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" 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 128
by George Albert Wentworth - 1888 - 386 pages
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Elements of Plane and Solid Geometry

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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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...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...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 322 pages
...By Art. 363, | = * Clearing of fractions, at = 6s. Again, 9:6:: 6-4, and 4 xg = 62. THEOREM III. If the product of two quantities is equal to the product of two others, the four quantities are proportional j the factors of either product being taken for the extremes,...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...we have, £ = £, or, A:B = C:DL, £ = 5, or, A:C=B:DIL, ~ = ~, or, B : A = D : C III. CA Hence, if the product of two quantities is equal to the product of two other quantities, one pair of factors may be made the extremes, and the other pair the means, of a...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...equal to the product of the meaiis ia merely clearing the equation of fractions. THEOREM II. 14i 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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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 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...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 6 d. Then ļ_. bd or,...
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Elements of Algebra

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 be made the extremes of a proportion and the other two the means. For, if ad = be, by dividing by bd, 2_ = _£ od ba ac PS' 343. The equation...
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The Inductive Algebra: Embracing a Complete Course for Schools and Academies

William James Milne - Algebra - 1881 - 360 pages
...What does ad, the first member of the equation, form in the proportion? What be? PRINCIPLE 3. — If the product of two quantities is equal to the product of two otlier quantities, two of them may be made the extremes, and the other two the means, of a proportion....
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Elements of Geometry

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...which the other two are made the means. Let ad = be. We are to prove a : b : : c : d. .. , Divide both members of the given equation by b d. Then or. ac...
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The national encyclopędia. Libr. ed, Volume 11

National cyclopaedia - 1884 - 670 pages
...term) can be obtained as easily ; for be . ad , ad a=— ,6 = — , and c = — . dcb Conversely, if the product of two quantities is equal to the product of two others, these four are proportionals ; example, 4 times 6 = 3 times 8 ; whence we see that 3 is to 4 as 6 is...
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