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.

48

DESCRIPTIVE GEOMETRY

123. Problem 61. Given a rectangular card whose dimensions are
6 units by 4 units, whose surface is parallel to V, whose long edges are
parallel to H, and whose right-hand upper vertex is E = 4, - 2, - 1;
required (1) to draw the projections of the card in the given position;
(2) to revolve the card about its right-hand vertical edge as an axis
until the surface of the card is inclined 30 degrees to V, and to draw
the corresponding projections; and (3) to revolve the card in its last
position about an axis through E perpendicular to VTuntil the vertical
projections of the edges of the card are inclined 45 degrees to G-L,
and to draw the corresponding projections.
124. Problem 62. Solve Problem 60, substituting a new value for A,
namely A =- 4, 1 1, locating the whole work in the first quadrant.
125. Problem 63. Given an hexagonal card whose side is 3 units,
whose surface is parallel to V, two of whose sides are parallel to H,
and whose extreme left-hand vertex is A = - 4,- 1,- 4; required (1) to
draw the projections of the card in the given position; (2) to revolve the
card about a vertical axis through A until the surface of the card makes
an angle of 60 degrees with V, and to draw the corresponding projections; and (3) to revolve the card in its last position about an axis
through A perpendicular to V until the vertical projections of the sides
which were parallel to H in the last position shall make an angle of
45 degrees with G-L, and to draw the corresponding projections.
Construction. See Fig. 58. The projections of the card in its
first position are a,-b,-d,-e,-f,-g, and a'-b'-d'-e'-f'-g'.
In taking its second position the card is revolved about a vertical axis through A. The surface of the card will remain perpendicular to H and its horizontal projection will take the position
a,-e,, equal to a,-e,, and making an angle of 60 degrees with a,-e,.
Its vertical projection will be a'-b"-d_-e"-flf-g", where a' has
made no change in position, where b" is at the intersection of a
straight line through b' parallel to G-L, with a straight line
through b,, perpendicular to G-L, where d" is at the intersection
of a straight line through d' parallel to G-L, with a straight line
through d,, perpendicular to G-L, etc.
In taking its third position the card is revolved about an axis
through A perpendicular to V. The vertical projection will change
in position but not in character.