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altitude APPLICATIONS approximate arcs base Book called circle circumscribed coincide common computed construct contains COROLLARY corresponding cube cylinder defined definite determined diameter difference dihedral angles distance draw edges element equal equidistant EXERCISES face angles figure Find Find the volume fixed follows formed four frustum geometry given line greater Hence inches increasing inscribed intersection lateral area length less limit measure meet oblique opposite parallel parallel planes parallelopiped pass perimeter perpendicular placed plane plane geometry polar triangle pole polyhedral angle polyhedrons prism PROBLEM projection Proof prove pyramid radius ratio rectangular regular relation respectively right angles right circular cone right section segment sequence Show sides SIGHT similar similitude slant height sphere spherical triangle square straight line Suggestion surface symmetrical tangent tetrahedron THEOREM third triangular trihedral unit vertex vertices volume
Σελίδα 45 - The sum of the face angles of any convex polyhedral angle is less than four right angles.
Σελίδα 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.
Σελίδα 105 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 191 - ... which is the ratio of the circumference to the diameter of a circle.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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'.
Σελίδα 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