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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. "
Elements of Geometry: With Practical Applications to Mensuration - Page 52
by Benjamin Greenleaf - 1863 - 320 pages
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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...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.) Adding...
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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
...be in proportion. sequents the same in both, the remaining terms will be in proportion. PROPOSITTON XI. — THEOREM. 147. If any number of magnitudes...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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New Elementary Algebra

Benjamin Greenleaf - 1870 - 334 pages
...Therefore, by Art. 38, Ax. 7, ^ = ¿, or, a : b : : с : d. THEOREM X. 324. If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedent» is to the sum of all the consequents. Let a : b : : с : d : : e : f; then a : b : : a...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1871 - 412 pages
...= -j. ; therefore r = -. ; " J Л J о а whence, a : b : : c : d. 319i If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents M to the sum of all the consequents. If a : b : : c : d : : e : f, then a : b : : a-\-c-\-e : b-\-d-\-f....
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...is 7=3 bd Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent...sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (A) and by (12) ad=bc (B) and also af=."be (C) Adding (A), (B), (C) a (b -fd +/) = b (a...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1872 - 268 pages
...7 = -, I d T-, a" c» Hence, = ie a" : bn = c" : ef THEOREM XII. 21 3. If any number of quantities are proportional', any antecedent is to its consequent...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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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 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 consequents. Let a : b = c : d=. e :f Now ab = ab (A) and by (12) ad=bc (B) and also af=be (C) Adding (A), (B), (C) a (b + d +/) = b (a +...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...two consequents the same in both, the remaining terms will be in proportion. THEOREM X. 115. If atiy number of magnitudes are proportional, any antecedent...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 adding AXB...
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