[Footnote 166: Cruice suggests that this was an astronomical instrument and quotes Cl. Ptolemy, _Harmon._, I, 2, in support.]
[Footnote 167: Why should the cosmos be masculo-feminine? The Valentinians said the same thing about their Sophia, who was, as I have said elsewhere (_Journal of the Royal Asiatic Society_, Oct. 1917), a personification of the Earth. The idea seems to go back to Sumerian times. Cf. _Forerunners_, II, 45, n. 1, and Mr. S. Langdon, _Tammuz and Ishtar_, Oxford, 1914, pp. 7, 43 and 115.]
[Footnote 168: The worshippers of the Greek Isis declared Isis to be the earth and Osiris water. See _Forerunners_, I, 73, for references. If Hippolytus is here recapitulating Books II and III, it is probable that the lacuna was occupied with some reference to the Alexandrian deities and their connection with the arithmetical speculations of the Neo-Pythagoreans. Could this be substantiated, we should not need to look further for the origin of the Simonian and Valentinian heresies.]
[Footnote 169: ψηφιζόμενα κὰι ἀναλυόμενα, _supputata et diversa_, Cr. The process seems to be that called earlier (p. 85 _supra_) the rule of 9.]
[Footnote 170: 361 ÷ 9 = 40 + 1; 605 ÷ 9 = 67 + 2.]
[Footnote 171: ἀπερίζυγον, lit., “unyoked.”]
[Footnote 172: εἰς ἐννάδα here appears in the text apparently as an alternative reading. Cruice suggests “with an ennead deducted.”]
[Footnote 173: Meaning that some reckon the numerical value of all the letters in a name, others that of the vowels only.]
[Footnote 174: What follows has nothing to do with divination, but treats of the celestial map as a symbolical representation of the Christian scheme of salvation. Hippolytus condemns the notion as a “heresy,” but if so, its place ought to be in Book V. It is doubtful from what author or teacher he derived his account of it; but all the quotations from Aratus’ _Phænomena_ which he gives are to be found in Cicero, _De Natura Deorum_, 41, where they make, as they do not here, a connected story.]
[Footnote 175: One of the passages favouring the conjecture that the book was originally in the form of lectures.]
[Footnote 176: οἱ ἐντυγχάνοντες, _legentibus_, Cr. It may just as easily mean “those who come across this.”]