 | William Betz - Geometry - 1916 - 536 pages
...spherical triangle is greater than the third side. SPHERICAL POLYGONS PROPOSITION XIV. THEOREM 829. The sum of the face angles of any convex polyhedral angle is less than four right angles. Given the convex polyhedral angle O-ABCDE. To prove that the sum of the face angles is less than 4... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...equal angles A OB and A OD, or ^.AOB+Z.BOC>'^.AOC. SPHERICAL POLYGONS PROPOSITION XIV. THEOREM 829. The sum of the face angles of any convex polyhedral angle is less than four right angles. Given the convex polyhedral angle O-ABCDE. To prove that the sum of the face angles is less than krt.A.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...AVB + ZBVC>ZDVC + ZAVD, or ZA VB + ZB VC > ZA VC. (Why ?) (Why ?) QED PROPOSITION XXIV. THEOREM 549. The sum of the face angles of any convex polyhedral angle is less than four right angles. v Given V-ABCDE, any convex polyhedral angle. To prove the sum of AA VB, B VC, etc., is less than four... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 240 pages
...drawn. Then prove (1) AB=AE, (2) AC<AB + BC, (3) EC < BC, (4) £EDC<£ BDC, (5) ^ ADC < £ ADB + Z BDC. SUM OF THE FACE ANGLES OF A POLYHEDRAL ANGLE...point in the base, and draw OA, OB, OC, etc. Then Z PBA + Z PEC > Z ABC, Z PCB + Z PCD > Z BCD, and so on. § 151 Now the sum of the A of the A OAB, OBC,... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 232 pages
...DB = DE, and that AB and BC are drawn. Then prove (1) AB = AE, (2) AC < AB + BC, (3) EC<BC, (4) 44 SUM OF THE FACE ANGLES OF A POLYHEDRAL ANGLE 152....point in the base, and draw OA, OB, OC, etc. Then Z PBA + Z PBC > Z ABC, Z FCB + Z PCD > Z BCD, and so on. § 151 Now the sum of the A of the A OAB, OBC,... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...the dihedral angles of a trihedral angle intersect in a common straight line. Proposition 246 Theorem The sum of the face angles of any convex polyhedral angle is less than four right angles. Hypothesis. A-BCDEF is a convex polyhedral Z-. Conclusion. Z BAG + Z CAD + etc. < 4 rt. A. Proof. Let... | |
 | United States. Office of Education - 1921 - 1286 pages
...45. The sum of any two face angles of a trihedral angle is greater than the third face angle. 4(1. The sum of the face angles of any convex polyhedral angle is less than four right angles. 47. Each side of a spherical triangle is less than the sum of the other two sides. 48. The sum of the... | |
 | Education - 1921 - 1190 pages
...45. The sum of any two face angles of a trihedral angle is greater than the third face angle. 4fi. The sum of the face angles of any convex polyhedral angle is less than four right angles. 47. Each side of a spherical triangle is lees than the sum of the other two sides. 48. The sum of the... | |
 | National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...equiangular. 45. The sum of any two face angles of a trihedral angle is greater than the third face angle. 46. The sum of the face angles of any convex polyhedral angle is less than four right angles. 47. Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...inequality the equal angles A OC and A OK, we have £AOC + Z.BOC >Z.AOK+Z.KOB. §139 Theorem 31 572. The sum of the face angles of any convex polyhedral angle is less than four right angles. P X 'Y \Z Given any polyhedral angle P with face angles XPY, YPZ, etc. To prove that XPY + YPZ+ •... | |
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The sum of the face angles of any convex polyhedral angle is less than four right angles. 
