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Evokation
  
 
Index
  

 

-
-
-
-
-
-
-
-
-
-
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
995
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
9+9+5
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
23
14
10
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
2+3
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

 

 

 

 

-
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
-
7
-
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
-
7
-
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
-
7
-
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
-
7
--
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
-
7
-
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
-
7
-
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
1
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
6
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
=
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
16
7
H
I
N
O
S
X
Z
-
-
29
-
-
7
-
43
-
25
1+6
-
-
9
-
-
9
-
-
-
-
2+9
-
-
-
-
4+3
-
2+5
7
7
H
I
N
O
S
X
Z
-
-
11
-
-
7
-
7
-
7
1+6
-
8
9
5
6
1
6
8
-
-
1+1
-
-
-
-
-
-
-
7
7
H
I
N
O
S
X
Z
-
-
2
-
-
7
-
7
-
7

 

 

7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
=
7
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
=
7
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
=
7
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
=
7
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
=
7
=
7
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
=
7
=
7
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
6
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
8
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
7
H
I
N
O
S
X
Z
-
-
29
-
-
7
-
43
-
25
-
-
9
-
-
9
-
-
-
-
2+9
-
-
-
-
4+3
-
2+5
7
H
I
N
O
S
X
Z
-
-
11
-
-
7
-
7
-
7
-
8
9
5
6
1
6
8
-
-
1+1
-
-
-
-
-
-
-
7
H
I
N
O
S
X
Z
-
-
2
-
-
7
-
7
-
7

 

 

7
H
I
N
O
S
X
Z
-
-
-
-
-
--
-
8
9
14
15
19
24
26
+
=
115
1+1+5
=
7
7
H
I
N
O
S
X
Z
-
-
-
-
-
--
-
8
9
5
6
1
6
8
+
=
43
4+3
=
7
7
H
I
N
O
S
X
Z
-
-
-
-
-
-
-
H
-
-
-
-
-
Z
-
-
-
-
-
-
-
8
-
-
-
-
-
8
+
=
16
1+6
=
7
-
-
I
-
-
-
X
-
-
-
-
-
-
-
-
-
9
-
-
-
6
-
+
=
15
1+5
=
6
-
-
-
N
-
S
-
-
-
-
-
-
-
-
-
-
-
5
-
1
-
-
+
=
6
-
-
6
-
-
-
-
O
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
+
=
6
-
-
6
7
H
I
N
O
S
X
Z
-
-
43
-
-
25
-
8
9
5
6
1
6
8
-
-
4+3
-
-
2+5
7
H
I
N
O
S
X
Z
-
-
7
-
-
7
-
8
9
14
15
19
24
26
-
-
-
-
-
-
7
H
I
N
O
S
X
Z
-
-
7
-
-
7

 

....

 

4
ZERO
64
28
1
3
ONE
34
16
7
-
-
-
-
-
-
-
-
-
-
3
TEN
39
12
3

 

 

-
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
8
-
-
6
+
=
14
1+4
=
5
=
5
-
-
26
-
-
15
+
=
41
4+1
=
5
=
5
-
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
-
5
9
-
+
=
14
1+4
=
5
=
5
-
-
-
5
18
-
+
=
23
2+3
=
5
=
5
-
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
26
5
18
15
+
=
64
6+4
=
10
1+0
1
-
-
8
5
9
6
+
=
28
2+8
=
10
1+0
1
-
4
Z
E
R
O
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
17
4
Z
E
R
O
-
-
28
-
-
4
-
28
1+7
-
-
-
9
-
-
-
2+8
-
-
-
-
2+8
8
4
Z
E
R
O
-
-
10
-
-
4
-
10
-
-
8
5
9
6
-
-
1+0
-
-
-
-
1+0
8
4
Z
E
R
O
-
-
1
-
-
4
-
1

 

 

4
Z
E
R
O
-
-
-
-
-
-
-
-
-
8
-
-
6
+
=
14
1+4
=
5
=
5
-
26
-
-
15
+
=
41
4+1
=
5
=
5
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
5
9
-
+
=
14
1+4
=
5
=
5
-
-
5
18
-
+
=
23
2+3
=
5
=
5
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
26
5
18
15
+
=
64
6+4
=
10
1+0
1
-
8
5
9
6
+
=
28
2+8
=
10
1+0
1
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
9
-
-
-
9
occurs
x
1
=
9
4
Z
E
R
O
-
-
28
-
-
4
-
28
-
-
-
9
-
-
-
2+8
-
-
-
-
2+8
4
Z
E
R
O
-
-
10
-
-
4
-
10
-
8
5
9
6
-
-
1+0
-
-
-
-
1+0
4
Z
E
R
O
-
-
1
-
-
4
-
1

 

 

 

 

4
ZERO
64
28
1
3
ONE
34
16
7
-
-
-
-
-
-
-
-
-
-
3
TEN
39
12
3

 

 

 

-
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
+
=
11
1+1
=
2
=
2
=
2
-
-
15
14
-
+
=
29
2+9
=
11
1+1
2
=
2
-
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
15
14
5
+
=
34
3+4
=
7
=
7
=
7
-
-
6
5
5
+
=
16
1+6
=
7
=
7
=
7
-
3
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
34
3
O
N
E
-
-
11
-
-
3
-
16
-
7
3+4
-
-
-
-
-
-
1+1
-
-
-
-
1+6
-
-
7
3
O
N
E
-
-
2
-
-
3
-
7
-
7
-
-
6
5
5
-
-
-
-
-
-
-
-
-
-
7
3
O
N
E
-
-
2
-
-
3
-
7
-
7

 

 

3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
6
5
-
+
=
11
1+1
=
2
=
2
=
2
-
15
14
-
+
=
29
2+9
=
11
1+1
2
=
2
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
5
+
=
5
-
=
5
=
5
=
5
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
15
14
5
+
=
34
3+4
=
7
=
7
=
7
-
6
5
5
+
=
16
1+6
=
7
=
7
=
7
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
3
O
N
E
-
-
11
-
-
3
-
16
-
7
-
-
-
-
-
-
1+1
-
-
-
-
1+6
-
-
3
O
N
E
-
-
2
-
-
3
-
7
-
7
-
6
5
5
-
-
-
-
-
-
-
-
-
-
3
O
N
E
-
-
2
-
-
3
-
7
-
7

 

 

-
3
T
W
O
-
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
T
W
O
-
-
-
-
-
-
-
-
-
-
2
5
-
+
=
7
-
=
7
=
7
-
-
20
23
-
+
=
43
4+3
=
7
=
7
-
3
T
W
O
-
-
-
-
-
-
-
-
-
-
20
23
15
+
=
58
5+8
=
13
1+3
4
-
-
2
5
6
+
=
13
1+3
=
4
=
4
-
3
T
W
O
T
-
-
-
-
-
-
-
1
-
3
-
3
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
---
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
32
3
T
W
O
-
-
13
-
-
3
-
13
3+2
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
3
T
W
O
-
-
4
-
-
3
-
4
-
-
2
5
6
T
-
-
-
-
-
-
-
5
3
T
W
O
-
-
4
-
-
3
-
4

 

 

3
T
W
O
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
T
W
O
-
-
-
-
-
-
-
-
-
2
5
-
+
=
7
-
=
7
=
7
-
20
23
-
+
=
43
4+3
=
7
=
7
3
T
W
O
-
-
-
-
-
-
-
-
-
20
23
15
+
=
58
5+8
=
13
1+3
4
-
2
5
6
+
=
13
1+3
=
4
=
4
3
T
W
O
T
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
6
occurs
x
1
=
6
3
T
W
O
-
-
13
-
-
3
-
13
-
-
-
-
-
-
1+3
-
-
-
-
1+3
3
T
W
O
-
-
4
-
-
3
-
4
-
2
5
6
T
-
-
-
-
-
-
-
3
T
W
O
-
-
4
-
-
3
-
4

 

 

-
5
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
+
=
8
-
=
8
=
8
=
8
-
-
-
8
-
-
-
+
=
8
-
=
8
=
8
=
8
-
5
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
9
5
5
+
=
21
2+1
=
3
=
3
=
3
-
-
20
-
18
5
5
+
=
48
4+8
=
12
1+2
3
=
3
-
5
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
20
8
18
5
5
+
=
56
5+6
=
11
1+1
2
=
2
-
-
2
8
9
5
5
+
=
29
2+9
=
11
1+1
2
=
2
-
5
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
21
5
T
H
R
E
E
-
-
24
-
-
5
-
29
-
20
2+1
-
-
-
9
-
-
-
-
2+4
-
-
-
-
2+9
-
2+0
3
5
T
H
R
E
E
-
-
6
-
-
5
-
11
-
2
-
-
2
8
9
5
5
-
-
-
-
-
-
-
1+1
-
-
3
5
T
H
R
E
E
-
-
6
-
-
5
-
2
-
2

 

 

5
T
H
R
E
E
-
-
-
-
-
=
-
-
-
-
-
-
8
-
-
-
+
=
8
-
=
8
=
8
=
8
-
-
8
-
-
-
+
=
8
-
=
8
=
8
=
8
5
T
H
R
E
E
-
-
-
-
-
=
-
-
-
-
-
2
-
9
5
5
+
=
21
2+1
=
3
=
3
=
3
-
20
-
18
5
5
+
=
48
4+8
=
12
1+2
3
=
3
5
T
H
R
E
E
-
-
-
-
-
=
-
-
-
-
-
20
8
18
5
5
+
=
56
5+6
=
11
1+1
2
=
2
-
2
8
9
5
5
+
=
29
2+9
=
11
1+1
2
=
2
5
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
=
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
5
T
H
R
E
E
-
-
24
-
-
5
-
29
-
20
-
-
-
9
-
-
-
-
2+4
-
-
-
-
2+9
-
2+0
5
T
H
R
E
E
-
-
6
-
-
5
-
11
-
2
-
2
8
9
5
5
-
-
-
-
-
-
-
1+1
-
-
5
T
H
R
E
E
-
-
6
-
-
5
-
2
-
2

 

 

-
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
+
=
15
1+5
=
6
=
6
=
6
-
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
-
3
9
+
=
18
1+8
=
9
=
9
=
9
-
-
6
-
21
18
+
=
45
4+5
=
9
=
9
=
9
-
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
15
21
18
+
=
60
6+0
=
6
=
6
=
6
-
-
6
6
3
9
+
=
24
2+4
=
6
=
6
=
6
-
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
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
occurs
x
1
=
9
=
9
27
4
F
O
U
R
-
-
18
-
-
4
-
24
-
15
2+7
-
-
-
-
9
-
-
1+8
-
-
-
-
2+4
-
1+5
9
4
F
O
U
R
-
-
9
-
-
4
-
6
-
6
-
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
4
F
O
U
R
-
-
9
-
-
4
-
6
-
6

 

 

4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
=
6
-
-
15
-
-
+
=
15
1+5
=
6
=
6
=
6
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
6
-
3
9
+
=
18
1+8
=
9
=
9
=
9
-
6
-
21
18
+
=
45
4+5
=
9
=
9
=
9
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
6
15
21
18
+
=
60
6+0
=
6
=
6
=
6
-
6
6
3
9
+
=
24
2+4
=
6
=
6
=
6
4
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
6
6
-
-
--
--
6
occurs
x
2
=
12
1+2
3
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
4
F
O
U
R
-
-
18
-
-
4
-
24
-
15
-
-
-
-
9
-
-
1+8
-
-
-
-
2+4
-
1+5
4
F
O
U
R
-
-
9
-
-
4
-
6
-
6
-
6
6
3
9
-
-
-
-
-
-
-
-
-
-
4
F
O
U
R
-
-
9
-
-
4
-
6
-
6

