Solid Geometry, with Problems and Applications |
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ABCD altitude angles are equal arcs axis b₁ center of similitude circle construct a plane COROLLARY corresponding cube diameter dihedral angles element equal respectively equidistant face angles figure Find the area Find the locus Find the ratio Find the volume frustum given line given point Hence inches incommensurable inscribed intersecting planes l₁ lateral area lateral edge lateral surface length limit line perpendicular line-segment meet parallel planes parallelogram perimeter plane angle plane geometry plane parallel plane-segment polar triangle pole polyhedral angle projection Proof prove radii rectangular parallelopiped regular polyhedrons regular pyramid right angles right circular cone right circular cylinder right prism right section segment sequence Show SIGHT skew lines slant height solid geometry spherical angle spherical cone spherical excess spherical polygon spherical triangle square straight line Suggestion T₁ tangent tetrahedron THEOREM triangles are equal trihedral vertex vertices
Popular passages
Page 6 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Page 45 - The sum of the face angles of any convex polyhedral angle is less than four right angles.
Page 199 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 44 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 65 - The volume of any parallelopiped is equal to the product of its base and altitude. Given any parallelopiped P with area of base b and altitude h.
Page 33 - The acute angle which a line makes with its own projection on a plane is the least angle which it makes with any line in that plane. Given the line AB, cutting plane P at 0, A'B' the projection of AB on P, and XX' any other line in P, through 0.
Page 33 - The projection of a straight line on a plane is a straight line in that plane.
Page 105 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 17 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular...
Page 6 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.