Chapter XI: Book IV: Diviners and Magicians (3)

[Footnote 66: The object of all these figures is apparently to prove that those of Archimedes are wrong and that the Platonic theory--said, one does not know with what truth, to have been inherited from Pythagoras, viz., that the intervals between the orbits of the different bodies of the cosmos are arranged like the notes on a musical scale--is to be preferred. This was perhaps to be expected from a Churchman as favouring the doctrine of creation by design. It is difficult at first sight to see how the figures in the text bear out Hippolytus’ contention, inasmuch as the distances here given of the seven planets (including therein the Sun and Moon) from the Earth proceed in an irregular kind of arithmetical progression ranging from one to fifty-four, the distance from the Earth to the Moon which Hippolytus accepts from Archimedes as correct being taken as unity. Thus, let us call this unit of distance _x_, and we have the table which follows:--

TABLE I (_of distances_)

Distance of Earth (♁) from ☽ = 5,544,130 stadia or _x_
“ ” “ ☉ = 16,632,390 ” 3_x_
“ ” “ ♀ = 33,264,780 ” 6_x_
“ ” “ ☿ = 55,441,300 ” 10_x_
“ ” “ ♂ = 105,338,470 ” 19_x_
“ ” “ ♃ = 149,691,510 ” 27_x_
“ ” “ ♄ = 299,383,020 ” 54_x_

But let us take the figures given in the text for the intervals between the Earth and the seven “planets” arranged in the same order, and again taking the Earth to Moon distance as unity, we have:--

TABLE II (_of intervals_)

Interval between ♁ and ☽ = 5,554,130 stadia or _x_
“ ” ☽ “ ☉ = 11,088,260 ” 2_x_
“ ” ☉ “ ♀ = 16,632,390 ” 3_x_
“ ” ♀ “ ☿ = 22,176,520 ” 4_x_(2²)
“ ” ☿ “ ♂ = 49,897,170 ” 9_x_(3²)
“ ” ♂ “ ♃ = 44,353,040 ” 8_x_(2³)
“ ” ♃ “ ♄ = 149,691,510 ” 27_x_(3³)

This agrees almost entirely with the theory which M. Bigourdan in the work mentioned in the last note has worked out as the Platonic theory of the distances of the different planets from the Earth, “the supposed centre of their movements” (p. 228). Thus:--

Planets ☽ ☉ ♀ ☿ ♂ ♃ ♄
Distances 1 2 3 4 8 9 27

which distances are, in his own words, “les termes enchevêtrés de deux progressions géométriques ayant respectivement pour raison 2 et 3, savoir 1, 2, 4, 8--1, 3, 9, 27; on voit que l’unité est, comme chez Pythagore, la distance de la Terre à la Lune.” This conclusion is amply borne out by Hippolytus’ figures, which, as given in Table II above, show a regular progression from 2 and 3 to 2² and 3², then to 2³ and 3³, which explains what our author means by increasing the Earth to the Moon distance, κατὰ τὰ διπλάσιον καὶ τριπλάσιον. The only discrepancy between this and M. Bigourdan’s table is that he has transposed the distances between ☿--♂ and ♂--♄ respectively; but as I do not know the details of the calculation on which he bases his figures, I am unable to say whether the mistake is his or Hippolytus’.]

[Footnote 67: Are we to conclude from this that these last calculations are those of Claudius Ptolemy, the author of the _Almagest_? He has certainly not been mentioned before, but his fame was so great that Hippolytus may have been certain that the allusion would be understood by his audience. Ptolemy lived, perhaps, into the last quarter of the second century.]

[Footnote 68: Genesis vi. 4. The subject seems to have had irresistible fascination for Christian converts of Asiatic blood, whether orthodox or heretic. Manes also wrote a book upon the Giants, cf. Kessler, _Mani_, Berlin, 1899, pp. 191 ff.]