 

 

-
4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
-
-
-
9
-
-
+
=
9
-
=
9
=
9
-
4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
6
-
4
5
+
=
15
1+5
=
6
=
6
-
-
6
-
22
5
+
=
33
3+3
=
6
=
6
-
4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
6
9
22
5
+
=
42
4+2
=
6
=
6
-
-
6
9
4
5
+
=
24
2+4
=
6
=
6
-
4
F
I
V
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
21
4
F
I
V
E
-
-
24
-
-
4
-
24
2+1
-
-
9
-
-
-
-
2+4
-
-
-
-
2+4
3
4
F
I
V
E
-
-
6
-
-
4
-
6
-
-
6
9
4
5
-
-
-
-
-
-
-
-
3
4
F
I
V
E
-
-
6
-
-
4
-
6

 

 

4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
-
-
9
-
-
+
=
9
-
=
9
=
9
4
F
I
V
E
-
-
-
-
-
-
-
-
-
6
-
4
5
+
=
15
1+5
=
6
=
6
-
6
-
22
5
+
=
33
3+3
=
6
=
6
4
F
I
V
E
-
-
-
-
-
-
-
-
-
6
9
22
5
+
=
42
4+2
=
6
=
6
-
6
9
4
5
+
=
24
2+4
=
6
=
6
4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
6
-
-
-
-
-
6
occurs
x
2
=
12
-
-
9
-
-
-
-
9
occurs
x
1
=
9
4
F
I
V
E
-
-
24
-
-
4
-
24
-
-
9
-
-
-
-
2+4
-
-
-
-
2+4
4
F
I
V
E
-
-
6
-
-
4
-
6
-
6
9
4
5
-
-
-
-
-
-
-
-
4
F
I
V
E
-
-
6
-
-
4
-
6

 

 

-
3
S
I
X
-
-
-
-
-
-
-
-
-
-
1
9
6
+
=
16
1+6
=
7
=
7
-
-
19
9
24
+
=
52
5+2
=
7
=
7
-
3
S
I
X
-
-
-
-
-
-
-
-
-
-
1
9
6
+
=
16
1+6
=
7
=
7
-
-
19
9
24
+
=
52
5+2
=
7
=
7
-
3
S
I
X
-
-
-
-
-
-
-
-
-
-
19
9
24
+
=
52
5+2
=
7
=
7
-
-
1
9
6
+
=
16
1+6
=
7
=
7
-
3
S
I
X
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
29
3
S
I
X
-
-
16
-
-
3
-
16
2+9
-
-
9
-
-
-
1+6
-
-
-
-
1+6
11
3
S
I
X
-
-
7
-
-
3
-
7
1+1
-
1
9
6
-
-
-
-
-
-
-
-
2
3
S
I
X
-
-
7
-
-
3
-
7

 

 

3
S
I
X
-
-
-
-
-
-
-
-
-
1
9
6
+
=
16
1+6
=
7
=
7
-
19
9
24
+
=
52
5+2
=
7
=
7
3
S
I
X
-
-
-
-
-
-
-
-
-
1
9
6
+
=
16
1+6
=
7
=
7
-
19
9
24
+
=
52
5+2
=
7
=
7
3
S
I
X
-
-
-
-
-
-
-
-
-
19
9
24
+
=
52
5+2
=
7
=
7
-
1
9
6
+
=
16
1+6
=
7
=
7
3
S
I
X
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
9
-
-
-
9
occurs
x
1
=
9
3
S
I
X
-
-
16
-
-
3
-
16
-
-
9
-
-
-
1+6
-
-
-
-
1+6
3
S
I
X
-
-
7
-
-
3
-
7
-
1
9
6
-
-
-
-
-
-
-
-
3
S
I
X
-
-
7
-
-
3
-
7

 

 

-
5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
5
+
=
6
-
=
6
=
6
=
6
-
-
19
-
-
-
14
+
=
33
3+3
=
6
=
6
=
6
-
5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
5
4
5
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
5
22
5
-
+
=
32
3+2
=
5
=
5
=
5
-
5
S
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
-
19
5
22
5
14
+
=
65
6+5
=
11
1+1
2
=
2
-
-
1
5
4
5
5
+
=
20
2+0
=
2
=
2
=
2
-
5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
35
5
S
E
V
E
N
-
-
10
-
-
5
-
20
-
11
3+5
-
-
5
-
5
5
-
-
1+0
-
-
-
-
2+0
-
1+1
8
5
S
E
V
E
N
-
-
1
-
-
5
-
2
-
2
-
-
1
5
4
5
5
-
-
-
-
-
-
-
-
-
-
8
5
S
E
V
E
N
-
-
1
-
-
5
-
2
-
2

 

 

5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
5
+
=
6
-
=
6
=
6
=
6
-
19
-
-
-
14
+
=
33
3+3
=
6
=
6
=
6
5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
-
5
4
5
-
+
=
14
1+4
=
5
=
5
=
5
-
-
5
22
5
-
+
=
32
3+2
=
5
=
5
=
5
5
S
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
19
5
22
5
14
+
=
65
6+5
=
11
1+1
2
=
2
-
1
5
4
5
5
+
=
20
2+0
=
2
=
2
=
2
5
S
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
5
S
E
V
E
N
-
-
10
-
-
5
-
20
-
11
-
-
5
-
5
5
-
-
1+0
-
-
-
-
2+0
-
1+1
5
S
E
V
E
N
-
-
1
-
-
5
-
2
-
2
-
1
5
4
5
5
-
-
-
-
-
-
-
-
-
-
5
S
E
V
E
N
-
-
1
-
-
5
-
2
-
2

 

 

