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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 Geometry, with Practical Applications

Benjamin Greenleaf - Geometry - 1875 - 204 pages
...will be in proportion. THEOREM X. 115. If any number of magnitudes are proportional, awy 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,...
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Eaton's Elementary Algebra, Designed for the Use of High Schools and Academies

William Frothingham Bradbury - 1875 - 280 pages
...5" = c" : <f THEOREM XII. 213. If any number of quantities are proportional, any antecedent is to us consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : 6 = с : d=e : f Now ab = ab (1) and by Theorem I. ad = be (2) and also af=be (3) Adding(l),(2),(3),...
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...: b + d+f+h + &c. :: a:b; (11) hence, the following principle : 10. In any continued proportion, the sum of all the antecedents is to the sum of all the consequents, as any antecedent is to the corresponding consequent. ь d " bc = ad. a — c' b a = ' " be = /•...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...B + F. -F; .-. A + E : В + F = E : F = С: D. THEOREM LXX. If there be any number of equal ratios, the sum of all the antecedents is to the sum of all the consequents as either antecedent is to its consequent. Let A : В = С : D = E : F. By Theorem LXIX., A + E:B +...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 394 pages
...be multiplied or divided by the same quantity. PROPOSITION VIII. THEOREM. In a continued proportion, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to the corresponding consequent. Assume the continued proportion, z 7 /• * df...
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Bradbury's Elementary Algebra

William Frothingham Bradbury - Algebra - 1877 - 302 pages
...a" : b" = c" : d" 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 = be (2) and also af=be (3) Adding (1),...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...C— D. PROPOSITION IX. THEOREM. 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,etc.; then will A:B:: A+C+E: B+D+F. For,since A:B::C:D, we have A x D=B x C. And,...
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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1877 - 468 pages
...(6 + d +/+ & + & +, etc.) : : a : 6, or c : d, or e : /, etc. That is, in a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents, as any antecedent is to its consequent ., aa SOLUTION. =- = r- or 06 = 60, oo ac . — = -T or ad =...
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 324 pages
...6:2 .-. 12 : 4 = 9 : 3 THEOREM X. Wlien 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, etc. Then a : b :: a + c + e : b + d+f, etc. For (Th. i), ad = be And,...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...as the squares of those sides. 1. Since the polygons are similar, AB: FG:: BC:GK::DC:LK, etc. Now, as the sum of all the antecedents is to the sum of all the consequents as any one anteB * a sequent, AB+BC+DC cedent is to any one con+ ED + AE:FG+GK + KL + LH + FH::AB:FG;...
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