Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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 Geometry and Trigonometry - Page 55
by Adrien Marie Legendre - 1871 - 187 pages
Full view - About this book

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

Thomas Sherwin - Algebra - 1841 - 314 pages
...Adding these equations q, or Dividing by 6 + d+f+h a-\-c-4-e-\-gac - ' In any series of equal ratios, the sum of the antecedents is to the sum of the consequents, as any one of the antecedents is to its consequent. 16. If a : b = c : d, and e :f= g : h, that is, — =...
Full view - About this book

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...
Full view - About this book

Elementary Algebra: For the Use of Schools

William Smyth - Algebra - 1851 - 272 pages
...: c : : b -f- d : d. Comparing this with the proposed, we derive the following principle : In every proportion, th~e sum of the antecedents is to the sum of the consequents, as any one anetcedent is to its consequent. In like manner it may be shown, that the difference of the antecedents...
Full view - About this book

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

Charles William Hackley - Trigonometry - 1851 - 524 pages
...Geom.), Aft : Aft' : : 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, A6 : A&' : : A& + be + cd + <fec., : A&' + be' + cd' + <fec. But...
Full view - About this book

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

Samuel Alsop - Algebra - 1856 - 152 pages
...§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...
Full view - About this book

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

Olinthus Gregory - 1863 - 482 pages
...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...
Full view - About this book

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

Edward Brooks - Geometry - 1868 - 284 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,...
Full view - About this book

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

Charles Davies - Geometry - 1872 - 464 pages
...1 ± —, and, n = 1 ± —,, we shall have, DD* A±*-A : *± P -B :: C±$C : D ± *D; PBOPOSITION XI. THEOREM. In any continued proportion, the sum...proportion (D. 3), A. : B : : C : D : : E : F : : G : E, &o, hence, _j = -T ; whence, BA = AB ; .&. jH 7? 7? -T = -=; ; whence, BC = AD ; 7? T) ^3. (/...
Full view - About this book

Annual Report, Volume 43

Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...moins son foyer, sa famille ; on s'accoutumne il s'en passer; on a son chez-soi partout. GEOMETRY. 1. In any continued proportion the sum of the antecedents is to the sum of the_ consequents, as any antecedent is to its consequent. Prove. 2. If two circumferences intersect...
Full view - About this book

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

Aaron Schuyler - Navigation - 1873 - 536 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...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF