[Footnote 200: ἀγαπητοί. The word generally used in a _sermon_.] [Footnote 201: This also reads like a peroration.] [Footnote 202: In this chapter Hippolytus for the first time sets himself seriously to prove the thesis which he has before asserted, _i. e._, that all the Gnostic systems are derived from the teachings of the Greek philosophers. His mode of doing so is to compare the elaborate systems of Aeons or emanations of deity imagined by heresiarchs like Simon Magus and Valentinus to the views attributed by him to Pythagoras which make all nature to spring from one indivisible point. Whether Pythagoras ever held such views may be doubted and we have no means of checking Hippolytus’ always loose statements on this point; but something like them appears in the _Theaetetus_ of Plato where arithmetic and geometry seem to be connected by talk about oblong as well as square numbers and the construction of solids from them. If we imagine with the Greeks (see n. on p. 37 _supra_) that numbers are not abstract things, but actual portions of space, there is indeed a strong likeness between the ideas of the later Platonists as to the construction of the world by means of numbers and those attributed to the Gnostic teachers as to its emanation from God. Whether these last really held the views thus attributed to them is another matter. Cf. _Forerunners_, II, pp. 99, 100.] [Footnote 203: ἀπὸ τοῦ σημείου seems to be repeated needlessly.] [Footnote 204: ῥυὲν, “flowing out.”] [Footnote 205: πέρος ἔχουσα σημεῖον. Surely it has two limits--a point at each end.] [Footnote 206: σῶμα. In the next sentence he uses the proper word στερεόν.] [Footnote 207: This is, I suppose, quoted from the Ἀποφάσις μεγαλή attributed to Simon, as he speaks afterwards (II, p. 9 _infra_) of the small becoming great, “as it is written in the _Apophasis_, if it ... come into being from the indivisible point. But the great will be in the boundless æon,” etc.] [Footnote 208: What follows from this point down to the end of the paragraph is an almost verbatim transcript of the passage in Book I (pp. 37 ff. _supra_), where it is given as the teaching of Pythagoras. The only substantial differences are: that hypostasis is written for hypothesis in the second sentence of the passage; the Tetractys is no longer said to be the “source” of eternal nature; and the 11, 12, etc., are now said to take, and not “share” their beginning from the 10.] [Footnote 209: ὑπόθεσιν ἑαυτοῖς ἐντεῦθεν σχεδιάσαντες, _suis dogmatibus fundamentum posuerunt_, Cr.] [Footnote 210: τὸ πνεῦμα. Cruice translates this by _spiritum_, and is followed by Macmahon. I think, however, he means the breath, it being the idea of the ancients that the arteries were air-vessels.] [Footnote 211: παρεγκεφαλίς.] [Footnote 212: κωνάριον.] [Footnote 213: νωτιαῖον μοελόν.] [Footnote 214: It is at any rate plain from this that the missing Books II and III at one time existed.]