Solid Geometry, with Problems and Applications |
Other editions - View all
Common terms and phrases
ABCD altitude angles are equal arcs B₁ base center of similitude circle 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 given point 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 polyhedrons 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 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 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 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 191 - ... which is the ratio of the circumference to the diameter of a circle.
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...
Page 7 - Two right triangles are equal if the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an acute angle of the other.
Page 66 - The volume of a triangular prism is equal to the product of its base by its altitude. A~ Let V denote the volume, B the base, and H the altitude of the triangular prism CEA-E'.
Page 120 - B' S' C,' C S' A' and the dicdral angles .S" A, SB, SC to the diedral angles 5" A,' S' B,' S' C.' Symmetrical spherical triangles arc those in which the sides and angles of the one are equal respectively to the sides and angles of the other, but arranged in the reverse order. Thus the spherical triangles ABC and A' B' C