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
| 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 extremes of a proportion. Let . ....... bo... | |
| 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
...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... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...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... | |
| 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
...: 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.... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION n. 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 Guy Peck - Algebra - 1875 - 348 pages
...Conversely, if we divide both members of (2) by ca, we have, - = -; or, a : b :: c : d; hence, ac If **the product of two quantities is equal to the product of two** other quantities, the first two may be made the means, and the second two the extremes, of a proportion.... | |
| William Guy Peck - Conic sections - 1876 - 412 pages
...then have the square of the mean equal to the product of the extremes. PROPOSITION III. THEOREM. If **the product of two quantities is equal to the product of two** other quantities, the first two may be made the means and the other two the extremes of a proportion.... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...extracting the square root, b = \ac7 QED PROPOSITION III. 261. If ihe product of two quantities be **equal to the product of two others, either two may...which the other two are made the means. Let ad = be.** We are to prove a : b : : с : d. Divide both members of the given equation by b d. Then ^=-i, bd or,... | |
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