| George Albert Wentworth, George Anthony Hill - 1894 - 150 páginas
...Theorem. If a : b = c : d, then a ; c — b : d a±b: b = c• ± d : d a:a±b = c: dd 218. 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. 219. Theorem. A line parallel to one side of a triangle divides the... | |
| George P. Lilley - 1894 - 522 páginas
...= d = = д • Therefore, a + c + e + rj : b + d+f+h :: a : b. Hence, XI. In a continued proportion the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. a2 + b3 ab + Ь с EXAMPLE 1. .If — r-^_- j- = -rj-x~-j-, prove... | |
| William Freeland - 1895 - 328 páginas
...composition, (л By division, iZ=°ri (2) Dividing (1) by (2), we have, a + b _c + d a — b с — d 292. IX. 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. If a:b = c:d = e:f=g:h. To prove (a + b + e + g) : (b + d +f+ K)=a:b.... | |
| John Macnie - 1895 - 390 páginas
...(232") PROPOSITION XII. THEOREM. 251. If any number of like quantities are in continued proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Given : A : B = C : D = K : V ; To Prow : A + C + E : B + D + F =... | |
| Henry Sinclair Hall, Samuel Ratcliffe Knight - 1895 - 508 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 - 68 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 is to the sum of the consequents as any antecedent is to its consequent. 304. The products of the corresponding terms of two or more proportions... | |
| George D. Pettee - 1896 - 272 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... | |
| Emerson Elbridge White - 1896 - 418 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 - 398 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 - 428 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 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... | |
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