Proof with Geometry.
intros...
assert (C ** A = - A ** C)...
assert (S P C A = - S P A C)...
assert (C ** B / C ** A = S P C B / S P C A)...
rewrite H3 in H4...
rewrite H2 in H4...
RewriteVar (C ** B) H4...
field...
Qed.
Hint Resolve A6_3: Geom.

Theorem A6_4 :
forall A B C P : Point,
A <> B -> ~ Col P A B -> Col A B C -> C ** A / A ** B = S P C A / S P A B.