-
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
`-
-
9
-
8
-
+
=
17
1+7
=
8
=
8
-
-
-
9
-
8
-
+
=
17
1+7
=
8
=
8
-
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
-
5
-
7
-
2
+
=
14
1+4
=
5
=
5
-
-
5
-
7
-
20
+
=
32
3+2
=
5
=
5
-
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
-
5
9
7
8
20
+
=
49
4+9
=
13
1+3
4
-
-
5
9
7
8
2
+
=
31
3+1
=
4
=
4
-
5
E
I
G
H
T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
14
5
E
I
G
H
T
-
-
31
-
-
5
-
31
1+4
-
-
9
-
-
-
-
-
3+1
-
-
-
-
3+1
5
5
E
I
G
H
T
-
-
4
-
-
5
-
4
-
-
5
9
7
8
2
-
-
-
-
-
-
-
-
5
5
E
I
G
H
T
-
-
4
-
-
5
-
4

 

 

5
E
I
G
H
T
-
-
-
-
-
-
-
-
`-
-
9
-
8
-
+
=
17
1+7
=
8
=
8
-
-
9
-
8
-
+
=
17
1+7
=
8
=
8
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
5
-
7
-
2
+
=
14
1+4
=
5
=
5
-
5
-
7
-
20
+
=
32
3+2
=
5
=
5
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
5
9
7
8
20
+
=
49
4+9
=
13
1+3
4
-
5
9
7
8
2
+
=
31
3+1
=
4
=
4
5
E
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
5
E
I
G
H
T
-
-
31
-
-
5
-
31
-
-
9
-
-
-
-
-
3+1
-
-
-
-
3+1
5
E
I
G
H
T
-
-
4
-
-
5
-
4
-
5
9
7
8
2
-
-
-
-
-
-
-
-
5
E
I
G
H
T
-
-
4
-
-
5
-
4

 

 

-
4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
9
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
14
9
14
-
+
=
37
3+7
=
10
1+0
1
=
1
-
4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
14
9
14
5
+
=
42
4+2
=
6
=
6
=
6
-
-
5
9
5
5
+
=
24
2+4
=
6
=
6
=
6
-
4
N
I
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
31
4
N
I
N
E
-
-
14
-
-
4
-
24
-
15
3+1
-
5
-
5
5
-
-
1+4
-
-
-
-
2+4
-
1+5
4
4
N
I
N
E
-
-
5
-
-
4
-
6
-
6
-
-
5
9
5
5
-
-
-
-
-
-
-
-
-
-
4
4
N
I
N
E
-
-
5
-
-
4
-
6
-
6

 

 

4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
5
9
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
14
9
14
-
+
=
37
3+7
=
10
1+0
1
=
1
4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
4
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
14
9
14
5
+
=
42
4+2
=
6
=
6
=
6
-
5
9
5
5
+
=
24
2+4
=
6
=
6
=
6
4
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
4
N
I
N
E
-
-
14
-
-
4
-
24
-
15
-
5
-
5
5
-
-
1+4
-
-
-
-
2+4
-
1+5
4
N
I
N
E
-
-
5
-
-
4
-
6
-
6
-
5
9
5
5
-
-
-
-
-
-
-
-
-
-
4
N
I
N
E
-
-
5
-
-
4
-
6
-
6

 

 

-
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
14
+
=
14
1+4
=
5
=
5
=
5
-
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
-
2
5
-
+
=
7
-
=
7
=
7
=
7
-
-
20
5
-
+
=
25
2+5
=
7
=
7
=
7
-
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
-
20
5
14
+
=
39
3+9
=
12
1+2
3
=
3
-
-
2
5
5
+
=
12
1+2
=
3
=
3
=
3
-
3
T
E
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
38
3
T
E
N
-
-
7
-
-
3
-
12
-
3
3+8
-
-
-
-
-
-
-
-
-
-
-
1+2
-
-
11
3
T
E
N
-
-
7
-
-
3
-
3
-
3
1+1
-
2
5
5
-
-
-
-
-
--
-
-
-
-
2
3
T
E
N
-
-
7
-
-
3
-
3
-
3

 

 

3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
14
+
=
14
1+4
=
5
=
5
=
5
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
2
5
-
+
=
7
-
=
7
=
7
=
7
-
20
5
-
+
=
25
2+5
=
7
=
7
=
7
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
20
5
14
+
=
39
3+9
=
12
1+2
3
=
3
-
2
5
5
+
=
12
1+2
=
3
=
3
=
3
3
T
E
N
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
3
T
E
N
-
-
7
-
-
3
-
12
-
3
-
-
-
-
-
-
-
-
-
-
-
1+2
-
-
3
T
E
N
-
-
7
-
-
3
-
3
-
3
-
2
5
5
-
-
-
-
-
--
-
-
-
-
3
T
E
N
-
-
7
-
-
3
-
3
-
3

 

 

-
6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
-
-
-
14
+
=
14
1+4
=
5
=
5
=
5
-
6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
-
5
3
5
4
5
-
+
=
22
2+2
=
4
=
4
=
4
-
-
5
12
5
22
5
-
+
=
49
4+9
=
13
1+3
4
=
4
-
6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
-
5
12
5
22
5
14
+
=
63
6+3
=
9
=
9
=
9
-
-
5
3
5
4
5
5
+
=
27
2+7
=
9
=
9
=
9
-
6
E
L
E
V
E
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
33
6
E
L
E
V
E
N
-
-
12
-
-
6
-
27
-
9
3+3
-
-
-
-
-
-
-
-
-
1+2
-
-
-
-
2+7
-
-
6
6
E
L
E
V
E
N
-
-
3
-
-
6
-
9
-
9
-
-
5
3
5
4
5
5
-
-
-
-
-
-
-
-
-
-
6
6
E
L
E
V
E
N
-
-
3
-
-
6
-
9
-
9

 

 

