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 one whose faces are all rectangles . A Cube is a rectangular parallelopipedon whose faces are squares . 8. A PYRAMID is a polyedron bounded by a polygon called the base , and by tri- angles meeting at a common point ...
... Parallelopipedon is one whose faces are all rectangles . A Cube is a rectangular parallelopipedon whose faces are squares . 8. A PYRAMID is a polyedron bounded by a polygon called the base , and by tri- angles meeting at a common point ...
Page 186
... , will be equal in all their parts 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 .
... , will be equal in all their parts 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 in all their parts , each to each , and their planes are parallel . E G Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For ...
... parallelopipedon , the opposite faces are equal in all their parts , each to each , and their planes are parallel . E G Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For ...
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 Badc - g is a right prism ... 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 Badc - g is a right prism ... 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 adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence