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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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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...G.— 8. Then (Theo. IlI), (a + c + e + g):b+d a : b ; that is, in a set of continued proportionals, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Cor. — If any number of fractions are equal each to each, the sum of the numerators divided by the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...—,, we have, AfA : BfB :: c|c : D!D; PROPOSITION XI. THEOREM. In any continued proItortion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A : B : : C...
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Shorter Course in Algebra

George Albert Wentworth - Algebra - 1886 - 284 pages
...obtained by: VI. Composition. a-\-c: c: :b -\- d: d. VII. Division. a — с : с : :b — d: d. 295. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. -i-7-f г may be put for each of these ratios. Then fr.Sr.ir.fr. oafn .'. a — br, с = dr, e =fr,...
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A Treatise on Algebra

James Edward Oliver, Lucien Augustus Wait - Algebra - 1887 - 428 pages
...reader may write in formula, and prove. THEOR. 9. If six or more numbers be in continued proportion, the sum of the antecedents is to the sum of the consequents...as any antecedent is to its consequent. Let a : 6 = с : d = e :/=•••, then will For •.• ad = bc, af=be, ••-, [th.6 .-. ab + ad + af-\...
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A Treatise on Algebra

James Edward Oliver - Algebra - 1887 - 436 pages
...reader may write in formula, and prove. THEOR. 9. If six or more numbers be in continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a: b = c: d = e:f= •••, then will For •.• od = &c, af=be, •••, [th.6 = ba + be -f be -\...
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A Treatise on Algebra

James Edward Oliver, Lucien Augustus Wait, George William Jones - Algebra - 1887 - 440 pages
...may write in formula, and prove. THEOR. 9. If six or more numbers be in continued proportion, tJie sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a : b = c: d = e : /= •••, then will For •.• ad = bc, af=be, ••-, [th. 6 ••, [ax. 2...
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Proceedings of the Edinburgh Mathematical Society, Volumes 5-6

Edinburgh Mathematical Society - Mathematics - 1887 - 312 pages
...then the terms D, E, F are proportional. Since A:B = B:C, by composition A + B:B = B + C:C; therefore the sum of the antecedents is to the sum of the consequents in the same ratio, that is, A + 2B + C:B + C = B + C:C. Now D = A + 2B + C, E = B + C, andF = C; therefore...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...<—- = — *— -j a — oc — d or, a-\-b: a — b= c-\-d: c — d. aE. D. PROPOSITION IX. 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 :f— g : h. To prove a-\-c + e-\-g :b + d-\-f-\- h = a: b. Denote each ratio by r. Then...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...AB'C'E' AC'D'E' &ABE+BCE+CDE _ A ABE _ = A BCE _ A CDE AA'B'E ' ' + B'C'E' + C''E ' AA'B'E' A 'i* (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). Q . E . D . 377. COR. 1. The areas of two similar polygons are to each other as the squares of any...
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A College Algebra

George Albert Wentworth - Algebra - 1888 - 514 pages
...to d. For, if a:b = c:d, HMultiplying by *, ^ = *, с ос cd o- с d .'. a: с — b : d. 193. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. For, if ? = - = - = 3-, bdfh r may be put for each of these ratios. rru a с e (7 1 hen - = r — =...
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