 | George Albert Wentworth, David Eugene Smith - Algebra - 1913 - 310 pages
...— 6n > or < ab — an, or as — bn > or < — an, or as 6 < or > a. 4. 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. и С в Consider the three ratios -,-,—, and let each equal... | |
 | George Wentworth, David Eugene Smith - Algebra - 1913 - 478 pages
...— 6n > or < ab — an, or as — bn > or < — an, or as b < or > a. 4. 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. Consider the three ratios -,-,-, and let each equal r. bdf... | |
 | William James Milne - Algebra - 1914 - 514 pages
...10 and a:b =c:d = e :f are multiple proportions. 489. PRINCIPLE 13. — In any multiple proportion the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. For, given 0:6= c:d = e:f, or - = - = - = r, the value of each... | |
 | Fletcher Durell - 1914 - 458 pages
...common third form. PROPORTION 233. Composition of Several Equal Ratios. 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. . a с eg Given, т = -j = -. = I Let each of the equal... | |
 | Fletcher Durell - Algebra - 1914 - 606 pages
...expressions to a common third form. 268. Composition of Several Equal Batios. 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. -,• а с eg GlVen' b=d=f = h Let each of the. equal... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...the ratio in the given proportion ? 346. Theorem. If any number of quantities are in proportion, then the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Given To prove that a _c _e _g b~d~f~h b+d+f+h+ a _c b~d' Proof... | |
 | 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... | |
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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. 
