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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 Text-book of Geometry

George Albert Wentworth - Geometry, Analytic - 1889 - 266 pages
...ABE = A BCE _ A CPE i.iata, AA>B>> AB'C'E' A C'D'E'' &ABE+BCE+CDE _AABE AB* AA'B'E' AB? J33 (in o series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). .: S:S' = AB* : A'B''. Q. E, D. 377. COR. 1. The areas of two similar polygons are to each other as...
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A College Algebra

James Morford Taylor - Algebra - 1889 - 344 pages
...ma:mb = nc:nd; (ii.) ma:nb = mc: nd; (iii.) a" : b" = c" : d„, n being any exponent. 196. If we have a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. T ace Let --2-7-...г/ Adding these equations, we obtain a + t...
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Numbers Symbolized: An Elementary Algebra

David Martin Sensenig - Algebra - 1889 - 388 pages
...Demonstrat1on : d = , and x = [P. I, Cor. 1] aa, L ' Therefore, x = d XVI. In any multiple proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given a:b::c:d::c:f Given Г ( e :b::с :/:•ff :</ :h (A)) (B) Prove, 1. aXe: ab bX f: d :cXg:...
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Numbers Universalized: An Advanced Algebra, Volume 2

David Martin Sensenig - Algebra - 1890 - 556 pages
...member by member, ab, , , — = -т ; whence а : с : : о : d. O 449. In any multiple proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given a :b : : с : d : : e :f : : g :h to prove e+g : b + d+f+h : : a : b Demonstration : Let т=г;-3-...
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A School Algebra

George Albert Wentworth - Algebra - 1891 - 382 pages
...с then 7 = -• bd Multiplying by —, — = — * 0 be cd ab or - = _ cd .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. •c, т a с g For, 1f - = - = - = J-, bdfh r may be put for each of these ratios. Then |=r,.|=r,i...
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A School Algebra

George Albert Wentworth - Algebra - 1891 - 380 pages
...i_ b ab bc Multiplying by —, 7- = —;' ' с be cd ab or - = -. с d л a : с — b : d. L\. 317. In a series of equal ratios, the sum of the antecedents...sum of the consequents as any antecedent is to its 7 Ju_.'. r may be put for each of these ratios. mi „ Я „ С- -' * _ J <Г i aen - = r, - — r,...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 426 pages
...quotients will form a proportion. SECTION IV.— CONTINUED PROPORTIONS. 299. PROP. XVI. In any proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. PROP. XVII. In any proportion, all the antecedents, or all the consequents, may be multiplied by any...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...Consult 298, 297, 296, and 299. 303. If any number of magnitudes of the same kind form a proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Post. Let the quantities a, x, c, n, d, and r form a continued proportion, so that a:x::c:n::d:r. We...
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A Higher Algebra

George Albert Wentworth - Algebra - 1891 - 556 pages
...о с— a V. Alternation ; that is, a will be to с as b is to d. 282. In a Series of Equal Batios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. For if aff-2, rui, 11 — — — i bdfh r may be put for each of these ratios. Then - = r - = r -...
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A Text-book of Geometry

George Albert Wentworth - Geometry, Plane - 1892 - 264 pages
...Let a:b = c:d. By division, ., a—bc—d or, a-\-b:a — b= c-\-d: c — d, PROPOSITION IX. QED 303. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a: b = c: d — e :/= g: h. To prove a+c+e+g : b+d+f+ h = a: b. Denote each ratio by r. '-iH-1 Whence,...
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