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
| William James Milne - Algebra - 1908 - 476 pages
...a:b =r, : d = e :f are multiple proportions. 489. PRINCIPLE 13. — In any multiple proportion the mm **of all the antecedents is to the sum of all the consequents** as any antecedent is to its consequent. For, given a:u=c:rf = e:/, or - = - = - = »-, the value of... | |
| Education - 1910 - 522 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... | |
| New York (State). Legislature. Assembly - Government publications - 1910 - 744 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... | |
| William James Milne - Algebra - 1911 - 378 pages
...Also, Ax. 3, ? - 2» = 2.u», OTma:nb = mc:nd. bndn 401. PRINCIPLE 10. — 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. For, given a : Ь = с : d = e :/, or - = - = - = r, the value... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
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