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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 they prophesy by
means of calculations and numbers,^{197}^{197}
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*. 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^{198}^{198}
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. 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,^{199}^{199} That is,
the division by 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,^{200}^{200} That is,
calculated according to the rule of a division by seven. 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^{201}^{201} We should
expect rather five instead of 9, if the division be by 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,^{202}^{202}
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. 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.^{203}^{203} Miller
says there is an error in the calculation here. Is there, then, not any annexed, and
(is there) not a proper name for Ulysses?^{204}^{204} This is as
near the sense of the passage as a translation in some respects
conjectural can make it. 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.

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