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" To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 248
by Thomas Malton - 1774 - 440 pages
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Electronic book - 1795 - 400 pages
...the laft definition, the ratio of A to C is compounded of the ratios of A to B, and of B to C ; but the ratio of A to B is equal to the ratio of B to C, becaufe A, B, C are continual proportionals ; therefore the ratio of A to C,by this definition,...
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Analytical Institutions in Four Books: Originally Written in ..., Volumes 1-2

Maria Gaetana Agnesi - Calculus - 1801
...proportion of three- or four terms, is thus expreffed : a . b :: b . c, when there are three terms; that is, the ratio of a to b is equal to the ratio of b to c. Alfo, a . b '.'. c . d means, that a is to b as c is to d. Laftly, the fign oo denotes infinite,...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...o^ : R : : c : D. But as p and o^are equal, by supposition, they have the same ratio to R, that is, the ratio of A to B is equal to the ratio of c to D, or A : B : : c : D. o^ ED Corol. 1. When the two means, namely, the second and third terms, are...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816
...Q : a : : c : D. But as r and q are equal, by supposition. they have the same ratio to R, that is, the ratio of A to B is equal to the ratio of c to D, or A - B : : c : D. q E. o. Carol. \ . When the two means, namely, the second and third terms, are...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822
...<l : R : : c : D. But as t and <j are equal, by supposition, they have the same ratio to R, that is, the ratio of A to B is equal to the ratio of c to D, or A : B : : c : DQEI). Carol. 1. When the two means, namely, the second and third terms, are equal,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...values that —is equal to—,, then A is said to have the same ratio AC to B, th.it C has to D, or the ratio of A to B is equal to the ratio of C 'to D. When four quantities have this relation to .each other, they are said to be in proportion. To indicate...
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The Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics ...

William Whewell - Mechanics - 1837 - 182 pages
...Ratio is the relation of quantities in respect of proportion, so that if a, b, c, d be proportional, the ratio of a to b is equal to the ratio of c to d. *LEMMA 1. If magnitudes be proportionals according to the algebraical definition of proportion,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...the last definition, the ratio of A to C is compounded of the ratios of A to B, and of B to C ; hut the ratio of A to B is equal to the ratio of B to 0, because A, B, C, are continual proportionals ; therefore the ratio of A to C, by this definition,...
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Elements of Algebra

Algebra - 1838 - 358 pages
...and D, having such values that BD then A is said to have the same ratio to B, that C has to D ; or, the ratio of A to B is equal to the ratio of C to D. When four quantities have this relation to each other, they are said to be in proportion. Hence,...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 252 pages
...other, they are said to be in proportion. Hence, proportion is an equality of ratios. To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D. The quantities which...
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