 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...b + mb :: c -\- 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... | |
 | 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
...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 is to the sum of the 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 ••,... | |
 | 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 - Algebra - 1888 - 514 pages
...HMultiplying by *, ^ = *£, с ос cd o-» с d .'. a: с — b : d. 193. 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. For, if ? = - = - = 3-, bdfh r may be put for each of these ratios. rru a с e (7 1 hen - = r — =... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...,6хс , ftxc r¥, _ r* --, Demonstrat1on : d = , and x = [P. I, Cor. 1] aa, L ' Therefore, x = d XVI. In any multiple proportion the sum of the antecedents...consequents as any antecedent is to its consequent. Given a:b::c:d::c:f Given Г ( e :b::с :/:•ff :</ :h (A)) (B)î Prove, 1. aXe: ab bX f: d :cXg: dXh 2.... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...= mc:nd; (iii.) a" : bn = c" : dn, n being any exponent. 196. If we have a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent. . ace Let - = -=7 = ...r,. Adding these equations, we obtain e... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...is to B as C is to D as E is to F as G is to H as / is to J. PROPOSITION XVI. 329. Theorem : In any proportion, the sum of the antecedents is to the sum...consequents as any antecedent is to its consequent. Statement : If A : B : : C : D : : E : F : : G : H, then, A + C + E + G : B + D + F + H : : A: B. Demonstration... | |
| |
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. 
