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.

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DESCRIPTIVE GEOMETRY

The plane of representation, or the plane upon which the representation is made, is cqlled the plane of projection, * and the process
by which reference to this plane is made is called projection.
Projection involves the assumption of a point of sight, or position for the observer, and a plane of projection.
When the point of sight and the plane of projection are given,
the projection of an object, for simplicity a point, is accomplished
when the point is literally thrown forward along its visual ray
until it rests upon the plane. In other words, the projection of a
point upon any plane is the intersection of the visual ray of the
point with that plane.
The point may occupy a position between the observer and the
plane of projection, or the plane of projection may stand between
the observer and the point; but in either case the projection of
the point is found by the process stated above.
If the point is in the plane of projection, it is evident that the
point and its projection will be identical.
5. Systems of Projection. It is evident that the character of the
projection of a magnitude, which consists of a collection of points,
will depend upon the relative positions of the magnitude, the
observer, and the plane of projection.
There are two principal systems of projection, depending upon
the position of the observer with reference to the plane of projection, - the scenographic projection and the orthographic projection.
The scenographic projection is that system in which the point
of sight is assumed within a finite distance of the plane of
projection.
As this is the position which would naturally be assumed by an
observer, the projection upon the plane will correspond with that
made upon the retina of the eye, and the picture will be true to
nature. This system is employed whenever it is desired to represent an object as it appears, rather than to show its exact dimensions; but on account of difficulties attending the operation of the
* Projection may be made upon various surfaces, such as cylindrical surfaces,
spherical surfaces, etc.; but in this work attention will be confined to projection
upon plane surfaces.
t A visual ray is any straight line passing through the point of sight.