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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.com › Word [ratio]

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ratio

RA'TIO, n. ra'sho. [L. from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like L. suppono; and setting gives the sense of a fixed rate or rule. See Reason.]

Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.

The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2, or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio, which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 6 is 4.

Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line cannot be compared with a superficies, and hence between a line and a superficies there can be no ratio.


Evolution (or devolution) of this word [ratio]

1828 Webster1844 Webster1913 Webster

RA'TIO, n. ra'sho. [L. from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like L. suppono; and setting gives the sense of a fixed rate or rule. See Reason.]

Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.

The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2, or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio, which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 6 is 4.

Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line cannot be compared with a superficies, and hence between a line and a superficies there can be no ratio.

RA'TIO, n. [ra'sho; L. from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like L. suppono; and setting gives the sense of a fixed rate or rule. See Reason.]

Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another without the intervention of a third. – Encyc. The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2 or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio, which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 8 is 4. Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line can not be compared with a superficies, and hence between a line and a superficies there can be no ratio. – Encyc.


Ra"ti*o
  1. The relation which one quantity or magnitude has to another of the same kind. It is expressed by the quotient of the division of the first by the second; thus, the ratio of 3 to 6 is expressed by ***frac36] or ½ of a to b by a/b; or (less commonly) the second term is made the dividend; as, a:b = b/a.

    * Some writers consider ratio as the quotient itself, making ratio equivalent to a number.

    The term ratio is also sometimes applied to the difference of two quantities as well as to their quotient, in which case the former is called arithmetical ratio, the latter, geometrical ratio. The name ratio is sometimes given to the rule of three in arithmetic. See under Rule.

  2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress.

    Compound ratio, Duplicate ratio, Inverse ratio, etc. See under Compound, Duplicate, etc. -- Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one.

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Ratio

RA'TIO, noun ra'sho. [Latin from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like Latin suppono; and setting gives the sense of a fixed rate or rule. See Reason.]

Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.

The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2, or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 6 is 4.

Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line cannot be compared with a superficies, and hence between a line and a superficies there can be no ratio

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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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miscreate

MISCREA'TE

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