6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
-
-
-
-
-
14
+
=
14
1+4
=
5
=
5
=
5
6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
5
3
5
4
5
-
+
=
22
2+2
=
4
=
4
=
4
-
5
12
5
22
5
-
+
=
49
4+9
=
13
1+3
4
=
4
6
E
L
E
V
E
N
-
-
-
-
-
--
-
-
-
-
-
5
12
5
22
5
14
+
=
63
6+3
=
9
=
9
=
9
-
5
3
5
4
5
5
+
=
27
2+7
=
9
=
9
=
9
6
E
L
E
V
E
N
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
5
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
6
E
L
E
V
E
N
-
-
12
-
-
6
-
27
-
9
-
-
-
-
-
-
-
-
-
1+2
-
-
-
-
2+7
-
-
6
E
L
E
V
E
N
-
-
3
-
-
6
-
9
-
9
-
5
3
5
4
5
5
-
-
-
-
-
-
-
-
-
-
6
E
L
E
V
E
N
-
-
3
-
-
6
-
9
-
9

 

 

-
-
-
-
0
ZERO
-
-
-
-
-
-
2
-
Z+E
31
13
4
-
-
-
1
-
R
18
9
9
-
-
-
1
-
O
15
6
6
Z
=
8
4
4
ZERO
64
28
19
-
-
-
-
-
-
9+1
1+9
1+9
Z
=
8
4
-
ZERO
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
Z
=
8
4
-
ZERO
10
10
10

 

 

-
-
-
-
1
ONE
-
-
-
-
-
-
1
-
O
15
6
6
-
-
-
1
-
N
14
5
5
-
-
-
1
-
E
5
5
5
O
=
6
3
4
ONE
34
16
16
-
-
-
-
-
-
3+4
1+6
1+6
O
=
6
3
4
ONE
7
7
7

 

 

-
-
-
-
2
TWO
-
-
-
-
-
-
1
-
T
20
2
2
-
-
-
1
-
W
23
5
5
-
-
-
1
-
O
15
6
6
T
=
2
3
4
TWO
58
13
13
-
-
-
-
-
-
5+8
1+3
1+3
T
=
2
3
4
TWO
13
4
4
-
-
-
-
-
-
1+3
-
-
T
=
2
3
4
TWO
4
4
4

 

 

-
-
-
-
3
THREE
-
-
-
-
-
-
1
-
T
20
2
2
-
-
-
1
-
H
8
8
8
-
-
-
1
-
R
18
9
9
-
-
-
2
-
E+E
10
10
1
T
=
2
5
4
THREE
56
29
20
-
-
-
-
-
-
5+6
2+9
2+0
T
=
2
5
4
THREE
11
11
2
-
-
-
-
-
-
1+1
1+1
-
T
=
2
5
4
THREE
2
2
2

 

 

-
-
-
-
4
FOUR
-
-
-
-
-
-
1
-
F
6
6
6
-
-
-
2
-
O+U
36
9
9
-
-
-
1
-
R
18
9
9
F
=
6
4
4
FOUR
60
24
24
-
-
-
-
-
-
6+0
2+4
2+4
F
-
6
4
4
FOUR
6
6
6

 

 

-
-
-
-
5
FIVE
-
-
-
-
-
-
1
-
F
6
6
6
-
-
-
1
-
I
9
9
9
-
-
-
2
-
V+E
27
9
9
F
=
6
4
4
FIVE
60
24
24
-
-
-
-
-
-
6+0
2+4
2+4
F
=
6
4
4
FIVE
6
6
6

 

 

-
-
-
-
6
SIX
-
-
-
-
-
-
1
-
S
19
10
1
-
-
-
1
-
I
9
9
9
-
-
-
1
-
X
24
6
6
S
=
1
3
4
SIX
52
25
16
-
-
-
-
-
-
5+2
2+5
1+6
S
=
1
3
4
SIX
7
7
7

 

 

-
-
-
-
7
SEVEN
-
-
-
-
-
-
1
-
S
19
10
1
-
-
-
2
-
E+V
27
9
9
-
-
-
2
-
E+N
19
10
1
S
=
1
5
4
SEVEN
65
29
11
-
-
-
-
-
-
6+5
2+9
1+1
S
=
2
5
4
SEVEN
11
11
2
-
-
-
-
-
-
1+1
1+1
-
S
=
2
5
4
SEVEN
2
2
2

 

 

-
-
-
-
8
EIGHT
-
-
-
-
-
-
1
-
E
5
5
5
-
-
-
1
-
I
9
9
9
-
-
-
3
-
G+H+T
35
17
8
E
=
5
5
4
EIGHT
49
31
4
-
-
-
-
-
-
4+9
3+1
-
E
=
5
5
4
EIGHT
13
4
4
-
-
-
-
-
-
1+3
-
-
E
=
5
5
4
EIGHT
4
4
4

 

 

-
-
-
-
9
NINE
-
-
-
-
-
-
1
-
N
14
5
5
-
-
-
1
-
I
9
9
9
-
-
-
2
-
N+E
19
10
1
N
=
5
4
4
NINE
42
24
13
-
-
-
-
-
-
4+2
2+4
1+3
N
=
5
3
4
NINE
6
6
6

 

 

-
-
-
10
-
TEN
--
-
-
-
-
-
-
1
T
20
2
2
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
T
=
2
10
3
TEN
39
12
12
-
-
-
-
-
-
3+9
1+2
1+2
T
=
2
10
3
TEN
12
3
3
-
-
-
-
-
-
1+2
-
-
T
=
2
10
3
TEN
3
3
3

 

 

-
-
-
11
-
ELEVEN
--
-
-
-
-
-
-
3
E+L+E
22
13
4
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
N
14
5
5
E
=
5
11
6
ELEVEN
63
27
18
-
-
-
-
-
-
6+3
2+7
1+8
E
=
5
11
6
ELEVEN
9
9
9

 

 

-
-
-
12
-
TWELVE
--
-
-
-
-
-
-
4
T+W+E+L
60
15
6
-
-
-
-
2
V+E
27
9
9
T
=
2
12
6
TWELVE
87
24
15
-
-
-
-
-
-
8+7
2+4
1+5
T
=
2
12
6
TWELVE
15
6
6
6
-
-
-
-
-
1+5
-
-
T
=
2
12
6
TWELVE
6
6
6

