| Webster Wells - Algebra - 1885 - 370 pages
...c—d Whence, a + b: a — b = c + d: c — d. 302. In a series of equal ratios, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents.** Let a: 6 = c: d = e :/. Then, by Art. 293, ad = be, and af= be. Also, a6 = ba. Adding, a(b + d+f) =... | |
| Webster Wells - Algebra - 1885 - 382 pages
...с— a Whence, a-\-b: a — b = c + d: c — d. 302. In a series of equal ratios, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents.** Let a:b = c:d = e:f. Then, by Art. 293, ad = &c, and af= be. Also, a& = ba. Adding, a(b + d+f) = b(a... | |
| Webster Wells - 1885 - 368 pages
...by (2), Whence, a + b: a — b = c + d: c — d. 302. In a series of equal ratios, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents.** Let a:b = c:d = e:f. Then, by Art. 293, ad = bc, and a/= be. Aîso, a6 = ba. Adding, a(b + d+f) = b(a+c... | |
| Webster Wells - Algebra - 1885 - 376 pages
...by (2), Whence, a + b: a — b = c + d: c — d. 302. In a series of equal ratios, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum** oj all the consequents. Let a:b = c:d = e:f. Then, by Art. 293, ad = be, and af=be. AÎSO, ab = ba.... | |
| Edward Albert Bowser - Algebra - 1888 - 876 pages
...••• a»:&»::c-:/«. 6» d" (14) If any number of quantities are in proportion, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents.** For if a : b : : c : d : : e : f, then by (1), ad = be, and of = be ; also ab = ba. Adding a(6 + d... | |
| Algebra - 1888 - 494 pages
...: : с -\- d : с — d. 374. X. Wlien any number of quantities are proportional, any antecedent is **to its consequent as the sum of all the antecedents is to the sum of all the consequents.** Thus, if a : b : : с : d : : e :f, etc., then а : b : : a -\- с -\- e, etc. : b + d + /, etc. And... | |
| Webster Wells - Algebra - 1889 - 584 pages
...d Whence, a + b: a — b = c + d:c — d. 318. In a series of equal ratios, any antecedent is to us **consequent, as the sum of all the antecedents is to the sum of all the consequents.** Let a: b — с: d= e :/. Then by Art. 309, ad = &e, and af= be. Also, ab = ba. Adding, a(b + d+f)=b(a+c... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...powers or like roots are in proportion. Proposition XI. A Theorem. 127. In a series of equal ratios **the sum of all the antecedents is to the sum of all the consequents** as any one antecedent is to its consequent. COROLLARY. The sura of any number of the antecedents is... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...consequents. Proposition X. A Theorem. Proposition XI. A Theorem. 127. In a series of equal ratios **the sum of all the antecedents is to the sum of all the consequents** as any one antecedent is to its consequent. COROLLARY. The sum of any number of the antecedents is... | |
| Charles Davies - Algebra - 1889 - 332 pages
...+ d+f+h+ &c. _ b Ac. a •/ Honce, the following principle : 10. In any continued proportion, tlie **sum of all the antecedents is to the sum of all the consequents,** as any antecedent is to the corresponding consequent. Let us assume the two equations, bd . fh - =... | |
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