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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. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 17
por International Correspondence Schools - 1906
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The Elements of Algebra

George Lilley - 1892 - 402 páginas
...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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A School Algebra

George Albert Wentworth - 1893 - 362 páginas
...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 - 1893 - 338 páginas
...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 - 1893 - 338 páginas
...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 - 1894 - 504 páginas
...= 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 - 1894 - 138 páginas
...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 - 1895 - 309 páginas
...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 - 1895 - 374 páginas
...(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 School Algebra

George Albert Wentworth - 1895 - 362 páginas
...ab or - = -• с d .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedent? is to the sum of the consequents as any antecedent is to its consequent. n • » a с ea For, if _ = - = - = £, oafп r may be put for each of these ratios. rm.™ a_ r c_.-r...
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A Text-book of Geometry

George Albert Wentworth - 1895 - 437 páginas
...+ 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...
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