 

 

-
-
-
13
-
THIRTEEN
--
-
-
-
-
-
-
2
T+H
28
10
1
-
-
-
-
1
I
9
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
4
T+E+E+N
44
17
8
T
=
2
13
8
THIRTEEN
99
45
27
-
-
-
-
-
-
9+9
4+5
2+7
T
=
2
13
8
THIRTEEN
18
9
9
6
-
-
-
-
-
1+8
-
-
T
=
2
13
8
THIRTEEN
9
9
9

 

 

-
-
-
14
-
FOURTEEN
--
-
-
-
-
-
-
1
F
6
6
6
-
-
-
-
2
O+U
36
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
4
T+E+E+N
44
17
8
F
=
6
14
8
FOURTEEN
104
41
32
-
-
-
-
-
-
1+0+4
4+1
3+2
F
=
6
14
8
FOURTEEN
5
5
5

 

 

-
-
-
15
-
FIFTEEN
--
-
-
-
-
-
-
1
F
6
6
6
-
-
-
-
1
I
9
9
9
-
-
-
-
5
F+T+E+E+N
50
23
5
F
=
6
15
7
FIFTEEN
65
38
20
-
-
-
-
-
-
6+5
3+8
2+0
F
=
6
15
7
FIFTEEN
11
11
2
6
-
-
-
-
-
1+1
1+1
-
F
=
6
15
7
FIFTEEN
2
2
2

 

 

-
-
-
16
-
SIXTEEN
--
-
-
-
-
-
-
1
S
19
10
1
-
-
-
-
1
I
9
9
9
-
-
-
-
4
X+T+E+E
54
18
9
-
-
-
-
1
N
14
5
5
S
=
1
16
7
SIXTEEN
96
42
24
-
-
-
-
-
-
9+6
4+2
2+4
S
=
1
16
7
SIXTEEN
15
6
6
6
-
-
-
-
-
1+5
-
-
S
=
1
16
7
SIXTEEN
6
6
6

 

 

-
-
-
17
-
SEVENTEEN
--
-
-
-
-
-
-
1
S
19
10
1
-
-
-
-
2
E+V
27
9
9
-
-
-
-
6
E+N+T+E+E+N
63
27
9
S
=
1
17
9
SEVENTEEN
109
46
19
-
-
-
-
-
-
1+0+9
4+6
1+9
S
=
1
17
9
SEVENTEEN
10
10
10
6
-
-
-
-
-
1+0
1+0
1+0
S
=
1
17
9
SEVENTEEN
1
1
1

 

 

-
-
-
18
-
EIGHTEEN
--
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
I
9
9
9
-
-
-
-
5
G+H+T+E+E
45
27
9
-
-
-
-
1
N
14
5
5
E
=
5
18
8
EIGHTEEN
73
46
28
-
-
-
-
-
-
7+3
4+6
2+8
E
=
5
18
8
EIGHTEEN
10
10
10
6
-
-
-
-
-
1+0
1+0
1+0
E
=
5
18
8
EIGHTEEN
1
1
1

 

 

-
TEEN
--
-
-
1
T
20
2
2
3
E+E+N
24
15
6
4
TEEN
44
17
8
-
-
4+4
1+7
-
4
TEEN
8
8
8

 

 

-
-
-
-
TEEN
--
-
-
-
-
-
1
T
20
2
2
-
-
-
1
E
5
5
5
-
-
-
1
E
5
5
5
-
-
-
1
N
14
5
5
T
=
2
4
TEEN
44
17
17
-
-
-
-
-
4+4
1+7
1+7
T
=
2
4
TEEN
8
8
8

 

 

G
=
7
-
7
GRAHAMS
67
31
4
N
=
5
-
6
NUMBER
73
28
1
-
-
12
Q
13
First Total
140
59
5
-
-
1+2
-
1+3
Add to Reduce
1+4+0
5+9
-
-
-
3
-
4
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
3
-
4
Essence of Number
5
5
5

 

 

Graham's number - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Graham's_numberCached -

Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory. The number ...

Graham's problem - Definition of Graham's number

Graham's number From Wikipedia, the free encyclopediaJump to: navigation, search
This article is about the large number named after Ronald Graham. For the investing term named after Benjamin Graham, see Graham number.
Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.

The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977, writing that, "In an unpublished proof, Graham has recently established ... a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof." The 1980 Guinness Book of World Records repeated Gardner's claim, adding to the popular interest in this number.

Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number. Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume. Even power towers of the form are useless for this purpose, although it can be easily described by recursive formulas using Knuth's up-arrow notation or the equivalent, as was done by Graham. The last ten digits of Graham's number are ...2464195387.

Specific integers known to be far larger than Graham's number have since appeared in many serious mathematical proofs (e.g., in connection with Friedman's various finite forms of Kruskal's theorem

The last ten digits of Graham's number are ...2464195387.

 

1234456789

 

 

-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
-
8
-
-
19
-
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
-
7
18
1
-
1
13
-
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
-
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
6
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
-
1+3
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
6
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
6
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
8
-
-
19
-
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
7
18
1
-
1
13
-
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
-
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
1+3
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
8
-
-
19
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
7
18
1
-
1
13
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
7
9
1
8
1
4
1
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
1+3
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
4
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
7
9
1
8
1
4
1
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
4
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

LIGHT DARK BALANCING TWILIGHT BALANCING DARK LIGHT

DARK LIGHT BALANCING TWILIGHT BALANCING LIGHT DARK

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
14
5
3
THE
33
15
6
5
LIGHT
56
29
2
7
BRINGER
73
46
1
22
Add to Reduce
234
126
27
2+2
Reduce to Deduce
2+3+4
1+2+6
2+7
4
Essence of Number
9
9
9

 

 

