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 - Page 1851839 - 355 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... | |
| 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... | |
| Charles Davies - Algebra - 1839 - 272 pages
...quantities, A, B, C, D, are so related to each other that AxD=BxC, we shall also have — =— ; A. L> , and hence, A : B : : C : D. That is : If the product...extremes, and the other two the means of a proportion. Thus, if we have 2x8 = 4x4, we also have 2 : 4 : : 4 : 8. 1 56. If we have three proportional quantities... | |
| Charles Davies - Algebra - 1839 - 264 pages
...B, C, D, are so related to each other that AxD=BxC, ,....., BD we shall also have — =— ; A. Lx and hence, A : B~: : C : D. That is : If the product of two quantities is equal to tJte product of two other quantities, two of them may be made the extremes, and the other two the means... | |
| Charles Davies - Algebra - 1840 - 264 pages
...quantities, A, B, C, D, are so related to each other that ta.ll.!! BD 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 otlier quantities, two of them may be made the extremes, and the other two the means of a proportion.... | |
| Charles Davies - Algebra - 1842 - 368 pages
...quantities, A, B, C, and D, are so related to each other that we shall also have — =— ., jfi O and hence, A : B : : C : D; that is, if the product...extremes, and the other two the means of a proportion. we have -=^; , BC hence, B 2 =AC; that is, the square of the middle term is equal to the product of... | |
| 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, what... | |
| 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... | |
| 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... | |
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