 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 254by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...c. Therefore, etc. PROPOSITION VI. — THEOREM. If four quantities are in proportion, they will be in proportion by composition; that is, the sum of the first two terms will be to the second term as the sum of the last two terms is to the fourth term. Suppose a : b =... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...of x and y. Ex. 524. If x - y : y = 2 : 3, find the ratio of x and y. PROPOSITION VIII. THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference as the sum of the last two terms... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...of x and y. Ex. 524. If x - y : y = 2 : 3, find the ratio of x and y. PROPOSITION VIII. THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference as the sum of the last two terms... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...Transform the proposition, m : x = p : q, so that x becomes the fourth term. PROPOSITION VI. 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... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...—, arranged by composition and division, 0 Ci becomes a + b _c + d PROPOSITION VII. THEOREM 431. If four quantities are in proportion, they are in proportion by composition and division. H. a — bc — d Proof. [Analyze and solve.] 432. EXERCISE. If 2 = -, bd prove ^l«... | |
 | Arthur Schultze - 1901 - 392 pages
...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... | |
 | Arthur Schultze - 1901 - 260 pages
...Transform the proposition, m : x = p : q, so that x becomes the fourth term. PROPOSITION VI. 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... | |
 | Middlesex Alfred Bailey - Algebra - 1902 - 336 pages
...as an equality of two fractions. See p. 214. PROPOSITION LXXXI. THEOREM In any proportion, the terms are in proportion by composition ; that is, the sum of the first two is to the first or second as the sum of the last two is to the corresponding term. Let a : b : : с... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...333. 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... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...obtain the first conclusion subtract 1 from each ratio. SUG. 2. See Sug. 2, Prop. VI. 151. Prop. VIII. If four quantities are in proportion, they are in proportion by composition and division. If a:b = c:d, then a + b : a - b = c + d: c - d. SUG. Divide result of Prop. VI by that... | |
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