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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. "
Solid Geometry - Page 254
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 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 tiie third term. Given the proportion a : b = c :...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...Therefore (by 201), ab: a = c - d: c. Similarly, a — b :b = c — d: d. QED PROPOSITION VII. 206. If four quantities are in proportion, they are in proportion by Composition and Division; that is, the sum of the first and second is to their difference as the sum of the third...
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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 : 6 = c :...
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Plane Geometry

George Albert Wentworth - Geometry, Plane - 1899 - 276 pages
...327 • Divide each member of the equation by ac. Then ac Or b:a = d:c. PROPOSITION VI. THEOREM. 332. If four quantities 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...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...simplifying as in § 97, a - b:b::c - d: d. The student should prove that a — b : a : : c - d : c. 99. If four quantities are in proportion, they are in proportion by composition and division. Let the proportion be a : 6 : : c : d. a+b c+d Then by § 97, bd a — bc — d ' 6 d...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...Then bd that is, —7— —-j— bd Or a — b : b — c — d : d. PROPOSITION VIII. THEOREM. 334. If four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first two terms is to their difference as the sum of the last...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...5-1; od a — bc— d that is, -y- = — Or a — b .b = c — d:d. PROPOSITION VIII. THEOREM. 334. If four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first two terms is to their difference as the sum of the last...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...If four quantities are in proportion, they are in proportion by division ; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth term. 335. In a series of equal ratios, the sum of...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...If four quantities are in proportion, they are in proportion by division ; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth term. Let a : b = c : d. To prove that a — b :b...
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Grammar School Algebra

George Edward Atwood - 1900 - 276 pages
...the third as the second is to the fourth. If a: b = c: d ad = bc .: a:c = b:d 431. If four numbers are in proportion, they are in proportion by composition; that is, the sum of the terms of the first ratio is to either term as the sum of the terms of the second ratio is to the corresponding...
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