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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. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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Educational Review, Volume 3

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...application of their methods. For instance, under the theory of proportion, it is sometimes stated that : " In a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent." This is a true proposition applied to numbers, but is not true of geometrical magnitudes unless these...
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The Elements of Algebra

George W. Lilley - Algebra - 1892 - 420 pages
...163), ÝSr;-7?H-Ý╗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 ~´~v~ţ~ = ~j,z 4. г > Prove that о as a mean proportional...
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A School Algebra

George Albert Wentworth - Algebra - 1893 - 370 pages
...ос Multiplying by -, — = — -. с ос cd ab or - = -у с d .'. a : с = b : d. 317. In a aeries of equal ratios, the sum of the antecedents is to...consequents as any antecedent is to its consequent. •c, -ta с ea For'lf ┐=5=7=f' r may be put for each of these ratios. Then |=г,.=^=г,j,.r. .-....
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An Academic Algebra

James Morford Taylor - Algebra - 1893 - 358 pages
...ma : mb = гtc : nd ; (ii.) ma : nb= me: nd. The proof is left as an exercise for the student. 224. In a series of equal ratios, the sum of the antecedents is to the киm of the consequents as any one antecedent is to its consequent. For assume a: b = c: d= e:f= ...,...
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An Academic Algebra

James Morford Taylor - Algebra - 1893 - 360 pages
...mb = nc : nd ; (ii.) ma : nb = me : nd. The proof is left as an exercise for tl1e student. 224. L1 a series of equal ratios, the sum of the antecedents is to the кит of the consequents as any one antecedent is to its consequent. For assume a:b = c: d = e:f=...
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Higher Algebra

George P. Lilley - Algebra - 1894 - 522 pages
...= d = = д • Therefore, a + c + e + rj : b + 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 + b3 ab + Ь с EXAMPLE 1. .If — r-^_- j- = -rj-x~-j-, prove that b is a mean proportional between...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...conversely, the greater angle is opposite the greater side. 2.- Show that in any continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent to its corresponding consequent. 3. Prove that, in equal circles, incommensurable angles at the centre...
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Algebra for Schools and Colleges

William Freeland - Algebra - 1895 - 328 pages
...composition, (л By division, iZ=░ri (2) Dividing (1) by (2), we have, a + b _c + d a — b с — d 292. IX. In a Series of Equal Ratios the sum of the antecedents...consequents as any antecedent is to its consequent. If a:b = c:d = e:f=g:h. To prove (a + b + e + g) : (b + d +f+ K)=a:b. If a:b=c:d = e:f=g:h, н=нALGEBPA....
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...(232") PROPOSITION XII. THEOREM. 251. If any number of like quantities are in continued 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 = K : V ; To Prow : A + C + E : B + D + F = A : B. Since a:b = c:d = e:f, (Hyp....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1895 - 458 pages
...+ d : c - d. as. D. PROPOSITION IX. 303. In a series of equal ratios, the sum of the an~ tecedents is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c:d = e :/= g : ft. To prove a + c + e+^r : 6+<f+/+ h = a : b. Denote each ratio by r. N rm_...
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