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" If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. "
Elementary Algebra - Page 230
by George William Myers, George Edward Atwood - 1916 - 338 pages
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...of the extremes. II. If ad = bc, then a : b = c : d. Proof. Divide the given equals by bd. Hence, If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. Ax. 7 If the rectangle...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...of the extremes. II. If ad = be, then a : b = c : d. Proof. Divide the given equals by bd. Hence, If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. Ax. 7 If the rectangle...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...PROPOSITION II. 230. Theorem. If ad = be, then a : b = c : d. Proof. Divide the given equals by bd. Hence If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. Ax. 7 If the rectangle...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...PROPOSITION II. 230. Theorem. If ad = be, then a : b = c : d. Proof. Divide the given equals by bd. Hence If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. Ax. 7 If the rectangle...
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Grammar School Algebra

George Edward Atwood - 1900 - 264 pages
...= bc bo * bc , ad ad a = — a = — b = — c = — 428. If the product of two numbers is equal to the product of two other numbers, the factors of either product may be made the extremes, and the factors of the other product the means, of a proportion. 1. 2. 3. 4. ad = bc ad =...
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School Algebra

John Marvin Colaw - Algebra - 1903 - 444 pages
...the product of the extremes by the other mean. Have the student give numerical illustrations. 406. If the product of two numbers equals the product of two other numbers, either two may be made the extremes, and the other two the means of a proportion. For, by Art. 405,...
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Elementary Algebra

John Henry Tanner - Algebra - 1904 - 396 pages
...numbers equals the product of two others, then these four numbers form a proportion of which the two factors of either product may be made the means, and those of the other product the extremes.* For, if ad = bc, then ?=~, [Dividing by bd ie, a:b = c:d. In the same way it may be shown that, if...
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Elementary Algebra

John Henry Tanner - Algebra - 1904 - 400 pages
...product of two ottiers, then tiese four numbers form a proportion of which tlie two factors of eitJier product may be made the means, and those of the other product the extremes* For, if ad = be, then -=-, [Dividing by bd bd ie, a:b = c:d. In the same way it may be shown that,...
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The Essentials of Algebra: For Secondary Schools

Robert Judson Aley, David Andrew Rothrock - Algebra - 1904 - 344 pages
...corollary results from the above theorem by letting (7= Д =:' or 1> = &, whence B^ MD THEOREM II. If the product of two numbers equals the product of two other numbers, then either pair may be taken as extremes, and the other pair as means, of a proportion. (Inverse of...
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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

John Charles Stone, James Franklin Millis - Algebra - 1905 - 792 pages
...т= jMultiplying by bd, ad=bc) wh ich -pro ves the principle. Thus, in 2:4=6:12, 2x12 = 4x6. 196. If the product of two numbers equals the product of two other numbers, then these four numbers form a proportion in which the extremes are the factors of either product and...
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