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.

68

DESCRIPTIVE GEOMETRY

Analysis 1. Pass a plane perpendicular to the line of intersection of the two given planes. This plane will intersect the given
planes in straight lines perpendicular to the line of intersection
at the same point. The angle between these two lines is the
required angle.
Analysis 2. Assume any point between the faces of the dihedral
angle. Through this point draw two straight lines, one perpendicular to one face and the other perpendicular to the other face.
/s, The angle formed by
t""<Xa~, ~ these two lines will be./ _*^. gthe supplement of the
/ /! \^^;\ i.,' required angle.
~~///,, \./e~ Construction. See Fig.,/ \' >b", 77. Let S and T repreU /le \ \ T< sent the given planes
G t,T L which intersect in the
\. ~\ I~/ line A-B.
\ \ / Following Analysis 1,
through any point of
\a -b, as c,, draw U-u,
^\/{, ~ perpendicular to a,-b,.
U-u, may be taken as the
horizontal trace of a plane
FIG. 77 U perpendicular to A-B
(see Section 45). The line cut from S by U, -the line forming
one side of the required plane angle,- pierces II at d,; the line cut
from T by U,- the line forming the other side of the same angle,
-pierces H at e,, and it only remains to find the vertex of the
angle, which is the point in which U is intersected by A-B.
U will cut the horizontal projecting plane of A-B in a straight
line perpendicular to A-B, piercing H at c,, and intersecting A-B
at the vertex of the angle sought.
Revolve the horizontal projecting plane of A-B about a,-b, as
an axis, into H. The line a,-bH is the revolved position of A-B,
and c,-fHH drawn through c, perpendicular to a,-b, is the revolved
position of the intersection of U and the horizontal projecting plane
of A-B. The point f, is the revolved position of the vertex, and