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 157
... edge of the angle , and the planes themselves are called faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the ...
... edge of the angle , and the planes themselves are called faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the ...
Page 158
... edges of the the portions of the planes lying called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but ...
... edges of the the portions of the planes lying called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but ...
Page 174
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle then will the sum of any two of the plane angles formed by them , as ASC and CSB , be greater than the third ASB . If the ...
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle then will the sum of any two of the plane angles formed by them , as ASC and CSB , be greater than the third ASB . If the ...
Page 175
... edges of any polyedral angle , is less than four right angles . Let S be the vertex of any polyedral angle whose edges are SA , SB , SC , SD , and SE ; then will the sum of the angles about S be less than four right angles . For , pass ...
... edges of any polyedral angle , is less than four right angles . Let S be the vertex of any polyedral angle whose edges are SA , SB , SC , SD , and SE ; then will the sum of the angles about S be less than four right angles . For , pass ...
Page 176
... edges of two triedral angles are equal , each to each , the planes of the equal angles are equally inclined to each other . Let S and T be the vertices of two triedral angles , and let the angle ASC be equal to DTF , ASB to DTE and BSC ...
... edges of two triedral angles are equal , each to each , the planes of the equal angles are equally inclined to each other . Let S and T be the vertices of two triedral angles , and let the angle ASC be equal to DTF , ASB to DTE and BSC ...
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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