[Footnote 131: Hippolytus gives as is usual with him a more detailed

account of Aristotle’s doctrines on these points later. (See Book VII,

II, pp. 62 ff. _infra_.) He there admits that he cannot say exactly

what was Aristotle’s doctrine about the soul. He also refers to books

of Aristotle on Providence and the like which, _teste_ Cruice, no

longer exist. Cf. Macmahon’s note on same page (p. 272 of Clark’s

edition).]

[Footnote 132: ἐπὶ τὸ συλλογιστικώτερον τὴν φιλοσοφίαν ηὔξησαν.

_Syllogisticæ artis expolitione philosophiam locupletarunt._]

[Footnote 133: Prof. Arnold in his lucid book on _Roman Stoicism_

(Cambridge, 1911, p. 219, n. 4) quotes this as a genuine Stoic

doctrine. But Diog. Laert., VII, _vit. Zeno_, c. 68, represents Zeno,

Cleanthes, Chrysippus, Archedemus and Posidonius as agreeing that

principles and elements differ from one another in being respectively

indestructible and destroyed, and because elements are bodies while

principles have none. For the Stoic idea of God, see _op. cit._, c. 70.

So Cicero, _De Natura Deorum_, Bk. I, cc. 8, 18, makes Zeno say that

the cosmos is God, but in the _Academics_, II, 41 that Aether is the

Supreme God, with which doctrine, he says, nearly all Stoics agree.

Perhaps Hippolytus is here quoting Clement of Alexandria, _Stromateis_,

VI, 71, who says that the Stoics dare to make the God of all things

“a corporeal spirit.” For the Stoic doctrine of Providence, see Diog.

Laert., _vit. Zeno_, c. 70.]

[Footnote 134: ποιῶν καὶ τὸ αὐτεξούσιον μετὰ τῆς ἀνάγκης οἷον τῆς

εἱμαρμένης. Τὸ αὐτεξούσιον is the recognized expression for free will.

Note the difference between ἀνάγκη, “compulsion,” and εἱμαρμένη,

“destiny.” For the Stoic doctrine of Fate, see Diog. Laert., _vit.

cit._, c. 74.]

[Footnote 135: Diog. Laert., _ubi cit._, c. 84.]

[Footnote 136: From ψῦξις, “cooling”--a bad pun.]

[Footnote 137: It is extremely doubtful whether the metempsychosis ever

formed part of Stoic doctrine.]

[Footnote 138: Zeno and Cleanthes both accepted the ecpyrosis. See

Diog. Laert., _ubi cit._, c. 70. The same author says that Panætius

said that the cosmos was imperishable.]

[Footnote 139: σῶμα διὰ σώματος μὲν χωρεῖν, _corpusque per corpus

migrare_, Cr. Macmahon inserts a “not” in the sentence, but without

authority. The Stoic resurrection assumed that in the new world created

out of the ashes of the old, individuals would take the same place as

in this last. See Arnold, _op. cit._, p. 193 for authorities.]

[Footnote 140: ἀτόμοι, “that cannot be cut.” The rest of this sentence

is taken from Diog. Laert., X, _vit. Epicur._, c. 24, and is quoted

there from Epicurus’ treatise on Nature.]

[Footnote 141: With the exception of the Deity’s seat in the

intercosmic spaces and the idea that the souls of men consist of blood,

all the above opinions of Epicurus are to be found in Diog. Laert., X,

_vit. Epic._]

[Footnote 142: οὐ μᾶλλον, “not rather.”]

[Footnote 143: See n. on p. 49 _supra_. The doctrines here given are

those of the Sceptics, and are to be found in Diog. Laert., IX, _vit.

Pyrrho_, c. 79 ff. and in Sextus Empiricus, _Hyp. Pyrrho_, I, 209 ff.

Diog. Laert. quotes from Ascanius of Abdera that Pyrrho introduced the

dogma of incomprehensibility, and Hippolytus seems to have copied this

without noticing that he has said the same thing about Xenophanes.]

[Footnote 144: Diog. Laert., I, _Prooem._, c. 1, mentions both

Gymnosophists and Druids, but if he ever gave any account of their

teaching it must be in the part of the book which is lost. Clem. Alex.,

_Stromateis_, I, c. 15, describes the two classes of Gymnosophists

as Sarmanæ and Brachmans. The Sarmanæ or Samanæi (Shamans?) seem the

nearer of the two to the Brachmans of our text.]

[Footnote 145: ἀκροδρύοι, hard-shelled fruit such as acorns or

chestnuts.]

[Footnote 146: Roeper suggests the Ganges.]

[Footnote 147: Megasthenes, for whom see Strabo V, 712, differs from

Hippolytus in making the abstinence of the Gymnosophists endure for

thirty-seven years only.]

[Footnote 148: Nothing has yet been said about any bank.]

[Footnote 149: The whole of this sentence is corrupt. Macmahon

following Roeper would read: “This discourse whom they name God they

affirm to be incorporeal, but enveloped in a body outside himself, just

as if one carried a covering of sheepskin to have it seen; but having

stripped off the body in which he is enveloped, he no longer appears

visibly to the naked eye.”]

[Footnote 150: ἐγείρας τρόπαιον, lit., “raised a trophy.”]

[Footnote 151: θεολογοῦσι. Eusebius, _Præp. Ev._, uses the word in this

sense. For the Dandamis and Calanus stories, see Arrian, _Anabasis_,

Bk. VII, cc. 2, 3.]

[Footnote 152: This is quite unintelligible as it stands. It probably

means that the Brachmans worship the light of which the Sun is the

garment, and that they think they are united with it when temporarily

freed from the body. Is he confusing them on the one hand with the

Yogis, whose burial trick is referred to later in connection with Simon

Magus, and on the other with some Zoroastrian or fire-worshipping sect

of Central Asia?]

[Footnote 153: ὃς ... ἐκεῖ χωρήσας αἴτιος τούτοις ταύτης τῆς φιλοσοφίας

ἐγένετο. Does the ἐκεῖ mean Galatia, whose inhabitants were Celts

by origin? Hippolytus has probably copied the sentence without

understanding it.]

[Footnote 154: Hesiod is treated by Aristotle, _Metaphysica_, Bk.

II, c. 15, as one who philosophizes, which perhaps accounts for the

introduction of his name here.]

[Footnote 155: διδαχθῆναι, _ut se edocerent_, Cr. So Macmahon. The

context, however, plainly requires that it is Hesiod and not the Muse

who is to be taught. The rendering of poetry into prose is seldom

satisfactory, so I have ventured to give here the version of Elton,

which is as close to the original as it is poetic in form.]

[Footnote 156: ὡς στέφανον δάσσαντο.]

[Footnote 157: Αἰθήρ τε καὶ Ἡμέρη. One would prefer to keep the word

“Aether,” which is hardly “sunshine.”]

[Footnote 158: ἶσον ἑαυτῇ.]

[Footnote 159: τὰ μυστικὰ. The expression generally used for Mysteries

such as those of Eleusis. Either he employs it here to include the

tricks of the magicians described in Book IV, or he did not mean to

describe these last when the sentence was written, but to go instead

straight from the astrologers to the heresies. The last alternative

seems the more probable.]

[Footnote 160: ἀδρανῆ, _infirmas_, Cr.]

[Footnote 161: The main question which arises on this First Book of our

text is, What were the sources from which Hippolytus drew the opinions

he here summarizes? Diels, who has taken much pains over the matter,

thinks that his chief source was the epitome that Sotion of Alexandria

made from Heraclides. As we have seen, however, Diogenes Laertius is

responsible for a fair number of Hippolytus’ statements, especially

concerning the opinions of those to whom he gives little space. Certain

phrases seem taken directly from Theophrastus or from whatever author

it was that Simplicius used in his commentaries on Aristotle, and the

likeness between Alcinous’ summary of Plato’s doctrines and those of

our author is too close to be accidental. It therefore seems most

probable that Hippolytus did not confine himself to any one source, but

borrowed from several. This would, after all, be the natural course for

a lecturer as distinguished from a writer to adopt, and goes some way

therefore towards confirming the theory as to the origin of the book

stated in the Introduction.]

BOOKS II AND III

(These are entirely missing, no trace of them having been found

attached to any of the four codices of Book I or to the present text of

Books IV to X. We know that such books must have once existed, as at

the end of Book IV (p. 117 _infra_) the author tells us that all the

famous opinions of earthly philosophy have been included by him in the

preceding _four_ books, of which as has been said only Books I and IV

have come down to us.

Our only ground for conjecture as to the contents of Books II and III

is to be found in Hippolytus’ statement at the end of Book I, that he

will _first_ make public the mystic rites[1] and then the fancies of

certain philosophers as to stars and magnitudes. As the promise in the

last words of the sentence seems to be fulfilled in Book IV, where he

gives not only the method of the astrologers of his time, but also the

calculations of the Greek astronomers as to the relative distances of

the heavenly bodies, it may be presumed that this was preceded and not

followed by a description of the Mysteries more elaborate and fuller

than the casual allusions to them which appear in Book V. So, too, in

Chap. 5 of the same Book IV, which he himself describes in the heading

as a “Recapitulation” of what has gone before, he refers to certain

dogmas of the Persians and the Babylonians as to the nature of God,

which have certainly not been mentioned in any other part of the book

which has come down to us. So, again, at the beginning of Book X, which

purports to be a summary of the whole work, he tells us that having now

gone through the “labyrinth of heresies,” it will be shown that the

Truth is not derived from “the wisdom (philosophy) of the Greeks, the

secret mysteries of the Egyptians,[2] the fallacies of the astrologers,

or the demon-inspired ravings of the Babylonians.” The Greek philosophy

and astrological fallacies are dealt with at sufficient length in Books

I and IV respectively, but nothing of importance is said in these or

elsewhere in the work as to the mysteries of the “Egyptians,” by whom

he probably means the worshippers of the Alexandrian divinities, and

nothing at all as to Babylonian demonolatry or magic. It is quite

true that he follows this up immediately by the statement that he

has included the tenets of all the wise men among the _Greeks_ in

four books, and the doctrines of the heretics in five; but it has

been explained in the Introduction (pp. 18 ff. _supra_) that there

are reasons why the summarizer’s recollection of the earlier books

may not be verbally accurate, nor does he say that the description

of the philosophic and heretical teachings exhausted the contents

of the first four books. On the whole, therefore, Cruice appears to

be justified in his conclusion that the missing books contained an

account of the “Egyptian” Mysteries and of “the sacred sciences of the

Babylonians.”)[3]

FOOTNOTES

[Footnote 1: τὰ μυστικά.]

[Footnote 2: Αἰγυπτίων δόγματα ... ὡς ἄρρητα διδαχθείς.]

[Footnote 3: M. Adhémar d’Alès in his work _La Théologie de St.

Hippolyte_, Paris, 1906, argues that the existing text of Book

IV contains large fragments of the missing Books II and III. His

argument is chiefly founded on the supposed excessive length of Book

IV, although as a fact Book V is in Cruice’s pagination some 20

pages longer than this and Book VI, 10. Apart from this, it seems

very doubtful if any author would describe the arithmomantic and

arithmetical nonsense in Book IV as either μυστικά or δόγματα ἄρρητα,

and it is certain that he cannot be alluding, when he speaks of the

Βαβυλωνίων ἀλογίστῳ μανίᾳ δι’ ἐν(εργί)ας δαιμόνων καταπλαγείς, to the

jugglery in the same book, which he there attributes not to the agency

of demons but to the tricks of charlatans.]

BOOK IV

DIVINERS AND MAGICIANS

(The first pages of this book have been torn away from the MS., and we

are therefore deprived of the small Table of Contents which the author

has prefixed to the other seven. From the headings of the various

chapters it may be reproduced in substance thus:--

1. The “Chaldæans” or Astrologers, and the celestial measurements of

the Greek astronomers.

2. The Mathematicians or those who profess to divine by the numerical

equivalents of the letters in proper names.

3. The Metoposcopists or those who connect the form of the body and the

disposition of the mind with the Zodiacal sign rising at birth.

4. The Magicians and the tricks by which they read sealed letters,

perform divinations, produce apparitions of gods and demons, and work

other wonders.

5. Recapitulation of the ideas of Greek and Barbarian on the nature of

God, and the views of the “Egyptians” or neo-Pythagoreans as to the

mysteries of number.

6. The star-diviners or those who find religious meaning in the

grouping of the constellations as described by Aratus.

7. The Pythagorean doctrine of number and its relation to the heresies

of Simon Magus and Valentinus.)

[Sidenote: p. 53.] [1. _About Astrologers_.[1]]

... (And they (_i. e._ the Chaldæans) declare there are “terms”[2]

of the stars in each zodiacal sign extending from one given part)[3]

to [another given part in which some particular star has most power.

About which there is no mere chance difference] among them [as appears

from their tables]. But they say that the stars are guarded[4] [when

they are midway between two other stars] in zodiacal succession.

For instance, if [a certain star should occupy the first part] of a

zodiacal sign and another [the last parts, and a third those of the

middle, the one in the middle is said to be guarded] by those occupying

the parts at the extremities. [And they say that the stars behold

one another and are in accord with one another] when they appear

triangularly or quadrangularly. Now those form a triangular [Sidenote:

p. 54.] figure[5] and behold one another which have an interval of

three zodiacal signs between them and a square those which have one of

two signs....

([6]Such then seems to be the character of the Chaldæan method. And

in that which has been handed down it remains easy to understand and

follow the contradictions noted. And some indeed try to teach a rougher

way as if earthly things have no sympathy[7] at all with the heavenly

ones. For thus they say, that the ambient[8] is not united as is the

human body, so that according to the condition) of the head the lower

parts [suffer with it and the head with the lower] parts, and earthly

things should suffer along with those above the moon. But there is a

certain difference and want of sympathy between them as they have not

one and [the] same unity.

2. Making use of these statements, Euphrates the Peratic and

Akembes the Carystian[9] and the rest of the band of these people,

miscalling the word of Truth, declare that there is a war of æons and

a falling-away of good powers to the bad, calling them Toparchs and

Proastii[10] and many other names. All which heresy undertaken by them,

I shall set forth and refute when we come to the discussion concerning

them. But now, lest any one should deem trustworthy and unfailing

the rules laid down[11] by the Chaldæans [Sidenote: p. 55.] for the

astrological art, we shall not shrink from briefly setting forth their

refutation and pointing out that their art is vain and rather deceives

and destroys the soul which may hope for vain things than helps it. In

which matters we do not hold out any expertness in the art, but only

that drawn from knowledge of the practical words.[12] Those who, having

been trained in this science, become pupils of the Chaldæans and who

having changed the names only, have imparted mysteries as if they were

strange and wonderful to men, have constructed a heresy out of this.

But since they consider the astrologers’ art a mighty one and making

use of the witness of the Chaldæans wish to get their own systems

believed because of them, we shall now prove that the astrological art

as it appears to-day is unfounded, and then that the Peratic heresy is

to be put aside as a branch growing from a root which does not hold.[13]

3.[14] Now the beginning and as it were the basis of the affair

is the establishment of the horoscope. From this the rest of the

cardinal points, and the cadents and succeedents and the trines and

the squares[15] and the configuration of the stars in them are known,

from all which things the predictions [Sidenote: p. 56.] are made.

Wherefore if the horoscope be taken away, of necessity neither the

midheaven nor the descendant nor the anti-meridian is known. But the

whole Chaldaic system vanishes if these are not disclosed. [And how

the zodiacal sign ascending is to be discovered is taught in divers

ways. For in order that this may be apprehended, it is necessary first

of all that the birth of the child falling under consideration be

carefully taken, and secondly that the signalling of the time[16] be

unerring, and thirdly that the rising in the heaven of the ascending

sign be observed with the greatest care. For at the birth[17] the

rising of the sign ascending in the heaven must be closely watched,

since the Chaldæans determining that which ascends, on its rising make

that disposition of the stars which they call the Theme,[18] from

which they declare their predictions. But neither is it possible to

take the birth of those falling under consideration, as I shall show,

nor is the time established [Sidenote: p. 57.] unerringly, nor is the

ascending sign ascertained with care. How baseless the system of the

Chaldæans is, we will now say. It is necessary before determining

the birth of those falling under consideration, to inquire whether

they take it from the deposition of the seed and its conception or

from the bringing forth. And if we should attempt to take it from the

conception, the accurate account of this is hard to grasp, the time

being short and naturally so. For we cannot say whether conception

takes place simultaneously with the transfer of the seed or not. For

this may happen as quick as thought, as the tallow put into heated

pots sticks fast at once, or it may take place after some time.[19]

For there being a distance from the mouth of the womb to the other

extremity, where conceptions are said by doctors to take place, it

is natural that nature depositing the seed should take some time to

accomplish this distance. Therefore the Chaldæans being ignorant of

the exact length of time will never discover exactly the time of

conception, the seed being sometimes [Sidenote: p. 58.] shot straight

forward and falling in those places of the womb fitted by nature for

conception, and sometimes falling broadcast to be only brought into

place by the power of the womb itself. And it cannot be known when the

first of these things happens and when the second, nor how much time is

spent in one sort of conception and how much in the other. But if we

are ignorant of these things, the accurate discovery of the nature of

the conception vanishes.[20] Nor if, as some physiologists say, seed

being first seethed and altered in the womb then goes forward to its

gaping vessels as the seeds of the earth go to the earth; why then,

those who do not know the length of time taken by this change will not

know either the moment of conception. And again, as women differ from

one another in energy and other causes of action in other parts of the

body, so do they differ in the energy of the womb, some conceiving

quicker and others slower. And this is not unexpected, since if we

compare them, they are seen now to be good conceivers and now not at

all so. This being so, it is impossible to say with exactness when the

seed deposited is secured, so that from this time the Chaldæans may

establish the horoscope[21] of the birth.

[Sidenote: p. 59.] 4. For this reason it is impossible to establish the

horoscope from the conception; nor can it be done from the bringing

forth. For in the first place, it is very hard to say when the bringing

forth is: whether it is when the child begins to incline towards the

fresh air or when it projects a little, or when it is brought down

altogether to the ground. But in none of these cases is it possible

to define the time of birth accurately.[22] For from presence of mind

and suitableness of body, and through preference of places and the

expertness of the midwife and endless other causes, the time is not

always the same when, the membranes being ruptured, the infant inclines

forward, or when [Sidenote: p. 60.] it projects a little, or when it

falls to the ground. But it is different with different women. Which,

again, the Chaldæans being unable to measure definitely and accurately,

they are prevented from determining as they should the hour of the

bringing forth.

That the Chaldæans, therefore, while asserting that they know the

sign ascending at the time of birth, do not know it, is plain from

the facts. And that there is no means either of unerringly observing

the time,[23] is easy to be judged. For when they say that the person

sitting by the woman in labour at the bringing forth signifies the

same to the Chaldæan who is looking upon the stars from a high place

by means of the gong,[24] and that this last gazing upon the heaven

notes down the sign then rising, we shall show that as the bringing

forth happens at no defined time,[25] it is not possible either to

signify the same by the gong. For even if it be granted that the actual

bringing forth can be ascertained, yet the time cannot be signified

accurately. For the sound of the gong, being capable of divisions

by perception into much and more time,[26] it happens that it is

[Sidenote: p. 61.] carried (late) to the high place. And the proof of

this is what is noticed when trees are felled a long way off.[27] For

the sound of the stroke is heard a pretty long time after the fall of

the axe, so as to reach the listener later. And from this cause it

is impossible for the Chaldæans to obtain accurately the time of the

rising sign and that which is in truth on the ascendant.[28] And indeed

not only does more time pass after the birth before he who sits beside

the woman in labour, strikes the gong, and again after the stroke

before it is heard by him upon the high place, but also before he can

look about and see in which sign is the moon and in which is each of

the other stars. It seems inevitable then that there must be a great

change in the disposition of the stars,[29] [from the movement of the

Pole being whirled along with indescribable swiftness] before the

hour of him who has been born as it is seen in heaven can be observed

carefully.[30]

[Sidenote: p. 62.] 5. Thus the art according to the Chaldæans has been

shown to be baseless. But if any one should fancy that by enquiries,

the geniture[31] of the enquirer is to be learned, we may know that

not in this way either can it be arrived at with certainty. For if

such great care in the practice of the art is necessary, and yet as we

have shown they do not arrive at accuracy, how can an unskilled person

take accurately the time of birth, so that the Chaldæan on learning

it may set up the horoscope truthfully?[32] But neither by inspection

of the horizon will the star ascending appear the same everywhere,

but sometimes the cadent sign will be considered the ascendant and

sometimes the succeedent, according as the coming in view of the places

is higher or lower. So that in this respect the prediction will not

appear accurate, many people being born all over the world at the same

hour, while every observer will see the stars differently.

But vain also is the customary taking of the time by water-jars.[33]

For the pierced jar will not give the same flow when full as when

nearly empty, while according to [Sidenote: p. 63.] the theory of these

people the Pole itself is borne along in one impulse with equal speed.

But if they answer to this that they do not take the time accurately

but as it chances in common use,[34] they will be refuted merely by

the starry influences themselves.[35] For those who have been born

at the same time have not lived the same life; but some for example

have reigned as kings while others have grown old in chains. None at

any rate of the many throughout the inhabited world at the same time

as Alexander of Macedon were like unto him, and none to Plato the

philosopher. So that if the Chaldæan observes carefully the time in

common use, he will not be able to say[36] if he who is born at that

time will be fortunate. For many at any rate born at that time, will be

unfortunate, so that the likeness between the genitures is vain.

Having therefore refuted in so many different ways the vain speculation

of the Chaldæans, we shall not omit this, that their prognostications

lead to impossibility. For if he who is born under the point of

Sagittarius’ arrow must be slain, as the astrologers[37] say, how

was it that so many [Sidenote: p. 64.] barbarians who fought against

the Greeks at Marathon or Salamis were killed at the same time? For

there was not at any rate the same horoscope for all. And again, if

he who is born under the urn of Aquarius will be shipwrecked, how was

it that some of the Greeks returning from Troy were sunk together in

the furrows of the Eubœan sea? For it is incredible that all these

differing much from one another in age should all have been born under

Aquarius’ urn. For it cannot be said often that because of one who was

destined to perish by sea, all those in the ship should be destroyed

along with him. For why should the destiny of this one prevail over

that of all, and yet that not all should be saved because of one who

was destined to die on land?

6. But since also they make a theory about the influence of the

zodiacal signs to which they say the things brought forth are likened,

we shall not omit this. For example, they say that he who is born

under Leo will be courageous,[38] and he who is born under Virgo

straight-haired, pale-complexioned, [Sidenote: p. 65.] childless

and bashful. But these things and those like them deserve laughter

rather than serious consideration.[39] For according to them an

Ethiopian can be born under Virgo, and if so they allow he will be

white, straight-haired and the rest. But I imagine that the ancients

gave the names of the lower animals to the stars rather because of

arbitrariness[40] than from natural likeness of shape. For what

likeness to a bear have the seven stars which stand separate from one

another? Or to the head of a dragon those five of which Aratus says:--

Two hold the temples, two the eyes, and one beneath

Marks the chin point of the monster dread.--

(Aratus, _Phainomena_, vv. 56, 57.)

7. That these things are not worthy of so much labour is thus proved

to the right-thinkers aforesaid, and to those who give no heed to the

inflated talk of the Chaldæans, who with assurance of indemnity make

kings to disappear [Sidenote: p. 66.] and incite private persons to

dare great deeds.[41] But if he who has given way to evil fails, he

who has been deceived does not become a teacher to all whose minds

the Chaldæans wish to lead endlessly astray by their failures. For

they constrain the minds of their pupils when they say that the same

configuration of the stars cannot occur otherwise than by the return

of the Great Year in 7777 years.[42] How then can human observation

agree[43] in so many ages upon one geniture? And this not once but many

times, since the destruction of the cosmos as some say will interrupt

the observation, or its gradual transformation will cause to disappear

entirely the continuity of historical tradition.[44]] The Chaldaic art

must be refuted by more arguments, although we have been recalling

it to memory on account of other matters and not for its own sake.

But since we have before said that we will omit none of the opinions

current among the Gentiles,[45] by reason of the many-voiced craft of

the heresies, let us see what they say also who have [Sidenote: p. 67.]

dared to speculate about magnitudes. Who, recognizing the variety of

the work of most of them, when another has been utterly deceived in a

different manner and has been yet held in high esteem, have dared to

say something yet more grandiose than he, so that they may be yet more

glorified by those who have already glorified their petty frauds. These

men postulate circles and triangular and square measures doubly and

triply.[46] There is much theory about this, but it is not necessary

for what lies before us.

8. I reckon it enough therefore to declare the marvels described by

them. Wherefore I shall employ their epitomes,[47] as they call them,

and then turn to other things. They say this:[48] he who fashioned the

universe, gave rule to the revolution of the Same and Like, for that

alone he left undivided; but the inner motion he divided 6 times and

made 7 unequal circles divided by intervals in ratios of 2 and 3, 3

of each, and bade the circles revolve in directions opposite to one

another--3 of them to revolve at equal pace, and 4 with a velocity

unlike that of the 3, but in [Sidenote: p. 68.] due proportion.[49] And

he says that rule was given to the orbit of the 7, not only because it

embraces the orbit of the Other, _i. e._, the Wanderers; but because

it has so much rule, _i. e._, so much power, that it carries along

with it the Wanderers to the opposite positions, bearing them from

West to East and from East to West by its own strength. And he says

that the same orbit was allowed to be one and undivided, first because

the orbits of all the fixed stars are equal in time and not divided

into greater and lesser times.[50] And next because they all have the

same appearance,[51] which is that of the outermost orbit, while the

Wanderers are divided into more and different kinds of movements and

into unequal distances from the Earth. And he says that the Other orbit

has been cut in 6 places into 7 circles according to ratio.[52] For as

many cuts as there are of each, so many segments are there _plus_ a

monad. For example if one cut be made,[53] there are 2 segments; if 2

cuts, 3 segments; and so, if a thing be cut 6 times there [Sidenote:

p. 69.] will be 7 segments. And he says that the intervals between

them are arranged alternately in ratios of 2 and 3, 3 of each, which

he has proved with regard to the constitution of the soul also, as to

the 7 numbers. For 3 among them, viz., 2, 4, 8, are doubles from the

monad onwards and 3 of them, viz., 3, 9, 27 [triples][54].... But the

diameter of the Earth is 80,008 stadia and its perimeter 250,543.[55]

And the distance from the Earth’s surface to the circle of the Moon,

Aristarchus of Samos writes as ...[56] stadia but Apollonius as

5,000,000 and Archimedes as 5,544,130. And Archimedes says that from

the Moon’s circle to that of the Sun is 50,262,065 stadia; from this

to the circle of Aphrodite 20,272,065; and from this to the circle of

Hermes 50,817,165; and from the same to the circle of [Sidenote: p.

70.] the Fiery One[57] 40,541,108; and from this to the circle of Zeus

20,275,065; but from this to the circle of Kronos, 40,372,065; and from

this to the Zodiac and the last periphery 20,082,005 stadia.

9. The differences from one another of the circles and the spheres

in height are also given by Archimedes. He takes the perimeter of

the Zodiac at 447,310,000 stadia, so that a straight line from the

centre of the Earth to its extreme surface is the sixth part of the

said number, and from the surface of the Earth on which we walk to

the Zodiac is exactly one-sixth of the said number less 40,000 stadia

which is the distance from the centre of the Earth to its surface.

And from the circle of Kronos to the Earth, he says, the interval is

2,226,912,711 stadia; and from the [Sidenote: p. 71.] circle of the

Fiery One to the Earth, 132,418,581; and from the Sun to the Earth,

121,604,454; from the Shining One to the Earth, 526,882,259; and from

Aphrodite to the Earth, 50,815,160.[58]

10. And about the Moon we have before spoken. The distances and

depths[59] of the spheres are thus given by Archimedes, but Hipparchus

speaks differently about them, and Apollonius the mathematician

differently again. But it is enough for us in following the Platonic

theory to think of the intervals between the Wanderers as in ratios

of 2 and 3. For thus is kept alive the theory of the harmonious

construction of the universe in accordant ratios[60] by the same

distances. But the numbers set out by Archimedes and the ratios quoted

by the others concerning the distances, if they are not in accordant

ratios, that is in those called by [Sidenote: p. 72.] Plato twofold

and threefold, but are found to be outside the chords,[61] would not

keep alive the theory of the harmonious construction of the universe.

For it is neither probable nor possible that their distances should

have no ratio to one another, that is, should be outside the chords

and enharmonic scales. Except perhaps the Moon alone, from her waning

and the shadows of the Earth, as to which planet alone you may trust

Archimedes, that is to say for the distance of the Moon from the Earth.

And it will be easy for those who accept this calculation to ascertain

the number and the other distances according to the Platonic method

by doubling and tripling as Plato demands.[62] If then, according to

Archimedes, the Moon is distant from the Earth 5,544,130 stadia, it

will be easy by increasing these numbers in ratios of 2 and 3 to find

her distance from the rest by taking one fraction of the number of

stadia by which the Moon is distant from the Earth.

But since the rest of the numbers stated by Archimedes about the

distance of the Wanderers are not in accordant ratios, it is easy to

know how they stand in regard to one [Sidenote: p. 73.] another and in

what ratios they have been observed to be. But that the same are not in

harmony and accord[63] when they are parts of the cosmos established

by harmony is impossible. So then, as the first number (of stadia)

by which the Moon is distant from the Earth is 5,544,130, the second

number by which the Sun is distant from the Moon being 50,262,065, it

is in ratio more than ninefold; and the number of the interval above

this being 20,272,065 is in ratio less than one-half. And the number of

the interval above this being 50,815,108 is in ratio more than twofold.

And the number of the interval above this being 40,541,108 is in ratio

more than one and a quarter.[64] And the number of the interval above

this being 20,275,065 is in ratio more than half. And the number of

the highest interval above this being 40,372,065 is in ratio less than

twofold.[65]

11. These same ratios indeed--the more than ninefold, [Sidenote: p.

74.] less than half, more than twofold, less than one and a quarter,

more than half, less than half and less than twofold are outside all

harmonies and from them no enharmonic nor accordant system can come to

pass. But the whole cosmos and its parts throughout are put together in

an enharmonic and accordant manner. But the enharmonic and accordant

ratios are kept alive as we have said before by the twofold and

threefold intervals. If then we deem Archimedes worthy of faith on the

distance given above, _i. e._, that from the Moon to the Earth, it is

easy to find the rest by increasing it in the ratios of 2 and 3. Let

the distance from the Earth to the Moon be, according to Archimedes,

5,544,130 stadia. The double of this will be the number of stadia by

which the Sun is distant from the Moon, viz., 11,088,260. But from

the Earth the Sun is distant 16,632,390 stadia and Aphrodite indeed

from the Sun--16,632,390 stadia, but from the Earth 33,264,780. Ares

indeed is distant from Aphrodite 22,176,520 stadia but from the Earth

105,338,470. But Zeus is distant from Ares 44,353,040 stadia, but from

[Sidenote: p. 75] the Earth 149,691,510. Kronos is distant from Zeus

40,691,510 stadia, but from the Earth 293,383,020.[66]

12. Who will not wonder at so much activity of mind produced by so

great labour? It seems that this Ptolemy[67] who busies himself with

these matters is not without his use to me. This only grieves me that

as one but lately born he was not serviceable to the sons of the

giants,[68] who, being ignorant of these measurements, thought they

were near high heaven and began to make a useless tower. Had he been at

hand to explain these measurements to them they would not have ventured

on the foolishness. But if any one thinks he can disbelieve this let

him take the measurements and be convinced; for one cannot have for

the unbelieving a more manifold proof than this. O puffing-up of

vainly-toiling soul and unbelieving belief, when Ptolemy is considered

wise in everything by those trained in the like wisdom![69]

13. Certain men in part intent on these things as judging [Sidenote:

p. 76.] them mighty and worthy of argument have constructed

measureless[70] and boundless heresies. Among whom is one

Colarbasus,[71] who undertakes to set forth religion by measures and

numbers. And there are others whom we shall likewise point out when

we begin to speak of those who give heed to Pythagorean reckoning as

if it were powerful and neglect the true philosophy for numbers and

elements, thus making vain divinations. Collecting whose words, certain

men have led astray the uneducated, pretending to know the future and

when they chance to divine one thing aright are not ashamed of their

many failures, but make a boast of their one success. Nor shall I pass

over their unwise wisdom, but when I have set forth their attempts to

establish a religion from these sources, I shall refute them as being

disciples of a school inconsistent and full of trickery.

2. _Of Mathematicians._[72]

[Sidenote: p. 77.] Those then who fancy that they can divine by means

of ciphers[73] and numbers, elements[74] and names, make the foundation

of their attempted system to be this. They pretend that every number

has a root:--in the thousands as many units as there are thousands.

For example, the root of 6000 is 6 units, of 7000, 7 units, of 8000,

8 units, and with the rest in the same way. In the hundreds as many

hundreds as there are, so the same number of units is the root of them.

For example, in 700 there are 7 hundreds: 7 units is their root. In 600

there are 6 hundreds: 6 units is their root. In the same way in the

decads: of 80 the root is 8 units, of 40, 4 units, of 10, 1 unit. In

the units, the units themselves are the root; for instance, the unit

of the 9 is 9, of the 8, 8, of the 7, 7. Thus then must we do with the

component parts [of names]. For each element is arranged according to

some number. For example, the Nu consists of 50 units; but of 50 units

the root is 5, and of the letter [Sidenote: p. 78.] Nu the root is 5.

Let it be granted that from the name we may take certain[75] of its

roots. For example, from the name Agamemnon there comes from the Alpha

one unit, from the Gamma 3 units, from the other Alpha 1 unit, from the

Mu 4 units, from the Epsilon 5 units, from the Mu 4 units, from the Nu

5 units, from the Omega 8 units, from the Nu 5 units, which together in

one row will be 1, 3, 1, 4, 5, 4, 5, 8, 5. These added together make 36

units. Again they take the roots of these and they become 3 for the 30,

but 6 itself for the 6. Then the 3 and the 6 added together make 9, but

the root of 9 is 9. Therefore the name Agamemnon ends in the root 9.

Let the same be done with another name, viz., Hector. The name Hector

contains five elements, Epsilon, Kappa, Tau, Omega and Rho.[76] The

roots of these are 5, 2, 3, 8, 1; these added together make 19 units.

Again, the root of the 10 is 1, of the 9, 9, which added together make

10. The root of the 10 is one unit. Therefore the name of Hector when

counted up[77] has made as its root one unit.

[Sidenote: p. 79.] But it is easier to work this way. Divide by 9 the

roots ascertained from the elements, as we have just found 19 units

from the name Hector, and read the remaining root. For example, if I

divide the 19 by 9, there remains a unit, for twice 9 is 18, and the

remainder is a unit. For if I subtract 18 from the 19, the remainder

is a unit. Again, of the name Patroclus[78] these numbers 8, 1, 3, 1,

7, 2, 3, 7, 2 are the roots; added together they make 34 units. The

remainder of these units is 7, viz., 3 from the 30 and 4 from the 4.

Therefore 7 units are the root of the name Patroclus. Those then who

reckon by the rule of 9 take the 9th part of the number collected from

the roots and describe the remainder as the sum of the roots; but those

who reckon by the rule of 7 take the 7th part. For example, in the name

Patroclus the aggregate of the roots is 34 units. This divided into

sevens makes 4 sevens, which are 28; the [Sidenote: p. 80.] remainder

is 6 units. He says that by the rule of 7, 6 is the root of the name

Patroclus.[79] If, however, it be 43, the 7th part, he says, is 42, for

7 times 6 is 42, and the remainder is 1. Therefore the root from the

43 by the rule of 7 becomes a unit. But we must take notice of what

happens if the given number when divided has no remainder,[80] as for

example, if from one name, after adding together the roots, I find, _e.

g._, 36 units. But 36 divided by 9 is exactly 4 enneads (for 9 times

4 is 36 and nothing over). Thus, he says the 9 itself is plainly the

root. If again we divide the number 45 we find 9 and no remainder (for

9 times 5 is 45 and nothing over), in such cases we say the root is 9.

And in the same way with the rule of 7: if, _e. g._, we divide 28 by

7 we shall have nothing over (for 7 times 4 is 28 and nothing left),

[and] they say the root is 7. Yet when he reckons up the names and

finds the same letter twice, he counts it only once. For example, the

name [Sidenote: p. 81.] Patroclus has the Alpha twice and the Omicron

twice,[81] therefore he counts the Alpha only once and the Omicron only

once. According to this, then, the roots will be 8, 3, 1, 7, 2, 3, 2,

and added together make 27,[82] and the root of the name by the rule of

9 will be the 9 itself and by that of 7, 6.

In the same way Sarpedon, when counted, makes by the rule of 9, 2

units; but Patroclus makes 9: Patroclus conquers. For when one number

is odd and the other even, the odd conquers if it be the greater. But

again if there were an 8, which is even, and a 5, which is odd, the 8

conquers, for it is greater. But if there are two numbers, for example,

both even or both odd, the lesser conquers. But how does Sarpedon by

the rule of 9 make 2 units? The element Omega is omitted; for when

there are in a name the elements Omega and Eta, they omit the Omega

[Sidenote: p. 82.] and use one element. For they say that they both

have the same power, but are not to be counted twice, as has been said

above. Again, Ajax (Αἴας)[83] makes 4 units, and Hector by the rule of

9 only one. But the 4 is even while the unit is odd. And since we have

said that in such cases the greater conquers, Ajax is the victor. Take

again Alexandros[84] and Menelaus. Alexandros has an individual[85]

name [Paris]. The name Paris makes by the rule of 9, 4; Menelaus by the

same rule 9, and the 9 conquers the 4. For it has been said that when

one is odd and the other even, the greater conquers, but when both are

even or both odd, the lesser. Take again Amycus and Polydeuces. Amycus

makes by the rule of 9, 2 units, and Polydeuces 7: Polydeuces conquers.

Ajax and Odysseus contended together in the funereal games. Ajax makes

by the rule of 9, 4 units, and Odysseus by the same rule 8.[86] Is

there not (here) then some epithet of Odysseus and not his individual

name, for he conquered? According to the numbers Ajax conquers, but

tradition says Odysseus. Or take again Achilles and Hector. Achilles by

the rule of 9 makes 4; [Sidenote: p. 83.] Hector 1; Achilles conquers.

Take again Achilles and Asteropæus. Achilles makes 4, Asteropæus 3;[87]

Achilles conquers. Take again Euphorbus and Menelaus. Menelaus has 9

units, Euphorbus 8; Menelaus conquers.

But some say that by the rule of 7, they use only the vowels, and

others that they put the vowels, semi-vowels and consonants by

themselves, and interpret each column separately. But yet others do not

use the usual numbers, but different ones. Thus, for example, they will

not have Pi to have as a root 8 units, but 5 and the element Xi as a

root 4 units; and turning about every way, they discover nothing sane.

When, however, certain competitors contend a second time,[88] they take

away the first element, and when a third, the two first elements of

each, and counting up the rest, they interpret them.

[Sidenote: p. 84.] 2. I should think that the design of the

arithmeticians has been plainly set forth, who deem that by numbers

and names they can judge life. And I notice that, as they have time

to spare and have been trained in counting, they have wished by means

of the art handed down to them by children to proclaim themselves

well-approved diviners, and, measuring the letters topsy-turvy, have

strayed into nonsense. For when they fail to hit the mark, they say in

propounding the difficulty that the name in question is not a family

name but an epithet; as also they plead as a subterfuge in the case

of Ajax and Odysseus. Who that founds his tenets on this wonderful

philosophy and wishes to be called heresiarch, will not be glorified?

3. _Of Divination by Metoposcopy._[89]

1. But since there is another and more profound art among the all-wise

investigators of the Greeks, whose disciples the heretics profess

themselves because of the use they make of their opinions for their

own designs, as we shall show before long, we shall not keep silence

about this. This is the divination or rather madness by metoposcopy.

[Sidenote: p. 85.] There are those who refer to the stars the forms of

the types and patterns[90] and natures of men, summing them up by their

births under certain stars. This is what they say: Those born under

Aries will be like this, to wit, long-headed, red-haired, with eyebrows

joined together, narrow forehead, sea-green eyes, hanging cheeks, long

nose, expanded nostrils, thin lips, pointed chin, and wide mouth. They

will partake, he says, of such a disposition as this: forethinking,

versatile, cowardly, provident, easy-going, gentle, inquisitive,

concealing their desires, equipped for everything, ruling more by

judgment than by strength, laughing at the present, skilled writers,

faithful, lovers of strife, provoking to controversy, given to desire,

lovers of boys, understanding, turning from their own homes, displeased

[Sidenote: p. 86.] with everything, litigious, madmen in their cups,

contemptuous, casting away somewhat every year, useful in friendship by

their goodness. Most often they die in a foreign land.[91]

2. Those born under Taurus will be of this type: round-headed,

coarse-haired, with broad forehead, oblong eyes and great eyebrows

if dark; if fair, thin veins, sanguine complexion, large and heavy

eyelids, great ears, round mouth, thick nose, widely-open nostrils,

thick lips. They are strong in their upper limbs, but are sluggish from

the hips downwards from their birth. The same are of a disposition

pleasing, understanding, naturally clever, religious, just, rustical,

agreeable, laborious[92] after twelve years old, easily irritated,

leisurely. Their appetite is small, they are quickly satisfied, wishing

for many things, provident, thrifty towards themselves, liberal towards

others; as a class they are sorrowful, useless in friendship, useful

because of their minds, enduring ills.

[Sidenote: p. 87.] 3. The type of these under Gemini: red-faced, not

too tall in stature, even-limbed, eyes black and beady,[93] cheeks

drawn downwards, coarse mouth, eyebrows joined together. They rule

all that they have, are rich at the last, niggardly, thrifty of their

own, profuse in the affairs of Venus, reasonable, musical, cheats. The

same are said (by other writers) to be of this disposition: learned,

understanding, inquisitive, self-assertive, given to desire, thrifty

with their own, liberal, gentle, prudent, crafty, wishing for many

things, calculators, litigious, untimely, not lucky. They are beloved

by women, are traders, but not very useful in friendship.

[Sidenote: p. 88.] 4. The type of those under Cancer: not great in

stature, blue-black hair, reddish complexion, small mouth, round

head, narrow forehead, greenish eyes, sufficiently beautiful, limbs

slightly irregular. Their disposition: evil, crafty, skilled in plots,

insatiable, thrifty, ungraced, servile, unhelpful, forgetful. They

neither give back what is another’s nor demand back their own; useful

in friendship.

5. The type of those under Leo: round head, reddish hair, large

wrinkled forehead, thick ears, stiff-necked, partly bald, fiery

complexion, green-gray eyes, large jaws, coarse mouth, heavy upper

limbs, great breast, lower parts small. Their disposition is:

self-assertive, immoderate, self-pleasers, wrathful, courageous,

scornful, arrogant, never deliberating, no talkers, indolent, addicted

to custom, given up to the things of Venus, fornicators, shameless,

wanting in faith, importunate for favour, audacious, niggardly,

rapacious, celebrated, helpful to the community, useless in friendship.

[Sidenote: p. 89.] 6. The type of those under Virgo: with fair

countenance, eyes not great but charming, with dark eyebrows close

together, vivacious and swimming.[94] But they are slight in body,

fair to see, with hair beautifully thick, large forehead, prominent

nose. Their disposition is: quick at learning, moderate, thoughtful,

playful, erudite, slow of speech, planning many things, importunate for

favour, observing all things and naturally good disciples. They master

what they learn, are moderate, contemptuous, lovers of boys, addicted

to custom, of great soul, scornful, careless of affairs giving heed

to teaching, better in others’ affairs than in their own; useful for

friendship.

7. The type of those under Libra: with thin bristling hair, reddish

and not very long, narrow wrinkled forehead, beautiful eyebrows close

together, fair eyes with black pupils, broad but small ears, bent head,

wide mouth. Their disposition is: understanding, honouring the gods,

talkative to one another, traders, laborious, not keeping [Sidenote: p.

90.] what they get, cheats, not loving to take pains in business,[95]

truthful, free of tongue, doers of good, unlearned, cheats, addicted

to custom, careless, unsafe to treat unjustly.[96] They are scornful,

derisive, sharp, illustrious, eavesdroppers, and nothing succeeds with

them. Useful for friendship.

8. The type of those under Scorpio: with maidenly countenance, well

shaped and pale,[97] dark hair, well-formed eyes, forehead not wide and

pointed nose, ears small and close (to the head), wrinkled forehead,

scanty eyebrows, drawn-in cheeks. Their disposition is: crafty,

sedulous, cheats, imparting their own plans to none, double-souled,

ill-doers, contemptuous, given to fornication, gentle, quick at

learning. Useless for friendship.

9. The type of those under Sagittarius: great in stature, square

forehead, medium eyebrows joined together, hair [Sidenote: p. 91.]

abundant, bristling and reddish. Their disposition is: gracious as

those who have been well brought up, simple, doers of good, lovers

of boys, addicted to custom, laborious, loving and beloved, cheerful

in their cups, clean, passionate, careless, wicked, useless for

friendship, scornful, great-souled, insolent, somewhat servile,[98]

useful to the community.

10. The type of those under Capricorn: with reddish body, bristling,

greyish hair,[99] round mouth, eyes like an eagle, eyebrows close

together, smooth forehead, inclined to baldness, the lower parts of the

body the stronger. Their disposition is: lovers of wisdom, scornful and

laughing at the present, passionate, forgiving, beautiful, doers of

good, lovers of musical practice, angry in their cups, jocose, addicted

to custom, talkers, lovers of boys, cheerful, friendly, beloved,

provokers of strife, useful to the community.

11. The type of those under Aquarius: square in stature, small mouth,

narrow small, fierce eyes. (Their disposition) is: commanding,

ungracious, sharp, seeking the easy path, [Sidenote: p. 92.] useful for

friendship and to the community. Yet they live on chance affairs and

lose their means of gain. Their disposition is:[100] reserved, modest,

addicted to custom, fornicators, niggards, painstaking in business,

turbulent, clean, well-disposed, beautiful, with great eyebrows. Often

they are in small circumstances and work at (several) different trades.

If they do good to any, no one gives them thanks.

12. The type of those under Pisces: medium stature, with narrow

foreheads like fishes, thick hair. They often become grey quickly.

Their disposition is: great-souled, simple, passionate, thrifty,

talkative. They will be sleepy at an early age, they want to do

business by themselves, illustrious, venturesome, envious, litigious,

changing their place of abode, beloved, fond of dancing.[101] Useful

for friendship.

13. Since we have set forth their wonderful wisdom, and have not

concealed their much-laboured art of divination by intelligence,[102]

neither shall we be silent on the folly into [Sidenote: p. 93.] which

their mistakes in these matters lead them. For how feeble are they in

finding a parallel between the names of the stars and the forms and

dispositions of men? For we know that those who at the outset chanced

upon the stars, naming them according to their own fancy, called them

by names for the purpose of easily and clearly recognizing them. For

what likeness is there in these names to the appearance of the Zodiacal

signs, or what similar nature of working and activity, so that any one

born under Leo should be thought courageous,[103] or he who is born

under Virgo moderate, or under Cancer bad, and those under[104]....

4. _The Magicians._[105]

(The gap here caused by the mutilation of the MS. was probably filled

by a description of the mode of divination by enquiry of a spirit or

dæmon which was generally made in writing, as Lucian describes in

his account of the imposture of Alexander of Abonoteichos. The MS.

proceeds.)

... And he (_i. e._, the magician) taking some paper, orders the

enquirer to write down what it is he wishes to enquire of the

dæmons.[106] Then he having folded up the paper and given it to the

boy,[107] sends it away to be burned so that the smoke carrying the

letters may go hence to the dæmons. But while the boy is doing what

he is commanded, he first tears off equal parts of the paper, and on

some other parts [Sidenote: p. 94.] of it, he pretends that the dæmons

write in Hebrew letters. Then having offered up the Egyptian magicians’

incense called Cyphi,[108] he scatters these pieces of paper over the

offering. But what the enquirer may have chanced to write having been

put on the coals is burned. Then, seeming to be inspired by a god, the

magician rushes into the inner chamber[109] with a loud and discordant

cry unintelligible to all. But he bids all present to enter and cry

aloud, invoking Phrēn[110] or some other dæmon. When the spectators

have entered and are standing by, he flings the boy on a couch and

reads to him many things, sometimes in the Greek tongue, sometimes

in the Hebrew, which are the incantations usual among magicians. And

having made libation, he begins the sacrifice. And he having put

copperas[111] in the libation bowl[112] and when the drug is dissolved

sprinkling with it the paper which had forsooth been discharged of

writing, he compels the hidden and concealed letters again to come to

light, whereby he learns what the enquirer has written.

[Sidenote: p. 95.] And if one writes with copperas and fumigates it

with a powdered gall-nut, the hidden letters will become clear. Also if

one writes (with milk) and the paper is burned and the ash sprinkled

on the letters written with the milk, they will be manifest.[113] And

urine and garum[114] also and juice of the spurge and of the fig will

have the same effect.

