| George Roberts Perkins - Geometry - 1856 - 460 pages
...incommensurable magnitudes A and B are proportional to two other incommensurable magnitudes A' and B', or that **the ratio of A to B is equal to the ratio of** A' to B', when we obtain for each the same numerical ratio at each successive step of the approximation.... | |
| Joseph Ray - Algebra - 1857 - 408 pages
...an equality of ratios. That is, when two ratios are equal, their terms are said to be proportional. **Thus, if the ratio of a to b, is equal to the ratio of c to d,** that is, if -=-, then a, b, c, d, form a proportion, and we say that a is to ac b as c is to d. Proportion... | |
| Charles Davies - Algebra - 1860 - 332 pages
...other, compared together two and two, they are said to form a geometrical proportion. 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 -Z? as C to D. The quantities which... | |
| Charles Davies - Algebra - 1860 - 332 pages
...expression of equality between two equal ratios. Thus, b -_ d a e' is a proportion, expressing the fact that **the ratio of a to b is equal to the ratio of c to d.** This proportion may also be written thus, a : b : : c : d. In either case, the proportion is read,... | |
| Euclides - 1860 - 288 pages
...the last 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, because A, B, C are continual proportionals ; therefore the ratio of A to C, by this definition,... | |
| George Roberts Perkins - Geometry - 1860 - 470 pages
...incommensurable magnitudes A and B are proportional to two other incommensurable magnitudes A' and B', or that **the" ratio of A to B is equal to the ratio of** A' to B', when we obtain for each the same numerical ratio at each successive step of the approximation.... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...often, with the sign : : between the ratios. Thus, A : B : : X : Y, expresses a proportion, and is read, **The ratio of A to B is equal to the ratio of** X to Y ; or, A is to B as X is to Y. 127. The first and third terms of a proportion are called the... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...often, with the sign : : between the ratios. Thus, A : B : : X : Y, expresses a proportion, and is read, **The ratio of A to B is equal to the ratio of** X to Yj or, A is to B as X is to Y. 127. The first and third terms of a proportion are called the ANTECEDENTS;... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...which is read, a is to b as с is to d ; or thus, a : Ъ = с ; d, which may be read as the other, or, **the ratio of a to b is equal to the ratio of** с to d. The second method of writing proportion is recommended as the more appropriate. 331. A Couplet... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...often, with the sign : : between the ratios. Thus, A : B : : X : Y, expresses a proportion, and is read, **The ratio of A to B is equal to the ratio of** X to Y ; or, A is to B as X is to Y. 127. Tlie first and third terms of a proportion are called the... | |
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