 | Admiralty - 1845 - 152 pages
...number of equal ratios, then will one antecedent be to its consequent, as the sum of all the antecedents to the sum of all the consequents. Let a : b : : c : d : : e : f ace that is, — =r— =— then will a : b : : a + c + e : b + d+f ab=ba •. ad— be af=be .-. ab... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...quantities, the first will have to the second the same ratio that t}ie 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::eif:igzhr Then a:l>::a+c+e+g:b+d+f+h.... | |
 | Anna Cabot Lowell - Geometry - 1846 - 216 pages
...This is called a continued proportion, being a series of equal ratios. In every continued proportion the sum of all the antecedents is to the sum of all the consequents as one antecedent is to its consequent. Therefore AB + BC + CD+DE + EA : ab+bc + cd -f- de-\-ea= AB... | |
 | 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 :... | |
 | 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... | |
 | 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 - 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... | |
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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. 