But when he has thus learned the enquiry, he thinks beforehand in what

fashion he need reply. Then he bids the spectators come inside bearing

laurel-branches and shaking them[115] and crying aloud invocations to

the dæmon Phrēn. For truly it is fitting that he should be invoked

by them and worthy that they should demand from dæmons what they do not

wish to provide on their own account, seeing that they have lost their

brains.[116] But the confusion of the noise and the riot prevents them

following what the magician is thought to do in secret. What this is,

it is time to say.

Now it is very dark at this point. For he says that it is impossible

for mortal nature to behold the things of the gods, for it is enough

to talk with them. But having made the boy lie down on his face, with

two of those little writing tablets on which are written in Hebrew

letters [Sidenote: p. 96.] forsooth[117] such things as names of

dæmons, on each side of him, he says (the god) will convey the rest

into the boy’s ears. But this is necessary to him, in order that he

may apply to the boy’s ears a certain implement whereby he can signify

to him all that he wishes. And first he rings[118] (a gong) so that

the boy may be frightened, and secondly he makes a humming noise, and

then thirdly he speaks through the implement what he wishes the boy to

say, and watches carefully the effect of the act. Thereafter he makes

the spectators keep silence, but bids the boy repeat what he has heard

from the dæmons. But the implement which is applied to the ears is a

natural one, to wit, the wind-pipe of the long-necked cranes or storks

or swans. If none of these is at hand, the art has other means at its

disposal. [Sidenote: p. 97.] For certain brass pipes, fitting one into

the other and ending in a point are well suited to the purpose through

which anything the magician wishes may be spoken into the ears. And

these things the boy hearing utters when bidden in a fearful way, as if

they were spoken by dæmons. And if one wraps a wet hide round a rod and

having dried it and bringing the edges together fastens them closely,

and then taking out the rod, makes the hide into the form of a pipe, it

has the same effect. And if none of these things is at hand, he takes a

book and, drawing out from the inside as much as he requires, pulls it

out lengthways and acts in the same way.[119]

But if he knows beforehand that any one present will ask a question,

he is better prepared for everything. And if he has learned the

question beforehand he writes it out with the drug (aforesaid) and

as being prepared is thought more adept for having skilfully written

what was about to be asked. But if he does not know, he guesses at it,

and exhibits some roundabout phrase of double and various meaning,

so that the answer of the oracle being meaningless will do for many

things at the beginning, but at the end of the events will be thought

a prediction of what has happened. [Sidenote: p. 98.] Then having

filled a bowl with water, he puts at the bottom of it the paper with

apparently nothing written on it, but at the same time putting in

the copperas. For thus there floats to the surface the paper bearing

the answer which he has written. To the boy also there often come

fearful fancies; for truly the magician strikes blows in abundance to

terrify him. For, again casting incense into the fire, he acts in this

fashion. Having covered a lump of the so-called quarried salts[120]

with Tyrrhenian wax and cutting in halves the lump of incense, he puts

between them a lump of the salt and again sticking them together throws

them on the burning coals and so leaves them. But when the incense is

burnt, the salts leaping up produce an illusion as if some strange

and wonderful thing were happening. But indigo black[121] put in the

incense produces a blood-red flame as we have before said.[122] And

he makes a liquid like blood by mixing wax with rouge and as I have

said, putting the wax in the incense. And he makes the coals to move by

putting under them stypteria[123] cut in pieces, and when it melts and

swells up like bubbles, the coals are moved.

[Sidenote: p. 99.] 2. And they exhibit eggs different (from natural

ones) in this way. Having bored a hole in the apex at each end and

having extracted the white, and again plunged the egg in boiling water,

put in either red earth from Sinope[124] or writing ink. But stop up

the holes with pounded eggshell made into a paste with the juice of a

fig.

3. This is the way they make sheep cut off their own heads. Secretly

anointing the sheep’s throat with a caustic drug, he fixes near the

beast a sword and leaves it there. But the sheep, being anxious to

scratch himself, leans (heavily) on the knife, rubs himself along it,

kills himself and must needs almost cut off his head. And the drug is

bryony and marsh salt and squills in equal parts mixed together. So

that he may not be seen to have the drug with him, he carries a horn

box made double, the visible part of which holds frankincense and the

invisible the drug. And he also puts quicksilver into the ears of the

animal that is to die. But this is a death-dealing drug.

4. But if one stops up the ears of goats with salve, they say they will

shortly die because prevented from breathing. [Sidenote: p. 100.] For

they say that this is with them the way in which the intaken air is

breathed forth. And they say that a ram dies if one should bend him

backwards against the sun.[125] But they make a house catch fire by

anointing it with the ichor of a certain animal called dactylus;[126]

and this is very useful because of sea-water. And there is a sea-foam

heated in an earthen jar with sweet substances, which if you apply to

it a lighted lamp catches fire and is inflamed, but does not burn at

all if poured on the head. But if you sprinkle it with melted gum, it

catches fire much better; and it does better still if you also add

sulphur to it.

5. Thunder is produced in very many ways. For very many large stones

rolled from a height over wooden planks and falling upon sheets of

brass make a noise very like thunder. And they coil a slender cord

round the thin [Sidenote: p. 101.] board on which the wool-carders

press cloth, and then spin the board by whisking away the string when

the whirring of it makes the sound of thunder. These tricks they play

thus; but there are others which I shall set forth which those who

play them also consider great. Putting a cauldron full of pitch upon

burning coals, when it boils they plunge their hands in it and are not

burned; and further they tread with naked feet upon coals of fire and

are not burned. And also putting a pyramid of stone upon the altar,

they make it burn and from its mouth it pours forth much smoke and

fire. Then laying a linen cloth upon a pan of water and casting upon it

many burning coals, the linen remains unburnt. And having made darkness

in the house, the magician claims to make gods or dæmons enter in,

and if one somehow asks that Esculapius shall be displayed he makes

invocation, saying thus:--

“Apollo’s son, once dead and again undying!

I call on thee to come as a helper to my libations.

[Sidenote: p. 102.] Who erst the myriad tribes of fleeting dead

In the ever-mournful caves of wide Tartarus

Swimming the stream hard to cross and the rising tide,

Fatal to all mortal men alike,

Or wailing by the shore and bemoaning inexorable things

These thyself did rescue from gloomy Persephoneia.

Whether thou dost haunt the seat of holy Thrace

Or lovely Pergamum or beyond these Ionian Epidaurus

Hither, O blessed one, the prince of magicians calls thee to be

present here.”[127]

6. But when he has made an end of this mockery a fiery Esculapius

appears on the floor. Then having put in the midst a bowl of

water,[128] he invokes all the gods and they are at hand. For if the

spectator lean over and gaze into the bowl, he will see all the gods

and Artemis leading on [Sidenote: p. 103.] her baying hounds. But we

shall not hesitate to tell the story of these things and how they

undertake them. For the magician plunges his hands in the cauldron

of pitch which appears to be boiling; but he throws into it vinegar

and soda[129] and moist pitch and heats the cauldron gently. And

the vinegar having mingled with the soda, on getting a little hot,

moves the pitch so as to bring bubbles to the surface and gives the

appearance of boiling only. But the magician has washed his hands

many times in sea-water, thanks to which it does not burn him much if

it be really boiling. And if he has after washing them anointed his

hands with myrtle-juice and soda and myrrh[130] mixed with vinegar

he is not burned (at all). But the feet are not burned if he anoints

them with icthyokolla and salamander.[131] And this is the true cause

of the pyramid flaming like a torch, although it is of stone. A paste

of Cretan earth[132] is moulded into the shape of a pyramid,--but the

colour is like a milk-white stone,--in this fashion. He has soaked

the piece of earth in much oil, has put it on the coals, and when

heated, has again soaked it and heated it a second and third time and

many a time afterwards, whereby he so prepares [Sidenote: p. 104.]

it that it will burn even if plunged in water; for it holds much

oil within itself. But the altar catches fire when the magician is

making libation, because it contains freshly-burned lime instead of

ashes and finely-powdered frankincense and much ... and of ... of

anointed torches and self-flowing and hollow nutshells having fire

within them.[133] But he also sends forth smoke from his mouth after

a brief delay by putting fire into a nutshell and wrapping it in tow

and blowing it in his mouth.[134] The linen cloth laid on the bowl of

water whereon he puts the coals is not burned, because of the sea-water

underneath, and its being itself steeped in sea-water and then anointed

with white of egg and a solution of alum. And if also one mixes with

this the juice of evergreens and vinegar and a long time beforehand

anoint it copiously with these, after being dipped in the drug it

remains altogether incombustible.[135]

7. Since then we have briefly set forth what can be done with the

teachings which they suppose to be secret, we have [Sidenote: p.

105.] displayed their easy system according to Gnosis.[136] Nor do we

wish to keep silence as to this necessary point, that is, how they

unseal letters and again restore them with the same seals (apparently

intact). Melting pitch, resin, sulphur and also bitumen in equal parts,

and moulding it into the form of a seal impression, they keep it by

them. But when the opportunity for unsealing a letter[137] arrives,

they moisten the tongue with oil, lick the seal, and warming the drug

before a slow fire press the seal upon it and leave it there until

it is altogether set, when they use it after the manner of a signet.

But they say also that wax with pine resin has the same effect and

so also 2 parts of mastic with 1 of bitumen. And sulphur alone does

fairly well and powdered gypsum diluted with water and gum.[138] This

certainly does most beautifully for sealing molten lead. And the effect

of [Sidenote: p. 106.] Tyrrhenian wax and shavings of resin and pitch,

bitumen, mastic and powdered marble in equal parts all melted together,

is better than that of the other (compounds) of which I have spoken,

but that of the gypsum is no worse. Thus then they undertake to break

the seals when seeking to learn what is written within them. These

contrivances I shrank from setting out in the book,[139] seeing that

some ill-doer taking hints from them[140] might attempt (to practise)

them. But now the care of many young men capable of salvation has

persuaded me to teach and declare them for the sake of protection

(against them). For as one person will use them for the teaching of

evil, so another by learning them will be protected (against them) and

the very magicians, corruptors of life as they are, will be ashamed

to practise the art. But learning that the same (tricks) have been

taught beforehand, they will perhaps be hindered in their perverse

foolishness. In order, however, that the seal may not be broken in this

way, let any one seal with swine’s fat and mix hairs with the wax.[141]

8. Nor shall I be silent about their lecanomancy[142] which is an

imposture. For having prepared some closed chamber [Sidenote: p. 107.]

and having painted its ceiling with cyanus, they put into it for the

purpose certain utensils of cyanus[143] and fix them upright. But in

the midst a bowl filled with water is set on the earth, which with the

reflection of the cyanus falling upon it shows like the sky. But there

is a certain hidden opening in the floor over which is set the bowl,

the bottom of which is glass, but is itself made of stone. But there is

underneath a secret chamber in which those in the farce[144] assembling

present the dressed-up forms of the gods and dæmons which the magician

wishes to display. Beholding whom from above the deceived person

is confounded by the magicians’ trickery and for the rest believes

everything which (the officiator) tells him. And (this last) makes

(the figure of) the dæmon burn by drawing on the wall the figure he

wishes, and then secretly anointing it with a drug compounded in this

way ...[145] with Laconian and Zacynthian bitumen. Then as if inspired

by Phœbus, he brings the lamp near the wall, and the drug having caught

light is on fire.

But he manages that a fiery Hecate should appear to be flying through

the air thus: Having hidden an accomplice in what place he wills, and

taking the dupes on one side, he prevails on them by saying that he

will show them the [Sidenote: p. 108.] fiery dæmon riding through the

air. To whom he announces that when they see the flame in the air,

they must quickly save their eyes by falling down and hiding their

faces until he shall call them. And having thus instructed them, on a

moonless night, he declaims these verses:--

Infernal and earthly and heavenly Bombo,[146] come.

Goddess of waysides, of cross-roads, lightbearer, nightwalker,

Hater of the light, lover and companion of the night,

Who rejoicest in the baying of hounds and in purple blood;

Who dost stalk among corpses and the tombs of the dead

Thirsty for blood, who bringest fear to mortals

Gorgo and Mormo and Mene and many-formed one.

Come thou propitious to our libations![147]

9. While he speaks thus, fire is seen borne through the air, and the

spectators terrified by the strangeness of the sight, cover their eyes

and cast themselves in silence on the earth. But the greatness of the

art contains this device. [Sidenote: p. 109.] The accomplice, hidden as

I have said, when he hears the incantation drawing to a close, holding

a hawk or kite wrapped about with tow, sets fire to it and lets it go.

