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

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20. Problem 5. Determine the projections of a point situated in
the fourth quadrant, 4 units from H and 4 units from V.
21. Problem 6.- Determine the projections of a point situated in
the second quadrant, 4 units from H and 2 units from V.
22. Problem 7. Determine the projections of a point situated in
G-L.
23. Projection of the Straight Line upon H and V in their
Primary Position. As a straight line may be regarded as made up
of an infinite number of consecutive points, the projection of the
straight line will be the locus of the projections of these points.
The projecting lines of these points, since they are drawn from
points in a straight line and perpendicular to a plane, constitute
a plane perpendicular to the plane of projection.
The plane made up of these projecting lines is called the projecting plane of the line. If the projection is being made upon
H, the projecting plane is called the horizontal projecting plane;
and if the projection is being made upon V, the projecting plane
is called the vertical projecting plane.
The projection of a straight line upon a plane, then, is a straight
line, and for this reason its position is fully known when two of
its points are determined.
In Fig. 6, which shows
H and V in their primary
position, M-N represents
a straight line in the Nthird quadrant. M and N represent any
two points of the line but in no sense
limit the length of the line. The hori- /
zontal projection of M is m,,, and the
vertical projection of M is m". The
horizontal projection of N is n,,, and IG. 6
the vertical projection of NVis n". The horizontal projection of the
line is then m,-n,, and the vertical projection of the line is m"-n".
The projection of a straight line, then, may be found by finding
the projections of two of its points and drawing a straight line
through these two projections. This will be true whatever the
quadrant occupied by the line.