 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...order, the polyhedral angles are said to be equal. PROPOSITION XXV. THEOREM '/ 494. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given the trihedral angle V-XYZ, with the face angle XVZ greater than either of the face angles XVYor... | |
 | George C. Shutts - 1913 - 212 pages
...equidistant from two given points? POLYHEDRAL ANGLES PROPOSITION XXX. 339 509. THEOREM. The sum of any two face angles of a trihedral angle is greater than the third. Given the trihedral A — BCD, in which face angle DAC is the greatest. To Prove Z CAB + Z BAD > Z... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...each face of a trihedral angle perpendicular to the opposite edge lie in the same plane. 147. THEOREM. The sum of two face angles of a trihedral angle is greater than the third face angle. 8 Given S-ABC, a trihedral Z having face Z ASC greater than either of the face A ASB or BSC. To prove... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...relation to that plane? Therefore LT is not in what relation to OV and RS? VIII THEOREM 35 The sum of any two face angles of a trihedral angle is greater than the third face angle. Draw the figure as here represented, making the edge OV heavy. Denote right edge by OS. For convenience... | |
 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...Find the area of a plane section of a sphere of radius 10, which passes 6 units from the center. 4. The sum of two face angles of a trihedral angle is greater than the third face angle. 5. Find the surface and volume of a regular octahedron having an edge 4 units long. 6. Given a solid... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...order. Hence, vertical, polyhedral angles are symmetrical. PROPOSITION XIX. THEOREM 566. The sum of any two face angles of a trihedral angle is greater than the third face angle. 0 Let ZAOC be greater than ZAOB and greater than ZBOC, in the trihedral angle O-ABC. To prove ZAOB+ZBOOZAOC.... | |
 | William Betz - Geometry - 1916 - 536 pages
...826. // two angles of a spherical triangle are equal the sides opposite are equal. 827. The sum of any two face angles of a trihedral angle is greater than the third face angle. Given the trihedral angle 0-ABC, and AOC its greatest face angle. To prove that /LA OB +Z.BOC >Z.4... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...are equal, the face angles opposite are equal. PROPOSITION XIII. THEOREM 827 . The sum of any tivo face angles of a trihedral angle is greater than the third face angle. Given the trihedral angle 0-ABC, and AOC its greatest face angle. To prove that ZA OB +/LBOC >ZA OC.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...angles are right angles. (d) The sum of the face angles of a polyhedral angle is less than 3(50°. (e) The sum of two face angles of a trihedral angle is greater than the third face angle. (/) If the opposite face angles of a tetrahedral angle are equal, the opposite dihedral angles are... | |
 | Eugene Randolph Smith, William Henry Metzler - Geometry, Solid - 1918 - 232 pages
...the other follows from the relations shown in §§ 242 and 243. 245. Theorem IV. (a) The sum of any two face angles of a trihedral angle is greater than the third face angle. (i) The sum of any two sides of a spherical triangle is greater than the third side. FIRST PROOF :... | |
| |
The sum of any two face angles of a trihedral angle is greater than the third face angle. 
