Elements of Geometry |
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Page 113
... angle CAE = DBF . Again , the plane ACE is parallel to the plane BDF ; for , let us suppose the plane parallel to DBF , drawn through the point A , to meet the lines CD , EF , in points different from C and E , for ... Solid Angles . 113.
... angle CAE = DBF . Again , the plane ACE is parallel to the plane BDF ; for , let us suppose the plane parallel to DBF , drawn through the point A , to meet the lines CD , EF , in points different from C and E , for ... Solid Angles . 113.
Page 115
... angle IIA e = HDƒ ; hence the triangles AHe , DHƒ , are similar ( 208 ) , and consequently the angle AHe DHf . It follows then , in the first place , that e Hƒ is a straight line , and that thus the three parallels Ee ... Solid Angles . 115.
... angle IIA e = HDƒ ; hence the triangles AHe , DHƒ , are similar ( 208 ) , and consequently the angle AHe DHf . It follows then , in the first place , that e Hƒ is a straight line , and that thus the three parallels Ee ... Solid Angles . 115.
Page 117
... angle APD formed by the two perpendiculars PA , PD , at the common intersection BP , measures the angle of the two planes AB , MN ; therefore , since this angle is a right angle , the two planes are perpendicular to ... Solid Angles . 117.
... angle APD formed by the two perpendiculars PA , PD , at the common intersection BP , measures the angle of the two planes AB , MN ; therefore , since this angle is a right angle , the two planes are perpendicular to ... Solid Angles . 117.
Page 118
... solid angle is formed by three plane angles , the sum of either two of these angles will be greater than the third . Demonstration . We need consider only the case in which the plane angle to be compared with the two others is greater ...
... solid angle is formed by three plane angles , the sum of either two of these angles will be greater than the third . Demonstration . We need consider only the case in which the plane angle to be compared with the two others is greater ...
Page 119
... angles about the point O is greater than the sum of the angles about the point S. But the sum of the angles about the point O is equal to four right angles ( 34 ) ; therefore the sum of the plane angles , which form a solid angle S , is ...
... angles about the point O is greater than the sum of the angles about the point S. But the sum of the angles about the point O is equal to four right angles ( 34 ) ; therefore the sum of the plane angles , which form a solid angle S , is ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence