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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
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A Second Course in Algebra, Book 2

Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1924 - 490 pages
...called transformation by addition and subtraction. T, 3 6, 3 + 4 6 + 8, 6. In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Proof : Tf a _ C _ g b = d=f Let r = the value of each of the...
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Annual Report of the Education Department

University of the State of New York - Education - 1905 - 998 pages
...inequality is increased by adding the same quantity to both its terms. 3 In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Proportion. 1 Necessary definitions. 2 If four quantities are...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 248 pages
...— In any continued proportion, that is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...the sum of all the consequents. Let a : b : : c : d : : m : n, &c. Then will a : b : : a+c+m : b+d+n ' Since a : b : : c : d, we have be=ad. Since a :...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 252 pages
...in, any number of proportions having the same ratio, any one antecedent is to Us consequent, as lite sum of all the antecedents is to the sum of all the consequents. Let a : b : : c : d : : in : n, &o. Then will a : b : : o+c+m : i+cZ+n ; Since a : b : : c : d, we have lc=ad. Since a...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 260 pages
...thai is, any number of proportions haciug the same ratio, any one antecedent is to its consilient, as the sum of all the antecedents is to the sum of all the consequents. . 9 Let a : b : : c : d : : m : n, úc. Then vcill a : 6 : : a+c+m : b+d+nj Since a : 6 : : c : d,...
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