Solid GeometryAmerican Book Company, 1912 - 188 Seiten |
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12 inches altitude by H axis circle circular sector circumference circumscribed common limit cube diagonals dihedral angles equal spheres equidistant face angles feet Find the area Find the locus Find the radius Find the total Find the volume frustum given plane given point HINT inscribed intersecting planes isosceles lateral area lateral edges lune number of sides oblique OUTLINE OF PROOF parallel planes parallelogram perimeter perpendicular Plane Geometry plane MN plane parallel points in space polyhedral angle polyhedron EC 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 317 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
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 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 387 - Every section of a cylinder made by a plane passing through an element is a parallelogram.
Seite 361 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Seite 321 - The acute angle that a straight line makes with its own projection upon a plane is the least angle that it makes with any line passing through its foot in the plane.
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 316 - Two lines perpendicular to the same plane are parallel. 6. If two lines are parallel, every plane containing one of the lines and only one is parallel to the other.
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 365 - ... the edge of a cube whose volume is double that of a given cube.