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 . Т S τ N 2+ K L + G H D a E A C k m d 7 B Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be ...
... pyramids , having equivalent bases and equal altitudes , are equivalent , or equal in solidity . Т S τ N 2+ K L + G H D a E A C k m d 7 B Let S - ABC , S - abc , be those two pyramids ; let their equiva- lent bases ABC , abc , be ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex