intros.
uniformize_dir_seg.
rewrite H.
auto.
Qed.
Hint Resolve dirseg_2: Geom.
(* Theorem dirseg_1 : (A,B,C,D:Point) C<>D -> -(A**B/C**D) = B**A /C**D. Proof with Geometry. Intros. Replace A**B with -B**A. Field. Symmetry. Qed.  Theorem dirseg_2 : (A,B,C,D:Point) C<>D -> -(A**B/C**D) = A**B /D**C. Proof with Geometry. Intros. Replace C**D with -D**C. Field. Symmetry. Qed.   Hints Resolve dirseg_1 dirseg_2 : Geom. *)

Theorem dirseg_3 :
forall A B C D : Point, C ** D <> 0 -> A ** B / C ** D = - (B ** A / C ** D).