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The Refutation of All Heresies
Authorship uncertain
Book 4 · Chapter 14 About this work A large heresiological work tracing contested Christian teachings to Greek philosophy, mystery traditions, astrology, and magic, then setting them against the author’s account of apostolic truth.
Author Authorship uncertain
Traditional attribution Hippolytus of Rome
Date Early 3rd century, probably c. AD 220s
Origin Rome (traditional)
Genre Heresiology Traditional attribution to Hippolytus remains disputed, and the author is often called the Refutator.
Chapter XIV.—System of the Arithmeticians; Predictions Through Calculations; Numerical Roots; Transference of These Doctrines to Letters; Examples in Particular Names; Different Methods of Calculation; Prescience Possible by These. Those , then , who suppose that
‹ Book 4 · Chapter 13 Book 4 · Chapter 15 ›
they
prophesy
by
means
of
calculations
and
numbers
,
and
elements
and
names
,
constitute
the
origin
of
their
attempted
system
to
be
as
follows
.
They
affirm
that
there
is
a
root
of
each
of
the
numbers
;
in
the
case
of
thousands
,
so
many
monads
as
there
are
thousands
:
for
example
,
the
root
of
six
thousand
,
six
monads
;
of
seven
thousand
,
seven
monads
;
of
eight
thousand
,
eight
monads
;
and
in
the
case
of
the
rest
,
in
like
manner
,
according
to
the
same
(
proportion
)
.
And
in
the
case
of
hundreds
,
as
many
hundreds
as
there
are
,
so
many
monads
are
the
root
of
them
:
for
instance
,
of
seven
hundred
there
are
seven
hundreds
;
the
root
of
these
is
seven
monads
:
of
six
hundred
,
six
hundreds
;
the
root
of
these
,
six
monads
.
And
it
is
similar
respecting
decades
:
for
of
eighty
(
the
root
is
)
eight
monads
;
and
of
sixty
,
six
monads
;
of
forty
,
four
monads
;
of
ten
,
one
monad
.
And
in
the
case
of
monads
,
the
monads
themselves
are
a
root
:
for
instance
,
of
nine
,
nine
;
of
eight
,
eight
;
of
seven
,
seven
.
In
this
way
,
also
,
ought
we
therefore
to
act
in
the
case
of
the
elements
(
of
words
)
,
for
each
letter
has
been
arranged
according
to
a
certain
number
:
for
instance
,
the
letter
n
according
to
fifty
monads
;
but
of
fifty
monads
five
is
the
root
,
and
the
root
of
the
letter
n
is
(
therefore
)
five
.
Grant
that
from
some
name
we
take
certain
roots
of
it
.
For
instance
,
(
from
)
the
name
Agamemnon
,
there
is
of
the
a
,
one
monad
;
and
of
the
g
,
three
monads
;
and
of
the
other
a
,
one
monad
;
of
the
m
,
four
monads
;
of
the
e
,
five
monads
;
of
the
m
,
four
monads
;
of
the
n
,
five
monads
;
of
the
(
long
)
o
,
eight
monads
;
of
the
n
,
five
monads
;
which
,
brought
together
into
one
series
,
will
be
1
,
3
,
1
,
4
,
5
,
4
,
5
,
8
,
5
;
and
these
added
together
make
up
36
monads
.
Again
,
they
take
the
roots
of
these
,
and
they
become
three
in
the
case
of
the
number
thirty
,
but
actually
six
in
the
case
of
the
number
six
.
The
three
and
the
six
,
then
,
added
together
,
constitute
nine
;
but
the
root
of
nine
is
nine
:
therefore
the
name
Agamemnon
terminates
in
the
root
nine
.
Let us do the same with another name — Hector . The name ( H ) ector has five letters — e , and k , and t , and o , and r . The roots of these are 5 , 2 , 3 , 8 , 1 ; and these added together make up 19 monads . Again , of the ten the root is one ; and of the nine , nine ; which added together make up ten : the root of ten is a monad . The name Hector , therefore , when made the subject of computation , has formed a root , namely a monad . It would , however , be easier to conduct the calculation thus : Divide the ascertained roots from the letters — as now in the case of the name Hector we have found nineteen monads — into nine , and treat what remains over as roots . For example , if I divide 19 into 9 , the remainder is 1 , for 9 times 2 are 18 , and there is a remaining monad : for if I subtract 18 from 19 , there is a remaining monad ; so that the root of the name Hector will be a monad . Again , of the name Patroclus these numbers are roots : 8 , 1 , 3 , 1 , 7 , 2 , 3 , 7 , 2 ; added together , they make up 34 monads . And of these the remainder is 7 monads : of the 30 , 3 ; and of the 4 , 4 . Seven monads , therefore , are the root of the name Patroclus .
