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" If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. "
A Text-book of Geometry - Page 130
by George Albert Wentworth - 1888 - 386 pages
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...equation by ac. Then bd ac PROPOSITION VI. THEOREM. 332. If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Let a: b = c : d. To...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...Proof. From (1), ad = be. (?) .-. b:a = d:c. (?) PROP. V. THEOREM. 237. In any proportion, the terms are in proportion by COMPOSITION ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term. Given the proportion a...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...by ac. Then - = -• ac PROPOSITION VI. THEOREM. 332. If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms ,s to the second term as the sum of the last two terms is to the fourth term. Let a: b = c: d. To prove...
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Plane Geometry

George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...are in proportion, they are in proportion by composition ; that in, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Let a : bc : d. To prove that a + b:b = c + d:d, -KT ac Now - = -• bd Then...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...are in proportion, they are in proportion by composition ; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Let a : b = c : d. QED PROPOSITION VII. THEOREM. 333. If four quantities are...
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Bulletin

Education - 1900 - 612 pages
...would have taken 10 hours. Find the rate of a) the crew in still water, b) the stream. 7 Prove that if four quantities are in proportion they will be in proportion by a) composition, b) alternation. 8 In a school of 25 boys and 18 girls how many classes could be formed...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 812 pages
...the same kind, the alternation may take place. 490. THEOREM VI. — In any proportion, the terms are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Let the proportion be...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...the same kind, the alternation may take place. 490. THEOREM VI. — In any proportion, the terms are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Let the proportion be...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term. Hyp. a : 6 = c: d. To prove a + b :b = c + d:d. Proof. = -". bd f+lf + <,...
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Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...Whence, a+ b :b = cf d : d. Similarly, a+ b : a = c + d: c. Therefore, etc. PROPOSITION VII. — THEOREM. If four quantities are in proportion, they will be in proportion by division; that is, the difference of the first two terms will be to the second term as the difference...
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