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.

56

DESCRIPTIVE GEOMETRY

Since the intersection of two planes is a straight line, the
straight line joining these two points must be the required line
of intersection.
Construction. See Fig. 65. Let Sand T represent the two given
planes. The horizontal traces intersect at a, vertically projected at a'.
The vertical traces intersect at
tk,/\ ~ b' horizontally projected at b,.
a, According to analysis A-B is
the required intersection.
/^ / i\~ ClCheck. Connect any point in
S0- a'-j^ - -— T L the line of intersection with any
point in the vertical trace of one
of the planes, and note whether
this line intersects Hill the horit;^Xb' \zontal trace of the same plane.
x~~ \s' Apply the same test with refFIG. 65 erence to the other plane.
CASE 2. When either the two horizontal traces or the two vertical
traces do not intersect within the limits of the drawing.
Analysis. Pass a series of
auxiliary planes parallel to the
plane of projection on which
the traces intersect. These W f --- -w,
planes will cut from the two
given planes straight lines U- 6 _ u,
which will be parallel to this b/'' /r
plane of projection and which
will intersect in points comnmon to both of the given
planes and therefore in their
line of intersection.
Construction. See Fig. 66. t//
Let S and T represent the
given planes whose horizontal FIG. 66
traces do not intersect within the limits of the drawing. The vertical traces intersect at a' horizontally projected at a,, locating one
point in the required intersection. Pass an auxiliary plane U