Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 . BE ; A E H G D B Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For , the ...
... parallelopipedon , the opposite faces are equal , each to each , and their planes are parallel . BE ; A E H G D B Let ABCD - H be a parallelopipedon : then will its opposite faces be equal and their planes will be parallel . For , the ...
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
From the Works of A. M. Legendre Adrien Marie Legendre. because their opposite sides are parallel , each to each ( B ... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE . PROPOSITION VIII ...
From the Works of A. M. Legendre Adrien Marie Legendre. because their opposite sides are parallel , each to each ( B ... 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following