Elements of Geometry and Trigonometry |
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Page 143
... pyramid , the point S the vertex ; and the triangles ASB , BSC , CSD , & c . form its convex or lateral sur- face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the remaining ...
... pyramid , the point S the vertex ; and the triangles ASB , BSC , CSD , & c . form its convex or lateral sur- face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the remaining ...
Page 145
... 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 , be cut ...
... 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 , be cut ...
Page 146
... pyramid is equal to the perime- ter of its base multiplied by half the slant height . For , since the pyramid is regular , the point O , in which the axis meets the base , is the centre of the polygon ABCDE ( Def . 14. ) ; hence the ...
... pyramid is equal to the perime- ter of its base multiplied by half the slant height . For , since the pyramid is regular , the point O , in which the axis meets the base , is the centre of the polygon ABCDE ( Def . 14. ) ; hence the ...
Page 147
... 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 the slant height . Cor . The convex surface of the frustum of a regular pyra- mid is equal ...
... 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 the slant height . Cor . The convex surface of the frustum of a regular pyra- mid is equal ...
Page 158
... pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . T K G at x + D A m Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be situated in the same plane ...
... pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . T K G at x + D A m Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be situated in the same plane ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex