Solid GeometryAmerican Book Company, 1912 - 188 Seiten |
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12 inches altitude altitude by H axis circle circular sector circumference circumscribed common limit cube diagonals dihedral angle equal spheres equidistant face angles feet Find the area Find the locus Find the radius Find the volume frustum given plane given point HINT inscribed isosceles lateral area lateral edges lateral faces lune number of sides oblique OUTLINE OF PROOF parallel planes parallelogram perimeter perpendicular Plane Geometry plane parallel points in space polyhedral angle polyhedron EC prismatic surface prismatoid proof is left PROPOSITION prove radii ratio rectangle rectangular parallelopiped regular polygon regular pyramid revolving right circular cone right circular cylinder slant height spherical angle spherical degrees spherical polygon spherical sector spherical triangle square inches square pyramid straight line student surface tangent tetrahedron THEOREM total area triangular prism triangular pyramid trihedral vertex vertices volume denoted zone
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Seite 455 - 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...
Seite 366 - 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
Seite 355 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...
Seite 399 - A pyramid is inscribed in a cone when its base is inscribed in the base of the cone and its vertex coincides with the vertex of the cone.
Seite 337 - If two face angles and the included dihedral angle of the one are respectively equal to two face angles and the included dihedral angle of the other...
Seite 397 - The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Hyp. S is the lateral area, P the perimeter of a right .section, and E an element of the cylinder AK; S...
Seite 296 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Seite 314 - If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line. Let...
Seite 365 - ... the edge of a cube whose volume is double that of a given cube...
Seite 315 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel.