| George Albert Wentworth - Geometry, Analytic - 1889 - 266 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... | |
| James Morford Taylor - Algebra - 1889 - 344 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 - 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:... | |
| 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 - 382 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,... | |
| Seth Thayer Stewart - Geometry - 1891 - 426 pages
...quotients will form a proportion. SECTION IV.— CONTINUED PROPORTIONS. 299. PROP. XVI. In any proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** PROP. XVII. In any proportion, all the antecedents, or all the consequents, may be multiplied by any... | |
| George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...Consult 298, 297, 296, and 299. 303. If any number of magnitudes of the same kind form a proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** Post. Let the quantities a, x, c, n, d, and r form a continued proportion, so that a:x::c:n::d:r. We... | |
| George Albert Wentworth - Algebra - 1891 - 556 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 -... | |
| George Albert Wentworth - Geometry, Plane - 1892 - 264 pages
...Let a:b = c:d. By division, ., a—bc—d or, a-\-b:a — b= c-\-d: c — d, PROPOSITION IX. QED 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 :/= g: h. To prove a+c+e+g : b+d+f+ h = a: b. Denote each ratio by r. '-iH-1 Whence,... | |
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