 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 - 1872 - 110 pagesFull view - About this book
 | Elias Loomis - Algebra - 1846 - 380 pages
...same ratio, the first will have to 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 o : b :... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...same ratio, the first will have to the second the same ratio thai the sum of all the antecedents has to the sum of all the consequents. Let a, b, c, d, e,/be any number of proportional quantities, suchthat a : b : : с : d : : e :f, then will a : b :... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...quantities, the first will have to 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, g, h be any number of proportional quantities, such that a : b : : c : d : : e :/: : g : h. Then... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...mA. A THEOREM L. 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 : mB : : wA : nB, &c. ; then will A : B : ; A + mA + nA : B + mB + nB, &c. B + mB + nB^(l +m... | |
 | 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 sum of all the consequents. Let a : b : : c : d : : m : n, &c. Then will a : b : : a+c+m : b+d+n ; Since a : 6 : : c : d, we have bc=ad. Since a :... | |
 | George Clinton Whitlock - Mathematics - 1848 - 338 pages
...a' : с : : a" : c" : : &.C., .'. PROPOSITION V. If any number of couplets have the same ratio: (41) The sum of all the antecedents is to the sum of all the consequents, as any one antecedent to its consequent. We should also have ± a =fc a ± a" ± ... : ± с ± c'... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...by ; al= bL .-. (§ 233) a+e+g-\-k : b+f+h+l—a :b = e:f, &c. Hence, In any number of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any one of the antecedents is to its consequent. Thus, if 1:2 = 3:6 = 4:8 = 5: 10, then 1+3+4+5... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...quantities are proportional, any one antecedent 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, since A :... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...am :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...the sum of all the consequents. Let a :b : :c : d : :m :n, &c. Then a : b : : a-\-c-\-m : b-\-d-\-n. Since a : b : : c : d, we have bc=ad (Art. 267).... | |
 | 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, we have a... | |
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