And the bird scared by the flame is carried into the height and makes

very speedy flight. Seeing which, the fools hide themselves as if they

had beheld something divine. But the winged one whirled about by the

fire, is borne whither it may chance and burns down now houses and now

farm-buildings. Such is the prescience of the magicians.

10. But they show the moon and stars appearing on the ceiling in this

way. Having previously arranged in the centre part of the ceiling a

mirror, and having placed a bowl filled with water in a corresponding

position in the middle of the earthen floor, but a lamp showing

dimly[148] has been placed between them and above the bowl, he thus

produces the appearance of the moon from the reflection by means of the

mirror. But often the magician hangs aloft[149] near the ceiling a drum

on end, the same being kept covered by the accomplice by some cloth so

that it may not show before its time; and a lamp having been put behind

it, when he makes the agreed signal to the accomplice, the last-named

takes away so much of the [Sidenote: p. 110.] covering as will give a

counterfeit of the moon in her form at that time.[150] But he anoints

the transparent parts of the drum with cinnabar and gum....[151] And

having cut off the neck and bottom of a glass flask, he puts a lamp

within and places around it somewhat of the things necessary for the

figures shining through, which one of the accomplices has concealed on

high. After receiving the signal, this last lets fall the contrivances

from the receptacle hung aloft, so that the moon appears to have been

sent down from heaven. And the like effect is produced by means of

jars in glass-like forms.[152] And it is by means of the jar that the

trick is played within doors. For an altar having been set up, the

jar containing a lighted lamp stands behind it; but there being many

more lamps (about), this nowise appears. When therefore the enchanter

invokes the moon, he orders all the lamps to be put out, but one is

left dim and then the light from the jar is reflected on to the ceiling

and gives the illusion of the moon to the spectators, the [Sidenote:

p. 111.] mouth of the jar being kept covered for the time which seems

to be required that the image of the crescent moon may be shown on the

ceiling.

11. But the scales of fishes or of the “hippurus”[153] make stars seem

to be when they are moistened with water and gum and stuck upon the

ceiling here and there.

12. And they create the illusion of an earthquake, so that everything

appears to be moving, ichneumon’s dung being burned upon coal with

magnetic iron ore[154]....

13. But they display a liver appearing to bear an inscription. On his

left hand (the magician) writes what he wishes, adapting it to the

enquiry, and the letters are written with nut-galls and strong vinegar.

Then taking up the liver, which rests in his left hand, he makes some

delay, and it receives the impression and is thought to have been

inscribed.

14. And having placed a skull on the earth, they make it speak in

this fashion. It is made out of the omentum of [Sidenote: p. 112.] an

ox,[155] moulded with Tyrrhenian wax and gypsum and when it is made

and covered with the membrane, it shows the semblance of a skull. The

which seems to speak by the use of the implement and in the way we have

before explained in the case of the boys. Having prepared the wind-pipe

of a crane or some such long-necked bird and putting it secretly into

the skull, the accomplice speaks what (the magician) wishes. And when

he wants it to vanish, he appears to offer incense and putting round it

a quantity of coals the wax receiving the heat of which melts, and thus

the skull is thought to have become invisible.[156]

15. These and ten thousand such are the works of the magicians, which,

by the suitableness of the verses and of the belief-inspiring acts

performed, beguile the fancy of the thoughtless. The heresiarchs struck

with the arts of these (magicians) imitate them, handing down some of

their doctrines in secrecy and darkness, but paraphrasing others as if

they were their own. Thanks to this, as we wish to remind the public,

we have been the more anxious to leave behind us no place for those

who wish to go astray. But we have been led away not without reason

into certain secrets of the magicians which were not [Sidenote: p.

113.] altogether necessary for the subject,[157] but which were thought

useful as a safeguard against the rascally and inconsistent art of

the magicians. Since, now, as far as one can guess,[158] we have set

forth the opinions of all, having bestowed much care on making it clear

that the things which the heresiarchs have introduced into religion as

new are vain and spurious, and probably are not even among themselves

thought worthy of discussion, it seems proper to us to recall briefly

and summarily what has been before said.

5. _Recapitulation._

1. Among all the philosophers and theologists[159] who are enquiring

into the matter throughout the inhabited world, there is no agreement

concerning God, as to what He is or whence (He came).[160] For some

say that He is fire, some spirit, some water, others earth. But every

one of these elements contains something inferior and some of them

are defeated by the others. But this has happened to the world’s

sages, which indeed is plain to those who think, [Sidenote: p. 114.]

that in view of the greatness of creation, they are puzzled as to the

substance of the things which are, deeming them too great for it to

be possible for them to have received birth from another. Nor yet do

they represent the universe itself taken collectively[161] to be God.

But in speculation about God every one thought of something which he

preferred among visible things as the Cause. And thus gazing upon the

things produced by God and on those which are least in comparison with

His exceeding greatness, but not being capable of extending their mind

to the real God, they declared these things to be divine.

The Persians, however, deeming that they were further within the truth

(than the rest) said that God was a shining light comprised in air. But

the Babylonians said that darkness was God, which appears to be the

sequence of the other opinion; for day follows night and night day.[162]

2. But the Egyptians, deeming themselves older than all, have subjected

the power of God to ciphers,[163] and calculating the intervals of the

fates by Divine inspiration[164] said that God [Sidenote: p. 115.] was

a monad both indivisible and itself begetting itself, and that from

this (monad) all things were made. For it, they say, being unbegotten,

begets the numbers after it; for example, the monad added to itself

begets the dyad, and added in the like way the triad and tetrad up

to the decad, which is the beginning and the end of the numbers. So

that the monad becomes the first and tenth through the decad being of

equal power and being reckoned as a monad, and the same being decupled

becomes a hecatontad and again is a monad, and the hecatontad when

decupled will make a chiliad, and it again will be a monad. And thus

also the chiliads if decupled will complete the myriad and likewise

will be a monad. But the numbers akin to the monad by indivisible

comparison are ascertained to be 3, 5, 7, 9.[165] There is, however,

also a more natural affinity of another number with the monad which

is that by the operation of the spiral of 6 circles[166] of the dyad

according to the [Sidenote: p. 116.] even placing and separation of

the numbers. But the kindred number is of the 4 and 8. And these

receiving added virtue from numbers of the monad, advanced up to the

four elements, I mean spirit and fire, water and earth. And having

created from these the masculo-feminine cosmos,[167] he prepared and

arranged two elements in the upper hemisphere, (to wit) spirit and

fire, and he called this the beneficent hemisphere of the monad and

the ascending and the masculine. For the monad, being subtle, flies to

the most subtle and purest part of the æther. The two other elements

being denser, he assigns to the dyad (to wit) earth and water, and he

calls this the descending hemisphere and feminine and maleficent. And

again the two upper elements when compounded with themselves have in

themselves the male and the female for the fruitfulness and increase of

the universals. And the fire is masculine, but the spirit feminine: and

again the water is masculine and the earth feminine.[168] And thus from

the beginning the fire lived with the spirit and the water with the

earth. For as the power of the spirit is the fire, so also (the power)

of the earth is the water....

[Sidenote: p. 117.] And the same elements counted and resolved by

subtraction of the enneads,[169] properly end some in the male number,

others in the female. But again the ennead is subtracted for this

cause, because the 360 degrees of the whole circle consist of enneads,

and hence the 4 quarters of the cosmos are (each) circumscribed by

90 complete degrees. But the light is associated with the monad and

the darkness with the dyad, and naturally life with the light and

death with the dyad, and justice with life and injustice with death.

Whence everything engendered among the male numbers is benefic,

and (everything engendered) among the female numbers is malefic.

For example, they reckon that the monad--so that we may begin from

this--becomes 361, which ends in a monad, the ennead(s) being

subtracted. Reckon in the same way: the dyad becomes 605; subtract

the enneads, it ends in a dyad and each is (thus) carried back to its

own.[170]

3. With the monad, then, as it is benefic, there are [Sidenote: p.

118.] associated names which end in the uneven number,[171] and they

say that they are ascending and male and benefic when observed; but

that those which end in an even number are considered descending and

female and malefic. For they say that nature consists of opposites,

to wit, good and bad, as right and left, light and darkness, night

and day, life and death. And they say this besides: that they have

calculated the name of God and that it results in a pentad [or in an

ennead],[172] which is uneven and which written down and wrapped about

the sick works cures. And thus a certain plant (whose name) ends in

this number when tied on in the same way is effective by the like

reckoning of the number. But a doctor also cures the sick by a like

calculation. But if the calculation be contrary, he does not make cures

easily. Those who give heed to these numbers count all numbers like it

which have the same meaning, some [Sidenote: p. 119.] according to the

vowels alone, others according to the total of the numbers.[173] Such

is the wisdom of the Egyptians, whereby, while glorifying the Divine,

they think they understand it.

6. _Of the Divination by Astronomy._[174]

We seem then to have set forth these things also sufficiently. But

since I consider that not one tenet of this earthy and grovelling

wisdom has been passed over, I perceive that our care with regard to

the same things has not been useless. For we see that our discourse

has been of great use not only for the refutation of heresies, but

also against those who magnify these things.[175] Those who happen to

notice the manifold care taken by us will both wonder at our zeal and

will neither despise our painstaking nor denounce Christians as fools

when they see what themselves have foolishly believed. And besides

this, the discourse will timely instruct those lovers of learning who

give heed to the truth, making them more wise to easily overthrow those

who have dared to mislead them--for they will have learned not only

the principles of the heresies, but also the so-called opinions of the

[Sidenote: p. 120.] sages. Not being unacquainted with which, they

will not be confused by them as are the unlearned, nor misled by some

who exercise a certain power, but will keep a watch upon those who go

astray.

2. Having therefore sufficiently set forth (our) opinions, it remains

for us to proceed to the subject aforesaid, when, after we have

proved what we arranged concerning the heresies, and have forced the

heresiarchs to restore to everyone his own, we shall exhibit (these

heresiarchs) stripped (of all originality) and by denouncing the

folly of their dupes we shall persuade them to return again to the

precious haven of the truth. But in order that what has been said may

appear more clearly to the readers,[176] it seems to us well to state

the conclusions of Aratus as to the disposition of the stars in the

heaven. For there are some who by likening them to the words of the

Scriptures turn them into allegories and seek to divert the minds of

those who listen to them by leading them with persuasive words whither

they wish, and pointing out to them strange marvels like those of the

transfers to the stars[177] alleged by them. They who while gazing upon

the outlandish wonder are caught by their admiration for trifles are

like the bird called the owl,[178] [Sidenote: p. 121.] whose example

it will be well to narrate in view of what follows. Now this animal

presents no very different appearance from that of the eagle whether in

size or shape; but it is caught in this way. The bird-catcher, when he

sees a flock alighting anywhere, claps his hands, pretends to dance,

and thus gradually draws near to the birds; but they, struck by the

unwonted sight, become blind to everything else. Others of the party,

however, who are ready on the ground coming behind the birds easily

capture them while they are staring at the dancer. Wherefore I ask that

no one who is struck by the wonders of whose who interpret the heaven

shall be taken in like the owl. For the dancing and nonsense of such

(interpreters) is trickery and not truth. Now Aratus speaks thus:--

“Many and like are they, going hither and thither,

Daily they wheel in heaven always and ever [that is, all the stars]

Yet none changes his abode[179] ever so little: but with perfect

exactness

Ever the Pole is fixed, and holds the earth in the midst of all

As equipoise of all, and around it leads Heaven itself.”--

(Aratus, _Phæn._, vv. 45, 46.)

[Sidenote: p. 122.] 3. He says that the stars in heaven are πολέας,

that is, turning,[180] because of their going about ceaselessly from

East to West and from West to East in a spherical figure. But he says

there is coiled round the Bears themselves, like the stream of some

river, a great marvel of a terrible dragon, and this it is, he says,

that the Devil in the (Book of) Job says to God: “I have been walking

to and fro under heaven and going round about,”[181] that is, turning

hither and thither and inspecting what is happening. For they consider

that the Dragon is set below the Arctic Pole, from this highest pole

gazing upon all things and beholding all things, so that none of those

that are done shall escape him. For though all the stars in the heaven

can set, this Pole alone never sets, but rising high above the horizon

inspects all things and beholds all things, and nothing of what is

done, he says, can escape him.

“Where (most)

Settings and risings mingle with one another.”--

(Aratus, _Phæn._, v. 61.)

