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" If the product of two quantities is equal to the product of two others, the... "
An Elementary Geometry - Page 27
by William Frothingham Bradbury - 1872 - 110 pages
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The Essentials of Geometry

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 = bc. (1)...
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Plane and Solid Geometry

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. Let...
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Plane and Solid Geometry

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. Data : ad...
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The Elements of Plane Geometry

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,...
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Grammar School Algebra

George Edward Atwood - 1900 - 276 pages
...— 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 = bc ad = bc ad=bc ad_bc_ ad_bc ad_bc ad_bc...
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College Algebra

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 of the...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 816 pages
..., lc n — -, b = — > с — -, ( = — 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 terms of the...
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High School Algebra

Middlesex Alfred Bailey - Algebra - 1902 - 318 pages
...of the means.) ae x dh = bf x eg (We multiply the equations member by member.) ae : bf : : cg : dh (If the product of two quantities is equal to the product of two others, etc.) Hence, the principle, QED PROPOSITION LXXXVII. THEOREM Equimultiples of two quantities have the...
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Mathematics

American School (Chicago, Ill.) - Engineering - 1903 - 428 pages
...the means. Let a : b = с : d ,, , . а с that is T =3 -, о а Clearing of fractions, ad = be П. 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 ТЧ-...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...b = b : q. Then b2 = ac. 327 Whence, extracting the square root, 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 tiuo are made the means. Let...
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