 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...Theorem VI. (a) The sum of the face angles of any polyhedral angle is less than a perigon. (b) The sum of the sides of any spherical polygon is less than the circumference of a great circle. Let ABCDEF be a plane section of the polyhedral angle with vertex F. Then at A, Z FA V + Z VAB > Z... | |
 | Eugene Randolph Smith, William Henry Metzler - Geometry, Solid - 1918 - 232 pages
...Theorem VI. (a) The sum of the face angles of any polyhedral angle is less than a perigon. (b) The sum of the sides of any spherical polygon is less than the circumference of a great circle. Let ABCDEF be a plane section of the polyhedral angle with vertex F. Then at A, Z FA V + Z VAB > Z.... | |
 | Henry Barnard - 1862 - 160 pages
...of a great circle which joins the two given points. The sum of the sides of a spherical triangle, or of any spherical polygon, is less than the circumference of a great circle. Poles of an arc of a great or small circle. — They serve to trace arcs of circles on the sphere.... | |
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The sum of all the sides of any spherical polygon is less than the circumference of a great circle. 
