

2. Mutual; done by each to the other; as reciprocal love; reciprocal benefits or favors; reciprocal duties; reciprocal aid.

3. Mutually interchangeable.

These two rules will render a definition reciprocal with the thing defined.

Reciprocal terms, in logic, those terms that have the same signification, and consequently are convertible and may be used for each other.

Reciprocal quantities, in mathematics, are those which, multiplied together, produce unity.

Reciprocal figures, in geometry, are those which have the antecedents and consequents of the same ratio in both figures.

Reciprocal ratio, is the ratio between the reciprocals of two quantities; as, the reciprocal ratio of 4 to 9, is that of 1/4 to 1/9.

RECIP'ROCAL, n. The reciprocal of any quantity, is unity divided by that quantity. Thus the reciprocal of 4 is 1/4.


RE-CIP'RO-CAL, a. [L. reciprocus; Sp. and It. reciproco; Fr. reciproque.]

  1. Acting in vicissitude or return; alternate. Corruption is reciprocal to generation. – Bacon.
  2. Mutual; done by each to the other; as, reciprocal love; reciprocal benefits or favors; reciprocal duties; reciprocal aid.
  3. Mutually interchangeable. These two rules will render a definition reciprocal with the thing defined. – Watts. Reciprocal terms, in logic, those terms that have the same signification, and consequently are convertible and may be used for each other. – Encyc. Reciprocal quantities in mathematics, are those which, multiplied together, produce unity. – Encyc. Reciprocal figures, in geometry, are those which have the antecedents and consequents of the same ratio in both figures. – Encyc. Reciprocal ratio, is the ratio between the reciprocals of two quantities; as, the reciprocal ratio of 4 to 9, is that of 1/4 to 1/9.

RE-CIP'RO-CAL, n.

The reciprocal of any quantity, is unit; divided by that quantity. Thus the reciprocal of 4 is 1/4.


Re*cip"ro*cal
  1. Recurring in vicissitude; alternate.
  2. That which is reciprocal to another thing.

    Corruption is a reciprocal to generation. Bacon.

  3. 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.

  4. The quotient arising from dividing unity by any quantity] thus, ¼ 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.
  5. Mutually interchangeable.

    These two rules will render a definition reciprocal with the thing defined. I. Watts.

  6. Reflexive; -- applied to pronouns and verbs, but sometimes limited to such pronouns as express mutual action.
  7. 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 ¼ to ***frac19]. -- 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, 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.

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Reciprocal

RECIP'ROCAL, adjective [Latin reciprocus.]

1. Acting in vicissitude or return; alternate.

Corruption is reciprocal to generation.

2. Mutual; done by each to the other; as reciprocal love; reciprocal benefits or favors; reciprocal duties; reciprocal aid.

3. Mutually interchangeable.

These two rules will render a definition reciprocal with the thing defined.

Reciprocal terms, in logic, those terms that have the same signification, and consequently are convertible and may be used for each other.

Reciprocal quantities, in mathematics, are those which, multiplied together, produce unity.

Reciprocal figures, in geometry, are those which have the antecedents and consequents of the same ratio in both figures.

Reciprocal ratio, is the ratio between the reciprocals of two quantities; as, the reciprocal ratio of 4 to 9, is that of 1/4 to 1/9.

RECIP'ROCAL, noun The reciprocal of any quantity, is unity divided by that quantity. Thus the reciprocal of 4 is 1/4.

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Word of the Day

importance

IMPORT'ANCE, n.

1. Weight; consequence; a bearing on some interest; that quality of any thing by which it may affect a measure, interest or result. The education of youth is of great importance to a free government. A religious education is of infinite importance to every human being.

2. Weight or consequence in the scale of being.

Thy own importance know.

Nor bound thy narrow views to things below.

3. Weight or consequence in self-estimation.

He believes himself a man of importance.

4. Thing implied; matter; subject; importunity. [In these senses, obsolete.]

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