Elements of Geometry and Trigonometry |
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Page 143
A pyramid is a solid formed by several triangular planes proceeding from the same point S , and terminating in the different sides of the same polygon ABCDE . The polygon ABCDE is called the base of the pyramid , the point S the vertex ...
A pyramid is a solid formed by several triangular planes proceeding from the same point S , and terminating in the different sides of the same polygon ABCDE . The polygon ABCDE is called the base of the pyramid , the point S the vertex ...
Page 145
If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . 2d . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , of which SO is the altitude ...
If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . 2d . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , of which SO is the altitude ...
Page 146
Let S - ABCDE , S S - XYZ be two pyramids , hav - b ing a common vertex and the apt to same altitude , or having their bases situated in the same plane ; if these pyramids are cut by a plane parallel to the plane of their bases , giving ...
Let S - ABCDE , S S - XYZ be two pyramids , hav - b ing a common vertex and the apt to same altitude , or having their bases situated in the same plane ; if these pyramids are cut by a plane parallel to the plane of their bases , giving ...
Page 147
to its base EA multiplied by half the perpendicular SF , which is the slant height of the pyramid : hence the area of all the tri- angles , or the convex surface of the pyramid , is equal to the perimeter of the base multiplied by half ...
to its base EA multiplied by half the perpendicular SF , which is the slant height of the pyramid : hence the area of all the tri- angles , or the convex surface of the pyramid , is equal to the perimeter of the base multiplied by half ...
Page 158
Two triangular pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . 72+ 2 . D H m B Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be situated in the ...
Two triangular pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . 72+ 2 . D H m B Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be situated in the ...
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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 |