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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 Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...this case, the square of the mean is equal to the product of the extremes. PROPOSITION II. THEOREM. jy 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....
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...mean proportional of two quantities is the square root of their product. * 18. Proposition — When the product of two quantities is equal to the product of two others, either two may be the extremes and the other two the means of a proportion. Let aXd = bXc represent the equal products....
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...tJte product of the means divided by the other extreme. (2) PROPOSITION II. — Conversely : — If the product of two quantities is equal to the product of two others, then two of them may be taken for the means, and the other two for the extremes of a proportion. Let...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 422 pages
...the ratio of 3 to 10, we have the two fractions I, aud y, ART. 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 bc=ad. Dividing...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common ..., Book 1

Joseph Ray - Algebra - 1866 - 252 pages
...2 : 5 is a false proportion, since 3X5 is not equal to 8x2. 245. 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 6c=ad. Dividing...
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 250 pages
...2 : 5 is a false proportion, since 3x5 is not equal to 8x2. 245. Proposition II. — Conversely, If the product of two quantities is equal to the product of two others, two of them may le made the means, and the other two the extremes of a proportion. Let be— ad. Dividing...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 444 pages
...mean proportional of two quantities is the square root of their product. 18. Proposition.- — When the product of two quantities is equal to the product, of two others, either two may be the extremes and the other two the means of a proportion. Let aXd=bXc represent the equal products....
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 270 pages
...d ac ie r = 3 bd Clearing of fractions, ad = bc P RATIO AND PROPORTION. 209 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...
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...Then | = J, Art. 292. Multiplying each of these equals by bd, we have ad—be. 9 300.^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....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 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',...
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