Solid GeometryC.E. Merrill Company, 1911 |
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Common terms and phrases
ABCD ABCDF altitude angles are equal axis bisects chord circle circular cone circumference circumscribed coincide cone of revolution conical surface construct cube cylinder of revolution diagonal diameter dihedral angle draw equidistant equivalent face angles Find the area Find the locus Find the radius Find the volume formula frustum geometry given line given point Hence homologous inscribed isosceles lateral area lateral edges lateral faces lateral surface line perpendicular lune parallel planes parallelogram pass a plane perimeter perpendicular plane MN plane parallel plane PQ polar triangle polyhedral angle prismatoid Proof prove quadrilateral radii rectangle rectangular parallelopiped regular polygon regular polyhedron regular pyramid regular square pyramid right angles right prism sides similar slant height spherical angle spherical excess spherical polygon spherical triangle straight line symmetrical tangent THEOREM triangular prism triangular pyramid trihedral vertex vertices zone
Popular passages
Page 495 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.
Page 495 - Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other...
Page 353 - The sum of the face angles of any convex polyhedral angle is less than four right angles.
Page 416 - Every section of a circular cone made by a plane parallel to the base is a circle. Let the section abcd of the circular cone S-ABCD be parallel to the base. To prove that abcd is a circle.
Page 421 - The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. Let V denote the volume, B the lewer base, b the upper base, H the altitude of a frustum of a circular cone.
Page 420 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 400 - Every section of a prism made by a plane parallel to a lateral edge is a parallelogram.
Page 315 - If two triangles have an angle of one equal to an angle of the other, and...
Page 419 - The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 311 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.