-
10
P
R
O
M
E
T
H
E
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
8
-
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
15
-
-
-
8
-
-
19
+
=
42
4+2
=
6
=
6
=
6
-
10
P
R
O
M
E
T
H
E
U
S
-
-
-
-
-
-
-
-
-
-
-
-
7
9
-
4
5
2
-
5
3
-
+
=
35
3+5
=
8
=
8
=
8
-
-
16
18
-
13
5
20
-
5
21
-
+
=
98
9+8
=
17
1+7
8
=
8
-
10
P
R
O
M
E
T
H
E
U
S
-
-
-
-
-
-
-
-
-
-
-
-
16
18
15
13
5
20
8
5
21
19
+
=
140
1+4+0
=
5
=
5
=
5
-
-
7
9
6
4
5
2
8
5
3
1
+
=
50
5+0
=
5
=
5
=
5
-
10
P
R
O
M
E
T
H
E
U
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
5
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
45
10
P
R
O
M
E
T
H
E
U
S
-
-
45
-
-
10
-
50
-
41
4+5
1+0
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
1+0
-
5+0
-
4+1
9
1
P
R
O
M
E
T
H
E
U
S
-
-
9
-
-
1
-
5
-
5
-
-
7
9
6
4
5
2
8
5
3
1
-
-
-
-
-
-
-
-
-
-
9
1
P
R
O
M
E
T
H
E
U
S
-
-
9
-
-
1
-
5
-
5

 

 

3
THE
33
15
6
5
LIGHT
56
29
2
7
BRINGER
73
46
1
15
Add to Reduce
162
90
9
1+5
Reduce to Deduce
1+6+2
9+0
-
6
Essence of Number
9
9
9

 

 

-
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
8
-
-
-
-
9
5
-
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
8
-
-
-
9
-
8
-
-
-
-
9
14
-
-
-
+
=
48
4+8
=
12
1+2
3
=
3
-
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
7
-
2
-
2
9
-
-
7
5
9
+
=
51
5+1
=
6
=
6
=
6
-
-
20
-
5
-
12
-
7
-
20
-
2
18
-
-
7
5
18
+
=
114
1+1+4
=
6
=
6
=
6
-
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
12
9
7
8
20
-
2
18
9
14
7
5
18
+
+
162
1+6+2
=
9
=
9
=
9
-
-
2
8
5
-
3
9
7
8
2
-
2
9
9
5
7
5
9
+
+
90
9+0
=
9
=
9
=
9
-
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
``-
2
-
-
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
9
-
-
9
occurs
x
4
=
36
-
9
11
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
34
-
-
15
-
90
-
36
1+1
1+5
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
9
-
-
3+4
-
-
1+5
-
5+4
-
3+6
2
6
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
7
-
-
6
-
9
-
9
-
-
2
8
5
-
3
9
7
8
2
-
2
9
9
5
7
5
9
-
-
-
-
-
-
-
-
-
-
2
6
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
7
-
-
6
-
9
-
9

 

 

5
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
8
-
-
-
-
9
5
-
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
8
-
-
-
9
-
8
-
-
-
-
9
14
-
-
-
+
=
48
4+8
=
12
1+2
3
=
3
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
7
-
2
-
2
9
-
-
7
5
9
+
=
51
5+1
=
6
=
6
=
6
-
20
-
5
-
12
-
7
-
20
-
2
18
-
-
7
5
18
+
=
114
1+1+4
=
6
=
6
=
6
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
12
9
7
8
20
-
2
18
9
14
7
5
18
+
+
162
1+6+2
=
9
=
9
=
9
-
2
8
5
-
3
9
7
8
2
-
2
9
9
5
7
5
9
+
+
90
9+0
=
9
=
9
=
9
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
-
-
-
-
-
-
-
-
``-
2
-
-
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
9
-
-
9
occurs
x
4
=
36
=
9
15
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
34
-
-
15
-
90
-
36
1+5
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
9
-
-
3+4
-
-
1+5
-
5+4
-
3+6
6
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
7
-
-
6
-
9
-
9
-
2
8
5
-
3
9
7
8
2
-
2
9
9
5
7
5
9
-
-
-
-
-
-
-
-
-
-
6
T
H
E
-
L
I
G
H
T
-
B
R
I
N
G
E
R
-
-
7
-
-
6
-
9
-
9

 

 

-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
+
=
31
3+1
=
4
=
4
=
4
-
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
+
=
67
6+7
=
13
1+3
4
=
4
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
+
=
51
5+1
=
6
=
6
=
6
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
+
=
141
1+4+1
=
6
=
6
=
6
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
+
=
82
8+2
=
10
1+0
1
=
1
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
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
12
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
33
-
-
15
-
82
-
37
1+2
1+5
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
3+3
-
-
1+5
-
8+2
-
3+7
3
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
3
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
1
-
1

 

 

15
ONE TWO THREE FOUR
208
82
1
-
--
-
-
-
4
FIVE
42
24
6
-
--
-
-
-
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
5
9
5
-
-
-
9
-
8
-
-
1
-
-
-
5
-
1
9
6
+
=
58
5+8
=
13
1+3
4
=
4
-
-
14
9
14
-
-
-
9
-
8
-
-
19
-
-
-
14
-
19
9
24
+
=
139
1+3+9
=
13
1+3
4
=
4
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
5
-
7
-
2
-
-
5
4
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
5
-
5
-
7
-
20
-
-
5
22
5
-
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
14
9
14
5
-
5
9
7
8
20
-
19
5
22
5
14
-
19
9
24
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
5
9
5
5
-
5
9
7
8
2
-
1
5
4
5
5
-
1
9
6
+
=
91
9+1
=
10
1+0
1
=
1
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
5
-
5
-
-
-
-
-
-
5
-
5
5
-
-
-
-
-
-
5
occurs
x
7
=
35
3+5
8
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
=
6
-
--
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
--
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
3
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
42
-
-
17
-
91
-
46
-
1+7
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
4+2
-
-
1+7
-
9+1
-
4+6
3
8
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
6
-
-
8
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
3
8
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
6
-
-
8
-
1
-
1

