| 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... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...—,, 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... | |
| 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.** 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,... | |
| 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-\... | |
| James Edward Oliver, Lucien Augustus Wait - Algebra - 1887 - 434 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 -\... | |
| James Edward Oliver, Lucien Augustus Wait - 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... | |
| Edinburgh Mathematical Society - Mathematics - 1887 - 316 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... | |
| George Albert Wentworth - Geometry - 1888 - 272 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... | |
| 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... | |
| 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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