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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. For, if ad = be, then, divide by bd, — = r~,> /n"- bd a- c or - = -• .'. a : b = с : d.
New School Algebra - Page 308
by George Albert Wentworth - 1898

## 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...

## 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...

## 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....

## First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 272 pages
...each other that AxD=BxC, we shall also have — =— ; A. L> , 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....

## 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....

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

Charles Davies - Algebra - 1842 - 284 pages
...Thus, if we have the proportion 3 : 6 : : 6 : 12, t we shall also have = 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 1 How ? — 156. If three quantities are proportional,...

## An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1842 - 326 pages
...Suppose we have ad = bc. Dividing both members by 6 and d, we have r = -, or a : b = c : d. Hence, oa If the product of two quantities is equal to the product of ttca other quantities, the two factors of either product may be made the means, and the two factors...

## Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - Algebra - 1844 - 568 pages
...products, 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...