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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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A School Algebra Complete

Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...Then ma :mb = nc: nd, And ma : pb = me : pd. 290. Equal Products made into a Proportion ; that is, if the product of two quantities is equal to the product of two other quantities, either two may be made the means, and the other two the extremes of a proportion....
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New School Algebra

George Albert Wentworth - 1898 - 424 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If the product of two quantities is equal to the product...either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, divide by bd. — = ;~; , bd bd ac or - = - •...
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 516 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If the product of two quantities is equal to the product...either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, divide by bd, -— = -—, od bd с b = d .'....
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 434 pages
...the two numbers that represent them when the quantities are expressed in a common unit. 338. If tbс product of two quantities is equal to the product...either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, divide by bd, — = — i н с or - = -r bd .'....
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 428 pages
...of the two numbers that represent them when the quantities are expressed in a common unit. 338. If the product of two quantities is equal to the product of two others, either two may be made th6 extremes of a proportion and the other two the means. For, if ad = be, , . . , ' . . ad bc then'...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...quantities is equal to the square root of their product. PROPOSITION II. THEOREM. 201. CONVERSELY, 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 = be. Dividing...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...Vac. Proof. From (1), b**= ac. ( 232) .-. b = Vac. PROP. II. THEOREM. 234. (Converse of Prop. I.) 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. Given ad — be....
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New School Algebra

George Albert Wentworth - 1898 - 436 pages
...quantities are expressed in a common unit. 338. If the product of two quantities is equal to the prodvet of two others, either two may be made the extremes of a proportion and the other two the means. For. if ad = be, then, divide by bd, — = — > bd bd ac or - = -•...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...b* = ac. 327 Whence, extracting the square root, & = Vac. QED PROPOSITION III. THEOREM. 329. If the product of two quantities is equal to the product...two others, either two may be made the extremes of the proportion in which the other two are made the means. Let ad = be. To prove that a:b = c:d. Divide...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...6 2 = ac. 327 Whence, extracting the square root, Z< = VCQED PROPOSITION III. THEOREM. 329. If the product of two quantities is equal to the product...two others, either two may be made the extremes of the proportion in which the other two are made the means. Let ad = be. To prove that a:b = c:d. Divide...
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