| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...proportion, consisting of three or more equal ratios, then either antécédent will be to its consequent, as the sum of all the antecedents is to the sum of all the coimequmUs. Suppose a : b = с : d = e : _/°— g : h =, etc. Then by comparing the ratio, a : b,... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...n : : p : q, we have mq = np; whence am X dy = bn X cp, or am : bn :: cp : dq. (14) PROP. IX. In 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. (Vide § SS16, def. ,7.) For, since a : b : : c : d, we have... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...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, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D... | |
| Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...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. t Let a : b = a : b (A) -Also, a : b = с : d (в) a : b =m : n (С) &c. = &c. We are to prove that... | |
| Joseph Ray - Algebra - 1866 - 250 pages
...that is, any number of proportions having the same ratio, 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 : :m-.n, etc. Then will a : 6 : : a+c+m : b-\-d-\-n. Since a : b : : c : d, And a... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...tlmt is, any number of proportions having the same ratio, 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 : : m :n, etc. Then will a : b : : a+c+wi : 6+d+n. Since a : b : : c : d, And a... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...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 : b : : c : d : : m ; n, etc. Then, ..... a : b : : a+C+W : 6+d+ n. Since... | |
| Joseph Ray - Algebra - 1852 - 420 pages
...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 consequent*Let a :b : :c: d : :m :n, die. Then a:b:\ a-\-c+m : b-\-d-\-n. Since a : b : : c : d, we... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...number of quantities be proportional, then 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::mA:»nB::nA:nB, &c. ; then will A: B:: A : B+mB+»B, &c. ^ B+mB+nB (l+»»+n)BB , For -T—... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...nd. n 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 — be; A (1.) and, since a: b :: e: /, «/=fe;... | |
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