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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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A Complete Course in Algebra for Academies and High Schools

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) =...
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A Complete Course in Algebra for Academies and High Schools

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...
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A Complete Course in Algebra

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. Aso, a6 = ba. Adding, a(b + d+f) = b(a+c...
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A Complete Course in Algebra for Academies and High Schools

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. ASO, ab = ba....
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College Algebra: For the Use of Academies, Colleges, and Scientific Schools ...

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...
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Sheldons' Complete Algebra: Part I Being Sheldon's Elements of ..., Parts 1-2

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...
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A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

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...
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Principles of Plane Geometry

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...
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Principles of Plane Geometry

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...
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University Algebra: Embracing a Logical Development of the Science with ...

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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