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
... SLANT 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 ...
... SLANT 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 ...
Page 184
... slant 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 ...
... slant 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 ...
Page 185
... slant 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 ...
... slant 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 ...
Page 212
... slant 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 ...
... slant 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 ...
Page 213
... slant height is BH . F H K E A B 7. SIMILAR CONES are those which may be generated by similar right - angled triangles revolving about homologous sides . " The axes of similar cones are proportional to the radi of their bases ( B. IV ...
... slant height is BH . F H K E A B 7. SIMILAR CONES are those which may be generated by similar right - angled triangles revolving about homologous sides . " The axes of similar cones are proportional to the radi of their bases ( B. IV ...
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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