Elements of Geometry and Trigonometry |
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Page 51
If we suppose AB - DE , the angle ACB will be equal to DCE . For , if these angles are not equal , suppose ACB to be the greater , and let ACI be taken equal to DCE . From what has just been shown , we shall have AI - DE : but ...
If we suppose AB - DE , the angle ACB will be equal to DCE . For , if these angles are not equal , suppose ACB to be the greater , and let ACI be taken equal to DCE . From what has just been shown , we shall have AI - DE : but ...
Page 52
Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained times in the angle ACB , and 4 times in ...
Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained times in the angle ACB , and 4 times in ...
Page 54
Let BAD be an inscribed angle , and let us first suppose that the centre of the circle lies within the angle BAD . Draw the diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum ...
Let BAD be an inscribed angle , and let us first suppose that the centre of the circle lies within the angle BAD . Draw the diameter AE , and the radii CB , CD . E The angle BCE , being exterior to the triangle ABC , is equal to the sum ...
Page 63
Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC , or suppose them to be drawn ; bisect those two lines by the perpendiculars DE , FG : the point O , where these perpendiculars meet , will be ...
Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC , or suppose them to be drawn ; bisect those two lines by the perpendiculars DE , FG : the point O , where these perpendiculars meet , will be ...
Page 66
Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall have FD = 2 : but EB contains FD once , plus GB ; therefore we have EB = 3 : CD ...
Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines . Put BG = 1 ; we shall have FD = 2 : but EB contains FD once , plus GB ; therefore we have EB = 3 : CD ...
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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 |