 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 128by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
 | 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. Let... | |
 | 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 of the... | |
 | 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 of the equation... | |
 | 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,... | |
 | 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.... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...term. This is a part of the well known rule of three, in Arithmetic. PROPOSITION II. Conversely. If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion. Let... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...equal to 8X2, we infer that the proportion is false. ART. 345. — PROPOSITION II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad. Dividing... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...2X8, we infer that 2, 3, 5, and 8, are not in proportion. ART. 268. PROPOSITION II. Conversely, If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let be— ad. Dividing... | |
 | G. Ainsworth - 1854 - 216 pages
...then -=-, and multiplying both sides by ac, —= — , Л С ' <to . • . bc=ad. And conversely, if the product of two quantities is equal to the product of two other quantities, the four are proportional. For (by hyp.) ad=bc, and dividing both sides by bd, we... | |
 | 1855 - 424 pages
...in both cases is the same. So, if na : Ь : : x : y, then a : Ь : : x : ny. 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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