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.

46

DESCRIPTIVE GEOMETRY

When the card is revolved through an angle of 45 degrees, its
two projections will be a,,,-b, and a"'-b'-d'-e."'
The projections of the card in the different positions are easily
determined when we remember that horizontal projections will
move in arcs of circles and that.a,,, ---,, vertical projections will move in
a r,,,,^ straight lines parallel to G-L (see
7,/ \ Section 98).
at: A\\120. Problem 58. Given a rect-:i a\\ angular card situated in the third
quadrant, whose dimensions are 6
ajei ',:d,,units by 4 units, whose surface is
' — --.... - - L parallel to If, and whose long edges
-a'-a" a"" b' are perpendicular to 1V; required
I l I (1) to draw the projections of the
I I lcard in the given position, and (2) to
I I revolve the card about its left-hand
I I edge as an axis, through angles of
i I 30 degrees, 45 degrees, 60 degrees,
I and 90 degrees, and to draw the
I I
1 ~I ~corresponding projections.
e" ae"'f e"" 121. Problem 59. Given a rectangular card situated in the first
FIG. 56
quadrant, whose dimensions are 6
units by 4 units, whose surface is parallel to V, and whose long edges
are perpendicular to H; required (1) to draw the projections of the
card in the given position, and (2) to revolve the card about one of its
vertical edges as an axis, through angles of 30 degrees, 45 degrees, 60
degrees, and 90 degrees, and to draw the corresponding projections.
122. Problem 60. Given a rectangular card whose dimensions are
5 units by 3 units, whose surface is parallel to H, whose long edges are
parallel to V, and whose left-hand back vertex is A = - 3, - 4, - 1;
required (1) to draw the projections of the card in the given position;
(2) to revolve the card about its left-hand edge as an axis until the
surface of the card is inclined 30 degrees to IT, and to draw the corresponding projections; and (3) to revolve the card in its last position
about a vertical axis through A until the horizontal projections of the