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 30by William Frothingham Bradbury - 1872 - 110 pagesFull view - About this book
| 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... | |
| 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... | |
| 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 :... | |
| 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... | |
| 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, £c. Then vcill a : 6 : : a+c+m : b+d+nj Since a : 6 : : c : d,... | |
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