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 228
... cylinder whose altitude is H : then is its convex surface equal to the circumference of its base multiplied by the altitude . For , inscribe in the cylinder a prism whose base is a regular polygon . The convex surface of this prism is ...
... cylinder whose altitude is H : then is its convex surface equal to the circumference of its base multiplied by the altitude . For , inscribe in the cylinder a prism whose base is a regular polygon . The convex surface of this prism is ...
Page 229
... cylinder : hence , the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude ; which was to be proved . Cor . The convex surfaces of cylinders having equal altitudes are to each other as the ...
... cylinder : hence , the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude ; which was to be proved . Cor . The convex surfaces of cylinders having equal altitudes are to each other as the ...
Page 230
... cylinders are to each other as the cubes of their altitudes , or as the cubes of the radii of their bases . For , the bases are as the squares of their radii ( B. V. , P. XIII . ) , and the cylinders being similar , these radii are to ...
... cylinders are to each other as the cubes of their altitudes , or as the cubes of the radii of their bases . For , the bases are as the squares of their radii ( B. V. , P. XIII . ) , and the cylinders being similar , these radii are to ...
Page 233
... cylinder having an equal base and an equal altitude . Cor . 2. Cones are to each other as the products of their bases and altitudes . Cones having equal bases are to each other as their altitudes . Cones having equal altitudes are to ...
... cylinder having an equal base and an equal altitude . Cor . 2. Cones are to each other as the products of their bases and altitudes . Cones having equal bases are to each other as their altitudes . Cones having equal altitudes are to ...
Page 239
... For , the cone generated by the right - angled triangle ADB , is equal to one third of the cylinder generated by the rectangle ADBF ( P. V. , C. 1 ) , and the cone generated by the triangle ADC , is equal to one third BOOK VIII . 239.
... For , the cone generated by the right - angled triangle ADB , is equal to one third of the cylinder generated by the rectangle ADBF ( P. V. , C. 1 ) , and the cone generated by the triangle ADC , is equal to one third BOOK VIII . 239.
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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