 | 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... | |
 | 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 — =... | |
 | George Albert Wentworth - Geometry, Analytic - 1889 - 264 pages
...ABE = A BCE _ A CPE i.iata, AA>B>£> AB'C'E' A C'D'E'' &ABE+BCE+CDE _AABE AB* AA'B'E' AB? J3°3 (in o series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). .: S:S' = AB* : A'B''. Q. E, D. 377. COR. 1. The areas of two similar polygons are to each other as... | |
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...Demonstrat1on : d = , and x = [P. I, Cor. 1] aa, L ' Therefore, x = d XVI. In any multiple proportion the sum of the antecedents is to the sum of the 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:... | |
 | James Morford Taylor - Algebra - 1889 - 340 pages
...ma:mb = nc:nd; (ii.) ma:nb = mc: nd; (iii.) a" : b" = c" : d„, 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. T ace Let --2-7-...г/ Adding these equations, we obtain a + t... | |
 | David Martin Sensenig - Algebra - 1890 - 556 pages
...member by member, ab, , , — = -т ; whence а : с : : о : d. û Oí 449. In any multiple proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given a :b : : с : d : : e :f : : g :h to prove e+g : b + d+f+h : : a : b Demonstration : Let т=г;-3-... | |
 | George Albert Wentworth - Algebra - 1891 - 380 pages
...с then 7 = -• bd Multiplying by —, — = — * 0 be cd ab or - = _ cd .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. •c, т a с à g For, 1f - = - = - = J-, bdfh r may be put for each of these ratios. Then |=r,.|=r,i... | |
 | George Albert Wentworth - Algebra - 1891 - 380 pages
...i_ b ab bc Multiplying by —, 7- = —;' ' с be cd ab or - = -. с d л a : с — b : d. L\. 317. In a series of equal ratios, the sum of the antecedents...sum of the consequents as any antecedent is to its 7 Ju_.'. r may be put for each of these ratios. mi „ Я „ С- -' * _ J <Г i aen - = r, - — r,... | |
 | George Albert Wentworth - Algebra - 1891 - 550 pages
...о с— a V. Alternation ; that is, a will be to с as b is to d. 282. In a Series of Equal Batios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. For if aff-2, rui, 11 — — — i bdfh r may be put for each of these ratios. Then - = r - = 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. 
