 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.  Algebra for Secondary Schools - Page 315by Webster Wells - 1906 - 462 pagesFull view - About this book
 | Webster Wells - Algebra - 1897 - 426 pages
...— d) == c(a — b). Whence, a — b: a = c — d: c. Similarly, a — b : b = с — d : d. 314. In any proportion, the terms are in proportion by...sum of the last two terms is to their difference. Let the proportion be a : b = с : d. Then by § 312, ÍL+Ь = £±A m а с And by §313, a--b = c_-d,... | |
 | Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...„, .. о — б с — d That is, — - — = — — » 6 d Or, a — b :b — c — d:d. 285. V. Composition and Division ; that is, the sum of the...sum of the last two terms is to their difference. Given, a : b = с : d. By composition (Art. 283), d By division (Art. 284), - = =- . . . . . (2) о... | |
 | Webster Wells - Algebra - 1897 - 386 pages
...a(c — d) = c(a — b). Whence, a — b: a = c — d: c. Similarly, a — b : b = e — d: d. 314. In any proportion, the terms are in proportion by...Division ; that is, the sum of the first two terms is to ¿heir difference as the sum of the last two terms is to their difference. Let the proportion be a... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...b). .•. a - b : a = c - d : c. (?) In like manner, a - b: b - c — d:d. PROP. VII. THEOREM. 239. In any proportion, the terms are in proportion by...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 a + b:a - b = c + d:c - d. Proof.... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 714 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...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 — b : b = с — d : d. Then... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 712 pages
...proportions are said to be derived from the given proportion by Division. 10. In any proportion, the mm of the first two terms is to their difference as the...sum of the last two terms is to their difference. Let a : b = c : d. By Art 8, a + b: b = c + d: d; and by Art. 9, a — b : b = c — d : d. Then by... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 712 pages
...said to be derived from the given proportion by Division. 10. In any proportion, the sum of theßrst 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 — b:b = c — d:d. or Then by... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...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 and fourth is to their difference. Let To... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...that of composition in Prop. VII. 187. PROPOSITION IX. When four numbers are in proportion, are they 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 and fourth is to their difference ? Is this... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...: a — b : a = c — d : c. (?) In like manner, a — b : b = c — d: d. PROP. VII. THEOREM. 239. In any proportion, the terms are in proportion by...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 a + b: a— b = c + d:c —... | |
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