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Evokation
  
 
Index
  

 

 

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

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
MULTIPLED
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

 

 

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

 

 

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

 

I

SAY

GODS I ME I GODS

REAL REALITY REVEALED REALITY REAL

AND WOULD IT HAVE BEEN WORTH IT AFTER ALL, WHEN ALL IS SAID AND DONE, TO DENY A GOD INSPIRED MAGICIAN. THE SCATTERING OF BLESSED STAR STARRY STARDUST UPON AND AROUND THE MINDS I MINDS EYE. I ASK YOU, O DEAR GOOD AND TRUSTED FRIENDS, TO ACCEPT THESE EXALTED NAMES AS GODS HOLY ACCOLADES, ACCORDED OF GODS CREATORS. AND I HUMBLY REQUEST YOU TO PLEASE ALLOW ME, WITH KINDLY GOOD GRACE, AND AN UNDERSTANDING CREATIVE VISION. THE ODD LIGHT TOUCHES OF FAIRY STAR DUST. SUCH WORDS OF POWER AS ARE IMPORTANT TO THE GREAT WORK, AND DAVID IS OBLIGATED TO THE SYMBOLICAL MARKING OF THESE MAGICALLLY ESOTERIC, AND MYSTERIOUS WORDS OF POWER MANIFESTING FORTH FROM OUT THE IN OF ETERNAL MIND. MIRACULOUSLY BIRTHED OF THE GREAT COSMIC MOTHER. THE BE ALL AND END ALL OF EVERYTHING. THE HE AS IN SHE THAT IS ALWAYS FATHER TO THE THOUGHT. IN HOMAGE TO THAT. GODS EVER AND FOREVER LIVING CONSCIOUSNESS. THE PERFECT SUBLIME CREATIVE EXPRESSION OF THE DIVINE. THAT THAT THAT, HOLY, WHOLLY HOLY, ISISIS. BELOVED, WE ARE LIVING WITHIN THE MYTH OF MYTHS THE STORY OF THE PHYSICAL, OF MIND, AND SPIRIT. IN SACRED RECOGNITION OF KARMAS GLORIOUSLY MAGIC MIND. ACKNOWLEDGING ONCE AND FOR ALL SWEET ALCHERINGA, GODS HOLY DREAM TIME. THAT FECUND FERTILE MEMORY STORE FROM OUT THE IN OF WHICH IS KNIT THE SUM OF EVERLASTING LIFE. O DREAMER OF DREAMS, READ DEAR, READ THE MYTH OF N THE EVERLASTING NOW. ALL IS NOT WHAT IT SEEMS. DEPENDS ON YOUR I ME STATE OF MIND. THE SEE OF THE SELF THAT FEELS.

 

 

 

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

 

 

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

 

 

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

 

 

ADVENT 999 ADVENT

 

 

F
=
6
6
FATHER
58
31
4
F
=
6
7
FORGIVE
82
46
1
T
=
2
4
THEM
46
19
1
F
=
6
3
FOR
39
21
3
T
=
2
4
THEY
58
22
4
K
=
2
4
KNOW
63
18
9
N
=
5
3
NOT
49
13
4
W
=
5
4
WHAT
52
16
7
T
=
2
4
THEY
58
22
4
D
=
2
4
DO
19
10
1
-
-
40
41
First Total
524
218
38
-
-
4+0
4+1
Add to Reduce
5+2+4
2+1+8
3+8
Q
-
4
5
Second Total
11
11
11
-
-
-
-
Reduce to Deduce
1+1
1+1
1+1
-
-
4
5
Essence of Number
2
2
2

 

 

7
WHITHER
91
46
1
5
GOEST
66
21
3
4
THOU
64
19
1
16
First Total
221
86
5
1+6
Add to Reduce
2+2+1
8+6
-
7
Second Total
5
14
5
-
Reduce to Deduce
-
1+4
-
7
Essence of Number
5
5
5

 

 

-
-
-
-
-
ENNEAD
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
2
A+D
5
5
5
E
=
5
-
6
ENNEAD
43
25
25
-
-
-
-
-
-
4+3
2+5
2+5
E
=
5
-
6
ENNEAD
7
7
7

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
3
THE
33
15
6
3
SON
48
12
3
2
OF
21
12
3
3
THE
33
15
6
3
SUN
73
10
1
21
First Total
280
91
37
2+1
Add to Reduce
2+8+0
9+1
3+7
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

2
RA
19
10
1
3
THE
33
15
6
3
SUN
54
9
9
2
OF
21
12
3
4
SUNS
73
10
1
14
First Total
200
56
20
1+4
Add to Reduce
2+0+0
5+6
2+0
5
Second Total
2
11
2
-
Reduce to Deduce
-
1+1
-
5
Essence of Number
2
2
2

 

F
=
6
6
FATHER
58
31
4
F
=
6
7
FORGIVE
82
46
1
T
=
2
4
THEM
46
19
1
F
=
6
3
FOR
39
21
3
T
=
2
4
THEY
58
22
4
K
=
2
4
KNOW
63
18
9
N
=
5
3
NOT
49
13
4
W
=
5
4
WHAT
52
16
7
T
=
2
4
THEY
58
22
4
D
=
2
4
DO
19
10
1
-
-
40
41
First Total
524
218
38
-
-
4+0
4+1
Add to Reduce
5+2+4
2+1+8
3+8
Q
-
4
5
Second Total
11
11
11
-
-
-
-
Reduce to Deduce
1+1
1+1
1+1
-
-
4
5
Essence of Number
2
2
2

 

 

7
WHITHER
91
46
1
5
GOEST
66
21
3
4
THOU
64
19
1
16
First Total
221
86
5
1+6
Add to Reduce
2+2+1
8+6
-
7
Second Total
5
14
5
-
Reduce to Deduce
-
1+4
-
7
Essence of Number
5
5
5

 

 

-
-
-
-
-
ENNEAD
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
2
A+D
5
5
5
E
=
5
-
6
ENNEAD
43
25
25
-
-
-
-
-
-
4+3
2+5
2+5
E
=
5
-
6
ENNEAD
7
7
7

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
3
THE
33
15
6
3
SON
48
12
3
2
OF
21
12
3
3
THE
33
15
6
3
SUN
73
10
1
21
First Total
280
91
37
2+1
Add to Reduce
2+8+0
9+1
3+7
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

2
RA
19
10
1
3
THE
33
15
6
3
SUN
54
9
9
2
OF
21
12
3
4
SUNS
73
10
1
14
First Total
200
56
20
1+4
Add to Reduce
2+0+0
5+6
2+0
5
Second Total
2
11
2
-
Reduce to Deduce
-
1+1
-
5
Essence of Number
2
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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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

 

 

ADVENT 797 ADVENT

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
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

 

 

PEACE BE UNTO YOU BELOVED CHILDREN OF THE RAINBOW LIGHT

 

 

1
I
9
9
9
2
AM
14
5
5
3
THE
33
15
6
8
OPPOSITE
115
43
7
2
OF
21
12
3
3
THE
33
15
6
8
OPPOSITE
115
43
7
1
I
9
9
9
2
AM
14
5
5
3
THE
33
15
6
8
OPPOSITE
115
43
7
2
OF
21
12
3
8
OPPOSITE
115
43
7
2
IS
28
19
1
3
THE
33
15
6
2
AM
14
5
5
1
I
9
9
9
6
ALWAYS
81
18
9
2
AM
14
5
5
64
First Total
793
325
109
6+4
Add to Reduce
7+9+3
3+2+5
1+0+9
10
Second Total
10
10
10
1+0
Reduce to Deduce
1+0
1+0
1+0
1
Essence of Number
1
1
1

 

 

6
BEYOND
65
29
2
3
THE
33
15
6
4
VEIL
48
21
3
7
ANOTHER
81
36
9
4
VEIL
48
21
3
7
ANOTHER
81
36
9
4
VEIL
48
21
3
6
BEYOND
65
29
2
41
First Total
469
208
37
4+1
Add to Reduce
4+6+9
2+0+8
3+7
5
Second Total
19
10
10
-
Reduce to Deduce
1+9
1+0
1+0
5
Third Total
10
1
1
-
Add to Reduce
1+0
-
-
5
Essence of Numbe
1
1
1

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
45
-
8
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
-
-
-
9
-
8
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
45
-
8
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
-
-
-
9
-
8
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
2
4
5
6
7
9
T
=
2
-
1
T
20
2
2
-
2
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
4
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
7
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
45
-
8
GEOMETRY
108
45
45
-
2
4
10
6
14
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
1+0
-
1+4
-
-
-
9
-
8
GEOMETRY
9
9
9
-
2
4
1
6
5
9

 

 

 

"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"

 

 

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

 

 

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

 

 

-
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
-
+
=
7
-
=
7
=
7
-
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
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
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
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
-
-
-
-
-
-
-
-
5
5
A
T
O
M
S
-
-
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
-
+
=
7
-
=
7
=
7
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
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

