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" If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. "
A Text-book of Geometry - Page 128
by George Albert Wentworth - 1888 - 386 pages
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...abd bed ~T ~ Т or ad = be. Thus, if 3 : 4 : : 9 : 12, then . 3 x 12 = 4 x 9. (213.) Conversely, if the product of two quantities is equal to the product of two others, the first two quantities may be made the extremes, and the other 'two the means of a proportion. Let...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1847 - 358 pages
...means is, in both cases the same. And if na: b :: x: y, then a: b:: x : ny. 375. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, when they are so arranged, that those on one side of the...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...in both cases is the same. So if na : b : : x : y, then a : b : : x : ny. 339. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion if they are so arranged, that those on one side of the equation...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1848 - 302 pages
...Thus, if we have the proportion 3 : 6 : : 6 : 12, we shall also have 6x6=62=3xl2=36. QUEST. — 155. If the product of two quantities is equal to the product of two other quantities, may the four be placed in a proportion ? How ? — 156. If three quantiiies are proportional,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...: : B : C ; then, by the proposition, I BOOK H. PROPOSITION ii. THEOREM (Converse of Prop. /.). If the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion....
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An Elementary Treatise on Algebra: Designed as First Lessons in that Science

Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...term. This is a part of the well known rule of three, in Arithmetic. PROPOSITION II. Conversely. If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion. Let...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...equal to 8X2, we infer that the proportion is false. ART. 345. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad. Dividing...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...2X8, we infer that 2, 3, 5, and 8, are not in proportion. ART. 268. PROPOSITION II. Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let be— ad. Dividing...
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A treatise on the elements of algebra, by G. Ainsworth and J. Yeats

G. Ainsworth - 1854 - 216 pages
...then -=-, and multiplying both sides by ac, —= — , Л С ' <to . • . bc=ad. And conversely, if the product of two quantities is equal to the product of two other quantities, the four are proportional. For (by hyp.) ad=bc, and dividing both sides by bd, we...
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The Popular Educator, Volume 6

1855 - 424 pages
...in both cases is the same. So, if na : Ь : : x : y, then a : Ь : : x : ny. On the other hand, if the product of two quantities is equal to the product of two others, the four quantities will form a proportion, if they are so arranged that those on one side of the equation...
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