To verify that a projection of a cubic curve is a cubic curve.
Rely on <a href=../../Bézier/Logic.html>this code</a> while replacing the identity function <tt>e</tt> with our 2D projection <tt>P</tt> given <a href=work.html>here</a>.
<pre>(define (P a b c d e f g h i) (lambda (p) (let ((x (car p)) (y (cdr p)))
  (let* ((D (/ (+ (* a x) (* b y) c))))
    (cons (* D (+ (* d x) (* e y) f)) (* D (+ (* g x) (* h y) i)))))))

(define e (P 2 4 3/4 -2 3 6 1 3 -5))</pre>
We conclude that a 2D projection transforms algebraic curves of orders 3, 4 and 5 into curves of the same order.