 | 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 +/)... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...find the ratio of x to y. PROPOSITION IX. THEOREM 336 In a continued proportion, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. PROOF ab = ba, I den. ad = be, § 328 and af = be. § 328 Adding, ab + ad -f <tf= ba + &c + be ; Ax.... | |
 | 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; - =... | |
 | Webster Wells - Algebra - 1906 - 550 pages
...-ï— = -^— • 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... | |
 | 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: f±£±i+|= f = 1 , etc.... | |
 | Webster Wells - Algebra - 1908 - 262 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... | |
 | Webster Wells - Algebra - 1908 - 456 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.... | |
 | 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 =... | |
 | Webster Wells - Geometry - 1908 - 336 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... | |
 | 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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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. 
