Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 8
... 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 , ..... Volume 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 , ..... Volume of the ...
Page 180
... frustum ; the base of the pyramid is cal- led the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a frustum of a right ...
... frustum ; the base of the pyramid is cal- led the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a frustum of a right ...
Page 185
... frustum , as AEea , is a trapezoid , whose altitude is equal to Ff , the slant height of the frustum ; hence , its area is equal to ( B. IV . , P. VII . ) . ( EA + ea ) × Fƒ But the area of the con- E vex surface of the frustum is equal ...
... frustum , as AEea , is a trapezoid , whose altitude is equal to Ff , the slant height of the frustum ; hence , its area is equal to ( B. IV . , P. VII . ) . ( EA + ea ) × Fƒ But the area of the con- E vex surface of the frustum is equal ...
Page 202
... frustum , and whose bases are the lower base of the frustum , the upper base of the frustum , and a mean proportional between the two bases . Let FGH - h be a fi ustum of any triangular pyramid : then will its volume be equal to that of ...
... frustum , and whose bases are the lower base of the frustum , the upper base of the frustum , and a mean proportional between the two bases . Let FGH - h be a fi ustum of any triangular pyramid : then will its volume be equal to that of ...
Page 203
... frustum into three pyramids . The pyra- mid g - FGH , has for its base the lower base FGH of the frustum , and its al- titude is equal to that of the frustum , because its vertex g , is in the plane of the upper base . The pyramid H ...
... frustum into three pyramids . The pyra- mid g - FGH , has for its base the lower base FGH of the frustum , and its al- titude is equal to that of the frustum , because its vertex g , is in the plane of the upper base . The pyramid H ...
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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