 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.  An Elementary Geometry - Page 30by William Frothingham Bradbury - 1873 - 110 pagesFull view - About this book
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...: Q. THEOREM VII. 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, C, D, E, etc., represent the several magnitudes which give the proportions A : B :: C : D A : B ::... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...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... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...— In any continued proportion, tlmt is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...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 : : m... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...— In any continued proportion, that is, any number of proportions having the same ratio, any one antecedent is to its consequent, as the sum of all...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: :m:n,... | |
 | Joseph Ray - Algebra - 1852 - 422 pages
...bn : : 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... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...15 : 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... | |
 | 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... | |
 | Benjamin Greenleaf - 1866 - 336 pages
...= ^, л ce and 5=7. Therefore, by Art, 38, Ax. 7, .т- = -з, or, a : b : : с : d. THEOREM X. 324. If any number of quantities are proportional, any antecedent is to its consequent as the sum of aU the antecedents is to the sum of att the consequents. « Let a : b : : с : d : : e : f; then a... | |
 | 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— !... | |
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