 | 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 of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...by bd. Hence If the product of two numAx. 7 bers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion. If the rectangle of two lines equals the rectangle of two other lines, either two may be made the means... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...proportion. Ax. 7 If the rectangle of two lines equals the rectangle of two other lines, either two may be made the means and the other two the extremes of a proportion. PROPOSITION III. 231. Theorem. If a : b = c : d, then (1) a : c = b : d, (2) d : b = c : a, and (3)... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...proportion. Ax. 7 If the rectangle of two lines equals the rectangle of two other lines, either two may be made the means and the other two the extremes of a proportion. PROPOSITION III. 231. Theorem. If a : b = c : d, then (1) a : c = b : d, (2) d : b = c : a, and (3)... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...equal to the square root of their product, Extracting the square root of both members, b = Vac. 94. If the product of two quantities is equal to the product of two other quantities, the factors of either product may be made the means, and the other two the extremes, of a proportion.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...the product of two equals the rectangle of two other numbers, either two may other lines, either two may be made the means and the other two the extremes of a be made the means and the other two the extremes of a proportion. proportion. PROPOSITION III. 231.... | |
 | 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 of two others, either two may be made the extremes of the proportion in which the other two are made the means.... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...6 2 = ac. § 327 Whence, extracting the square root, Z< = V«CQED PROPOSITION III. THEOREM. 329. If the product of two quantities is equal to the product of two others, either two may be made the extremes of the proportion in which the other two are made the means.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...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... | |
 | Wooster Woodruff Beman, David Eugene Smith - Algebra (Elements) - 1900 - 460 pages
...6 334. Theorem. If the product of two abstract numbers equals the product of two others, either two may be made the means and the other two the extremes of a proportion. Proof. 1. If ad = bc, then, by dividing by bd, 2- l b Similarly, - = - , etc. a с \ 335. Theorem.... | |
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If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion. 
