Proof with try solve [ Geometry | congruence ].
intros...
assert (P ** M / Q ** M = M ** P / M ** Q)...
assert (M ** P / M ** Q = S A M P / S A M Q)...
assert (S A M P = S P A M)...
assert (S A M Q = S Q A M)...
Qed.
Hint Resolve A6_1: Geom.

Theorem A6_2 :
forall P Q R A : Point,
P <> Q -> ~ Col Q A P -> Col P Q R -> P ** R / P ** Q = S R A P / S Q A P.