 | Mathematics - 1898 - 228 pages
...line. 5. If two planes be perpendicular to the same straight line they are parallel or coincident. 6. The sum of the face angles of any convex polyhedral angle is less than four right angles. 7. Compare the areas of two mutually equiangular spherical triangles, the one on a sphere of radius... | |
 | Yale University - 1898 - 212 pages
...perpendicular frcni a point to a plane is the shortest line that can be drawn from that point to the plane. 2. The sum of the face angles of any convex polyhedral angle is less tl an four right angles. 3. What is a cone of revolution? State and prove the theorem regarding the... | |
 | William James Milne - Geometry - 1899 - 404 pages
...to the face angles of this polyhedral. How does their sum compare with four right angles ? Theorem. The sum of the face angles of any convex polyhedral angle is less than four right angles. Datum : Any convex polyhedral angle, as Q. To prove that the sum of the face angles of Q is less than... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...DC. Ax. 5 In the A BSC and DSC, SC = SC, and SB = SD, but BC > DC. PROPOSITION XXVII. THEOREM. 581. The sum of the face angles of any convex polyhedral angle is less than four right angles. Let S be a convex polyhedral angle, and let all its edges be cut by a plane, making the section ABCDE.... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
....45Z) + Z DSC. That is, Z ASB + Z 55(7 is greater than Z .45(7. Q ED PROPOSITION XXVII. THEOREM. 581. The sum of the face angles of any convex polyhedral angle is less than four right angles. Let S be a convex polyhedral angle, and let all its edges be cut by a plane, making the section ABODE.... | |
 | William James Milne - Geometry - 1899 - 396 pages
...angles of this polyhedral. How does their sum compare with four right angles ? Theorem. Tlie sum of thc face angles of any convex polyhedral angle is less than four right angles. Datum : Any convex polyhedral angle, as Q. To prove that the sum of the face angles of Q is less than... | |
 | Universities and colleges - 1917 - 140 pages
...the locus of P? (Give no proof.) Find the total length of this locus. Monday 2 pm Two hours 1. Prove: The sum of the face angles of any convex polyhedral angle is less than four right angles. 2. Prove: If two perpendicular planes intersect in a line x, a line through any point of x, perpendicular... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...Z EAD. (Art. 80.) Therefore the sum of Zs BAC and CAD is greater than Z BAD. PROPOSITION XXIII 460. The sum of the face angles of any convex polyhedral angle is less than four right angles. Let A-BCDE be any convex polyhedral angle. It is required to prove that the sum of the face angles... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...Any face angle of a polyhedral angle is less than the sum of the remaining face angles. ยง 459. (3) The sum of the face angles of any convex polyhedral angle is less (4) If two trihedral angles have the three face angles of one equal, respectively, to the three face... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...> DC. Ax. 5 In the A -BSC and DSC, SC = SC, and SB = SD, but BODC. PROPOSITION XXVII. THEOREM. 581. The sum of the face angles of any convex polyhedral angle is less than four right angles. Let S be a convex polyhedral angle, and let all its edges be cut by a plane, making the section ABCDE.... | |
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The sum of the face angles of any convex polyhedral angle is less than four right angles. 
