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

Charles Davies - Algebra - 1889 - 332 pages
...equality between two equal ratios. Thus, b ^ d a c' is n proportion, expressing the fact that the ratio ol 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,...
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College Algebra

Webster Wells - Algebra - 1890 - 560 pages
...the ratio 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 - Algebra - 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, b,...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...number to the first number. It A, B be two magnitudes such that times A is equal to n times It, the ratio of A to B is equal to the ratio of n to HI. Similarly, if m times A be greater than n times /.', the ratio of A to B is greater than that...
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An Academic Algebra

James Morford Taylor - Algebra - 1893 - 358 pages
...incommensurable ratio. 214. Proportion. Four numbers, a, b, c, d, are said to be in proportion, when the ratio of a to b is equal to the ratio of с to d. The proportion is written in the form - = -, a : 6 = с : d, or a : b : : с : d, and is read...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...POLYGONS. DEFINITIONS. 227. A Proportion is a statement that two ratios are equal. The statement that the ratio of a to b is equal to the ratio of c to d, may be written in either of the forms a:b — c: d, or - = -. bd ^ Of C 39? The first and fourth terms...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...Thus A (1 each of the equalities A : B = C : D, — = —, expresses a proportion that may be read, the ratio of A to B is equal to the ratio of C to D ; or more briefly, A is to B as C is to D. 229. The first and fourth terms of a proportion are called...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...second number to the first number. If A, B be two magnitudes such that m times A is equal to n times B, the ratio of A to B is equal to the ratio of n to m. Similarly, if m times A be greater than n times B, the ratio of A to B is greater than that...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1896 - 152 pages
...Circles are circles having the same centre. 84. Proportionals are four quantities, a, b, c, d, such that the ratio of a to b is equal to the ratio of c to d; that is, such that a : b = c : d. The quantity d is called the fourth proportional to a, b, and c....
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Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1897 - 524 pages
...also expressed a : b. b SOL A Proportion is a statement that two ratios are equal. The statement that the ratio of a to b is equal to the ratio of с to d, may be written in either of the forms a : b = с : d, or - = -• bd 302. The first and fourth...
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