[Footnote 69: Hippolytus seems to have been entirely ignorant that the calculations he derides were anything but mere guesswork. They were not only singularly accurate considering the imperfection of the observations at the disposal of their author, but have also been of the greatest use to science as laying the foundation of all future astronomy.]

[Footnote 70: ἀμέτρους. Another pun on their _measurements_.]

[Footnote 71: Nothing definite is known of this Colarbasus or his supposed astrological heresy. The accounts given of him by Irenæus and Epiphanius describe him as holding tenets identical with those of Marcus. Hort, following Baur, believes that he never existed, and that his name is simply a Greek corruption of _Qol arba_, “the Voice of the Four.” See _D.C.B._, s.h.v.]

[Footnote 72: περὶ μαθηματικῶν. The article is omitted; but he must mean the students and not the study. This is curious, because Mathematicus in the Rome of Hippolytus must have meant astrologer and nothing else, and what follows has nothing to do with astrology. Rather is it what was called in the Renaissance Arithmomancy. Cruice refers us to Athanasius Kircher’s _Arithmologia_ on the subject. Cornelius Agrippa, _De vanitate et incertitudine Scientiarum_, writes of it as “The Pythagorean lot,” and it is described in Gaspar Peucer’s _De præcipuis Divinationum generibus_, 1604.]

[Footnote 73: ψῆφοι, lit., pebbles, _i. e._ counters.]

[Footnote 74: στοιχεῖα: letters as the component parts or elements of words.]

[Footnote 75: Reading with the text τινὰς for Cruice’s τινὰ.]

[Footnote 76: In the text the Kappa and Tau are written at full length, the other numbers in the usual Greek notation, a proof that the scribe was here writing from dictation and not copying MS.]

[Footnote 77: ψηφισθὲν.]

[Footnote 78: The name is spelt Πάτροκλος.]

[Footnote 79: So that the “root” may be either 7 or 6 according as you use the “rule of 9” or of 7. A _reductio ad absurdum_.]

[Footnote 80: ἐὰν ἀπαρτίσῃ, “is even or complete.”]

[Footnote 81: I omit the Rho, which in the Codex precedes the Alpha. Cruice suggests it is put for Π.]

[Footnote 82: They do not, but make 26. Cruice adds an Alpha between the 8 and the 3: but in any case the rule just enunciated is broken by the reckoning in of two 2’s.]

[Footnote 83: Αἴας. Α = 1, ι = 10 = 1, α = 1 (omitted), ς = 200 = 2. 1 + 1 + 2 = 4.]

[Footnote 84: The Homeric name for Paris.]

[Footnote 85: κύριον ὄνομα as opposed to μεταφορὸν ὄνομα, a name transferred from one to another, or family name.]

[Footnote 86: Not 8 but 4. ο = 70 = 7, δ = 4, υ = 400 = 4, σ = 200 = 2, ε = 5 (with duplicate omitted) = 22, which divided by 9 leaves 4, or by 7, only 1. The next sentence and a similar remark at the last sentence but one of the chapter are probably by a commentator or scribe and have slipped into the text by accident. Oddly enough, nothing is said as to what happens if the “roots” are equal, as they seem to be in this case.]

[Footnote 87: Another mistake. Α = 1, σ = 200 = 2, τ = 300 = 3, ε = 5, ρ = 100 = 1, ο = 70 = 7, π = 80 = 8, ι = 10 = 1 (with duplicates omitted) = 28, which divided by 9 leaves 1, or by 7, 0 = 7.]

[Footnote 88: ὅταν μέντοι δευτερόν τινες ἀγωνίζωνται. _Quum vero quidam iterum decertant de numeris_, Cr. But the allusion is almost certainly to two charioteers or combatants meeting in successive contests. Half the divination and magic of the early centuries refers to the affairs of the circus, and the text has nothing about _de numeris_.]

[Footnote 89: Lit., inspection of the forehead (or face), or what Lavater called physiognomy. The word was known to Ben Jonson, who uses it in his _Alchymist_. “By a rule, Captain. In metoposcopy, which I do work by. A certain star in the forehead which you see not,” etc.]

[Footnote 90: ἰδέας.]

[Footnote 91: I have not thought it worth while to set down the various readings suggested by the different editors and translators for these “forms and qualities.” The whole of this chapter is taken from Ptolemy’s _Tetrabiblos_, and was corrupted by every copyist. The common type suggested with eyebrows meeting over the nose is plainly Alexandrian, as we know from the portraits on mummy-cases in Ptolemaic times.]

[Footnote 92: κοπιαταὶ. The dictionaries give “grave-digger,” which makes no sense.]

[Footnote 93: ὀφθαλμοῖς μέλασιν ὡς ἠλειμμένοις, “eyes black as if oiled.” Not a bad description of the eyes of a certain type of Levantine.]

[Footnote 94: The text has κολυμβῶσιν, which must refer to the eyes.]

[Footnote 95: Yet he twice calls them ψεῦσται, or “cheats.”]

[Footnote 96: Miller thinks this last characteristic interpolated.]

[Footnote 97: Reading λευκῷ for ἀλυκῷ, “salt,” which seems impossible.]

[Footnote 98: Reading ὑποδούλιοι for ὑπόδουλοι.]

[Footnote 99: Is any one born with grey hair?]

[Footnote 100: οἱ αὐτοὶ φύσεως. A similar phrase has just occurred under the same sign: a proof of the utter corruption of the text.]

[Footnote 101: ὀρχησταί in codex. Probably a mistake for εἰς κοινωνίαν εὔχρηστοι, “useful to the community.”]

[Footnote 102: δι’ ἐπινοίας; probably a sarcasm.]

[Footnote 103: It is hardly necessary to point out the futility of this astrology, its base being the theory that the earth is the centre of the universe. Nearly all the characteristics given above have, however, less to do with the stars than with those supposed to distinguish the different animals named. This is really sympathetic magic, or what was later called “the signatures of things.”]

[Footnote 104: A lacuna in the text here extending to the opening words of the next chapter.]

[Footnote 105: Richard Ganschinietz, in a study on _Hippolytus’ Capitel gegen die Magier_ appearing in Gebhardt’s and Harnack’s _Texte und Untersuchungen_, dritte Reihe Bd. 9, Leipzig, 1913, says it is not doubtful that Hippolytus took this chapter from Celsus’ book κατὰ μάγων, which he discovers in Origen’s work against the last-named author. He assumes that Lucian of Samosata in his Ἀλέξανδρος ἢ Ψευδόμαντις borrowed from the same source.]

[Footnote 106: τῶν δαιμόνων, _a demonibus_, Cr. But the word δαίμων is hardly ever used in classic or N.T. Greek for a devil or evil spirit, generally called δαιμόνιον. Δαίμων here and elsewhere in this chapter plainly means a god of lesser rank or spirit. Cf. Plutarch _de Is. et Os._, cc. 25-30.]

[Footnote 107: τῷ παιδὶ, the magician’s assistant necessary in all operations requiring confederacy or hypnotism.]

[Footnote 108: For the composition of this see Plutarch, _op. cit._, c. 81.]

[Footnote 109: ὁ μυχός. Often used for the women’s chamber or gynaeceum.]

[Footnote 110: Clearly the Egyptian sun-god Ra or Rê, the Phi in front being the Coptic definite article. It is a curious instance of the undying nature of any superstition that in the magical ceremonies of the extant Parisian sect of Vintrasists, Ammon-Ra, the Theban form of this god, is invoked apparently with some idea that he is a devil. See Jules Bois’ _Le Satanisme et la Magie_, Paris, 1895.]

[Footnote 111: χαλκάνθον, sulphate of iron, which, mixed with tincture or decoction of nut-galls, makes writing ink. Our own word copperas is an exact translation.]

[Footnote 112: φιάλη. A broad flat pan used for sacrificial purposes.]

[Footnote 113: There is some muddle here, probably due to Hippolytus not having any practical acquaintance with the tricks described. The smoke of nut-galls would hardly make the writing visible. On the other hand, letters written in milk will turn brown if exposed to the fire without the application of any ash.]

[Footnote 114: A sauce made of brine and small fish.]

[Footnote 115: See the roughly-drawn vignettes usual in magic papyri, _e. g._ Parthey, _Zwei griechische Zauberpapyri_, Berlin, 1866, p. 155; Karl Wessely, _Griechische Zauberpapyri von Paris und London_, Vienna, 1888, p. 118.]

[Footnote 116: τὰς φρένας. One of Hippolytus’ puns.]

[Footnote 117: Hebrew was used in these ceremonies, because they were largely in the hands of the Jews. See _Forerunners and Rivals of Christianity_, II, pp. 33, 34, for references.]

[Footnote 118: ἠχεῖ. Particularly appropriate to the striking of a metal disc.]

[Footnote 119: The book of course was a long roll of parchment, the inner coils of which could be drawn out as described.]

[Footnote 120: ὀρυκτῶν ἁλῶν. Cruice translates fossil salts. Does he mean rock-salt?]

[Footnote 121: τὸ ἰνδικὸν μέλαν. Either indigo dye or pepper. Cayenne pepper put in the flame might have a startling effect on the audience.]

[Footnote 122: Where?]

[Footnote 123: Said to be an astringent earth made from rock-alum, and containing both alum and vitriol. Known to Hippocrates.]

[Footnote 124: Red lead or vermilion? The idea seems to be to frighten the dupe by the supposed prodigy of a hen laying eggs which have red or black inside them instead of white.]

[Footnote 125: Pliny, _Nat. Hist._, VIII, c. 75, says the sheep is compelled when it feeds to turn away from the sun by reason of the weakness of its head. This is probably the story which Hippolytus or the author has exaggerated. Something is omitted from the text.]

[Footnote 126: Seal or porpoise oil?]

[Footnote 127: Hymns like these are to be found in the two collections of magic papyri quoted in n. on p. 93 _supra_.]

[Footnote 128: He tells us how this trick is performed on p. 100 _infra_. Lecanomancy or divination by the bowl was generally performed by means of a hypnotized boy, as described in Lane’s _Modern Egyptians_. This, however, is a more elaborate process dependent on fraud.]

[Footnote 129: Reading νάτρον for νίτρον. It was common in Egypt, and saltpetre would not have the same effect, which seems to depend on the expulsion of carbonic acid.]

[Footnote 130: μυρσίνη. Cruice suggests μάλφη, a mixture of wax and pitch, which hardly seems indicated. Storax is the ointment recommended by eighteenth-century conjurers. Water is all that is needful.]

[Footnote 131: ἰχθυοκόλλα. Presumably fish-glue. Macmahon suggests isinglass. The salamander, the use of which is to be sought in sympathetic magic, was no doubt calcined and used in powder. σκολοπένδριον, “millipede” and σκολόπενδρον, “hart’s tongue fern” are the alternative readings suggested. Fern-oil is said to be good for burns.]

[Footnote 132: Probably chalk or gypsum.]

[Footnote 133: αὐτορρύτων κηκίδων τε κενῶν. Κήκις here evidently means any sort of nut-shell. But how can it be “self-flowing”? Miller’s suggested φορυτὸν makes no better sense.]

[Footnote 134: The lion-headed figure of the Mithraic worship is shown thus setting light to an altar in Cumont’s _Textes et Monuments de Mithra_, II, p. 196, fig. 22. A similar figure with an opening at the back of the head to admit the “wind-pipe” described in the text shows how this was effected. See the same author’s _Les Mystères de Mithra_, Brussels, 1913, p. 235, figs. 26, 27.]

