 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
 | 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... | |
 | 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.... | |
 | 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
...extremes. 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
...we 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,... | |
 | William Frothingham Bradbury - Algebra - 1877 - 302 pages
...product of the extremes is equal to the product of the means. Let a : 6 = c : d i=5 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 - Conic sections - 1877 - 458 pages
...this proposition, A x C=B x B, which is equal to B'. PROPOSITION ii. THEOREM. (Converse of Prop. I.) If the product of two quantities is equal to the product of two others, the one pair may be made the extremes, and the other t/ie means of a proportion. Thus, suppose we have... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...means). Whence, extracting the square root, PROPOSITION III. 261. lf the product of two quantities be equal to the product of two others, either two may be made the extremes nf a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : с... | |
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