Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 20
Page viii
... Frustum of a Cone , Area of the Surface of a Sphere , 121 122 Area of a Zone , 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 , 126 ...
... Frustum of a Cone , Area of the Surface of a Sphere , 121 122 Area of a Zone , 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 , 126 ...
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 · E ( EA + ea ) × Fƒ F B area of the con- ( B. IV . , P. VII . ) . But the vex surface of the frustum is ...
... frustum , as AEea , is a trapezoid , whose altitude is equal to Ff , the slant height of the frustum ; hence , its area is equal to · E ( EA + ea ) × Fƒ F B area of the con- ( B. IV . , P. VII . ) . But the vex surface of the frustum is ...
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 frustum 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 frustum 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 ...
Other editions - View all
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