[Footnote 135: The solution of alum would be effective without any other ingredients.]

[Footnote 136: That is, not by guesswork. Another pun.]

[Footnote 137: The letter was of course in the form of a writing-tablet bound about with silk or cord, to which the seal was attached.]

[Footnote 138: This would make something like plaster of Paris.]

[Footnote 139: This book or the former one. Lucian describes the same process in his _Alexander_, which he dedicates to Celsus; _v._ n. on p. 92 _supra_.]

[Footnote 140: ἀφορμὰς λαβών, “taking them as starting-points.”]

[Footnote 141: Cruice suggests that this sentence has either got out of place or is an addition by an annotator. Probably an afterthought of Hippolytus’.]

[Footnote 142: See n. on p. 97 _supra_.]

[Footnote 143: κύανος. A dark-blue substance which some think steel, others lapis lazuli.]

[Footnote 144: συμπαῖκται, “playfellows.” Here, as elsewhere in the text, accomplices or confederates.]

[Footnote 145: Several words missing here, perhaps by intention. It would be interesting to know if the “drug” was any preparation of phosphorus.]

[Footnote 146: Should be Baubo, a synonym of Hecate in the hymn to that goddess published by Miller, _Mélanges de Litt. Grecque_, Paris, 1868, pp. 442 ff.]

[Footnote 147: Most of the epithets and names here used are to be found in the hymn quoted in the last note. The goddess is there identified not only with Artemis and Persephone, but with the Sumerian Eris-ki-gal, lady of hell.]

[Footnote 148: A sort of magic lantern? κάτοπτρον, which I have translated mirror, _might_ be a lens. One is said to have been found in Assyria.]

[Footnote 149: πόρρωθεν. Better, perhaps, πόρροτεθεν.]

[Footnote 150: Full moon, or half, or quarter, as the case may be.]

[Footnote 151: Schneidewin seems to be right in suggesting a lacuna here.]

[Footnote 152: ἐν ὑαλώδεσι τύποις. Schneidewin suggests τόποις unreasonably. Many alabaster jars are nearly transparent.]

[Footnote 153: Cf. Aristotle, _De Hist. Animal._, V, 10, 2. Said to be _Coryphæna hippurus_.]

[Footnote 154: The hiatus leaves us in doubt how this operated. Perhaps it liberated free ammonia.]

[Footnote 155: Reading ἐπίπλοον βοείου instead of, with Cruice, ἐπίπλεον βώλου, “filled with clay.”]

[Footnote 156: ἀφανὲς, “unapparent.”]

[Footnote 157: ἀπηνέχθημεν. An admission that this chapter was an afterthought.]

[Footnote 158: ὡς εἰκάσαι, ἐστι, _ut patet_, Cr.]

[Footnote 159: θεολόγοι. It does not mean “theologians” in our sense, but narrator of stories about the gods. Orpheus is always considered a θεολόγος.]

[Footnote 160: ποδαπός. Not, as Cruice translates, _quale_, which would be better expressed by the ποίον of Aristotle.]

[Footnote 161: τὸ σύμπαν αὐτὸ.]

[Footnote 162: It is fairly certain that Hippolytus in this “Recapitulation” must here be summarizing the missing Books II and III. He has said nothing in any part of the work that has come down to us about the Persian theology, and in Book I he calls Zaratas or Zoroaster a Chaldæan and not a Persian.]

[Footnote 163: ψήφοις ὑπέβαλον καὶ are supplied by Schneidewin in the place of three words rubbed out.]

[Footnote 164: Reading with Schneidewin μοιρῶν for μυρῶν and ἐπιπνοίας for ἐπίνοιας.]

[Footnote 165: By indivisible comparison (σύγκρισις) he seems to imply that these numbers cannot be divided except by 1. Hence Cruice would omit 9 as being divisible by 3. Perhaps he means “like indivisibility.”]

[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.”]

