(* set (X_C := S O U C). set (X_A := S O U A). set (X_B := S O U B). set (X_D := S O U D). set (Y_C := S O V C). set (Y_A := S O V A). set (Y_B := S O V B). set (Y_D := S O V D). *)

Lemma free_points_ratio_elimination_8 : forall O U V A B C D: Point,
parallel A B C D ->
C<>D ->
~ Col O U V ->
~ Col V A C ->
Col A C D ->
A**B / C**D =
( S O U V * (S O V B - S O V A) + S O V A * S O U B - S O V B * S O U A) /
( S O U V * (S O V D - S O V C) + S O V C * S O U D - S O V D * S O U C).