Elements of Geometry and Trigonometry |
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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
... parallel hence , the opposite faces are equal , each to each , and their planes are parallel ; which was to be proved . Cor . 1. Any two opposite faces of a parallelopipedon may be taken as bases . Cor . 2. In a rectangular parallelo ...
... parallel hence , the opposite faces are equal , each to each , and their planes are parallel ; which was to be proved . Cor . 1. Any two opposite faces of a parallelopipedon may be taken as bases . Cor . 2. In a rectangular parallelo ...
Page 188
... parallelopipedon . PROPOSITION VII . THEOREM . If a plane be passed through the diagonally opposite edger 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 edger of a parallelopipedon , it will divide the parallelopipedon into two equal triangular prisms . Let ABCD - H be a parallelopipedon ...
Page 189
Adrien Marie Legendre. because their opposite sides are parallel , each to each ( B. VI . , P. X. ) ; they will also be ... parallelopipedon AG , which has the same triedral angle A , and the same edges AB , AD , and AE PROPOSITION VIII ...
Adrien Marie Legendre. because their opposite sides are parallel , each to each ( B. VI . , P. X. ) ; they will also be ... 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
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence