 | 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 =... | |
 | 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.... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...V- = ac. § 327 Whence, extracting the square root, b — -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
...Then b2 = ae. § 327 Whence, extracting the square root, b = 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.... | |
 | William James Milne - Geometry - 1899 - 398 pages
...proportion the product of whose extremes or means is 60 ; 72; 84; 80; 64; 144; x2y3, xyz; xyzv. Theorem. If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion of which the other two are the means. Data... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...Vac.' Proof. From (1), V = 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... | |
 | 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... | |
 | William James Milne - Geometry - 1899 - 396 pages
...proportion the product of whose extremes or means is 60 ; 72; 84; 80; 64; 144; x2y2, xyz; xyzc. Theorem. 1f the product, of two quantities is equal to the product of two others, either two may be made the extremes of a proportion of which tlie other two are the means.... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...from the equation ad = be: thus, he , ad ad ] be 486. THEOREM III.— (The converse of Theorem I.) If the product of two quantities is equal to the product of two others, the four are proportionals, the terms of either product being taken as the means, and the terms... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
..., lc n — -, b = — > с — -, (í = — deba 488. THEOREM III.— (The converse of Theorem I.) If the product of two quantities is equal to the product of two others, the four <trc proportionals, the terms of either product being taken as the means, and the... | |
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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. 
