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 165
... 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 straight lines , one in each face , and both perpendicular to the edge at ...
... 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 straight lines , one in each face , and both perpendicular to the edge at ...
Page 166
... edges of the angle , and the portions of the planes lying between the edges are 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 ...
... edges of the angle , and the portions of the planes lying between the edges are 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 ...
Page 182
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle : then is the sum of any two of the plane angles formed by them , as ASC and CSB , greater than the third ASB . If the plane ...
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle : then is the sum of any two of the plane angles formed by them , as ASC and CSB , greater than the third ASB . If the plane ...
Page 183
... 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 is the sum of the angles about S less than four right angles . For , pass a ...
... 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 is the sum of the angles about S less than four right angles . For , pass a ...
Page 184
... 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 ...
... 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 ...
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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