 If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, dividing by bd, ad_ be bd~bd' ac or j- — -  A School Algebra - Page 295by George Albert Wentworth - 1895 - 362 pagesFull view - About this book
 | 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 be made the extremes of a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : с : d. Divide both... | |
 | 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... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...if ab :: c: d, then f = ^ 6 a By multiplying by bd, ad = bc. 342. If the product of two numbers be equal to the product of two others, either two may...proportion and the other two the means. For, if ad = be, by dividing by bd, 2_ = _£ od ba ac PS' 343. The equation ad = be gives be , ad a = -r I 0 = — ;... | |
 | George Albert Wentworth - 1881 - 266 pages
...extracting the square root, b = V/ac. QED PROPOSITION III. 261. If the product of two quantities be 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. Let ad = be. We are to prove a : b : : с : d. Divide both... | |
 | George Albert Wentworth - Algebra - 1881 - 406 pages
...multiplying by bd, ad = be. 342. If the product of two num bcrs be equal to the product of two others, cither two may be made the extremes of a proportion and the other two the means. For, if ad=bc, by dividing by bd, 2_ = -1, od oa rl 343. The equation ad = be gives lie . , ad . a'~~d' ' ~... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...the square root, b = \l ac. QE o. PROPOSITION III. 261. If the product of two quantities be equal lo the product of two others, either two may be made the extremes of a proportion in which the other two are made the means. Let ad = be. We are to prove a : b : : c : d. .. , Divide... | |
 | George Albert Wentworth - 1883 - 536 pages
...means. For, if a : b : : с : d, By multiplying by bd. ad = be. 342. If the product of two numbers be equal to the product of two others, either two may...proportion and the other two the means. For, if ad = 6e, by dividing by bd, 2- = -£-, od ba or 2-56 d' 343. The equation ad = be gives be , ad a = -j\... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...a : b : : с : d, then а.1 od By multiplying by bd, ad= be. 287. If the product of two numbers be equal to the product of two others, either two may...proportion, and the other two the means. For, if ad = be, by dividing by bd, ^- = —, bd bd M 288. The equation ad = bc gives bс , ad a = -j ; ° — — ;... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...proportional (II., 36) between two 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 ah 9 = a\ then, dividing by bb... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...proportional (II., 36) between tico numbers is equal to the square root of their product. 8. Conversely, if the product of two numbers is equal to the product of two others, either tico may be made the extremes, and the other two the means, of a proportion. For, if we have given... | |
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