 | 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 — =... | |
 | 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... | |
 | 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 - 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 - 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 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... | |
 | 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... | |
| |
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. 
