Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 8
... Pyramid , Area of the Frustum of a Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , Volume of a Prism , .... PAGE . 120 120 121 ... 122 122 123 124 124 125 .... 126 127 128 132 Volume of a Pyramid ...
... Pyramid , Area of the Frustum of a Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , Volume of a Prism , .... PAGE . 120 120 121 ... 122 122 123 124 124 125 .... 126 127 128 132 Volume of a Pyramid ...
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 : 1o . The edges and the altitude will be divided proportionally : 2 ° . 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 : 1o . The edges and the altitude will be divided proportionally : 2 ° . 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 - XY2 , 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 abcd ...
... pyramids S - ABCDE , and S - XY2 , 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 abcd ...
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Common terms and phrases
AB² 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