Schultze and Sevenoak's Plane and Solid Geometry |
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Page 321
... DIHEDRAL ANGLES 517. If a plane ABC rotates about the line BC until it reaches the position FBC , then the amount of rotation is called a dihedral angle . The line BC is called the edge and the planes ABC and FBC are called the faces of ...
... DIHEDRAL ANGLES 517. If a plane ABC rotates about the line BC until it reaches the position FBC , then the amount of rotation is called a dihedral angle . The line BC is called the edge and the planes ABC and FBC are called the faces of ...
Page 322
... dihedral angle is the angle formed by perpendiculars to the edge at the same point , one in each face . Thus , CDE is a plane angle of dihedral angle AB if CD is perpendicular to AB and ED is per- pendicular to AB . Two plane angles of ...
... dihedral angle is the angle formed by perpendiculars to the edge at the same point , one in each face . Thus , CDE is a plane angle of dihedral angle AB if CD is perpendicular to AB and ED is per- pendicular to AB . Two plane angles of ...
Page 323
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION XV . THEOREM 524. Two dihedral angles are equal if their plane angles are equal . Given the dihedral angles AB and A'B ' with equal plane angles CBD and C'B'D ' respectively . To prove ...
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION XV . THEOREM 524. Two dihedral angles are equal if their plane angles are equal . Given the dihedral angles AB and A'B ' with equal plane angles CBD and C'B'D ' respectively . To prove ...
Page 324
... dihedral angles are equal . HINT . Construct a plane MN1 EB , the inter- section of two planes . PROPOSITION XVI . THEOREM C 526. A dihedral angle is measured by its plane angle . D B Given To prove ABC the plane angle of dihedral △ BD ...
... dihedral angles are equal . HINT . Construct a plane MN1 EB , the inter- section of two planes . PROPOSITION XVI . THEOREM C 526. A dihedral angle is measured by its plane angle . D B Given To prove ABC the plane angle of dihedral △ BD ...
Page 325
... dihedral angles are respectively 30 ° and 40 ° , find the dihedral angle formed by the planes which bisect these dihedral angles . PROPOSITION XVII . THEOREM 527. If a straight line is perpendicular to a plane , every plane passed ...
... dihedral angles are respectively 30 ° and 40 ° , find the dihedral angle formed by the planes which bisect these dihedral angles . PROPOSITION XVII . THEOREM 527. If a straight line is perpendicular to a plane , every plane passed ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.