Those , then , that conduct their calculations according to the rule of the number nine , take the ninth part of the aggregate number of roots , and define what is left over as the sum of the roots . They , on the other hand , ( who conduct their calculations ) according to the rule of the number seven , take the seventh ( part of the aggregate number of roots ) ; for example , in the case of the name Patroclus , the aggregate in the matter of roots is 34 monads . This divided into seven parts makes four , which ( multiplied into each other ) are 28 . There are six remaining monads ; ( so that a person using this method ) says , according to the rule of the number seven , that six monads are the root of the name Patroclus . If , however , it be 43 , ( six ) taken seven times , he says , are 42 , for seven times six are 42 , and one is the remainder . A monad , therefore , is the root of the number 43 , according to the rule of the number seven . But one ought to observe if the assumed number , when divided , has no remainder ; for example , if from any name , after having added together the roots , I find , to give an instance , 36 monads . But the number 36 divided into nine makes exactly 4 enneads ; for nine times 4 are 36 , and nothing is over . It is evident , then , that the actual root is 9 . And again , dividing the number forty - five , we find nine and nothing over — for nine times five are forty - five , and nothing remains ; ( wherefore ) in the case of such they assert the root itself to be nine . And as regards the number seven , the case is similar : if , for example we divide 28 into 7 , we have nothing over ; for seven times four are 28 , and nothing remains ; ( wherefore ) they say that seven is the root . But when one computes names , and finds the same letter occurring twice , he calculates it once ; for instance , the name Patroclus has the pa twice , and the o twice : they therefore calculate the a once and the o once . According to this , then , the roots will be 8 , 1 , 3 , 1 , 7 , 2 , 3 , 2 , and added together they make 27 monads ; and the root of the name will be , according to the rule of the number nine , nine itself , but according to the rule of the number seven , six .
In like manner , ( the name ) Sarpedon , when made the subject of calculation , produces as a root , according to the rule of the number nine , two monads . Patroclus , however , produces nine monads ; Patroclus gains the victory . For when one number is uneven , but the other even , the uneven number , if it is larger , prevails . But again , when there is an even number , eight , and five an uneven number , the eight prevails , for it is larger . If , however , there were two numbers , for example , both of them even , or both of them odd , the smaller prevails . But how does ( the name ) Sarpedon , according to the rule of the number nine , make two monads , since the letter ( long ) o is omitted ? For when there may be in a name the letter ( long ) o and ( long ) e , they leave out the ( long ) o , using one letter , because they say both are equipollent ; and the same must not be computed twice over , as has been above declared . Again , ( the name ) Ajax makes four monads ; ( but the name ) Hector , according to the rule of the ninth number , makes one monad . And the tetrad is even , whereas the monad odd . And in the case of such , we say , the greater prevails — Ajax gains the victory . Again , Alexander and Menelaus ( may be adduced as examples ) . Alexander has a proper name ( Paris ) . But Paris , according to the rule of the number nine , makes four monads ; and Menelaus , according to the rule of the number nine , makes nine monads . The nine , however , conquer the four ( monads ) : for it has been declared , when the one number is odd and the other even , the greater prevails ; but when both are even or both odd , the less ( prevails ) . Again , Amycus and Polydeuces ( may be adduced as examples ) . Amycus , according to the rule of the number nine , makes two monads , and Polydeuces , however , seven : Polydeuces gains the victory . Ajax and Ulysses contended at the funeral games . Ajax , according to the rule of the number nine , makes four monads ; Ulysses , according to the rule of the number nine , ( makes ) eight . Is there , then , not any annexed , and ( is there ) not a proper name for Ulysses ? for he has gained the victory . According to the numbers , no doubt , Ajax is victorious , but history hands down the name of Ulysses as the conqueror . Achilles and Hector ( may be adduced as examples ) . Achilles , according to the rule of the number nine , makes four monads ; Hector one : Achilles gains the victory . Again , Achilles and Asteropæus ( are instances ) . Achilles makes four monads , Asteropæus three : Achilles conquers . Again , Menelaus and Euphorbus ( may be adduced as examples ) . Menelaus has nine monads , Euphorbus eight : Menelaus gains the victory .
Some , however , according to the rule of the number seven , employ the vowels only , but others distinguish by themselves the vowels , and by themselves the semi - vowels , and by themselves the mutes ; and , having formed three orders , they take the roots by themselves of the vowels , and by themselves of the semi - vowels , and by themselves of the mutes , and they compare each apart . Others , however , do not employ even these customary numbers , but different ones : for instance , as an example , they do not wish to allow that the letter p has as a root 8 monads , but 5 , and that the ( letter ) x ( si ) has as a root four monads ; and turning in every direction , they discover nothing sound . When , however , they contend about the second ( letter ) , from each name they take away the first letter ; but when they contend about the third ( letter ) , they take away two letters of each name , and calculating the rest , compare them .
Notes 1 The subject of the numerical system employed by the Gnostics, and their occult mysteries, is treated of by the learned Kircher, Œdipi Ægypt., tom. ii. part i., de Cabalâ Hebræorum; also in his Arithmolog. in the book De Arithmomantia Gnosticor., cap. viii., de Cabalâ Pythagoreâ. See also Mersennes, Comment. on Genes.
2 This subject is examined by Cornelius Agrippa in his celebrated work, De vanitate et incertitudine Scientiarum, chap. xi., De Sorte Pythagoricâ. Terentius Maurus has also a versified work on Letters and Syllables and Metres, in which he alludes to similar interpretations educible from the names Hector and Patroclus.
3 That is, the division by nine.
4 That is, calculated according to the rule of a division by seven.
5 We should expect rather five instead of 9, if the division be by nine.
6 There is some confusion in the text. Miller conjectures that the reading should be: “As, for instance, the name Patroclus has the letter o occurring twice in it, they therefore take it into calculation once.” Schneidewin suggests that the form of the name may be Papatroclus.
7 Miller says there is an error in the calculation here.
8 This is as near the sense of the passage as a translation in some respects conjectural can make it.
