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.

7O

DESCRIPTIVE GEOMETRY

Revolve the plane of these two lines about the first line as an
axis until perpendicular to H. The second line in this position
must be a line of the plane whose vertical trace is sought, and
must pierce V at a point in this trace.
By assuming other points in the given horizontal trace and
proceeding as above, other points in the required vertical trace
may be obtained.
Construction. See Fig. 78. Let S-s, represent the given horizontal trace, and let the angle A represent the measure of the
given angle which the plane makes with H.
Through b,, aly point on S-s,, draw b,-d, perpendicular to S-s,.
Through b, also draw b,-d,, making the given angle A with b,-d,.
The line b,-d, is, by analysis,
s^'N^ ~ the revolved position of a line
of the plane whose vertical trace
-ai~ Er —"V is sought.
\ ~/ \^ Through d, draw d,-d' perpen\ dicular to G-L; also through d,
|di L draw d,-dHperpendicular to b,-d,
*-A - ^ >~ ~intersecting b,-d. at d,.
Revolve the plane of the three
I/ Ad'~ ^lines, b,-d,, b6-d,, and d,-d. about
b,-d, as an axis until the plane
occupies its true position, which
FIG. 78 is perpendicular to H. The line
d,-dH will take the position d,-d' perpendicular to G-L, and the
point d= will take the position d' on the line d,-d', and at the distance d,-dH below G-L. The point d', then, is the point in which
B-D, in true position, pierces V, and is therefore a point in the
required vertical trace. S-d'-s' is the required vertical trace.
In case the given horizontal trace does not intersect G-L within
the limits of the drawing, assume another point upon the horizontal trace and proceed as above to find another point in the
vertical trace.
Check. Assume some point on the horizontal trace other than
those already used, and proceed as above to locate an additional
point on the vertical trace already determined.