 | Horatio Nelson Robinson - 1869 - 276 pages
...D :: P : Q. THEOREM VII. X If any number of magnitudes are proportional, 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, (7, D, E, etc., represent the several magnitudes which give the proportions To which we may... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...72. 278. Proposition XII. — -In any number of proportions having the same ratio, any antecedent is to its consequent as the sum. of all the antecedents is to the sum of all the contequents. Let ...... a : 6 : : c : d : : m : n, etc. Then, ..... a : b : : a+c+m : 6+d+n. Since... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...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 = e :f Now ab = ab (A) and by (12) ad=bc (B) and also af=."be (C) Adding (A), (B),... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...proved. 23. If any number of quantities are proportional, any antecedent is to its consequent as tl;e 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),... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...be in proportion. THEOREM X. 115. If atiy number of magnitudes 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 will A:B::A+C+E:B\-D + F. For, from the given proportion, we have... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...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 the 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... | |
 | 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 :... | |
 | 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,... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...PROPOSITION VIII. — If there be a proportion, consisting of three or more equal ratios, then either antecedent will be to its consequent, as the sum of...antecedents is to the sum of all the consequents. Suppose a:b=c:d — e:f = g:h=, etc. Then by comparing the ratio, a : b, first with itself, and afterward... | |
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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. 
