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 210
... convex surface , is , in any position , called an element of the surface ; the elements are all perpendicular to the planes of the bases , and any one of them is equal to the altitude of the cylinder . Any line of the generating ...
... convex surface , is , in any position , called an element of the surface ; the elements are all perpendicular to the planes of the bases , and any one of them is equal to the altitude of the cylinder . Any line of the generating ...
Page 212
... convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ; and the point S ... convex surface , is , in any position , called an element of the surface ; the elements are all equal , and any one ...
... convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ; and the point S ... convex surface , is , in any position , called an element of the surface ; the elements are all equal , and any one ...
Page 215
... 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 whose altitude is H : then will its convex surface be equal to the circum ference of its base ...
... 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 whose altitude is H : then will its convex surface be equal to the circum ference of its base ...
Page 216
... convex surface of the cylinder is equal to the circumference of its base multiplied by the altitude ; which was to be proved . Cor . The convex surfaces of cylinders having equal alti- tudes are to each other as the circumferences of ...
... convex surface of the cylinder is equal to the circumference of its base multiplied by the altitude ; which was to be proved . Cor . The convex surfaces of cylinders having equal alti- tudes are to each other as the circumferences of ...
Page 217
... convex surface of a cone is equal to the circumference of its base multiplied by half the slant height . Let S - ACD be a cone whose base is ACD , and whose slant height is SA : then will its convex surface be equal to the circumference ...
... convex surface of a cone is equal to the circumference of its base multiplied by half the slant height . Let S - ACD be a cone whose base is ACD , and whose slant height is SA : then will its convex surface be equal to the circumference ...
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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