[Footnote 177: “Catasterisms” was the technical term for these transfers, of which the _Coma Berenices_ is the best-known example. Cf. Bouché-Leclercq, _op. cit._, p. 23.]

[Footnote 178: The long-eared owl (_strix otus_). According to Ælian it had a reputation for stupidity, and was therefore a type of the easy dupe, Athenæus, _Deipnosophistæ_, IX, 44, 45, tells a similar story to that in the text about the bustard.]

[Footnote 179: Reading μετανάσσεται for μετανίσσεται or μετανείσεται.]

[Footnote 180: στρεπτούς, _volventes_, Cr. An attempt to pun on πόλος, the Pole.]

[Footnote 181: Job i. 7. The Book of Job according to some writers comes from an Essene school, which may give us some clue to the origin of these ideas. The Enochian literature to which the same tendency is assigned is full of speculations about the heavenly bodies. See _Forerunners_, I, p. 159, for references.]

[Footnote 182: ὁ ἐν γόνασιν. Aratus calls this constellation ὁ ἐν γόνασι καθήμενος, Cicero _Engonasis_, Ovid _Genunixus_, Vitruvius, Manilius and J. Firmicus Maternus, _Ingeniculus_.]

[Footnote 183: A perversion of the “it shall bruise thy head and thou shall bruise his heel,” of Genesis iii. 15.]

[Footnote 184: From his attitude the Kneeler resembles the figure of Atlas supporting the world, who as Omophorus plays a great part in Manichæan mythology. Cumont derives this from a Babylonian original, for which and his connection with Mithraic cosmogony see his _Recherches sur le Manichéisme_, Brussels, 1908, I, p. 70, figs. 1 and 2. The constellation is now known as Hercules.]

[Footnote 185: Hippolytus here evidently quotes not from Aratus, but from some unnamed Gnostic or heretic writer, whom Cruice thinks must have been a Jew. Yet he was plainly a Christian, as appears from his remarks about the “Second Creation.” An Ebionite writer might have preserved many Essene superstitions.]

[Footnote 186: Cruice, following Roeper, says these words have slipped in from an earlier page.]

[Footnote 187: ὀφιοῦχος. The “Ophiuchus huge” of Milton or Anguitenens.]

[Footnote 188: Ἑλίκη. So Aratus and Apollonius Rhodius. Said to be so called from its perpetually revolving. Cruice remarks on this sentence that it does not seem to have been written by a Greek, and quotes Epiphanius as to the addiction of the Pharisees to astrology. But see last note but one.]

[Footnote 189: ἑλίκη. A pun quite in Hippolytus’ manner.]

[Footnote 190: πρὸς ἣν ... ναυτίλλονται. Cruice and Macmahon alike translate this “towards which,” but Aratus clearly means “steer by” both here and earlier.]

[Footnote 191: Herodotus I, 1. He does not say, however, that the Greeks were Phœnicians.]

[Footnote 192: Rather the conceiver, from κύω, to conceive. γεννάω is used of the mother by Aristotle, _De Gen. Animal._, 3, 5, 6.]

[Footnote 193: λογικῆς.]

[Footnote 194: Reading Ιάσαδος for Cruice’s Ἰασίδαο. The text is said to have εἰς ἀΐδαο.]

[Footnote 195: γράμματα, elementa, Cr. But I think the allusion is to the story they contain for those who can read them.]

[Footnote 196: The Swan.]

[Footnote 197: τὰς ἰδέας.]

[Footnote 198: If Hippolytus’ words are here correctly transcribed, the “heretic” quoted seems to have two inconsistent ideas about the stars. One is that the constellations are types or allegories of what takes place in man’s soul; the other, that they are the patterns after which the creatures of this world were made. This last is Mithraic rather than Christian.]

[Footnote 199: τῆς τούτων ὑπολήψεως, _ab horum cogitationibus_, Cr.]

[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.]

[Footnote 215: These words appear in the MS. at the foot of this Book.]