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
| Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...in proportion, they are in proportion by division. SECTION II.— EQUAL PRODUCTS. 297. PROP. VI. If **the product of two quantities is equal to the product of two** other quantities, the two quantities that form either product may be made the extremes, and the other... | |
| George W. Lilley - Algebra - 1892 - 420 pages
...(l С Divide by bd, 6 = 5 ' By definition, a : b :: с : d. Hence, II. 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 tJie other two the means. A Mean Proportional is a number used for both means of a proportion ;... | |
| William Chauvenet - 1893 - 340 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',... | |
| George P. Lilley - Algebra - 1894 - 522 pages
...Divide by Id, т = ~¡ • By definition, a : Ь ;: с : d. Hence, II. 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. A Mean Proportional is a number used for both means of a proportion ;... | |
| John Macnie - Geometry - 1895 - 390 pages
...show that ZAOC: Z ABC = 7:2. PROPOSITION III. THEOREM. 240. Conversely, 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 its means. Given: ad = bc; To Prove : a:b = c:d. Since ad = bc, (Hyp.) ... dividing... | |
| George Albert Wentworth - Mathematics - 1896 - 68 pages
...296. A mean proportional between two quantities is equal to the square root of their product. 297. If **the product of two quantities is equal to the product...proportion in which the other two are made the means.** 298. If four quantities of the same kind are in proportion, they will be in proportion by alternation;... | |
| George D. Pettee - Geometry, Modern - 1896 - 272 pages
...equations, such as squaring the equation, are applicable to proportions. PROPOSITION II 188. Theorem. //' **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 product the means... | |
| George Albert Wentworth - Algebra - 1896 - 302 pages
...a:b::c:d, Î-Î By multiplying by bd, ad = be. 287. If the product of two numbers be equal to the prorfwt **of two others, either two may be made the extremes of a proportion,** and the other two the means. For, if ad = be, by dividing by bd, ^=*£, bd bd И 288, The equation... | |
| Webster Wells - Algebra - 1897 - 422 pages
...mean is equal to the product of the extremes divided by the other mean. 309. (Converse of § 306.) If **the product of two quantities is equal to the product of two others,** one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = bс. Dividing... | |
| Webster Wells - Algebra - 1897 - 426 pages
...mean is equal to the product of the extremes divided by the other mean. 309. (Converse of § 306.) If **the product of two quantities is equal to the product of two others,** one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = bc. Whence... | |
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