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. A Treatise on Algebra - Page 220by Elias Loomis - 1879 - 384 pagesFull view - About this book
| Joseph Ray - Algebra - 1866 - 250 pages
...Proposition XII. — In any continued proportion, that is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum...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 :b:... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...Proposition XII. — In any continued proportion, tlmt is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum...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 : b... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...: 135 : : 8 : 72. 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 contequents. Let ...... a : b : : c : d : : m ; n, etc. Then, ..... a : b : : a+C+W : 6+d+ n. Since... | |
| Joseph Ray - Algebra - 1852 - 422 pages
...: cr : ds. 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... | |
| 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... | |
| 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
...' 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 - 340 pages
...ill proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes are proportional, any 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 will A:B::A+C + E:B + D+F. For, from the given proportion, we have... | |
| William Frothingham Bradbury - Algebra - 1868 - 270 pages
...Hence, F = ^ ie 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...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 (1),... | |
| Benjamin Greenleaf - 1869 - 516 pages
...in proportion. PROPOSITTON XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. feet A:B::C:D::E:F; then will A:B::A + C + E:B + D + F. For, from the given proportion, we have AXD... | |
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