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.

THE POINT, LINE, AND PLANE

17

27. To assume a Straight Line at Random. To assume a straight
line at random, we may, within certain limitations, draw its two
projections at random.
28. To assume a Point upon a Straight Line. In Fig. 21 let
m,-n, and m'-n' represent the horizontal and vertical projections
of a straight line in the third quadrant.
Assume one of the projections of the point,
say the horizontal, o,, anywhere on the _ _,
line m,-n,. Through o, draw a straight G ' L
line perpendicular to G-L and note its
intersection o' with m'-n'. The point o'
is the vertical projection of the required
point. F 21
If a point is situated on a line, its horizontal projection must be on the horizontal projection of the line,
and its vertical projection must be on the vertical projection of
the line.
29. To assume Two Straight Lines which intersect. See Fig. 22.
Draw at random the two projections, m,-n, and m'-n', of one of
the lines. Assume upon this line any point as P. Through p,
and p' respectively draw at random the horizontal and vertical
projections of the other line.
/, n30. The Projections of Parallel
Straight Lines. The projecting planes
>^ ^', of parallel straight lines are necessarily
A - - L parallel whatever the plane of projec\I 1 / z tion; therefore the intersections of these!' >4[ planes with the plane of projection, or
in other words the projections of the
lines, must be parallel.
FIG. 22 31. The Projections of Straight Lines
which are Perpendicular to Each Other. The projections of two
straight lines which are perpendicular to each other are perpendicular to each other only when one or both of the lines are
parallel to the plane of projection, since it is only under these conditions that the projecting planes of the lines are perpendicular
to each other.