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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