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.

DEFINITIONS AND ASSUMPTIONS

3

system, owing to the obliquity of the visual rays to the plane of
projection, the system is not practicable for problematic work.
The orthographic projection -the system which will be employed
throughout this work -is that system in which the point of sight
is assumed at an infinite distance from the plane of projection.
In this system, since magnitudes are assumed within a finite
distance of the plane of projection, visual rays to the various
points of such magnitudes may be regarded as parallel lines, and
may be assumed perpendicular to the plane of projection.
Under these conditions the orthographic projection of a point
upon any plane is the point in which a straight line drawn through
the point perpendicular to the plane pierces the plane.
6. Planes of Projection. As a rule it is not possible to learn all
the characteristics of magnitudes of three dimensions from a single
standpoint of observation, and for this reason more than one plane
of projection is usually needed.
There are two principal planes of projection, - a horizontal plane
called the horizontal plane of projection or H, and a vertical plane
perpendicular to H and called the vertical plane of projection or V.
7. The Ground Line. The intersection of H and V is called the
ground line, or G-L.
8. Quadrants. The planes H and V divide space into four right
dihedral angles known as the first quadrant, the second quadrant,
the third quadrant, and the fourth quadrant.
The first quadrant is above H and in front of V, the second
quadrant is above H and back of V, the third quadrant is below H
and back of V, and the fourth quadrant is below H and in front of V.
9. Projecting Lines. In orthographic projection the visual rays
are called projecting lines, and are assumed perpendicular to the
plane on which projection is made.
10. Position of the Observer. When projecting on H the observer
is supposed to be above H and at an infinite distance from it.
When projecting on V the observer is supposed to be in front
of V and at an infinite distance from it.
11. Horizontal and Vertical Projections. Projections on H are
called horizontal projections, and projections on V are called vertical
projections.