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 180
... HEIGHT of a frustum of a right pyramid , is that portion of the slant height of the pyramid which lies between the planes of its upper and lower bases . 16. SIMILAR POLYEDRONS are those which are bounded by the same number of similar ...
... HEIGHT of a frustum of a right pyramid , is that portion of the slant height of the pyramid which lies between the planes of its upper and lower bases . 16. SIMILAR POLYEDRONS are those which are bounded by the same number of similar ...
Page 184
... height . Let S be the vertex , ABCDE the base , and SF , perpendicular to EA , the slant height of a right pyramid : then will the convex surface be equal to , ( AB + BC + CD + DE + EA ) × † SF . Draw SO perpendicular to the plane of ...
... height . Let S be the vertex , ABCDE the base , and SF , perpendicular to EA , the slant height of a right pyramid : then will the convex surface be equal to , ( AB + BC + CD + DE + EA ) × † SF . Draw SO perpendicular to the plane of ...
Page 185
... height of the pyramid . Now , the area of any lateral face , as SEA , is equal to its base EA , multiplied by half its altitude SF : hence , the sum of the areas of the lateral faces , or the convex sur- face of the pyramid , is equal ...
... height of the pyramid . Now , the area of any lateral face , as SEA , is equal to its base EA , multiplied by half its altitude SF : hence , the sum of the areas of the lateral faces , or the convex sur- face of the pyramid , is equal ...
Page 197
... height . Cor . 2. The volume of a rectangular parallelopipedon is equal to the product of its base and altitude ; that is , the number of times which it contains the unit of volume , is equal to the number of superficial units in its ...
... height . Cor . 2. The volume of a rectangular parallelopipedon is equal to the product of its base and altitude ; that is , the number of times which it contains the unit of volume , is equal to the number of superficial units in its ...
Page 212
... height of the cone ; and the per- pendicular distance from the vertex to the plane of the base , is called the altitude of the cone . The line SB , which generates the convex surface , is , in any position , called an element of the ...
... height of the cone ; and the per- pendicular distance from the vertex to the plane of the base , is called the altitude of the cone . The line SB , which generates the convex surface , is , in any position , called an element of the ...
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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