| Joseph Ray - Algebra - 1866 - 250 pages
...: 2 : 5 is a false proportion, since 3x5 is not equal to 8x2. 245. Proposition II. — Conversely, **If the product of two quantities is equal to the product of two others,** two of them may le made the means, and the other two the extremes of a proportion. Let be— ad. Dividing... | |
| Joseph Ray - Algebra - 1852 - 420 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... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...: 2 : 5 is a false proportion, since 3X5 is not equal to 8x2. 245. 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 6c=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...factors of the other the means of a proportion. Let ad** = lc Dividing by bd, j- = ie a : b = c : d THEOREM III. 204 t If four quantities are in proportion,... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...c : d ac ie r = 3 bd Clearing of fractions, ad = bc P RATIO AND PROPORTION. 209 THEOREM II. 203 • **If the product of two quantities is equal to the product...factors of the other the means of a proportion. Let** ad=bc Dividing by bd, ^ = ^ ie a : b = c : d THEOREM III. 204, If four quantities are in proportion,... | |
| Eli Todd Tappan - Geometry - 1868 - 436 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 - 268 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. Let... | |
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