Plane and solid geometry . Given two equal dihedral A BC and B^C^ whose plane A areA MNO and M^no\ respectively. To prove Z MNO = Z J^N^O* Argument 1. Superpose dihedral Z BC upon its equal, dihedral Z Bc, so that point iV ofedge BC shall fall upon point N ofedge ^C/. 2. Then MX and 3fN^, two lines in plane AB, are J. BC at point -Y. 3. .*. MX and j/iV are collinear. 4. Likewise NO and iVo are collinear. 6. ,.Z MNO = Z mno. Reasons1. § 54, 14. 2. § 670. 3. § 62. 4. §§ 670, 62. 5. § 18. 674. Cor. I. The plane angle of a right dihedral angleis a right angle, 675. Cor. II. If two intersect
Plane and solid geometry . Given two equal dihedral A BC and B^C^ whose plane A areA MNO and M^no\ respectively. To prove Z MNO = Z J^N^O* Argument 1. Superpose dihedral Z BC upon its equal, dihedral Z Bc, so that point iV ofedge BC shall fall upon point N ofedge ^C/. 2. Then MX and 3fN^, two lines in plane AB, are J. BC at point -Y. 3. .*. MX and j/iV are collinear. 4. Likewise NO and iVo are collinear. 6. ,.Z MNO = Z mno. Reasons1. § 54, 14. 2. § 670. 3. § 62. 4. §§ 670, 62. 5. § 18. 674. Cor. I. The plane angle of a right dihedral angleis a right angle, 675. Cor. II. If two intersecting planes are each per-pendicular to a third plane, their intersections with tJiethird plane intersect each other. BOOK VI 325 Given planes ABand CI) JL plane 3fiVand intersecting eachother in line DB; alsolet AE and FC be theintersections of planesAB and CD with plane J/xV. To prove that AEand FC intersect eachother. Argu:ment 1. Either AE 11 FC or AE and i^C intersect each other. 2. Suppose J-E: 11 FC. Then throug
Size: 1474px × 1695px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
