The Elements of Solid Geometry
University Press, 1905 - Geometry, Solid - 122 pages
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ABCD altitude axis base bisect called centre circle circumscribed common section concurrent cone containing corresponding cube cylinder diagonals diameter dicular dihedral angle distance divided draw drawn equal equidistant EXERCISES faces figure find the volume fixed point formed four frustum given given plane greater height inscribed intersect lateral surface length less lies line joining meet middle points opposite edges pair of opposite parallel planes parallelepiped parallelogram perpen perpendicular to BC plane angles plane parallel plane passing plane perpendicular pole polygon polyhedra polyhedron portion prism produced PROP prove pyramid radii radius rectangle respectively revolves right angles segment sides similar Similarly sphere spherical triangle square straight line tangent-lines tetrahedron three planes touch traces triangle ABC trihedral vertex vertices volume
Page 82 - A Cone is a solid figure, described by the revolution of a right.angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 77 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Page 118 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.
Page 116 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 10 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 57 - COR. The lateral area of a frustum of a regular pyramid is equal to one-half the sum of the perimeters of the bases multiplied by the slant height.
Page 26 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.
Page 20 - Straight lines which are parallel to the same straight line are parallel to one another.
Page 110 - The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them.
Page 53 - In any quadrilateral the squares on the diagonals are together equal to twice the sum of the squares on the straight lines joining the middle points of opposite sides.