 | Elias Loomis - 1846 - 376 σελίδες
...becomes 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 ad... | |
 | Jeremiah Day - 1847 - 358 σελίδες
...then a : b :: mx : y. For the product of the 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...side of the equation shall constitute the means, and (hose on the other side, the extremes. If my=nh, then m : n:: h : y, that is, 2==_ ny For by dividing... | |
 | Jeremiah Day, James Bates Thomson - 1848 - 264 σελίδες
...product of 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...others, the four quantities will form a proportion if they are so arranged, that those on one side of the equation shall constitute the means, and those... | |
 | Joseph Ray - 1848 - 252 σελίδες
...equul to 8X2, we infer that the proportion isfalie. .\,.t-'2l't. — 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... | |
 | Charles Davies - 1848 - 300 σελίδες
...Thus, if we have the proportion 3 : 6 : : 6 : 12, we shall also have 6x6=6a=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 ? — 150. If three quartiues are proportional,... | |
 | Elias Loomis - 1849 - 252 σελίδες
...: B : : 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 - 1850 - 256 σελίδες
...first 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 - 1848 - 250 σελίδες
...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 - 1852 - 408 σελίδες
...to 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 σελίδες
...d, 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... | |
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Conversely, 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. 
