p. 203, Copt. Why there should be 24, when the dodecad or group of Aeons in the world above was only 12, it is difficult to say. But Hippolytus supplies a sort of explanation when he says (_op. cit._ Bk VI. c. 33, p. 292, Cruice): Ταῦτά ἐστιν ἃ λέγουσιν· ἔτι [δὲ] πρὸς τούτοις, ἀριθμητικὴν ποιούμενοι τὴν πᾶσαν αὐτῶν διδασκαλίαν, ὡς προεῖπον [τοὺς] ἐντὸς Πληρώματος Αἰῶνας τριάκοντα πάλιν ἐπιπροβεβληκέναι αὐτοῖς κατὰ ἀναλογίαν Αἰῶνας ἄλλους, ἵν’ ᾖ τὸ Πλήρωμα ἐν ἀριθμῷ τελείῳ συνηθροισμένον. Ὡς γὰρ οἱ Πυθαγορικοὶ διεῖλον εἰς δώδεκα καὶ τριάκοντα καὶ ἑξήκοντα, καὶ λεπτὰ λεπτῶν εἰσὶν ἐκείνοις, δεδήλωται· οὕτως οὗ τοι τὰ ἐντὸς Πληρώματος ὑποδιαιροῦσιν. “This is what they say. But besides this, they make their whole teaching arithmetical, since they say that the thirty Aeons within the Pleroma again projected by analogy other Aeons, so that thereby the Pleroma may be gathered together in a perfect number. For the manner in which the Pythagoreans divide [the cosmos] into 12, 30, and 60 parts, and each of these into yet more minute ones, has been made plain” [see _op. cit._ Bk VI. c. 28, p. 279, where Hippolytus tells us how Pythagoras divided each Sign of the Zodiac into 30 parts “which are days of the month, these last into 60 λεπτὰ, and so on”]. “In this way do they [the Valentinians] divide the things within the Pleroma.” Cf. Μέρος τευχῶν Σωτῆρος p. 364, Copt. In another book of the Philosophumena (Bk IV. c. 7 Περὶ τῆς ἀριθμετικῆς τέχνης) he explains how the Pythagoreans derived infinity from a single principle by a succession of odd and even or male and female numbers, in connection with which he quotes Simon Magus (_op. cit._ p. 132, Cruice). The way this was applied to names he shows in the chapter Περὶ μαθηματικῶν (_op. cit._ Βk IV. c. 11, pp. 77 _sqq._, Cruice) which is in fact a description of what in the Middle Ages was called Arithmomancy, or divination by numbers. Footnote 492: p. 224, Copt. See also p. 241, Copt.—a very curious passage where the Ineffable One is called “the God of Truth without foot” (cf. Osiris as a mummy) and is said to live apart from his “members.” Footnote 493: In the beginning of the Μέρος τευχῶν Σωτῆρος (p. 252, Copt.) it is said of the Ineffable that “there are many members, but one body.” But this statement is immediately followed by another that this is only said “as a pattern (παράδειγμα) and a likeness and a resemblance, but not in truth of shape” (p. 253, Copt.). Footnote 494: What he does say is that the Ineffable One has two χωρήματα or receptacles and that the second of these is the χώρημα of the First Mystery. It is, I think, probable that an attempt to describe both these χωρήματα is made in one of the documents of the Bruce Papyrus. See pp. 191, 192 _infra_. Footnote 495: