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" 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- — - "
Elementary Algebra - Page 321
by George Albert Wentworth - 1906 - 421 pages
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The Popular Educator, Volumes 1-2; Volume 12

Geography - 1867 - 964 pages
...9. Sow, 12 and 3 are the extremes, and 4 and 9 are the means, oí tie given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since — 8 x 3 = « x 4 or,...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...the means is equal to the product of the extremes ; as, 6 : 4 : : 15 : 10, hence 10.6=15.4. Prop. 2. If the product of two numbers is equal to the product of two other numbers, the four may be arranged in a proportion; as, 8.3=12.2, hence 8: 12: : 2 : 3. Scholium....
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Bourdon's Arithmetic: Containing a Discussion of the Theory of Numbers

Bourdon (M., Louis Pierre Marie) - Arithmetic - 1858 - 262 pages
...multiplication, they must have been equal at first. Hence the property is proved. 161. Reciprocally. — If the product of two numbers is equal to the product of two other numbers, these four numbers form a proportion of which either pair of factors will constitute...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...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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Arithmetic for school and college use. With a chapter on the metric system

Thomas Percy Hudson - Arithmetic - 1866 - 268 pages
...45 ' Now, 12 and 3 are the extremes, and 4 and 9 are the means, of the given proportion. Conversely, if the product of two numbers is equal to the product of any other two numbers, the four numbers will form a proportion. Thus, since 8X3 = 6X4, 8, 4, 6, 3 form...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 pages
...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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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...mean proportional 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 ab' = a'b, then, dividing by bb',...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...mean proportional 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 ab' = a'b, then, dividing by bb',...
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An Elementary Algebra

Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...Theorem II. 332. If the product of two quantities be equal to the product of two other quantities, either two may be made the extremes of a proportion, and the other two the means. Let ad = bc; Dividing by bd, — = — ; bd Theorem III. 333. In a proportion, either extreme is equal...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...mark the fourth term by x — 12 : 108 : : n : x. And from what has already been said — («). When the product of two numbers is equal to the product of two othtrs they form a proportion in four different ways. Thus the four numbers (5, 54, 6, 45) form a proportion...
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