 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
 | Richard Wormell - 1876 - 268 pages
...the difference of the first two terms is to the difference of the last two in the same ratio ; also the sum of the first two terms is to their difference as the sum of the last two is to their difference. Proof. — The proportion A: B = C : D gives, by transposing the means, A :... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...we may prove that a — b : 6 = e — d : d. 349. If four quantit1es are in proportion, they will be in proportion by COMPOSITION AND DIVISION ; that is, the sum of the first two terms will be to their difference, as the sum of the last two terms is to their difference. Thus, if a :... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...B : A -B = 0+ D : C- D. Comparing this with the given proportion, we learn that In any proportion, the sum of the first two terms is to their difference as the sum of the last two is to their difference. Apply this principle to the proportion 9:6 = 3:2, and test the result. 201.... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...or, а(c — d) = c(a — b). Whence, a — b:a = c — d : c. Similarly, a — b:b = c — d:d. 301. In any proportion the terms are in proportion by Composition...sum of the last two terms is to their difference. Let a : b — с : d. Then, by Art. 299, = m а с And, by Art. 300, i^ = c-^. (2) ac Dividing (1)... | |
 | Webster Wells - 1885 - 368 pages
...or, a(c — d) = c(a — b). Whence, a — b:a = c — d:c. Similarly, a — b:b = c — d:d. 301. In any proportion the terms are in proportion by Composition...sum of the last two terms is to their difference. Let a : b = с : d. Then, by Art. 299, - = (1) a с And, by Art. 300, ^n* = ^L^. (2) Dividing (1) by... | |
 | Webster Wells - Algebra - 1885 - 372 pages
...or, a(c — d) = c(a — &). Whence, a — b: a = c — d:c. Similarly, a — b:b = c — d:d. 301. In any proportion the terms are in proportion by Composition...sum of the last two terms is to their difference. Let a : b = с : d. Then, by Art. 299, = (1) a с And, by Art. 300, £=± = c-^- (2) a Dividing (1)... | |
 | Webster Wells - Algebra - 1885 - 324 pages
...or, a(c — d) = c(a — b). Whence, a — b:a = c — d:c. Similarly, a — b: b = c — d: d. 301. In any proportion the terms are in proportion by Composition...two terms is to their difference, as the sum of the Zosi two terms is to their difference. Let a : b = с : d. Then, by Art. 299, = . (1) And, by Art.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...— d:c. In like manner it may be proved that a — b:b = c — did. PROPOSITION VII. THEOREM. 249. In any proportion the terms are in proportion by COMPOSITION...sum of the last two terms is to their difference. Let a : b = c : d. Then by §247, = . (i) ct c And by §248, ^ = ~ (2) Dividing (1) by (2), a+b _ PROPOSITION... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...— bc — d that is, — ; — = — — , bd or, a — b : b = c — d : d. PROPOSITION VIII. 302. In any proportion the terms are in proportion by composition...their difference as the sum of the last two terms to their difference. Let a : 6 = c : d. Then, by §300, a + b =c±d_ ac And, by § 301, By division,... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...member of the equation. Then f _l=i_l ; bd that is, bd or, a — b:b--=c — d:d. PROPOSITION VIII. 302. In any proportion the terms are in proportion by composition and division; that is, the sum of tlic first two terms is to their difference as the sum of the last two terms to their difference. Let... | |
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