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" In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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A School Algebra

George Albert Wentworth - Algebra - 1895 - 376 pages
...ab or - = -• с d .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedent? is to the sum of the consequents as any antecedent is to its consequent. n • a с ea For, if _ = - = - = , oafп r may be put for each of these ratios. rm.™ a_ r c_.-r...
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Elementary Algebra

Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...= -> = 7. , each of these ratios = , - =- . • b 9 f b+d+f a result which may be thus enunciated : In a series of equal ratios the sum of the antecedents is to he sum of the consequents as any antecedent is to its consequent. Example. 1. If - = — find tho...
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A Complete Algebra: For High Schools, Academies and Normal Schools

George Washington Hull - Algebra - 1895 - 358 pages
...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 а:Ь = c:d= e: f. Let г = the common ratio....
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...the first two terms is to their difference as the sum of the last two terms to their difference. 303. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 304. The products of the corresponding terms of two or more proportions are in proportion. 305. Like...
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Elements of Algebra

George Albert Wentworth - Algebra - 1896 - 344 pages
...obtained by: VI. Composition, и --\- c : c : : b + d : d. VII. Division. — c:c::b — d : d. 350. In a series of equal ratios, the sum of the antecedents...sum of the consequents as any antecedent is to its т-. -taceg For-lf b = d = J=V r may be put for each of these ratios. , ., aeeg Then - = f,- = r,j=r,0...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...equations ma me multiplying as ot fractions a _ c PROPOSITION VIII 195. Theorem. In a continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let ————-- b~d~f'~ ['value of each ratio e=fr ,.] clearing of fractions separately a + c + e =...
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A School Algebra: Designed for Use in High Schools and Academies

Emerson Elbridge White - Algebra - 1896 - 422 pages
...Dividing (1) by (2), member by member, _ ab~cd' that is, о + b • a — b = с + d : с — d. 530. In a series of equal ratios, the sum of the antecedents is tc the sum of the consequents as any antecedent is toits consequent. --i-7-' then, by 522,...
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Elements of Analytic Geometry

Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...equal. 21. In every proportion the product of the extremes is equal to the product of the means. 22. lu a series of equal ratios, the sum of the antecedents is to the sum of the conseqnents as any antecedent is to its conseqnent. 23. If a line be drawn through two sides of a triangle...
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 428 pages
...kind as a and b. In applying alternation, however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. _, .. a с eg For'lf -b = d = f = -h' r may be put for each of these ratios. г_, a с eg Then, -b...
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New School Algebra

George Albert Wentworth - Algebra - 1898 - 442 pages
...however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of th e antecedents is to the sum of the consequents as any antecedent is to its consequent. _< .„ aeet) For, if - = - = - = , bdfh r may be put for each of these ratios. . aeeg Then, - -...
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