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If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
An Elementary Geometry - Page 30
by William Frothingham Bradbury - 1872 - 110 pages

## Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...powers or like roots are in proportion. Proposition XI. A Theorem. 127. In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. COROLLARY. The sura of any number of the antecedents is...

## Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...consequents. Proposition X. A Theorem. Proposition XI. A Theorem. 127. In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. COROLLARY. The sum of any number of the antecedents is...

## University Algebra: Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1889 - 330 pages
...+ d+f+h+ &c. _ b Ac. a •/ Honce, the following principle : 10. In any continued proportion, tlie sum of all the antecedents is to the sum of all the consequents, as any antecedent is to the corresponding consequent. Let us assume the two equations, bd . fh - =...

## Elements of Algebra: For Colleges, Schools, and Private Students

Joseph Ray - Algebra - 1894 - 422 pages
...15 : 135 : : 8 : 72. 278. Propositioa XII. — In any number of proportions having the same ratio, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a : b : : С : d : : m : n, etc. Then, a : b : : a+c+wi : o+ d+n. Since a : b : : с : d, we have be— .ad...

## College Algebra

Webster Wells - Algebra - 1890 - 604 pages
...(1) by (2), a — oc — a Whence, a + 6 : a — b = c + d:c — d. 390. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a:b = c:d = e:f. Then by Art. 381, ad = be, and af= be. Also, ab = ba. Adding, a(6 + d+/) = 6(a + c...

## A Drill-book in Algebra

George William Jones - Algebra - 1892 - 300 pages
...and like roots of the terms of a proportion are proportional. THEOR. 9. In a continued proportion, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. For, let a : b - с : d= e :/= - - then va/a = b/b, с/а -...

## The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...by the second, we have a -f- bc -\- d PROPOSITION VIII. THEOREM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of...of all the consequents. . Let a :b = c : d = e :f. To prove a:b=a+c+e:b+d+f. Let r denote the value of each of the given ratios. Then, r = ;hy = rWhence,...

## The Elements of Geometry

Webster Wells - Geometry - 1894 - 256 pages
...the second, we have a -\- b _ c -f- d PROPOSITION VIII. THEOREM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of...the sum of all the consequents. Let a : b = c: d = e if. To prove a:b = a-\-c-\-e:b-\-d-\-f. Let r denote the value of each of the given ratios. lli-, Whence,...