Elements of Geometry and Trigonometry |
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Page 142
The prism is a solid bounded by several parallelograms , which are terminated at both ends by equal and parallel polygons . f B C To construct this solid , let ABCDE be any polygon ; then if in a plane parallel to ABCDE , the lines FG ...
The prism is a solid bounded by several parallelograms , which are terminated at both ends by equal and parallel polygons . f B C To construct this solid , let ABCDE be any polygon ; then if in a plane parallel to ABCDE , the lines FG ...
Page 143
A prism is right , when the sides AF , BG , CH , & c . are perpendicular to the planes of the bases ; and then each of them is equal to the altitude of the prism . In every other case the prism is oblique , and the altitude less than ...
A prism is right , when the sides AF , BG , CH , & c . are perpendicular to the planes of the bases ; and then each of them is equal to the altitude of the prism . In every other case the prism is oblique , and the altitude less than ...
Page 144
The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude . Let ABCDE - K be a right prism : then will its convex surface be equal to ( AB + BC + CD + DE + EA ) × AF .
The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude . Let ABCDE - K be a right prism : then will its convex surface be equal to ( AB + BC + CD + DE + EA ) × AF .
Page 145
Every section in a prism , if drawn parallel to the base , is also equal to the base . PROPOSITION III . THEOREM . If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally .
Every section in a prism , if drawn parallel to the base , is also equal to the base . PROPOSITION III . THEOREM . If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally .
Page 146
The triangles , therefore , which E form the convex surface of the prism are all equal to each other . But the area of either of these triangles , as ESA , is equal F B C to its base EA multiplied by half the perpendicular SF 146 ...
The triangles , therefore , which E form the convex surface of the prism are all equal to each other . But the area of either of these triangles , as ESA , is equal F B C to its base EA multiplied by half the perpendicular SF 146 ...
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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 |