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Books Books 1 - 10 of 149 on To express that the ratio of A to B is equal to the ratio of C to D, we write the....  
" 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. "
Elements of Algebra: Including Strums' Theorem - Page 175
by M. Bourdon (Louis Pierre Marie) - 1847 - 368 pages
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A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ...

Thomas Malton - 1774 - 440 pages
...either greater or lefs than E to F; the Ratio of A to B is alfo greater or lefs, than E to Ft For, the Ratio of A to B is equal to the Ratio of C to Dl therefore, their Ratios are the fame, in refpect to any other. -Note. By miftake, the 7th and 8th...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 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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Of the integral calculus

Maria Gaetana Agnesi, John Hellins, Francis Maseres - Mathematics - 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, Olinthus Gregory - 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 equal,...
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A course of mathematics ...: For the use of academies, as well as ..., Volume 1

Charles Hutton, Robert Adrain - 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, Robert Adrain - 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 - 1837
...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, they...
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Elements of plane geometry according to Euclid

Andrew Bell, Robert Simson, John Playfair - 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

Charles Davies, Bourdon (Louis Pierre Marie, M.) - Algebra - 1838 - 355 pages
...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,...the ratio of A to B is equal to the ratio of C to 1), 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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