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 179
... Parallelopipedon is a right parallelopipedon , all of whose faces are rect- angles ; a cube is a rectangular parallelo- pipedon , all of whose faces are squares . 8. A PYRAMID is a polyedron bounded by a polygon called the base , and by ...
... Parallelopipedon is a right parallelopipedon , all of whose faces are rect- angles ; a cube is a rectangular parallelo- pipedon , all of whose faces are squares . 8. A PYRAMID is a polyedron bounded by a polygon called the base , and by ...
Page 186
... angle of the one , will be equal to the faces which include the corresponding triedral angle of the other , each to each , and they will be similarly placed . PROPOSITION VI . THEOREM . In any parallelopipedon , the 186 GEOMETRY .
... angle of the one , will be equal to the faces which include the corresponding triedral angle of the other , each to each , and they will be similarly placed . PROPOSITION VI . THEOREM . In any parallelopipedon , the 186 GEOMETRY .
Page 187
... parallelopipedon , the opposite faces are equal , each to each , and their planes are parallel . A E H G B Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For , the bases ...
... parallelopipedon , the opposite faces are equal , each to each , and their planes are parallel . A E H G B Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For , the bases ...
Page 188
... parallelopipedon . PROPOSITION VII . THEOREM . If a plane be passed through the diagonally opposite edges of a parallelopipedon , it will divide the parallelopipedon into two equal triangular prisms . Let ABCD - H be a parallelopipedon ...
... parallelopipedon . PROPOSITION VII . THEOREM . If a plane be passed through the diagonally opposite edges of a parallelopipedon , it will divide the parallelopipedon into two equal triangular prisms . Let ABCD - H be a parallelopipedon ...
Page 189
... parallel , each to each ( B. VI . , P. X. ) ; they will also be equal ( P. II . ) : edron Bade - g is a right prism ( D ... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE PROPOSITION VIII ...
... parallel , each to each ( B. VI . , P. X. ) ; they will also be equal ( P. II . ) : edron Bade - g is a right prism ( D ... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE PROPOSITION VIII ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence