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" In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. "
Elements of Plane and Solid Geometry - Page 134
by George Albert Wentworth - 1877 - 398 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents an any antecedent is to its consequent. Let a : b= c : d = e :/. Let r = the common ratio, Then r = r> ar>da == or- (1) b '- = r, and c = dr. (2) 7=r, ande=/r....
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 320 pages
...antecedents, is to the sum or difference of the consequents, as either antecedent is to its consequent ; the sum of the antecedents is to the sum of the consequents, as the difference of the antecedents is to the difference of the consequents; also, the sum of the, antecedents...
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Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...last the same principle, we have and thus in order, whatever the number of equal ratioS. Therefore, in a series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one antecedent is to its consequent. Let us take next the two proportions If we now multiply these...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 372 pages
...A4 : A4' : : be : be' : : cd : cd', &c. PLANE SAILING. therefore, since by the theory of proportion the sum of the antecedents is to the sum of the consequents as any one antecedent is to its consequent, A* : A6' : : A4 + be + cd + &c., : A4' + be' + cd' + >fec. But...
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First Lessons in Algebra: In which the Elements of the Science are ...

Samuel Alsop - Algebra - 1856 - 150 pages
...1O5. If any number of like magnitudes be proportionals, one antecedent will be to its consequent as the sum of the antecedents is to the sum of the consequents. Let a : Ъ : : с : d : : e :f, then a:b::a-\-c-{-e:b-{-d -)-/• For since a : b : : с : d, and a...
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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863 - 482 pages
...series of equal ratios represented by f we shall have - - * - V - • T • - Tj Therefore, in a series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one antecedent is to its consequent. If there be two proportions, as 30 : 1 5 : : 6 : 3, and 2 : 3...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 455 pages
...shall have, APA : B*-B :: C 2,0 : 2>^D; PEOPOSITION XI. THEOEEM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A : B : : 0...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...THEOREM XII. If any number of quantities are in proportion, any antecedent will be to its consequent as the sum of the antecedents is to the sum of the consequents. Let A:B:: C: D:\E\F, etc. A : B : : E : F; we have A x .D = S X C, and AXF= B X E; adding to these,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...have, DD* A*-A : * P -B :: C$C : D *D; PBOPOSITION XI. THEOREM. In any continued proportion, the sum of the antecedents is to the sum of the consequents, as any antecedent to its corresponding consequent. From the definition of a continued proportion (D. 3), A. : B : : C...
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Surveying and Navigation: With a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Navigation - 1873 - 482 pages
...give the continued proportions: AB : AE : : BC : BF :: CD : CG. AB : EB :: BC : FC :: CD : GD. Since the sum of the antecedents is to the sum of the consequents as one antecedent is to its consequent, we have, AD : AE+BF + CG : : AB : AE. NAVIGATION. Now let a right...
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