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 94
... upper , and the other , the lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A ...
... upper , and the other , the lower base . 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A ...
Page 95
... upper base of the parallelogram , or in the prolongation of that base . equal to From A , draw AE parallel to BC , forming the par- allelogram ABCE . This parallelogram will be the parallelogram ABFD , from Proposition I. But the ...
... upper base of the parallelogram , or in the prolongation of that base . equal to From A , draw AE parallel to BC , forming the par- allelogram ABCE . This parallelogram will be the parallelogram ABFD , from Proposition I. But the ...
Page 178
... upper , and the make up the lateral or convex surface of the prism ; lines in which the lateral faces meet , are called lateral edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its ...
... upper , and the make up the lateral or convex surface of the prism ; lines in which the lateral faces meet , are called lateral edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its ...
Page 180
... upper base of the frustum ; the base of the pyramid is cal- led the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a ...
... upper base of the frustum ; the base of the pyramid is cal- led the lower base of the frustum . 14. The ALTITUDE of a frustum of a pyramid , is the per- pendicular distance between the planes of its bases . 15. The SLANT HEIGHT of a ...
Page 185
... upper and lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then will the section abcde be similar to the base ABCDE , and their homologous sides will be parallel , ( P ...
... upper and lower bases , multiplied by the slant height . Let ABCDE - e be a frustum of a right pyramid , whose vertex is S : then will the section abcde be similar to the base ABCDE , and their homologous sides will be parallel , ( P ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence