 | 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
...= 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... | |
 | 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 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... | |
 | 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 -... | |
 | George Albert Wentworth - Algebra - 1891 - 380 pages
...Multiplying by —, — = — * 0 be cd ab or - = _ cd .'. a : с = b : d. 317. 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. •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
...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 is to the 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 - Geometry, Plane - 1892 - 266 pages
...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 is to the sum of the consequents...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, a = br, c = dr,... | |
 | George W. Lilley - Algebra - 1892 - 420 pages
...163), íSr;-7?H-í»HTherefore, a + c + e + g :l+d+f + h::a:b. Hence, XI. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. a2 + Ь* а Ъ + b с EXAMPLE 1. .If ~ï~v~î~ = ~j,z 4. г > Prove that о as a mean proportional... | |
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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. Let a: b = c: d — e :/= g: h. 
