Elements of Geometry and Trigonometry |
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Page 32
Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . In every parallelogram , the opposite sides and angles are equal . Let ABCD be a parallelogram : then will AB = DC ...
Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . In every parallelogram , the opposite sides and angles are equal . Let ABCD be a parallelogram : then will AB = DC ...
Page 35
If there be four magnitudes A , B , C , and D , having such B. D values that is equal to- then A is said to have the same ratio A to B , that C has to D , or the ratio of A to B is equal to the ratio of C to D. When four quantities have ...
If there be four magnitudes A , B , C , and D , having such B. D values that is equal to- then A is said to have the same ratio A to B , that C has to D , or the ratio of A to B is equal to the ratio of C to D. When four quantities have ...
Page 36
When four quantities are in proportion , the product of the two extremes is equal to the product of the two means X Let A , B , C , D , be four quantities in proportion , and M : N :: P : Q be their numerical representatives ; then will ...
When four quantities are in proportion , the product of the two extremes is equal to the product of the two means X Let A , B , C , D , be four quantities in proportion , and M : N :: P : Q be their numerical representatives ; then will ...
Page 37
Let and then will For , by alternation If there be four proportional quantities , and four other proportional quantities , having the antecedents the same in both , the consequents will be proportional . and M : N :: P : Q M : R :: P ...
Let and then will For , by alternation If there be four proportional quantities , and four other proportional quantities , having the antecedents the same in both , the consequents will be proportional . and M : N :: P : Q M : R :: P ...
Page 38
Let , as before , M , N , P , Q , be the numerical representatives of the four quantities , so that M : N :: P : Q ; then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or Nx P = M × Q ; Add each of ...
Let , as before , M , N , P , Q , be the numerical representatives of the four quantities , so that M : N :: P : Q ; then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or Nx P = M × Q ; Add each of ...
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |