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NUCLEAR FAMILY 19769

 

 

 

 

 

 

 

 

THE

MAGICALALPHABET

 

..................

 

 

-
-
-
-
-
THE RAINBOW LIGHT
-
-
-
T
=
2
-
3
THE
33
15
6
R
=
9
-
7
RAINBOW
82
37
1
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
THE RAINBOW LIGHT
171
81
9
-
-
1+4
-
1+5
-
1+7+1
8+1
-
Q
-
5
-
6
THE RAINBOW LIGHT
9
9
9

 

 

 

 

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Midway this way of life we're bound upon

I woke to find myself in a dark wood,

Where the right road was wholly lost and gone."

 

 

M
=
4
-
6
MIDWAY
75
30
3
T
=
2
-
4
THIS
56
20
2
W
=
5
-
3
WAY
49
13
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
4
LIFE
32
23
5
W
=
5
-
4
WE'RE
51
24
6
B
=
2
-
5
BOUND
56
20
2
U
=
3
-
4
UPON
66
21
3
-
-
30
-
32
-
406
163
28
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
W
=
5
-
4
WOKE
54
18
9
T
=
2
-
2
TO
35
8
8
F
=
6
-
4
FIND
33
24
6
M
=
4
-
6
MYSELF
80
26
8
I
=
9
-
2
IN
23
14
5
A
=
1
-
1
A
1
1
1
D
=
4
-
4
DARK
34
16
7
W
=
5
-
4
WOOD
57
21
3
-
-
45
-
28
-
326
137
56
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WHERE
59
32
5
T
=
2
-
3
THE
33
15
6
R
=
9
-
5
RIGHT
62
35
8
R
=
9
-
4
ROAD
38
20
2
W
=
5
-
3
WAS
43
7
7
W
=
5
-
6
WHOLLY
95
32
5
L
=
3
-
4
LOST
66
12
3
A
=
1
-
3
AND
19
10
1
G
=
7
-
4
GONE
41
23
5
-
-
46
-
37
-
456
186
42
-
-
-
-
-
-
-
-
-
-
-
121
-
97
First Total
1188
486
126
-
-
1+2+1
-
9+7
Add to Reduce
1+1+8+8
4+8+6
1+2+6
Q
-
4
-
16
Second Total
18
18
9
-
-
-
-
1+6
Reduce to Deduce
1+8
1+8
-
-
-
4
-
7
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Power failed high fantasy here; yet, swift to move

Even as a wheel moves equal, free from jars,

Already my heart and will were wheeled by love,

The Love that moves the sun and other stars."

 

P
=
7
-
5
POWER
77
32
5
F
=
6
-
6
FAILED
37
28
1
H
=
8
-
4
HIGH
32
32
5
F
=
6
-
7
FANTASY
86
23
5
H
=
8
-
4
HERE
36
27
9
Y
=
7
-
3
YET
50
14
5
S
=
1
-
5
SWIFT
77
23
5
T
=
2
-
2
TO
35
8
8
M
=
4
-
4
MOVE
55
19
1
-
-
49
-
40
First Total
485
206
44
-
-
4+9
-
4+0
Add to Reduce
4+8+5
2+0+6
4+4
Q
-
13
-
4
Second Total
17
8
8
-
-
1+3
-
-
Reduce to Deduce
1+7
-
-
-
-
4
-
4
Essence of Number
8
8
8

 

 

E
=
5
-
4
EVEN
46
19
1
A
=
1
-
2
AS
20
2
2
A
=
1
-
1
A
1
1
1
W
=
5
-
5
WHEEL
53
26
8
M
=
4
-
5
MOVES
74
20
2
E
=
5
-
5
EQUAL
56
20
2
F
=
6
-
4
FREE
34
25
7
F
=
6
-
4
FROM
52
25
7
J
=
1
-
4
JARS
48
12
3
-
-
34
-
34
First Total
384
150
33
-
-
3+4
-
3+4
Add to Reduce
3+8+4
1+5+0
3+3
Q
-
7
-
7
Second Total
15
6
6
-
-
-
-
-
Reduce to Deduce
1+5
-
-
-
-
7
-
7
Essence of Number
6
6
6

 

 

A
=
1
-
7
ALREADY
66
30
3
M
=
4
-
2
MY
38
11
2
H
=
8
-
5
HEART
52
25
7
A
=
1
-
3
AND
19
10
1
W
=
5
-
4
WILL
56
20
2
W
=
5
-
4
WERE
51
24
7
W
=
5
-
7
WHEELED
62
35
8
B
=
2
-
2
BY
27
9
9
L
=
3
-
4
LOVE
54
18
9
-
-
34
-
38
First Total
425
182
47
-
-
3+4
-
3+8
Add to Reduce
4+2+5
1+8+2
4+7
Q
-
7
-
11
Second Total
11
11
11
-
-
-
-
1+1
Reduce to Deduce
1+1
1+1
1+1
-
-
7
-
2
Essence of Number
2
2
2

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LOVE
54
18
9
T
=
2
-
4
THAT
49
13
4
M
=
4
-
5
MOVES
74
20
2
T
=
2
-
3
THE
33
15
6
S
=
1
-
3
SUN
54
9
9
A
=
1
-
3
AND
19
10
1
O
=
6
-
5
OTHER
66
30
3
S
=
1
-
5
STARS
77
14
5
-
-
22
-
35
First Total
459
144
45
-
-
2+2
-
3+5
Add to Reduce
4+5+9
1+4+4
4+5
Q
-
4
-
8
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
HOLY
60
24
6
7
MESSAGE
-
-
-
2
M+E
18
9
9
1
S
19
10
1
3
S+A+G
27
18
9
1
E
5
5
5
7
MESSAGE
69
42
24
14
Add
162
81
36
1+4
Reduce
1+6+2
8+1
3+6
5
Deduce
9
9
9

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly, too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the / Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry in the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 360° in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus. Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillana adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

The Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656 years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, multiply this by 2 and again we have the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as-the interesting number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes difficult to escape the suspicion that many signs (number and otherwise) - indicate that early man observed the results of the movement of Precession and that the - transmission of this information was considered of prime importance.

With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would have constituted the construction-of a 'Unified Field Theory' for nothing less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced, that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two, four. Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radius ekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up his piece of stripped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

CITY OF REVELATION

John Michell

1972

Page 109

"At the root of our traditional units of measurement is the ancient, mystical science of numbers, to which Plato makes an obscure reference towards the end of Epinomis, here quoted from Lamb's translation.

The most important and first (study) is of numbers in themselves: not of those which are corporeal, but of the whole origin of the odd and the even and the greatness of their influence on the nature of reality. When he has learnt these things, there comes next what they call by the very ridiculous name of geometry, when it proves to be a manifest likening of numbers not like one another by nature in respect of the province of planes; and this will be clearly seen by him who is able to understand it to be a marvel, not of human but of divine origin. And then, after that, the numbers thrice increased and like to the solid nature, and those again which have been made unlike, he likens by another art, namely that which its adepts call stereometry.'

The text is probably corrupt, the expressions are unfamiliar and it is hard to follow Plato's meaning. But the reference, both here and in another passage in Laws, is to some method of relating different classes of phenomena to one numerical system, by which the adept may come to understand the unifying principle in nature. Of this knowledge Plato declares that it is the greatest of all blessings both to him who possessed it and to his community, but if it can not be acquired, the best substitute is simple faith in God since, on the / Page 110 / word of an initiate, matters are far better arranged than we can possibly conceive. He continues,'Every diagram and system of number and every combination of harmony and the agreement of the revolution of the stars must be made manifest as one in all to him who learns in the proper way, and will be made manifest if a man learns aright by keeping his eyes on unity; for it will be manifest to us as we reflect, that there is one bond naturally uniting all these things.'

The number 666 in metrology

The number which above all others acts as a bond between the various units of measurement is the perfect number of Chaldean mathematics, 666. For example, 666 feet = 150 cubits + 150 MY while 666 square feet = 90 square MY. Also 6660 square yards = 902 square MY and 66,600 square feet = 1502 square cubits. The Babylonians had a decimal system, but they also reckoned in units of 6, 60 and 600 and a curious survival of this system is found in the letters which the Romans used as numerals, for the sum of I, V, X, L, C and D is 666. "

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH NUMBER WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLIED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
10
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

 

THE JOURNEYMAN 1977

 

 

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

 

 

 

...

 

 

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
9
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLIED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
14
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

“THE WORLD IS BUILT UPON THE POWER OF NUMBERS”

"Pythagoras, the old master philosopher and mathematician, who lived in the sixth century BC, propounded the theory that nothing in the universe could exist without numbers. He established a Mystery School in Italy when he was 52 years old. He was born in Greece and lived between 582 and 507 BC, much of his life spent in study and travel. His Mystery School taught esoteric knowledge, which included the secret of number and vibration."

“The World is built upon the power of Numbers” ...Pythagoras – 6th century BC.

 

“THE WORLD IS BUILT UPON THE POWER OF NUMBERS”

 

T
=
2
Q
3
THE
33
15
6
W
=
5
-
5
WORLD
72
27
9
I
=
9
-
2
IS
28
10
1
B
=
2
Q
5
BUILT
64
19
1
U
=
3
-
4
UPON
66
21
3
T
=
2
Q
3
THE
33
15
6
P
=
7
Q
5
POWER
77
32
5
O
=
6
-
2
OF
21
12
3
N
=
5
-
7
NUMBERS
92
29
2
-
-
41
-
36
First Total
486
180
36
-
-
4+1
-
3+6
Add to Reduce
2+7+9
1+8+0
3+6
-
-
5
-
9
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
5
-
9
Essence of Number
9
9
9

 

 

I

ME

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

 

THE GROWTH OF SCIENCE

A.P. Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

 

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
6
3
8
9

 

 

THE

MISSING

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

 

10
PYTHAGORAS
130
49
4
8
OURABORUS
130
31
4
5
SAMOS
67
13
4
7
MILETUS
99
27
9
8
THIRTEEN
99
45
9

 

 

PLATO

 

Sacred Geometry is the theory of dimensional evolution which assumes the ... door to his academy stating,

"Let no one unacquainted with geometry enter here.". ...
ezinearticles.com/?An-Overview-Of-Sacred-Geometry

 

AN OVERVIEW OF SACRED GEOMETRY

Gregg Hall

Sacred Geometry is the theory of dimensional evolution which assumes the universe is a living system kept together by the existence of a sacred geometry that encompasses the entire cosmos and makes for the blueprint for the manifestation of what we know as our material universe and in addition organizes the context through which all love evolves.

Our universe was designed to be highly efficient and is capable of performing a wide range of multiple functions at the same time. The very same geometry which provides structure to physical reality also allows for the perceptual environments that people and civilizations must move through as part of a systematic learning process on the path towardsevolution.

Each dimension of this sacred geometry holds a unique place of perceptual space and a context of learning both for personaland social evolution. As each new dimension appears a new set of perceptions and potentials is awakened which we are free to accept and actualize or ignore. It is in understanding the dimensional structure which exists all around us that allows us to be able to understand the path and direction of personal and social evolution.

Even though our modern science generally believes there is nothing of deeper meaning to the dimensional geometry of the universe other than the actual physical aspects, there is a view that is almost diametrically opposed to this that began with the Greek philosopher Pythagoras in 500 B.C. Pythagoras believed and taught the theory or belief that all of the mathematical patterns in the universe were actually expressions of divine intelligence and signified a divine intention.

According to Pythagoras, we are surrounded by organizational intelligence that is shown in its purest from through mathematical formulas and musical harmonies and allowing ourselves to be at the center of our experience; we can know and share the organizing patterns and principles that pervadethe universe. This is a thought that was even held by Albert Einstein, who stated that he received his greatest breakthroughs after praying and sleeping. The answers to the questions he was seeking came to him from the Universe while he slept! This is also the way that it can be explained for someone who is blind to be able to sculpt and for a deaf person, such as Beethoven to be able to compose intricate musical scores.

Plato, who taught over a hundred years after Pythagoras, continued in the teachings of Pythagorean thought in espousing that the universe or cosmos as Pythagoras termed it was a place of "harmonious and beautiful order" and placed such a high regard on geometry that he placed a sign above the door to his academy stating, "Let no one unacquainted with geometry enter here."

 

 

the aims of studying plane geometry and how to attain them - Jstor
https://www.jstor.org/stable/27949586

by EP Sisson - 1908
Plato had written over the porch of his famous school,

"Let no one who is unacquainted with geometry enter here."

 

 

The Cyclopædia, Or, Universal Dictionary of Arts, Sciences, and ...

Abraham Rees - 1819 - ?Encyclopedias and dictionaries
But to these arguments it has been replied, 1. ... he placed this inscription, Ovcel; 2) souárpolo; a`To

“Let no one, who is unacquainted with geometry, enter here.

 

 

A history of elementary mathematics -

Page 61

C. Florian - 1914 - History

Let no one who is unacquainted with geometry enter here,” was inscribed over the entrance to his school.

Likewise Xenocrates, a successor of Plato, as teacher ...

 

 

A History of Mathematics

Page 26

Florian Cajori - 1999 - Mathematics
Like them, he sought in arithmetic and geometry the key to the universe. ...

inscription over his porch, "Let no one who is unacquainted with geometry enter here".

 

Geometry. Part 2 - ChestofBooks.com
https://chestofbooks.com › American-Cyclopaedia-V7

Plato is said to have inscribed over his door, "Let no one enter here who is unacquainted with geometry."

 

"Let no one enter here who is unacquainted with geometry."

 

L
=
3
3
LET
37
10
1
N
=
5
2
NO
29
11
2
O
=
6
3
ONE
34
16
7
E
=
5
5
ENTER
62
26
8
H
=
8
4
HERE
36
27
9
W
=
5
3
WHO
46
19
1
I
=
9
2
IS
28
19
1
U
=
3
12
UNACQUAINTED
130
49
4
W
=
5
4
WITH
60
24
6
G
=
7
8
GEOMETRY
108
45
9
-
-
56
46
First Total
570
246
48
-
-
5+6
4+6
Add to Reduce
5+7+0
2+4+6
4+8
-
-
11
10
Second Total
12
12
12
-
-
1+1
1+0
Reduce to Deduce
1+2
1+2
1+2
-
-
2
1
Essence of Number
3
3
3

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
8
-
12
UNACQUAINTED
130
49
4
-
-
-
-
4
-
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
-
-
-
-
-
-
9
-
-
56
-
-
-
46
First Total
570
246
48
-
3
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+6
Add to Reduce
5+7+0
2+4+6
4+8
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
10
Second Total
12
12
12
-
3
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
1+0
Reduce to Deduce
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
1
Essence of Number
3
3
3
-
3
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
-
-
-
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
8
-
12
UNACQUAINTED
130
49
4
-
-
-
-
4
-
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
-
-
-
-
-
-
9
-
-
56
-
-
-
46
First Total
570
246
48
-
3
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+6
Add to Reduce
5+7+0
2+4+6
4+8
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
10
Second Total
12
12
12
-
3
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
1+0
Reduce to Deduce
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
1
Essence of Number
3
3
3
-
3
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
3
-
5
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
3
-
5
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
3
-
5
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
3
-
5
-
-
-
-
U
=
3
-
8
-
12
UNACQUAINTED
130
49
4
-
-
-
3
4
-
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
3
-
5
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
3
-
5
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
3
-
5
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
3
-
5
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
3
-
5
-
-
-
9
-
-
56
-
-
-
46
First Total
570
246
48
-
3
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+6
Add to Reduce
5+7+0
2+4+6
4+8
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
10
Second Total
12
12
12
-
3
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
1+0
Reduce to Deduce
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
1
Essence of Number
3
3
3
-
3
2
3
4
5
6
7
8
9

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

THE

MISSING

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

 

-
PLATO
-
-
-
2
PL
28
10
1
3
ATO
36
9
9
5
PLATO
64
19
10
-
--
6+4
1+9
1+0
5
PLATO
10
10
1
-
-
1+0
1+0
-
5
PLATO
1
1
1

 

 

5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
-
1
+
=
1
-
=
1
-
1
-
-
-
A
-
-
-
-
-
-
-
-
-
-
-
-
3
-
2
-
+
=
5
=
5
-
5
-
-
L
-
T
-
-
-
-
-
-
-
-
-
-
7
-
-
-
6
+
=
13
1+3
=
4
-
4
-
P
-
-
-
O
-
-
-
-
-
-
-
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-

 

 

-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
16
12
1
20
15
+
+
64
6+4
=
10
1+0
1
-
-
7
3
1
2
6
+
+
19
1+9
=
10
1+0
1
-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
26
5
P
L
A
T
O
-
-
19
-
-
5
-
19
2+6
-
-
-
-
-
-
-
-
1+9
-
-
-
-
1+9
8
5
P
L
A
T
O
-
-
10
-
-
5
-
10
-
-
7
3
1
2
6
-
-
1+0
-
-
-
-
1+0
8
5
P
L
A
T
O
-
-
1
-
-
5
-
1

 

 

-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
3
-
-
--
-
--
--
--
-
-
-
3
THREE
-
-
-
-
-
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
6
-
--
--
-
--
--
--
-
-
-
6
SIX
-
-
-
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
-
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
-
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
-
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

KEEPER OF GENESIS

A QUEST FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock 1996

Page 254

"...Is there in any sense an interstellar Rosetta Stone?

We believe there is a common language that all technical civilizations, no matter how different, must have.

That common language is science and mathematics.

The laws of Nature are the same everywhere:..."

 

 

R
=
9
-
7
ROSETTA
98
26
8
S
=
1
-
5
STONE
73
19
1
-
-
10
-
12
Add to Reduce
171
45
9
-
-
1+0
-
1+2
Reduce to Deduce
1+7+1
4+5
-
Q
-
1
-
3
Essence of Number
9
9
9

 

 

-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
22
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
2+2
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 38

"In the sphere of the natural sciences and of mathematics there have been endless disputes as to how much the Greeks borrowed from their neighbours, and the disputes are likely to continue, for the evidence is scanty and unreliable. It is safe to assume that the Greeks (noted then as now for commercial enterprise) took all they could get. Their own writers say as much, for they attribute the origin of very many useful inventions to other peoples. But this one thing, the scientific outlook and method, was not there to take; they had to invent it themselves. It is well to be clear on this point, for European civilization rests on three legs. They are Greek science, Jewish religion and Roman law. / Page 39 / Roman law may well be considered the Roman development of Greek scientific method. I will therefore deal with two examples in some little detail. These are taken from the sphere of mathematics and astronomy, for it was in these two sciences that the Greeks had their most outstanding success, doing about as much as could possibly be done under the conditions of their day and laying the foundations on which all subsequent work has been based.

The Egyptians knew of many useful methods of -geo- metrical calculation, for finding the area of a field, the volume of a barrel and so on. The Babylonians and earlier Mesopotamians had made accurate observations of sun, moon and stars over long periods and developed ingenious methods for calculating their future positions in the sky. In these arts of calculation these people had nothing to learn from the Greeks; it was the other way about. But there is no evidence that they ever dreamt of turning the art of calculation into the science of mathematics. Solving particular problems, however ingeniously, is not necessarily science any more than is playing chess (though all chess problems are geometrical) or keeping accounts (though all money reckoning is arithmetical). Mathematical science in the proper sense of the word attains its end by two means : (1) generalizing as far as is possible all problems and their solutions, so that one solution solves any number of particular cases; (2) finding proofs that solutions are correct as opposed to finding solutions which might be right by chance, not by necessity. The method used is the method of discussion in its specifically mathematical form.

The Egyptians could set out a right-angle on the ground, for building or for land surveying, by means of a cord knotted at intervals of 3, 4 and 5 units of length. They adjusted three pegs to make a triangle with the knots at the pegs when the cord was stretched tight round them. The Greeks, seeing this trick, generalized the problem and looked for a proof of the solution. The final result, after two centuries of effort, is the First Book of Euclid's Elements, leading up to Proposition 47—that the square on the hypotenuse of a right-angled triangle equals the sum of / Page 40 / the squares on the other sides, and that this must be so, granted the assumptions made at the beginning. (The proposition is further generalized in, Euclid VI, 31.) In this way a technical dodge of the land surveyor, depending upon the fact that 32+42= 52, was turned into science.

Page 38 Notes

1 Thucydides IV, 104—V, 26.
2 Hippocrates, Vol. ii, pp. 138 seq. Loeb Classical Library.

 

 

-
PYTHAGORAS
-
-
-
5
PYTHA
70
25
7
5
GORAS
60
24
6
10
PYTHAGORAS
130
49
13
-
-
1+3+0
4+9
3+1
-
-
4
13
4
8
THIRTEEN
99
45
9

 

 

-
PYTHAGORAS
-
-
-
-
PYT
61
16
7
-
HA
9
9
9
-
GO
22
13
4
-
R
18
9
9
-
AS
20
11
2
10
PYTHAGORAS
130
58
31
1+0
  
1+3+0
5+8
3+1
1
PYTHAGORAS
4
13
4
-
-
-
1+3
-
1
PYTHAGORAS
4
4
4

 

 

-
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
+
=
130
1+3
=
18
1+8
4
-
4
-
-
7
7
2
8
1
7
6
9
1
1
+
=
49
4+9
=
13
1+3
4
-
4
-
8
P
Y
T
H
A
G
O
R
A
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
1
occurs
x
3
=
3
-
3
-
-
-
-
2
-
-
-
-
-
-
-
--
--
2
occurs
x
1
=
2
-
2
3
--
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
-
-
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
--
7
7
-
-
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
9
-
9
12
8
P
Y
T
H
A
G
O
R
A
S
-
-
33
-
-
8
-
49
-
31
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
3+3
-
-
-
-
4+9
-
3+1
3
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
13
-
4
-
-
7
7
2
8
1
7
6
9
1
1
-
-
-
-
-
-
-
1+3
-
-
3
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
4
-
4

 

 

-
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
+
=
15
1+5
=
6
-
6
-
6
-
-
-
-
-
8
-
-
15
-
-
19
+
=
42
4+2
=
6
-
6
-
6
-
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
+
=
34
3+4
=
7
-
7
-
7
-
`-
16
25
20
-
1
7
-
18
1
-
+
=
88
8+8
=
16
1+6
7
-
7
-
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
+
=
 130
1+3
=
18
1+8
4
-
4
-
-
7
7
2
8
1
7
6
9
1
1
+
=
49
4+9
=
13
1+3
4
-
4
-
8
P
Y
T
H
A
G
O
R
A
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
1
occurs
x
3
=
3
-
3
-
-
-
-
2
-
-
-
-
-
-
-
--
--
2
occurs
x
1
=
2
-
2
3
--
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
--
7
7
-
-
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
9
-
9
12
8
P
Y
T
H
A
G
O
R
A
S
-
-
33
-
-
8
-
49
-
31
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
3+3
-
-
-
-
4+9
-
3+1
3
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
13
-
4
-
-
7
7
2
8
1
7
6
9
1
1
-
-
-
-
-
-
-
1+3
-
-
3
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
4
-
4

 

 

8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
+
=
15
1+5
=
6
-
6
-
6
-
-
-
-
8
-
-
15
-
-
19
+
=
42
4+2
=
6
-
6
-
6
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
+
=
34
3+4
=
7
-
7
-
7
`-
16
25
20
-
1
7
-
18
1
-
+
=
88
8+8
=
16
1+6
7
-
7
8
P
Y
T
H
A
G
O
R
A
S
-
-
-
-
-
--
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
+
=
 130
1+3
=
18
1+8
4
-
4
-
7
7
2
8
1
7
6
9
1
1
+
=
49
4+9
=
13
1+3
4
-
4
8
P
Y
T
H
A
G
O
R
A
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
1
occurs
x
3
=
3
-
3
-
-
-
2
-
-
-
-
-
-
-
--
--
2
occurs
x
1
=
2
-
2
--
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
6
--
7
7
-
-
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
9
-
9
8
P
Y
T
H
A
G
O
R
A
S
-
-
33
-
-
8
-
49
-
31
-
-
-
-
-
-
-
-
9
-
-
-
-
3+3
-
-
-
-
4+9
-
3+1
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
13
-
4
-
7
7
2
8
1
7
6
9
1
1
-
-
-
-
-
-
-
1+3
-
-
8
P
Y
T
H
A
G
O
R
A
S
-
-
6
-
-
8
-
4
-
4

 

 

PYTHAGORAS

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

-
-
-
-
10
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
6
3
8
9

 

A BRIEF HISTORY OF INFINITY

"The Quest to Think the Unthinkable

Brian Clegg 2003

Page 66

"When dealing with such ratios, they would know that there was a clear relationship in terms of a full unit - so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4..."

 

The Theorem of Pythagoras 25 Nov 2001 ... Brief description and proof of the Pythagorean theorem by dissection, ... Ancient Egyptian builders may have known the (3,4,5) triangle and ... arc.iki.rssi.ru/mirrors/stern/stargaze/Spyth.htm - Cached - Similar -

 

Pythagorean Triangles and Triples Jump to The 3-4-5 Triangle‎: 3 4 5 on graph paper But all Pythagorean triangles are even easier to draw on squared paper because all their sides are ... www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html - Cached - Similar

 

-3:4:5 triangle definition - Math Open Reference - Sep 23
You could of course use any dimensions you like, and then use Pythagoras' theorem to see if it is a right triangle. But the numbers 3,4,5 are easy to ...
www.mathopenref.com/triangle345.html - Cached - Similar

 

-The Pythagorean Theorem and the Maya Long Count Various ancient cultures based some of their artwork on the 3-4-5 right triangle, frequently referred to by geometrists as a perfect triangle. Pythagoras is ... www.earthmatrix.com/pythagoras.html - Cached - Similar

 

-Our Ancient Friend and Brother, the Great Pythagoras The evidence that the particular triangle alluded to in the Monitor is the 3,4,5 right triangle can be derived from the odd comments about Pythagoras' ... www.sricf-ca.org/paper1.htm - Similar

 

-The 3-4-5 Rule is the Pythagorean Theorem: Set Control Lines for ... The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or ...
homerenorepair.suite101.com/.../the_345_rule_is_the_pythagorean_theorem - Cached - Similar

 

-pythagoras For integers m and n, {n2-m2, 2mn, n2+m2}is a pythagorean triangle. For m=1, n=2, you'll get {3, 4, 5}. I'll add a diagram so that this isn't completely ... www.mathpuzzle.com/pythagoras.html - Cached - Similar

-The Pythagorean Theorem First described by the Greek mathematician Pythagoras 2500 years ago, the Pythagorean ... For example: 3,4,5 or 6,8,10 or 9,12,15 or 12,16,20 ... etc ... www.worsleyschool.net/.../pythagoras/pythagoreantheorem.html - Cached - Similar

 

-pythagoras Pythagoras the 3-4-5 fallacy. ... Traditionally the example used to illustrate the Pythagorean theorem is the 3-4-5 diagram. This is a fallacy, ... www.marques.co.za/duke/pythagoras.htm - Cached - Similar -

 

PYTHAGORAS = 7728176911 = PYTHAGORAS

1112345677789

123456789

1112345677789

PYTHAGORAS = 7728176911 = PYTHAGORAS

 

 

THE GROWTH OF SCIENCE

A.P.Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
12
-
-
-
14
-
13
First Total
158
77
14
1+2
-
-
-
1+4
-
1+3
Add to Reduce
1+5+8
7+7
1+4
12
-
-
-
5
-
4
Second Total
14
14
5
-
-
-
-
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
-
-
5
-
4
Essence of Number
5
5
5

 

 

JUST SIX NUMBERS

The Deep Forces that Shape the Universe

Martin Rees 1999

Chapter 1

THE COSMOS AND THE MICROWORLD

Man is . . . related inextricably to all reality, known and unknowable . . . plankton, a shimmering phosphorescence on the sea and the spinning planets and an expanding universe, all bound together by the elastic string of time. It is advisable to look from the tide pool to the stars and then back to the tide pool again.

John Steinbeck, The Log from the Sea of Cortez

SIX NUMBERS

Mathematical laws underpin the fabric of our universe — not just atoms, but galaxies, stars and people. The properties of atoms — their sizes and masses, how many different kinds there are, and theiorces linking them together — determine the chemistry of our everyday world. The very existence of atoms depends on forces and particles deep inside them. The objects that astronomers study — planets, stars and galaxies — are controlled by the force of gravity. And everything takes place in the arena of an expanding universe, whose properties were imprinted into it at the time of the initial Big Bang.
Science advances by discerning patterns and regularities in nature, so that more and more phenomena can be subsumed into general categories and laws. Theorists aim to encapsulate the essence of the physical laws in a unified set of equations,

Page 7

"Lengths spanning sixty powers of ten are depicted in the ouraborus,"

Page 8

FIGURE 1.1 (omitted)

"The ouraborus, There are links between the micro world of particles, nuclei and atoms (left) and the cosmos (right)"

Page 161

"A theme of this book has been the intimate links between the micro world and the cosmos symbolized by the ouraborus"

 

THE

OURABORUS PYTHAGORAS  OURABORUS

THAT

SERPENT I PRESENT

 

3
THE
33
15
6
-
OURABORUS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
A+B+O
18
9
9
1
R
18
9
9
2
U+S
40
13
4
-
OURABORUS
-
-
-
12
First Total
163
64
46
1+2
Add to Reduce
1+6+3
6+4
4+6
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

B HOURS OF HORUS B

 

-
OURABORUS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
A+B+O
18
9
9
1
R
18
9
9
2
U+S
40
13
4
9
OURABORUS
130
49
40
-
-
1+3+0
4+9
9
OURABORUS
4
13
4
-
-
1+3
-
9
OURABORUS
4
4
4

 

 

THE GROWTH OF SCIENCE

A.P. Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

 

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
12
-
-
-
14
-
13
First Total
158
77
14
1+2
-
-
-
1+4
-
1+3
Add to Reduce
1+5+8
7+7
1+4
12
-
-
-
5
-
4
Second Total
14
14
5
-
-
-
-
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
-
-
5
-
4
Essence of Number
5
5
5

 

 

THE

MISSING

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

THE MISSING NUMBERS FROM THE NAME PYTHAGORAS ARE 3 4 5

so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4."

 

TRANSCRIBE THE WORD PYTHAGORAS INTO NUMBER

VIA

THE ENGLISH ALPHABET

ADD TO REDUCE REDUCE TO DEDUCE

NOTA BENE

PYTHAGORAS = 7728176911 = PYTHAGORAS

WHEN REARRANGED IN NUMERICAL ORDER THE ONLY NUMBERS MISSING ARE REVEALED AS

 

1112 3 4 5 677789

1112 3 4 5 677789

1112 3 4 5 677789

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
10
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
10
PYTHAGORAS
-
-
-
-
1
2
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
6
3
8
9

 

THE MISSING NUMBERS FROM THE NAME PYTHAGORAS ARE 3 4 5

 

so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4."

 

-
-
-
-
10
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

PYTHAGORAS = 7728176911 = PYTHAGORAS

1112345677789

123456789

1112345677789

PYTHAGORAS = 7728176911 = PYTHAGORAS

 

A BRIEF HISTORY OF INFINITY

"The Quest to Think the Unthinkable

Brian Clegg 2003

Page 66

"When dealing with such ratios, they would know that there was a clear relationship in terms of a full unit - so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4..."

 

The Theorem of Pythagoras 25 Nov 2001 ... Brief description and proof of the Pythagorean theorem by dissection, ... Ancient Egyptian builders may have known the (3,4,5) triangle and ... arc.iki.rssi.ru/mirrors/stern/stargaze/Spyth.htm - Cached - Similar -

 

Pythagorean Triangles and Triples Jump to The 3-4-5 Triangle‎: 3 4 5 on graph paper But all Pythagorean triangles are even easier to draw on squared paper because all their sides are ... www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html - Cached - Similar

 

-3:4:5 triangle definition - Math Open Reference - Sep 23
You could of course use any dimensions you like, and then use Pythagoras' theorem to see if it is a right triangle. But the numbers 3,4,5 are easy to ...
www.mathopenref.com/triangle345.html - Cached - Similar

 

-The Pythagorean Theorem and the Maya Long Count Various ancient cultures based some of their artwork on the 3-4-5 right triangle, frequently referred to by geometrists as a perfect triangle. Pythagoras is ... www.earthmatrix.com/pythagoras.html - Cached - Similar

 

-Our Ancient Friend and Brother, the Great Pythagoras The evidence that the particular triangle alluded to in the Monitor is the 3,4,5 right triangle can be derived from the odd comments about Pythagoras' ... www.sricf-ca.org/paper1.htm - Similar

 

-The 3-4-5 Rule is the Pythagorean Theorem: Set Control Lines for ... The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or ...
homerenorepair.suite101.com/.../the_345_rule_is_the_pythagorean_theorem - Cached - Similar

 

-pythagoras For integers m and n, {n2-m2, 2mn, n2+m2}is a pythagorean triangle. For m=1, n=2, you'll get {3, 4, 5}. I'll add a diagram so that this isn't completely ... www.mathpuzzle.com/pythagoras.html - Cached - Similar

-The Pythagorean Theorem First described by the Greek mathematician Pythagoras 2500 years ago, the Pythagorean ... For example: 3,4,5 or 6,8,10 or 9,12,15 or 12,16,20 ... etc ... www.worsleyschool.net/.../pythagoras/pythagoreantheorem.html - Cached - Similar

 

-pythagoras Pythagoras the 3-4-5 fallacy. ... Traditionally the example used to illustrate the Pythagorean theorem is the 3-4-5 diagram. This is a fallacy, ... www.marques.co.za/duke/pythagoras.htm - Cached - Similar -

 

THE MISSING NUMBERS FROM THE NAME PYTHAGORAS ARE 3 4 5

so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4."

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
6
3
8
9

 

THE MISSING NUMBERS FROM THE NAME PYTHAGORAS ARE 3 4 5

so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4."

 

A BRIEF HISTORY OF INFINITY

"The Quest to Think the Unthinkable

Brian Clegg 2003

Page 66

"When dealing with such ratios, they would know that there was a clear relationship in terms of a full unit - so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4..."

 

The Theorem of Pythagoras 25 Nov 2001 ... Brief description and proof of the Pythagorean theorem by dissection, ... Ancient Egyptian builders may have known the (3,4,5) triangle and ... arc.iki.rssi.ru/mirrors/stern/stargaze/Spyth.htm - Cached - Similar -

 

Pythagorean Triangles and Triples Jump to The 3-4-5 Triangle‎: 3 4 5 on graph paper But all Pythagorean triangles are even easier to draw on squared paper because all their sides are ... www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html - Cached - Similar

 

-3:4:5 triangle definition - Math Open Reference - Sep 23
You could of course use any dimensions you like, and then use Pythagoras' theorem to see if it is a right triangle. But the numbers 3,4,5 are easy to ...
www.mathopenref.com/triangle345.html - Cached - Similar

 

-The Pythagorean Theorem and the Maya Long Count Various ancient cultures based some of their artwork on the 3-4-5 right triangle, frequently referred to by geometrists as a perfect triangle. Pythagoras is ... www.earthmatrix.com/pythagoras.html - Cached - Similar

 

-Our Ancient Friend and Brother, the Great Pythagoras The evidence that the particular triangle alluded to in the Monitor is the 3,4,5 right triangle can be derived from the odd comments about Pythagoras' ... www.sricf-ca.org/paper1.htm - Similar

 

-The 3-4-5 Rule is the Pythagorean Theorem: Set Control Lines for ... The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or ...
homerenorepair.suite101.com/.../the_345_rule_is_the_pythagorean_theorem - Cached - Similar

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
P
=
7
-
10
PYTHAGORAS
130
58
4
T
=
2
-
7
THEOREM
84
39
3
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
4
-
4
-
1+7
-
2+1+4
9+7
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
4
-
4
-
-
-
-
1+6
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7

 

The Babylonians were using Pythagoras' Theorem over 1,000 years before he was born. An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.4 Aug 2021

The Babylonians were using Pythagoras’ Theorem over 1,000 years before he was born Subscribe to BBC Science Focus Magazine and get 6 issues for just £9.99
An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.

By Sara Rigby

Published: 04th August, 2021 at 17:05

Students may not believe that Pythagoras’ Theorem has real-world uses, but a 3,700-year-old tablet proves that their maths teachers are right. The artifact, named Si.427, shows how ancient land surveyors used geometry to draw boundaries accurately.

Discovered in central Iraq in 1894, Si.427 sat in a museum in Istanbul for over a century. Now, mathematician Dr Daniel Mansfield from the University of New South Wales, Australia, has studied the clay tablet and uncovered its meaning.

“Si.427 dates from the Old Babylonian (OB) period – 1900 to 1600 BCE,” said Mansfield. “It’s the only known example of a cadastral document from the OB period,

which is a plan used by surveyors define land boundaries. In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off.


A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13.

Any triangle with sides of these lengths must be a right-angled triangle.

This fact is useful for marking out accurate rectangles: constructing a triangle whose sides are a Pythagorean triple gives you a right angle every time. This makes Si.427 the earliest-known example of applied geometry.

Read more about ancient maths:
40,000-year-old yarn suggests Neanderthals had basic maths skills
Archimedes: inventor of war machines and calculus (almost)
“Nobody expected that the Babylonians were using Pythagorean triples in this way,” Mansfield said. “It is more akin to pure mathematics, inspired by the practical problems of the time.

“The discovery and analysis of the tablet have important implications for the history of mathematics,” he said. “For instance, this is over a thousand years before Pythagoras was born.

“This is from a period where land is starting to become private – people started thinking about land in terms of ‘my land and your land’, wanting to establish a proper boundary to have positive neighbourly relationships. And this is what this tablet immediately says. It’s a field being split, and new boundaries are made.”

However, this mathematics wasn’t always simple for the Babylonians. Their number system was different from the one we use now. Ours is in a system called base 10: numbers are written by breaking them down into hundreds, tens, units, and so on. The Babylonian number system, however, used the much more complex base 60, similar to how we keep time: 60 seconds make up one minute, and 60 minutes make up one hour.

“This raises a very particular issue – their unique base 60 number system means that only some Pythagorean shapes can be used,” said Mansfield.

In 2017, Mansfield studied another tablet from later in the same time period. This one, called Plimpton 322, contained what he calls ‘proto-trigonometry’: a table studying different types of triangle.

“It seems that the author of Plimpton 322 went through all these Pythagorean shapes to find these useful ones,” he said. “This deep and highly numerical understanding of the practical use of rectangles earns the name ‘proto-trigonometry’ but it is completely different to our modern trigonometry involving sin, cos, and tan.”

The issue of geometry and land ownership came up over and over for the ancient Babylonians, highlighting just how important this mathematics was.

“Another tablet refers to a dispute between Sin-bel-apli – a prominent individual mentioned on many tablets including Si.427 – and a wealthy female landowner,” Mansfield said.

“The dispute is over valuable date palms on the border between their two properties. The local administrator agrees to send out a surveyor to resolve the dispute. It is easy to see how accuracy was important in resolving disputes between such powerful individuals.”

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
P
=
7
-
10
PYTHAGORAS
130
58
4
T
=
2
-
7
THEOREM
84
39
3
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
4
-
4
-
1+7
-
2+1+4
9+7
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
4
-
4
-
-
-
-
1+6
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7

 

The Babylonians were using Pythagoras’ Theorem over 1,000 years before he was bornSubscribe to BBC Science Focus Magazine and get 6 issues for just £9.99
An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.

By Sara Rigby

Published: 04th August, 2021 at 17:05


As many will remember from their school days, Pythagoras’ Theorem states that the sides of a right-angled triangle obey the formula a2 + b2 = c2, where a and b are the lengths of the short sides, and c is the length of the longest side.

A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13.

Any triangle with sides of these lengths must be a right-angled triangle.

This fact is useful for marking out accurate rectangles: constructing a triangle whose sides are a Pythagorean triple gives you a right angle every time. This makes Si.427 the earliest-known example of applied geometry.

 

A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13.

Any triangle with sides of these lengths must be a right-angled triangle.

 

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PYTHAGORAS
130
58
4
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
17
PYTHAGORAS THEOREM
214
97
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
PYTHAGORAS THEOREM-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
12
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
14
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
15
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
17
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
4
3
4
10
12
21
16
18
-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
-
-
-
-
1+0
3+0
2+1
1+6
1+8
P
=
7
-
10
PYTHAGORAS
130
58
4
-
3
4
3
4
1
3
3
7
9
T
=
2
4
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
1+7
-
2+1+4
9+7
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7
-
3
4
3
4
1
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PYTHAGORAS
130
58
4
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
17
PYTHAGORAS THEOREM
214
97
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
3
-
-
-
7
-
-
T
=
2
3
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
A
=
1
9
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
H
=
8
12
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
O
=
6
14
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
R
=
9
15
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
E
=
5
16
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
M
=
4
17
1
M
13
4
4
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
4
3
4
10
12
21
16
18
-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
-
-
-
-
1+0
1+2
2+1
1+6
1+8
P
=
7
-
10
PYTHAGORAS
130
58
4
-
3
4
3
4
1
3
3
7
9
T
=
2
4
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
1+7
-
2+1+4
9+7
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7
-
3
4
3
4
1
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PYTHAGORAS
130
58
4
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
17
PYTHAGORAS THEOREM
214
97
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
M
=
4
17
1
M
13
4
4
-
-
-
3
4
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
O
=
6
14
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
3
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
H
=
8
12
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
R
=
9
8
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
15
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
3
4
3
4
10
12
21
16
18
-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
-
-
-
-
1+0
1+2
2+1
1+6
1+8
P
=
7
-
10
PYTHAGORAS
130
58
4
-
3
4
3
4
1
3
3
7
9
T
=
2
4
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
1+7
-
2+1+4
9+7
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7
-
3
4
3
4
1
3
3
7
9

 

 

THE PYTHAGOREAN EQUATION

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
T
=
2
-
3
THE
33
15
6
P
=
7
-
11
PYTHAGOREAN
130
58
4
E
=
5
-
8
EQUATION
102
39
3
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
4
-
4
-
-
-
1+3
-
-
-
4
9
4
4
THE PYTHAGOREAN EQUATION
4
4
4

 

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
20
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
21
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
4
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
4
-
-
7
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
4
-
-
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
4
-
-
-
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
4
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
I
=
9
20
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
O
=
6
21
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
U
=
3
17
1
U
21
3
3
-
-
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
O
=
6
21
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
4
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
4
-
-
7
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
4
-
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
4
-
-
-
-
9
I
=
9
20
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

THE GROWTH OF SCIENCE

A.P.Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

dic Astrology and Numerology, ROHIT KR RAO

www.rohitkrrao.com/numerology.html‎

The history of numbers is as old as the recorded history of man. Numerology was in use in ancient Greece, Rome, Egypt, China and India and is to be found in ...

What are the Numbers?

The most familiar form of numbers are natural numbers 0, 1, 2, 3, 4 5, 6, 7, 8, 9.

The numbers 1 to 9 can be called as unit numbers and the numbers from 10 onwards (up to 99) can be called as double-digit numbers which denotes the fusion of two numbers however these can still be reduced to unit numbers, eg; 24 (2+4=6) is reduced to 6. Then, there are Master Numbers such as 11, 22, 33, 44 and so on which are never reduced to a unit number as they carry their own intensified vibration and potency.

Every number expresses its qualities in the form of strengths and challenges. Therefore, no number is good or bad, lucky or unlucky and auspicious or inauspicious as each and every number is equally necessary and important, and each gives strength to the next one and takes what it needs from the one before. Numbers have two aspects viz; exoteric or external and esoteric or inner. In a nut shell, every number possesses its own unique quality and power.

Our ancient seers believed that numbers symbolize divinity and however our mathematicians believed that study of numbers can possibly reveal the principles of creation and laws of time & space. Numbers can be seen as fundamental in art, poetry, architecture, music, and so on.

“The World is built upon the power of Numbers” ...Pythagoras – 6th century BC.


What is Numerology?

The word Numerology comes from the Latin word "Numerus," which means number, and the Greek word "Logos," which means word, thought, and expression.

Numerology, based upon the sacred science of numbers, is an advanced offshoot of the melodious rhythm of the mathematical precision that controls all creation. It influences every aspect of our life unconsciously or consciously whether we are aware of this or not.

Numerology is the science and philosophy of numbers (1 to 9) where each numbers has its own strength, potential and challenge. The whole idea behind this is to know the hidden expression contained in these numbers so as to understand their relationship and progression in our numerology chart. This can help us in knowing the difficulties we may have experienced in the past or under present circumstances and then working towards doing some inner work in our life for bringing harmony, peace and joy.
The belief in Numerology is easier to understand when we put it into a context with realizing how the entire world revolves around numbers and mathematical equations.

 

What is the origin and history of Numerology? top

The history of numbers is as old as the recorded history of man. Numerology was in use in ancient Greece, Rome, Egypt, China and India and is to be found in the ancient books of wisdom, such as the Hebrew Kabala. Most commonly used system for Numerology were developed by the Chaldeans, the Hindus, the Mayans, the Hebrews (Kabala), the Chinese (Book of Changes), and the work of Pythagoras, to name a few. The basic intent behind these systems originally was to understand the relationship between man and his god.

Pythagoras, the old master philosopher and mathematician, who lived in the sixth century BC, propounded the theory that nothing in the universe could exist without numbers. He established a Mystery School in Italy when he was 52 years old. He was born in Greece and lived between 582 and 507 BC, much of his life spent in study and travel. His Mystery School taught esoteric knowledge, which included the secret of number and vibration. The knowledge was passed down by word of mouth and a few manuscripts. The academic teaching rested on a foundation of Mathematics, Music and Astronomy. Much of Pythagoras' background in Egyptian philosophy and religion was based upon Number and Kabalistic principle. He postulated that the triangle was particularly important, as it was the first complete shape, and constituted a blueprint. Thus form is preceded by a blueprint, and each stage of this process is measured through numbers, hence nothing exists without numbers.

 

 

Free Numerology School | A Brief History of Pythagorean Numerology

numerology-school.com/brief-history-of-numerology.html‎

The history of Numerology is closely related to the invention of alphabet. Since letters of alphabet were also used to record numbers, each and every word could ...

A Brief History of Pythagorean Numerology

There are as many different numerologies in the world as there are developed cultures, since wise people have grasped the connection between Creation, Numbers and the reality of our world a long time ago. In this section, we are going to focus on only one kind of numerology: the one associated with Pythagoras.

The Life of Pythagoras

It all began more than 2500 years ago on Samos, a small island in the Mediterranean. Born there was a person who can rightfully be called the very first philosopher of humanity. This is because it was Pythagoras who in fact coined the word philosophy.

In those times, the Mediterranean was a major center of world's civilization, and the young Pythagoras traveled around a great deal in order to find all the available sources of ancient wisdom. He spent 22 years in Egypt absorbing the knowledge of its ancient civilization, he studied with the wise people of Babylon, and journeyed to Persia in order to familiarize himself with the Zoroastrian tradition, and he even met the mysterious Hyperboreans. The sphere of his interests was not limited to the sciences (particularly those of of mathematical nature), but also included religious systems. As a result, Pythagoras was initiated into the mysteries of several cultures.

By the time he was 40, Pythagoras had settled in Southern Italy, established his school and presented his teachings to humanity. The scale of that teaching and its impact on human civilization were so great that even now, after several millennia, the name of Pythagoras is known to every shool kid.

Ironically, though, the proof of the theorem present in school books is probably one of his least achievements. After all, the fact that the sum of the squares of two legs gives the square of hypotenuse was already well known in Egypt and Babylon long before Pythagoras came along. Yet his philosophical system was so impressive that the ever-famous Plato could even be thought of as merely one of Pythagoras’s followers.

However, the interests of Pythagoras weren't exclusively abstract or theoretical. He spent plenty of time researching music (And, again, not simply as an intellectual pursuit — those familiar with the theory of music can confirm that it is quite close to mathematics.) and its application to healing, and as a means of restoring the vibrational structure of one's system. Pythagoras believed that music is an art in which Numbers reach directly to the heart, whereas in mathematics, they just occupy the brain.

It is clear that philosophy, as understood by Pythagoras, was very different from how it is understood now. It had more in common with the concepts in Indian yoga. Consider this: Pythagoras completely accepted the idea of a cycle of numerous incarnations of a human soul and believed that the exit from that circle was found not through religious rituals but through philosophy, i.e., contemplation and comprehension of the main principles of Creation. Philosophy, in his understanding, was a path to perfect the soul, a path towards immortality.

Numbers are at the very core of Pythagoras’s teachings, but as you can see, his understanding of numbers was very different from the contemporary one. Now we understand numbers in a concrete, utilitarian way (two apples, three dollars, etc.), or like a sort of exercise for one's brain (the dreaded math with which we were all fed up at school and believed we’d never use in real life).

For Pythagoras, numbers, especially the first ten, are the highest manifestations of the Creative Principle in the creation of our world. They can be called the different aspects of the Creator of the Universe. Interacting and gradually descending from the world of ideas into the world of matter, the numbers create, according to their rules, everyone and everything.

And to show that this idea might not be not just wild speculation, consider that according to contemporary physics, at some deep level, microparticles and the quanta of energy are indistinguishable. In other words, material particles are in fact bundles of energy, or electromagnetic waves. And waves—or vibrations—are directly related to the numbers that define their frequency.

From Theory to Practice

Enough theoretical speculations for now. Let's concentrate on life’s utilitarian, practical application of numbers. We are all used to counting things, using money, applying numbers to our cars, telephones, addresses, and so on. The day, month and year of a person's birth also contains their numbers. Numbers surround us everywhere. And even though this is true, we do not think about them in terms of bearing some special mystical properties, but rather we are simply using them for convenience, taking one or another sequence of numbers as yet another random thing in our chaotic and senseless world.

Still, sooner or later many of us start asking questions the answers to which cannot be found in either schoolbooks or academic treatises. What are we doing in this world? Is there any reason for our existence here? Is the world really as chaotic and void of any sense as it seems to be? Are we really here simply to hang around in this chaos and somehow come to our natural end? Or does our existence have some purpose? Is there perhaps something that we are supposed to learn in our lives? Is there someone or something that can help us to understand what's going on, which path to take so that we can eventually reach our true destination?

Questions like these have been asked since man’s beginning on this Earth. To some people, these kinds of questions come early in youth, while others need to gain some life experience before they start asking these things, and others still who simply can't be bothered with them.

Understanding the connection between the everyday numbers that surround us and the Numbers (with a capital N), which are the acting principles of the universe, is important in our search for the answers to the questions above. This is where numerology comes in.

In the lessons that follow, I will share with you my fascination with the wonders of the universe, as seen with the help of the tools of practical numerology. I don't promise that you will understand everything about your life and the surrounding world, but if you were to get even the smallest glimpse of understanding, this could prove to be very important. After all, even a tiny lantern is much better than complete darkness.

More History

Below you'll find a collection of bits and pieces of information that will help you to better understand the history of Numerology. I plan to add more to this collection from time to time.

isopsephy and Gematria

The history of Numerology is closely related to the invention of alphabet. Since letters of alphabet were also used to record numbers, each and every word could be given a numeric value. The process of adding together the numeric values of separate letters to obtain a value for the whole word was called by the Greeks isopsephy. Later, when this method was used to interpret the Torah, it was called Gematria.

isopsephy was widely used by the Greeks in magic and interpretation of dreams. According to tradition, Pythagoras used isopsephy for divination. The idea is that if two words or two phrases have the same numeric value, then there is some kind of an invisible link between them. For example, Jesus in Greek (Ιησούς) adds up to 888, as well as the phrase "I am life" (η ζωη ειμι). Clearly, Christians felt this made a lot of sense.

As you will see, the approach that is used today to obtain the numeric value of a name or a word is substantially different from the method used in isopsephy.

 

 

Free Numerology School | A Brief History of Pythagorean Numerology

numerology-school.com/brief-history-of-numerology.html‎

The history of Numerology is closely related to the invention of alphabet. Since letters of alphabet were also used to record numbers, each and every word could be given a numeric value. The process of adding together the numeric values of separate letters to obtain a value for the whole word was called by the Greeks isopsephy. Later, when this method was used to interpret the Torah, it was called Gematria.

isopsephy was widely used by the Greeks in magic and interpretation of dreams. According to tradition, Pythagoras used isopsephy for divination. The idea is that if two words or two phrases have the same numeric value, then there is some kind of an invisible link between them. For example, Jesus in Greek (Ιησούς) adds up to 888, as well as the phrase "I am life" (η ζωη ειμι). Clearly, Christians felt this made a lot of sense.

As you will see, the approach that is used today to obtain the numeric value of a name or a word is substantially different from the method used in isopsephy.

 

 

-
-
-
-
-
ISOPSEPHY
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
1
1
I
9
9
9
-
-
2
3
4
-
-
-
-
9
S
=
1
2
1
S
19
10
1
-
1
2
3
4
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
2
3
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
S
=
1
5
1
S
19
10
1
-
1
2
3
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
2
3
4
5
-
-
-
-
P
=
7
7
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
2
3
4
-
-
-
8
-
Y
=
7
9
1
Y
25
7
7
-
-
2
3
4
-
-
7
-
-
-
-
51
-
9
ISOPSEPHY
132
69
51
-
2
2
3
4
5
6
21
8
9
-
-
5+1
-
-
-
1+3+2
6+9
5+1
-
-
-
-
-
-
-
2+1
-
-
-
-
6
-
9
ISOPSEPHY
6
15
6
-
2
2
3
4
5
6
3
8
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
ISOPSEPHY
6
6
6
-
2
2
3
4
5
6
3
8
9

 

 

-
-
-
-
-
ISOPSEPHY
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
2
1
S
19
10
1
-
1
2
3
4
-
-
-
-
-
S
=
1
5
1
S
19
10
1
-
1
2
3
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
2
3
4
5
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
2
3
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
P
=
7
7
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
Y
=
7
9
1
Y
25
7
7
-
-
2
3
4
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
2
3
4
-
-
-
8
-
I
=
9
1
1
I
9
9
9
-
-
2
3
4
-
-
-
-
9
-
-
51
-
9
ISOPSEPHY
132
69
51
-
2
2
3
4
5
6
21
8
9
-
-
5+1
-
-
-
1+3+2
6+9
5+1
-
-
-
-
-
-
-
2+1
-
-
-
-
6
-
9
ISOPSEPHY
6
15
6
-
2
2
3
4
5
6
3
8
9
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
ISOPSEPHY
6
6
6
-
2
2
3
4
5
6
3
8
9

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

THE GROWTH OF SCIENCE

A.P.Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

-
-
-
-
SESHAT
-
-
-
S
=
1
1
S
19
10
1
E
=
5
1
E
5
5
5
S
=
1
1
S
19
10
1
H
=
8
1
H
8
8
8
A
=
1
1
A
1
1
1
T
=
2
1
T
20
2
2
-
-
18
6
SESHAT
72
36
18
-
-
1+8
-
-
7+2
3+6
1+8
Q
-
9
6
SESHAT
10
9
9

 

 

5
THOTH
-
-
-
-
T+H
28
10
1
1
O
15
6
6
1
T+H
28
10
1
5
THOTH
-
-
-

 

 

-
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
8
6
-
8
-
-
5
-
-
1
-
1
8
-
-
+
=
37
3+7
=
10
1+0
1
-
1
-
-
-
8
15
-
8
-
-
14
-
-
19
-
19
8
-
-
+
=
91
9+1
=
10
1+0
1
-
1
-
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
1
-
4
-
-
5
-
-
1
2
+
=
21
2+1
=
3
=
3
-
3
-
-
20
-
-
20
-
-
1
-
4
-
-
5
-
-
1
20
+
=
75
7+5
=
12
1+2
3
-
3
-
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
20
8
15
20
8
-
1
14
4
-
19
5
19
8
1
20
+
=
162
1+6+2
=
9
=
9
-
9
-
-
2
8
6
2
8
-
1
5
3
-
1
5
1
8
1
2
+
=
54
5+4
=
9
-
9
-
9
-
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
1
-
-
-
1
occurs
x
4
=
4
-
4
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
-
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
3
=
24
2+4
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
19
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
26
-
-
14
-
54
-
27
1+9
1+4
-
-
-
-
-
-
--
-
-
-
--
-
--
-
--
-
-
-
2+6
-
-
1+4
-
5+4
-
2+7
10
5
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
8
-
-
5
-
9
-
9
1+0
-
2
8
6
2
8
-
1
5
3
-
1
5
1
8
1
2
-
-
-
-
-
-
-
-
-
-
1
5
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
8
-
-
5
-
9
-
9

 

 

14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
8
6
-
8
-
-
5
-
-
1
-
1
8
-
-
+
=
37
3+7
=
10
1+0
1
-
1
-
-
8
15
-
8
-
-
14
-
-
19
-
19
8
-
-
+
=
91
9+1
=
10
1+0
1
-
1
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
1
-
4
-
-
5
-
-
1
2
+
=
21
2+1
=
3
=
3
-
3
-
20
-
-
20
-
-
1
-
4
-
-
5
-
-
1
20
+
=
75
7+5
=
12
1+2
3
-
3
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
20
8
15
20
8
-
1
14
4
-
19
5
19
8
1
20
+
=
162
1+6+2
=
9
=
9
-
9
-
2
8
6
2
8
-
1
5
3
-
1
5
1
8
1
2
+
=
54
5+4
=
9
-
9
-
9
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
1
-
-
-
1
occurs
x
4
=
4
-
4
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
8
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
14
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
26
-
-
14
-
54
-
27
1+4
-
-
-
-
-
-
--
-
-
-
--
-
--
-
--
-
-
-
2+6
-
-
1+4
-
5+4
-
2+7
5
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
8
-
-
5
-
9
-
9
-
2
8
6
2
8
-
1
5
3
-
1
5
1
8
1
2
-
-
-
-
-
-
-
-
-
-
5
T
H
O
T
H
-
A
N
D
-
S
E
S
H
A
T
-
-
8
-
-
5
-
9
-
9

 

 

5
THOTH
-
-
-
-
T+H
28
10
1
1
O
15
6
6
1
T+H
28
10
1
5
THOTH
-
-
-

 

 

-
-
-
-
SESHAT
-
-
-
S
=
1
1
S
19
10
1
E
=
5
1
E
5
5
5
S
=
1
1
S
19
10
1
H
=
8
1
H
8
8
8
A
=
1
1
A
1
1
1
T
=
2
1
T
20
2
2
-
-
18
6
SESHAT
72
36
18
-
-
1+8
-
-
7+2
3+6
1+8
Q
-
9
6
SESHAT
10
9
9

 

 

13
PROMISE THEE US
-
-
-
-
P+R+O+M
62
26
8
1
I+S
28
19
1
1
E
5
5
5
-
T+H+E
33
15
6
1
E
5
5
5
1
U+S
40
4
4
13
PROMISE THEE US
-
-
-

 

PROMETHEUS

 

8
CEREMONY
98
44
8

 

 

S
=
1
10
STRETCHING
123
51
6
O
=
6
2
OF
21
12
3
T
=
2
3
THE
33
15
6
C
=
3
4
CORD
40
22
4
-
-
12
19
First Total
217
100
19
-
-
1+2
1+9
Add to Reduce
2+1+7
1+0+0
1+9
Q
-
3
10
Second Total
10
1
10
-
-
-
1+0
Reduce to Deduce
1+0
-
1+0
-
-
3
1
Essence of Number
1
1
1

 

 

-
19
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
8
9
5
-
-
6
-
-
-
8
-
-
-
6
-
-
+
=
43
4+3
=
7
-
7
-
7
-
-
19
-
-
-
-
-
8
9
14
-
-
15
-
-
-
8
-
-
-
15
-
-
+
=
88
8+8
=
16
1+6
7
-
7
-
19
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
-
-
-
-
-
-
-
-
-
-
-
2
18
5
2
3
-
-
-
7
-
-
6
-
2
-
5
-
3
-
18
4
+
=
75
7+5
=
12
1+2
3
-
3
-
-
-
20
9
5
20
3
-
-
-
7
-
-
6
-
20
-
5
-
3
-
9
4
+
=
111
1+1+1
=
3
-
3
-
3
-
19
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
-
-
-
-
-
-
-
-
-
-
19
20
18
5
20
3
8
9
14
7
-
15
6
-
20
8
5
-
3
15
18
4
+
=
217
2+1+7
=
10
1+0
1
-
1
-
-
1
2
9
5
2
3
8
9
5
7
-
6
6
-
2
8
5
-
3
6
9
4
+
=
100
1+0+0
=
1
-
1
-
1
-
19
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
``-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
``-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
45
19
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
45
-
-
10
-
100
-
55
4+5
1+9
-
-
9
-
-
-
-
9
-
-
-
-``
-
-
-
-
-
-
-
-``
9
-
-
-
4+5
-
-
1+0
-
1+0+0
-
5+5
9
10
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
9
-
-
1
-
1
-
10
-
1+0
1
2
9
5
2
3
8
9
5
7
-
6
6
-
2
8
5
-
3
6
9
4
-
-
-
-
-
-
-
-
-
1+0
9
1
S
T
R
E
T
C
H
I
N
G
-
O
F
-
T
H
E
-
C
O
R
D
-
-
9
-
-
1
-
1
-
1

 

 

3
ALL
25
7
7
3
ARE
24
15
6
5
EQUAL
56
20
2
4
UNTO
70
16
7
3
GOD
26
17
8
18
First Total
201
75
30
1+8
Add to Reduce
2+0+1
7+5
3+0
9
Second Total
3
12
3
-
Reduce to Deduce
-
1+2
-
9
Essence of Number
3
3
3

 

 

2
IS
28
10
1
5
EQUAL
56
20
2
4
UNTO
70
16
7
3
GOD
26
17
8
14
Add to Reduce
180
63
18
1+4
Reduce to Deduce
1+8+0
6+3
1+8
5
Essence of Number
9
9
9

 

 

3
GOD
26
17
8
2
IS
28
10
1
6
ALWAYS
81
18
9
11
Add to Reduce
135
45
18
1+1
Reduce to Deduce
1+3+5
4+5
1+8
2
Essence of Number
9
9
9

 

 

-
20
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
1
-
-
-
-
-
6
-
-
-
-
-
5
9
5
-
+
=
34
3+4
=
7
-
7
-
7
-
-
-
8
-
-
-
-
-
19
-
-
-
-
-
15
-
-
-
-
-
14
9
14
-
+
=
79
7+9
=
16
1+6
7
-
7
-
20
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
4
5
1
-
3
18
5
18
-
-
6
-
4
5
1
-
-
-
7
+
=
66
6+6
=
12
1+2
3
-
3
-
-
20
-
5
-
13
5
1
-
21
9
5
9
-
-
6
-
13
5
1
-
-
-
7
+
=
138
1+3+8
=
12
1+2
3
-
3
-
20
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
13
5
1
19
21
18
5
18
-
15
6
-
13
5
1
14
9
14
7
+
=
217
2+1+7
=
10
1+0
1
-
1
-
-
2
8
5
-
4
5
1
1
3
9
5
9
-
6
6
-
4
5
1
5
9
5
7
+
=
100
1+0+0
=
1
  
1
-
1
-
20
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
2
``-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
``-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
5
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
5
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
8
-
8
9
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
9
-
-
9
occurs
x
3
=
27
2+7
9
45
20
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
45
-
-
20
-
100
-
46
4+5
2+0
-
-
-
--
-
-
-
-
-
9
-
9
--
-``
-
--
-
-
-
-
9
-
-
-
-
4+5
-
-
2+0
-
1+0+0
-
4+6
9
2
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
9
-
-
2
-
1
-
10
-
-
2
8
5
-
4
5
1
1
3
9
5
9
-
6
6
-
4
5
1
5
9
5
7
-
-
-
-
-
-
-
-
-
1+0
9
2
T
H
E
-
M
E
A
S
U
R
E
R
-
O
F
-
M
E
A
N
I
N
G
-
-
9
-
-
2
-
1
-
1

 

 

3
THE
33
15
6
5
HOUSE
68
23
5
2
OF
21
12
3
4
LIFE
32
23
5
14
First Total
154
73
19
1+4
Add to Reduce
1+5+4
7+3
1+9
5
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
1
Essence of Number
1
1
1

 

 

11
HOUSE OF LIFE
121
58
4

 

 

-
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
1
-
1
8
-
-
+
=
10
1+0
=
10
1+0
1
-
-
19
-
19
8
-
-
+
=
46
4+6
=
10
1+0
1
-
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
-
5
-
-
1
2
+
=
8
-
=
8
=
8
-
-
-
5
-
-
1
20
+
=
26
2+6
=
8
-
8
-
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
19
5
19
8
1
20
+
=
72
7+2
=
9
=
9
-
-
1
5
1
8
1
2
+
=
18
1+8
=
9
-
9
-
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
1
occurs
x
3
=
3
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
29
6
S
E
S
H
A
T
-
-
16
-
-
6
-
18
2+9
-
-
-
-
-
-
-
-
-
1+6
-
-
-
-
1+8
11
6
S
E
S
H
A
T
-
-
7
-
-
6
-
9
1+1
-
1
5
1
8
1
2
-
-
-
-
-
-
-
-
2
6
S
E
S
H
A
T
-
-
7
-
-
6
-
9

 

 

6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
1
-
1
8
-
-
+
=
10
1+0
=
10
1+0
1
-
19
-
19
8
-
-
+
=
46
4+6
=
10
1+0
1
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
-
5
-
-
1
2
+
=
8
-
=
8
=
8
-
-
5
-
-
1
20
+
=
26
2+6
=
8
-
8
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
19
5
19
8
1
20
+
=
72
7+2
=
9
=
9
-
1
5
1
8
1
2
+
=
18
1+8
=
9
-
9
6
S
E
S
H
A
T
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
1
occurs
x
3
=
3
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
6
S
E
S
H
A
T
-
-
16
-
-
6
-
18
-
-
-
-
-
-
-
-
-
1+6
-
-
-
-
1+8
6
S
E
S
H
A
T
-
-
7
-
-
6
-
9
-
1
5
1
8
1
2
-
-
-
-
-
-
-
-
6
S
E
S
H
A
T
-
-
7
-
-
6
-
9

 

 

THE EGYPT CODE

Robert Bauval 1988

Page 30

"It is quite natural, therefore, that the divine tutors of Time and and Calendar should be Thoth, God of Science, and Seshat, Goddess of Writings and Annals.47

Page 31

"It is generally agreed by Egyptologists that the king's first jubilee (or heb-sed festival, as it called by the ancients) was celebrated in the thirtieth year of his reign. But some others are of the opinion that the 30- year period was calendrical, i.e. that it fell in cycles of 30 years irrespective of the number of years the king had reigned. At any rate, it is evident from the text quoted by Budge that the term 'thirty-year festivals' is a euphemism for royal jubilees. Also the mention of the 'Thirty-Years periods' alongside the term 'years of Ra' should affirm to us that the computations of this period had something to do with the sun or rather its yearly cycle, and thus, by extension, the solar calendar. Such an association with the sky and Seshat's royal duties is also evident in the 'stretching of the cord' ceremony, since, as we shall see, this entailed observing the motion and position of the circumpolar stars. Indeed, because of this last role / Page 32 / Seshat was also called 'Lady of Builders', 'Goddess of Construction', 'Founder of Architecture' and perhaps more aptly, 'Lady of the Stars'. To be concise, we can think of Seshat as the royal librarian, the royal scribe, the royal astronomer, the royal architect, the royal engineer, the royal herald and perhaps even the royal adviser all rolled into one" — a sort of Condoleeza Rice to the pharaohs.


It is well established that the 'stretching of the cord' ceremony was practised from at least the Second Dynasty (e. 2900 Bc). As Egyptologist George Hart further explains: 'As early as Dynasty II she (Seshat) assisted the monarch . . . in hammering boundary poles into the ground for the ceremony of "stretching the cord". This is a crucial part of a temple foundation ritual.'50
To be precise, it is fair to say that much of the knowledge we have about the'stretching of the cord' ceremony comes from very late inscriptions, mostly trom the temples at -Edfu and Dendera. Earlier evidence of the ceremony is found only in drawing form, without any explanatory captions. Nonetheless, as I.E.S. Edwards correctly argued:

In spite of the relative late date of the inscriptions referring to the episodes of the foundation ceremonies, there is no reason to doubt that they preserved an ancient tradition. Some indication that similar ceremonies were already current in the pyramid Age is provided by a fragmentary relief found in the Vth Dynasty sun-temple of Niuserre, which shows the king and a priestess impersonating Seshat, each holding a mallet and a stake to which a measuring cord is attached. The scene is in complete agreement with the text in the temple at Edfu which represents the king saying: take the stake and I hold the handle of the mallet. I hold the cord with Seshat' .51
In the many depictions of the ceremony found all over Egypt, Seshat always faces the king and each is seen carrying a peg in one hand and a mallet in the other. A short cord is looped between the two pegs, and it is evident from this scene that the protagonists are aligning the axis of a temple or pyramid by stretching cord and aiming it at a distant object, and then fixing the alignment by hammering the two pegs into the ground. Here are some of the inscriptions from the temples at Edfu and Dendera which describe the scene:

[The king says:] I hold the peg. I grasp the handle of the mallet and grip the measuring-cord with Seshat. I turn my eyes to the movements of the stars. I direct my gaze towards the bull's thigh [meskhetiu; Plough]. . . I make - firm the corners of the temple . .52

[A priest says:] The king stretches joyously the cord, having turned his head towards thebull's thigh and establishes the temple in the manner of ancient times.53

[The king says] I grasp the peg and the mallet; I stretch the cord with Seshat; I observed the trajectory of the stars with my eye which is fixed on the bull's thigh; I have been the god who indicates Time with the Merkhet instrument. I have established the- four corners of the temple.54 / Page 33 / [A priest says:] The king . . . while observing the sky and the stars, turns his sight towards the bull's thigh . . .55

 

 

7
READEST
72
27
9
2
ME
18
9
9
7
DEAREST
72
27
9
16
Add to Reduce
162
63
27
1+6
Reduce to Deduce
1+6+2
6+3
2+7
7
Essence of Number
9
9
9

 

 

5
DREAM
-
-
-
-
ME
18
9
9
1
READ
28
19
1
1
ME
18
9
9
7
DREAMER
-
-
-

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

Babylonia - Wikipedia
https://en.wikipedia.org/wiki/Babylonia

Babylonia was an ancient Akkadian-speaking state and cultural area based in central-southern .... Sumer rose up again with the Third Dynasty of Ur in the late 22nd century BC, and ejected the Gutians from southern Mesopotamia. They also ...
?Babylonian religion · ?Amorites · ?Neo-Babylonian Empire · ?First Babylonian dynasty

Babylonia (/?bæb?'lo?ni?/) was an ancient Akkadian-speaking state and cultural area based in central-southern Mesopotamia (present-day Iraq). A small Amorite-ruled state emerged in 1894 BC, which contained the minor administrative town of Babylon.[1] It was merely a small provincial town during the Akkadian Empire (2335–2154 BC) but greatly expanded during the reign of Hammurabi in the first half of the 18th century BC and became a major capital city. During the reign of Hammurabi and afterwards, Babylonia was called "the country of Akkad" (Mat Akkadi in Akkadian), a deliberate archaism in reference to the previous glory of the Akkadian Empire.[2][3]

It was often involved in rivalry with the older state of Assyria to the north and Elam to the east in Ancient Iran. Babylonia briefly became the major power in the region after Hammurabi (fl. c. 1792–1752 BC middle chronology, or c. 1696–1654 BC, short chronology) created a short-lived empire, succeeding the earlier Akkadian Empire, Third Dynasty of Ur, and Old Assyrian Empire. The Babylonian empire, however, rapidly fell apart after the death of Hammurabi and reverted to a small kingdom.

Like Assyria, the Babylonian state retained the written Akkadian language (the language of its native populace) for official use, despite its Northwest Semitic-speaking Amorite founders and Kassite successors, who spoke a language isolate, not being native Mesopotamians. It retained the Sumerian language for religious use (as did Assyria), but already by the time Babylon was founded, this was no longer a spoken language, having been wholly subsumed by Akkadian. The earlier Akkadian and Sumerian traditions played a major role in Babylonian and Assyrian culture, and the region would remain an important cultural center, even under its protracted periods of outside rule.

The earliest mention of the city of Babylon can be found in a clay tablet from the reign of Sargon of Akkad (2334–2279 BC), dating back to the 23rd century BC. Babylon was merely a religious and cultural centre at this point and neither an independent state nor a large city; like the rest of Mesopotamia, it was subject to the Akkadian Empire which united all the Akkadian and Sumerian speakers under one rule. After the collapse of the Akkadian empire, the south Mesopotamian region was dominated by the Gutian people for a few decades before the rise of the Third Dynasty of Ur, which restored order to the region and which, apart from northern Assyria, encompassed the whole of Mesopotamia, including the town of Babylon.

Pre-Babylonian Sumero-Akkadian period[edit]

Mesopotamia had already enjoyed a long history prior to the emergence of Babylon, with Sumerian civilisation emerging in the region c. 3500 BC, and the Akkadian-speaking people appearing by the 30th century BC.[citation needed]

During the 3rd millennium BC, an intimate cultural symbiosis occurred between Sumerian and Akkadian-speakers, which included widespread bilingualism.[4] The influence of Sumerian on Akkadian and vice versa is evident in all areas, from lexical borrowing on a massive scale, to syntactic, morphological, and phonological convergence.[4] This has prompted scholars to refer to Sumerian and Akkadian in the third millennium as a sprachbund.[4]

Akkadian gradually replaced Sumerian as the spoken language of Mesopotamia somewhere around the turn of the third and the second millennium BC (the precise timeframe being a matter of debate).[5]

From c. 3500 BC until the rise of the Akkadian Empire in the 24th century BC, Mesopotamia had been dominated by largely Sumerian cities and city states, such as Ur, Lagash, Uruk, Kish, Isin, Larsa, Adab, Eridu, Gasur, Assur, Hamazi, Akshak, Arbela and Umma, although Semitic Akkadian names began to appear on the king lists of some of these states (such as Eshnunna and Assyria) between the 29th and 25th centuries BC. Traditionally, the major religious center of all Mesopotamia was the city of Nippur where the god Enlil was supreme, and it would remain so until replaced by Babylon during the reign of Hammurabi in the mid-18th century BC.[citation needed]

The Akkadian Empire (2334–2154 BC) saw the Akkadian Semites and Sumerians of Mesopotamia unite under one rule, and the Akkadians fully attain ascendancy over the Sumerians and indeed come to dominate much of the ancient Near East.

The empire eventually disintegrated due to economic decline, climate change and civil war, followed by attacks by the Gutians from the Zagros Mountains. Sumer rose up again with the Third Dynasty of Ur in the late 22nd century BC, and ejected the Gutians from southern Mesopotamia. They also seem to have gained ascendancy over much of the territory of the Akkadian kings of Assyria in northern Mesopotamia for a time.[citation needed]

Followed by the collapse of the Sumerian "Ur-III" dynasty at the hands of the Elamites in 2002 BC, the Amorites ("Westerners"), a foreign Northwest Semitic-speaking people, began to migrate into southern Mesopotamia from the northern Levant, gradually gaining control over most of southern Mesopotamia, where they formed a series of small kingdoms, while the Assyrians reasserted their independence in the north. The states of the south were unable to stem the Amorite advance, and for a time may have relied on their fellow Akkadians in Assyria for protection.[citation needed]

King Ilu-shuma (c. 2008–1975 BC) of the Old Assyrian Empire (2025–1750 BC) in a known inscription describes his exploits to the south as follows:

The freedom[n 1] of the Akkadians and their children I established. I purified their copper. I established their freedom from the border of the marshes and Ur and Nippur, Awal, and Kish, Der of the goddess Ishtar, as far as the City of (Ashur).[6]

Past scholars originally extrapolated from this text that it means he defeated the invading Amorites to the south and Elamites to the east, but there is no explicit record of that, and some scholars believe the Assyrian kings were merely giving preferential trade agreements to the south.

These policies were continued by his successors Erishum I and Ikunum.

However, when Sargon I (1920–1881 BC) succeeded as king in Assyria in 1920 BC, he eventually withdrew Assyria from the region, preferring to concentrate on continuing the vigorous expansion of Assyrian colonies in Anatolia and the Levant, and eventually southern Mesopotamia fell to the Amorites, a Northwest Semitic-speaking people from the northern Levant. During the first centuries of what is called the "Amorite period", the most powerful city states in the south were Isin, Eshnunna and Larsa, together with Assyria in the north.

First Babylonian dynasty – Amorite Dynasty, 1894–1595 BC[edit]

Main article: First Babylonian dynasty

Hammurabi (standing), depicted as receiving his royal insignia from Shamash (or possibly Marduk). Hammurabi holds his hands over his mouth as a sign of prayer[7] (relief on the upper part of the stele of Hammurabi's code of laws).
One of these Amorite dynasties founded a small kingdom of Kazallu which included the then still minor town of Babylon circa 1894 BC, which would ultimately take over the others and form the short-lived first Babylonian empire, also called the First Babylonian dynasty.

An Amorite chieftain named Sumu-abum appropriated a tract of land which included the then relatively small city of Babylon from the neighbouring Amorite ruled Mesopotamian city state of Kazallu, of which it had initially been a territory, turning his newly acquired lands into a state in its own right. His reign was concerned with establishing statehood amongst a sea of other minor city states and kingdoms in the region. However Sumuabum appears never to have bothered to give himself the title of King of Babylon, suggesting that Babylon itself was still only a minor town or city, and not worthy of kingship.[8]

He was followed by Sumu-la-El, Sabium, Apil-Sin, each of whom ruled in the same vague manner as Sumuabum, with no reference to kingship of Babylon itself being made in any written records of the time. Sin-Muballit was the first of these Amorite rulers to be regarded officially as a king of Babylon, and then on only one single clay tablet. Under these kings, the nation in which Babylon lay remained a small nation which controlled very little territory, and was overshadowed by neighbouring kingdoms that were both older, larger, and more powerful, such as; Isin, Larsa, Assyria to the north and Elam to the east in ancient Iran. The Elamites occupied huge swathes of southern Mesopotamia, and the early Amorite rulers were largely held in vassalage to Elam.

Empire of Hammurabi[edit]

Babylon remained a minor town in a small state until the reign of its sixth Amorite ruler, Hammurabi, during 1792–1750 BC (or c. 1728 – 1686 BC in the short chronology). He conducted major building work in Babylon, expanding it from a small town into a great city worthy of kingship. A very efficient ruler, he established a bureaucracy, with taxation and centralized government. Hammurabi freed Babylon from Elamite dominance, and indeed drove the Elamites from southern Mesopotamia entirely. He then systematically conquered southern Mesopotamia, including the cities of Isin, Larsa, Eshnunna, Kish, Lagash, Nippur, Borsippa, Ur, Uruk, Umma, Adab, Sippar, Rapiqum, and Eridu. His conquests gave the region stability after turbulent times, and coalesced the patchwork of small states into a single nation; it is only from the time of Hammurabi that southern Mesopotamia acquired the name Babylonia.

Hammurabi turned his disciplined armies eastwards and invaded the region which a thousand years later became Iran, conquering Elam, Gutians, Lullubi and Kassites. To the west, he conqured the Amorite states of the Levant (modern Syria and Jordan) including the powerful kingdoms of Mari and Yamhad.

Hammurabi then entered into a protracted war with the Old Assyrian Empire for control of Mesopotamia and dominance of the Near East. Assyria had extended control over much of the Hurrian and Hattian parts of southeast Anatolia from the 21st century BC, and from the latter part of the 20th century BC had asserted itself over the north east Levant and central Mesopotamia. After a protracted struggle over decades with the powerful Assyrian kings Shamshi-Adad I and Ishme-Dagan I, Hammurabi forced their successor Mut-Ashkur to pay tribute to Babylon c. 1751 BC, giving Babylonia control over Assyria's centuries-old Hattian and Hurrian colonies in Anatolia.[9]

One of Hammurabi's most important and lasting works was the compilation of the Babylonian law code, which improved the much earlier codes of Sumer, Akkad and Assyria. This was made by order of Hammurabi after the expulsion of the Elamites and the settlement of his kingdom. In 1901, a copy of the Code of Hammurabi was discovered on a stele by Jacques de Morgan and Jean-Vincent Scheil at Susa in Elam, where it had later been taken as plunder. That copy is now in the Louvre.

From before 3000 BC until the reign of Hammurabi, the major cultural and religious center of southern Mesopotamia had been the ancient city of Nippur, where the god Enlil was supreme. Hammurabi transferred this dominance to Babylon, making Marduk supreme in the pantheon of southern Mesopotamia (with the god Ashur, and to some degree Ishtar, remaining the long-dominant deity in northern Mesopotamian Assyria). The city of Babylon became known as a "holy city" where any legitimate ruler of southern Mesopotamia had to be crowned. Hammurabi turned what had previously been a minor administrative town into a large, powerful and influential city, extended its rule over the entirety of southern Mesopotamia, and erected a number of impressive buildings.

The Amorite-ruled Babylonians, like their predecessor states, engaged in regular trade with the Amorite and Canaanite city-states to the west, with Babylonian officials or troops sometimes passing to the Levant and Canaan, and Amorite merchants operating freely throughout Mesopotamia. The Babylonian monarchy's western connections remained strong for quite some time. Ammi-Ditana, great-grandson of Hammurabi, still titled himself "king of the land of the Amorites". Ammi-Ditana's father and son also bore Amorite names: Abi-Eshuh and Ammi-Saduqa.

Decline[edit]

Southern Mesopotamia had no natural, defensible boundaries, making it vulnerable to attack. After the death of Hammurabi, his empire began to disintegrate rapidly. Under his successor Samsu-iluna (1749–1712 BC) the far south of Mesopotamia was lost to a native Akkadian-speaking king Ilum-ma-ili who ejected the Amorite-ruled Babylonians. The south became the native Sealand Dynasty, remaining free of Babylon for the next 272 years.[10]

Both the Babylonians and their Amorite rulers were driven from Assyria to the north by an Assyrian-Akkadian governor named Puzur-Sin c. 1740 BC, who regarded king Mut-Ashkur as both a foreign Amorite and a former lackey of Babylon. After six years of civil war in Assyria, a native king named Adasi seized power c. 1735 BC, and went on to appropriate former Babylonian and Amorite territory in central Mesopotamia, as did his successor Bel-bani.

Amorite rule survived in a much reduced Babylon, Samshu-iluna's successor Abi-Eshuh made a vain attempt to recapture the Sealand Dynasty for Babylon, but met defeat at the hands of king Damqi-ilishu II. By the end of his reign Babylonia had shrunk to the small and relatively weak nation it had been upon its foundation, although the city itself was far larger than the small town it had been prior to the rise of Hammurabi.

He was followed by Ammi-Ditana and then Ammi-Saduqa, both of whom were in too weak a position to make any attempt to regain the many territories lost after the death of Hammurabi, contenting themselves with peaceful building projects in Babylon itself.

Samsu-Ditana was to be the last Amorite ruler of Babylon. Early in his reign he came under pressure from the Kassites, a people speaking an apparent language isolate originating in the mountains of what is today northwest Iran. Babylon was then attacked by the Indo-European-speaking, Anatolia-based Hittites in 1595 BC. Shamshu-Ditana was overthrown following the "sack of Babylon" by the Hittite king Mursili I. The Hittites did not remain for long, but the destruction wrought by them finally enabled their Kassite allies to gain control.

 

 

Tower of Babel - Wikipedia
https://en.wikipedia.org/wiki/Tower_of_Babel

The Tower of Babel (Hebrew: Migdal Bavel) as told in Genesis 11:1–9 is an origin myth meant to explain why the world's peoples speak different languages. ... God, observing their city and tower, confounds their speech so that they can no longer understand each other, and scatters them around the world.
The Tower of Babel (Bruegel) · Tower of Babel (disambiguation) · Etemenanki

The Tower of Babel (Hebrew:, Migdal Bavel) as told in Genesis 11:1–9 is an origin myth meant to explain why the world's peoples speak different languages.[1][2][3][4]
According to the story, a united humanity in the generations following the Great Flood, speaking a single language and migrating eastward, comes to the land of Shinar (????????). There they agree to build a city and a tower tall enough to reach heaven. God, observing their city and tower, confounds their speech so that they can no longer understand each other, and scatters them around the world.
Some modern scholars have associated the Tower of Babel with known structures, notably the Etemenanki, a ziggurat dedicated to the Mesopotamian god Marduk by Nabopolassar, the king of Babylonia circa 610 BCE.[5][6] The Etemenanki was nearly 91 metres (300 ft) in height. Alexander the Great ordered it to be demolished circa 331 BCE in preparation for a reconstruction that his death forestalled.[7][8] A Sumerian story with some similar elements is told in Enmerkar and the Lord of Aratta.[9]

1 And the whole earth was of one language, and of one speech.
2 And it came to pass, as they journeyed from the east, that they found a plain in the land of Shinar; and they dwelt there.
3 And they said one to another, Go to, let us make brick, and burn them throughly. And they had brick for stone, and slime had they for morter.
4 And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth.
5 And the LORD came down to see the city and the tower, which the children of men builded.
6 And the LORD said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.
7 Go to, let us go down, and there confound their language, that they may not understand one another's speech.
8 So the LORD scattered them abroad from thence upon the face of all the earth: and they left off to build the city.
9 Therefore is the name of it called Babel; because the LORD did there confound the language of all the earth: and from thence did the LORD scatter them abroad upon the face of all the earth.

Etymology[edit]

The phrase "Tower of Babel" does not appear in the Bible; it is always "the city and the tower" or just "the city". The original derivation of the name Babel (also the Hebrew name for Babylon) is uncertain. The native, Akkadian name of the city was Bab-ilim, meaning "gate of God". However, that form and interpretation itself are now usually thought to be the result of an Akkadian folk etymology applied to an earlier form of the name, Babilla, of unknown meaning and probably non-Semitic origin.[11][12] According to the Bible, the city received the name "Babel" from the Hebrew verb ??????? (balal), meaning to jumble or to confuse.[13][14]

Composition[edit]

Genre[edit]

The narrative of the tower of Babel (Genesis 11.1–9) is an etiology or explanation of a phenomenon. Etiologies are narratives that explain the origin of a custom, ritual, geographical feature, name, or other phenomenon.[15]:426 The story of the Tower of Babel explains the origins of the multiplicity of languages. God was concerned that humans had blasphemed by building the tower to avoid a second flood so God brought into existence multiple languages.[15]:51 Thus, humans were divided into linguistic groups, unable to understand one another.

Themes[edit]

The story's theme of competition between God and humans appears elsewhere in Genesis, in the story of Adam and Eve in the Garden of Eden.[16] The 1st-century Jewish interpretation found in Flavius Josephus explains the construction of the tower as a hubristic act of defiance against God ordered by the arrogant tyrant Nimrod. There have, however, been some contemporary challenges to this classical interpretation, with emphasis placed on the explicit motive of cultural and linguistic homogeneity mentioned in the narrative (v. 1, 4, 6).[17] This reading of the text sees God's actions not as a punishment for pride, but as an etiology of cultural differences, presenting Babel as the cradle of civilization.

Authorship and source criticism[edit]

Tradition attributes the whole of the Pentateuch to Moses; however, in the late 19th century, the documentary hypothesis was proposed by Julius Wellhausen.[18] This hypothesis proposes four sources: J, E, P and D. Of these hypothetical sources, proponents suggest that this narrative comes from the J or Yahwist source. The etiological nature of the narrative is considered typical of J. In addition, the intentional word play regarding the city of Babel, and the noise of the people's "babbling" is found in the Hebrew words as easily as in English, and is considered typical of the Yahwist source.[15]:51

Comparable myths[edit]

See also: Comparative mythology and Mythical origins of language

Sumerian and Assyrian parallel[edit]

There is a Sumerian myth similar to that of the Tower of Babel, called Enmerkar and the Lord of Aratta,[9] where Enmerkar of Uruk is building a massive ziggurat in Eridu and demands a tribute of precious materials from Aratta for its construction, at one point reciting an incantation imploring the god Enki to restore (or in Kramer's translation, to disrupt) the linguistic unity of the inhabited regions—named as Shubur, Hamazi, Sumer, Uri-ki (Akkad), and the Martu land, "the whole universe, the well-guarded people—may they all address Enlil together in a single language."[19]

In addition, a further Assyrian myth, dating from the 8th century BC during the Neo-Assyrian Empire (911–605 BC) bears a number of similarities to the later written Biblical story.[20]

Mexico[edit]

Various traditions similar to that of the tower of Babel are found in Central America. Some writers[who?] connected the Great Pyramid of Cholula to the Tower of Babel. The Dominican friar Diego Durán (1537–1588) reported hearing an account about the pyramid from a hundred-year-old priest at Cholula, shortly after the conquest of Mexico. He wrote that he was told when the light of the sun first appeared upon the land, giants appeared and set off in search of the sun. Not finding it, they built a tower to reach the sky. An angered Lord of the Heavens called upon the inhabitants of the sky, who destroyed the tower and scattered its inhabitants. The story was not related to either a flood or the confusion of languages, although Frazer connects its construction and the scattering of the giants with the Tower of Babel.[21]

Another story, attributed by the native historian Fernando de Alva Cortés Ixtlilxóchitl (c. 1565–1648) to the ancient Toltecs, states that after men had multiplied following a great deluge, they erected a tall zacuali or tower, to preserve themselves in the event of a second deluge. However, their languages were confounded and they went to separate parts of the earth.[22]

Arizona[edit]

Still another story, attributed to the Tohono O'odham people, holds that Montezuma escaped a great flood, then became wicked and attempted to build a house reaching to heaven, but the Great Spirit destroyed it with thunderbolts.[23][24]

Nepal[edit]

Traces of a somewhat similar story have also been reported among the Tharu of Nepal and northern India.[25]

Africa[edit]

According to David Livingstone, the Africans whom he met living near Lake Ngami in 1849 had such a tradition, but with the builders' heads getting "cracked by the fall of the scaffolding".[26]

Other traditions[edit]

In his 1918 book, Folklore in the Old Testament, Scottish social anthropologist Sir James George Frazer documented similarities between Old Testament stories, such as the Flood, and indigenous legends around the world. He identified Livingston's account with a tale found in Lozi mythology, wherein the wicked men build a tower of masts to pursue the Creator-God, Nyambe, who has fled to Heaven on a spider-web, but the men perish when the masts collapse. He further relates similar tales of the Ashanti that substitute a pile of porridge pestles for the masts. Frazer moreover cites such legends found among the Kongo people, as well as in Tanzania, where the men stack poles or trees in a failed attempt to reach the moon.[21] He further cited the Karbi and Kuki people of Assam as having a similar story. The traditions of the Karen people of Myanmar, which Frazer considered to show clear 'Abrahamic' influence, also relate that their ancestors migrated there following the abandonment of a great pagoda in the land of the Karenni 30 generations from Adam, when the languages were confused and the Karen separated from the Karenni. He notes yet another version current in the Admiralty Islands, where mankind's languages are confused following a failed attempt to build houses reaching to heaven.

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

 

10
PYTHAGORAS
130
49
4
9
OURABORUS
130
40
4

 

PYTHAGORASOURABORUS

 

19
PYTHAGORASOURABORUS
260
89
8
1+9
-
2+6+0
8+9
-
10
PYTHAGORASOURABORUS
8
17
8
1+0
-
-
1+7
-
1
PYTHAGORASOURABORUS
8
8
8

 

 

JUST SIX NUMBERS

THE DEEP FORCES THAT SHAPE THE UNIVERSE

Martin Rees 1999

Page 7

"Lengths spanning sixty powers of ten are depicted in the ouraborus,"

Page 8

FIGURE 1.1 (omitted)

"The ouraborus, There are links between the microworld of particles, nuclei and atoms (left) and the cosmos (right)"

Page 161

"A theme of this book has been the intimate links between the microworld and the cosmos symbolized by the ouraborus"

 

 

Solar Plexus; snake swallowing its own tail 11 posts - 4 authors - Last post: 19 Feb 2005
The ouraborous is the flow of a kind of kundalini which bypasses the heart. Kundalini is the Luciferic initiation. ...
www.astralpulse.com/.../metaphoric_phenomenon-t16782.0.html;... - Cached - Similar

The ouraborous is the flow of a kind of kundalini which bypasses the heart. Kundalini is the Luciferic initiation.

 

 

THE

OURABORUS PYTHAGORAS OURABORUS

THAT

SERPENT I PRESENT

 

 

3
THE
33
15
6
-
OURABORUS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
A+B+O
18
9
9
1
R
18
9
9
2
U+S
40
13
4
-
OURABORUS
-
-
-
12
First Total
163
64
46
1+2
Add to Reduce
1+6+3
6+4
4+6
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

3
THE
33
15
6
9
OURABORUS
130
40
40
12
First Total
163
55
46
1+2
Add to Reduce
1+6+3
5+5
4+6
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

-
12
T
H
E
-T
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
6
-
-
-
-
6
-
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
-
8
-
--
15
-
-
-
-
15
-
-
19
+
=
57
5+7
=
12
1+2
3
=
3
-
12
T
H
E
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
-
3
9
1
2
-
9
3
-
+
=
34
3+4
=
7
=
7
=
7
-
`-
20
-
5
--
-
21
18
1
2
-
18
21
-
+
=
106
1+0+6
=
7
=
7
=
7
-
12
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R
A
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-
-
-
-
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20
8
5
-
15
21
18
1
2
15
18
21
19
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1+6+3
=
10
1+0
1
=
1
-
-
2
8
5
-
6
3
9
1
2
6
9
3
1
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5+5
=
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1
=
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-
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-
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=
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--
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T
H
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9
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1+2
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5+5
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3+7
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12
T
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S
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-
--
-
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6
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-
-
6
-
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21
2+1
=
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=
3
=
3
-
-
8
-
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15
-
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-
15
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19
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=
12
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=
3
12
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5
-
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3
9
1
2
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9
3
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34
3+4
=
7
=
7
=
7
`-
20
-
5
--
-
21
18
1
2
-
18
21
-
+
=
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1+0+6
=
7
=
7
=
7
12
T
H
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-
O
U
R
A
B
O
R
U
S
-
-
-
-
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--
-
-
-
-
`-
20
8
5
-
15
21
18
1
2
15
18
21
19
+
=
163
1+6+3
=
10
1+0
1
=
1
-
2
8
5
-
6
3
9
1
2
6
9
3
1
+
=
55
5+5
=
10
1+0
1
=
1
12
T
H
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-
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S
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-
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1
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1
-
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1
occurs
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2
=
2
=
2
-
2
-
-
-
-
-
-
-
2
-
-
-
-
--
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2
occurs
x
2
=
4
=
4
--
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
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2
=
6
=
6
-
-
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5
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
--
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
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-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
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9
-
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9
occurs
x
2
=
18
1+8
9
12
T
H
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-
O
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R
A
B
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R
U
S
-
-
34
-
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55
-
37
1+2
-
-
-
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6
-
-
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-
9
-
-
-
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3+4
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1+2
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3+7
3
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A
B
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-
-
7
-
-
3
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10
-
10
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2
8
5
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6
3
9
1
2
6
9
3
1
-
-
-
-
-
-
-
1+0
-
1+0
3
T
H
E
-
O
U
R
A
B
O
R
U
S
-
-
7
-
-
3
-
1
-
1

 

 

-
OURABORUS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
A+B+O
18
9
9
1
R
18
9
9
2
U+S
40
13
4
9
OURABORUS
130
49
40
-
-
1+3+0
4+9
9
OURABORUS
4
13
4
-
-
1+3
-
9
OURABORUS
4
4
4

 

 

-
-
-
-
-
OURABORUS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
40
-
9
OURABORUS
130
49
40
-
2
2
6
4
5
12
7
8
18
-
-
4+0
-
-
-
1+3+0
5+8
4+9
-
-
-
-
-
-
1+2
-
-
1+8
-
-
4
-
9
OURABORUS
4
13
13
-
2
2
6
4
5
3
7
8
9
-
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
OURABORUS
4
4
4
-
2
2
6
4
5
3
7
8
9

 

 

-
-
-
-
-
OURABORUS
-
-
-
-
1
2
3
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
40
-
9
OURABORUS
130
49
40
-
2
2
6
12
18
-
-
4+0
-
-
-
1+3+0
5+8
4+9
-
-
-
-
1+2
1+8
-
-
4
-
9
OURABORUS
4
13
13
-
2
2
6
3
9
-
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
4
-
9
OURABORUS
4
4
4
-
2
2
6
3
9

 

 

9
OURABORUS
130
40
4
10
PYTHAGORAS
130
49
4
19
-
260
97
7
1+9
-
2+6+8
9+7
-
10
-
16
16
7
1+0
-
1+6
1+6
-
1
-
7
7
7

 

 

10
PYTHAGORAS
130
49
4
3
AND
19
10
1
9
OURABORUS
130
40
4
22
First Total
279
99
9
2+2
Add to Reduce
2+7+9
9+9
-
4
Second Total
18
18
9
-
Reduce to Deduce
1+8
1+8
-
4
Essence of Number
9
9
9

 

 

-
22
P
Y
T
H
A
G
O
R
A
S
-T
A
N
D
-T
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
-
5
-
-
6
-
-
-
-
6
-
-
1
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
8
-
-
15
-
-
19
--
-
14
-
--
15
-
-
-
-
15
-
-
19
+
=
105
1+0+5
=
6
=
6
=
6
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
1
-
4
-
-
3
9
1
2
-
9
3
-
+
=
66
6+6
=
12
1+2
3
=
3
-
`-
16
25
20
-
1
7
-
18
1
-
--
1
-
4
--
-
21
18
1
2
-
18
21
-
+
=
174
1+7+4
=
12
1+2
3
=
3
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
1
14
4
-
15
21
18
1
2
15
18
21
19
+
=
279
2+7+9
=
18
1+8
9
=
9
-
-
7
7
2
8
1
7
6
9
1
1
-
1
5
4
-
6
3
9
1
2
6
9
3
1
+
=
99
9+9
=
18
1+8
9
=
9
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
1
-
1
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
6
=
6
=
6
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
3
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
6
--
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-
-
45
-
-
22
-
99
-
54
4+5
2+2
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
4+5
-
-
2+2
-
9+9
-
5+4
9
4
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
4
-
18
-
9
-
-
7
7
2
8
1
7
6
9
1
1
-
1
5
4
-
6
3
9
1
2
6
9
3
1
-
-
-
-
-
-
-
1+8
-
-
9
4
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
4
-
9
-
9

 

 

PYTHAGORAS OURABORUS

 

10
PYTHAGORAS
130
49
4
9
OURABORUS
130
40
4
19
First Total
260
89
8
1+9
Add to Reduce
2+6+0
8+9
-
10
Second Total
8
17
8
1+0
Reduce to Deduce
-
1+7
-
1
Essence of Number
8
8
8

 

 

-
22
P
Y
T
H
A
G
O
R
A
S
-T
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
6
-
-
-
-
6
-
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
8
-
-
15
-
-
19
--
15
-
-
-
-
15
-
-
19
+
=
91
9+1
=
10
1+0
1
=
1
-
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
-
3
9
1
2
-
9
3
-
+
=
61
6+1
=
7
=
7
=
7
-
`-
16
25
20
-
1
7
-
18
1
-
--
-
21
18
1
2
-
18
21
-
+
=
169
1+6+9
=
16
1+6
7
=
7
-
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
15
21
18
1
2
15
18
21
19
+
=
260
2+6+0
=
17
1+7
8
=
8
-
-
7
7
2
8
1
7
6
9
1
1
-
6
3
9
1
2
6
9
3
1
+
=
89
8+9
=
17
1+7
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
--
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
--
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
--
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
9
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
36
-
-
19
-
89
-
44
-
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
1
-
-
-
-
1
-
-
3+6
-
-
1+9
-
8+9
-
4+4
9
10
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
10
-
17
-
8
-
1+0
7
7
2
8
1
7
6
9
1
1
-
6
3
9
1
2
6
9
3
1
-
-
-
-
-
1+0
-
1+7
-
-
9
1
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
1
-
8
-
8

 

PYTHAGORAS OURABORUS

 

22
P
Y
T
H
A
G
O
R
A
S
-T
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
6
-
-
-
-
6
-
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
8
-
-
15
-
-
19
--
15
-
-
-
-
15
-
-
19
+
=
91
9+1
=
10
1+0
1
=
1
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
-
3
9
1
2
-
9
3
-
+
=
61
6+1
=
7
=
7
=
7
`-
16
25
20
-
1
7
-
18
1
-
--
-
21
18
1
2
-
18
21
-
+
=
169
1+6+9
=
16
1+6
7
=
7
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
15
21
18
1
2
15
18
21
19
+
=
260
2+6+0
=
17
1+7
8
=
8
-
7
7
2
8
1
7
6
9
1
1
-
6
3
9
1
2
6
9
3
1
+
=
89
8+9
=
17
1+7
8
=
8
22
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
36
-
-
19
-
89
-
44
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
1
-
-
-
-
1
-
-
3+6
-
-
1+9
-
8+9
-
4+4
10
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
10
-
17
-
8
1+0
7
7
2
8
1
7
6
9
1
1
-
6
3
9
1
2
6
9
3
1
-
-
-
-
-
1+0
-
1+7
-
-
1
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
A
B
O
R
U
S
-
-
9
-
-
1
-
8
-
8

 

 

PYTHAGORASOURABORUS

 

19
PYTHAGORASOURABORUS
260
89
8
1+9
-
2+6+0
8+9
-
10
PYTHAGORASOURABORUS
8
17
8
1+0
-
-
1+7
-
1
PYTHAGORASOURABORUS
8
8
8

 

 

-
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
6
-
-
-
-
6
-
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
8
-
-
15
-
-
19
15
-
-
-
-
15
-
-
19
+
=
91
9+1
=
10
1+0
1
=
1
-
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
3
9
1
2
-
9
3
-
+
=
61
6+1
=
7
=
7
=
7
-
`-
16
25
20
-
1
7
-
18
1
-
-
21
18
1
2
-
18
21
-
+
=
169
1+6+9
=
16
1+6
7
=
7
-
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
15
21
18
1
2
15
18
21
19
+
=
260
2+6+0
=
17
1+7
8
=
8
-
-
7
7
2
8
1
7
6
9
1
1
6
3
9
1
2
6
9
3
1
+
=
89
8+9
=
17
1+7
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
--
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
--
--
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
--
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
9
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
36
-
-
19
-
89
-
44
-
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
1
-
-
-
-
1
-
-
3+6
-
-
1+9
-
8+9
-
4+4
9
10
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
9
-
-
10
-
17
-
8
-
1+0
7
7
2
8
1
7
6
9
1
1
6
3
9
1
2
6
9
3
1
-
-
-
-
-
1+0
-
1+7
-
-
9
1
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
9
-
-
1
-
8
-
8

 

 

22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
6
-
-
-
-
6
-
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
8
-
-
15
-
-
19
15
-
-
-
-
15
-
-
19
+
=
91
9+1
=
10
1+0
1
=
1
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
3
9
1
2
-
9
3
-
+
=
61
6+1
=
7
=
7
=
7
`-
16
25
20
-
1
7
-
18
1
-
-
21
18
1
2
-
18
21
-
+
=
169
1+6+9
=
16
1+6
7
=
7
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
15
21
18
1
2
15
18
21
19
+
=
260
2+6+0
=
17
1+7
8
=
8
-
7
7
2
8
1
7
6
9
1
1
6
3
9
1
2
6
9
3
1
+
=
89
8+9
=
17
1+7
8
=
8
22
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
--
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
36
-
-
19
-
89
-
44
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
1
-
-
-
-
1
-
-
3+6
-
-
1+9
-
8+9
-
4+4
10
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
9
-
-
10
-
17
-
8
1+0
7
7
2
8
1
7
6
9
1
1
6
3
9
1
2
6
9
3
1
-
-
-
-
-
1+0
-
1+7
-
-
1
P
Y
T
H
A
G
O
R
A
S
O
U
R
A
B
O
R
U
S
-
-
9
-
-
1
-
8
-
8

 

B HOURS OF HORUS B

 

-
OURABORUS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
A+B+O
18
9
9
1
R
18
9
9
2
U+S
40
13
4
9
OURABORUS
130
49
40
-
-
1+3+0
4+9
4+0
-
OURABORUS
4
13
4
-
-
-
1+3
-
9
OURABORUS
4
4
4

 

 

-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
1
+
=
13
1+3
=
4
=
4
=
4
-
-
15
-
-
-
-
15
-
-
19
+
=
49
4+9
=
13
1+3
4
=
4
-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
3
9
1
2
-
9
3
-
+
=
27
2+7
=
9
=
9
=
9
-
`-
-
21
18
1
2
-
18
21
-
+
=
81
8+1
=
9
=
9
=
9
-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
`-
15
21
18
1
2
15
18
21
19
+
=
130
1+3
=
4
=
4
=
4
-
-
6
3
9
1
2
6
9
3
1
+
=
40
4+0
=
4
=
4
=
4
-
9
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
1
=
2
=
2
-
--
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
-
--
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
24
9
O
U
R
A
B
O
R
U
S
-
-
21
-
-
9
-
49
-
22
2+4
-
-
-
9
-
-
-
9
-
-
-
-
2+1
-
-
-
-
4+9
-
2+2
6
9
O
U
R
A
B
O
R
U
S
-
-
3
-
-
9
-
13
-
4
-
-
6
3
9
1
2
6
9
3
1
-
-
-
-
-
-
-
1+3
-
-
6
9
O
U
R
A
B
O
R
U
S
-
-
3
-
-
9
-
4
-
4

 

 

-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
1
+
=
13
1+3
=
4
=
4
=
4
-
-
15
-
-
-
-
15
-
-
19
+
=
49
4+9
=
13
1+3
4
=
4
-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
3
9
1
2
-
9
3
-
+
=
27
2+7
=
9
=
9
=
9
-
`-
-
21
18
1
2
-
18
21
-
+
=
81
8+1
=
9
=
9
=
9
-
9
O
U
R
A
B
O
R
U
S
-
-
-
-
-
--
-
-
-
-
-
`-
15
21
18
1
2
15
18
21
19
+
=
130
1+3
=
4
=
4
=
4
-
-
6
3
9
1
2
6
9
3
1
+
=
40
4+0
=
4
=
4
=
4
-
9
O
U
R
A
B
O
R
U
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
1
=
2
=
2
-
--
-
3
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
--
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
24
9
O
U
R
A
B
O
R
U
S
-
-
21
-
-
9
-
49
-
22
2+4
-
-
-
9
-
-
-
9
-
-
-
-
2+1
-
-
-
-
4+9
-
2+2
6
9
O
U
R
A
B
O
R
U
S
-
-
3
-
-
9
-
13
-
4
-
-
6
3
9
1
2
6
9
3
1
-
-
-
-
-
-
-
1+3
-
-
6
9
O
U
R
A
B
O
R
U
S
-
-
3
-
-
9
-
4
-
4

 

 

9
OURABORUS
130
40
4
10
PYTHAGORAS
130
49
4
19
First Total
260
89
8
1+9
Add to Reduce
2+6+0
8+9
-
10
Second Total
8
17
8
1+0
Reduce to Deduce
-
1+7
-
1
Essence of Number
8
8
8

 

 

OURABORUS

OUROBOROS OUROBOROS

ANOTHER

SERPENT I PRESENT

 

 

9
OURABORUS
130
31
4
9
OUROBOROS
138
48
3

 

 

9
OUROBOROS
138
48
3
10
PYTHAGORAS
130
49
4
19
First Total
268
97
7
1+9
Add to Reduce
2+6+8
9+7
-
10
Second Total
16
16
7
1+0
Reduce to Deduce
1+6
1+6
-
1
Essence of Number
7
7
7

 

 

10
PYTHAGORAS
130
49
4
3
AND
19
10
1
9
OUROBOROS
138
48
3
22
First Total
287
107
8
2+2
Add to Reduce
2+8+7
1+0+7
-
4
Second Total
17
8
8
-
Reduce to Deduce
1+7
-
-
4
Essence of Number
8
8
8

 

 

-
22
P
Y
T
H
A
G
O
R
A
S
-T
A
N
D
-T
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
-
5
-
-
6
-
-
6
-
6
-
6
1
+
=
45
4+5
=
9
=
9
=
9
-
-
-
-
-
8
-
-
15
-
-
19
--
-
14
-
--
15
-
-
15
-
15
-
15
19
+
=
135
1+3+5
=
9
=
9
=
9
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
1
-
4
-
-
3
9
-
2
-
9
-
-
+
=
62
6+2
=
8
=
8
=
8
-
`-
16
25
20
-
1
7
-
18
1
-
--
1
-
4
--
-
21
18
-
2
-
18
-
-
+
=
152
1+5+2
=
8
=
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
1
14
4
-
15
21
18
15
2
15
18
15
19
+
=
287
2+8+7
=
17
1+7
8
=
8
-
-
7
7
2
8
1
7
6
9
1
1
-
1
5
4
-
6
3
9
6
2
6
9
6
1
+
=
107
1+0+7
=
8
=
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
1
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
3
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
6
--
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
7
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
18
1+8
9
--
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
45
22
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-
-
45
-
-
22
-
107
-
44
4+5
2+2
7
7
2
8
1
7
6
9
1
1
-
1
5
4
-
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
2+2
-
1+0+7
-
4+4
9
5
P
Y
T
H
A
G
O
R
A
S
-
A
N
D
-
O
U
R
O
B
O
R
O
S
-
-
6
-
-
5
=
8
3+0
8

 

 

10
PYTHAGORAS
130
49
4
3
AND
19
10
1
9
OUROBOROS
138
48
3
22
First Total
287
107
8
2+2
Add to Reduce
2+8+7
1+0+7
-
4
Second Total
17
8
8
-
Reduce to Deduce
1+7
-
-
4
Essence of Number
8
8
8

 

 

-
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
5
-
6
-
-
6
-
6
-
6
1
+
=
45
4+5
=
9
=
9
=
9
-
-
-
-
-
8
-
-
15
-
-
19
-
14
-
15
-
-
15
-
15
-
15
19
+
=
135
1+3+5
=
9
=
9
=
9
-
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
1
-
4
-
3
9
-
2
-
9
-
-
+
=
62
6+2
=
8
=
8
=
8
-
`-
16
25
20
-
1
7
-
18
1
-
1
-
4
-
21
18
-
2
-
18
-
-
+
=
152
1+5+2
=
8
=
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
1
14
4
15
21
18
15
2
15
18
15
19
+
=
287
2+8+7
=
17
1+7
8
=
8
-
-
7
7
2
8
1
7
6
9
1
1
1
5
4
6
3
9
6
2
6
9
6
1
+
=
107
1+0+7
=
8
=
8
=
8
-
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
1
1
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
3
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
6
--
-
-
-
-
-
-
6
-
-
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
7
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
--
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
45
22
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
45
-
-
22
-
107
-
44
4+5
2+2
7
7
2
8
1
7
6
9
1
1
1
5
4
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
2+2
-
1+0+7
-
4+4
9
5
P
Y
T
H
A
G
O
R
A
S
A
N
D
O
U
R
O
B
O
R
O
S
-
-
6
-
-
5
=
8
3+0
8

 

 

10
PYTHAGORAS
130
49
4
9
OUROBOROS
138
48
3
19
First Total
268
97
7
1+9
Add to Reduce
2+6+8
9+7
-
10
Second Total
16
16
7
1+0
Reduce to Deduce
1+6
1+6
-
4
Essence of Number
7
7
7

 

 

-
19
P
Y
T
H
A
G
O
R
A
S
-T
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
6
-
-
6
-
6
-
6
1
+
=
40
4+0
=
4
=
4
=
4
-
-
-
-
-
8
-
-
15
-
-
19
--
15
-
-
15
-
15
-
15
19
+
=
121
1+2+1
=
4
=
4
=
4
-
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
-
3
9
-
2
-
9
-
-
+
=
57
5+7
=
12
1+2
3
=
3
-
`-
16
25
20
-
1
7
-
18
1
-
--
-
21
18
-
2
-
18
-
-
+
=
147
1+4+7
=
12
1+2
3
=
3
-
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
15
21
18
15
2
15
18
15
19
+
=
268
2+8+7
=
16
1+6
7
=
7
-
-
7
7
2
8
1
7
6
9
1
1
-
6
3
9
6
2
6
9
6
1
+
=
97
9+7
=
16
1+6
7
=
7
-
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
--
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
-
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
9
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
19
-
97
-
44
-
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1+9
-
9+7
-
4+4
-
=
-
-
-
-
-
-
6
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
10
-
16
-
8
9
10
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
45
-
-
1+0
-
1+6
-
-
-
1+0
7
7
2
8
1
7
6
9
1
1
-
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
=
-
=
-
=
9
1
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
6
-
-
1
=
7
3+0
8

 

 

9
P
Y
T
H
A
G
O
R
A
S
-T
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
-
6
-
-
6
-
6
-
6
1
+
=
40
4+0
=
4
=
4
=
4
-
-
-
-
8
-
-
15
-
-
19
--
15
-
-
15
-
15
-
15
19
+
=
121
1+2+1
=
4
=
4
=
4
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
-
3
9
-
2
-
9
-
-
+
=
57
5+7
=
12
1+2
3
=
3
`-
16
25
20
-
1
7
-
18
1
-
--
-
21
18
-
2
-
18
-
-
+
=
147
1+4+7
=
12
1+2
3
=
3
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
-
15
21
18
15
2
15
18
15
19
+
=
268
2+8+7
=
16
1+6
7
=
7
-
7
7
2
8
1
7
6
9
1
1
-
6
3
9
6
2
6
9
6
1
+
=
97
9+7
=
16
1+6
7
=
7
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
-
-
-
-
-
6
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
19
-
97
-
44
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1+9
-
9+7
-
4+4
=
-
-
-
-
-
-
6
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
10
-
16
-
8
10
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
45
-
-
1+0
-
1+6
-
-
1+0
7
7
2
8
1
7
6
9
1
1
-
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
=
-
=
-
=
1
P
Y
T
H
A
G
O
R
A
S
-
O
U
R
O
B
O
R
O
S
-
-
6
-
-
1
=
7
3+0
8

 

 

19
PYTHAGORAS OUROBOROS
268
97
7
1+9
-
2+6+8
9+7
-
10
PYTHAGORAS OUROBOROS
16
16
7
1+0
-
-
1+6
-
1
PYTHAGORAS OUROBOROS
7
7
7

 

 

-
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
6
-
-
6
-
6
-
6
1
+
=
40
4+0
=
4
=
4
=
4
-
-
-
-
-
8
-
-
15
-
-
19
15
-
-
15
-
15
-
15
19
+
=
121
1+2+1
=
4
=
4
=
4
-
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
3
9
-
2
-
9
-
-
+
=
57
5+7
=
12
1+2
3
=
3
-
`-
16
25
20
-
1
7
-
18
1
-
-
21
18
-
2
-
18
-
-
+
=
147
1+4+7
=
12
1+2
3
=
3
-
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
15
21
18
15
2
15
18
15
19
+
=
268
2+8+7
=
16
1+6
7
=
7
-
-
7
7
2
8
1
7
6
9
1
1
6
3
9
6
2
6
9
6
1
+
=
97
9+7
=
16
1+6
7
=
7
-
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
--
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
-
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
9
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
19
-
97
-
44
-
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1+9
-
9+7
-
4+4
-
=
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
10
-
16
-
8
9
10
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
45
-
-
1+0
-
1+6
-
-
-
1+0
7
7
2
8
1
7
6
9
1
1
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
=
-
=
-
=
9
1
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
6
-
-
1
=
7
3+0
8

 

 

9
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
-
-
6
-
-
1
6
-
-
6
-
6
-
6
1
+
=
40
4+0
=
4
=
4
=
4
-
-
-
-
8
-
-
15
-
-
19
15
-
-
15
-
15
-
15
19
+
=
121
1+2+1
=
4
=
4
=
4
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
7
7
2
-
1
7
-
9
1
-
-
3
9
-
2
-
9
-
-
+
=
57
5+7
=
12
1+2
3
=
3
`-
16
25
20
-
1
7
-
18
1
-
-
21
18
-
2
-
18
-
-
+
=
147
1+4+7
=
12
1+2
3
=
3
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
`-
16
25
20
8
1
7
15
18
1
19
15
21
18
15
2
15
18
15
19
+
=
268
2+8+7
=
16
1+6
7
=
7
-
7
7
2
8
1
7
6
9
1
1
6
3
9
6
2
6
9
6
1
+
=
97
9+7
=
16
1+6
7
=
7
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
--
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
--
7
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
-
-
-
19
-
97
-
44
1+9
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1+9
-
9+7
-
4+4
=
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
6
-
6
-
-
-
-
-
-
10
-
16
-
8
10
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
45
-
-
1+0
-
1+6
-
-
1+0
7
7
2
8
1
7
6
9
1
1
6
3
9
6
2
6
9
6
1
-
-
4+5
-
-
=
-
=
-
=
1
P
Y
T
H
A
G
O
R
A
S
O
U
R
O
B
O
R
O
S
-
-
6
-
-
1
=
7
3+0
8

 

 

Ouroboros - Wikipedia, the free encyclopedia - 8:55am
The Ouroboros often represents self-reflexivity or cyclicality, especially in the sense of something constantly re-creating itself, the eternal return, ...

Historical representations - See also - References - External links
en.wikipedia.org/wiki/Ouroboros - Cached - Similar

 

-Ouroboros - Crystalinks Ouroboros is an ancient alchemy symbol depicting a snake or dragon [DNA] swallowing its own tail, constantly creating itself and forming a circle. ...
www.crystalinks.com/ouroboros.html - Cached - Similar

 

-Ouroboros From there it moved to the Phonecians and then to the Greeks, who called it the Ouroboros, which means devouring its tail. ...
www.dragon.org/chris/ouroboros.html - Cached - Similar -

 

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Spira Solaris and the Universal Ouroboros. Spira Solaris Archytas ... - 2 visits - 9:04am
"Ouroboros was and is the name for the Great World Serpent, ...... Pythagoras is often mentioned in Arabic philosophy and in gnomic literature. ...
www.spirasolaris.ca/sbb4f.html - Cached - Similar

 

-The Egyptian Ouroboros and the Enigma of - Stephen Linsteadt Studio alchemy, ouroboros, stephen linsteadt. Image by: sashkin. Scientists have seen Pythagoras and Euclid's view, that the universe operates according to ...
www.stephenlinsteadtstudio.com/articles/ouroboros.html - Cached - Similar

 

-The Ouroboros Collective on MySpace Music - Free Streaming MP3s ... Download The Ouroboros Collective Experimental / / music singles, ... nudity, various instruments being set ablaze/sacrificed to Pythagoras, paint slinging, ...
www.myspace.com/ouroboroscollective - Cached - Similar

 

-Ouroboros Press Catalogue - Alchemy: The Royal Art - tribe.net 20 Feb 2009 ... From Pythagoras to the Thrice-Greatest ... ouroboros@bookarts.org] We wrap our packages securely for safe shipping. ...
alchemical.tribe.net/.../31214a99-3baa-451f-bf40-51cde8df81de - Cached - Similar -Tetraktys inside Ouroboros - Vox 10 Nov 2008 ... The ten pointed tetraktys is an ancient Pythagorean symbol of Kosmic unity. The ouroboros herein emphasizes Oneness. ...
kyotoobserver.vox.com/.../tetraktys-inside-ouroboros.html - Cached - Similar

 

-Ouroboros Press' Journal 14 Aug 2007 ... From Pythagoras to the Thrice-Greatest Hermes, ... This Limited Edition produced by Ouroboros Press continues the tradition of fine ...
community.livejournal.com/ouroboros_press/ - Cached - Similar

 

-statemaster - Encyclopedia: Ouroboros The Ouroboros, also spelled Ourorboros, Oroborus, Uroboros or Uroborus (IPA: .... from ancient Egypt and developed in the teachings of Pythagoras. ...
www.statemaster.com/encyclopedia/Ouroboros - Cached - Similar

 

-thelastdayprophet Calendar of Human Sacrifices The Occult Calendar ... ... Orwelliian, New Age, Occult, Satanism, Nazi, Guillotines, Ouroboros, Theosophy. ... Pythagoras who was an initiate in the Eleusinian Mysteries, ...
www.geocities.com/.../CalendarOfHumanSacrifices.html - Cached - Similar

 

-Kyr Ouroboros - "I am DEEPLY GRATEFUL for My Being!" - My Care2 Kyr Ouroboros: "...finally freed from the tyrannous bondage of his own mind ... including Edison, Einstein, Gandhi, Kafka, Pythagoras, da Vinci, Tesla, ...
www.care2.com/c2c/people/profile.html?pid=415192164 - Cached - Similar

 

-PENTACLE HEALER'S Ring - S Silver Ouroboros SNAKE RING - ebay ... ebay: Find PENTACLE HEALER'S Ring - S Silver Ouroboros SNAKE RING in the Jewelry ... The Greek philosopher, Pythagoras, thought the symbol represented the ...
cgi.ebay.com/PENTACLE-HEALER'S-Ring----S-Silver-Ouroboros-SNAKE-RING_W0QQitemZ380159594516QQcmdZViewItemQQim... - Cached - Similar

 

 

-
OUROBOROS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
O+B+O
32
14
5
1
R
18
9
9
2
O+S
34
7
7
9
OUROBOROS
138
48
30
-
-
1+3+8
4+8
3+0
9
OUROBOROS
12
12
3
-
1+2
1+2
-
9
OUROBOROS
3
3
3

 

 

-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
6
-
6
-
6
1
+
=
25
2+5
=
7
=
7
=
7
-
-
15
-
-
15
-
15
-
15
19
+
=
79
7+9
=
16
1+6
7
=
7
-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
3
9
-
2
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
`-
-
21
18
-
2
-
18
-
-
+
=
59
5+9
=
14
1+4
5
=
5
-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
15
21
18
15
2
15
18
15
19
+
=
138
1+3+8
=
12
1+2
3
=
3
-
-
6
3
9
6
2
6
9
6
1
+
=
48
4+8
=
12
1+2
3
=
3
-
9
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
1
=
2
=
2
-
--
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
--
--
5
FIVE
5
-
-
-
-
-
-
--
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
4
=
24
2+4
6
7
--
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
24
9
O
U
R
O
B
O
R
O
S
-
-
21
-
-
9
-
48
-
21
2+4
-
6
-
-
6
-
6
-
6
-
-
-
2+1
-
-
-
-
4+8
-
2+1
6
9
O
U
R
O
B
O
R
O
S
-
-
3
-
-
9
-
12
-
3
-
-
6
3
9
6
2
6
9
6
1
-
-
-
-
-
-
-
1+2
-
-
6
9
O
U
R
O
B
O
R
O
S
-
-
3
-
-
9
-
3
-
3

 

 

-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
6
-
6
-
6
1
+
=
25
2+5
=
7
=
7
=
7
-
-
15
-
-
15
-
15
-
15
19
+
=
79
7+9
=
16
1+6
7
=
7
-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
3
9
-
2
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
`-
-
21
18
-
2
-
18
-
-
+
=
59
5+9
=
14
1+4
5
=
5
-
9
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
15
21
18
15
2
15
18
15
19
+
=
138
1+3+8
=
12
1+2
3
=
3
-
-
6
3
9
6
2
6
9
6
1
+
=
48
4+8
=
12
1+2
3
=
3
-
9
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
1
=
2
=
2
-
--
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
24
9
O
U
R
O
B
O
R
O
S
-
-
21
-
-
9
-
48
-
21
2+4
-
6
-
-
6
-
6
-
6
-
-
-
2+1
-
-
-
-
4+8
-
2+1
6
9
O
U
R
O
B
O
R
O
S
-
-
3
-
-
9
-
12
-
3
-
-
6
3
9
6
2
6
9
6
1
-
-
-
-
-
-
-
1+2
-
-
6
9
O
U
R
O
B
O
R
O
S
-
-
3
-
-
9
-
3
-
3

 

 

-
-
-
-
-
OUROBOROS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
48
-
9
OUROBOROS
138
57
48
-
1
2
3
4
5
24
7
8
18
-
-
4+8
-
-
-
1+3+8
5+7
4+8
-
-
-
-
-
-
2+4
-
-
1+8
-
-
12
-
9
OUROBOROS
12
12
12
-
1
2
3
4
5
6
7
8
9
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
OUROBOROS
3
3
3
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
OUROBOROS
-
-
-
-
1
2
3
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
48
-
9
OUROBOROS
138
57
48
-
1
2
3
24
18
-
-
4+8
-
-
-
1+3+8
5+7
4+8
-
-
-
-
2+4
1+8
-
-
12
-
9
OUROBOROS
12
12
12
-
1
2
3
6
9
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
-
-
-
-
-
-
3
-
9
OUROBOROS
3
3
3
-
1
2
3
6
9

 

 

THE

OUROBOROS

THAT

SERPENT I PRESENT

 

 

3
THE
33
15
6
-
OUROBOROS
-
-
-
2
O+U
36
9
9
1
R
18
9
9
3
O+B+O
32
14
5
1
R
18
9
9
2
O+S
34
16
7
-
OUROBOROS
-
-
-
12
Add to Reduce
171
72
45
1+2
Reduce to Deduce
1+7+1
7+2
4+5
3
Essence of Number
9
9
9

 

 

3
THE
33
15
6
9
OUROBOROS
138
48
3
12
Add to Reduce
171
63
9
1+2
Reduce to Deduce
1+7+1
6+3
-
3
Essence of Number
9
9
9

 

 

-
12
T
H
E
-T
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
6
-
-
6
-
6
-
6
1
+
=
33
3+3
=
6
=
6
=
6
-
-
-
8
-
--
15
-
-
15
-
15
-
15
19
+
=
87
8+7
=
15
1+5
6
=
6
-
12
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
-
3
9
-
2
-
9
-
-
+
=
30
3+0
=
3
=
3
=
3
-
`-
20
-
5
--
-
21
18
-
2
-
18
-
-
+
=
84
7+5
=
12
1+2
3
=
3
-
12
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
20
8
5
-
15
21
18
15
2
15
18
15
19
+
=
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
6
3
9
6
2
6
9
6
1
+
=
63
6+3
=
9
=
9
=
9
-
12
T
H
E
-
O
U
R
O
B
O
R
O
S
-T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
--
--
2
occurs
x
2
=
4
=
4
-
--
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
-
--
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
4
=
24
2+4
6
7
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
12
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
34
-
-
12
-
63
-
36
1+1
1+2
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
3+4
-
-
1+2
-
6+3
-
3+6
2
3
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
7
-
-
3
-
9
-
9
-
-
2
8
5
-
6
3
9
6
2
6
9
6
1
-
-
-
-
-
-
-
-
-
-
2
3
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
7
-
-
3
-
9
-
9

 

 

12
T
H
E
-T
O
U
R
O
B
O
R
O
S
-
-
-
-
-
--
-
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Spira Solaris and the Universal Ouroboros. Spira Solaris Archytas ... - 8:52am
"Ouroboros was and is the name for the Great World Serpent, ...... Pythagoras is often mentioned in Arabic philosophy and in gnomic literature. ... www.spirasolaris.ca/sbb4f.html - Cached - Similar

PART VI. SPIRA SOLARIS AND THE UNIVERSAL OUROBOROS

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A. THE OUROBOROS
In general, if not universal terms, the Ouroboros may be defined as a self-sustaining, tail-eating snake, but it is clear that there is far more to the matter than this, for the concept is almost global in its distribution and evidently has far deeper meanings in many cultures. In researching the ouroborus it soon became apparent that a number of people had not only concerned themselves with the topic, they had also placed their understanding of it on the Internet. The graphical representations and insights below are all from this rapidly expanding resource.

Fom left to right, the first Ouroboros is one of the better known examples, which according to the source (Chris McCoy) was from: "The Chrysopoeia ('Gold-Making') of Cleopatra during the Alexandrian Period. The enclosed words mean ' the all is one.'" The same source also explains that: "In the above drawing, from a book by an early Alchemist, Cleopatra, the black half symbolizes the Night, Earth, and the destructive force of nature, yin. the light half represents Day, Heaven, the generative, creative force, yang. Alchemically, the ouroboros is also used as a purifying glyph ...The 'tail-devourer' is the symbolization of concepts such as completion, perfection and totality, the endless round of existence, etc. It is usually represented as a worm or serpent with its tail in its mouth."
The second example and the following expansion on the topic is by Chris Aynesworth (The World Tree) "Of The Androgyne: The Serpent Ouroboros."

"Ouroboros was and is the name for the Great World Serpent, encircling the earth. The word 'Ouroboros' is really a term that describes a similar symbol which has been cross-pollinated from many different cultures. From "Ouroboros," there is the serpent or dragon gnawing at its own tail. The symbolic connotation from this owes to the returning cyclical nature of the seasons; the oscillations of the night sky; self-fecundation; disintegration and re-integration; truth and cognition complete; the Androgyne (see below); the primaeval waters; the potential before the spark of creation; the undifferentiated; the Totality; primordial unity; self-sufficiency, and the idea of the beginning and the end as being a continuous unending principle. It represents the conflict of life as well in that life comes out of life and death. 'My end is my beginning.' In a sense life feeds off itself, thus there are good and bad connotations which can be drawn. It is a single image with the entire actions of a life cycle - it begets, weds, impregnates, and slays itself, but in a cyclical sense, rather than linear. Thus, it fashions our lives to a totality more towards what it may REALLY be - a series of movements which repeat. "As Above, So Below" - we are born from nature, and we mirror it, because it is what man wholly is a part of.
Born from this symbolic notion, there are many different cultures which share this great dragon-serpent symbol (the serpent Jormungandr, from the myth of Yggdrasil, is just one). There are some cultures that see the image as not being beneficial, but evil - like Satan. These more specific re-interpretations will be spoken of later.
It is of interest to mention that a symbol such as that of the Ouroboros is something which Carl Jung refers to as an archetype; it seems to makes its way into our conscious mind time and time again in varying forms. The 19th century German chemist named Kekule dreamed of a snake with its tail in its mouth one day after dosing off. He had been researching the molecular structure of benzene, and was at a stop point in his work until after waking up he interpreted the dream to mean that the structure was a closed carbon ring. This was the breakthrough he needed.
There is another mention of the Ouroboros laying at the edge of "the sea which surrounds the world," called Pontus. The Ouroboros encircles the Universe; everything known and unknown is encompassed in its embracing coils, supporting and maintaining the earthly balance. It injects life into death and death into budding life. Its form suggests immobility with its locked jaws upon itself, yet at the same time it pushes the insistent message of perpetual movement through its twined coils. The first clues to this symbol go back as far as 1600-1700 BC in Egypt. Through the years the serpent moved on to the Phoenicians and the Greeks-who were what gave it the name "Ouroboros." The Greek translation means, "tail eater."
It has a strong relation to what is known as the Androgyne. The androgyne is the united male and female principles together. This is the prime primordial end to human endeavor, the reunion which births totality and creation. It is not unlike the idea of androgyny, which is a duality complete. "A return to wholeness."
The third is apparently an Aztec Ouroboros (with proportions that even Hermes would have found pleasing) originally from: Project Ouroborus at the University of Minnesota, which has a large and diverse selection of these impressive archtypes. The following commentary from this source links with what has already been said and also adds further points of interest:
This symbol appears principally among the Gnostics and is depicted as a dragon, snake or serpent biting its own tail. In the broadest sense, it is symbolic of time and the continuity of life. It sometimes bears the caption Hen to pan - 'The One, the All', as in the Codex Marcianus, for instance, of the 2nd century A.D. It has also been explained as the union between the chthonian principle as represented by the serpent and the celestial principal as signified by the bird (a synthesis which can also be applied to the dragon). Ruland contends this proves that it is a variant of the symbol for Mercury - the duplex god. In some versions of the Ouroboros, the body is half light and half dark, alluding in this way to the successive counterbalancing of opposing principls as illustrated in the Chinese Yin-Yang symbol for instance. Evola asserts that it represents the dissolution of the body, or the universal serpent which (to quote the Gnostic saying) 'passes through all things'. Poison, the viper and the universal solvent are all symbols of the undifferentiated-of the 'unchanging law' which moves through all things, linking them by a common bond. Both the dragon and the bull are symbolic antagonists of the solar hero. The Ouroboros biting its own tail is symbolic of self-fecundation, or the primitive idea of a self-sufficient Nature - a Nature, that is which, à la Nietzsche, continually returns, within a cyclic pattern, to its own beginning. There is a Venetian manuscript on alchemy which depicts the Ouroboros with its body half-black (symbolizing earth and night) and half-white (denoting heaven and light).
Continuing in the same locale and context, Solar Architect Dennis Holloway more than twenty years ago defined the Ouroboros as: ".. the ancient Greek mythical serpent that survived by devouring itself." He also linked the Ouroboros with the following quotation from Plato's Timæus:
"It had no need of eyes, for there was nothing outside it to be seen; nor of ears, for there was nothing outside to be heard. There was no surrounding air to be breathed, nor was it in need of any organ by which to supply itself with food or to get rid of it when digested. Nothing went out from or came into it anywhere, for there was nothing. Of design it was made thus, its own waste providing its own food, acting and being acted upon entirely with and by itself, because its designer considered that a being which was sufficient unto itself would be far more excellent than one which depended upon anything." from Timaeus, (33 -The Construction of the World)
The fourth ouroboros is from Alciato's Book of Emblems and the Memorial Web Library at Memorial University of Newfoundland. The latter source also provided the fifth example (Emblem 2.40) and the following amplification:
Emblem 2.40 from George Wither's A Collection of Emblemes, Ancient and Moderne (London, 1635), page 102. A demanding poem to read on a screen. The plate was engraved by Crispin de Passe and son, and was first used in Gabriel Rollenhagen's Nucleus emblematum selectissimorum, quae Itali vulgo impresas vocant ... (Arnhem and Utrecht, 1611-13). The Greek running around the picture (aionion kai proskairon) means something like "timeless, and timely." In a later emblem (3.23) Wither explains further the snake swallowing its tail (ouroboros):
Old Sages by the Figure of the Snake
Encircled thus) did oft expression make
Of Annual-Revolutions; and of things,
Which wheele about in everlasting-rings;
There ending, where they first of all begun ..
... These Roundells, help to shew the Mystery
of that immense and blest Eternitie,
From whence the CREATURE sprung, and into whom
It shall again, with full perfection come ...
The sixth, a more ornate dragon-like example, is one of twelve emblems discussed in detail by Adam Mclean in terms of psychological and alchemical symbolism. (A Threefold Alchemical Journey Through the Book of Lambspring). As Mclean leads up to the latter example, he explains that:
The first layer of five emblems deal with the different facets of polarities in our inner world.
The second emblem shows a different aspect to polarities in the fight between the inner dragon and an armed knight (a St George figure) in the Forest of the Soul. In this emblem there is a sense that the polarities must struggle to overcome each other.
Next in Emblem 3 we have the beautiful picture of the meeting in a clearing in the forest of a magnificent Stag and a graceful Unicorn. The Stag as a symbol is often associated with the Sun and the Unicorn is usually linked with the Moon. These polarities are to be coupled together through the alchemist's work.
Next, in Emblem 4, the polarities are seen in their manifestation as masculine and feminine, pictured here in the meeting of Lion and Lioness. We note how they raise their opposite paws (Lion - right, Lioness - left) mirroring the posture of the Stag and Unicorn in the previous emblem.
The fifth emblem, which completes this part of the sequence shows the wild Wolf and the tamed Dog fighting for supremacy. These polarities are further linked in the verse with the directions West (Dog) and East (Wolf). Thus we can see that the first five emblems show us different ways in which the polarities appear in our inner world. The dynamically opposed though balanced way of the two fishes, the battling of the Dragon and Knight elements, or Wolf and Dog, and the meeting and relationship indicated in the Stag-Unicorn and Lion-Lioness emblems.
The next five emblems seem to indicate different ways in which we must inwardly work to unite these polarities in our beings.
Emblem 6 is a clear statement of the Ouroborus, the serpent dragon that siezes its own tail and unites these polarities in forming its circle in the Soul.
The next example (7 and 8) and following description:
"The symbol Ouroboros, a snake or dragon biting its own tail, engraved on a bronze receptacle from the Chou dynasty, China about 1200 B.C. The Ouroboros symbolizes the continuity of life, and intimates that each ending in a perpetual renewal corresponds to a new beginning. A suitable symbol for the life cycle philosophy"
were made available on the Internet by the Swedish Engineering concern ivf/ep (The Symbol Ouroboros.) while another representation of the ouroborus serves as the logo of the J.R. Ritman Library (Bibliotheca Philosophica Hermetica Site) in the Netherlands.
These are but a few representations of the Ouroboros; there are many others, some more ornate, some less, and many in more complex configurations, especially in the alchemical context. Moreover, as Jack Lindsay explains in The Origins of Alchemy in Græco-Roman Egypt, (1970, pp.267-268):1

Ideas about the Ouroboros found their way into the literary world, e.g., in Artemidoros and Acrobius. The former, in his dream-book, remarks that 'the dragon also signifies Time because it is long and undulant.' The latter declares the two-headed Roman god Janus is the world:
'that is, the heavens, and his name Janus comes from eundo [by going] since the world always goes rolling on itself in its globe-form ... So the Phoenicians have represented it in their temples as a dragon curled in a circle and devouring its tail, to denote the way in which the world feeds on itself and returns on itself ...

"It is also clear that it's the Sun honoured under the name of Mercurius [Hermes] according to the cadeuceus that the Egyptians have consecrated to the god in the figure of the Two Serpents, male and female, interlaced. Their upper extremities bend round together, and, embracing one another, form a circle, while the tails, after forming a knot, come together at the haft of the caduceus and are provided with wings that start off at this point.
Even more interesting is the passage that ends the second book of Claudian's poem, On the Consulship of Stilicho. Claudian came from Egypt and his imagery shows the Egyptian idea of the night-journey of the sun through the cave or tunnel in the earth. But the introduction of the Ouroboros in association with Natura (Physis), the various metals, and the Aged Seer strongly suggests one of the alchemic visions of revelation or initiation:

Far off, unknown, beyond the range of thought,
scarce reached by gods, the years' rough haggard mother,
stands a primeval Cave in whose vast breast,
is Time's cradle and womb. A Serpent encloses,
the Cave, consuming all things with slow power,
and green scales always glinting. Its mouth devours,
the backbent tail as with mute motion it traces,
its beginning. At the entrance Nature sits,
the threshold-guardian, aged and yet lovely,
and round her gather and flit on every side
Spirits. A Venerable Man writes down
immutable laws. He fixes the number of stars
in every constellation, makes some of them move and others hang at rest.
So all things live or die by predetermined laws...
When the Sun rested on the cave's wide threshold,
Nature ran in her might to meet him; the Old Man bent
grey hairs to the proud rays. Of its own accord
the admantine door swung open, revealing
the huge interior, displaying the House
the Secrets of Time. Here in appointed places
the Ages dwell, with varying Metals marking
their aspect. Those of brass are there upheaped,
there stiff the iron, there the silver gleaming;
shy of earth-contacts, in a distinguished section,
is set the flock of golden years."
From the above descriptions and the widespread occurrence of this Jungian archtype in both time and place it is also apparent that the Ouroboros embraces cyclic regeneration, rebirth, and the very foundations of life itself.

--------------------------------------------------------------------------------

B. SPIRA SOLARIS, ALCHEMY, AND EGYPT
The antiquity, complexity, and the wider presence of the Ouroboros in mythological contexts is discussed further in the following passage (Towards a Taxonomy of the Pure Ones Parallels within Gnosticism, Graeco-Roman Mythology and Hermeticism by Frater IAM, Magister Templi of the Ordo Rosae Crucis, 1994):
The next aeon, usually called the Aeon of Jupiter or Zeus, was created from Chronos and rebelled against it. The Greek Myth tells us that Chronos feared that his children would one day rebel as he had rebelled against his father, so he ate them. This could correspond to a will to stop the descent into matter by closing himself into an Ouroboros, the snake biting its own tail and incidentally also a symbol for the death/rebirth so intimately linked with Time. But this was broken by the stone Abadir (also called Baetylus) given to him by Rhea (who could in fact have been Ialdabaoth!), which he devoured instead of his son, who eventually defeated him. It is interesting to speculate if this stone is not the original archetype of the Holy Grail (which has been alternately described as a cup, a stonelight by different mystics) or the Philosophers Stone, which has the ability to open up the Ouroboros or close it". [emphasis supplied]

Here the speculation concerning the Ouroboros extends to embrace the philosopher's Stone, with the intriguing suggestion that the two are in a special relationship, one that points again to the subject of Alchemy.
In Section IV we have already examined the inter-related natures of the periods, distances and velocities pertaining to the Phi-series period spiral and the manner in which the outer and inner regions may be considered to feed back on one another. We have also touched upon the similar type of feedback inherent in the inverse-velocity phenomena evident in the modern Solar System and briefly considered the complications that arise from periodic variations in planetary motion in Section III. But there are additional themes running throughout all this with strong religious and biological undertones that link the whole with the Sun and its undoubted influence on life as we understand it. But to what exact degree such complexities and consequences were known and understood in the earlier period and the Middle Ages has still to be fully assessed. It would seem that great pains were taken to ensure that it was passed on, hence the multiplicity of methods, keys and approaches adopted - so much so, in fact that partial confusion may well have been an inevitable consequence. To this problem must also be added the waxing and waning of empires, changing religious beliefs, and the consequences of the Dark and Middle Ages. Perhaps it was originally intended that all roads should indeed lead to Rome - a location unfortunately rendered untenable by Roman degeneration and excesses which forced the disastrous relocation to Constantinople. In any event it would seem that it was not until the Middle Ages that the matter resurfaced, perhaps not entirely intact, but sufficiently coherent enough for its understanding among those who avidly studied the writings of the ancients. The resurgence of "Alchemy" in the Middle Ages on the other hand may have had both ancient origins and modern insights. Here again, Thomas Taylor supplies the linkage and incidentally the humour:2
They say, therefore, conformably to Cephalus, that the rich have many consolations.... if you are willing also, it may be said, that gold and silver, and each of the metals, as likewise other things, grow on earth, from the celestial Gods, and from an effluxion thence derived. It is said, therefore that gold pertains to the Sun, silver to the Moon, lead to Saturn, and iron to Mars. Hence these are generated from thence. But they subsist in the earth,. and not in the celestial Gods who emit the effluxions. For they do not receive anything from material natures." [Commentaries of Proclus on the Timæus of Plato, Book I, p. 36. (emphasis supplied)]
The references linking gold with the Sun, silver to the Moon, lead to Saturn, and iron to Mars are all clearly alchemical, even for those with only a passing knowledge of the subject. In more detail, however, it seems that one could present an argument that there was always more than the unlikely transformation of base metals into physical gold at stake here. In fact, a sound mathematical case can undoubtedly be made from extant writings that it was predominantly the "Golden" Section itself - the phi-based mean period of Mars and also the mean velocity of Mercury - in something akin to our present astronomical context that was always under consideration (e.g., mathematical transformations involving the black "lead" of Saturn, the "Tin" of Jupiter, the synodic "Oil" of "Antimony" and parameters pertaining to Mercury, Venus and Mars as discussed below). From this viewpoint, if "The Great Work" of the Alchemists was indeed essentially the preservation of a complex corpus of knowledge concerning the Sun and the structure of the Solar System, then the description is both apt and well-merited. And it is also a far more fitting and reasonable occupation for highly regarded scholars such as Francis Bacon, Robert Boyle and Sir Isaac Newton who (among others) became involved in this seemingly dubious enterprise.
It is not the intention here to discuss the multifarious aspects of Alchemy in detail, the subject is simply too vast and too complex for the present discourse. But to give some idea just how complex the matter can become, consider the following line of inquiry and where it ultimately leads, i.e., it is relevant to note that the erudite Thomas Taylor's comments concerning the construction of the universe in Plato's Timæus (33b) have some similarity with helpful (but equally cryptic) remarks provided near the end of an alchemical work (ca.1600 A.D.) entitled: The Twelve Keys of Basil Valentine. Thus Thomas Taylor states:3

It is well observed here by Proclus that, the whole universe being luminous, it is most lucid according to its external superficies, and full of divine splendour... But of this luminous subsistence smoothness is a symbol. Why, therefore, are the extremities of the universe smooth? We reply, That it may be harmoniously adapted to supermundane lights, through similitude to them. Smoothness, therefore, is significant of extreme aptitude, through which the universe is able to receive the illuminations proceeding from intellect and soul; just as mirrors, by their smoothness, receive the representations of things. Proclus further observes that a mirror was assumed by ancient theologists as a symbol of the aptitude of the universe to be filled with intellectual illumination. Hence, says he, they say that Vulcan made a mirror for Bacchus, into which the God, looking and beholding the image of himself, proceeded into the whole divisible fabrication. And you may say that the smoothness of the external surface of the universe, which is mentioned by Plato, reminds us of the above-mentioned catoptric apparatus." [emphasis supplied]
while "Basil Valentine" adds in The Twelve Keys :
As a parting kindness to you, I am constrained to add that the spirit may also be extracted from black Saturn and benevolent Jupiter. When it has been reduced to a sweet oil, we have a means of robbing the common liquid quicksilver of its vivacity, or rendering it firm and solid, as is also set forth in my book. [emphasis supplied]
The similarity lies in the mirroring of numeric values associated with the extremal locations of the planets Mercury and Saturn, i.e., the phi-series mean velocity for the synodic difference cycle between Jupiter and Saturn provides the value of 0.3819660112 which also occurs as the mean distance of Mercury and again as the mean synodic period between the latter and Venus (see Table 5a in Part IV for the complete relationship).
To understand the above it is necessary to recognize that the first astronomical parameters normally obtained from the observation of the planets and major luminaries are the periods of revolution. Subject to further observation and refinement, a planetary model and estimates for both the mean distances and the mean velocities may (or may not) follow. In the second context we are dealing with material that post-dates both the heliocentric model of Copernicus and the publication of Kepler's Harmonic Law (1618). We also know from the fundamental synodic period relationship given in Section Two that the intermediate mean synodic period (or mean lap time) for adjacent co-orbital bodies is obtained from the product of the mean sidereal periods divided by their difference. From the Phi-series mean periods for Jupiter and Saturn of 11.090169944 and 29.034441854 years respectively we therefore obtain an intermediate mean synodic period of: 17.944271910 years. The resulting period, the Harmonic Law (exponent = 2/3) and the velocity variant (exponent = -1/3) respectively produce a corresponding mean distance of 6.854101966 A.U and a mean relative velocity of 0.3819660112, the latter as noted above. Table 1 below provides the numeric data and a simple cipher that connects the "Period-Distance-Velocity" and "Soul-Body-Spirit" triads in the present context.


POSITION Planet/Synodic Phi N PERIOD "SOUL" DISTANCE "BODY" VELOCITY "SPIRIT"
MERCURY - 3 0.23606797 0.38196601 1.618033988
Synodic/(Oil) - 2 0.38196601 0.52644113 1.378240772
VENUS/Copper - 1 0.61803398 0.72556263 1.173984996
Synodic/Earth 0 1 1 1
MARS/Iron 1 1.61803398 1.37824077 0.851799642
(Asteriod Belt)

JUPITER/Tin 5 11.0901699 4.97308025 0.448422366
Syn./Antimony 6 17.9442719 6.85410196 0.381966011
SATURN/Lead 7 29.0344418 9.44660278 0.325358511

Table 1. The Phi-Series Planetary Framework, Mercury through Mars, and Jupiter
to Saturn. Unity provides the frame of reference, "Gold" = Phi = 1.6180339887499

In keeping with the hint provided by Thomas Taylor and Proclus ("Vulcan made a mirror for Bacchus, into which the God, looking and beholding the image of himself, proceeded into the whole divisible fabrication"), if one is aware that the mean period of Mercury is approximately 0.24 years and that Phi - 3 is 0.23606774 (years) the Harmonic Law yields the mean distance for Mercury from: (Phi- 3) 2/3 = Phi - 2 with the mean velocity similarly obtained from (Phi - 3) - 1/3 = Phi.1 This is perhaps looking at the matter in reverse (the mirror image, if you wish); one could also proceed forward from Table 1 to obtain both the harmonic law and the velocity variants from another direction altogether, but either way the reference to mirrors appears to be singularly appropriate as well as helpful. In passing one might also note that the mirror analogy includes the equality between the mean period ("Soul") of Mercury and the mean velocity ("spirit") of the next outer planet, Uranus; i.e., a mean sidereal period of 0.2360679774 Years in the first instance and a mean orbital velocity (relative to unity) of 0.2360679774 in the second. Unlikely, perhaps, but not entirely improbable, for in spite of its relatively recent discovery (by William Herschel in 1781), as Jeffrey K. Wagner observed in Introduction to the Solar System (Holt, Rinehart and Winston, Orlando, 1991:334) "Uranus is just bright enough to be visible to the naked eye, and it is surprising that it escaped detection for so long. Even a sharp eyed ancient Greek astronomer could have spotted it... 4

Those who balk at the inclusion of planetary velocities in the above context in general might wish to consider Thomas Taylor's translation of the commentary by Proclus on "The Construction of the World Soul" (Book III: The TIMÆUS OF PLATO): 5

He first took one part from the whole. In the next place he took away the double of this.
And after this, a third part, which was sequialter indeed of the second, but triple of the first. [Timæus, 35b:]
We have observed, that it is not proper to understand what is here said by Plato, mathematically, but physically, or philosophically. For the essence of the soul, does not consist of mathematical numbers and ratios, but all these numbers and ratios, adumbrate its truly existing essence, and the demiurgic and vivific divisions in it. But of what things the mathematical ratios are images, and how they develop the essence of the soul of the universe, it is not easy for those to assign, who do not look to the conceptions of Plato. But this is manifest from the discord of the interpreters; and the opposition of the modern to the more ancient expositors, evinces the difficulty of this theory. For some of them think fit to refer to the seven spheres, the first seven terms, to which we have assumed as analogous the numbers that exhibit the whole diagram. But others refer them to the distances of the spheres from the center of the earth, in which place they arrange the monad. Others again, refer them to the motions of the spheres. [Others the magnitudes of the stars. And others adapt them to the velocities of the celestial orbs.] But others, refer them to other such like explanations. Their interpretations, however, are attended with many difficulties, and among the rest with this, that they are discordant with the observations of recent astronomers, and to the demonstrations given by them. To which it may also be added that Plato nowhere defines, either the magnitude, or the distance, or the swiftness, or the motion of the stars; but admitting that one star is greater than another, he does not add how much, and after what manner, it is greater. And that the thing proposed by him to be discussed in this part is psychogony, and not cosmogony {hereafter follows a discussion of various interpretations, etc,}. [Vol II, Book III, pp. 89-90; emphases supplied].
The part that refers to "magnitudes" and "velocities" (included by Thomas Taylor in square brackets) is from the obscure writings of Nicholæus Leonicus Thomæus.
The triadic sets: Period/Distance/Velocity and Soul/Body/Spirit represent a specialized application of what appears to have been a wider comprehension of the nature of the Soul. Proclus, for example, tells us [The Commentaries of Proclus on the Timeus of Plato, transl. Thomas Taylor, Kessinger Books, Kila, pp.115-118; the emphases are also Thomas Taylor's]: 6

... we may say, that a line is adapted to the soul. For intellect indeed, though some should give it motion, yet it has this energy intransitive. For it surveys at once the whole of the intelligible, having an eternal life, and energizing about the same things, in the same nature, according to the same. But soul possesses a transitive energy. For at different times, it applies itself to different forms, and this is true even of the soul of the universe. For, as Plato says in the Phaedrus, it is the peculiarity of soul to energize through time. But every transitive motion is a line. For it has whence and whither, and the rectilinear, and one thing for the beginning, and another for the end. So that in this respect we refer a line to psychical life.
... In what is said, therefore, about the admixture of the soul, and also in what is said concerning numbers and middles, Plato unfolds the being itself of the soul, and shows how it is one and many, what progression it has, and what regressions both to superior natures, and to itself; how it produces and converts things posterior to itself; how it fills ratios, and binds together the whole world. But in what he says concerning the right line and circles, he delivers to us the vital and intellectual peculiarity of the soul, and indicates how it participates of the life in intellect, and how it is converted to itself, so far as it is self-vital and self-moved.
...In short therefore, the essence of the soul, being a whole and consisting of parts, is harmonized number. But its life is rectilinear, and is uniform and biformed.. And its intellect is dianetic and doxastic. For there are in it being, life, and intellect. Or rather prior to the gnostic, perceiving that the vital powers are in themselves at one and the same time transitive, and self-motive, we must say, that the right line adumbrates the transitive, but the circle, the self-motive nature of these powers. For they are moved from themselves to themselves. Hence Timeus delivering to us in what is here said, the vital motion by itself alone, assumes the rectilinear, and the circular motion, but in what follows unfolds the gnostic motions of the circles; the soul now becoming self-motive, in consequence of the whole of it moving itself. If therefore, we now admit that the right lines are lives, and these essential; on which account also, the Demiurgus made the composition of the soul itself to be rectilinear, as possessing life by its very existence;--if we admit this, then we must say, that the circle manifests what the quality is of the form of this life, viz. that it is self-moved, beginning from, and returning to itself; and that it is not like the life of irrational natures, tending to externals as it were in a right line, as never being able to converge to itself, and as having an appetite directed to other things placed externally to itself. For the self-motive nature is moved from itself to itself, sees itself, and is present with itself. Hence also, such a form of life as this is circular. For in a circle, the same thing is the end and the beginning, in the same manner as in that which is converted to, begins from, and ends in itself. The right line therefore and the circle of the soul, are without interval; the former being the image of life [simply], but the latter of life converting to itself, and not absolutely of all life. For both these may be surveyed in souls; the right line indeed, according to the transitions of appetites; but the circle according to a circumduction from the same thing to the same. And this Socrates knowing, says in the Phaedrus, that souls are carried round in a circle, revolving under intelligibles as objects of desire, being at different times happily affected by different things, and returning from the same objects to the same. Why therefore, should we any longer fear those skillful Peripatetics who ask us, what kind of line Plato here assumes ? Is it physical line ? But this would be absurd: for this is the end of bodies. Is it then a mathematical line ? But this is not self-motive, and is not essence: Plato however says, that the soul is an essence, and is separate from bodies. We say therefore, that they in vain make these inquiries. For long before this, we have not ceased asserting that this line is essential. And prior to us Xenocrates calls a line of this kind indivisible. For it would be ridiculous in any one to think that there is an indivisible magnitude. It is evident however, that Xenocrates thought it requisite to call the essential reason of a line an indivisible line. But Plato, for the sake of concealment, employed mathematical names, as veils of the truth of things, in the same manner as theologists employed fables, and the Pythagoreans symbols. For it is possible in images to survey paradigms, and through the former to pass to the latter. Against such men however, as these Peripatetics, who are contentious, no arguments are sufficient. But let us return to the words of Plato, and direct our attention to each of them.
Since therefore, the soul is one, is divided according to its parts, and is both one and many, Plato denominates it this, as being one, but all, as being multitude, and composition, as both; which also shows that the essence of it differs both from things discrete, and things continuous. For these are without communion with each other. But the soul is one, and at the same time multitude, and is discrete, and continued. Since however the psychical reasons are biformed; for the soul is of an ambiguous nature, and has two faces, conformably to its paradigm, so that it intellectually perceives the impartible essence through the circle of the same, but contains and connects the partible essence, through the circle of the different; --hence Plato calls it double. But because it has the same reasons or ratios, above and beneath, and not as some fancy, the duple ratios here, but the triple there, on this account, he delivers it to us divided according to length. For this division alone, preserves every where the same ratios. But the scission itself exhibits demiurgic section, which is appropriate to the Demiurgus. For the duad is seated by him, and is refulgent with intellectual sections, as some one of the Gods says. Moreover, the words "middle to middle" indicate perhaps, that the division and contact of things intangible, are adapted to the psychical middle: for they subsist in a middle way. For in intellect also there is division, because there is difference, but it subsists primarily, and as it were occultly, and indivisibly. In sensibles likewise there is division, but according to an ultimate distribution into parts. Hence also the union in these is obscure and evanescent. But in the soul both have a middle subsistence, in a way adapted to it. And if indeed Plato had spoken concerning intellect and soul, he would have said, that the Demiurgus applied the.first to the middle, and if about body and soul, that he applied the middle to the last. But since he teaches us concerning the psychical duad, lie says that the Demiurgus applied middle to middle. Perhaps too, he says this, because the contact of the soul is properly of a middle nature. For the last part of the dianoetic. and the summit of the doxastic power, form tile media of all tile psychical composition. But these are conjoined to each other, and conformably to these, one union is produced of these two lives. For in every order of beings, the bases of first are united to the summits of secondary natures. The figure X however, produced by this application, has a great affinity to the universe, and also to the soul. And as Porphyry relates, a character of this kind, vis. X, surrounded by a circle, is with the Egyptians a symbol of the mundane soul. For perhaps it signifies, through the right lines indeed, the biformed progression of the soul, but through the circle its uniform life, and regression according to an intellectual circle. We must not however conceive, that Plato thought a divine essence could be discovered through these things. For the truth of real beings cannot, as some fancy, be known from characters, positions, and vocal emissions. But these are after another manner symbols of divine natures. For as a certain motion, so likewise a certain figure. and colour, are symbols of this kind, as the initiators into mysteries say. For different characters and also different signatures are adapted to different Gods; just as the present character is adapted to the soul. For the complication of the right lines indicates the union of a biformed life. For a right line itself also, is a symbol of a life which flows from on high. In order however, that we may not, omitting the things themselves, be too busily employed about. the theory of the character, Plato adds "as it were," indicating that this is assumed as a veil, and for the sake of concealment, thus endeavouring to invest with figure the unfigured nature of the soul.
Returning to the relative simplicity of the triadic sets in question, with respect to both inferior planets (Mercury and Venus), Earth, and Mars it should be noted that the mean velocity (or "Spirit") of Mercury is itself the "Golden Ratio" Phi = 1.6180339887499 while the inverse (0.61803989 ) represents the mean period of revolution of Venus. Lastly, Phi (1.618033989) is in turn the mean period of revolution of Mars. These special inter-relationships are stated (albeit cryptically) in further alchemical works, i.e., The philosophical canons of Paracelus in the 17th Century Sloane Ms 3506, and An hundred aphorisms containing the whole body of magic, in Sloane Ms 1321 (both transcribed by Adam Mclean). In the first, bearing in mind the relationship between the two triadic sets, "Gold," Mars, and Mercury, we find the following aphorisms:
12. The sulphur of Mars is the best, and this joined with the sulphur of gold makes a medicine.
14. Nature makes and generates minerals by degrees, also out of one root are generated all metals till the end of all which is gold.
39. The Sulphur is the soul, but the Mercury is the matter.
49. They who take the Sulphur of Venus are cheated.
56. The Mercury receives the form of gold by the mediation of the spirit.
57. Gold resolved into Mercury is spirit and soul.
145. The highest secret of all is to know that Mercury is both matter and Menstruum, and that the Mercury of perfect bodies is the form.
152. The greatest arcanum of the work, is the physical dissolution into Mercury, and reduction into Mercury.
Aphorism 14 is undoubtedly correct as far as the Phi-series planetary framework is concerned since all the mean parameters (periods, distances and velocities) may be consistantly expressed as fractional exponents of Phi as shown earlier in Table 5a. Moreover, in so much as the period/soul of Venus is both Phi -1 and the reciprocal of Phi Aphorism 49 also quite appropriate. Aphorism 56 is correct. Aphorism 57 provides a succinct summation of the relationship between the velocity/spirit of Mercury and the period/soul of Mars as shown in Table 1.
The second reference is divided into three parts with the first concerned with "Twelve conclusions upon the Nature of the Soul ". Statements 1 through 11 are from this source; the remainder are from additional sections:

1. The whole world is animated with the first supreme and intellectual Soul possessing in itself the seminary reasons of all things, which proceeding from the brightness of the ideas of the first Intellect are as it were the instrument by which this great body is governed and are the links of the golden chain of providence.
2. While the operations of the Soul are terminated or bounded, the body is generated or produced out of the power of the Soul, and is diversely formed according to the imagination thereof, hence it hath the denominating power over the body which it could not have except the body did fully and wholly depend upon it.
3. In this production whilst the Soul fashions to itself a body, there is some third thing the mean between them both by which the Soul is now inwardly joined to the body, and by which the operation of all natural things are dispensed, and this is called the Vital Spirit.
9. This Spirit is somewhere or rather every where found as it were free from the body, and he that knows how to join it with a body agreeably, possesses a treasure better than all the riches of the world.
11. The organs by which this Spirit works are the qualities of things, which merely and purely considered are able to do no more than the eyes can see without life, as being nothing else but modification of the matter of the body.
15. Neither Souls nor pure Spirits, nor Intelligences can work upon bodies but by means of this Spirit, for two extremes cannot be joined without a mean ...
18. In generation the Spirit is mixed with the body, and directs the intent of Nature to its end.
64. By natural application it is done when the Spirit of one body is implanted in another, by means of those things which are apt to intercept the Spirit, and to communicate it to another, and they are known by the signature, and by the ancients called amatoria or such things as love one another. [emphases supplied]
Before returning to "antimony," it is clear from Table 1 that "Gold" ( Phi,1.6180339887499), the mean velocity of Mercury, and the mean period/soul of Mars ("iron") are identical. This relationship may well have provided the basis for the allegorical "War of the Knights" by Johann Sternhals (1595) concerning the resolution of the "conflict," i.e.,.

"The Lord Chief Justice pronounced sentence to the quarreling and disputing metals, introduced in this Allegory by Sternhals as so many Knights. The Judge's name was Mercury."
Mercury says to Gold:
'Whilst Thou, O Gold, as plaintiff against Iron, appeal to me concerning thy nobility and nature, and as I am well acquainted with thy origin but am likewise no stranger to the nature, property, and operation of the defendant Iron, I can, for the sake of truth and justice, not omit to declare that you have both boasted of great things, which none of you separately can verify. Thou, Gold, knowest well if I Mercury do not deal kindly with thee and unite with thee in perpetual love and harmony, that thy power over the diseased Knights (the inferior metals) is nothing! Thou hast mentioned my perfect knowledge of thy exalted state amongst the Knights. Thou hast spoken rightly, because thy nature and power proceed from mine (from the Sophic or animated Mercury). Thy nature must be retrograded and converted into mine, if thou meanest ever to be of any service to the diseased poor knights.'
'Thou, Defendant, O Iron, knowest well that I do perfectly understand thy nature and complexion Thou canst much less than Gold effect anything useful without my assistance; and I, Mercury, am a declared enemy to thy external dirty appearance and thy dirty works. Therefore, I complain justly against you both!'
'Yet, from a motive of special goodness and friendship towards my fellow-creatures, I will never refuse to grant to thee, O Iron, a power to procure riches, and I have often given thee that power, as thou well knowest when thou and I did sweat in our hot bath and dried ourselves afterwards. Recollect then what friendship and services we rendered to Lady Luna, which we are able to do again, if we please. Which, however, thou canst not do without my assistance. I must further tell you both (Iron and Gold) that you stand both in need of my counsel and help, whilst I can do with very little of your assistance.'
'Thou, Gold, hast said that thou art the true Stone, about which the Philosophers contest. Dost thou not know that there are greater, nobler, and more powerful subjects than thee? and all other metals containing the four elements as well as they do. Dost thou not know that there is a mother of all metals and their greatest substance? All things have been subdued unto man! and thou haughty Gold do not elevate thyself too much, as there are creatures of God far above thee in power and virtue!'
'I then,' continued the supreme Lord, Mercury, 'unite you both, Iron and Gold, with a perpetual union.'
'Thou, Gold, shalt henceforth not vex nor despise Iron, but I order thee to make good use of its noble beautiful red flowers (when a crocus Mars is sublimated with Sal Ammoniac, it ascends in beautiful red flowers - this must be repeated three or four times) which Iron has got in his garden for the sake of multiplying thy active power. Thou shalt unite with Iron in friendship.'
'And thou, Iron! I order thee to accept and make use of the sweet heaven or ferment of Gold for thy good and nourishment.'
And thus they departed, united in friendship to be of use to all that knew them. [ Sigismund Backstrom's embedded notes are omitted for clarity]
With respect to alchemical "metals" in general, "Antimony" also looms large - a "metal" that in fact attracted Isaac Newton's attention (see: Newton And Flamel On Star Regulus Of Antimony And Iron Part 1, by Mark House and also the numeric relationship between "Iron" and "Antimony" in the Biblical Aesch-Mezareph). In such contexts it would appear that there were two types of "Antimony," the first (in the positional and also the numerical sense) between the "Iron" of Mars and the "Tin" of Jupiter, and the second ("Saturnine Antimony") similarly positioned between the "Tin" of Jupiter and the "Lead" of Saturn, i.e., the Jupiter-Saturn synodic cycle, or as Basil Valenttine informs the reader in his Triumphal Chariot of Antimony: "By our Art it (antimony) can also become an oil." The Secret Book of Artephius notes also that: "Antimony is a mineral participating of saturnine parts, and has in all respects the nature thereof. This saturnine antimony agrees with sol, and contains in itself argent vive, in which no metal is swallowed up, except gold, and gold is truly swallowed up by this antimonial argent vive..." The same source later states that: "... there is a double substance of argentum vivum, the one from antimony, and the other from mercury sublimated, it does give a double weight and substance of fixed argent vive, and also augments therein the native color, weight, substance and tincture thereof." Moreover, Betty Jo Teeter Dobbs, in The foundations of Newton's Alchemy (1975) discusses the occurrence of a special symbol introduced by Isaac Newton in some of his later alchemical writings that may have some bearing on our present discussion. After tentatively assigning the name "quintessentia" to the symbol in question Dobbs explains that: 7
Some pages of the manuscript seem to identify the quintessence with antimony (presumably the ore), but another renders the symbol ...as "Bism,." probably meaning an ore of bismuth. Either of these designations would at least make it appear to have been a concrete substance to Newton, yet elsewhere in the same manuscript he defined the quintessence as a "corporeal spirit" and a "spiritual body" and the "condensed spirit of the world."(The foundations of Newton's Alchemy, Cambridge University Press, Cambridge, 1975:165)
Table 1 shows that the "Spirit" of "Saturnine Antimony" (the mean velocity of the Saturn-Jupiter synodic cycel) is equal to the "body" (mean distance) of Mercury and it also follows that this parameter may in turn be reduced from the "Spirit" (mean velocity) of Mercury, itself the golden ratio, etc. On a more general but nevertheless ourobotic level, Roger Bacon's Tract on the Tincture and Oil of Antimony also contains the following aside:

"The Philosophers, when they have thus prepared our Antimonium in secret, have remarked how its outermost nature and power has collapsed into its interior, and its interior thrown out and has now become an oil that lies hidden in its innermost and depth, well prepared and ready." [emphasis supplied].

Those who feel that "Antimony" in this context is more reasonably construed in terms of metallurgy, chemistry, or medicine might wish to consider the following words of caution expressed by Basil Valentine in The Triumphal Chariot of Antimony:
Many Anatomists have subjected Antimony to all manner of singular torments and excruciating processes, which it is difficult either to believe or to describe. Their studies have led to no result, because they did not seek the true soul of Antimony, and, therefore, did not soon find that fictitious soul of which they were in search their path being obscured with black colours which rendered invisible what they desired to see. Antimony, like Mercury, is comparable to a circle, without beginning or end, composed of all colours; and the more is always found in it, the more diligent and prudent the search which is made. One man's life is too short to discover all these mysteries. [emphasis supplied]
The latter writer also provides an additional cautionary remark in The Twelve Keys along with the following expansion:
Know that our seed is produced in the following way. A celestial influence descends from above, by the decree and ordinance of God, and mingles with the astral proper ties. When this union has taken place, the two bring forth a third namely, an earth-like substance, which is the principle of our seed, of its first source, so that it can shew an ancestry, and from which three the elements, such as water, air, and earth, take their origin. These elements work underground in the form of fire, and there produce what Hermes, and all who have preceded me, call the three first principles, viz., the internal soul, the impalpable spirit, and visible bodies, beyond which we can find no earlier beginning of our Magistery. In the course of time these three unite, and are changed through the action of fire into a palpable substance, viz., quicksilver, sulphur, and salt. If these three substances be mixed, they are hardened and coagulated into a perfect body, which represents the seed chosen and appointed by the Creator. This is a most important and certain truth. If the metallic soul, the metallic spirit, and the metallic form of body be present, there will also be metallic quicksilver, metallic sulphur, and metallic salt, which together make up the perfect metallic body. If you cannot perceive what you ought to understand herein, you should not devote yourself to the study of philosophy. [emphasis supplied]
Moreover, the relationships between Antimony, Mars, Venus and Mercury are also stated in alchemical Aphorisms 117 and 119 below (source: 153 Chymical Aphorisms, ca.1680):
Aph. 111. And among Minerals there is none found which can perfect the colour of pale Gold, and facilitate its Flux, and render it more penetrating, but Antimony only.
Aph. 112. Therefore that appeareth to be the only Mineral, of which, and by which, the said Mercury may be obtained.
Aph. 113. For, seeing that Antimony cannot communicate more Tincture to Gold, than the natural perfection of Gold requireth
Aph. 114. And Gold, as hath been already said, ought to be more perfectly Tinged by the Mercury of philosophers.
Aph. 115. This Mercury cannot be had of Antimony alone;
Aph. 116. But by it, as a Medium, from other imperfect Metallick Bodies, which abound with the Tincture of Gold;
Aph. 117. Of which sort there are found only two, to wit, Mars and Venus.
Aph. 118. Whence we conclude, That of Antimony, and by its help, of Mars also, and Venus, our Royal Menstruum is to be elicited, by the work of Art and Nature.
Aph. 119. Antimony, Mars and Venus, consist of Sulphur and Mercury. [italics supplied]
Numerically, in this and similar contexts, it would therefore appear that "soul" can be equated with the mean period of revolution, "body" with the mean distance, and "spirit" with the mean velocity; for as The Book of Krates says, 'Know that copper, just like a man, has a spirit and a body' (Jack Lindsay, p.113) while in the writings of Kleopatra it is also stated that: "...the body and the soul and the spirit were all united in love and had become one: in which unity and the mystery has been concealed." (Lindsay, p.259).8
This representation appears to be one of a number of triadic keys and much further analysis will be required to clarify them all. Moreover, matters do not necessarily become simpler as as result, e.g., the symbolism also expands to include (among other things) animals of the land, denizens of the sea, and birds of the air, etc (see: Animal Symbolism in the Alchemical Tradition and The Birds in Alchemy by Adam McLean).
In case it is assumed that "alchemy" can be completely deciphered from the above information alone, it is necessary to point out that the significance of the Moon has been omitted here and the various terms and names associated with the subject are still as confusingly intermingled as the names of the Heroes and Gods of the ancient Greeks. For example, in an Arab MS called The Twelve Chapters by Ostanes the Philosopher on the Philosopher's Stone we find that: 9

"The style of the Twelve Chapters shows that it derives from the period when alchemic ideas were set out in elaborate rhetorical fashion, with much antithesis and heaping-up of synonyms. But the essential ideas are much earlier; and as the points are strongly and clearly made, we may cite some more passages that seek to stress the paradoxical nature of the secret. Needless to say, the Aristotle here cited is an apocryphal figure:
'I have heard Aristotle say: 'Why do these seekers turn away from the stone? It is however well known thing, characterised, existent, possible,'
"I replied, 'What are its qualities? Where is it found? What is its possibility?
He told me. 'I'll characterise it by telling you it's like lightning on a dark night. How can one fail to recognise something white showing up against a black background? The separation isn't painful for anyone accustomed to distance. Night cannot be dubious for him who owns two eyes.' [emphasis supplied]
"Another Sage has said: 'I've lived now forty years and I've never spent a single day without seeing the Stone day and night so well that I was fearing nobody could help seeing it too. I then used yet more enigmatic expressions than those I'd used at first and I have increased the obscurity of the phrases out of fear that their sense was already too plain.'
'Know then that the authors in their books have used a great number of words to denote the Stone. I'm going to mention the easiest ones. Leaving aside the majority of such words and choosing those which are, as far as I know, the ones best known in the world. It is called:
Lion, dragon, serpent, viper, scorpion, water,
fire, torrent, congealed or dissolved [body], vinegar,
salt, dog, Hermes, mercury, jackal, page,
serving-maid, gazelle, courser, wolf, panther, monkey,
sulphur, arsenic, tutty, foam of silver, iron,
copper, lead, tin, silver, gold, talc,
tulac, tirac, tarc, dumb man, oppressor, submitted[being]
magnet, fat, spirit, soul, oil, collyrium,
urine, bone, vein, Saturn,Barkis[Balti=Venus?],
Mars, Sun, Moon.' [emphasis supplied]
From a somewhat wider viewpoint there is also the following description of the "Stone" provided in another alchemical treatise, The Glory of the World, (ca.1620):
I have called it by various names, but the simplest is perhaps that of "Hyle," or first principle of all things. It is also denominated the One Stone of the Philosophers, composed of hostile elements, the Stone of the Sun. the Stone of the Metals, the runaway slave, the aeriform Stone, the Thirnian Stone, Magnesia, the corporeal Stone, the Stone of the jewel, the Stone of the free, the golden Stone, the fountain of earthly things, Xelis, or Silex (flint), Xidar, or Radix (root), Atrop, or Porta (gate). By these and many other names it is called, yet it is only one.
Next, it is worth repeating here Jack Linday's assessment of the Ouroborus in alchemical contexts:10
In the symbolism of Kleopatra and the alchemists in general, then, the Ouroboros was used to represent the All, which was One, in its aspect of Time: that is, as a system in a ceaseless development, yet revealing a comprehensive structure which could be defined in the triadic formula. (The Origins of Alchemy in Graeco-Roman Egypt, 1970:265.)
Lastly, although the inter-relationships between the mean planetary periods, mean distances and mean velocities have been discussed here largely in tabular form, there are rare references to the spiral configuration and further allusions to the Ouroborus in other alchemical works. In a very small selection from: The Hermetic Arcanum, ca.1623 ("The Secret Work of the Hermetic Philosophy, The work of an anonymous author, penes nos unda tagi") for example, we find the following information: 11
61. The extremes of the Stone are natural Argent vive and perfect Elixir: the middle parts which lie between, by help whereof the work goes on, are of three sorts; for they either belong unto matter, or operations, or demonstrative signs: the whole work is perfected by these extremes and means.
63. The operative means (which are also called the Keys of theWork) are four: the first is Solution or Liquefaction; the second is Ablution; the third Reduction; the fourth Fixation. By Liquefaction bodiescreate the Jupiter of Saturn, which is done by the conversion of the Body into Spirit. The Office of Reduction is to restore the soul to the stone exanimated, and to nourish it with dew and spiritual milk, until it shall attain unto perfect strength. In both these latter operations the Dragon rageth against himself, and by devouring his tail, doth wholly exhaust himself, and at length is turned into the Stone. Lastly, the operation of the Fixation fixeth both the White and the Red Sulphurs upon their fixed body, by the mediation of the spiritual tincture; it decocteth the Leaven or Ferment by degrees ripeneth things unripe, and sweeteneth the bitter. In fine by penetrating and tincturing the flowing Elixir it generateth, perfecteth, and lastly, raiseth it up to the height of sublimity. return into their first form, things concocted are made raw again and the combination between the position and negative is effected, from whence the Crow is generated lastly the Stone is divided into four confused elements, which happeneth by the retrogradation of the Luminaries. The Ablution teacheth how to make the Crow white, and to
83. The Circulation of the Elements is performed by a double Whorl, by the greater or extended and the less or contracted. The Whorl extended fixeth all the Elements of the Earth, and its circle is not finished unless the work of Sulphur be perfected. The revolution of the minor Whorl is terminated by the extraction and preparation of every Element. Now in this Whorl there are three Circles placed, which always and variously move the Matter, by an Erratic and Intricate Motion, and do often (seven times at least) drive about every Element, in order succeeding one another, and so agreeable, that if one shall be wanting the labour of the rest is made void. These Circulations are Nature's Instruments, whereby the Elements are prepared. Let the Philosopher therefore consider the progress of Nature in the Physical Tract, more fully described for this very end. [emphases supplied
The above discussion began with a relatively limited inquiry concerning "Antimony" and as a consequence it skimmed over colors, properties, animal symbolism, medicinal aspects, alchemical "recipes," and wider issues associated with religious beliefs and origins. But even though the subject is to some extent shrouded by secrecy it can nevertheless still be examined in terms of methodology and mathematics rather than numerology or mysticism. Such analysis is undoubtedly hindered by the proliferation of names, the many allegories, and the diversity of methods employed; for one last example, see the erudite H. P. Blavatsky's minor Kabbalistic excursion into the numbers of the "Dove," the "Raven," and the approximation Pi = 355/113 in "The Mystery of Blackness," The Secret Doctrine (2-12). - a work that is dated in some respects yet timeless in another:
Fortunately, in spite of many complications, the Great Work of the Alchemists appears to be a continuing process. There is in fact a wealth of Alchemical material now available, especially on the Internet, thanks largely to the massive presence of the Alchemy Web Site. organised by Adam McLean, the Bibliotheca Philosphica Hermetica in Holland, and works such as The Pythagorean Pentacle and The Rotation of the Elements by John Opsopaus - the latter replete with three-dimensional spiral, the ouroboros and an initial quotation by the alchemist George Ripley (1490) of some significance:

"When thou hast made the quadrangle round, Then is all the secret found ..."

 

--------------------------------------------------------------------------------

E G Y P T
For our present purposes, however, it is necessary to again consider origins and the links between Ancient Greece, Mesopotamia and Egypt. The source in this case is "Alchemy in Islamic Times" by Prof. Hamed Abdel-reheem Ead (University of Cairo Giza-Egypt and director of Science Heritage Center). A partial listing from this source is given below with emphasis on those of the Greek school already discussed; additional emphasis on the Egyptian contribution appears necessary to put the matter in its proper historical perspective before proceeding further.
"Pythagoras (Fithaghurus)
Pythagoras is often mentioned in Arabic philosophy and in gnomic literature. Jaldaki calls him al-muallim al-awwal because he acquired the science from hermetic texts. Jabir refers to him as an alchemic author and speaks of Ta'ifat Fthaghurus, the school of Pythagoras, and of his book Kitab almusahhahat (Book of Adjustments). Other quotations refer to Pythagoras's theory of numbers. Tughra'i mentions him several times and refers to his treatise about 'natural numbers'. The fragments of texts which are attributed to him could have come either from Turba philosophorum, where he is among the participants, or from other texts.
Socrates
Socrates is considered not only as a wise man but also as an alchemist. Jabir calls him 'the father and mother of all philosophers' and considers him as the prototype of the real chemist. From Socrates to Jabir, there is a continuous tradition which attributes entire treatises to him. Jabir affirms that Socrates was opposed to the writing down of alchemic knowledge to avoid its exposition to the ignorance of the masses. Most references to Socrates refer to his arithmetical speculations (theory of the balance) and also to artificial generation.
Plato (Aflatun)
Olympiodorus already (at the end of the sixth century) considered Plato as an alchemist and Ibn al-Nadlm mentions him in the list of alchemists. Butrus al-Ilmlml mentions an alchemic device called, hammam Aflatun (Plato's bath). Among the books attributed to him by the Arabs we can mention the Summa Platonis of which we only have the Latin version. There is a commentary to this book - the Kitab al-Rawabi' - whose Arabic text was edited by Badawi and whose Latin translation is known by the name Liber quartorum. The contents of this work are mainly alchemic but it contains also information on geometry, physiology and astrology. The ancient authors cited are Plato, Aristotle, Ptolemy, Hipparchus, Proclus, the Sophists, Ostanes, Hermes, Asclepius and Hippocrates....
Aristotle (Aristu)
Aristotle is considered as an alchemist author not so much because of his fourth book Meteorologica but because of his reputation as an all-round scholar. He wrote a book on alchemy for his disciple Alexander. In 618, by order of Heraclius, the book was translated into Syriac by the monk Jean, and the Bishop of Nisibis, Eliyya bar Shinaya, made sure of its orthodoxy. Finally Abdishu' bar Brika, Bishop of Sinjar, and later of Nisibis, made a commentary on it in Syriac of which there still exists an Arabic translation. The text contains an introduction in which Abdlshu reports the legendary history of the text followed by a Ietter from Alexander to Aristotle where the former poses questions to which the latter responds. This dialogue is called sahifat kanz Allah al-akbar (Epistle of the Great Treasure of God). it includes three chapters: (1) About the great principles of alchemy; (2) Alchemic operations; (3) The elixir. Pythagoras, Democritus, Asclepiades, Hermes, Plato, Ostanes and Balmas are mentioned in the text....
Bolos the Democritean of Mendes
Bolos the Democritean lived in the second century before Christ. The work of this scholar is varied: alchemy, astrology, medicine.... the school of Bolos brings to the Egyptian technique a philosophical reasoning which will open the way to the science of the Great Work. 'Once again', says Festugiere, 'we see the union of the Greek spirit and the Oriental art.' The art exists, from ancient times; the goldsmiths of Egypt work metals, stones and purple... About the same time alchemy was practiced in most Egyptian towns. This first alchemy is a mixture of hermetic or Gnostic elements and old Greek philosophy: Heraclitus, Empedocles and their speculations about the four elements, Parmenides with his theory on the unity of the whole, the Platonic cosmogony of Timaeus. [emphasis supplied]
Zosimus
The most famous character of this time is Zosimus of Panopolis (Akhmim, in Upper Egypt). He probably lived at the end of the third and beginning of the fourth century...Zosimus can be placed at the end of an evolution in alchemy. With Bolos, it became philosophical; with Zosimus it becomes a mystical religion where the idea of salvation is predominant. In fact, the period which separates Bolos the Democritean from Zosimus saw intense alchemic activity. Vastly different elements - Egyptian magic, Greek philosophy, neo-Platonism, Babylonian astrology, Christian theology, pagan mythology - can be found in Zosimus' texts. He is full of gnostic and hermetic books, he knows the Jewish speculations about the Old Testament. He gives to alchemy a religious character which will remain forever, at least in its traditional course, since with the Arab alchemists it will retain its concrete technical character before meeting the Ismaeli gnostic speculations.
Zosimus and his contemporaries who collected their predecessors' traditions insist on their connection with the Egypt of the Pharaohs or with the Persia of Zoroastra and Ostanes. We can find texts under the name of Agathodaimon compared with Hermes....
This Greek-Egyptian alchemy survived in Alexandria for several centuries. From here it will go to Constantinople, where several recensions of the 'collection of Greek alchemists' were compiled, and to the Arabs when they conquered Egypt in the seventh century.
Hermes and Hermetic literature
According to Ibn al-Nadlm (351, 19) Arab alchemists considered the Babylonian Hermes as the first one to have mentioned the art of alchemy. Exiled by his countrymen, he came to Egypt where he became king. He wrote a certain number of books on alchemy and was equally interested in the study of the hidden forces of nature." [emphases and italics supplied]
Further information concerning the roles played by Bolos, Zosimos and especially Hermes may be found in Jack Lindsay's The Origins of Alchemy in Graeco-Roman Egypt [1970], who informs the reader, among other things, that:12
Zosimos looked to Hermes as the originator of the notion of the alchemic process as triadic. 'The present [chemical] composition, once set in movement, leaves the state of monad in order to constitute itself as a triad by driving out the mercury. Constituted as a monad that overflows as a triad, it is a continuum; but in return, constituted as a triad with three separated elements, it constitutes the world by the providence of the First Author, Cause and Demiurge of Creation, who henceforth is called Trismegistos in the sense that he has envisaged what he produced, and what produces it, under a triadic mode.' This important statement deepens the triadic concept by applying it directly to the moment of change, in which simultaneously there occur an act of union and an act of expulsion, of negation. This pattern is not a chance product, it is something that has only a limited application; it is the creative or formative pattern of all process. The alchemist is re-enacting the role of the demiurge.
At which point we arrive back at the Triad and to some extent the Oracles to take up the occurrence of the universal constant phi, this time its underlying importance in the construction of major monuments in Ancient Egypt - a topic treated at length by R.A.Schwaller de Lubicz [1891-1962] with respect to the construction the Temple of Luxor (Le Temple de l'Homme).13 The latter's "symbolist" interpretations were subsequently championed by John Anthony West and made generally available by West's 1978 publication Serpent in the Sky. Because of the significance of Phi in both these works West gave considerable space to the topic, and in addition suggested that:14
Perhaps the greatest single achievement within Schwaller de Lubricz's reinterpretation is the solution of the ultimate meaning of the Golden Section - a problem that has occupied many of the greatest thinkers and artists of history. When this significance is divulged, the reader may well be puzzled as to why so apparently elementary an explanation should have remained a mystery so long. Yet the fact is that the solution eluded the genius of Leonardo and of Kepler, of a number of brilliant modern biologists, and a host of astute artists and researchers in aesthetics. The answer to the mystery's amazing persistence can only lie in the fact that the cause of number, the Primordal Scission, was never grasped. Yet it is known that phi controls the proportions of innumerable living organisms, that the spiral of the 'spiral galaxy" is a phi spiral, that the orbits of the planets of our solar system are in complex phi relationships to each other, and that the proportions of Gothic cathedrals and Greek temples are commanded by phi. Though long before Swaller de Lubicz's work a number of scholars had noted phi proportions in the pyramids and other Egyptian remains, only in the past few years has this been acknowledged by Egyptologists. Even now, attempts are made to show how the Egyptians might have used the Golden Section without actually realizing they were doing so. But the fact is that the Egyptians knew and used phi from the earliest dynasties - as well as the so-called Fibonacci numbers that devolve from phi. Evidently the Egyptians - and builders of the Greek temples and Gothic cathedrals and to a certain extent the painters and Neoplatonists of the Renaissance - also knew the significance of phi and the manner in which to employ it effectively; knowledge which they either deliberately kept secrect or which was later inadvertently lost. Even those modern artists who have been intrigued by phi and attempted to use it (Mondrian and le Corbusier, for example) did not understand its meaning and met with but partial success. [emphasis added]
Le Corbusier in fact made use of the phi-series itself in his blue and red series as Kappraff [1991] has explained in some detail.15 Moreover, from what has been discussed so far, it would appear that a case can indeed be made for the statement that: "the orbits of the planets of our solar system are in complex phi relationships to each other," although this does not seem to be a current or universal understanding, to say the least.
In the final analysis, the present work - unavoidably condensed - cannot in fact claim to be a distinct discovery per se, nor can it constitute restoration of lost wisdom if the latter was never truly lost. What is supplied here is a beginning and a partial integration of a complex corpus of information that may have ramifications yet to be recognized. The same may also be said regarding the background part played throughout the ages by those who elected to preserve and pass the information on. Only they know their true roles in all of this; perhaps the rest of us never will.

As for the role of Ancient Egypt, consider again (or refer to Part B of the previous Section) Kepler's "frank confession" in the Harmonies of the World published in the year 1618:16

The very nature of things, in order to reveal herself to mankind, was at work in the different interpreters of different ages, and the finger of God-to use the Hebrew expression; and here, in the minds of two men, who had wholly given themselves up to the contemplation of nature, there was the same conception as to the configuration of the world, although neither had been the others guide in taking this route. But now since the first light eight months ago, since broad day three months ago, and since the sun of my wonderful speculation has shone fully a very few days ago: nothing holds me back. I am free to give myself up to the sacred madness, I am free to taunt mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build a temple for my God, far from the territory of Egypt. If you pardon me, I shall rejoice; if you are enraged, I shall bear up. The die is cast, and I am writing the book-whether to be read by my contemporaries or by posterity matters not. Let it await its reader for a hundred years, if God Himself has been ready for His contemplator for six thousand years.
Lux e Tenebris
Almost four centuries have elapsed since Kepler wrote his frank confession and moving epilogue. Although much work remains, perhaps the time has now come for the "Golden Vessels of the Egyptians" to be repatriated and their place in the scheme of things acknowledged, along with the sacrifices of all those who laboured to preserve them through the intervening centuries of darkness.

 

--------------------------------------------------------------------------------

REFERENCES

Lindsay, Jack. The origins of Alchemy in Graeco-Roman Egypt, Ebenezer Baylis & Son, Trinity Press London 1970.
Taylor, Thomas, Commentaries of Proclus on the Timæus of Plato, Book I. Kessinger Books, Kila. p.36.

Taylor, Thomas, T. PLATO: The Timæus and The Critias, Bollingen Series, Pantheon Books, Washington 1944:118.
Wagner, Jeffrey K. Introduction to the Solar System, Holt, Rinehart and Winston, Orlando 1991.
Taylor, Thomas, Commentaries of Proclus on the Timæus of Plato, Vol II, Book III. pp. 89-90.

The Commentaries of Proclus on the Timeus of Plato, transl. Thomas Taylor, Kessinger Books, Kila, pp.115-118.
Dobbs, Betty Jo Teeter.The foundations of Newton's Alchemy, Cambridge University Press, Cambridge, 1975:165.
Lindsay, Jack, The Origins of Alchemy in Græco-Roman Egypt, Ebenezer Baylis & Son, Trinity Press, London, 1970:259.
ibid., pp.144-145.

ibid., p.265.

The Hermetic Arcanum
Lindsay, Jack, The Origins of Alchemy in Græco-Roman Egypt, Ebenezer Baylis & Son, Trinity Press London 1970:177.
de Lubicz, Schwaller, Le Temple de l'Homme, Translated by Robert and Deborah Lawlor, Autumn Books 2000.
West, J. A., Serpent in the Sky, Quest Books, Theosophical Publishing House, Wheaton. 1993:61-62.
Kappraff, J. CONNECTIONS: The Geometric Bridge between Art and Science, McGraw-Hill, New York 1991:21-25.
Kepler, Johannes. Harmonies of the World, Great Books of the Modern World 16, Robert Maynard Hutchins, Editor in Chief. William Benton, Chicago 1952.
Copyright © 1997. John N. Harris, M.A.(CMNS). Last Updated on February 22, 2004.

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12
THE OUROBOROS
171
63
9
12
THE OURABORUS
163
55
1

 

 

A

SERPENT I PRESENT

 

 

METRO

Free 01.12.09

The snake that ate itself

By Tariq Tahir

Page 3

Serpent sees rival. Serpent tries to eat rival. Serpent is in bother...

"IT MUST have seemed like the perfect opportunity for Reggie the hungry King snake.

When confronted by a .free lunch, it was natural for him to want a bite. But the greedy reptile was literally chasing his own tail.

Reggie's owner found him with a mouthful of himself, and headed straight for the vets. Little did he know that Reggie was close to digesting himself. Removing his tail required patience and skill because the snake's teeth face inward.

'Its teeth were acting like a ratchet,' said vet Bob Reynolds ,from Faygate, West Sussex.

'If a snake like this one is kept in a space that is too small. then there is always a temptation for it to lunge at its own tail. They can't spread themselves out and think there tails aew another snake.'

Reggie was close to being put down because his tail was nearly in his stomach, where it would have begun being digested. King snakes are native to California and feed. on rattlesnakes:.and lizards. And, it seems, themselves."

"Bitter end: Loopy Reggie before his life-saving visit to the vet and afterwards (image omitted) in safe hands"

 

 

9
OUROBOROS
138
48
4
9
OURABORUS
130
40
4
10
PYTHAGORAS
130
49
4
6
PYTHIA
79
34
7
6
PYTHON
98
35
8
7
PYTHONS
117
36
9
5
EGYPT
73
28
1
8
EGYPTIAN
97
43
7

 

EGYPT 57772 EGYPT

5+2 = 7 - 7 = 5+2

EGYPT 57772 EGYPT

 

10
PYTHAGORAS
130
49
4
-
-
-
-
-
-
-
-
-
-
10
PYTHAGORAS
130
49
4
5
EGYPT
73
28
1
1
E
5
5
5
4
PYTG
68
23
5
5
EGYPT
73
28
1

 

 

I

ME

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OUROBOROS PYTHAGORAS

 

 

-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
+
=
54
5+4
=
9
=
9
=
9
-
-`
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
+
=
126
1+2+6
=
9
=
9
=
9
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
20
8
18
5
5
-
6
6
21
18
-
6
9
22
5
+
=
158
8+6
=
5
=
5
=
5
-
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
+
=
77
4+1
=
14
1+4
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
37
-
-
13
-
77
-
41
-
1+3
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+7
-
-
1+3
-
7+7
-
4+1
8
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
10
-
-
4
-
14
-
5
-
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
-
1+0
-
-
-
-
1+4
-
-
8
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
1
-
-
4
-
5
-
5

 

 

-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
+
=
54
5+4
=
9
=
9
=
9
-
-`
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
+
=
126
1+2+6
=
9
=
9
=
9
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
20
8
18
5
5
-
6
6
21
18
-
6
9
22
5
+
=
158
8+6
=
5
=
5
=
5
-
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
+
=
77
4+1
=
14
1+4
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
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"1,2,3,4: Pythagoras and the Cosmology of Number ... to multiplicity via duality and trinity, is expressed even more graphically in ... Michell, The Dimensions of Paradise: The Proportions and Symbolic Numbers of ... vedicmaths.org/Free Resources/Articles/1234_pythagoras.asp - Cached

Free Resources
1,2,3,4: PYTHAGORAS

1,2,3,4: PYTHAGORAS AND THE COSMOLOGY OF NUMBER

At the heart of vedic mathematics lies a principle that underscores most, if not all, of the ancient wisdom traditions, the conveying of knowledge through cryptic, highly compressed expressions, open to multiple levels of interpretation. A prime example of this is the teaching of the Greek mathematician and sage Pythagoras. According to his ancient biographers:

"In the Pythagorean school, knowledge was transmitted symbolically, through the use of cryptic statements and riddles, in which a small number of words was pregnant with multiple levels of interpretation. Students were required to find meaning in these enigmatic lessons, sometimes through questioning and dialogue, sometimes by meditating upon their many possible meanings." (1)

If this was true of Pythagorean teachings, it was even more significant in more ancient schools of knowledge; it was, after all, at these schools, in Egypt, Babylon, and elsewhere, that Pythagoras gained his knowledge. In the case of the Indian tradition, both in Vedic times and later in the Hindu and Buddhist periods, the term most commonly encountered for this kind of cryptic literature was the sutra or collection of sutras. While this is often translated as "aphorism," or "formula," the word comes from the Sanskrit root for "thread," a usage that persists in the modern word "suture." As doctors use sutures to sow us up after surgery, the ancient sutras tie together our knowledge and integrate our awareness. There is no better example than the teachings contained in Patanjali's Yoga Sutras whose terse expressions contain instructions for the development of higher states of consciousness. Similarly, all the principles of vedic mathematics are encapsulated in sixteen sutras, which, along with thirteen sub-sutras, provide the basis for all the operations described in "The Cosmic Computer" (2).
If vedic mathematics can be counted as part of vedic literature, its ultimate source is the Rg Veda. This is certainly not concise, consisting of over 10,000 verses, but, as His Holiness Maharishi Mahesh Yogi has explained, it has a unique structure in which the essence of the whole text is essentially contained in one highly compressed expression--its first word. "It is the purpose of all ciphers to invest a few signs with much meaning," Carlo Suarès tells us. "In the severity of its beginning, in its first chapter, in its first sequence of letter numbers, is the seed, and in the seed is the whole." (3)
Suarès is referring to the beginning of Genesis, in which the process of creation is described, using the symbolism of gematria, in which each letter is given a numerical value. (4) According to Maharishi, the Rg Veda also sets forth a cosmogony in its first word-- Agni, but using a purely linguistic symbolism based on the physiology of speech. The first letter, or sound, AAAAAA…, pronounced with the mouth and throat fully open, and thus with a fully open sound, represents the fullness of the unmanifest, unbounded Brahman. But the letter G, a full glottal stop, introduces the first boundary on the full openness of the sound AAAAAA…. As the wave value of a sub-atomic particle collapses onto a point value when observed, so the unity, or samhita, value of Brahman collapses onto a point and becomes the triadic value of rishi, devata and chhandas, observer, process of observing, and object of observation. From here the process of manifestation begins. As the full stream of manifestation emerges, it leads on to the fullness of creation, and this is represented by the syllable NI, the same name given to the leading tone in Indian music (Sa, Re, Ga, Me Pa, Dha, Ni.....). The details of the process, and the content of manifestation and evolution, are unfolded through the rest of the verses of Rg Veda and commented upon by the rest of Vedic literature, including vedic mathematics.
Unity, duality, diversity, wholeness. These are the mechanics of creation described in different symbolic formulations in different knowledge traditions. To find it in purely mathematical or numerical form we return to the Pythagorean tradition, and its most concise expression comes from his successor Plato. Considered the most Pythagorean of Platonic dialogues, the Timaeus begins with a question by Socrates: "One, two, three ? but where, my dear Timaeus, is the fourth of my guests of yesterday who were to entertain me today?" (5) Commentators usually ignore this statement, but, as we have seen, in ancient literature every expression is "pregnant with multiple levels of meaning." This is particularly true when dealing with numbers.

"He [Pythagoras] held that the ultimate substances of all things, material and immaterial, were numbers, which had two distinct and complimentary aspects. On the one hand, they had a spatial and dynamic existence, and, on the other, they were fundamental formulating principles which were purely abstract. Thus, for example, the monad was understood by the Pythagoreans both as the number one, which had physical properties that could be manipulated in nature, and as an idea, which embodied the original unity at the source of all creation." (6)

The fundamental formulating principles in the universe are those values of unity, duality, diversity and wholeness we have already encountered. In Pythagorean thought these principles are clearly expressed in the first four numbers. Furthermore, this symbolism can be interpreted in terms of the Quadrivium, the four Pythagorean mathematical disciplines: arithmetic, music, geometry and astronomy.
Arithmetic was seen as the study of the abstract essence of things. Thus each number had a cosmological, as well as mathematical, significance. The monad, manifest as the number one, denotes the primordial unity at the basis of creation. The transition from one to two, from the monad to the dyad, represents the first step in the process of creation--unity polarizing within itself becomes duality. Three, the triad, is the first true number. One contains the seed, and two introduces potential. Three brings number into being, causing the potential contained within the monad to manifest into its true expression, the world of plurality and multitude.
If one and two initiate creation, three and four complete the process. Therefore, the tetrad, four, represents completion. Everything in the universe, both natural and numerical, is completed in the progression from one to four as 1 + 2 + 3 + 4 = 10, which brings us to the decad, also known to the Pythagoreans as the tetraktys, and representing their most sacred symbol. The same sequence, from unity to multiplicity via duality and trinity, is expressed even more graphically in the simplest and most basic musical relationships, those expressed through the numbers 1,2,3,4. The simplest and most fundamental musical relationship is the octave, discovered by Pythagoras to be the 1:2 relationship, and by Joseph Saveur (1653-1716) many centuries later, to be the first relationship in the harmonic overtone series. The experience of the octave is of two notes that are the same and yet different, and these values, sameness and difference are the fundamental substances used by the Demiurge to create the World-Soul in the Timaeus. Further, the octave provides the boundary conditions within which the musical universes contained within scales are formed, the values of Do in Do, Re, Mi, Fa, So, La, Ti, Do. Of these intervals, the central ones are those found to be next in the overtone series, 2:3, known as the fifth and 3:4 known as the fourth. These values are found in the first four harmonics of the overtone series, first 1:2 (octave), then 2:3 (fifth) then 3:4 (fourth) recapitulating the octave at the next power of two. In four simple sounds the whole process of unity, duality, multiplicity and wholeness is presented to the awareness.
In subsequent centuries, the science of geometry was developed into a sacred form in which the same process is represented by the circle (unity), contrasted with the square (diversity), and reconciled in the squaring of the circle, in alchemical practice, and the development of the mandala in Eastern art and architecture. "The object of sacred geometry being to depict that fusion of opposites, the squared circle is therefore its first symbol. Temples and cosmological cities throughout antiquity were founded on its proportions." (7) For Pythagoras, the symbolism of wholeness (kosmos) and order (harmonia) extended beyond mathematical to astrological phenomena. A theoretical planet called the counter-earth was posited to bring the number of heavenly bodies in the Pythagorean firmament to ten, the perfect number, the number of the tetraktys. And over time, an association between planets and musical notes was developed and elaborated into the famous "music of the spheres," a beautiful image of the kosmos as a divine harmony.
Having seen its range of implications, it could almost be stated that the sequence 1,2,3,4 sums up, in a compressed symbolism, the whole range of Pythagoreanism. But if we delve deeper into Platonic thought, a further dimension is revealed. In one of his most potent allegories, known as the "Divided Line," Plato sets out his theories of ontology and epistemology, and again it is done in terms of the number four. In this analogy, Plato makes a distinction between the outer realm of the world, illuminated by the sun and the inner realm of the mind, illuminated by the Good. The Divided Line passage divides each of these realms into two further sections. Plato also deals with the state of mind in which the resultant four realms are apprehended, resulting in the following scheme:

Level Object Faculty Type of Knowledge

IV Forms dialectic transcendental cognition } internal III mathematics thinking, scientific understanding } world Etc. reasoning

--------------------------------------------------------------------------------

II physical sense common-sense belief } external objects perception } world I shadows illusory illusion (8) perception

It can be seen from this scheme that within the subjective realm of the mind, Plato posits a level of knowledge higher than that which deals with mathematical objects through the processes of thinking and reasoning. This is the level of the forms and it is reached, Plato tells us, through the use of the "second phase" of the dialectic, a technique that, according to Jonathan Shear is similar to the practice of jñana yoga. (9) This again reflects the Pythagorean approach to mathematics, one that must, on some level at least, apply to vedic maths also:

"For Pythagoras, mathematics served as a bridge between the visible and invisible worlds. He pursued the discipline of mathematics not only as a way of understanding and manipulating nature, but also as a means of turning the mind away from the physical world, which he held to be transitory and unreal, and leading it to the contemplation of eternal and truly existing things that never vary. He taught his students that by focusing on the elements of mathematics, they could calm and purify the mind, and ultimately, through disciplined effort, experience true happiness." (10)

Notes:

(1) John Strohmeier and Peter Westbrook. Divine Harmony: The Life and Teachings of Pythagoras. (Berkeley, CA: Berkeley Hills Books, 1999), p. 54.
(2) Williams and Gaskell, The Cosmic Computer (Inspiration Books, 1997.
(3) Carlo Suarès The Cipher of Genesis (York Beach, Maine: Samuel Weiser, Inc., 1992), p. 72.
(4) For more information on gematria see John Michell, The New View Over Atlantis (London: Thames & Hudson Ltd., 1983) and Gordon Strachan, Jesus the Master Builder: Druid Mysteries and the Dawn of Christianity. (Edinburgh: Floris Books, 1998).
(5) Plato, Timaeus, 17a.
(6) Strohmeier & Westbrook (1999), p. 66.
(7) John Michell, The Dimensions of Paradise: The Proportions and Symbolic Numbers of Ancient Cosmology (San Francisco: Harper & Row, 1988), pp. 66-67.
(8) Jonathan Shear, The Inner Dimension: Philosophy and the Experience of Consciousness (New York: Peter Lang, 1990), p. 12, n2.
(9) It is interesting note that the Greek word harmonia has a similar etymology to the Sanskrit yoga, viz. a joining together of opposite values.
(10) Strohmeier & Westbrook (1999), p. 66"

 

 

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Iamblichus - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Iamblichus

Iamblichus, also known as Iamblichus Chalcidensis, or Iamblichus of Apamea was a Syrian Neoplatonist philosopher who determined the direction taken by ...
‎Iamblichus' life - ‎Iamblichus' cosmology - ‎Theurgy - ‎List of editions and translations


Iamblichus

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Iamblichus

Other names
"Iamblichus Chalcidensis", "Iamblichus of Chalcis", "Iamblichus of Apamea"

Born
c. 245

Died
c. 325

Era
Ancient philosophy

Region
Western philosophy

School
Neoplatonism

Influenced by[show]


Influenced[show]

Iamblichus, also known as Iamblichus Chalcidensis, or Iamblichus of Apamea (Greek: Ἰάμβλιχος, probably from Syriac or Aramaic ya-mlku, "He is king", c. 245 – c. 325), was a Syrian[1][2] Neoplatonist philosopher who determined the direction taken by later Neoplatonic philosophy.

