 | David Martin Sensenig - 1889 - 388 σελίδες
...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 - 1889 - 340 σελίδες
...= 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 - 1890 - 556 σελίδες
...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 - 1891 - 208 σελίδες
...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 - 1891 - 426 σελίδες
...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 - 1891 - 550 σελίδες
...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 - 1891 - 380 σελίδες
...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 - 1891 - 380 σελίδες
...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 - 1892 - 266 σελίδες
...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 - 1892 - 420 σελίδες
...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. 