6
DECODE
-
-
-
-
D+E
9
9
9
1
C+O
18
9
9
-
D+E
9
9
9
6
DECODE
36
27
27
-
-
3+6
2+7
2+7
6
DECODE
9
9
9

 

 

-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
9
-
14
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
2
9
-
1
-
7
3
5
+
=
27
2+7
=
9
=
9
=
9
-
-
20
18
-
1
-
7
12
5
+
=
63
6+3
=
9
=
9
=
9
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
20
18
9
1
14
7
12
5
+
=
86
8+6
=
14
1+4
5
=
5
-
-
2
9
9
1
5
7
3
5
+
=
41
4+1
=
5
=
5
=
5
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
8
T
R
I
A
N
G
L
E
-
-
27
-
-
8
-
41
-
23
1+8
-
-
9
9
-
-
-
-
-
-
-
2+7
-
-
-
-
4+1
-
2+3
9
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5
-
-
2
9
9
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
9
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5

 

 

8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
9
-
14
-
-
-
+
=
23
2+3
=
5
=
5
=
5
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
2
9
-
1
-
7
3
5
+
=
27
2+7
=
9
=
9
=
9
-
20
18
-
1
-
7
12
5
+
=
63
6+3
=
9
=
9
=
9
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
20
18
9
1
14
7
12
5
+
=
86
8+6
=
14
1+4
5
=
5
-
2
9
9
1
5
7
3
5
+
=
41
4+1
=
5
=
5
=
5
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
T
R
I
A
N
G
L
E
-
-
27
-
-
8
-
41
-
23
-
-
9
9
-
-
-
-
-
-
-
2+7
-
-
-
-
4+1
-
2+3
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5
-
2
9
9
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5

 

 

T
=
2
-
8
TRIANGLE
86
41
5
P
=
7
-
7
PYRAMID
86
41
5

 

 

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
-
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

 

 

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

 

 

-
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
3
5
+
=
16
1+6
=
7
=
7
=
7
-
-
1
-
7
12
5
+
=
25
2+5
=
7
=
7
=
7
-
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
14
7
12
5
+
=
39
3+9
=
12
1+2
3
=
3
-
-
1
5
7
3
5
+
=
21
2+1
=
3
=
3
=
3
-
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
29
5
A
N
G
L
E
-
-
16
-
-
5
-
21
-
12
2+0
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3
-
-
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3

 

 

5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
7
3
5
+
=
16
1+6
=
7
=
7
=
7
-
1
-
7
12
5
+
=
25
2+5
=
7
=
7
=
7
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
1
14
7
12
5
+
=
39
3+9
=
12
1+2
3
=
3
-
1
5
7
3
5
+
=
21
2+1
=
3
=
3
=
3
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
5
A
N
G
L
E
-
-
16
-
-
5
-
21
-
12
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3
-
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3

 

 

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

 

 

-
5
A
N
G
E
L
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
5
A
N
G
E
L
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
5
3
+
=
16
1+6
=
7
=
7
=
7
-
-
1
-
7
5
12
+
=
25
2+5
=
7
=
7
=
7
-
5
A
N
G
E
L
-
-
-
-
-
-
-
-
-
-
-
-
1
14
7
5
12
+
=
39
3+9
=
12
1+2
3
=
3
-
-
1
5
7
5
3
+
=
21
2+1
=
3
=
3
=
3
-
5
A
N
G
E
L
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
29
5
A
N
G
E
L
-
-
16
-
-
5
-
21
-
12
2+0
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
2
5
A
N
G
E
L
-
-
7
-
-
5
-
3
-
3
-
-
1
5
7
5
3
-
-
-
-
-
-
-
-
-
-
2
5
A
N
G
E
L
-
-
7
-
-
5
-
3
-
3

 

 

ANGELS AND ANGLES ANGLES AND ANGELS

 

 

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
6
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 ANGLES ANGELS O ANGELS TRY ANGLES

 

 

THREE FOUR FIVE FIVE FOUR THREE

 

 

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

 

 

-
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

 

 

I

ME

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OUROBOROS 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

 

 

-
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
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
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
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
-
-
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
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
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
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
-
-
4
T
H
R
E
E
F
O
U
R
F
I
V
E
-
-
1
-
-
4
-
5
-
5

 

 

PYTHAGORAS 7728176911 PYTHAGORAS

NUMBERS REARRANGED IN NUMERICAL ORDER

1112 - 6789

PYTHAGORAS 7728176911 PYTHAGORAS

 

PYTHAGORAS THE MISSING NUMBERS IN THE NAME PYTHAGORAS

3 4 5

PYTHAGORAS THE MISSING NUMBERS PYTHAGORAS

 

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

One of the most famous triangles is the 345 triangle. It is also known as Egyptian Triangle. Mystically, the upright side, the perpendicular, is likened to the male; the base to the female and the hypotenuse to the child of both.The 345 Triangle – Symbolism of Mathematics
mathsymbolism.wordpress.com/2019/10/11/the-345-triangle/In other words, a 3-4-5 triangle has the ratio of the sides in whole numbers called Pythagorean Triples. This ratio can be given as: Side 1: Side 2: Hypotenuse = 3n: 4n: 5n = 3: 4: 5 We can prove this by using the Pythagorean Theorem as follows:

https://robertedwardgrant.com/the-3-4-5-pythagorean-triangle-is...
Feedback
The 3-4-5 Pythagorean Triangle is... - Robert Edward …
https://www.facebook.com/robertedwardgrant/posts/1722870857921833
The 3-4-5 Pythagorean Triangle is inherent to the Flower of Life.....AND it is the PRECISE foundational geometry upon which the Giza Plateau's Center Pyramid ("Khafre": the Dynastic …

The numbers 3, 4, and 5 are called Pythagorean triples since…
https://www.justanswer.com/math-homework/2zz8n-numbers-3-4-called...
12/01/2010 · The numbers 5, 12, and 13 are also Pythagorean triples since 5^2+12^2=13^2. Can you find any other Pythagorean triples? Actually there is a set of formulas that will generate an …

From
mathworld.wolfram.com
3, 4, 5 Triangle -- from Wolfram MathWorld
The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have lengths 3 and 4 and the hypotenuse length 5. It satisfies the Pythagorean theorem since 3^2+4^2=5^2. (1) It has inradius r=1. (2) Triangle line picking for points picked at random in a 3, 4, 5 triangle gives a mean line segment length of l^__(Delta(3,4,5)) = 1/(22500)(20460+9728ln2+5103ln3) (3)…

 

 

-
-
-
-
-
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

 

 

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..."

 

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 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 -

 

 

-
-
-
-
-
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

 

 

-
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

 

 

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.

 

 

-
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

 

 

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

 

 

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

SERPENT I PRESENT

 

9
OURABORUS
130
31
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

 

 

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

 

 

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
-
-
4
4
4
-
-
-
-
9
S
=
1
2
1
S
19
10
1
-
1
4
4
4
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
4
4
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
4
4
4
-
-
7
-
-
S
=
1
5
1
S
19
10
1
-
1
4
4
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
4
4
4
5
-
-
-
-
P
=
7
7
1
P
16
7
7
-
-
4
4
4
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
4
4
4
-
-
-
8
-
Y
=
7
9
1
Y
25
7
7
-
-
4
4
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
4
4
4
-
-
-
-
-
S
=
1
5
1
S
19
10
1
-
1
4
4
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
4
4
4
5
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
4
4
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
4
4
4
-
-
7
-
-
P
=
7
7
1
P
16
7
7
-
-
4
4
4
-
-
7
-
-
Y
=
7
9
1
Y
25
7
7
-
-
4
4
4
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
4
4
4
-
-
-
8
-
I
=
9
1
1
I
9
9
9
-
-
4
4
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

 

 

A

SERPENT I PRESENT

 

9
OURABORUS
130
31
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

 

 

10
PYTHAGORAS
130
49
4
-
SARAH
-
-
-
2
SA
20
11
2
1
R
18
9
9
2
AH
9
9
9
5
SARAH
47
29
20
-
-
4+7
2+9
2+0
5
SARAH
11
11
2
-
-
1+1
1+1
-
5
SARAH
2
2
2
-
-
-
-
-
-
-
-
-
-
10
PYTHAGORAS
130
49
4
5
HAGOR
49
31
4
5
SARAH
47
20
2
7
ABRAHAM
44
26
8
-
BRAHMAN
-
-
-
-
A
1
1
1
7
BRAHMAN
-
-
-
1
B
2
2
2
3
RAH
27
18
9
3
MAN
28
10
1
7
BRAHMAN
57
30
12
-
  
5+7
3+0
-
7
BRAHMAN
12
3
3
-
-
1+2
-
-
7
BRAHMAN
3
3
3

 

 

9
OURABORUS
130
40
4
10
PYTHAGORAS
130
49
4
19
Add to Reduce
260
80
8
1+9
Reduce to Deduce
2+6+0
8+0
-
10
Essence of Number
8
8
8

 

 

10
PYTHAGORAS
130
49
4
9
OURABORUS
130
40
4

 

 

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

 

 

-
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
First Total
260
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

 

BE HOURS OF HORUS BE

 

-
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

 

 

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

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
8
8
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
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-
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
7
7
-
OUROBOROS
-
-
-
12
First Total
171
63
45
1+2
Add to Reduce
1+7+1
6+3
4+5
3
Second Total
9
9
9
-
Reduce to Deduce
-
-
-
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
-
-
-
-
-
--
-
-
-
-
-
-
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
-
-
-
5
-
-
-
-
-
-
-
-
-
-
--
--
5
occurs
x
1
=
5
=
5
--
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
34
-
-
12
-
63
-
36
1+2
-
-
-
-
6
-
-
6
-
6
-
6
-
-
-
3+4
-
-
1+2
-
6+3
-
3+6
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
-
-
-
-
-
-
-
-
-
-
3
T
H
E
-
O
U
R
O
B
O
R
O
S
-
-
7
-
-
3
-
9
-
9

 

 

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

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

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.

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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 ..."

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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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10
PYTHAGORAS
130
49
4
9
OURABORUS
130
40
4

 

 

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

 

 

-
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

 

 

10
P
Y
T
H
A
G
O
R
A
S
               

16
25
20
8
1
7
15
18
1
19
+
=
130
1+3+0
=
4

FOUR

4

10
P
Y
T
H
A
G
O
R
A
S
               
                                     

O
U
R
A
B
O
R
U
S
               

15
21
18
1
2
15
18
21
19
+
=
130
1+3+0
=
4

FOUR

4
                                     

O
U
R
A
B
O
R
U
S
               

 

 

10
P
Y
T
H
A
G
O
R
A
S

16
25
20
8
1
7
15
18
1
19
+
=
130

1+3
=
4

4

FOUR

4

1+6

2+5

2+0

1+5

1+8

1+9

7

7

2

 

6

9

10
+
=
                

1+0

 
7
7
2
8
1
7
6
9
1
1
+
=
49
4+9
=

13

1+3

4
FOUR

4

10
P
Y
T
H
A
G
O
R
A
S
           
                                         
                                         

10
P
Y
T
H
A
G
O
R
A
S
           

1

1
1
+
=
3

3

3

THREE
3

2

2

2

2

TWO
2

6

6

6

6

SIX

6

7
7

7

+
=
21
2+1
=
3

3

THREE
3

8

8

8

8

EIGHT
8

9

9

9

NINE
9

10
P
Y
T
H
A
G
O
R
A
S
                   
                                         
                                         

10
P
Y
T
H
A
G
O
R
A
S

O
U
R
A
B
O
R
U
S

15
21
18
1
2
15
18
21
19
+
=

130

1+3+0

=

4

4

FOUR

4

1+5
2+1

1+8

1+5
1+8

2+1

1+0

6

3

9

6

9

3

1

+

=

37

3+7

=
10

1+0
1
ONE
1

O
U
R
A
B
O
R
U
S

10
P
Y
T
H
A
G
O
R
A
S
           

16
25
20
8
1
7

+
=
77

7+7

=

14

1+4

5

FIVE

5

7

7

2

1

7

+

=

24

2+4

=
6

6

SIX

6

10
P
Y
T
H
A
G
O
R
A
S
                   
                                         
                                         
3
  
O
U
R
                               
   
15
21
18
           

+

=
54
5+4

=

9

9
NINE
9
   
1+5
2+1

1+8

                                

6

3

9

+

=

18

1+8

=

9

9

NINE

9
3
  
O
U
R
                               

9

O
U
R
A
B
O
R
U
S

O
R
U
S

15
18
21
19
+
=

73

7+3
=
10

1+0
1
ONE
1

1+5

1+8

2+1

1+9
+
=
28

2+8
=
10

1+0
1
ONE
1

6

9

3

1
+
=

19

1+9

=
10

1+0
1
ONE
1

O
R
U
S

10
P
Y
T
H
A
G
O
R
A
S

O
R
A
S

             
15
18
1
19
+
=
53
5+3
=
8
  
8
EIGHT
8
             

1+5

1+8

2+1

1+9

                  
             

6

9

1

1
+
=
17
1+7
=
8
  
8
EIGHT
8
             
O
R
A
S
                 
10
P
Y
T
H
A
G
O
R
A
S
                 

8

8

8

EIGHT

8

6

10
+
=
16
1+6
=
7

7

SEVEN
7

1+5

1+9

8

15

19

+

=

42

4+2

=

6

6

SIX

6

10
P
Y
T
H
A
G
O
R
A
S
                   
                                         
                                         

10
P
Y
T
H
A
G
O
R
A
S

 

16
25
20
8
1
7
15
18
1
19
+
=
130
1+3
=

4

4
FOUR

4

1+6
2+5
2+0

1+5
1+8

1+9

 

7
7
2

6
9

10
+
=
41
4+1

=

5

5

FIVE

5

1+0

1

1

1

1

ONE

1

8
1
7

1

+
=
17
1+7
=
8

8

EIGHT
8

7
7
2
8
1
7
6
9
1
1
+
=
130

1+3
=
4

4

FOUR

4

10
P
Y
T
H
A
G
O
R
A
S

 

 

10
P
Y
T
H
A
G
O
R
A
S

16
25
20
8
1
7
15
18
1
19
+
=
130

1+3
=
4

4

FOUR

4

7
7
2
8
1
7
6
9
1
1
+
=
49
4+9
=

13

1+3

4
FOUR

4

10
P
Y
T
H
A
G
O
R
A
S

O
U
R
A
B
O
R
U
S

15
21
18
1
2
15
18
21
19
+
=

130

1+3+0

=

4

4

FOUR

4
6
3
9
1
2

6

9

3

1
+
=
40
4+0
=
4

4

FOUR

4

O
U
R
A
B
O
R
U
S

O
U
R
A
B
15
21
18
1
2
+
=
57
5+7
=
12
1+2
3
THREE
3
6
3
9
1
2
+
=
21
2+1
=
3
3
THREE
3
O
U
R
A
B
O
R
U
S

10
P
Y
T
H
A
G
O
R
A
S

16
25
20
8
1
7

+
=
77

7+7

=

14

1+4

5

FIVE

5

7

7

2

8

1

7

+

=

32

3+2

=
5

5

FIVE

5
                                         

9

O
U
R
A
B
O
R
U
S

O
R
U
S

15
18
21
19
+
=

73

7+3
=
10

1+0
1
ONE
1

1+5

1+8

2+1

1+9
+
=
28

2+8
=
10

1+0
1
ONE
1

6

9

3

1
+
=

19

1+9

=
10

1+0
1
ONE
1

O
R
U
S

10
P
Y
T
H
A
G
O
R
A
S

O
R
A
S

           
15
18
1
19
+
=
53
5+3
=
8
  
8
EIGHT
8
           

1+5

1+8

2+1

1+9

                  
           

6

9

1

1
+
=
17
1+7
=
8
  
8
EIGHT
8
           
O
R
A
S
                 
10
P
Y
T
H
A
G
O
R
A
S
                   
                                         
                                         
10
P
Y
T
H
A
G
O
R
A
S
                 
         
1
  
6
9
  
1
+
=
17
1+7
=
8
  
8
EIGHT
8

9

O
U
R
A
B
O
R
U
S

                                         
                                         

9

O
U
R
A
B
O
R
U
S
                   
             
O
R
U
                     
             
6
9
3
  
+
=

18

1+8

=

9

9

NINE

9
   
6
3
9
                              
3
  
O
U
R
                             
   
15
21
18
           

+

=
54
5+4

=

9

9
NINE
9
   
1+5
2+1

1+8

                              

6

3

9

+

=

18

1+8

=

9

9

NINE

9
3
  
O
U
R
                               
       
A
B
                            
       
1
2
        

+

=
3
3
3
THREE
3
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Pythagoras - Wikipedia, the free encyclopedia
He believed in transmigration, or the reincarnation of the soul again and again into the .... Wandering Souls: The Doctrine of Transmigration in Pythagorean ... en.wikipedia.org/wiki/Pythagoras - Cached - Similar

 

Pythagoras
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"Pythagoras of Samos" redirects here. For the Samian statuary of the same name, see Pythagoras (sculptor).
For other uses, see Pythagoras (disambiguation).
Pythagoras Pythagoras
Pre-Socratic philosophy

Bust of Pythagoras of Samos in the Capitoline Museums, Rome
Full name Pythagoras (Πυθαγόρας)
School/tradition Pythagoreanism
Main interests Metaphysics, Music, Mathematics, Ethics, Politics
Notable ideas Musica universalis, Golden ratio, Pythagorean tuning, Pythagorean theorem
Influenced by[show]Thales, Anaximander, Pherecydes
Influenced[show]Philolaus, Alcmaeon, Parmenides, Plato, Euclid, Empedocles, Hippasus, Kepler

Pythagoras of Samos (Greek: Ὁ Πυθαγόρας ὁ Σάμιος, O Pūthagoras o Samios, "Pythagoras the Samian", or simply Ὁ Πυθαγόρας; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy. Herodotus referred to him as "the most able philosopher among the Greeks". His name led him to be associated with Pythian Apollo; Aristippus explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian (Pyth-)," and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and beneficial to humankind.[1]

He is best known for the Pythagorean theorem, which bears his name. Known as "the father of numbers", Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. According to Iamblichus of Chalcis, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and daemons."

He was the first man to call himself a philosopher, or lover of wisdom,[2] and Pythagorean ideas exercised a marked influence on Plato. Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.

Contents [hide]
1 Life
2 Pythagoreans
2.1 Musical theories and investigations
3 Influence
4 Religion and science
5 Literary works
6 Lore
7 Other accomplishments
8 Groups influenced by Pythagoras
8.1 Influence on Plato
8.2 Roman influence
8.3 Influence on esoteric groups
9 See also
10 References
11 Sources
11.1 Classical secondary sources
11.2 Modern secondary sources
12 External links

Life
Pythagoras was born on Samos, a Greek island in the eastern Aegean, off the coast of Asia Minor. He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father, a Phoenician merchant from Tyre). As a young man, he left his native city for Croton, Calabria, in Southern Italy, to escape the tyrannical government of Polycrates. According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. He was also discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles which eventually inspired his formulation of the theorem that is now called by his name. This possible inspiration is presented as an extraordinaire problem in the Berlin Papyrus. Upon his migration from Samos to Croton, Calabria, Italy, Pythagoras established a secret religious society very similar to (and possibly influenced by) the earlier Orphic cult.


Bust of Pythagoras, VaticanPythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoreans. Very strict rules of conduct governed this cultural center. He opened his school to both male and female students uniformly. Those who joined the inner circle of Pythagoras's society called themselves the Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a mainly vegetarian diet (meat that could be sacrificed was allowed to be eaten). Other students who lived in neighboring areas were also permitted to attend Pythagoras's school. Known as Akousmatikoi, these students were permitted to eat meat and own personal belongings. Richard Blackmore, in his book The Lay Monastery (1714), saw in the religious observances of the Pythagoreans, "the first instance recorded in history of a monastic life."

According to Iamblichus, the Pythagoreans followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. Music featured as an essential organizing factor of this life: the disciples would sing hymns to Apollo together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid the memory.

Flavius Josephus, in his polemical Against Apion, in defence of Judaism against Greek philosophy, mentions that according to Hermippus of Smyrna, Pythagoras was familiar with Jewish beliefs, incorporating some of them in his own philosophy.

Towards the end of his life he fled to Metapontum because of a plot against him and his followers by a noble of Croton named Cylon. He died in Metapontum around 90 years old from unknown causes.

Bertrand Russell, in A History of Western Philosophy, contended that the influence of Pythagoras on Plato and others was so great that he should be considered the most influential of all western philosophers.

Pythagoreans
Main article: Pythagoreans

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by RaphaelThe so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

—Aristotle, Metaphysics 1-5 , cc. 350 BC
The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. It was based upon the religious teachings of Pythagoras and was very secretive. At first, the school was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism, and devote themselves to the mathematics of nature.

Pythagoras's followers were commonly called "Pythagoreans". They are generally accepted as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.

The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. This was because the Pythagoreans believed that a man's words were usually careless and misrepresented him and that when someone was "in doubt as to what he should say, he should always remain silent". Another rule that they had was to help a man "in raising a burden, but do not assist him in laying it down, for it is a great sin to encourage indolence", and they said "departing from your house, turn not back, for the furies will be your attendants"; this axiom reminded them that it was better to learn none of the truth about mathematics, God, and the universe at all than to learn a little without learning all. (The Secret Teachings of All Ages by Manly P. Hall).

In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi ("listeners"). Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborated version of this knowledge, the akousmatikoi (were) those who had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition." According to Iamblichus, the akousmatikoi were the exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a veil.

The akousmatikoi were not allowed to see Pythagoras and they were not taught the inner secrets of the cult. Instead they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. The akousmatikoi recognized the mathematikoi as real Pythagoreans, but not vice versa. After the murder of a number of the mathematikoi by the cohorts of Cylon, a resentful disciple, the two groups split from each other entirely, with Pythagoras's wife Theano and their two daughters leading the mathematikoi.

Theano, daughter of the Orphic initiate Brontinus, was a mathematician in her own right. She is credited with having written treatises on mathematics, physics, medicine, and child psychology, although nothing of her writing survives. Her most important work is said to have been a treatise on the philosophical principle of the golden mean. In a time when women were usually considered property and relegated to the role of housekeeper or spouse, Pythagoras allowed women to function on equal terms in his society.[3]

The Pythagorean society is associated with prohibitions such as not to step over a crossbar, and not to eat beans. These rules seem like primitive superstition, similar to "walking under a ladder brings bad luck". The abusive epithet mystikos logos ("mystical speech") was hurled at Pythagoras even in ancient times to discredit him. The prohibition on beans could be linked to favism, which is relatively widespread around the Mediterranean.

The key here is that akousmata means "rules", so that the superstitious taboos primarily applied to the akousmatikoi, and many of the rules were probably invented after Pythagoras's death and independent from the mathematikoi (arguably the real preservers of the Pythagorean tradition). The mathematikoi placed greater emphasis on inner understanding than did the akousmatikoi, even to the extent of dispensing with certain rules and ritual practices. For the mathematikoi, being a Pythagorean was a question of innate quality and inner understanding.

There was also another way of dealing with the akousmata — by allegorizing them. We have a few examples of this, one being Aristotle's explanations of them: "'step not over a balance', i.e. be not covetous; 'poke not the fire with a sword', i.e. do not vex with sharp words a man swollen with anger, 'eat not heart', i.e. do not vex yourself with grief," etc. We have evidence for Pythagoreans allegorizing in this way at least as far back as the early fifth century BC. This suggests that the strange sayings were riddles for the initiated.

The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods.

Much of their mysticism concerning the soul seem inseparable from the Orphic tradition. The Orphics advocated various purificatory rites and practices as well as incubatory rites of descent into the underworld. Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks", or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (ugieia).

Musical theories and investigations
Pythagoras was very interested in music, and so were his followers. The Pythagoreans were musicians as well as mathematicians. Pythagoras wanted to improve the music of his day, which he believed was not harmonious enough and was too hectic.

According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on." (See Pythagorean tuning.)

The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras believed in something called the "harmony of the spheres." He believed that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.[4]

Academic Genealogy
Notable teachers Notable students
Anaximander

Pherecydes of Syros
Hermodamas of Samos
Thales

Ameinias

Bathyllus
Brontinus
Calliphon
Cercops
Echecrates
Empedocles
Eurytus
Hippasus
Leon
Lysis of Tarentum
Milon, whose house was used as a Pythagorean meeting place
Parmeniscus
Petron
Philolaus of Croton
Theano, Pythagoras' Wife/Daughter of Milon
Xenophilus of Chalcidice
Zalmoxis,


Influence

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle), c, is equal to the sum of the squares of the other two sides, b and a—that is, a² + b² = c².

While the theorem that now bears his name was known and previously utilized by the Babylonians and Indians, he, or his students, are often said to have constructed the first proof. It must, however, be stressed that the way in which the Babylonians handled Pythagorean numbers, implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources.[5] Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck, down the centuries up to modern times.[6] The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.

Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato. But Pythagoras also had his critics, such as Heraclitus who said that "much learning does not teach wisdom; otherwise it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus".[7]

Religion and science
Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. Religiously, Pythagoras was a believer of metempsychosis. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were influenced by ancient Greek religion. He was one of the first to propose that the thought processes and the soul were located in the brain and not the heart. He himself claimed to have lived four lives that he could remember in detail, and heard the cry of his dead friend in the bark of a dog.

One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an unseen characteristic that can be encountered by the study of mathematics.

Literary works
No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. Ancient Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature of his teaching. Pythagoras appears as a character in the last book of Ovid's Metamorphoses, where Ovid has him expound upon his philosophical viewpoints. Pythagoras has been quoted as saying, "No man is free who cannot command himself."

