 | 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 - 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 -\... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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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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. 
