An elementary treatise on cubic and quartic curves, by A. B. Basset.

CHAPTER XII.
THEORY OF PROJECTION.
351. THE theory of projection is explained in treatises on
Conics, but since it affords a powerful method of deducing
general properties of curves from those of curves of a more simple
form we shall explain its leading features, and then apply it
to deduce properties of cubic and quartic curves.
If a curve S be drawn in any plane z, and if with any point V
as vertex a cone be described whose generators pass through S,
the curve of intersection of the cone with any plane z' is called
the projection of S.
If any straight line through the vertex cut the planes z and z'
in P and P', these points are called corresponding points. In
other words, the projection of P on the plane z' is called the point
corresponding to P.
The projection of any straight line is obviously another
straight line. Also if any straight line cuts a curve in n points
PI, P2,.., P, its projection will cut the projection of the curve in
n corresponding points P1', P2',... Pn'. But since every straight
line cuts a curve of the nth degree in n real or imaginary points,
it follows that the projections of the line and curve cut one
another in the same number of points. Hence the projection
of a curve of the nth degree is another curve of the same degree;
also a tangent to a curve projects into a tangent to the projection
of the curve, and every singularity on a curve projects into the
same singularity on the projected curve.
It can be shown by elementary geometry that the projection
of a triangle on any parallel plane is a similar triangle; from
which it follows that the projection of a polygon on a parallel