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. New School Algebra - Page 308by George Albert Wentworth - 1898 - 407 pagesFull view - About this book
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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.... | |
| 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,... | |
| 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... | |
| 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... | |
| James Bates Thomson - Algebra - 1844 - 272 pages
...the means 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... | |
| 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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