Proof with Geometry.
intros.
unfold not in |- *; intro.
assert (Col A O P)...
assert (Col A O B)...
assert (Col A P B)...
eauto with Geom...
Qed.
Hint Resolve col_not_col_1.

Theorem A6_1 :
forall P Q A M : Point,
M <> Q -> ~ Col Q A M -> Col P Q M -> P ** M / Q ** M = S P A M / S Q A M.