 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...Hence -,- = -=a n c n 6 n rf" that is a" : 6" = c" : d n THEOREM IX. 23. If any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. Let a :b = e : d=.e :f Now ab = ab (A) and by (12) ad —be (B) and also af=be (C) Adding (A), (B), (C) a (b... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...ma _mc nb ~ nd1 or ma : nb : : me : 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 : ft af=be; (2.) also ab =... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...: b—dl У 2. COR. — 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 : h, etc., a... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...= 3 bd a" cn Hence -6- = Jn that is an : 6n = c" : dn THEOREM IX. 23« If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedentt is to the sum of all the consequents. Let a : 6 = c : d = e :f Now ab = a 6 (A) and by... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...115. If any number of magnitiides are proportional, any antecedent is to its consequent as the sitm of all the antecedents is to the sum of all the consequents. Let A : B : : C : D : : E : F; then will A : B: : A + C + E : B \-D-\-F. For, from the given proportion, we have AXD = BXC, and AXF = BX E.... | |
 | Horatio Nelson Robinson - Algebra - 1874 - 340 pages
...PROPOSITION Xin. 275. If any number of proportionals have the same ratio, any one of the antecedents will be to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = a : b (A) Also, a : b = с : d (B) a : b =m : n (С) &c. = &c. We are to prove that a : b = (a +... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...remaining terms will be in proportion. THEOREM X. 115. If any number of magnitudes are proportional, awy antecedent is to its consequent as the sum of all...consequents. Let A : B : : C : D : : E : F; then will A : B: :A+C+E: B-\-D + F. For, from the given proportion, we have By adding AXB to the sum of the corresponding... | |
 | Benjamin Greenleaf - Algebra - 1875 - 338 pages
...Therefore, by Art. 38, Ax. 1, | = ^, or, a : b : : c : d, THEOREM X. 324. -//'' any number of quantities are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. Let a:b::c:d::e:f; then a : b : : a -f- c -|- e : b -\- d -|- f. For, by Theo. I., ad = bc, and af=be;... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 340 pages
...Х1П. 275. If any number of proportionals have the same ratio, any one of the antecedents will be to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a:b=a:b.... (A), a:f=c:d.... (B), / a : b = m: n. . . . (C), &c. = &c. We are to prove that a: b= (a... | |
 | William Frothingham Bradbury - 1875 - 280 pages
...5" = c" : <f THEOREM XII. 213. If any number of quantities are proportional, any antecedent is to us consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : 6 = с : d=e : f Now ab = ab (1) and by Theorem I. ad = be (2) and also af=be (3) Adding(l),(2),(3),... | |
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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. 
