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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 242
by Thomas Malton - 1774 - 440 pages
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Principles of Arithmetic

Homersham Cox (the younger) - 1885 - 248 pages
...to the number which expresses A in terms of C, or in other words the ratio of B to C multiplied by the ratio of A to B is equal to the ratio of A to C. In order to establish the properties of multiplication we require the two following theorems....
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 372 pages
...: b, a is the antecedent and b the consequent. 289. A Proportion is an equality of ratios. Thus, if the ratio of a to b is equal to the ratio of с to d, they form a proportion, which ma\' be written in either of the forms : а с a:b — с: d,...
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A Complete Course in Algebra for Academies and High Schools

Webster Wells - Algebra - 1885 - 370 pages
...: 6, a is the antecedent and b the consequent. 289. A Proportion is an equality of ratios. Thus, if the ratio of a to b is equal to the ratio of с to d, they form a proportion, which may be written in either of the forms : / j а с , , a : b...
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Algebra: An Elementary Text Book for the Higher Classes of Secondary ..., Part 1

George Chrystal - Algebra - 1886 - 572 pages
...of the same kind as A and B), whose ratio is c:d, then A, B, C, D are said to be proportional when the ratio of A to B is equal to the ratio of C to D, that is, when a:b = c\d. We may speak of the ratio A : B, of the concrete magnitudes themselves,...
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Algebra for Beginners

Isaac Todhunter - Algebra - 1887 - 378 pages
...for shortness we may say that the ratio of a to b is equal to y or is r . 349. Hence we may say that the ratio of a to b is equal to the ratio of c to d, when r = 3 • bd 350. If the terms of a ratio be multiplied or divided by t/ie same quantity the...
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Shorter Course in Algebra

George Albert Wentworth - Algebra - 1887 - 274 pages
...in proportion. 285. If the ratios a : b and c : d form a proportion, the proportion is written (read the ratio of a to b is equal to the ratio of c to cZ) , or a:b::c:d (read a is to b in the same ratio as c is to d). The first and last terms, a and...
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Shorter Course in Algebra

George Albert Wentworth - 1888 - 268 pages
...If the ratios a : Ъ and с : d form a proportion, the proportion is written a : Ъ = с : d (read the ratio of a to b is equal to the ratio of с to d) , or a:b::c:d (read я is to 6 in the same ratio as с is to d). The first and last terms,...
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A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

Webster Wells - Algebra - 1889 - 584 pages
...a to b is - ; and it is also expressed a : b. 305. A Proportion is an equality of ratios. Thus, if the ratio of a to b is equal to the ratio of с to d, they form a proportion, which may be written in either of the forms : a: & = c:d, • - =...
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College Algebra

Webster Wells - Algebra - 1890 - 560 pages
...of a to b is -; and it is also expressed a: b. 377. A Proportion is an equality of ratios. Thus, if the ratio of a to b is equal to the ratio of c to d, they form a proportion, which may be written in either of the forms : a:b = c:d, - = -, or a : b...
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Elementary Algebra

Walter William Rouse Ball - Mathematics - 1890 - 512 pages
...proportion is equal to the product of the means. For if a, b, c, d be in proportion, then, by definition, the ratio of a to b is equal to the ratio of c to d. That is, a _ c b~d" Multiply each side by bd, .'. ad = be. 300. Conversely, if four quantities a,...
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