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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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...=-jtyeducing the fractions, ad=bc. Thus 12: 8:: IS: 10, therefore 12x10=8x15. 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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 352 pages
...is, in both cases the same. And if no : b'. '.x : yy 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

Algebra - 1838 - 372 pages
...other that AxD=B*C, i „ , , BD we shall also have ~T=~r' A. O and hence, A : B : : C : D; that is, if the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion....
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 264 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 quantities are proportional,...
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Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...related to each other that we shall also have — =— ., jfi O and hence, A : B : : C : D; that is, if the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion....
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 pages
...each other that AxD=BxC, we shall also have — =— ; .AO and hence, A : B : : C : D. That is : If the product of two quantities is equal to the product of two other quantities, two of tJiem may be made the extremes, and the other two the means of a proportion....
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - Algebra - 1844 - 266 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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Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - Algebra - 1844 - 568 pages
...and each is divided by irf, ad be acc _ a that is, a : b::c : d, or c '. d:'.a '. b. Wherefore, if the product of two quantities is equal to the product of two others, the four quantities are convertible into a proportion of which the multiplicand and multiplier of either...
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - Algebra - 1845 - 382 pages
...other that A x D — B x C, we shall also have, — = — , -AO and hence, A : B : : C : D ; that is If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion....
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...becomes abd bed T=T 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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