 | James Bates Thomson - Algebra - 1878 - 322 pages
...That is. a : b = e : d od Again, 12 : 4 = 6 : 2, and 9:3 = 6:2 .-. 12 : 4 = 9 : 3 THEOREM X. Wlien any number of quantities are proportional, any antecedent...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,... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...as 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;... | |
 | 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 the consequents, as any one antecedent is to its consequent. DEM. — If a :b : : с : d : : e :f: :g :n, etc., a +... | |
 | 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,... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...E : F. TTK AC A EC ^f AE Proposition 16. Theorem. — If any number of quantities be in proportion, any antecedent is to its consequent, as the sum of...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= mD and E = m F, etc.... | |
 | Benjamin Greenleaf - Algebra - 1879 - 322 pages
...-=- = j, ce and - = -. Therefore, by Art 38, Ax. 7, | = ^, or, a : b : : c : d. THEOREM X. 324i If any number of quantities are proportional, any antecedent...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., arf=4c, an daj... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...other. Thus, if a:b = e:f and c:d — e:f ae с е then, -=- and -d = -f Therefore, - = od 351. If any number of quantities are proportional, any antecedent...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
...— -, , с n and d=f Therefore, by Art 38, Ax. 7, f = ¿, or. a : b : : с : d. THEOREM X. 324. If any number of quantities are proportional, any antecedent is to its consequent as the sum of аи the antecedents is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a :... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...d ac that is j = 5 Hence 6» = #> C" C B that is a n : b" = c n : d* ._ -~> . ^ THEOREM IX. 23i If any number of quantities are proportional, any antecedent....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... | |
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Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 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... 
