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 . E S B C 12. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced if necessary .
... the remaining solid ABCDE - d , is called a truncated pyramid , or the frustum of a pyramid . E S B C 12. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced if necessary .
Page 147
The convex surface of the frustum of a regular pyra- mid 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 pyra- mid 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 equi- valent 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 equi- valent 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 rea- son ; 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 rea- son ; 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 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 this is a mean proportional between the bases FGH and fgh .
But 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 this is a mean proportional between the bases FGH and fgh .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |