theorem
  for r being Real st P,Q,R are_collinear &
  P <> R & Q <> R & P <> Q &
  r = affine-ratio(P,Q,R) holds
  affine-ratio(P,R,Q) = 1 / r &
  affine-ratio(Q,P,R) = r / (r - 1) &
  affine-ratio(Q,R,P) = (r - 1) / r &
  affine-ratio(R,P,Q) = 1 / (1 - r) &
  affine-ratio(R,Q,P) = 1 - r by Th09,Th10,Th11,Th12,Th13;
