Abū al-Wafā’ al-Būzjānī proposed, in a fragment established and translated herein, two methods to build a parabolic mirror. The lack of demonstration, particularly for the first method, raises a difficult question of interpretation. To understand this method, O. Neugebauer used, in an unpublished article translated herein, concepts of descriptive geometry. He then eliminated the space construction used, to keep only simple geometrical considerations known by the Greeks. The second interpretation, given by R. Rashed, is based on the geometrical practices of al-Būzjānī's contemporaries, like al-Qūhī and Ibn Sahl, i.e. on the methods of conical projections. The second method borrowed by al-Būzjānī from Ibn Sinān seems to support this last interpretation.