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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. "
An Elementary Geometry - Page 30
by William Frothingham Bradbury - 1872 - 110 pages
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A Treatise on Algebra

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 :...
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A Treatise on Algebra

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 :...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

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...
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Elementary Course of Geometry ...

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...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

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 :...
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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

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'...
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A Treatise on Algebra: For the Use of Schools and Colleges

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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Elements of Geometry and Conic Sections

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 :...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

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)....
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A Practical Treatise on Algebra: Designed for the Use of Students in High ...

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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