 In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.  College Algebra - Page 520by James Harrington Boyd - 1901 - 777 pagesFull view - About this book
 | Edward Olney - 1878 - 360 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...consequents, as any one antecedent is to its consequent. DEM. — If a :b : : с : d : : e :f: :g :n, etc., a + c + e+g + etc. : b + d+f+h + etc. : : a : b,... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...the squares of those sides. 1. Since the polygons are similar, AB: FG:: BC:GK::DC:LK, etc. Now, as the sum of all the antecedents is to the sum of all the consequents as any one anteB * a sequent, AB+BC+DC cedent is to any one con+ ED + AE:FG+GK + KL + LH + FH::AB:FG; or, since... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...THEOREM X. Wlien 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, etc. Then a : b :: a + c + e : b + d+f, etc. For (Th. i), ad = be And,... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...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)... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...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 - 350 pages
...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... | |
 | 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...consequents, as any one antecedent is to its consequent. DEM. — If a : b : : e : d : : e :f: : g : A, etc., a + c + e+g + etc. : b + d+f+h + etc. : : a :... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...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 - 1881 - 506 pages
...24. If a : b : : c : d : : e : f : : g : li : : i : k, etc., show that 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. dd , d C 7 , Solution. -, = T or ab = Zra, = - or ad = fo, 66 6 d... | |
 | James Mackean - 1881 - 510 pages
...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... | |
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