The geometry section (chapters 5-8) of the so-called Fragmentum Censorini (date of composition unknown) is a faithful translation of the definitions (ὅροι), of the postulates (αἰτήματα) and of the common notions (κοιναὶ ἔννοιαι) of Book I of the Elements written by the Greek mathematician Euclid (IV-III B.C.). Within the Latin tradition, numerous translations, spanning several centuries (from the 1st to the 6th ) and directly or indirectly connected to Euclid, do survive. This contribution is a critical edition of the Fragmentum; it also includes an essay where the connections which can be established with the tradition of Euclides Latinus are scrutinized and assessed.