 | George W. Lilley - Algebra - 1892 - 420 pages
...163), íSr;-7?H-í»HTherefore, a + c + e + g :l+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 + Ь* а Ъ + b с EXAMPLE 1. .If ~ï~v~î~ = ~j,z 4. г > Prove... | |
 | George Albert Wentworth - Algebra - 1893 - 370 pages
...ос Multiplying by -, — = — -. с ос cd ab or - = -у с d .'. a : с = b : d. 317. In a aeries of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. •c, -ta с ea For'lf ¿=5=7=f' r may be put for each of these ratios.... | |
 | James Morford Taylor - Algebra - 1893 - 358 pages
...mb = гtc : nd ; (ii.) ma : nb= me: nd. The proof is left as an exercise for the student. 224. In a series of equal ratios, the sum of the antecedents is to the киm of the consequents as any one antecedent is to its consequent. For assume a: b = c: d= e:f= ...,... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...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 - Algebra - 1894 - 522 pages
...= 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 - Algebra - 1895 - 328 pages
...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 - Geometry - 1895 - 390 pages
...(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 =... | |
 | 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 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 - 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... | |
 | Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...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... | |
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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. 
