Let ABC, A'B'C' be orthologic with orthologic centers O, O' and perspective with center S. Define A" as the intersection between AO and A'O', and analogously B", C". The triangle A"B"C" is perspective with ABC and A'B'C' with perspective centers O, O' and is orthologic with ABC and A'B'C' with two orthologic centers S and the other two O and O'.