| Henry Sinclair Hall, Samuel Ratcliffe Knight - 1895 - 478 páginas
...= -> = 7. , each of these ratios = , - =- . • b 9 f b+d+f a result which may be thus enunciated : **In a series of equal ratios the sum of the antecedents is to** ¡he sum of the consequents as any antecedent is to its consequent. Example. 1. If - = — find tho... | |
| George Albert Wentworth - 1896 - 50 páginas
...the first two terms is to their difference as the sum of the last two terms to their difference. 303. **In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent.** 304. The products of the corresponding terms of two or more proportions are in proportion. 305. Like... | |
| George Albert Wentworth - 1896 - 324 páginas
...obtained by: VI. Composition, и --\- c : c : : b + d : d. VII. Division. « — c:c::b — d : d. 350. **In a series of equal ratios, the sum of the antecedents...sum of the consequents as any antecedent is to its** т-. -taceg For-lf b = d = J=V r may be put for each of these ratios. , ., aeeg Then - = f,- = r,j=r,0... | |
| George D. Pettee - 1896 - 253 páginas
...equations ma me multiplying as ot fractions a _ c PROPOSITION VIII 195. Theorem. In a continued proportion, **the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.** Let ————-- b~d~f'~ ['value of each ratio e=fr ,.] clearing of fractions separately a + c +... | |
| Emerson Elbridge White - 1896 - 394 páginas
...Dividing (1) by (2), member by member, _ ab~cd' that is, о + b • a — b = с + d : с — d. 530. **In a series of equal ratios, the sum of the antecedents is** tc the sum of the consequents as any antecedent is toits consequent. ï-ï-i-7-î' then, by § 522,... | |
| Joseph Johnston Hardy - 1897 - 365 páginas
...equal. 21. In every proportion the product of the extremes is equal to the product of the means. 22. lu **a series of equal ratios, the sum of the antecedents is to the sum of the** conseqnents as any antecedent is to its conseqnent. 23. If a line be drawn through two sides of a triangle... | |
| George Albert Wentworth - 1898 - 407 páginas
...kind as a and b. In applying alternation, however, all four quantities must be of the same kind. 340. **In a Series of Equal Ratios, the sum of the antecedents...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 - 407 páginas
...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, - -... | |
| William James Milne - 1899 - 242 páginas
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. **In a series of equal ratios, the sum of the antecedents...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 - 473 páginas
...A'B' = BC : B'C' = CD: C'D', 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...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 trapezoid... | |
| |