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 213
... cone , whose bases are ECDB and FKH , whose altitude is AG , and whose slant height is BH . F H K E A B 7. SIMILAR ... cone , when its base is inscribed in the base of the cone , and when its vertex coincides with that of the cone . The ...
... cone , whose bases are ECDB and FKH , whose altitude is AG , and whose slant height is BH . F H K E A B 7. SIMILAR ... cone , when its base is inscribed in the base of the cone , and when its vertex coincides with that of the cone . The ...
Page 214
... cone , when its bases are inscribed in the bases of the frustum of the cone . The lateral edges of the inscribed frustum of a pyramid are elements of the surface of the circumscribing frustum of a cone . 11. A frustum of a pyramid is ...
... cone , when its bases are inscribed in the bases of the frustum of the cone . The lateral edges of the inscribed frustum of a pyramid are elements of the surface of the circumscribing frustum of a cone . 11. A frustum of a pyramid is ...
Page 215
... CONE , and the SPHERE , are sometimes called THE THREE ROUND BODIES . PROPOSITION I. THEOREM . The convex surface of a cylinder is equal to the circum- ference of its base multiplied by the altitude . Let ABD be the base of a cylinder ...
... CONE , and the SPHERE , are sometimes called THE THREE ROUND BODIES . PROPOSITION I. THEOREM . The convex surface of a cylinder is equal to the circum- ference of its base multiplied by the altitude . Let ABD be the base of a cylinder ...
Page 217
... cone whose base is ACD , and whose slant height is SA : then will its convex surface be equal to the circumference ... cone , the perimeter of the base of the pyramid coincides with the circumference of the base of the cone , and the ...
... cone whose base is ACD , and whose slant height is SA : then will its convex surface be equal to the circumference ... cone , the perimeter of the base of the pyramid coincides with the circumference of the base of the cone , and the ...
Page 218
... cone , BIA and EGD its two bases , and EB its slant height : then is its convex surface equal to half the sum of the ... cone , the perimeters of its bases coincide with the circumferences of the bases of the frustum of the cone , and ...
... cone , BIA and EGD its two bases , and EB its slant height : then is its convex surface equal to half the sum of the ... cone , the perimeters of its bases coincide with the circumferences of the bases of the frustum of the cone , and ...
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Common terms and phrases
AB² 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 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