 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 College Algebra - Page 110by James Morford Taylor - 1889 - 363 pagesFull view - About this book
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...Consult 298, 297, 296, and 299. 303. If any number of magnitudes of the same kind form a proportion, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Post. Let the quantities a, x, c, n, d, and r form a continued proportion,... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...of their methods. For instance, under the theory of proportion, it is sometimes stated that : " 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." This is a true proposition applied to numbers, but is not true of... | |
 | 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 - 362 pages
...mb = nc : nd ; (ii.) ma : nb = me : nd. The proof is left as an exercise for tl1e student. 224. L1 a series of equal ratios, the sum of the antecedents is to the кит 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
...(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 - 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 =... | |
 | 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... | |
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