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

49

Upon a', which makes no change in position, construct the
polygon a'-b"V-d"'-el"-f" —g"' equal in every respect to a'-b"-d"e"-f"-g", but having the sides which were originally parallel to
G-L now inclined at an angle of 45 degrees to G-L. This is the
vertical projection of the card in its final position.
The horizontal projection of A will remain at a,.
The horizontal projection of B must be in a straight line through
b,, parallel to G-L, and
also in a straight line 7
through b"t perpendicu-
lar to G-L, or at,,,. / \"
The horizontal pro- / / '
jection of D must be in
a straight line through 9 - l-b,,,,
d,, parallel to G-L, and /\,, '
also in a straight line a,,, 'e
through d"' perpendicu- -
lar to G-L, or at d,,,.
The horizontal pro- b" bL'",L
jection of E must be in /i,
a straight line through / \
e,, parallel to G-L, and
also in a straight line ea"..
through e"' perpendicu-
lar to G-L, or at e,,,. /
The horizontal projec- " I f
tion of the card in its, '
final position is a,-b,,,- f" F
FoIG. 58
d, _ellif,_ll-g,,.
126. Problem 64. Given an hexagonal card whose side is 3
units, whose surface is parallel to H, two of whose sides are parallel
to V, and whose extreme left-hand vertex is A =-4, -4, - 1;
required (1) to draw the projections of the card in the given position;
(2) to revolve the card about an axis through A perpendicular to V until
the surface of the card makes an angle of 60 degrees with H, and to
draw the corresponding projections; and (3) to revolve the card in
its last position about an axis through A perpendicular to H until