 | 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... | |
 | 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...two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 180. If we have three proportional quantities,... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | Charles Davies - Algebra - 1848 - 300 pages
...other that AxD=Bx C, we shall also have — =— ; .AL/ and hence, A : B : : C : D. That is .• If the product of two quantities is equal to the product...two other quantities, two of them may be made the extremes, and the other two the means of a proportion. Thus, if we have 2x8=4x4, we also have 2 : 4... | |
 | 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, what... | |
 | 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... | |
 | 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. Thus, suppose... | |
 | Charles Davies - Algebra - 1850 - 292 pages
...related each other that we shall also have — — ~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 tie made the extremes, and the other two the means of a proportion. Thus, if we have = 4x4, we also... | |
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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. 