Lore
There is another side to Pythagoras, as he became the subject of elaborate legends surrounding his historic persona. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure, attributing to him such aspects as a golden thigh, which was a sign of divinity. According to Aristotle and others' accounts, some ancients believed that he had the ability to travel through space and time, and to communicate with animals and plants.[8] An extract from Brewer's Dictionary of Phrase and Fable's entry entitled "Golden Thigh":

Pythagoras is said to have had a golden thigh, which he showed to Abaris, the Hyperborean priest, and exhibited in the Olympic games.[9]

Another legend, also taken from Brewer's Dictionary, describes his writing on the moon:

Pythagoras asserted he could write on the moon. His plan of operation was to write on a looking-glass in blood, and place it opposite the moon, when the inscription would appear photographed or reflected on the moon's disc.[10]

Other accomplishments
This section does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. (May 2008)


The number is irrational.One of Pythagoras's major accomplishments was the discovery that music was based on proportional intervals of the numbers one through four. He believed that the number system, and therefore the universe system, was based on the sum of these numbers: ten. Pythagoreans swore by the Tetrachtys of the Decad, or ten, rather than by the gods. Odd numbers were masculine and even were feminine. He discovered the theory of mathematical proportions, constructed from three to five geometrical solids. One member of his order, Hippasos, also discovered irrational numbers, but the idea was unthinkable to Pythagoras, and according to legend, Hippasos was executed. Pythagoras (or the Pythagoreans) also discovered square numbers. They found that if one took, for example, four small stones and arranged them into a square, each side of the square was not only equivalent to the other, but that when the two sides were multiplied together, they equaled the sum total of stones in the square arrangement, hence the name "Square Root"[11]. He was one of the first to think that the earth was round, that all planets have an axis, and that all the planets travel around one central point. He originally identified that point as Earth, but later renounced it for the idea that the planets revolve around a central “fire” that he never identified as the sun. He also believed that the moon was another planet that he called a “counter-Earth” – furthering his belief in the Limited-Unlimited.

Groups influenced by Pythagoras

Influence on Plato
Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. b) there is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals". c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.[12]

Plato's harmonics were clearly influenced by the work of Archytas, a genuine Pythagorean of the third generation, who made important contributions to geometry, reflected in Book VIII of Euclid's Elements.

Roman influence
In the legends of ancient Rome, Numa Pompilius, the second King of Rome, is said to have studied under Pythagoras. This is unlikely, since the commonly accepted dates for the two lives do not overlap.

Influence on esoteric groups
Pythagoras started a secret society called the Pythagorean brotherhood devoted to the study of mathematics. This had a great effect on future esoteric traditions, such as Rosicrucianism and Freemasonry, both of which were occult groups dedicated to the study of mathematics and both of which claimed to have evolved out of the Pythagorean brotherhood. The mystical and occult qualities of Pythagorean mathematics are discussed in a chapter of Manly P. Hall's The Secret Teachings of All Ages entitled "Pythagorean Mathematics".

Pythagorean theory was tremendously influential on later numerology, which was extremely popular throughout the Middle East in the ancient world. The 8th-century Muslim alchemist Jabir ibn Hayyan grounded his work in an elaborate numerology greatly influenced by Pythagorean theory.[citation needed]

See also
Apollonius of Tyana
Hippasus
Pythagoreanism
Pythagorean comma
Pythagorean cup
Pythagorean theorem
Sacred geometry
Heliopolis-Pythagoras connection
Lute of Pythagoras
Pythagoras tree
Harmony of the spheres

References
1.^ Riedweg, Christoph (2005). Pythagoras: His Life, Teaching and Influence. Cornell University. pp. 5–6, 59, 73.
2.^ Cicero, Tusculan Disputations, 5.3.8-9 = Heraclides Ponticus fr. 88 Wehrli, Diogenes Laertius 1.12, 8.8, Iamblichus VP 58. Burkert attempted to discredit this ancient tradition, but it has been defended by C.J. De Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97-102, and C. Riedweg, Pythagoras: His Life, Teaching, And Influence (2005), p. 92.
3.^ Lynn M. Osen (1975). Women in Mathematics. MIT Press. ISBN 9780262650090. http://books.google.com/books?id=81kQ9VtTal4C&pg=PA17&dq=Theano+golden-mean&ei=jTJhSaDwJIbokATf7tD-BA.
4.^ Christoph Riedweg, Pythagoras: His Life, Teaching and Influence, Cornell: Cornell University Press, 2005 .
5.^ There are about 100,000 unpublished cuneiform sources in the British Museum alone. Babylonian knowledge of proof of the Pythagorean Theorem is discussed by J. Høyrup, 'The Pythagorean "Rule" and "Theorem" - Mirror of the Relation between Babylonian and Greek Mathematics,' in: J. Renger (red.): Babylon. Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne (1999).
6.^ From Christoph Riedweg , Pythagoras, His Life, Teaching and Influence, Cornell: Cornell University Press, 2005: "Had Pythagoras and his teachings not been since the early Academy overwritten with Plato’s philosophy, and had this ‘palimpsest’ not in the course of the Roman Empire achieved unchallenged authority among Platonists, it would be scarcely conceivable that scholars from the Middle Ages and modernity down to the present would have found the Presocratic charismatic from Samos so fascinating. In fact, as a rule it was the image of Pythagoras elaborated by Neopythagoreans and Neoplatonists that determined the idea of what was Pythagorean over the centuries."
7.^ Diog. L. ix. 1 (Fr. 40 in Vorsokratiker, i3, p. 86. 1-3)
8.^ Huffman, Carl. Pythagoras (Stanford Encyclopedia of Philosophy) [1]
9.^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable [2]
10.^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable [3]
11.^ Alioto, Anthony. A History of Western Science- 2nd ed. New York:Prentice Hall, 1992. p. 39-42
12.^ R.M. Hare, Plato in C.C.W. Taylor, R.M. Hare and Jonathan Barnes, Greek Philosophers, Socrates, Plato, and Aristotle, Oxford: Oxford University Press, 1999 (1982), 103-189, here 117-9.

Sources
No primary sources about Pythagoras have survived. This article describes the classical interpretation of Pythagoras, which is based on a small set of texts by later writers. As most of the surviving information was written down centuries after Pythagoras lived, their accuracy is uncertain.

It is suggested that the mathematical significance of the early Pythagoreans (pre-450 BC) has been exaggerated (with the exception of their theory of harmonics), and that the Pythagoreans were an Orphic-like cult with an emphasis on numerology who only later evolved into serious mathematicians as geometry became popular across Greece.[citation needed]

Classical secondary sources
Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information in these works.

Diogenes Laertius, Vitae philosophorum VIII (Lives of Eminent Philosophers), c. 200 AD, which in turn reference the lost work Successions of Philosophers by Alexander Polyhistor) — Pythagoras, Translation by C.D. Yonge
Porphyry, Vita Pythagorae (Life of Pythagoras), c. 270 AD
Iamblichus, De Vita Pythagorica (On the Pythagorean Life), c. 300 AD
Apuleius also writes about Pythagoras in Apologia, including a story of him being taught by Babylonian disciples of Zoroaster, c. 150 AD
Hierocles of Alexandria, Golden Verses of Pythagoras, Concord Grove Pr., 1983 c.430 AD

Modern secondary sources
Burkert, Walter. Lore and Science in Ancient Pythagoreanism. Harvard University Press, June 1, 1972. ISBN 0-674-53918-4
Burnyeat, M. F. "The Truth about Pythagoras". London Review of Books, 22 February 2007.
Guthrie, W. K. A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans, Cambridge University Press, 1979. ISBN 0-521-29420-7
Kingsley, Peter. Ancient Philosophy, Mystery, and Magic: Empedocles and the Pythagorean Tradition. Oxford University Press, 1995.
Hermann, Arnold. To Think Like God: Pythagoras and Parmenides—the Origins of Philosophy. Parmenides Publishing, 2005. ISBN 978-1-930972-00-1
O'Meara, Dominic J. Pythagoras Revived. Oxford University Press, 1989. ISBN 0-19-823913-0 (paperback), ISBN 0-19-824485-1 (hardcover)

External links
Wikiquote has a collection of quotations related to: Pythagoras
Wikimedia Commons has media related to: Pythagoras

Pythagoreanism Web Site
References for Pythagoras
Pythagoras, Internet Encyclopedia of Philosophy
Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University
Pythagoras and Pythagoreanism, The Catholic Encyclopedia
Pythagoreanism Web Article
Occult conception of Pythagoreanism
Pythagoras of Samos
Stanford Encyclopedia of Philosophy entry
Tetraktys
Golden Verses of Pythagoras
Pythagoras on Vegetarianism Quotes from primary source historical literature on Pythagoras' view on Vegetarianism, Justice and Kindness
Wandering Souls: The Doctrine of Transmigration in Pythagorean Philosophy, by Dr. James Luchte
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pythagoras.html

 

 

The Philosophy of Pythagoras
Pythagoras, Mathematician and Philosopher. Is the secret of the world hidden in ... Spirits, ghosts, souls, and transmigration were obviously things he ... www.thebigview.com/greeks/pythagoras.html - C

Pythagoras [Samos, 582 - 500 BC]

Like Thales, Pythagoras is rather known for mathematics than for philosophy. Anyone who can recall math classes will remember the first lessons of plane geometry that usually start with the Pythagorean theorem about right-angled triangles: a²+b²=c². In spite of its name, the Pythagorean theorem was not discovered by Pythagoras. The earliest known formulation of the theorem was written down by the Indian mathematician Baudhāyana in 800BC. The principle was also known to the earlier Egyptian and the Babylonian master builders. However, Pythagoras may have proved the theorem and popularised it in the Greek world. With it, his name and his philosophy have survived the turbulences of history.

His immediate followers were strongly influenced by him, and even until today Pythagoras shines through the mist of ages as one of the brightest figures of early Greek antiquity. The Pythagorean theorem is often cited as the beginning of mathematics in Western culture, and ever since mathematics -the art of demonstrative and deductive reasoning- has had a profound influence on Western philosophy, which can be observed down to Russell and Wittgenstein.

Pythagoras’ influence found an expression in visual art and music as well, particularly in the renaissance and baroque epoch. The far-reaching imprint of his ideas is yet more impressive if we consider that he did not leave any original writings. Instead, all what is known about Pythagoras was handed down by generations of philosophers and historiographers, some of whom, like Heraclitus, opposed his views. In this light it is remarkable that Pythagoras’ teachings have survived relatively undistorted until the present day.

Pythagoras was a native of the island of Samos. During his early life, Samos was governed by the powerful, unscrupulous tyrant Polycrates. Pythagoras did not sympathise with his government and thus emigrated to Croton in Southern Italy. Like the ancient Greek cities in Ionia, Croton was a flourishing commercial city that lived from importing and exporting goods. Obviously it was in Croton where Pythagoras developed most of his important ideas and theories.

Pythagoras founded a society of disciples which has been very influential for some time. Men and women in the society were treated equally -an unusual thing at the time- and all property was held in common. Members of the society practised the master’s teachings, a religion the tenets of which included the transmigration of souls and the sinfulness of eating beans. Pythagoras’ followers had to obey strict religious orders where it was forbidden to eat beans, to touch white cocks, or to look into a mirror beside a light.

If all of this seems a bit odd, it might lead us to suspect that Pythagoras’ personality reflects the inseparable blend of genius and madness that we associate with many other great men. It is said that once Pythagoras was walking up a lane in Croton when he came by a dog being ill-treated. Seeing this he raised his voice: “Stop, don’t hit it! It is a soul of a friend. I knew it when I heard its voice.” Spirits, ghosts, souls, and transmigration were obviously things he believed in deeply.

There was an opposition -if not rivalry- in ancient Greece between the gods of the Olympus and the lesser gods of more primitive religions. Pythagoras, like no other, embodied the contradistinctions of the mystical and rational world, which is woven into his personality and philosophy. In his mind, numbers, spirits, souls, gods and the mystic connections between them formed one big picture. The following text tells the legend of his own existences:

“He was once born as Aethalides and was considered to be the son of Hermes. Hermes invited him to choose whatever he wanted, except immortality; so he asked that, alive and dead, he should remember what happened to him. Thus, in life he remembered everything, and when he died he retained the same memories. [...] He remembered everything - how he first had been Aethalides, then Euphorbus, then Hermotimus, then Pyrrhus, the Delian fisherman. When Pyrrhus died, he became Pythagoras.” (Diogenes Laertius, Live of Philosophers, VIII 4-5)

“Pythagoras believed in metempsychosis and thought that eating meat was an abominable thing, saying that the souls of all animals enter different animals after death. He himself used to say that he remembered being, in Trojan times, Euphorbus, Panthus’ son who was killed by Menelaus. They say that once when he was staying at Argos he saw a shield from the spoils of Troy nailed up, and burst into tears. When the Argives asked him the reason for his emotion, he said that he himself had borne that shield at Troy when he was Euphorbus.

They did not believe him and judged him to be mad, but he said he would provide a true sign that it was indeed the case: on the inside of the shield there had been inscribed in archaic lettering EUPHORBUS. Because of the extraordinary nature of his claim they all urged that the shield be taken down - and it turned out that on the inside the inscription was found.” (Diogenes Laertius)

After Pythagoras introduced the idea of eternal recurrence into Greek thought, which was apparently motivated by his studies of earlier Egyptian scriptures, the idea soon became popular in Greece. It was Pythagoras’ ambition to reveal in his philosophy the validity and structure of a higher order, the basis of the divine order, for which souls return in a constant cycle.

This is how Pythagoras came to mathematics. It could be said that Pythagoras saw the study of mathematics as a purifier of the soul, just like he considered music as purifying. Pythagoras and his disciples connected music with mathematics and found that intervals between notes can be expressed in numerical terms. They discovered that the length of strings of a musical instrument correspond to these intervals and that they can be expressed in numbers. The ratio of the length of two strings with which two tones of an octave step are produced is 2:1.

Music was not the only field that Pythagoras considered worthy of study, in fact he saw numbers in everything. He was convinced that the divine principles of the universe, though imperceptible to the senses, can be expressed in terms of relationships of numbers. He therefore reasoned that the secrets of the cosmos are revealed by pure thought, through deduction and analytic reflection on the perceptible world.

This eventually led to the famous saying that “all things are numbers.” Pythagoras himself spoke of square numbers and cubic numbers, and we still use these terms, but he also spoke of oblong, triangular, and spherical numbers. He associated numbers with form, relating arithmetic to geometry. His greatest contribution, the proposition about right-angled triangles, sprang from this line of thought:

“The Egyptians had known that a triangle whose sides are 3, 4, 5 has a right angle, but apparently the Greeks were the first to observe that 3²+4²=5², and, acting on this suggestion, to discover a proof of the general proposition. Unfortunately for Pythagoras this theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy. In a right-angled isosceles triangle, the square on the hypotenuse is double of the square on either side.

Let us suppose each side is an inch long; then how long is the hypotenuse? Let us suppose its length is m/n inches. Then m²/n²=2. If m and n have a common factor, divide it out, then either m or n must be odd. Now m²=2n², therefore m² is even, therefore m is even, therefore n is odd. Suppose m=2p. Then 4p²=2n², therefore n²=2p² and therefore n is even, contra hyp. Therefore no fraction m/n will measure the hypotenuse. The above proof is substantially that in Euclid, Book X.” (Bertrand Russell, History of Western Philosophy)

This shows how Pythagoras’ formulation immediately led to a new mathematical problem, namely that of incommensurables. At his time the concept of irrational numbers was not known and it is uncertain how Pythagoras dealt with the problem. We may surmise that he was not too concerned about it. His religion, in absence of theological explanations, had found a way to blend the “mystery of the divine” with common-sense rational thought.

From Pythagoras we observe that an answer to a problem in science may give raise to new questions. For each door we open, we find another closed door behind it. Eventually these doors will be also be opened and reveal answers in a new dimension of thought. A sprawling tree of progressively complex knowledge evolves in such manner. This Hegelian recursion, which is in fact a characteristic of scientific thought, may or may not have been obvious to Pythagoras. In either way he stands at the beginning of it.

 

 

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3
ONE
34
16
7
4
ZERO
64
28
1
5
THREE
56
29
2
12
First Total
154
73
10
1+2
Add to Reduce
1+5+4
7+3
1+0
3
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
3
Essence of Number
1
1
1

 

 

-
12
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T
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6
5
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8
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6
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8
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33
3+3
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6
-
6
-
6
-
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15
14
-
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26
-
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15
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8
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78
7+8
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6
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9
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9
5
5
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40
4+0
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4
-
4
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4
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5
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5
18
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20
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5
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76
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4
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-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
15
14
5
-
26
5
18
15
-
20
8
18
5
5
+
=
154
1+5+4
=
10
1+0
1
-
1
-
-
6
5
5
-
8
5
9
6
-
2
8
9
5
5
+
=
73
7+3
=
10
1+0
1
-
1
-
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
-
-
-
-
-
-
5
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-``
-
-
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
15
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
30
-
-
12
-
73
-
28
1+5
1+2
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
3+0
-
-
1+2
-
7+3
-
2+8
6
3
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
3
-
-
3
-
10
-
10
-
-
6
5
5
-
8
5
9
6
-
2
8
9
5
5
-
-
-
-
-
-
-
1+0
-
1+0
6
3
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
3
-
-
3
-
1
-
1

 

 

12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
6
5
-
-
8
-
-
6
-
-
8
-
-
-
+
=
33
3+3
=
6
-
6
-
6
-
15
14
-
-
26
-
-
15
-
-
8
-
-
-
+
=
78
7+8
=
15
1+5
6
-
6
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
9
-
-
2
-
9
5
5
+
=
40
4+0
=
4
-
4
-
4
-
-
-
5
-
-
5
18
-
-
20
-
18
5
5
+
=
76
7+6
=
13
1+3
4
-
4
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
15
14
5
-
26
5
18
15
-
20
8
18
5
5
+
=
154
1+5+4
=
10
1+0
1
-
1
-
6
5
5
-
8
5
9
6
-
2
8
9
5
5
+
=
73
7+3
=
10
1+0
1
-
1
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
5
5
-
-
5
-
-
-
-
-
-
5
5
-
-
5
occurs
x
5
=
25
2+5
7
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
30
-
-
12
-
73
-
28
1+2
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
3+0
-
-
1+2
-
7+3
-
2+8
3
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
3
-
-
3
-
10
-
10
-
6
5
5
-
8
5
9
6
-
2
8
9
5
5
-
-
-
-
-
-
-
1+0
-
1+0
3
O
N
E
-
Z
E
R
O
-
T
H
R
E
E
-
-
3
-
-
3
-
1
-
1

 

 

-
7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
1
9
6
-
5
9
5
-
+
=
35
3+5
=
8
=
8
=
8
-
-
19
9
24
-
14
9
14
-
+
=
89
8+9
=
17
1+7
8
=
8
-
7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
19
9
24
-
14
9
14
5
+
=
94
9+4
=
13
1+3
4
=
4
-
-
1
9
6
-
5
9
5
5
+
=
40
4+0
=
1
=
1
=
1
-
7
S
I
X
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
24
7
S
I
X
-
N
I
N
E
-
-
21
-
-
7
-
40
-
22
2+4
-
-
9
-
-
-
9
-
-
-
-
2+1
-
-
-
-
4+0
-
2+2
6
7
S
I
X
--
N
I
N
E
-
-
3
-
-
7
-
4
-
4
-
-
1
9
6
--
5
9
5
5
-
-
-
-
-
-
-
-
-
-
6
7
S
I
X
--
N
I
N
E
-
-
3
-
-
7
-
4
-
4

 

 

7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
1
9
6
-
5
9
5
-
+
=
35
3+5
=
8
=
8
=
8
-
19
9
24
-
14
9
14
-
+
=
89
8+9
=
17
1+7
8
=
8
7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
7
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
19
9
24
-
14
9
14
5
+
=
94
9+4
=
13
1+3
4
=
4
-
1
9
6
-
5
9
5
5
+
=
40
4+0
=
1
=
1
=
1
7
S
I
X
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
7
S
I
X
-
N
I
N
E
-
-
21
-
-
7
-
40
-
22
-
-
9
-
-
-
9
-
-
-
-
2+1
-
-
-
-
4+0
-
2+2
7
S
I
X
-
N
I
N
E
-
-
3
-
-
7
-
4
-
4
-
1
9
6
-
5
9
5
5
-
-
-
-
-
-
-
-
-
-
7
S
I
X
-
N
I
N
E
-
-
3
-
-
7
-
4
-
4

 

 

-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
-
-
-
1
-
-
-
-
-
--
-
--
--
1
--
--
--
--
--
2
-
-
-
-
-
--
-
--
--
2
--
--
--
--
--
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
--
-
--
-
-
--
--
6
--
--
--
--
--
7
-
-
--
-
--
--
-
--
--
7
--
--
--
--
--
8
-
-
--
-
--
--
-
--
--
8
--
--
--
--
--
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
24
11
E
U
C
L
I
D
-
-
21
-
-
6
-
27
2+4
1+1
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+7
6
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
6
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
11
E
U
C
L
I
D
-
-
21
-
-
6
-
27
1+1
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+7
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

-
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
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1
-
-
5
-
1

 

 

COMET COMETH COMET COMETH COMET

 

 

 

SEVEN EVENS SEVEN


neoplatonism : Message: Re: [neoplatonism] Re: hieroglyphs ...
Minotaurus"), and the > Egyptian "Rhadamanthys" ("Ra of Ament," "Ruler of Hades"; Naville, "La > ... M.C. There is a good account of them in F. Boll's Sphaera. Neue ... groups.yahoo.com/group/neoplatonism/message/680?l=1 - 66k - Cached

 

The 7 Heaven's and Earth's Below - David Icke's Official Forums 2 posts - 2 authors - Last post: 10 Feb
The 7 Heaven's and Earth's Below Meditation / Human Consciousness / Spirituality / Ascension / 2012 Mayan Calendar.
www.davidicke.com/forum/showthread.php?p=1058301618 - Similar

 

SEVEN EVENS SEVEN

 

The 7 Heaven's and Earth's Below

This section of the angels story has been given different names by different theologians. It has been called:
- The seven heavens and the 7 hells
- The 7 celestial mansions and the 7 palaces
of darkness
- The 7 heavens and the seven earths.

These would be similar to the lowlands and highlands of our world. The seven heavens stack one over the top of each other in a straight line.

I am presenting this information by combining in order both 7 Heavens & 7 Earths.

The portrayal of the synthesis for - The 7 Heavens - was made by me using as much as possible the information in hand. Steli :-)

 

Seven is the maximum number of eclipses of the Sun and Moon that can occur in any one year.

Luicifer is responsible for bringing all below to above.
__________________
Going around the merry go around is revolution
Been aware of your journey, is evolution

The Seventh Heaven
Araboth
The 7th heaven is the holiest of the holy heavens. Araboth is ruled by Archangel Cassiel and is home to God and his Divine Throne it is also the abode of human souls waiting to be born. It is also home to the highest orders of angels - the Seraphim, Cherubim, and Thrones. It is in the 7th Heaven that Isaiah has a glimpse of God and the Christ and "hears the Most high dictating the program on his (Christs) earthly manifestation and return."

The Seventh Earth
This world's form is very much like that of Earth's, having hills, mountains, valleys and flatlands. Here lies 365 different types of bizarre creatures. These creatures range from having two heads, to having multiple bodies, but are considered to be righteous. They are considered quite superior and live off the aquatic life found there. They have the unique ability to prolong life or bring the dead back to life.

More References
In Enoch 2,8, the Garden of Eden and the Tree of Life are both found in the 3rd Heaven.
The Zohar mentions 390 Heavens and 70,000 worlds.
The gnostic Basilides vouched for 365 Heavens.
Jellenek (in Beth Ha-Midrasch) recalls a legend which tells of 955 Heavens.
In Enoch 2 the Heavens number 10. Here the 8th Heaven is called Muzaloth. The 9th Heaven, home of the 12 signs of the zodiac, is called Kukhavim. The 10th, where Enoch saw the "vision of the face of the Lord", is called Aravoth (Hebrew term for the 12 signs of the Zodiac).
The confusion of the Heavens is clear here from the fact that the signs of the zodiac do not lodge in the Heavens named after them.

The notion of the 7 Heavens appears in The Testament of the Twelve Patriarchs and other Jewish apocrypha, and was familiar to the ancient Persians and Babylonians.
The Persians pictured the Almighty in the highest of the 7 Heavens, "seated on a great white throne, surrounded by winged cherubim."
The Koran also speaks of 7 Heavens.

namaste

 

The 7 Deadly Sins

* Gula (gluttony)
* Fornicatio (fornication, lust)
* Avaritia (avarice/greed)
* Tristitia (sorrow)
* Ira (wrath)
* Acedia (acedia)
* Vanagloria (vainglory)
* Superbia (Pride)

7 colours of light

7 steps from creation to divine

7 steps to heaven

7 realities of existense

7 states of being

 

The 7 Tetragonal crystal classes.

Topologists have been able to prove that 7 colors may be needed on a donut shaped map to ensure that no adjacent areas are the same.

There are seven different ways of linking four hexagons together.

7 is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.

The Chemical Element Nitrogen has an atomic number of 7.

The 7 directions: north, south, east, west, up, down and the center.

In Humans: the 7 Endocrine glands.

The 7 colors of the rainbow.

The 7 double letters of the Hebrew Alphabet.

The 7 classical planets.

The 7 bodies of the Human microcosm.

In Humans: the 7 chakras.

Seventh heaven is the farthest of the concentric spheres containing the stars in the Moslem and cabalist systems.

 

SEVEN EVENS SEVEN

 

movie1.search.biglobe.ne.jp/video/watch/af38f248523e931f - Cached - Similar -lightgiver and the Book of Revelations: - Page 26 - David Icke's ... 10 posts - 2 authors - Last post: 8 Jun
'I'm not telling you up to seven times, I'm telling you up to seventy seven times!' " http://www.973-eht-namuh-973.com/col...s_1_cont_6.htm ...
www.davidicke.com/forum/showthread.php?

Seven

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

Seven generation sustainability is an ecological concept that urges the current generation of humans to live sustainably and work for the benefit of the seventh generation into the future.

Our generation, the seventh generation since the Alter Rebbe . . . and this generation (the last generation of the exile) immediately becomes the generation of the Geula .

"In every deliberation, we must consider the impact on the seventh generation... even if it requires having skin as thick as the bark of a pine."

