indications of what is to follow immediately, which can hardly be anything else than announcements in advance of the subject of the next lecture. Thus, at the end of Book I, he promises to explain the mystic rites[47]--a promise which is for us unfulfilled in the absence of Books II and III; at the end of Book IV, he tells us that he will deal with the disciples of Simon and Valentinus[48]; at that of Book VII, that he will do the same with the Docetæ[49]; and at that of Book VIII that he will “pass on” to the heresy of Noetus.[50] In none of these cases does he more than mention the first of the heresies to be treated of in the succeeding book, which the reader could find out for himself by turning over the page, or rather by casting his eye a little further down the roll. Again, there are repetitions in our text excusable in a lecturer who does not, if he is wise, expect his hearers to have at their fingers’ ends all that he has said in former lectures, and who may even find that he can best root things in their memory by saying them over and over again; but quite unpardonable in a writer who can refer his readers more profitably to his former statements. Yet, we find our author in Book I giving us the supposed teaching of Pythagoras as to the monad being a male member, the dyad a female and so on up to the decad, which is supposed to be perfect.[51] This is gone through all over again in Book IV with reference to the art of arithmetic[52] and again in Book VI where it is made a sort of shoeing-horn to the Valentinian heresy[53]. The same may be said of the “Categories” or accidents of substance which Hippolytus in one place attributes to Pythagoras, but which are identical with those set out by Aristotle in the _Organon_. He gives them rightly to Aristotle in Book I, but makes them the invention of the Pythagoreans in Book VI only to return them to Aristotle in Book VII.[54] Here again is a mistake such as a lecturer might make by a slip of the tongue, but not a writer with any pretensions to care or seriousness.