Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

RELATING TO POINT, LINE, AND PLANE

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the distance c,-fH is the distance of the vertex, in true position,
from the line U-u,.
With the vertex in true position revolve U about U-u, as an
axis, into H. The points d, and e, will remain stationary and the
vertex F will fall at f, where c,-fH is equal to c,-fIH.
The angle d,-fH-e, is the measure of the required angle.
Check. Pass another plane perpendicular to A-B.
190. Problem 128. Find the angle between the two planes
S= - 5, 140~, 40~ and T = 5, 30, 120~.
191. Problem 129. Find the angle between the two planes
S= - 2, 90, 90~ and T= 4, 30~, 60~.
192. Problem 130. Find the angle between the two planes
S = 0~, - - 2 and T= 0~, - 2, - 5.
193. Problem 131. Find the angle between the plane S= - 4,
30~, 60~ and the plane EH.
Suggestion. In this case the edge of the dihedral angle is the
horizontal trace of the given plane. The auxiliary plane, which
is perpendicular to the edge, is therefore perpendicular to H. Its
horizontal trace will be perpendicular to the horizontal trace of the
given plane, and its vertical trace will be perpendicular to G-L.
194. Problem 132. Find the angle between the plane S==-3,
20~, 60~, and the plane V.
195. Problem 133. Given either trace of a plane and the angle
which the plane makes with the corresponding plane of projection;
required to determine the other trace.
Analysis. Suppose the horizontal trace of the plane and the
angle which the plane makes with H are given.
Any plane perpendicular to this horizontal trace will cut from
the plane whose vertical trace is sought a straight line, and from
H another straight line, both of which will be perpendicular to
the horizontal trace at the same point. These two lines will form
a plane angle measuring the given dihedral angle, and if revolved
into H about the side in H, will be seen in true size.
Through any point of the given horizontal trace draw two
straight lines in H, the first perpendicular to the trace and the
second making an angle with the first equal to the measure of the
given dihedral angle.