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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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Elementary Algebra

Henry Sinclair Hall, Samuel Ratcliffe Knight - 1895 - 478 páginas
...= -> = 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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Syllabus of Geometry

George Albert Wentworth - 1896 - 50 páginas
...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 - 1896 - 324 páginas
...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 - 1896 - 253 páginas
...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 +...
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A School Algebra: Designed for Use in High Schools and Academies

Emerson Elbridge White - 1896 - 394 páginas
...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. ï-ï-i-7-î' then, by § 522,...
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Elements of Analytic Geometry

Joseph Johnston Hardy - 1897 - 365 páginas
...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 - 1898 - 407 páginas
...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 - 1898 - 407 páginas
...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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Plane Geometry

William James Milne - 1899 - 242 páginas
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a:b = c:d = e :/= g : h. To prove a + c + e + g:b + d +/+ ft...
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Plane and Solid Geometry

George Albert Wentworth - 1899 - 473 páginas
...A'B' = BC : B'C' = CD: C'D', etc. § 351 .-. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trapezoid...
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