 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...: PROPOSITION X. THEOEEM. If any number of magnitudes are proportionals, any one antecedent will be to its consequent, as the sum of all the antecedents to the sum of the consequents. Let M : N :: P : Q :: B : S, £c. Then since, M : N :: P : Q, we have M x Q=Nx P,... | |
 | Joseph Ray - Algebra - 1848 - 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 the antecedents i» to the sum of all the conseqtients. Let a : b : : c : d : : m : n, &c. Then will a:b: : o+e+m :... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...:bn: :cr:ds. ART. 278. 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 consequents. Let a :b : :c : d : :m :n, &c. Then a : b : : a-\-c-\-m : b-\-d-\-n.... | |
 | Benjamin Greenleaf - Algebra - 1853 - 370 pages
...proportionals, any antecedent has the same ratio to its consequent that the sum of all the antecedents has to the sum of all the consequents. Let a : b : : c : d : : e : f : : g : h ; then, also, a '. b : : o+c +e+g : b+d+f+k. Since ab=ba, ad=bc, af=be, ah=bg,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...55 PROPOSITION X. THEOREM. If any number of magnitudes are proportionals, any one antecedent will be to its consequent, as the sum of all the antecedents to the sum of tl1e consequents. Let M : N : : P : Q : : R : S, &c. Then since, M : N : : P : Q, we have Mx Q=NxP,... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...number of homogeneous magnitudes be proportionals, then as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. First, let there be four proportionals, and let any equimultiples of the antecedents and any equimultiples... | |
 | John Radford Young - 1855 - 218 pages
...of quantities of the same kind are proportionals, then as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. Let there be a, : b : : c : d : : e : f, &c. Put j=-=- &e. =m; then a=mb, c=md, e=mf, &c. &c.) .'. a :... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...same ratio, the first will have ti> the second the same ratio that the sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e, f be any number of proportional quantities, such that a: b: :c:d: : e:f, then will a:b: :a+c+e:b+d+f.... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...quantities are proportional, any one ante cedent is to its consequent, as the sum of all the antecedents, it to the sum of all the consequents. Let A : B : : C : D : : E : F, &c. ; then will A : B : : A+C+E : B+D+F For, since A : B : : C : D, we have AxD=BxC. And,... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...6, (387) " " a + b :ab : : c+d : c—d Q. K D. PROPOSITION (394.) 13. In a continued proportion, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. DEMONSTRATION. Let a : b : : с : d : : e :f::y: h : : &c. We... | |
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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. 
