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
... Frustum of a Cone , 121 Area of the Surface of a Sphere , 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 , 121 Area of the Surface of a Sphere , 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 call- ed 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 call- ed 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 of a right pyramid is equal to half the sum of the perimeters of its upper and lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then will the section abcde be ...
... frustum of a right pyramid is equal to half the sum of the perimeters of its upper and lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then will the section abcde be ...
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- itude is equal to that of the frustum , because its vertex g , is in the plane of he upper base . The pyramid H - fgh ...
... frustum into three pyramids . The pyra- mid g - FGH , has for its base the lower base FGH of the frustum , and its al- itude is equal to that of the frustum , because its vertex g , is in the plane of he upper base . The pyramid H - fgh ...
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Common terms and phrases
ABē ACē 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence