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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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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 484 pages
...т TI "VCl Vс In like manner, -1— = — — 344. 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 : b = c: d = e :/. Then by 331, ad — be, and af= be. Also, a6 = ba. Adding, а(b + d +/)...
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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 570 pages
...-— = -^— • л/о л/d 344. //ia series of equal ratios, any antecedent is to its consequent an the sum of all the antecedents is to the sum of all the consequents. Let a:b = c:d = e:f. Then by 331, ad = be, and of= be. Also, ab = ba. Adding, a(b + d +/) = b(a...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...a : b = c : r. ) Proof : am = 6c.and ar = be (?) (290). 301. THEOREM. 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: Set each given ratio = m; thus, acea = m; - = m; - =...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...a : b = c : r. \ Proof : am = be and ar = bc (?) (290). 301. THEOREM. 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. „. acea Glven: I-2-/-T To Prove: fi+|= f = 1 , etc....
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A First Course in Algebra ; A Second Course in Algebra

Webster Wells - Algebra - 1908 - 470 pages
...bd b" d" In like manner, — = ^- • П,, ",~i 152. 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. e). :b + d+f. (141) In like manner, the theorem may be proved for any number of equal ratios. 153....
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A First Course in Algebra

Webster Wells - Algebra - 1908 - 260 pages
...the proportions be ?=v and - = ?• 6 a / ft frl. 149. 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:b = c:d = e:f. Then, - ---/ b b+d+f EXERCISE 59 The following problems lead both to integral...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 206 pages
...- a2 _ 2 a + 6 _ x — va;2 — a2 2 a — 6 PROP. VIII. THEOREM 224. 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. We have ba = ab. And from (1), be = ad, and be =...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...division to the following: x + Vx2 - n" _ 2 q + 6 PROP. VIII. THEOREM 224. 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. !_!_!. a) To Prove a + c + e = g. b+d+fb Proof. We have ba...
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Standard Algebra

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...
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Education Department Bulletin

Education - 1910 - 520 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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