 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.  Academic Algebra - Page 202by George Wentworth, David Eugene Smith - 1913 - 458 pagesFull view - About this book
 | Webster Wells - Geometry - 1898 - 284 pages
...the second, a + b _ c + d a — bc — d .-. a + b:a — b = c + d:c — d. PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum of all the antecedents...consequents as any antecedent is to its consequent. Given a:b = c:d=e:f. (1) To Prove a+ c + e:b + d+f= a: b. Proof. We have ba = ab. Also, from (1), be... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...(1), 5L±i = <L±A, (§ 237) ac and a__6 = c j - 1 d (§238) ac PROP. VIII. THEOREM. 240. In a aeries of equal ratios, the sum of all the antecedents is...consequents as any antecedent is to its consequent. Given a : b = c : d = e : f. (1) To Prove a + c + e :b + d+f= a : b. Proof. We have ba = ab. Also,... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...- b = c + d:c - d. Proof. From(l), o_ = c- (§ 237) ac and o^-ft^Cj-d. ac PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum, of all the antecedents...to the sum of all the consequents as any antecedent 18 to its consequent. Given a:b = c:d=e:f. (1) To Prove a + c + e:b + d +/= a : b. Proof. We have ba... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...: W~C'*— CD : C' D' . Now substitute these values in your first equations. By proportion, §198, the sum of all the antecedents is to the sum of all...consequents as any antecedent is to its consequent. Can you write an equation so that the sum of the AS in the first figure shall be to the sum of the... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...proportion. PROPOSITION IX. THEOREM. 209. 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. To prove a + c + e:b + d +/= a : b = c : d = e : f. Let r be the value of... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...the second, a + b _ c + d a — bc — d .: a + b: a — 6 = c + d:c — d. PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum of all the antecedents...consequents as any antecedent is to its consequent. Given a:b = c:d = e:f. (1) To Prove a + c + e :b + d+f= a: b. Proof. We have ba = ab. Also, from (1),... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...the second, a + b _ c + d a—b c—d .-. a + b : a — b = c + d: c — d. PROP. VIII. THEOREM. 240. In a series of equal ratios, the sum of all the antecedents...consequents as any antecedent is to its consequent. Given a:b = c:d=e:f. (1) To Prove a+ c + e: b + d+f= a: b. Proof. We have ba = ab. Also, from (1),... | |
 | George Egbert Fisher - Algebra - 1900 - 438 pages
...Art. 8, &2 = ac ; whence b = 19. 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 % : d¡ = пi : d? = пя : d3 — ••• = v, П, Wo îi, or -. = v, ~ = v, -f = v, — . di... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...5L±^ = e±4 [?490] ac (2) "---$ = e=± [1491] ac By dividing (1) by (2), J±| = ^ 493. THEOREM IX. — In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent w to its consequent. Let the ratios be (1) •£• = -£• = £ = ..... = r. A Jj... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...proportion be j- = ^. (2) -° = ?^*. [{491] ac By dividing (1) by (2), 2-±| = e-±± 493. THEOREM IX. — 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. Let the 'ratios be (1) j- = J- = ± = = r. (2) a = Ar, b = Br,... | |
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