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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. "
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages
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College Algebra

Webster Wells - Algebra - 1890 - 560 pages
...— d Whence, a + b: a — b = c + d: c — d. 390. 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. 381, ad = be, and af= be. Also, ab = ba. Adding, a(b + d +/) = b(a...
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A Drill-book in Algebra

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 -...
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Regents Examination Papers

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...
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A Complete Algebra: For High Schools, Academies and Normal Schools

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 ™=....
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Essentials of Algebra for Secondary Schools: By Webster Wells

Webster Wells - Algebra - 1897 - 448 pages
...— t* Whence, a + b : 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...
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Essentials of Algebra

Webster Wells - 1897 - 422 pages
...a Whence, a + b : a — 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)...
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Essentials of Algebra: For Secondary Schools

Webster Wells - Algebra - 1897 - 422 pages
...(2), Whence, a + b: 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 = Ьe, and af= be. Also, ab = ba. Adding, a(b + d+,f)=b(a +...
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A School Algebra Complete

Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 478 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...
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Elements of Geometry

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...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...terms are in proportion. PROPOSITION IX. THEOREM. 209. 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. To prove a + c + e:b + d +/= a : b = c : d = e : f. Let r be the value of...
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