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" In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art. "
Elements of Plane Geometry: For the Use of Schools - Page 54
by Nicholas Tillinghast - 1844 - 96 pages
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New Elementary Algebra: Containing the Rudiments of Science for Schools and ...

Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...PROPOSITION xm. 275, If any number of proportionals have the same ratio, 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. t Let a : b = a : b (A) -Also, a : b = с : d (в) a : b =m : n (С) &c. = &c. We are to prove that...
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 252 pages
...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 is to the sum of all the consequents. Let a :b : : c :d : :m-.n, etc. Then will a : 6 : : a+c+m : b-\-d-\-n. Since a : b : : c : d, And a...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools ...

Joseph Ray - Algebra - 1866 - 252 pages
...continued proportion, tlmt is, any number of proportions having the same ratio, any one 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, etc. Then will a : b : : a+c+wi : 6+d+n. Since a : b : : c : d, And a...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 420 pages
...ART. 27. 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 consequent*Let a :b : :c: d : :m :n, die. Then a:b:\ a-\-c+m : b-\-d-\-n. Since a : b : : c : d, we...
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The University Algebra

John Fair Stoddard, William Downs Henkle - Algebra - 1866 - 546 pages
...c+d : cd QED PROPOSITION (>94.) 13. In a continued proportion, any antecedent it to its sjnscquent as the sum of all the antecedents is to the sum of all the consequents. DEMONSTRATION. Let a : b :: c : d :: e :/:: g : h :: &o. We are to prove that a ib '.\a + c + e+g,...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...ratio. mA A ' THEOREM VII. 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:nB::nA:nB, &c. ; then will A: B:: A : B+mB+B, &c. ^ B+mB+nB (l++n)BB , For -T—...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...proportion. PROPOSITION XI. — THEOREM. 147. 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. Let A : B : : C : D : : E : F ; then will A:B::A+C + E:B + D+F. For, from the given proportion, we...
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...nd 1 or ma: nb :: me: nd. n 309. If any number of quantities are proportional, any one 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; then, since a: b:: c: d, ad — be; A (1.) and, since a: b :: e: /, /=fe;...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 270 pages
...a" : J" = c" : <f THEOREM XII. 213. 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. ad = bc (2) and also af=be (3) Adding...
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New University Algebra: A Theoretical and Practical Treatise Containing Many ...

Horatio Nelson Robinson - 1868 - 430 pages
...PROPOSITION VIII. — If there be a proportion, consisting of three or more equal ratios, then either antecedent will be to' its consequent, as the sum of all the antecedents to the sum of all the consequents. Suppose a : b =: с : d = e : _/= g : h =, etc. Then by comparing...
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