—Great Law of the Iroquois

“Adah and Zillah, hear my voice;
Wives of Lamech, listen to my speech!
For I have killed a man for wounding me,
Even a young man for hurting me.

If Cain shall be avenged sevenfold,
Then Lamech seventy-sevenfold.”

—Genesis 4:19-24 (NKJV)

. Read Genesis 4 and 5 carefully and you'll discover that the full flowering of wickedness or righteousness becomes apparent in the seventh generation from Adam in each respective line.

7th pineal/crown crown Saturn Rosslyn (King of the Grail)

The word chakra is Sanskrit for wheel or disk and signifies one of seven basic energy centers in the body that correspond to nerve ganglia branching out from the spinal column, as well as states of consciousness, developmental stages of life, archetypal elements, body functions, colors, sounds, and much, much more.

7 seals, 7 trumpets, 7 bowls
Seven churches, seven seals, seven trumpets, seven bowls ordered in a big picture. Three great earthquakes and 14 judgments from God.

the seventh "trumpet" is an announcement that the "king" and his kingdom have arrived.

7. The Seventh Bowl

This next judgement is the last and final judgement.

THE SEVENTH SEAL

“And when he had opened the seventh seal, there was silence in heaven about the space of half an hour.” Revelation 8:1.

The 7th seal, remember, has still to be opened. Chapter seven was inserted between the 6th and 7th seals simply because that is when the sealing work will occur in the stream of time. But once the 144,000 are sealed, the four angels standing at the four corners of the earth are allowed to release the four winds which will hurt the earth, the sea and the trees. The hurting of the earth, the sea and the trees is in fact the beginning of the 7th seal.

7 candles of the Menorah

There are seven planets, namely: Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon.

The Seventh Sign is a 1988 film written by Clifford and Ellen Green and directed by Carl Schultz.( The seals have been broken. The prophecies have begun.)

Seven (also marketed as Se7en) is a 1995 American crime film ,(remember the head in the box at the end)could this have represented John the baptist?)

Chapter 7: 144,000 Sealed on Earth and a Throne Scene of Delivered Saints

7th Chakra of the earth, Great Pyramid & Mt Sinai & Mt of Olives Throat Chakra & air Spinner Wheel Egypt Middle East.http://www.earthchakras.org/

"Each of the major cathedrals along the pilgrimage were on ancient sites representing the seven major chakras of Europe.

The sites were:

Cathedral of St. James at Compostela (Moon Oracle) - base chakra
Notre-Dame de Dalbade Tolouse (Mercury Oracle) - sacral chakra
Orleans Cathedral (Venus Oracle) - solar pelxus chakra
Chartres Cathedral ( Sun Oracle) - heart chakra
Notre Dame de Paris (Mars Oracle) - throat chakra
Amiens Cathedral (Jupiter Oracle) - brow chakra
Rosslyn Chapel (Saturn Oracle) - crown chakra" (7,10)

THE SEVEN CHURCHES

Moving to the book of Revelation, we find letters to seven churches in Asia Minor. These seven churches, while they were literal congregations, they are also understood to be a description of a spectrum of seven conditions any church can find itself in. They are also considered symbolic for seven consecutive periods of time, from the Apostolic church to the time of the second coming as follows:

Ephesus ("desirable"), Rev. 2:1-7 — The Apostolic church of the 1st century.
Smyrna ("sweet smelling"), Rev. 2:8-11 — Persecuted by Ancient Pagan Rome.
Pergamos ("elevated by marriage"), Rev. 2:12-17 — Apostate church-state union.
Thyatira ("sacrifice of contrition"), Rev. 2:18-29 — The church of the middle ages.
Sardis ("escape of the remnant"), Rev. 3:1-6 — The Reformation era.
Philadelphia ("brotherly love"), Rev. 3:7-13 — The early 19th century to 1844.
Laodicea ("a people judged"), Rev. 3:14-19 — From 1844 to the second coming.

Knight of the Eagle and Pelican is one of the titles applied to a Rose-Croix ...... The number 7 is the sacred number in all theogo- nies and in all symbolisms. ..... the keystone of the Temple, the symbol of occult Ma- sonry ; — the cross, that central .... Mithra, it was said in the ancient Sabean Mysteries,

7/7 ripple effect

7 days in a week

More to come,there is a lot more to it.

 

SEVEN EVENS SEVEN


__________________
"Ye shall know them by their fruits"
~ Matthew 7:16

"Believe nothing. No matter where you read it, or who said it, even if I have said it, unless it agrees with your own reason and your own common sense."
~ Buddha

--------------------------------------------------------------------------------
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In astronomy, the Pleiades, or seven sisters, (Messier object 45) are an open star cluster in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky. Pleiades has several meanings in different cultures and traditions.

The cluster is dominated by hot blue stars that have formed within the last 100 million years. Dust that forms a faint reflection nebulosity around the brightest stars was thought at first to be left over from the formation of the cluster (hence the alternate name Maia Nebula after the star Maia), but is now known to be an unrelated dust cloud in the interstellar medium that the stars are currently passing through. Astronomers estimate that the cluster will survive for about another 250 million years, after which it will disperse due to gravitational interactions with its galactic neighbourhood.

The Babylonian star catalogues name them MUL.MUL or "star of stars", and they head the list of stars along the ecliptic, reflecting the fact that they were close to the point of vernal equinox around the 23rd century BC. Some Greek astronomers considered them to be a distinct constellation, and they are mentioned by Hesiod, and in Homer's Iliad and Odyssey. They are also mentioned three times in the Bible (Job 9:9 and 38:31, as well as Amos 5:8). The Pleiades (Krittika) are particularly revered in Hindu mythology as the six mothers of the war god Skanda, who developed six faces, one for each of them. Some scholars of Islam suggested that the Pleiades (Al thuraiya) are the Star in Najm which is mentioned in the Quran.

I sometimes wish someone else had started this thread,I am getting an aversion to the term Grand secretary,it should be petite secretary.

The Stargate Conspiracy: The Truth about Extraterrestrial life and the Mysteries of Ancient Egypt

In recent years, alternative historians have gained remarkable insight into the mysteries of ancient Egypt-but according to Lynn Picknett and Clive Prince, their discoveries tie into a dangerous conspiracy nearly fifty years in the making.

At the centre of this conspiracy is a group of respected, powerful individuals who believe that the ancient Egyptian gods are real extraterrestrials who will soon return to earth. The conspirators have intimate and exclusive knowledge of this momentous second coming-but they insist on keeping it to themselves. In this riveting, well-researched book, Picknett and Price reveal what this conspiracy means for the rest of mankind-and expose the insidious motivations of the individuals and organizations behind it...

The Greys were bugging me this morning while I slept,yeah 3 to 4 foot with their little probes and Needles.

The notion of an intellectual elite as a distinguished social stratum can be traced far back in history. Examples are the philosopher-kings and guardians of Plato's Republic and monks in medieval Europe, who are now seen as custodians of history and culture.

Their well-conceived United Religions Initiative will become a powerful tool to influence the masses toward their desired globalist agenda through a syncretic theology, which rabidly opposes religions, which do not conform to their syncretic doctrines, labelling them as intransigent and intolerant, narrow-minded bigots.

and on the 7 th day God took a break.

The Sirius Mystery - Robert Temple
Our own planet Earth is, significantly, 'the place where Ogo's umbilical cord was ..... When the seventh year comes round, a kind of trident is drawn on the outside ...... And near Knossos is a site called Omphalos which is one degree of ...... which is called 'path of the Nommo'.18 He is guardian of the 'spiritual

http://www.scribd.com/doc/2045191/Th...-Robert-Temple

'I'm not telling you up to seven times, I'm telling you up to seventy seven times!' "

 

SEVEN EVENS SEVEN

 

http://www.973-eht-namuh-973.com/col...s_1_cont_6.htm

The Illuminati and the Masonic "G":

7 = 3+4 = C+T = G

http://illuminatusobservor.blogspot....masonic-g.html

In Morals and Dogma, Albert Pike writes that Sirius was "the inventor of language, grammar, ... to the second degree in Masonry, whilst the seventh initiation makes the Adept a Master Mason of the Brotherhood of Sirius. ...

http://www.whale.to/b/melanson.html

seventh degree Melchizedek Ambassador of Light. http://www.waking-up.com/issue001/service.html

Noble Realms / The Matrix built by Sirians ? Sirius Serious ?:

 

 

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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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

 

 

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

 

3 4 5

PYTHAGORAS

THE MISSING NUMBERS IN THE WORD

PYTHAGORAS

3 4 5

 

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..."

 

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

3 4 5

PYTHAGORAS

THE MISSING NUMBERS IN THE WORD

PYTHAGORAS

3 4 5

 

-
-
-
-
-
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

 

 

A

SERPENT I PRESENT

 

9
OURABORUS
130
31
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

 

 

 

 

 

 

 
 
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