Elements of Geometry and Trigonometry |
From inside the book
Page 21
For , if these sites are not equal , suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ...
For , if these sites are not equal , suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ...
Page 22
A Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and Ddraw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and .
A Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and Ddraw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and .
Page 23
Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side AB is common , and the angle CBA - ABE ; hence the sides AC and AE are equal ( Prop . V. Cor . ) ...
Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side AB is common , and the angle CBA - ABE ; hence the sides AC and AE are equal ( Prop . V. Cor . ) ...
Page 24
Now , if it be possible , suppose these two sides to be unequal , and that BC is the greater . D CE On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side ...
Now , if it be possible , suppose these two sides to be unequal , and that BC is the greater . D CE On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side ...
Page 47
Suppose the chord AB = DE . Bisect these chords by the perpendiculars CF , CG , and draw the radii CA , CD . M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB ...
Suppose the chord AB = DE . Bisect these chords by the perpendiculars CF , CG , and draw the radii CA , CD . M D A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB ...
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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 |