A Course in Descriptive Geometry And Photogrammetry for the Mathematical Laborat
A Course in Descriptive Geometry And Photogrammetry for the Mathematical Laborat
E L Edward Lindsay Ince
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In order to find the angle A, consider a plane drawn through a point on the third edge whose projection is D, perpendicular to the third edge. Since OA' is a rabatment of the third edge, the intersection of this new plane with the face ft will be a perpendicular to OA' at D'. If this perpendicular be D'N, the new plane will meet OC in N, and if D"M be drawn perpendicular to OA" the new plane will meet OB in M, and thus MN will be the actual 36 DESCRIPTIVE GEOMETRY [CH. II intersection of the ne...w plane with the plane BOG. A triangle therefore exists in the new plane whose sides when ra batted on to the plane BOG are D"M, MN, and ND'. Rabat this triangle around MN, so that it becomes MPN where MP MD" and B FIG. 22. = ND f . Now PM and PN are the rabatments of two lines perpendicular to the third edge, drawn through a point on it, and hence the angle MPN is the required angle A. Examples:!, a = 60, /3 = II. A = 22J, /3 = III. A = 120, 3 = = 45. = 30. = 75. 29. Problem XVII. Given two faces and one angle of a trihedral angle, to find the other face and angles.
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