 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...<#• that is a" : 6" = cn : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all...the sum of all the consequents. Let a :b = c : d = e :/ Now ab = ab (A) and by (12) ad=be (B) and also af=be (C) Adding (A), (B), (C) q(ft + «l+/)=6(a... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...B : : C+D : C— D. PROPOSITION IX. THEOREM. If any number of quantities are proportional, any one antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. Let A:B::C:D::E:F,etc.; then will A:B:: A+C+E: B+D+F. For,since A:B::C:D, we have A x D=B x C. And, since... | |
 | Edward Olney - Algebra - 1877 - 466 pages
...(6 + d +/+ & + & +, etc.) : : a : 6, or c : d, or e : /, 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 SOLUTION. =- = r- or 06 = 60, oo ac . — = -T or ad =... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...2, and 9:3 = 6:2 .-. 12 : 4 = 9 : 3 THEOREM X. Wlien any number of quantities are proportional, any antecedent is to its consequent, as the sum of all...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, " of = be Also, ai> = 6a Adding... | |
 | 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 - 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 - 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 +... | |
 | Benjamin Greenleaf - Algebra - 1879 - 322 pages
...Ax. 7, | = ^, or, a : b : : c : d. THEOREM X. 324i If any number of quantities are proportional, any antecedent is to its consequent as 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 — be; also, ab = b a. Adding, ab-\-ud-\-af=ba-\-bc-\... | |
 | Benjamin Greenleaf - Algebra - 1879 - 376 pages
...7, -r = -,, or. a : b : : c : d. THEOREM X. 324 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. Let « : 4 : : c : d : : e : f; then g:t: : m -\- c -\- e : l-\-d-\- f. For, by Theo. I., ad = bc, and... | |
 | Elias Loomis - Algebra - 1879 - 398 pages
...n, ma _mc •rib ~ nd1 or ma :nb::mc: nd. 309. If any number of quantities are proportional, any one antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. Let a:b::c:d::e:f; then, since a : b : : c : d, ad=bc; (1.) and, since a:b::e:f, af=be; (2.) also ab —... | |
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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 (1) and by Theorem I. 
