 | Aaron Schuyler - Geometry - 1876 - 384 pages
...perpendicular is the shortest distance from one of these lines to the other. 16. The sum of the facial angles of any convex polyhedral angle is less than four right angles. 17. Two isosceles trihedral angles are equal if the three facial angles of the one are respectively... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
....-.¿ASB + ZBSOZASD + ZDSC, that is Z ASB+Z BSOZ. ASC. GEOMETRY. BOOK VI. PROPOSITION XXIV. THEOREM. 488. The sum of the face angles of any convex polyhedral angle is less than four right angles. S Let the polyhedral angle S be cut by a plane, making: the section ABСDE a convex polygon. We are... | |
 | Education - 1902 - 730 pages
...its own projection on a plane is the least angle it makes with any line in that plane. 3. (a) Prove: The sum of the face angles of any convex polyhedral angle is less than a perigon (four right angles). (b) In how many ways can a polyhedral angle be made with regular triangles... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...lines? 27. How many planes can be determined by four parallel lines ? PROPOSITION XX. THEOREM. 92. The sum of the face angles of any convex polyhedral angle is less than four right angles. Notation. Let S be any polyhedral angle formed by the face angles 17, Q, K, etc. To prove 77 + 6 +... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...5. Compare the sum of Zs DAB and BAC with Z.DAC. LINES AND PLANES. PROPOSITION XXXII. THEOREM. 389. The sum of the face angles of any convex polyhedral angle is less than four right angles. A -BCDEF represent a convex 'polyhedral angle. To prove that the sum of the face angles BAC, CAD, etc.,... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...auth. SUG. 5. Compare the sum of /^s DAB and BAC with Z.DAC. Therefore PROPOSITION XXXII. THKORBM. 389. The sum of the face angles of any convex polyhedral angle is less than four Tight angle*. A liet A-BCDEF represent a convex polyhedral angle. To prove that the sum of the face... | |
 | John Macnie - Geometry - 1895 - 390 pages
...perpendicular to only one edge or to two faces of a polyhedral angle. PROPOSITION XXVI. THEOREM. 492. The sum of the face angles of any convex polyhedral angle is less than four right angles. s IB \0 Given: ASB, BSC, CSD, etc,, face angles of a polyhedral angle S-ABCDE; To Prove : The sum of... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...angles. 2. Use the method of proof adopted in Prop. 21, Part 1, to prove that the sum of the plane angles of any convex polyhedral angle is less than four right angles. 36—2 PROPOSITION 21. PART 2. The sum of the plane angles of any convex polyhedral angle is less than... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...539. The sum of any two; face angles of a trihedral angle is greater than the third face angle. 540. The sum of the face angles of any convex polyhedral angle is less than four right angles. 541. Two trihedral angles are equal or symmetrical, if the three face angles of the one are respectively... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...ASB + /.BSC) > (/.ASD + Z-DSC), Or (Z ASB + Z BSC) > Z 4SC. QED PROPOSITION XXVII. THEOREM. 424. TJie sum of the face angles of any convex polyhedral angle is less than four right angles. Given—8—ABCDE a convex polyhedral angle. To Prove—Z ASB + Z BSC + Z CSD + Z DSE + Z-JSS4 < four... | |
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The sum of the face angles of any convex polyhedral angle is less than four right angles. 
