| 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 - 268 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 - 338 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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