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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In Fig. 23, S-s, represents the horizontal trace, and S-s' represents the vertical trace of a plane S which is oblique to both H
and V. The plane is supposed to extend without limit in all
directions, and therefore passes through all the quadrants, although
in the diagram only that portion of the plane which lies in the
third quadrant is represented.
Fig. 24 shows how the traces of the plane in Fig. 23 will
appear after H and V take their position of coincidence.
It will be observed that the traces S-s, and S-s' make the same
angle with G-L after revolution as before, and therefore reveal
just as much in regard to the location of the plane.
38. Representation of the Plane by Two Intersecting Straight
Lines in Space. Since any two intersecting straight lines or any
s8
FIG. 25 FIG. 26
two parallel straight lines may be used to determine a plane, we
may represent a plane by giving the projections of such lines.
By producing these lines until they intersect H and V we shall
find points in the horizontal and vertical traces of the plane, if
such traces are needed.
39. Representation of Planes occupying Various Positions with
Reference to H and V. Fig. 25 represents a plane in the third
quadrant, perpendicular to H but oblique to V. Under these conditions the vertical trace must be perpendicular to G-L and the
horizontal trace must make the same angle with G-L that the
plane makes with V.
Fig. 26 shows how the traces of the plane in Fig. 25 will appear
after H and V take their position of coincidence, no change taking
place in the relation of the traces to G-L.