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A-BCD adjacent altitude axis B₁ b₂ centre circle arc circumscribed coincide conical surface convex COROLLARY cube cuboid cuts the plane cutting plane cylindrical surface DEFINITION diagonal diameter dihedral angle distance element equal respectively equally distant equivalent face angles figure find the volume four right angles frustum hedron hence homologous lines icosahedron inscribed lateral edges lateral faces lateral surface length line of intersection lower base lune whose angle mid-section nappe octahedron opposite edges parallel planes parallelepiped parallelogram perpendicular plane angle plane geometry plane meet plane section plane ẞ pole polyhedral angle prismatoid quadrants radius rectangle regular dodecahedron regular octahedron regular polyhedrons regular tetrahedron right circular cone right prism right section set of prisms slant height solid sphere spherical excess spherical polygon spherical triangle square straight line surface and volume THEOREM three sides trihedral truncated upper base V₂ vertex vertices
Page 78 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 109 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 47 - Find a point in a given straight line such that the sums of its distances from two given points (not in the same plane with the given straight line) may be the least possible.
Page 139 - If two triangles have two angles, and the included side of the one equal to two angles and the included side of the other, each to each, the two triangles will be equal...
Page 139 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...