## Solid Geometry, with Problems and Applications |

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altitude APPLICATIONS approximate arcs base called center of similitude circle circumscribed coincide common Compare computed construct contains COROLLARY corresponding cube cylinder defined definite determined diameter difference dihedral angles dimensions distance draw edges element equal EXERCISES face angles figure Find Find the volume fixed follows formed four frustum geometry Give given line greater Hence inches increasing inscribed intersection lateral area length less limit line-segment measure meet oblique opposite parallel parallel planes parallelopiped pass perimeter perpendicular placed plane plane geometry plane parallel pole polyhedral angle polyhedrons prism PROBLEM projection Proof prove pyramid radius ratio rectangular regular relation respectively right circular cone right section segment sequence Show sides SIGHT similar slant height sphere spherical triangle square straight line Suggestion surface symmetrical tangent tetrahedrons THEOREM third trihedral unit vertex vertices volume

### 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