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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.
Manual of Geometry and Conic Sections: With Applications to Trigonometry and ... - Page 70
by William Guy Peck - 1876 - 366 pages

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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....

## Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

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...

## New Elementary Algebra: Embracing the First Principles of the Science

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...

## University Algebra : Embracing a Logical Development of the Science with ...

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,...

## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

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,...

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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....

## Elements of Geometry and Trigonometry: With Practical Applications

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...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

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;...