Elements of Geometry |
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Page 147
... frustum which remains , after taking away the smaller pyramid , is equal to the sum of three pyramids , which have for their com- mon altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its ...
... frustum which remains , after taking away the smaller pyramid , is equal to the sum of three pyramids , which have for their com- mon altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its ...
Page 148
... frustum of a triangular pyramid . Let FGH - hfg ( fig . 218 ) , be the frustum of a triangular pyra- mid ; through the points F , g , H , suppose a plane Fg H to pass , cutting off from the frustum the triangular pyramid g - FGH . This ...
... frustum of a triangular pyramid . Let FGH - hfg ( fig . 218 ) , be the frustum of a triangular pyra- mid ; through the points F , g , H , suppose a plane Fg H to pass , cutting off from the frustum the triangular pyramid g - FGH . This ...
Page 149
... frustum of a triangular pyramid is equal to three pyramids , which have for their common altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional be- tween ...
... frustum of a triangular pyramid is equal to three pyramids , which have for their common altitude the altitude of the frustum , and whose bases are the inferior base of the frustum , its superior base , and a mean proportional be- tween ...
Page 156
... frustum of a pyramid , and let A , B , be the bases ; then AB will be the mean proportion between them , and the solidity of the frustum will be + H × ( A + B + √AB ) . Let B be the base of a truncated triangular prism , H , H ' , H ...
... frustum of a pyramid , and let A , B , be the bases ; then AB will be the mean proportion between them , and the solidity of the frustum will be + H × ( A + B + √AB ) . Let B be the base of a truncated triangular prism , H , H ' , H ...
Page 177
... frustum of a cone . It may be conceived to be generated by the revolution of the trapezoid ABHG , of which the angles A and Gare right angles , about the side AG . The fixed line AG is called the axis or altitude of the frustum , the ...
... frustum of a cone . It may be conceived to be generated by the revolution of the trapezoid ABHG , of which the angles A and Gare right angles , about the side AG . The fixed line AG is called the axis or altitude of the frustum , the ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition pyramid S-ABC radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence