 | George William Jones - Algebra - 1892 - 300 pages
...and like roots of the terms of a proportion are proportional. THEOR. 9. In a continued proportion, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. For, let a : b - с : d= e :/= - - then va/a = b/b, с/а - d/b, e/a... | |
 | George Washington Hull - Algebra - 1895 - 358 pages
...nq Multiplying, $P--JJ26n dq Whence, am :bn = cp: dq. THEOREM XVI. In a series of equal ratios, (he sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Let a : 6 = с : d, And m:n=p:q. Then а с t Ь d' And ™=£. Let... | |
 | University of the State of New York. Examination dept - Examinations - 1895 - 436 pages
...imaginary. 6-7 Complete and prove the following theorem : if any number of quantities are in proportion the sum of all the antecedents is to the sum of all the consequents as ... 8-9 Write three terms of the expansion of [a -\- b~\ n and prove that it is true when n is any... | |
 | Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...+ d: c — d. 286. VI. Composition of Several Equal Batios ; that is, 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. а с eg eLet each of the equal ratios equal r. mu а с eg Then jr, --r, j =... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...are proportional. §111 §111 Ax. 2 PROPOSITION XV. THEOREM. QED 133. In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Let a: b— c : d= e:f. Let r •» the common ratio, Then £ = r,... | |
 | Webster Wells - Algebra - 1897 - 422 pages
...— b = с + d : с — d. 315. 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 = с : d = e : f. Then by § 306, ad = bс, and af= be. Also, ab = ba. Adding, a(b + d+f)... | |
 | Webster Wells - Algebra - 1897 - 434 pages
...: a — 6 = c + d:c — d. 315. 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 § 306, ad = be, and q/= be. Also, ab = ba. ft a -h In like manner, the... | |
 | Webster Wells - Algebra - 1904 - 384 pages
...a — b = c + d: с — d. 315. 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 § 306, ad = be, and a/= be. Also, ab = ba. Adding, a (6 + d +/) = b... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...From(l), o_ = c- (§ 237) ac and o^-ft^Cj-d. ac PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum, of all the antecedents is to the sum of all the consequents as any antecedent 18 to its consequent. Given a:b = c:d=e:f. (1) To Prove a + c + e:b + d +/= a : b. Proof.... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...: W~C'*— CD : C' D' . Now substitute these values in your first equations. By proportion, §198, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Can you write an equation so that the sum of the AS in the first figure... | |
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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. 
