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" In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. "
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages
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Documents of the Assembly of the State of ..., Volume 15; Volume 133, Issue 15

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...
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First Year Algebra

William James Milne - Algebra - 1911 - 380 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...
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Academic Algebra

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...
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School Algebra, Book 2

George 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...
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Durell's Algebra: Two Book Course. Book One, Book 1

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...
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Standard Algebra

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...
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Durell's School Algebra

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...
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General Mathematics, Book 2

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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A Second Course in Algebra, Book 2

Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1924 - 492 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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