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.

40 DESCRIPTIVE GEOMETRY
97. Problem 35. GCiven a straight line in space parallel to G-L,
also given a point in space; required to revolve the point about
the line as an axis until the plane of the point and the line is
parallel to H, and again until the plane of the point and the line is
parallel to V.
98. Problem 36. Given a straight line perpendicular to H, also
given a point in space; required to revolve the point about the line
as an axis.
Analysis. In Fig. 49, which is a pictorial drawing, let M-N
represent the line and let 0 (o,, o') represent the point.
Since the point O must move in a plane perpendicular to M-N
and therefore parallel to H, and since the point 0 must retain a: -L
/I OFFS 4t- X'I C 0, ' I id '.
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FIG. 49 FIG. 50
constant distance from the axis M-N, the horizontal projection o,
of the point must move in the arc of a circle with center at the
point where the axis pierces H; and its vertical projection o' must
move in a straight line od-omt drawn through o' parallel to G-L.
Now if the point 0 occupy the several positions indicated in
the diagram, the projections will fall at o,, o'; o,,, o"; o,,,, o"'; etc.
Construction. Fig. 50 shows how the work is done when the planes
Hand V occupy their position of coincidence. The line m'-n' represents the vertical projection of the given line, and the point m, represents the horizontal projection of the same line. The points o, and o'
represent the two projections of the given point in its first position.