 In any proportion the terms 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 two terms is to their difference.  Elementary Treatise on Algebra - Page 48by Benjamin Peirce - 1865 - 276 pagesFull view - About this book
 | Webster Wells - Geometry - 1899 - 450 pages
...THEOREM. 239. In any proportion, the terms 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 two terms is to their difference. Given the proportion a : b = c : d, . (1) in which a > b and c > d. To... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...THEOREM. 239. In any proportion, the terms 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 two terms is to their difference. Given the proportion a:b = c:d, (1) in which a > b and c > d. To Prove... | |
 | George Egbert Fisher - Algebra - 1899 - 506 pages
...two proportions are said to be derived from the given proportion by Division. 10. In any proportion, the sum of the first two terms is to their difference as the sum of the last tivo terms is to their difference. Let a : b = c : d. By Art. 8, a + b:b = c + d:d; and by Art. 9,... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 512 pages
...two proportions are said to be derived from the given proportion by Division. 15. In any proportion, the sum of the first two terms is to their difference as the sum of the last two terms is to their difference. Let a : b = с : d. By Art. 13, a + b:b = c + d:d; and by Art. 14, a... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...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 is to their difference. Hyp. a:b = c:d. To prove a + b: a — b = c + d: c — d. Proof. « ±... | |
 | George Egbert Fisher - 1901 - 320 pages
...two proportions are said to be derived from the given proportion by Division. 15. In any proportion, the sum of the first two terms is to their difference as the sum of the last two terms is to their difference. Let a : b = с : d. By Art. 13, a + b:b = c + d:d; and by Art. 14, a... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 646 pages
...two proportions are said to be derived from the given proportion by Division. 10. In any proportion, the sum of the first two terms is to their difference as the sum of the last two terms is to their difference. Let a : b — с : d. By Art. 8, a + b:b = c + d:d; and by Art. 9, a... | |
 | Arthur Schultze - 1901 - 260 pages
...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 is to their difference. Hyp. a: 6 = c : d. To prove a + b: a — b = c + d: c — d. Proof. 5L+J?... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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 is to their difference. Hyp. a : b = c : d. To prove a + b: a — b = c + d: c — d. Proof.... | |
 | Arthur Schultze - 1901 - 260 pages
...four quantities are in proportion, they are in proportion by composition and division, ie the suni of the first two terms is to their difference as the sum of the last two terms is to their difference. Hyp. a : 6 = c : d. To prove a + b: a — b = c + d:c — d. Proof. -.... | |
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