Proof with try solve [ Geometry | congruence ].
intros...
assert (P ** R / P ** Q = S A P R / S A P Q)...
assert (S A P R = S R A P)...
assert (S A P Q = S Q A P)...
Qed.
Hint Resolve A6_2: Geom.

Theorem A6_3 :
forall A B C P : Point,
A <> C -> ~ Col P A C -> Col A B C -> C ** B / A ** C = S P C B / S P A C.