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 , ... 184 134 135 Area of the Surface of a Sphere ,. 136 Area of a Zone , 137 Area of a Spherical Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid , ........ 189 Volume of the Frustum of a Pyramid , 139 ...
... Frustum of a Cone , ... 184 134 135 Area of the Surface of a Sphere ,. 136 Area of a Zone , 137 Area of a Spherical Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid , ........ 189 Volume of the Frustum of a Pyramid , 139 ...
Page 191
... frustum ; the base of the pyramid is called the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the perpendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a frustum of a right pyra ...
... frustum ; the base of the pyramid is called the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the perpendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a frustum of a right pyra ...
Page 196
... 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 the section abcde is similar ...
... 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 the section abcde is similar ...
Page 213
... 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 is its volume equal to that of three ...
... 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 is its volume equal to that of three ...
Page 214
... frustum into three pyramids . The pyra- mid g - FGH , has for its base the lower base FGH of the frustum , and its alti- tude is equal to that of the frustum , because its vertex g is in the plane of the 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 alti- tude is equal to that of the frustum , because its vertex g is in the plane of the upper base . The pyramid H - fgh ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence