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 - 378 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 - 336 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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