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" In any proportion the terms 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. "
Solid Geometry - Page 254
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...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 prove that a + b :b = c + d:d....
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...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 prove that a + b : b = c + d...
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Plane and Solid Geometry

Arthur Schultze - 1901 - 392 pages
...PROPOSITION VII. THEOREM 271. If four quantities are in proportion, they are in proportion by division, ie the difference of the first two terms is to the second term as the difference between the last two terms is to the fourth term. Hyp. a : 6 = c : d. To prove a— 6:6 = c — d:d....
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Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...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 of the last two terms is to the fourth term. Suppose a...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...THEOREM 270. If four 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 : b = c : d. To prove a + b : b = c + d : d....
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...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 fc By adding unity to each member,...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...THEOREM 270. If four 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....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...THEOREM 270. If four 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....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...THEOREM 270. If four 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....
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High School Algebra

Middlesex Alfred Bailey - Algebra - 1902 - 318 pages
...of two others, etc.) Hence, the principle, QED PROPORTION — PRINCIPLES PROPOSITION LXXXII. THEOREM In any proportion, the terms are in proportion by division; that is, the difference of the first two is to tIie first or second as the difference of the last two is to the corresponding term. Let a:b::c:d...
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