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.

50

DESCRIPTIVE GEO,(METIY

the horizontal projections of the sides which were parallel to V in the
last position shall be inclined 45 degrees to G-L, and to draw the
corresponding projections.
127. Problem 65. Solve Problem 63, substituting a new value for
A, namely A =-4, 1, 4, locating the whole work in the first quadrant.
128. Problem 66. To find the points in which a given straight
line intersects H and V.
CASE 1. To find the point in which the line intersects H.
Analysis. Since the point in which the line intersects H must
be both in H and in the line itself, its vertical projection must be
both in G-L and in the vertical projection of the line, and therefore at their intersection. The horizontal projection of the required
t au,
'a
~at\
b
FIG. 59 Fi;*. 60
point must be both in a straight line perpendicular to G-L through
the vertical projection just found and also in the horizontal projection of the line, and therefore at their intersection.
Since the required point is in H, it must be coincident with its
horizontal projection just found.
Construction. See Figs. 59 and 60. Let T-NT represent the
given line.
Produce the vertical projection m'-n' to meet G-L at a'. The
point a' is by analysis the vertical projection of the required point.
At a' draw a straight line perpendicular to G-L to meet the
horizontal projection of the line at a,, which is both the horizontal