Solid Geometry, with Problems and Applications |
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ABCD altitude angles are equal arcs b₁ base center of similitude circle circumscribed prisms convex COROLLARY corresponding cosine cube decreasing sequence defined definite diameter dihedral angle distance element equal respectively equidistant face angles figure Find the area Find the locus Find the ratio Find the volume frustum given plane Hence inches incommensurable inscribed intersection l₁ lateral area lateral surface length limit line-segment meet number of sides parallel planes perimeter plane geometry plane parallel plane perpendicular plane-segment polar triangle polyhedral angle Proof prove radii radius rectangle rectangular parallelopiped regular polyhedrons regular pyramid right angles right circular cone right circular cylinder right section right triangle segment Show similar tetrahedrons skew lines slant height solid geometry sphere spherical angle spherical cone spherical excess spherical polygon spherical triangle square straight line Suggestion T₁ tangent THEOREM triangular trihedral variable 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 44 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 33 - Theorem. 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 191 - ... which is the ratio of the circumference to the diameter of a circle.
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 5 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 199 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
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.
Page 74 - The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Given L the lateral area, P...