 | Joseph Ray - Algebra - 1852 - 422 pages
...than the ratio of 3 to 10, we have the two fractions I, aud y, 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 bc=ad. Dividing... | |
 | Charles Davies - Algebra - 1867 - 322 pages
...Thus, if we have the proportion 3 : 6 : • 6 : 12, we shall also have 6 x 6 — 62 = 3 x 12 = 36. 155i If the product of two quantities is equal to the product of hre ether quantities, may the four be placed in a proportion \ Hew ? 157. If we have RD A : B : : C... | |
 | William Frothingham Bradbury - Algebra - 1868 - 264 pages
...product of the extremes is equal to the product of the means. Let a : b = c : d ' 1 = 3 THEOREM II. 203, If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means of a proportion.... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...mean proportional of two quantities is the square root of their product. 18. Proposition.- — When the product of two quantities is equal to the product, of two others, either two may be the extremes and the other two the means of a proportion. Let aXd=bXc represent the... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...d. Then | = J, Art. 292. Multiplying each of these equals by bd, we have ad—be. 9 300.^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.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION II. THEOREM. If the product of two quantities is equal to the product of two other quantities, two of them may be made the means, and the other two the extremes of a proportion.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...extremes equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 141 If the product of two quantities is equal to the product of two others, the factors of either product may be made the extremes, and the factors of the other the means of a proportion.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...extremes equal to the product of the means is merely clearing the equation of fractions. THEOREM II. 14, If the product of two quantities is equal to the product of two others, the factors of eiIher product may be made the extremes, and the factors of the other the means of a proportion.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...this case, the square of the mean w equal to the product of the extremes. PROPOSITION II. THEOREM. If the product of two quantities is equal to the product of two other quantit1es, two nf them may be made the means, and the other two the extremes of a proportion.... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...c : d. Then | = |,Art.292. Multiplying each of these equals by bd, we have ad=bc. 300. 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.... | |
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: 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 product of two quantities is equal to the product of two others, the four quantities... 
