| Edward Olney - Algebra - 1878 - 516 pages
...: (6 + d+/+ ^ + fc+,ete.) : : a : b, or c : d, or e : f, etc. That is, 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 SOLUTION. =- = r or a& = ba, oo ac , , — = -j or ad = be,... | |
| Edward Olney - 1878 - 362 pages
...Ъ— dt 72. Сов. — If there be a series of equal ratios in the form of a continued proportion, **the sum of all the antecedents is to the sum of all the consequents,** as any one antecedent is to its consequent. DEM. — If a :b : : с : d : : e :f: :g :n, etc., a +... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...^f AE Proposition 16. Theorem. — If any number of quantities be in proportion, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents. If** A : B : : C : D : : E . F, etc., then A : B :: A+C+E,etc. : B+D + F,etc. Let A = mB, then (IV. 6) (7=... | |
| Webster Wells - Algebra - 1879 - 468 pages
...and -d = -f Therefore, - = od 351. If any number of quantities are proportional, any antecedent is **to its consequent, as the sum of all the antecedents is to the sum of all the consequents.** Thus, if a : b = c: d = e :f then (Art. 343), ad = bc and af=be also, ab = ab Adding, a (b + d +/)... | |
| Benjamin Greenleaf - Algebra - 1879 - 352 pages
...or. a : b : : c : d. THEOREM X. 321. If any number of quantities are proportional, any antecedent is **to its consequent as the sum of all the antecedents is to the sum of all the consequents.** Let a : b : : c : d : : e : f; then a : b :: a -\-c-\- e :b -\-d-\- f. For, by Theo. I., ad=bc, and... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...n : d* ._ -~> . ^ THEOREM IX. 23i If any number of quantities are proportional, any antecedent. is **to its consequent as the sum of all the antecedents is to the sum of all the consequents.** Let a :b = c : d =e :f Now ab — ab (A) and by (12) ad = bc (B) and also af = be (C) Adding (A), (B),... | |
| Edward Olney - Algebra - 1880 - 354 pages
...Ъ—dl У£. СОЕ. — If there be a series of equal ratios in the form of a continued proportion, **the sum of all the antecedents is to the sum of all the consequents,** as any one antecedent is to its consequent. DEM. — If a : b : : e : d : : e :f: : g : A, etc., a... | |
| James Mackean - 1881 - 510 pages
...Mixing. PROP. XIV. — When several quantities are in continued proportion, any one of the antecedents is **to its consequent as the sum of all the antecedents is to the sum of all the consequents.** a ma + ne + pe Theorem IX., l=mb + nd+pf, and if mnp-1, a a+c+e . . then т = f,i _r~?; ... a:o::a... | |
| Edward Olney - Algebra - 1881 - 504 pages
...,eíc.) : (b + d+f+h + k + ,etc.) ::a:ö,or с : d, or e : f, etc. That is, 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. _ aa -, -, а с , , Solution, v — т or ab = ba, - = ^01... | |
| Edward Olney - Algebra - 1882 - 358 pages
...:b—d1 72. Сок. — If there be a series of equal ratios in the form of a continued proportion, **the sum of all the antecedents is to the sum of all the consequents,** as any one antecedent is to its consequent. DEM. — If a : b : : с : d : : e :/: : g : h, etc., a... | |
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