[Sidenote: p. 123.] he says, indeed, that his head is set. For over

against the rising and setting of the two hemispheres lies the head

of Draco, so that, he says, nothing escapes him immediately either

of things in the West or of things in the East, but the Beast knows

all things at once. And there over against the very head of Draco is

the form of a man made visible by reason of the stars, which Aratus

calls “a wearied image,” and like one in toil; but he names it the

“Kneeler.”[182] Now Aratus says that he does not know what this toil

is and this marvel which turns in heaven. But the heretics, wishing

to found their own tenets on the story of the stars, and giving their

minds very carefully to these things, say that the Kneeler is Adam, as

Moses said, according to the decree of God guarding the head of the

Dragon and the Dragon (guarding) his heel.[183] For thus says Aratus:--

“Holding the sole of the right foot of winding Draco.”--

(_Phæn._, vv. 63-65.)

4. But he says there are placed on either side of him (I mean the

Kneeler) Lyra and Corona; but that he bends the knee and stretches

forth both hands as if making confession [Sidenote: p. 124.] of

sin.[184] And that the lyre is a musical instrument fashioned by the

Logos in extreme infancy. But that Hermes is called among the Greeks

Logos. And Aratus says about the fashioning of the lyre:--

“which, while he was yet in his cradle

Hermes bored and said it was to be called lyre.”--

(_Phæn._, v. 268.)

It is seven-stringed, and indicates by its seven strings the entire

harmony and constitution with which the cosmos is suitably provided.

For in six days the earth came into being and there was rest on the

seventh. If, then, he says,[185] Adam making confession and guarding

the head of the Beast according to God’s decree, will imitate the lyre,

that is, will follow the word of God, which is to obey the Law, he will

attain the Crown lying beside it. But if he takes no heed, he will be

carried downwards along with the Beast below him, and will have his

lot, he says, with the Beast. But the Kneeler seems to stretch forth

his hands on either side and here to grasp the Lyre and there the Crown

[and this is to make confession],[186] [Sidenote: p. 125.] as is to be

seen from the very posture. But the Crown is plotted against and at

the same time drawn away by another Beast, Draco the Less, who is the

offspring of the one which is guarded by the foot of the Kneeler. But

(another) man stands firmly grasping with both hands the Serpent, and

draws him backwards from the Crown, and does not permit the Beast to

forcibly seize it. Him Aratus calls Serpent-holder,[187] because he

restrains the rage of the Serpent striving to come at the Crown. But

he, he says, who in the shape of man forbids the Beast to come at the

Crown is Logos, who has mercy upon him who is plotted against by Draco

and his offspring at once.

And these Bears, he says, are two hebdomads, being made up of seven

stars each, and are images of the two creations. For the First

Creation, he says, is that according to Adam in his labours who is seen

as the Kneeler. But the Second Creation is that according to Christ

whereby we are born [Sidenote: p. 126.] again. He is the Serpent-holder

fighting the Beast and preventing him from coming at the Crown prepared

for man. But Helica[188] is the Great Bear, he says, the symbol of the

great creation, whereby Greeks sail, that is by which they are taught,

and borne onwards by the waves of life they follow it, such a creation

being a certain revolution[189] or schooling or wisdom, leading back

again those who follow such (to the point whence they started). For

the name Helica seems to be a certain turning and circling back to the

same position. But there is also another Lesser Bear, as it were an

image of the Second Creation created by God. For few, he says, are they

who travel by this narrow way. For they say that Cynosura is narrow,

by which, Aratus says, the Sidonians navigate.[190] But Aratus in turn

says the Sidonians are Phœnicians on account of the wisdom of the

Phœnicians being wonderful. But they say that the Greeks are Phœnicians

who removed from the Red Sea to the land [Sidenote: p. 127.] where

they now dwell. For thus it seemed to Herodotus.[191] But this Bear he

says is Cynosura, the Second Creation, the small, the narrow way and

not Helica. For she leads not backwards, but guides those who follow

her forwards to the straight way, being the (tail) of the dog. For the

Logos is the Dog (Cyon) who at the same time guards and protects the

sheep against the plans of the wolves, and also chases the wild beasts

from creation and slays them, and who begets all things. For Cyon, they

say, indeed means the begetter.[192] Hence, they say, Aratus, speaking

of the rising of Canis, says thus:--

“But when the Dog rises, no longer do the crops play false.”--

(_Phæn._ v. 332.)

This is what he means: Plants that have been planted in the earth up

to the rising of the Dog-star take no root, but yet grow leaves and

appear to beholders as if they will bear fruit and are alive, but have

no life from the root in them. But when the rising of the Dog-star

occurs, the living plants are distinguished by Canis from the dead,

for [Sidenote: p. 128.] he withers entirely those which have not taken

root. This Cyon, he says then, being a certain Divine Logos has been

established judge of quick and dead, and as Cyon is seen to be the star

of the plants, so the Logos, he says, is for the heavenly plants, that

is for men. For some such cause as this, then, the Second Creation

Cynosura stands in heaven as the image of the rational[193] creature.

But between the two creations Draco is extended below, hindering the

things of the great creation from coming to the lesser, and watching

those things which are fixed in the great creation like the Kneeler

lest they see how and in what way every one is fixed in the little

creation. But Draco is himself watched as to the head, he says, by

Ophiuchus. The same, he says, is fixed as an image in heaven, being a

certain philosophy for those who can see.

But if this is not clear, through another image, he says, creation

teaches us to philosophize, about which Aratus speaks thus:--

“Nor of Ionian[194] Cepheus are we the miserable race.”--

(_Phæn._ v. 353.)

[Sidenote: p. 129.] But near Draco, he says, are Cepheus and Cassiopeia

and Andromeda and Perseus, great letters of[195] the creation to

those who can see. For he says that Cepheus is Adam, Cassiopeia Eve,

Andromeda the soul of both, Perseus the winged offspring of Zeus and

Cetus the plotting Beast. Not to any other of these comes Perseus the

slayer of the Beast, but to Andromeda alone. From which Beast, he

says, the Logos Perseus, taking her to himself, delivers Andromeda

who had been given in chains to the Beast. But Perseus is the winged

axis which extends to both poles through the middle of the earth and

makes the cosmos revolve. But the spirit which is in the Cosmos is

Cycnus,[196] the bird which is near the Bears, a musical animal, symbol

of the Divine Spirit, because only when it is near the limits of life,

its nature is to sing, and, as one escaping with good hope from this

evil creation it sends up songs of praise to God. But crabs and bulls

and lions and rams and goats and kids [Sidenote: p. 130.] and all the

other animals who are named in heaven on account of the stars are, he

says, images and paradigms whence the changeable nature receives the

patterns[197] and becomes full of such animals.[198]

Making use of these discourses, they think to deceive as many as

give heed to the astrologers, seeking therefrom to set up a religion

which appears very different from their assumptions.[199] Wherefore,

O beloved,[200] let us shun the trifle-admiring way of the owl. For

these things and those like them are dancing and not truth. For the

stars do not reveal these things; but men on their own account and for

the better distinguishing of certain stars (from the rest) gave them

names so that they might be a mark to them. For what likeness have

the stars strewn about the heaven to a bear, or a lion, or kids, or

a water-carrier, or Cepheus, or Andromeda, or to the Shades named in

Hades--for many of these persons and the names of the stars alike came

into existence long after the stars themselves--so that the [Sidenote:

p. 131.] heretics being struck with the wonder should thus labour by

such discourses to establish their own doctrines?[201]

7. _Of the Arithmetical Art._[202]

Seeing, however, that nearly all heresy has discovered by the art of

arithmetic measures of hebdomads and certain projections of Æons, each

tearing the art to pieces in different ways and only changing the

names,--but of these (men) Pythagoras came to be teacher who first

transmitted to the Greeks such numbers from Egypt--it seems good not

to pass over this, but after briefly pointing it out to proceed to

the demonstration of the objects of our enquiries. These men were

arithmeticians and geometricians to whom especially it seems Pythagoras

first supplied the principles (of their arts). And they took the first

beginnings (of things), discovered apparently by reason alone, from

the numbers which can always proceed to infinity by multiplication and

the figures (produced by it). For the beginning of geometry, as may

be seen, is an indivisible point; but from that point the generation

of the infinite figures from [Sidenote: p. 132.] the point[203] is

discovered by the art. For the point when extended[204] in length

becomes after extension a line having a point as its limit:[205] and a

line when extended in breadth produces a superficies and the limits of

the superficies are lines: and a superficies extended in depth becomes

a (solid) body:[206] and when this solid is in existence, the nature

of the great body is thus wholly founded from the smallest point. And

this is what Simon says thus: “The little will be great, being as it

were a point; but the great will be boundless,”[207] in imitation of

that geometrical point. But the beginning of arithmetic, which includes

by combination philosophy, is[208] a number which is boundless and

incomprehensible, containing within itself all the numbers capable

of coming to infinity by multitude. But the beginning of the numbers

becomes by hypostasis the first monad, which is a male unit begetting

as does a father all the other numbers. Second comes the dyad, a female

number, and the same is called even by the arithmeticians. Third comes

the triad, a male number; this also has been ordained to be called odd

by the arithmeticians. After all these comes the tetrad, [Sidenote: p.

133.] a female number, and this same is also called even, because it is

female. Therefore all the numbers taken from the genus are four--but

the boundless genus is number--wherefrom is constructed their perfect

number, the decad. For 1, 2, 3, 4 become 10, as has before been shown,

if the name which is proper to each of the numbers be substantially

kept. This is the sacred Tetractys according to Pythagoras which

contains within itself the roots of eternal nature, that is, all the

other numbers. For the 11, 12 and the rest take the principle of birth

from the 10. Of this decad, the perfect number, the four parts are

called: number, monad, square and cube. The conjunctions and minglings

of which are for the birth of increase, they completing naturally the

fruitful number. For when this square is multiplied into itself, it

becomes a square squared; but when a square into a cube, it becomes a

square cubed; but when a cube into a cube, it becomes a cube cubed. So

that all the numbers are seven, in order that the birth of the existing

numbers [Sidenote: p. 134.] may come from a hebdomad, which is number,

monad, square, cube, square of a square, cube of a square, cube of a

cube.

Of this hebdomad Simon and Valentinus, having altered the names,

recount prodigies, hastening to base upon it their own systems.[209]

For Simon calls (it) thus: Mind, Thought, Name, Voice, Reasoning,

Desire and He who has Stood, Stands and will Stand: and Valentinus:

Mind, Truth, Word, Life, Man, Church and the Father who is counted with

them. According to these (ideas) of those trained in the arithmetic

philosophy, which they admired as something unknowable by the crowd,

and in pursuance of them, they constructed the heresies excogitated by

them.

Now there are some also who try to construct hebdomads from the healing

art, being struck by the dissection of the brain, saying that the

substance, power of paternity, and divinity of the universe can be

learned from its constitution. [Sidenote: p. 135.] For the brain, being

the ruling part of the whole body rests calm and unmoved, containing

within itself the breath.[210] Now such a story is not incredible, but

a long way from their attempted theory. For the brain when dissected

has within it what is called the chamber, on each side of which are the

membranes which they call wings, gently moved by the breath, and again

driving the breath into the cerebellum.[211] And the breath, passing

through a certain reed-like vein, travels to the pineal gland.[212]

Near this lies the mouth of the cerebellum which receives the breath

passing through and gives it up to the so-called spinal marrow.[213]

From this the whole body gets a share of pneumatic (force), all the

arteries being dependent like branches on this vein, the extremity of

which finishes in the genital veins. Whence also the seeds proceeding

from the brain through the loins are secreted. But the shape of the

cerebellum is like the head of a dragon; concerning which there is much

talk among those of the Gnosis falsely so called, as we have shown. But

there are other six pairs (of vessels) growing from the brain, which

making their way round the head and finishing within it, connect the

bodies together. But the [Sidenote: p. 136.] seventh (goes) from the

cerebellum to the lower parts of the rest of the body, as we have said.

And about this there is much talk since Simon and Valentinus have found

in it hints which they have taken, although they do not admit it,

being first cheats and then heretics. Since then it seems that we have

sufficiently set out these things, and that all the apparent dogmas

of earthly philosophy have been included in (these) four books,[214]

it seems fitting to proceed to their disciples or rather to their

plagiarists.

