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 viii
... Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , 128 Volumes of Regular Polyedrons ,. 132 ELEMENTS OF GEOMETRY . INTRODUCTION , 1. QUANTITY is anything viii ...
... Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , 128 Volumes of Regular Polyedrons ,. 132 ELEMENTS OF GEOMETRY . INTRODUCTION , 1. QUANTITY is anything viii ...
Page 179
... pyramid . The triangles taken together make up the lateral or convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges of the pyramid . 9. Pyramids are named from the number of sides of ...
... pyramid . The triangles taken together make up the lateral or convex surface of the pyramid ; the lines in which the lateral faces meet , are called the lateral edges of the pyramid . 9. Pyramids are named from the number of sides of ...
Page 180
... pyramid . 12. The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which cuts the ...
... pyramid . 12. The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which cuts the ...
Page 182
... pyramid be cut by a plane parallel to the base : 1 ° . The 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 ...
... pyramid be cut by a plane parallel to the base : 1 ° . The 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 ...
Page 183
... pyramids S - ABCDE , and S - XYZ , having a common vertex S , and their bases in the same plane , be cut by a plane abc , parallel to the plane of their bases , the sections will be to each other as the bases . For , the polygons abed ...
... pyramids S - ABCDE , and S - XYZ , having a common vertex S , and their bases in the same plane , be cut by a plane abc , parallel to the plane of their bases , the sections will be to each other as the bases . For , the polygons abed ...
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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