## Solid Geometry |

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### Common terms and phrases

ABCD altitude approaches arranged axis base called circle circular cylinder circumscribed coincide common congruent Construct COROLLARY corresponding cube cylinder determine diagonal diameter dihedral angle dimensions distance divided Draw drawn edges element equal equidistant EXERCISES face angles faces figure Find formed formula four frustum geometry given line given point greater half Hence included inscribed intersection joining lateral area lateral edges lateral faces length lies limit locus measured meet opposite parallel lines parallelepiped parallelogram passed perpendicular placed plane plane geometry polar pole polyhedral angle polyhedron prism projection Proof PROPOSITION prove pyramid radii radius ratio rays rectangular regular respectively revolves right circular cone segment Show sides similar slant height solid space sphere spherical polygon spherical triangle square straight line surface symmetric tangent tetrahedron THEOREM third triangular trihedral values vertex vertices volume

### Popular passages

Page 439 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.

Page 439 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 319 - ... the third side of the first is greater than the third side of the second.

Page 362 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.

Page 495 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.

Page 322 - If two triangles have an angle of one equal to an angle of the other, and...

Page 479 - If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles; P and Q their polar triangles. Since the angles are equal in the triangles A and B, the sides will be equal in.

Page 361 - If two planes are perpendicular to each other, a line drawn in one of them perpendicular to their intersection is perpendicular to the other.

Page 338 - The sum of the face angles of any polyhedron is equal to four right angles taken as many times, less two, as the polyhedron has vertices.

Page 480 - 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...