 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.  Solid Geometry - Page 254by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...the equation. Then thatis, bd a~bc~d bd or, a — b : b : : с — d : d. QED PROPOSITION VIII. 266. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a : b = с : d = e :/=<7 : h. We are to prove a + c+e + g: b + d+f-\-h: :a:b. Denote each ratio... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...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... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...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... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...£ _ 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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...-\- 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... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...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.... | |
 | 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 - 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 ••,... | |
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