 If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means.  A Text-book of Geometry - Page 132by George Albert Wentworth - 1892 - 437 pagesFull view - About this book
 | Joseph Ray - Algebra - 1866 - 420 pages
...: 8, is not a true proportion, since 3X5 is not equal to 2x8. 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 extreme* of a proportion. Let ........ bc... | |
 | 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... | |
 | 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 equal products.... | |
 | 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... | |
 | 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 Chauvenet - Geometry - 1871 - 380 pages
...numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb',... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...numbers is equal to the square root of their product. 6. Conversely, if the product of two numbers is equal to the product of two others, either two may be made the extremes, and the other two the means, of a proportion. For, if we have given ab' = a'b, then, dividing by bb',... | |
 | 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... | |
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