 | George Washington Hull - 1897 - 408 σελίδες
...THEOREM. QED 133. 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. Let a: b— c : d= e:f. Let r •» the common ratio, Then £ = r, and a = br. (1) b Let And Then And Multiplying, Whence... | |
 | George Albert Wentworth - 1898 - 428 σελίδες
...alternation, however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. _, .. a с eg For'lf -b = d = f = -h' r may be put for each of these ratios. г_, a с eg Then, -b... | |
 | George Albert Wentworth - 1898 - 434 σελίδες
...however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of th e antecedents is to the sum of the consequents as any antecedent is to its consequent. _< .„ aeet) For, if - = - = - = £, bdfh r may be put for each of these ratios. . aeeg Then, - -... | |
 | George Albert Wentworth - 1899 - 498 σελίδες
...to their difference. Let a : b = c : d. PROPOSITION IX. THEORKM. 335. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c;d = e:f=g:h. To prone that a + c+e + g:b-\-d+f+h = a:b. T acea Let r = - = - = - = fbdfh Then... | |
 | George Albert Wentworth - 1899 - 278 σελίδες
...Or a + b : a — b = c + d : c — d. QED PROPOSITION IX. THEOREM. 335. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a:b = c:d = e:f= g:h. To prove that a + c + e + y:b + d+f+k = a:b. Then a = br, c = dr, e =fr, g =... | |
 | George Albert Wentworth - 1899 - 248 σελίδες
...term as the difference of the last two terms is to the fourth term. 335. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 338. Like powers of the terms of a proportion are in proportion. 342. If a line is drawn through two... | |
 | George Albert Wentworth - 1899 - 272 σελίδες
...etc. § 351 /. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trape.... | |
 | William James Milne - 1899 - 258 σελίδες
...consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a:b = c:d = e :/= g : h. To prove a + c + e + g:b + d +/+ ft... | |
 | George Albert Wentworth - 1899 - 496 σελίδες
...etc. § 351 .-. AB + BC + etc. : AB' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent). That is, P:P' = AB: A'B'. QKI) Ex. 252. If the line joining the middle points of the bases of a trapezoid... | |
 | George Albert Wentworth - 1899 - 272 σελίδες
...etc. § 351 .'. AB + BC + etc.: A'B' + B'C' + etc. = AB: A'B', § 335 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to Us consequent). That is, P:P' = AB: A'B'. Q . ED Ex. 252. If the line joining the middle points of... | |
| |
In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a: b = c: d — e :/= g: h. 
