 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.  Secondary Algebra - Page 314by George Egbert Fisher, Isaac Joachim Schwatt - 1900 - 442 pagesFull view - About this book
 | Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...— - — = — — » 6 d Or, a — b :b — c — d:d. 285. V. Composition and Division ; that is, the sum of the first two terms is to their difference...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
...are in proportion by Composition and 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 : b = с : d. Then by § 312, And by §313, !^ = £П. , (2) а Dividing (1) by... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 714 pages
...of Art. 8. These two proportions are said to be derived from the given proportion by Division. 10. In any proportion, the sum of the first two terms...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 by Art. 7, or a — о с —a... | |
 | 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...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 Art 7, «±... | |
 | Webster Wells - Geometry - 1898 - 264 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...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 - 712 pages
...members of (1) by the corresponding members of (2), we have ac^ x_z a b_c t d b d' x' y~ z ' и У м 8. In any proportion^ the sum of the first two terms is to the first (or the second) tenu as the sum of the last two terms is to thv third (or the fourth) term.... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 506 pages
...of Art. 8. These 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. Let a : b = с : d. By Art. 8, a + b:b = c + d:d; and by Art. 9, a — b:b = c — d:d. Then by Art. 7, «±&:1=£±*:1, a— b... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...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...the last two terms is to their difference. Let a : b = c : d. Then = J . And -. = -=. §3 33 ac a + b _ r + d a — bc — d a-\-b:a — b = c + d:c —... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...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...the last two terms is to their difference. Let a : b = c: d. Then a ±j , = c ± d . ac And ?LzJ = £nA §333 ac „. ., a + bc + d Divide, r = _• a —... | |
 | 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...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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