 | Horatio Nelson Robinson - 1866 - 328 σελίδες
...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 - 1866 - 250 σελίδες
...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 - 1866 - 252 σελίδες
...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 - 1852 - 422 σελίδες
...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 - 1866 - 546 σελίδες
...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 - 1867 - 474 σελίδες
...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 - 1868 - 340 σελίδες
...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 - 1868 - 386 σελίδες
...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 - 1868 - 270 σελίδες
...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 σελίδες
...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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In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. 
