Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 190
... PARALLELOPIPEDON is a prism whose bases are parallelograms . A Right Parallelopipedon is one whose lateral edges are perpendicular to the planes of the bases . A Rectangular Parallelopipedon is one whose faces are all rectangles . A ...
... PARALLELOPIPEDON is a prism whose bases are parallelograms . A Right Parallelopipedon is one whose lateral edges are perpendicular to the planes of the bases . A Rectangular Parallelopipedon is one whose faces are all rectangles . A ...
Page 197
... of the one , are equal in all respects to the faces which include the corresponding triedral angle of the other , each to each , and they are similarly placed . PROPOSITION VI . THEOREM . In any parallelopipedon , the BOOK VII . 197.
... of the one , are equal in all respects to the faces which include the corresponding triedral angle of the other , each to each , and they are similarly placed . PROPOSITION VI . THEOREM . In any parallelopipedon , the BOOK VII . 197.
Page 198
... parallelopipedon , the opposite faces are equal in all respects , each to each , and their planes are parallel . Let ABCD - H be a parallelopipedon : then its opposite faces are equal and their planes are parallel . For , the bases ...
... parallelopipedon , the opposite faces are equal in all respects , each to each , and their planes are parallel . Let ABCD - H be a parallelopipedon : then its opposite faces are equal and their planes are parallel . For , the bases ...
Page 199
... parallelopipedon , it divides the parallelopipedon into two equal triangular prisms . Let ABCD - H be a parallelopipedon , and let a plane be passed through the edges BF and DH ; then are the prisms ABD - H and BCD - H equal in volume ...
... parallelopipedon , it divides the parallelopipedon into two equal triangular prisms . Let ABCD - H be a parallelopipedon , and let a plane be passed through the edges BF and DH ; then are the prisms ABD - H and BCD - H equal in volume ...
Page 200
... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a 200 GEOMETRY .
... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a 200 GEOMETRY .
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence