(* elimination of ratios for euclidean constructions *)
(* the condition A<>Y is required *)

Theorem elim_ratio_on_perp_d_spec_b :
forall Y P Q A C : Point, forall r: F,
on_perp_d Y P Q r->
~ Col A P Y  ->
parallel A Y C Y ->
C<>Y ->
A**Y / C**Y = Py A P Q / Py C P Q.