| George Albert Wentworth - Algebra - 1895 - 376 pages
...ab or - = -• с d .'. a : с = b : d. 317. In a series of equal ratios, the sum of the antecedent? is to the sum of the consequents as any antecedent is to its consequent. n • » a с ea For, if _ = - = - = £, oafп r may be put for each of these ratios. rm.™ a_ r c_.-r... | |
| Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...-> = 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 - Mathematics - 1896 - 68 pages
...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 - Algebra - 1896 - 344 pages
...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 - Geometry, Modern - 1896 - 272 pages
...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 + e =... | |
| Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...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 Washington Hull - Geometry - 1897 - 408 pages
...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,... | |
| George Albert Wentworth - Algebra - 1898 - 434 pages
...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 - Geometry, Modern - 1899 - 258 pages
...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 - Geometry, Modern - 1899 - 272 pages
...= EC : 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 trape.... | |
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