Elements of Geometry and Trigonometry |
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Page 8
... Frustum of a Cone , Arca of the Surface of a Sphere , Area of a Zone , 121 122 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 ...... Volume of the Frustum of a Pyramid , 125 Volume of a Sphere ...
... Frustum of a Cone , Arca of the Surface of a Sphere , Area of a Zone , 121 122 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 ...... Volume of the Frustum of a Pyramid , 125 Volume of a Sphere ...
Page 180
... FRUSTUM OF A PYRAMID , and the inter- section of the cutting plane with the pyramid , is called the upper base of the frustum ; the base of the pyramid is call- ed the lower base of the frustum . 14. The ALTITUDE of a frustum of a ...
... FRUSTUM OF A PYRAMID , and the inter- section of the cutting plane with the pyramid , is called the upper base of the frustum ; the base of the pyramid is call- ed the lower base of the frustum . 14. The ALTITUDE of a frustum of a ...
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 ( EA + ea ) × Fƒ ( B. IV . , P. VII . ) . But the area of the con- 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 ( EA + ea ) × Fƒ ( B. IV . , P. VII . ) . But the area of the con- 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 FGI - 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 FGI - 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
ABCD AC² 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