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 178
... edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its bases . 4. A RIGHT PRISM is one whose lateral edges are perpendicular to the planes of the bases , In this case , any lateral edge ...
... edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its bases . 4. A RIGHT PRISM is one whose lateral edges are perpendicular to the planes of the bases , In this case , any lateral edge ...
Page 179
... edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases are triangles ; a ...
... edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases are triangles ; a ...
Page 180
... edges , or angles , are called homologous . 17. A DIAGONAL of a polyedron , is a straight line join- ing the vertices of two polyedral angles not in the same face . 18. The VOLUME OF A POLYEDRON is its numerical value 180 GEOMETRY .
... edges , or angles , are called homologous . 17. A DIAGONAL of a polyedron , is a straight line join- ing the vertices of two polyedral angles not in the same face . 18. The VOLUME OF A POLYEDRON is its numerical value 180 GEOMETRY .
Page 181
... edge . PROPOSITION . I. THEOREM . The convex surface of a right prism is equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its conver surface equal to , ( AB + BC + CD + DE + EA ) ...
... edge . PROPOSITION . I. THEOREM . The convex surface of a right prism is equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its conver surface equal to , ( AB + BC + CD + DE + EA ) ...
Page 182
... edges and the altitude will be divided proportionally : 2o . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , whose altitude is So , be cut by the plane abcde , parallel to the base ABCDE 1o . The edges ...
... edges and the altitude will be divided proportionally : 2o . The section will be a polygon similar to the base . Let the pyramid S - ABCDE , whose altitude is So , be cut by the plane abcde , parallel to the base ABCDE 1o . The edges ...
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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