Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" 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. "
An Elementary Geometry - Page 30
by William Frothingham Bradbury - 1872 - 110 pages
Full view - About this book

Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...powers or like roots are in proportion. Proposition XI. A Theorem. 127. In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. COROLLARY. The sura of any number of the antecedents is...
Full view - About this book

Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 80 pages
...consequents. Proposition X. A Theorem. Proposition XI. A Theorem. 127. In a series of equal ratios the sum of all the antecedents is to the sum of all the consequents as any one antecedent is to its consequent. COROLLARY. The sum of any number of the antecedents is...
Full view - About this book

University Algebra: Embracing a Logical Development of the Science with ...

Charles Davies - Algebra - 1889 - 330 pages
...+ d+f+h+ &c. _ b Ac. a •/ Honce, the following principle : 10. In any continued proportion, tlie sum of all the antecedents is to the sum of all the consequents, as any antecedent is to the corresponding consequent. Let us assume the two equations, bd . fh - =...
Full view - About this book

Elements of Algebra: For Colleges, Schools, and Private Students

Joseph Ray - Algebra - 1894 - 422 pages
...15 : 135 : : 8 : 72. 278. Propositioa XII. — In any number of proportions having the same ratio, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a : b : : С : d : : m : n, etc. Then, a : b : : a+c+wi : o+ d+n. Since a : b : : с : d, we have be— .ad...
Full view - About this book

College Algebra

Webster Wells - Algebra - 1890 - 604 pages
...(1) by (2), a — oc — a Whence, a + 6 : a — b = c + d:c — d. 390. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a:b = c:d = e:f. Then by Art. 381, ad = be, and af= be. Also, ab = ba. Adding, a(6 + d+/) = 6(a + c...
Full view - About this book

A Drill-book in Algebra

George William Jones - Algebra - 1892 - 300 pages
...and like roots of the terms of a proportion are proportional. THEOR. 9. In a continued proportion, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. For, let a : b - с : d= e :/= - - then va/a = b/b, с/а -...
Full view - About this book

The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...by the second, we have a -f- bc -\- d PROPOSITION VIII. THEOREM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of...of all the consequents. . Let a :b = c : d = e :f. To prove a:b=a+c+e:b+d+f. Let r denote the value of each of the given ratios. Then, r = ;hy = rWhence,...
Full view - About this book

The Elements of Geometry

Webster Wells - Geometry - 1894 - 256 pages
...the second, we have a -\- b _ c -f- d PROPOSITION VIII. THEOREM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of...the sum of all the consequents. Let a : b = c: d = e if. To prove a:b = a-\-c-\-e:b-\-d-\-f. Let r denote the value of each of the given ratios. lli-, Whence,...
Full view - About this book

The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...by the second, we have a -\- bc -f- d PROPOSITION VIII. THEOKEM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a:b = c:d = e:f. To prove a\b — a-\-c-\-e:b-\-d-\-f. Let r denote the value of each of the given...
Full view - About this book

The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...VIII. THEOREM. 239. In a series of equal ratios, any antecedent is to its consequent as the sum of nil the antecedents 'is to the sum of all the consequents. Let a : b = e : d = e :f. To prove a : b = a -f- c -f- e : b -\- d -f- f. Let r denote the value of each of the...
Full view - About this book




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