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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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## Elements of Plane Geometry

Franklin Ibach - 1882 - 196 páginas
...on \ Then or a ± £- a : b ± £- b :: a : b. QED THEOREM XIII. 168. In any 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 :: g : h. To prove that a -\- c -\- e -\- y : b -{- d -\- f -\- h :: a...
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## Elements of Geometry

George Albert Wentworth - 1879 - 250 páginas
...QED PROPOSITION VIII. 266. In a series of equal ratios, of which all the terms are of the same kind, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a :6 = c : d — e : f = g : h. We are to prove -a + c+e + g: b + d+f+h: : a: b. Denote each ratio*by...
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## Elements of Geometry

George Albert Wentworth - 1882 - 250 páginas
...£ _ i = 1 _ i b ' ' d l> that is, -, bd or, a — b : b : : c — d : d. QED PROPOSITION VIIL 266. In a series of equal ratios, the sum of the antecedents is to the sum of tlie consequents as any antecedent is to its consequent. Let a : b = c : d = e :f — g : h. We are...
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## Essentials of Geometry

Alfred Hix Welsh - 1883 - 267 páginas
...-\- nc : d + nd. 4. State ' 2' and " 3' in general terms. r THEOREM XII. In a continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its corresponding consequent. Let a : b :: c : d :: e : f :: g : h ; then will a + c + e + g + etc. : b...
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## Elements of Plane and Solid Geometry

George Albert Wentworth - 1885 - 398 páginas
...of similar polygons arc proportional). .-.AB + BC, etc. : A'B' + B'C ' , etc. : : AB : A'B', § 260 (in a series of equal ratios the sum of the antecedents is to the sum of (he consequents ns any antecedent is to Us consequent). That is P : P' :: AB : A'B'. PROPOSITION XVII....
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## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 512 páginas
...—,, we have, A±fA : B±fB :: 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 - 1886 - 165 páginas
...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. î-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, George William Jones - 1887 - 412 páginas
...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 ••,...
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## Proceedings of the Edinburgh Mathematical Society, Volúmenes5-6

...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 College Algebra

George Albert Wentworth - 1888 - 494 páginas
...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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