THE FOURTH BOOK OF PHILOSOPHUMENA[215]

FOOTNOTES

[Footnote 1: This is the beginning of the Mt. Athos MS., the first

pages having disappeared. With regard to the first chapter περὶ

ἀστρολόγων, Cruice, following therein Miller, points out that nearly

the whole of it has been taken from Book V with the same title of

Sextus Empiricus’ work, Πρὸς Μαθηματικούς, and also that the copying

is so faulty that to make sense it is necessary to restore the text

in many places from that of Sextus. Sextus’ book begins, as did

doubtless that of Hippolytus, with a description of the divisions of

the zodiac, the cardinal points (Ascendant, Mid-heaven, Descendant,

and Anti-Meridian), the cadent and succeedent houses, the use of

the clepsydra or water-clock, the planets and their “dignities,”

“exaltations” and “falls,” and finally, their “terms,” with a

description of which our text begins. It is, perhaps, a pity that

Miller did not restore the whole of the missing part from Sextus

Empiricus; but the last-named author is not very clear, and the reader

who wishes to go further into the matter and to acquire some knowledge

of astrological jargon is recommended to consult also James Wilson’s

_Complete Dictionary of Astrology_, reprinted at Boston, U.S.A., in

1885, or, if he prefers a more learned work, M. Bouché-Leclercq’s

_L’Astrologie Grecque_, Paris, 1899. But it may be said here that

the astrologers of the early centuries made their predictions from a

“theme,” or geniture, which was in effect a map of the heavens at the

moment of birth, and showed the ecliptic or sun’s path through the

zodiacal signs divided into twelve “houses,” to each of which a certain

significance was attached. The foundation of this was the horoscope or

sign rising above the horizon at the birth, from which they were able

to calculate the other three cardinal points given above, the cadent

houses being those four which go just before the cardinal points and

the four succeedents those which follow after them. The places of the

planets, including in that term the sun and moon, in the ecliptic were

then calculated and their symbols placed in the houses indicated. From

this figure the judgment or prediction was made, but a great mass of

absurd and contradictory tradition existed as to the influence of the

planets on the life, fortune, and disposition of the native, which

was supposed to depend largely on their places in the theme both in

relation to the earth and to each other.]

[Footnote 2: Bouché-Leclercq, _op. cit._, p. 206, rightly defines

these terms as fractions of signs separated by internal boundaries

and distributed in each sign among the five planets. Cf. J. Firmicus

Maternus, _Matheseos_, II, 6, and Cicero, _De Divinatione_, 40. Wilson,

_op. cit_., s.h.v., says they are certain degrees in a sign, supposed

to possess the power of altering the nature of a planet to that of the

planet in the term of which it is posited. All the authors quoted say

that the astrologers could not agree upon the extent or position of

the various “terms,” and that in particular the “Chaldæans” and the

“Egyptians” were hopelessly at variance upon the point.]

[Footnote 3: In the translation I have distinguished Miller’s additions

to the text from Sextus Empiricus’ by enclosing them in square

brackets, reserving the round brackets for my own additions from the

same source, which I have purposely made as few as possible. So with

other alterations.]

[Footnote 4: δορυφορεῖσθαι, _lit._, “have spear-bearers.” “Stars” in

Sextus Empiricus nearly always means planets.]

[Footnote 5: This is the famous “trine” figure or aspect of modern

astrologers. Its influence is supposed to be good; that of the square

next described, the reverse.]

[Footnote 6: Hippolytus here omits a long disquisition by Sextus on the

position of the planets and the Chaldæan system. Where the text resumes

the quotation it is in such a way as to alter the sense completely;

wherefore I have restored the sentence preceding from Sextus.]

[Footnote 7: συμπάσχει, “suffer with.”]

[Footnote 8: τὸ περίεχον. The term used by astrologers to denote

the whole æther surrounding the stars or, in other words, the whole

disposition of the heavens. “Ambient” is its equivalent in modern

astrology.]

[Footnote 9: This is an anticipation of the Peratic heresy to which a

chapter in Book V (pp. 146 ff. _infra_) is devoted. Ἀκεμβὴς is there

spelt Κελβὴς, but Ἀκεμβὴς is restored in Book X and is copied by

Theodoret. “Peratic” is thought by Salmon (_D.C.B._, s.h.v.) to mean

“Mede.”]

[Footnote 10: “Toparch” means simply “ruler of a place.” Proastius

(προάστιος) generally the dweller in a suburb. Here it probably means

the powers in some part of the heavens which is near to a place or

constellation without actually forming part of it.]

[Footnote 11: νενομισμένα. Cf. νενομισμένως, “in the established

manner,” Callistratus, _Ecphr._, 897.]

[Footnote 12: τῶς πρακτικῶν λόγων, or, perhaps, “of the systems used.”]

[Footnote 13: ἀσύστατον, _lit._, “not holding together,” punningly used

as epithet for both the art and the heresy.]

[Footnote 14: What follows to the concluding paragraph of Chap. 7 is

taken nearly _verbatim_ from Sextus Empiricus.]

[Footnote 15: For these terms see n. on p. 67 _supra_.]

[Footnote 16: ὡροσκόπιον seems here put for ὡροσκοπεῖον = _horologium_,

or clock.]

[Footnote 17: ἀπότεξις, “the bringing-forth” is the word used by Sextus

throughout. As Sextus was a medical man it is probably the technical

term corresponding to our “parturition.” Miller reads ἀποτάξις which

does not seem appropriate.]

[Footnote 18: διάθεμα. See n. on p. 67 _supra_.]

[Footnote 19: I have here followed Sextus’ division of the sentence.

Cruice translates στέαρ, _farina aqua subacta_, for which I can see no

justification. Macmahon here follows him.]

[Footnote 20: Restoring from Sextus οἴχεται for ἦρται.]

[Footnote 21: ὡροσκόπον, “the ascending sign.” So Sextus.]

[Footnote 22: Restoring from Sextus ἐφ’ ἑκάστου for ἐν ἑκάστῳ; τὸν

ἀκριβῆ for τὸ ἀκριβὲς and omitting καταλαβέσθαι.]

[Footnote 23: See n. on p. 74 _infra_.]

[Footnote 24: Sextus has described earlier (p. 342, Fabricius) the

whole process of warning the astrologer of the moment of birth by

striking a metal disc, which I have called “gong.”]

[Footnote 25: ἀορίστου τυγχανούσης.]

[Footnote 26: ἐν πλείονι χρόνῳ καὶ ἐν συχνῷ πρὸς αἴσθησιν δυνάμενον

μερίζεσθαι, _majori et longiori temporis spatio ad aurium sensum

dividatur_, Cr.; “with proportionate delay,” Macmahon. I do not

understand how either his or Cruice’s construction is arrived at.]

[Footnote 27: Sextus has “on the hills.”]

[Footnote 28: ὡροσκοποῦντος might mean “which marks the hour.”]

[Footnote 29: φαίνεται ... ἀλλοιότερον ... διάθεμα.]

[Footnote 30: _quam diligenter observari possit in coelo nativitas_,

Cr., (before) “the nativity can be carefully observed in the sky.”]

[Footnote 31: γένεσις. The word in Greek astrological works has the

same meaning as “geniture” or “nativity” in modern astrological jargon.

Identical with “theme.”]

[Footnote 32: The whole of this sentence is corrupt, and the scribe

was probably taking down something from Sextus which was read to him

without his understanding it. I have given what seems to be the sense

of the passage.]

[Footnote 33: ὑδρίαι, Sextus (p. 342, Fabr.), has described the

clepsydra or water-clock and its defects as a measurer of time.]

[Footnote 34: ἐν πλάτει.]

[Footnote 35: τὰ ἀποτελέσματα. A technical expression for the results

or influence on sublunary things of the position of the heavenly

bodies. Cf. Bouché-Leclercq, _op. cit._, p. 328, n. 1.]

[Footnote 36: Sextus adds παγίως, “positively.”]

[Footnote 37: οἱ μαθηματικοί. The only passage in our text where

Hippolytus uses the word in this sense. He seems to have taken it from

Sextus’ title κατὰ τὸν μαθηματικὸν λόγον.]

[Footnote 38: A play of words upon Λέω and ἀνδρεῖος.]

[Footnote 39: σπουδῆς. Hippolytus inserts an unnecessary οὐ before the

word. See Sextus, p. 355.]

[Footnote 40: οἰκειώσεως χάριν, _gratia consuetudinis_, Cr.]

[Footnote 41: Does this refer to Otho’s encouragement by the astrologer

Ptolemy to rebel against Galba? See Tacitus, _Hist._, I, 22. The

sentence does not appear in Sextus.]

[Footnote 42: Sextus says 9977 years.]

[Footnote 43: φθάσει συνδραμεῖν, “arrive at concurrence with.” Sextus

answers the question in the negative.]

[Footnote 44: Here the quotations from Sextus end.]

[Footnote 45: παρ’ ἔθνεσι “among the nations.” A curious expression in

the mouth of a Greek, although natural to a Jew.]

[Footnote 46: Is this an allusion to trigonometry? The rest of the

sentence, as will presently be seen, refers to Plato’s _Timæus_. Cf.

also _Timæus the Locrian_, c. 5.]

[Footnote 47: Διὸ τοῖς ἐπιτόμοις χρησάμενος. An indication that

Hippolytus’ knowledge of Plato was not first-hand.]

[Footnote 48: The passage which follows is from the _Timæus_, XII,

where Plato describes how the World-maker set in motion two concentric

circles revolving different ways, the external called the Same and

Like, and the internal the Other, or Different.]

[Footnote 49: This seems to be generally accepted as Plato’s meaning.

Jowett says the three are the orbits of the Sun, Venus and Mercury, the

four those of the Moon, Saturn, Mars and Jupiter. The Wanderers are of

course the planets.]

[Footnote 50: _i. e._, swifter and slower.]

[Footnote 51: ἐπιφανεία.]

[Footnote 52: Perhaps the following extract from the pseudo-Timæus the

Locrian, now generally accepted as a summary of the second century, may

make this clearer. After explaining that the cosmos and its parts are

divided into “the Same” and “the Different,” he says: “The first of

these leads from without all that are within them, along the general

movement from East to West. But the latter, belonging to the Different,

lead from within the parts that are carried along from West to East,

and are self-moved, and they are whirled round and along, as it may

happen, by the movement of the Same which possesses in the Cosmos

a superior power. Now the movement of the Different, being divided

according to a harmonical proportion, takes the form of 7 circles,” and

he then goes on to describe the orbits of the planets.]

[Footnote 53: Lit., “if one section be severed.”]

[Footnote 54: Cf. Plato, _Timæus_, c. 12.]

[Footnote 55: A palpable mistake. As Cruice points out, if the Earth’s

diameter is as said in the text, its perimeter must be 251,768

stadia, which is not far from the 252,000 stadia assigned to it by

Eratosthenes.]

[Footnote 56: Lacunæ in both these sentences.]

[Footnote 57: The common Greek name for the planet Ares or Mars (♂).]

[Footnote 58: All these numbers are hopelessly corrupt in the text and

the scribe varies the notation repeatedly. I have given the figures as

finally settled by Cruice and his predecessors. The Shining One is the

planet Hermes or Mercury (☿).]

[Footnote 59: βάθη, “depths”; rather height if we consider the orbits

of the planets as concentric and fitting into one another like

jugglers’ caps or the skins of an onion.]

[Footnote 60: ἐν λόγοις συμφώνοις. Cruice would read τόνοις for λόγοις

on the strength of what Pliny, _Hist. Nat._, II, 20, says about

Pythagoras having taught that the intervals between the planets’ orbits

were musical tones. He seems to mean the gamut or chromatic scale as

contrasted with the enharmonic.]

[Footnote 61: See last note.]

[Footnote 62: See note on p. 81 _infra_ as to what this doubling and

tripling means.]

[Footnote 63: συμφωνίᾳ.]

[Footnote 64: ἐπιτετάρτῳ, _superquarta_, Cr., 1 + ¼; see Liddell and

Scott, quoting Nicomachus Gerasenus Arithmeticus.]

[Footnote 65: It is not easy to see from this confused statement

whether it is the system of Plato or Archimedes at which Hippolytus

is aiming. The one, however, that it most resembles is that of

the neo-Pythagoreans, of which the following table is given in M.

Bigourdan’s excellent work on _L’Astronomie: Evolution des Idées et des

Méthodes_, Paris 1911, p. 49:--

Planets ♁ ☽ ☿ ♀ ☉ ♂ ♃ ♄ Fixed

stars

Interval { in tones 1 ½ ½ 1½ 1 ½ ½ ½

{ in thousands of } 126 63 63 189 126 63 63 63

{ stadia }

Absolute distances }

in thousands } 0 126 189 252 441 567 630 693 756

of stadia }

]

[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.]