 

Contents [hide]
1 Iamblichus' life
2 Iamblichus' cosmology
3 Theurgy
4 List of editions and translations
5 See also
6 Notes
7 References
8 External links

Iamblichus' life[edit]

Iamblichus was the chief representative of Syrian Neoplatonism,[2][3] though his influence spread over much of the ancient world. The events of his life and his religious beliefs are not entirely known, but the main tenets of his beliefs can be worked out from his extant writings. According to the Suda, and his biographer Eunapius, he was born at Chalcis (modern Qinnasrin) in Syria. He was the son of a rich and illustrious family, and he is said to have been the descendant of several priest-kings of Royal family of Emesa. He initially studied under Anatolius of Laodicea, and later went on to study under Porphyry, a pupil of Plotinus, the founder of Neoplatonism. It was with Porphyry that he is known to have had a disagreement over the practice of theurgy, the criticisms of which Iamblichus responds to in his attributed De Mysteriis Aegyptiorum (On the Egyptian Mysteries).

Around 304, he returned to Syria to found his own school at Apameia (near Antioch), a city famous for its Neoplatonic philosophers. Here he designed a curriculum for studying Plato and Aristotle, and he wrote grand commentaries on the two that survive only in fragments. Still, for Iamblichus, Pythagoras was the supreme authority. He is known to have written the Collection of Pythagorean Doctrines, which, in ten books, comprised extracts from several ancient philosophers. Only the first four books, and fragments of the fifth, survive.

Iamblichus was said to have been a man of great culture and learning. He was also renowned for his charity and self-denial. Many students gathered around him, and he lived with them in genial friendship. According to Fabricius, he died during the reign of Constantine, sometime before 333.

Only a fraction of Iamblichus' books have survived. For our knowledge of his system, we are indebted partly to the fragments of writings preserved by Stobaeus and others. The notes of his successors, especially Proclus, as well as his five extant books and the sections of his great work on Pythagorean philosophy also reveal much of Iamblichus' system. Besides these, Proclus seems to have ascribed to him the authorship of the celebrated treatise Theurgia, or On the Egyptian Mysteries. However, the differences between this book and Iamblichus' other works in style and in some points of doctrine have led some to question whether Iamblichus was the actual author. Still, the treatise certainly originated from his school, and in its systematic attempt to give a speculative justification of the polytheistic cult practices of the day, it marks a turning-point in the history of thought where Iamblichus stood.

As a speculative theory, Neoplatonism had received its highest development from Plotinus. The modifications introduced by lamblichus were the detailed elaboration of its formal divisions, the more systematic application of the Pythagorean number-symbolism, and, under the influence of Oriental systems, a thoroughly mythical interpretation of what Neoplatonism had formerly regarded as notional. Unlike Plotinus who broke from Platonic tradition and asserted an undescended soul, Iamblichus re-affirmed the soul's embodiment in matter believing matter to be as divine as the rest of the cosmos.[4]

It is most likely on this account that lamblichus was looked upon with such extravagant veneration.

Iamblichus was highly praised by those who followed his thought. By his contemporaries, Iamblichus was accredited with miraculous powers. The Roman emperor Julian, not content with Eunapius' more modest eulogy that he was inferior to Porphyry only in style, regarded Iamblichus as more than second to Plato, and claimed he would give all the gold of Lydia for one epistle of Iamblichus. During the revival of interest in his philosophy in the 15th and 16th centuries, the name of Iamblichus was scarcely mentioned without the epithet "divine" or "most divine".

Iamblichus' cosmology[edit]

At the head of his system, Iamblichus placed the transcendent incommunicable "One", the monad, whose first principle is intellect, nous. Immediately after the absolute One, lamblichus introduced a second superexistent "One" to stand between it and 'the many' as the producer of intellect, or soul, psyche. This is the initial dyad. The first and highest One (nous), which Plotinus represented under the three stages of (objective) being, (subjective) life, and (realized) intellect, is distinguished by Iamblichus into spheres of intelligible and intellective, the latter sphere being the domain of thought, the former of the objects of thought. These three entities, the psyche, and the nous split into the intelligible and the intellective, form a triad.

Between the two worlds, at once separating and uniting them, some scholars think there was inserted by lamblichus, as was afterwards by Proclus, a third sphere partaking of the nature of both. But this supposition depends on a merely conjectural emendation of the text. We read, however, that in the intellectual triad he assigned the third rank to the Demiurge.[5] The Demiurge, the Platonic creator-god, is thus identified with the perfected nous, the intellectual triad being increased to a hebdomad. The identification of nous with the Demiurge is a significant moment in the Neoplatonic tradition and its adoption into and development within the Christian tradition. St. Augustine follows Plotinus by identifying nous, which bears the logos, with the creative principle. Whereas the Hellenes call that principle the Demiurge, Augustine identifies the activity and content of that principle as belonging to one of the three aspects of the Divine Trinity—the Son, who is the Word (logos). Iamblichus and Plotinus commonly assert that nous produced nature by mediation of the intellect, so here the intelligible gods are followed by a triad of psychic gods.

The first of these "psychic gods" is incommunicable and supramundane, while the other two seem to be mundane, though rational. In the third class, or mundane gods, there is a still greater wealth of divinities, of various local position, function, and rank. Iamblichus wrote of gods, angels, demons and heroes, of twelve heavenly gods whose number is increased to thirty-six or three hundred and sixty, and of seventy-two other gods proceeding from them, of twenty-one chiefs and forty-two nature-gods, besides guardian divinities, of particular individuals and nations. The realm of divinities stretched from the original One down to material nature itself, where soul in fact descended into matter and became "embodied" as human beings. Basically, Iamblichus greatly multiplied the ranks of being and divine entities in the universe, the number at each level relating to various mathematical proportions. The world is thus peopled by a crowd of superhuman beings influencing natural events and possessing and communicating knowledge of the future, and who are all accessible to prayers and offerings.

The whole of Iamblichus's complex theory is ruled by a mathematical formalism of triad, hebdomad, etc., while the first principle is identified with the monad, dyad and triad; symbolic meanings being also assigned to the other numbers. The theorems of mathematics, he says, apply absolutely to all things, from things divine to original matter. But though he subjects all things to number, he holds elsewhere that numbers are independent existences, and occupy a middle place between the limited and unlimited.

Another difficulty of the system is the account given of nature. It is said to be bound by the indissoluble chains of necessity called fate, and is distinguished from divine things that are not subject to fate. Yet, being itself the result of higher powers becoming corporeal, a continual stream of elevating influence flows from them to it, interfering with its necessary laws and turning to good ends the imperfect and evil. Of evil no satisfactory account is given; it is said to have been generated accidentally in the conflict between the finite and the infinite.

Theurgy[edit]

Despite the complexities of the make-up of the divine cosmos, Iamblichus still had salvation as his final goal. The embodied soul was to return to divinity by performing certain rites, or theurgy, literally, 'divine-working'. Some translate this as "magic", but the modern connotations of the term do not exactly match what Iamblichus had in mind, which is more along the lines of a sacramental religious ritual. Still, these acts did involve some of what would today be perceived as attempts at 'magic'.

Though the embodied souls are dominated by physical necessities, they are still divine and rational. This contains a conflict, being part of an immortal, divine nature, as well as genuinely part of a material, imperfect mortal domain. The personal soul, a kind of 'lost' embodied soul, has lost touch with its deeper, divine nature and has become self-alienated. In this conflict can perhaps be glimpsed Iamblichus' ideas about the origin of evil, though Iamblichus does not comment on this himself.

This was also the area where Iamblichus differed from his former master, Porphyry, who believed mental contemplation alone could bring salvation. Porphyry wrote a letter criticizing Iamblicus' ideas of theurgy, and it is to this letter that On the Egyptian Mysteries was written in response.

Iamblichus' analysis was that the transcendent cannot be grasped with mental contemplation because the transcendent is supra-rational, aka trans-rational. Theurgy is a series of rituals and operations aimed at recovering the transcendent essence by retracing the divine 'signatures' through the layers of being. Education is important for comprehending the scheme of things as presented by Aristotle, Plato and Pythagoras but also by the Chaldaean Oracles. The theurgist works 'like with like': at the material level, with physical symbols and 'magic'; at the higher level, with mental and purely spiritual practices. Starting with correspondences of the divine in matter, the theurgist eventually reaches the level where the soul's inner divinity unites with God.

List of editions and translations[edit]
On the mysteries (De mysteriis), ed. Gustav Parthey, Teubner, 1857 online; ed. Edouard des Places, Collection Budé, 1989 English translations: Thomas Taylor, 1821 online (Google books), online (HTML); Alexander Wilder, 1911 online (Google books), online (HTML); Emma C. Clarke, John M. Dillon, and Jackson P. Hershbell, 2003, ISBN 1-58983-058-X

On the Pythagorean Way of Life (De vita pythagorica), ed. Theophil Kießling, Leipzig, 1816 online; ed. August Nauck, St. Petersburg, 1884; ed. Ludwig Deubner, Teubner, 1937 (rev. Ulrich Klein, 1975) English translations: Taylor, 1818 (PDF); Kenneth Sylvan Guthrie, 1919 online (HTML); Gillian Clark, 1989, ISBN 0-85323-326-8; John M. Dillon and Jackson Hershbell, 1991, ISBN 1-55540-523-1

On general mathematical science (Περὶ τῆς κοινῆς μαθηματικῆς ἐπιστήμης, De communi mathematica scientia), ed. Nicola Festa, Teubner, 1891 (reprint 1975) online
Protrepticus, ed. Ermenegildo Pistelli, Teubner, 1888 (repr. 1975) online; ed. des Places, Budé, 1989 English translation: Thomas Moore Johnson, Iamblichus' exhortation to the study of philosophy, Osceola, Mo., 1907 (repr. 1988, ISBN 0-933999-63-1)

In Nicomachi arithmeticam introductionem, Teubner, ed. Pistelli, Teubner, 1894 online (rev. Klein, 1975)
Letters: John M. Dillon and Wolfgang Polleichtner, Iamblichus of Chalcis: The Letters, 2009, ISBN 1-58983-161-6
Fragmentary commentaries on Plato and Aristotle Bent Dalsgaard Larsen, Jamblique de Chalcis: exégète et philosophe (vol. 2, appendix: Testimonia et fragmenta exegetica), Universitetsforlaget i Aarhus, 1972 (Greek texts only)
Dillon (ed. and trans.), Iamblichi Chalcidensis in Platonis dialogos commentariorum fragmenta, Leiden: Brill, 1973
John F. Finamore and John M. Dillon, Iamblichus De Anima: Text, Translation, and Commentary, Leiden: Brill, 2002, ISBN 1-58983-468-2

Theological principles of arithmetic (Theologumena arithmeticae, an anonymous work sometimes ascribed to Iamblichus), ed. Friedrich Ast, Leipzig, 1817 online; ed. Vittorio de Falco, Teubner, 1922 English translation: Robin Waterfield, 1988, ISBN 0-933999-72-0

See also[edit]
Henotheism

Notes[edit]

1.Jump up ^ George Sarton (1936). "The Unity and Diversity of the Mediterranean World", Osiris 2, pp. 406–463 [430]; Brill's New Pauly, "Iamblichus", 2.
2.^ Jump up to: a b Shaw, Gregory; Shaw, George (1971-09-01). Theurgy and the Soul: The Neoplatonism of Iamblichus. Penn State Press. ISBN 978-0-271-02322-9. Retrieved 4 June 2010.
3.Jump up ^ Dudley, Charles. Library of the World's Best Literature, Ancient and Modern (1899).
4.Jump up ^ Sgaw, Gregory, ‘Neoplatonism I: Antiquity’, in Dictionary of Gnosis & Western Esotericism, ed. by Wouter J. Hanegraff (Leiden & Boston: Brill, 2006), pp. 834-835
5.Jump up ^ O'Meara', Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity, Oxford University Press.

References[edit]
Fowden, Garth. The Egyptian Hermes: A Historical Approach to the Late Pagan Mind. Princeton, Princeton University Press 1986 (has an excellent section on Iamblichus' and the Neoplatonists' relation to the works attributed to Hermes Trismegistus)
Shaw, Gregory. Theurgy and the Soul: The Neoplatonism of Iamblichus. Pennsylvania, Pennsylvania State University Press 1995
Public Domain This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.

 

3
THE
33
15
6
6
COSMOS
84
21
3
9
Add to Reduce
117
36
9
-
Reduce to Deduce
1+1+7
3+6
-
9
Essence of Number
9
9
9

 

 

-
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
6
1
-
6
1
+
=
22
2+2
=
4
=
4
-
4
-
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-
8
-
-
-
15
19
-
15
19
+
=
76
7+6
=
13
1+3
4
-
4
-
9
T
H
E
-
C
O
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M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
3
-
-
4
-
-
+
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14
1+4
=
5
1+0
5
-
5
-
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20
-
5
-
3
-
-
13
-
-
+
=
41
4+1
=
5
=
5
-
5
-
9
T
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E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
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20
8
5
-
3
15
19
13
15
19
+
=
117
1+1+7
=
9
-
9
-
9
-
-
2
8
5
-
3
6
1
4
6
1
+
=
36
3+6
=
9
1+0
9
-
9
-
9
T
H
E
-
C
O
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M
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T
-
-
-
-
-
-
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-
-
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-
-
-
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1
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2
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2
=
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-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
-
-
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-
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-
-
3
occurs
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1
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=
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-
-
-
-
-
-
-
-
-
4
-
-
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4
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=
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-
--
-
-
5
-
-
-
-
-
-
-
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5
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--
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
--
-
8
-
-
-
-
-
-
-
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-
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8
occurs
x
1
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8
9
-
-
-
-
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7
-
7
7
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-
9
NINE
9
-
-
-
-
-
16
9
T
H
E
-
C
O
S
M
O
S
-
-
29
-
-
9
-
36
-
27
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
3+6
-
2+7
7
9
T
H
E
-
C
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S
-
-
11
-
-
9
-
9
-
9
-
-
2
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5
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3
6
1
4
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1
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 -
1+1
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-
-
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7
9
T
H
E
-
C
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2
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9
-
9
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9

 

 

9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
8
-
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6
1
-
6
1
+
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76
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=
13
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4
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9
T
H
E
-
C
O
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S
-
-
-
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-
-
-
2
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5
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+
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=
5
1+0
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5
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3
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4+1
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T
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-
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-
-
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20
8
5
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13
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=
9
-
9
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-
2
8
5
-
3
6
1
4
6
1
+
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=
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1+0
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9
T
H
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3
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1+2
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--
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8
-
-
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-
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8
occurs
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9
T
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29
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9
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1
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 -
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9
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2
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9
-
9
-
9

 

 

-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
1
+
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=
7
=
7
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-
-
-
15
-
19
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=
34
3+4
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7
=
7
-
5
A
T
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S
-
-
-
-
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-
-
-
-
1
2
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4
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+
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7
-
=
7
=
7
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-
1
20
-
13
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+
=
34
3+4
=
7
=
7
-
5
A
T
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M
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-
-
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1
20
15
13
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+
=
68
6+8
=
14
1+4
5
-
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
-
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
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1
-
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1
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1
occurs
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=
2
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2
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1
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2
3
-
-
-
-
-
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3
THREE
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-
-
-
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-
-
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4
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-
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4
occurs
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1
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4
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
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1
=
6
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
5
A
T
O
M
S
-
-
13
-
-
5
-
14
3+2
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
-
1
2
6
4
1
-
-
-
-
-
-
-
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5
5
A
T
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-
4
-
-
5
-
5

 

 

5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
2
-
4
-
+
=
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=
7
=
7
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1
20
-
13
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+
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=
7
=
7
5
A
T
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M
S
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-
-
-
--
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
5
A
T
O
M
S
-
-
13
-
-
5
-
14
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 

-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
-
1
20
-
13
+
=
34
3+4
=
7
=
7
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
-
1
2
6
4
+
=
13
1+3
=
4
=
4
-
4
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
A
T
O
M
-
-
13
-
-
4
-
13
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
4
A
T
O
M
-
-
4
-
-
4
-
4
-
-
1
2
6
4
-
-
-
-
-
-
-
-
5
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
-
1
20
-
13
+
=
34
3+4
=
7
=
7
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
-
1
2
6
4
+
=
13
1+3
=
4
=
4
-
4
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
A
T
O
M
-
-
13
-
-
4
-
13
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
4
A
T
O
M
-
-
4
-
-
4
-
4
-
-
1
2
6
4
-
-
-
-
-
-
-
-
5
4
A
T
O
M
-
-
4
-
-
4
-
4

 

THE ATOM THE

 

THE ATUM THE

 

6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
4
occurs
x
1
=
4
6
A
T
U
M
-
-
10
-
-
4
-
10
-
1
2
3
4
-
-
1+0
-
-
-
Q
1+0
6
A
T
U
M
-
-
1
-
-
4
-
2

 

 

THE HERMETICA

THE LOST WISDOM OF THE PHARAOHS

Timothy Freke & Peter Gandy

To the Memory of Giordano Bruno 1548 - 1600

Mundus Nihil Pulcherrimum

The World is a Beautiful Nothing

Page 23

"Although we have used the familiar term 'God' in the explanatory notes which accompany each chapter, we have avoided this term in the text itself. Instead we have used 'Atum - one of the ancient Egyptian names for the Supreme One God."

 

Page 45

The Being of Atum

"Atum is Primal Mind."

 

Page 45

The Being of Atum

Give me your whole awareness, and concentrate your thoughts, for Knowledge of Atum's Being requires deep insight, which comes only as a gift of grace.

It is like a plunging torrent of water whose swiftness outstrips any man who strives to follow it, leaving behind not only the hearer, but even the teacher himself.

To conceive of Atum is difficult.

To define him is impossible.

The imperfect and impermanent cannot easily apprehend the eternally perfected.

Atum is whole and conconstant.

In himself he is motionless, yet he is self-moving.

He is immaculate, incorruptible and ever-lasting.

He is the Supreme Absolute Reality. He is filled with ideas which are imperceptible to the senses, and with all-embracing Knowledge.

Atum is Primal Mind.

Page 46

He is too great to be called by the name 'Atum'. He is hidden, yet obvious everywhere.

His Being is known through thought alone, yet we see his form before our eyes.

He is bodiless, yet embodied in everything. There is nothing which he is not. He has no name, because all names are his name. He is the unity in all things, so we must know him by all names and call everything 'Atum'.

He is the root and source of all. Everything has a source, except this source itself, which springs from nothing.

Atum is complete like the number one, which remains itself whether multiplied or divided, and yet generates all numbers.

Atum is the Whole which contains everything. He is One, not two.

He is All, not many.

The All is not many separate things, but the Oneness that subsumes the parts.

The All and the One are identical.

You think that things are many when you view them as separate, but when you see they all hang on the One, /Page 47/ and flow from the One, you will realise they are united­linked together, and connected by a chain of Being from the highest to the lowest, all subject to the will of Atum.

The Cosmos is one as the sun is one, the moon is one and the Earth is one.

Do you think there are many Gods? That's absurd - God is one.

Atum alone is the Creator of all that is immortal, and all that is mutable.

If that seems incredible, just consider yourself. You see, speak, hear, touch, taste, walk, think and breathe.

It is not a different you who does these various things, but one being who does them all.

To understand how Atum makes all things, consider a farmer sowing seeds; here wheat - there barley,
now planting a vine - then an apple tree.

Just as the same man plants all these seeds, so Atum sows immortality in heaven and change on Earth.

Throughout the Cosmos he disseminates Life and movement­the two great elements that comprise Atum and his creation, and so everything that is.

Page 48

Atum is called 'Father' because he begets all things, and, from his example, the wise hold begetting children the most sacred pursuit of human life. Atum works with Nature, within the laws of Necessity, causing extinction and renewal, constantly creating creation to display his wisdom.

Yet, the things that the eye can see are mere phantoms and illusions.

Only those things invisible to the eye are real. Above all are the ideas of Beauty and Goodness.

Just as the eye cannot see the Being of Atum, so it cannot see these great ideas.

They are attributes of Atum alone, and are inseparable from him.

They are so perfectly without blemish that Atum himself is in love with them.

There is nothing which Atum lacks, so nothing that he desires.

There is nothing that Atum can lose, so nothing can cause him grief. Atum is everything.

Atum makes everything, and everything is a part of Atum.

Atum, therefore, makes himself.

This is Atum's glory - he is all-creative, and this creating is his very Being.

It is impossible for him ever to stop creating­for Atum can never cease to be.

Page 49

Atum is everywhere.

Mind cannot be enclosed, because everything exists within Mind.

Nothing is so quick and powerful.

Just look at your own experience. Imagine yourself in any foreign land, and quick as your intention you will be there!

Think of the ocean - and there you are.

You have not moved as things move, but you have travelled, nevertheless.

Fly up into the heavens - you won't need wings!

Nothing can obstruct you - not the burning heat of the sun, or the swirling planets.

Pass on to the limits of creation. Do you want to break out beyond the boundaries of the Cosmos?

For your mind, even that is possible.

Can you sense what power you possess? If you can do all this, then what about your Creator?

Try and understand that Atum is Mind.

This is how he contains the Cosmos. All things are thoughts which the Creator thinks."

 

 

-
6
A
T
U
M
-
-
-
-
-
--
-
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
-
1
2
3
4
+
=
10
1+0
=
1
-
1
-
6
A
T
U
M
-
-
-
-
-
--
-
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
-
1
2
3
4
+
=
10
1+0
=
1
-
1
-
6
A
T
U
M
-
-
-
-
-
--
-
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
-
1
2
3
4
+
=
10
1+0
=
1
-
1
-
6
A
T
U
M
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
35
6
A
T
U
M
-
-
10
-
-
4
-
10
3+5
-
1
2
3
4
-
-
1+0
-
-
-
Q
1+0
8
6
A
T
U
M
-
-
1
-
-
4
-
2

 

 

6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-
-
-
-
-
--
-
-
`-
1
20
21
13
+
=
55
5+5
=
10
1+0
1
-
1
2
3
4
+
=
10
1+0
=
1
=
1
6
A
T
U
M
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
4
occurs
x
1
=
4
6
A
T
U
M
-
-
10
-
-
4
-
10
-
1
2
3
4
-
-
1+0
-
-
-
Q
1+0
6
A
T
U
M
-
-
1
-
-
4
-
2

GOD ONE GOD

AND ONE CHOSEN RACE THE HUMAN RACE

 

 

HOLY BIBLE

Scofield References

C 1 V 16

THE ACTS OF THE APOSTLES

Page 1148 (Part quoted)

"MEN AND BRETHREN THIS SCRIPTURE MUST NEEDS HAVE BEEN FULFILLED

WHICH THE HOLY GHOST BY THE MOUTH OF DAVID SPAKE"

 

 

YEA

THOUGH

I

WALK THROUGH

THE

VALLEY OF THE SHADOW OF DEATH

I

WILL FEAR NO EVIL FOR THOU ART WITH

ME

 

 

http://cyberconnects.com/forum/index.php?topic=20378.0

Quote from: Vyse Dyne on November 22, 2008, 07:16:32 PMThe word occult comes from the Latin word occultus (clandestine, hidden, secret), referring to "knowledge of the hidden"

Or occulti, occulto, occultum, occulto, occulti, occultorum, occultis, occultos, or occultis.
Depends on where it is in the sentence.

 

 

TIMELESS EARTH

Peter Kolosimo 1974

Chapter

NINETEEN

Page 192

"The Indians say that thousands of years ago their ancestors travelled on great golden discs which were kept airborne by means of sound vibrations at a certain pitch, produced by continual hammer-blows. This is not so absurd as it may seem. Vibrations of a set frequency may have had the effect of increasing the atomic energy of gold, thus reducing the weight of the disc and enabling it to overcome gravity.'
'… To quote Pauwels and Bergier (op. Cit.,p. 197: ' The U.S. archaeologist Hyatt Verrill spent thirty years investigating the lost civilizations of Central and South America. . . In his fine novel, The Bridge of Light, he described a pre-Incaic city protected by a rocky defile which could only be crossed by a bridge constructed of ionized matter which could be made to appear and diappear at will. Verrill,who died at the age of eighty, insisted to the last that this was much more than a legend, and his wife who survives him, is of the same opinion."

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT

PLANETS STARS AND LIFE

Page 24

A

proton

is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'

 

 

O

NAMUH

BELOVED CHILDREN OF THE LIGHT BLESSED

DREAMER OF DREAMS

AWAKEN

THE

ETERNAL MOMENT

BIRTHS

ITS

FUTURE

 

 

1
1
9
9
9
2
AM
14
5
5
10
EVERYTHING
133
61
7
4
THAT
49
13
4
3
WAS
43
7
7
4
THAT
49
13
4
2
IS
28
10
1
2
OR
33
15
6
4
EVER
50
23
5
4
WILL
56
20
2
2
BE
7
7
7
38
First Total
471
183
57
3+8
Add to Reduce
4+7+1
1+8+3
5+7
11
Second Total
12
12
12
1+1
Reduce to Deduce
1+2
1+2
1+2
2
Essence of Number
3
3
3

 

 

I

NAME THAT HOLY NAME HAT HOLY NAME I NAME

AH ME AND YOU AND I AND YOU AND ME AH ME

NAME THAT HOLY AMEN AND AMEN THAT HOLY NAME

 

3
THE
33
15
6
4
HOLY
60
24
6
4
AMEN
33
15
6

 

 

4
AMEN
33
15
6
3
THE
33
15
6
4
NAME
33
15
6
11
First Total
99
45
18
1+1
Add to Reduce
9+9
4+5
1+8
2
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
2
Essence of Number
9
9
9

 

 

1
I
9
9
9
4
MEAN
33
15
6
4
AMEN
33
15
6
4
THAT
49
13
4
4
NAME
33
15
6
17
First Total
157
67
31
1+7
Add to Reduce
1+5+7
6+7
3+1
8
Second Total
13
13
4
-
Reduce to Deduce
1+3
1+3
-
8
Essence of Number
4
4
4

 

 

ANGEL AND ANGLE AND ANGLE AND ANGEL

 

 

THE ENGLISH ANGEL

Peter Burton & Harland Walshaw 2000

Page 5

Angles & Angels

The Venerable Bede tells the story of the slave boys from Northumbria in the Forum at Rome. St Gregory, struck by their fair hair and blue eyes, asks their nationality. When told that they are Angles, he replies, with one of those rare puns that work in two languages, 'Non Angli, sed angeli.' Not Angles, but angels.

 

"NON ANGLI SED ANGELI"

NOT ANGLES BUT ANGELS

 

 

A
=
1
-
5
ANGLE
39
21
3
-
-
-
-
-
-
-
-
-
A
=
1
-
5
ANGEL
39
21
3

 

 

A
=
1
-
6
ANGELS
58
22
4
A
=
1
-
3
AND
19
10
1
A
=
1
-
6
ANGLES
58
22
4
-
-
3
-
15
Add to Reduce
135
54
9
-
-
-
-
1+5
Reduce to Deduce
1+3+5
5+4
-
Q
-
3
-
6
Essence of Number
9
9
9

 

 

-
15
A
N
G
E
L
S
-
A
N
D
-
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
---
-
5
-
---
-
5
-
-
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
-
14
-
-
-
19
---
-
14
-
---
-
14
-
-
-
19
+
=
80
8+0
=
8
=
8
=
8
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
5
3
-
--
1
-
4
--
1
-
7
3
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
1
-
7
5
12
-
--
1
-
4
--
1
-
7
12
5
-
+
=
55
5+5
=
10
1+0
1
=
1
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
14
7
5
12
19
--
1
14
4
--
1
14
7
12
5
19
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
5
7
5
3
1
--
1
5
4
--
1
5
7
3
5
1
+
=
54
5+4
=
9
=
9
=
9
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
2
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
3
-
--
-
-
-
--
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
--
-
-
4
--
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
--
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
---
-
-
-
---
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
--
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
--
-
-
-
-
--
-
-
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
--
-
-
-
-
--
-
-
25
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
20
-
-
15
-
54
-
27
2+5
1+5
1
5
7
5
3
1
---
1
5
4
---
1
5
7
3
5
1
-
-
2+0
-
-
1+5
-
5+4
-
2+7
7
6
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
2
-
-
6
-
9
-
9

 

 

5
A
N
G
E
L
S
-
A
N
D
-
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
---
-
5
-
---
-
5
-
-
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
14
-
-
-
19
---
-
14
-
---
-
14
-
-
-
19
+
=
80
8+0
=
8
=
8
=
8
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
-
7
5
3
-
--
1
-
4
--
1
-
7
3
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
1
-
7
5
12
-
--
1
-
4
--
1
-
7
12
5
-
+
=
55
5+5
=
10
1+0
1
=
1
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
14
7
5
12
19
--
1
14
4
--
1
14
7
12
5
19
+
=
135
1+3+5
=
9
=
9
=
9
-
1
5
7
5
3
1
--
1
5
4
--
1
5
7
3
5
1
+
=
54
5+4
=
9
=
9
=
9
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
-
-
3
-
--
-
-
-
--
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
--
-
-
4
--
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
7
-
-
-
--
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
--
-
-
-
-
--
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
--
-
-
-
-
--
-
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
--
-
-
-
-
--
-
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
20
-
-
15
-
54
-
27
1+5
1
5
7
5
3
1
---
1
5
4
---
1
5
7
3
5
1
-
-
2+0
-
-
1+5
-
5+4
-
2+7
6
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
2
-
-
6
-
9
-
9

 

 

THREE ANGLES THREE ANGELS THREE ANGELS THREE ANGLES

TRY ANLES ANGELS O ANGELS TRY ANGLES

 

 

 

 
 
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