The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets”. However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded the note with the (...) observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form. (shrink)