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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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...remaining terms will be ill proportion. PROPOSITION XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent...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 have AXD = BXC, and AXF = BX E....
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...ma me nb ~- 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...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; (2.) also ab ~ ba. (3.)...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...proportional, any one of the antecedents will be to its consequent as the sum of all thf tnlfcedents is to the sum of all the consequents. Let A, B, C, D, 13, etc., represent the several magm tudes whi ih give the proportions A : B :: C : J) A : B :: E :...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...remaining terms will be in proportion. PROPOSITTON XI. — THEOREM. 147. If any number of magnitudes are proportional, any antecedent is to its consequent...antecedents is to the sum of all the consequents. feet A:B::C:D::E:F; then will A:B::A + C + E:B + D + F. For, from the given proportion, we have AXD...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...Q. THEOREM VII. X If any number of magnitudes are proportional, 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, (7, D, E, etc., represent the several magnitudes which give the proportions To which we may annex the...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 268 pages
...proved. 23. If any number of quantities are proportional, any antecedent is to its consequent as tl;e sum of all the antecedents is to the sum of all the...ad=bc (B) and also af=be (C) Adding (A), (B), (C) a (b + d +/) = b (a + c + e) Hence, by (14) a :b = a -\-c-\-e:b -\-d-\-f THEOREM X. 21. If there are two...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1872 - 268 pages
...proportion. Let a : b = c : d ac 1.0. 7 = -, I d T-, a" c Hence, = ie a" : bn = c" : ef THEOREM XII. 21 3. If any number of quantities are proportional', any...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 (1), (2),...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...same in both, the remaining terms will be in proportion. THEOREM X. 115. If atiy number of magnitudes are proportional, any antecedent is to its consequent...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 have AXD = BXC, and AXF = BX E. By...
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A Treatise on Algebra

Elias Loomis - Algebra - 1873 - 396 pages
...ma _mc nb ~ nd1 or ma : nb : : me : nd. 309. If any number of quantities are proportional, any one antecedent is to its consequent as the sum of all...antecedents is to the sum of all the consequents. Let a:b::c:d::e:f; then, since a:b::c:d, ad=bc; (1.) and, since a : b : : e : ft af=be; (2.) also ab =...
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A University Algebra ...

Edward Olney - Algebra - 1873 - 354 pages
...: b—dl У 2. COR. — If there be a series of equal ratios in the form of a continued proportion, the sum of all the antecedents is to the sum of all the consequents, as any one antecedent is to its consequent. DEM. — If a : b : : e : d : : e :f: : g : h, etc., a...
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