Elements of Geometry and Trigonometry |
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Page 143
... the remaining solid ABCDE - d , is called a truncated pyramid , or the frustum of a pyramid . A B 12. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced if necessary . 13.
... the remaining solid ABCDE - d , is called a truncated pyramid , or the frustum of a pyramid . A B 12. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced if necessary . 13.
Page 147
The convex surface of the frustum of a regular pyramid is equal to half the perimeters of its upper and lower bases multiplied by its slant height . For , since the section abcde is similar to the base ( Prop . III . ) ...
The convex surface of the frustum of a regular pyramid is equal to half the perimeters of its upper and lower bases multiplied by its slant height . For , since the section abcde is similar to the base ( Prop . III . ) ...
Page 161
If a pyramid be cut by a plane parallel to its base , the frustum that remains when the small pyramid is taken away , is equivalent to the sum of three pyramids having for their common altitude the altitude of the frustum , and for ...
If a pyramid be cut by a plane parallel to its base , the frustum that remains when the small pyramid is taken away , is equivalent to the sum of three pyramids having for their common altitude the altitude of the frustum , and for ...
Page 162
The whole pyramids S - ABCDE , T - FGH are equivalent for the same reason ; hence the frustums ABD - dab , FGH - hfg are equivalent ; hence if the proposition can be proved in the single case of the frustum of a triangular pyramid ...
The whole pyramids S - ABCDE , T - FGH are equivalent for the same reason ; hence the frustums ABD - dab , FGH - hfg are equivalent ; hence if the proposition can be proved in the single case of the frustum of a triangular pyramid ...
Page 163
But plane of the base : hence these pyramids are equivalent . the pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the frustum : as to its base FKH , we are now to show that ...
But plane of the base : hence these pyramids are equivalent . the pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the frustum : as to its base FKH , we are now to show that ...
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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 |