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

47

edges of the card are inclined 45 degrees to G-L, and to draw the
corresponding projections.
Construction. See Fig. 57. The projections of the card in its
first position are a,-b,-d,-e, and a'-b'-d'-e.
In taking its second position the card is revolved about an
axis through A perpendicular to V. The surface of the card will
remain perpendicular to V and its vertical projection will take the
position a'-b" equal to a'-bl, and making an angle of 30 degrees
with a'-b. Its horizontal projection will be a,-b,,-d,,-e,, where
A and E have made no change in position and where b, and d,,
fall in a straight line through b" b,,
perpendicular to G-L.
In taking its third position the
card is revolved about an axis /. d
through A perpendicular to H. a,
The horizontal projection of the \/
card will change in position but \ /
not in character. i,
Upon a,, which makes no e, --- -
change in position, construct the a_, _ _L L
rectangle a,-b,,,-d,,,-e,, equal in ae' e blef'
every respect to a,-b,,-d,,-e, but: i
having its edges inclined 45 degrees to G-L. This is the hori-,
zontal projection of the card in b d
its final position. FIG. 57
The vertical projection of A will remain at a'. The vertical projection of B must be in a straight line through b" parallel to G-L, and
also in a straight line through b,,, perpendicular to G-L, or at b"'
The vertical projection of D must be in a straight line through
d" parallel to G-L, and also in a straight line through d,,, perpendicular to G-L, or at d"'.
The vertical projection of E must be upon a straight line
through e' parallel to G-L, and also upon a straight line through
e,, perpendicular to G-L, or at e".
The vertical projection of the card in its final position is
a'-b"'-d"'-e"