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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. Let a: b = c: d — e :/= g: h. "
Elements of Plane and Solid Geometry - Σελίδα 132
των George Albert Wentworth - 1877 - 398 σελίδες
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - 1807 - 398 σελίδες
...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....

An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - 1841 - 300 σελίδες
...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...

A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - 1851 - 372 σελίδες
...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...

Elementary Algebra: For the Use of Schools

William Smyth - 1851 - 236 σελίδες
...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...

First Lessons in Algebra: In which the Elements of the Science are ...

Samuel Alsop - 1856 - 135 σελίδες
...§1O«5. 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...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

CHARLES DAVIES, LL.D. - 1863
...shall have, A±PA : 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...

Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863
...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...

The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - 1868 - 275 σελίδες
...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,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 455 σελίδες
...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...

Surveying and Navigation: With a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1873 - 482 σελίδες
...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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