| Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...PROPOSITION xm. 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.** 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 - 252 pages
...continued proportion, 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
...continued proportion, 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 - 1852 - 420 pages
...ART. 27§. 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** consequent*Let a :b : :c: d : :m :n, die. Then a:b:\ a-\-c+m : b-\-d-\-n. Since a : b : : c : d, we... | |
| John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...c+d : cd QED PROPOSITION («>94.) 13. In a continued proportion, any antecedent it to its sjnscquent **as the sum of all the antecedents is to the sum of all the consequents.** DEMONSTRATION. Let a : b :: c : d :: e :/:: g : h :: &o. We are to prove that a ib '.\a + c + e+g,... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...ratio. mA A ' THEOREM VII. If any 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—... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...proportion. PROPOSITION XI. — THEOREM. 147. If any 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... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...nd 1 or ma: nb :: me: 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;... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...a" : J" = c" : <f THEOREM XII. 213. 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. ad = bc (2) and also af=be (3) Adding... | |
| Horatio Nelson Robinson - 1868 - 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 all the antecedents** ù to the sum of all the consequents. Suppose a : b =: с : d = e : _/= g : h =, etc. Then by comparing... | |
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