Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 157
... edge of the angle , and the planes themselves are called faces of the angle . A 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 . A 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 between the 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 ...
... edges of the the portions of the planes lying between the 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 ...
Page 174
... edges of a triedral angle , is greater than the third . Let SA , SB , and angle : then will the sum formed by them , as ASC third ASB . SC , be the edges of a triedral of any two of the plane angles and CSB , be greater than the If the ...
... edges of a triedral angle , is greater than the third . Let SA , SB , and angle : then will the sum formed by them , as ASC third ASB . SC , be the edges of a triedral of any two of the plane angles and CSB , be greater than the 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 ...
... 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following