author of a book Περὶ τῆς τοῦ πάντος οὐσίας, and Photius ascribes a book with the same title to the Roman Caius (§ 31, 7), Baur attributes to the latter the composition of the Elenchus. Photius, however, founds his opinion simply upon an apocryphal note on the margin of his copy of the book. Incomparably more important are the evidences for the Hippolytus authorship, which is now almost universally admitted. The Elenchus is not, indeed, enumerated in the list of works on the statue. The book Περὶ τῆς τοῦ πάντος οὐσίας, however, appears there, and it contains the statement that its author also wrote the Elenchus. The author of the Elenchus also states that he had previously written a similar work in a shorter form, and Photius describes such a shorter writing of Hippolytus, dating from the time of his intercourse with Irenæus, under the title Σύνταγμα κατὰ πασῶν αἱρέσεων. Lipsius has made it appear extremely probable that in the _Libellus adv. omnes hæreticos_ appended to Tertullian’s _De præscriptione hæreticorum_, and so usually styled a treatise of the Pseudo-Tertullian, we have an abbreviated Latin reproduction of that work; for this one as well as the other begins with Dositheus and ends with Noëtus, and both deal with thirty-two heresies. Epiphanius and Philastrius [Philaster] have used it largely in their heresiological works. The discussion in the Elenchus agrees therewith in many passages but also in many is essentially different, which, however, when we consider the much later date of the first named treatise affords no convincing evidence against the theory that both are by one author. The Elenchus thereby wins a high importance as giving information about the condition of the Roman church during the first decades of the 3rd century, about the position of the author who describes himself in his treatise as a pupil of Irenæus, about his own and his opponents’ way of viewing things, and about his conflict with them leading to schism, though all is told from the standpoint of an interested party (§§ 33, 5; 41, 1). A considerable fragment directed against the errors of Noëtus (§ 33, 5) was perhaps originally a part of his Syntagma,--though not perhaps of the anonymous, so-called Little Labyrinth against the Artemonites (§ 33, 3) or probably against the Monarchians generally, from which Eusebius makes extensive quotations, especially about the Theodotians. This work is ascribed by Photius to the Roman Caius, but without doubt wrongly. Great probability has been given to the recently advanced idea that this book too may have been written by Hippolytus.[72] § 31.4. =The Alexandrian Church Teachers.=