 

 

15
ONE TWO THREE FOUR
208
82
1
-
--
-
-
-
4
FIVE
42
24
6
-
--
-
-
-
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S THE 5FIVE5S THE 5FIVE5S

 

 

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

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
112
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
256
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
113
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
266
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
522
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
225
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
5
-
-
-
6
-
6
-
-
-
-
--
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
45
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
5
-
-
-
-
5
4+5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
112
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
256
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
113
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
266
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
522
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
225
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
5
-
-
-
6
-
6
-
-
-
-
--
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
45
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
5
-
-
-
-
5
4+5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9

 

 

Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
8
-
-
6
6
5
-
-
-
6
-
8
-
-
-
-
6
-
-
-
9
-
-
1
9
6
1
-
-
-
5
-
9
-
8
-
5
9
5
-
112
26
-
-
15
15
14
-
-
-
15
-
8
-
-
-
-
15
-
-
-
9
-
-
19
9
24
19
-
-
-
14
-
9
-
8
-
14
9
14
-
256
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
5
9
-
-
-
5
2
5
-
2
-
9
5
5
6
-
3
9
6
-
4
5
-
-
-
-
5
4
5
-
5
-
7
-
2
-
-
-
5
113
-
5
18
-
-
-
5
20
23
-
20
-
18
5
5
6
-
21
18
6
-
22
5
-
-
-
-
5
22
5
-
5
-
7
-
20
-
-
-
5
266
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
26
5
18
15
15
14
5
20
23
15
20
8
18
5
5
6
15
21
18
6
9
22
5
19
9
24
19
5
22
5
14
5
9
7
8
20
14
9
14
5
522
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
225
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
-
-
5
-
5
5
5
-
-
-
6
6
-
-
-
--
6
-
-
-
-
-
6
6
-
-
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
9
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
9
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
45
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
5
5
-
-
-
5
4+5
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
-
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9

 

LOOK AT THE 5S LOOK AT THE 5S LOOK AT THE 5S THE 5S THE 5S

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
40
4+0
=
4
-
4
-
4
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
+
=
112
1+1+2
=
4
-
4
-
4
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
+
=
256
2+5+6
=
13
1+3
4
-
4
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
+
=
113
1+1+3
=
5
-
5
-
5
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
+
=
266
2+6+6
=
14
1+4
5
-
5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
+
=
522
5+2+2
=
9
-
9
-
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
+
=
225
2+2+5
=
9
-
9
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
4
occurs
x
2
=
8
-
8
-
5
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
+
=
5
occurs
x
14
=
70
7+0
7
-
-
-
6
-
6-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
  
-
-
-
-
+
=
6
occurs
x
7
=
42
4+2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
+
=
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
occurs
x
3
=
24
2+4
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
+
=
9
occurs
x
7
=
63
6+3
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
45
-
-
40
-
225
-
54
-
5
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
-
-
4+5
-
-
4+0
-
2+2+5
-
5+4
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
9
-
-
4
-
9
-
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
-
-
-
-
-
-
-
-
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
9
-
-
4
-
9
-
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
56
29
2
3
-
T
=
2
-
5
THREE
52
16
7
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
65
20
2
6
-
S
=
1
-
3
SIX
42
24
6
7
-
S
=
1
-
5
SEVEN
58
13
4
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
56
29
2
3
-
T
=
2
-
5
THREE
52
16
7
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
65
20
2
6
-
S
=
1
-
3
SIX
42
24
6
7
-
S
=
1
-
5
SEVEN
58
13
4
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

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
56
29
2
3
-
T
=
2
-
5
THREE
52
16
7
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
65
20
2
6
-
S
=
1
-
3
SIX
42
24
6
7
-
S
=
1
-
5
SEVEN
58
13
4
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

 

 

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

 

 

O
=
6
3
ONE
34
16
7
T
=
2
3
TWO
58
13
4
T
=
2
5
THREE
56
29
2
F
=
6
4
FOUR
60
24
6
F
+
6
4
FIVE
42
24
6
S
=
1
3
SIX
52
16
7
S
=
1
5
SEVEN
65
20
2
E
=
5
5
EIGHT
49
31
4
N
=
5
4
NINE
42
24
6
-
-
39
36
-
458
197
44
-
-
3+9
3+6
-
4+5+8
1+9+7
4+4
-
-
12
9
-
17
17
8
-
-
1+2
-
-
-
-
-
-
-
3
9
-
8
8
8

 

 

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

 

 

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

 

 

O
=
6
3
ONE
34
16
7
T
=
2
3
TWO
58
13
4
T
=
2
5
THREE
56
29
2
F
=
6
4
FOUR
60
24
6
F
+
6
4
FIVE
42
24
6
S
=
1
3
SIX
52
16
7
S
=
1
5
SEVEN
65
20
2
E
=
5
5
EIGHT
49
31
4
N
=
5
4
NINE
42
24
6
-
-
39
36
-
458
197
44
-
-
3+9
3+6
-
4+5+8
1+9+7
4+4
-
-
12
9
-
17
17
8
-
-
1+2
-
-
-
-
-
-
-
3
9
-
8
8
8

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Page 32

5


To Sorcerers and Magicians number FIVE is the most powerful - five is the mark of the pentacle, a five pointed star drawn by extending the sides of a Pentagon. Five surely is in the possession of the occult. And the Pentagon is the geometric figure in which the golden ratio of classical art and architecture is found most.

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

 

 

O
=
15
-
3
ONE
34
16
7
-
1
T
=
20
-
3
TWO
58
13
4
-
2
T
=
20
-
5
THREE
56
29
2
-
3
F
=
6
-
4
FOUR
60
24
6
-
4
-
-
61
-
15
Add
208
82
19
-
10
-
-
6+1
-
1+5
Reduce
2+0+8
8+2
1+9
-
1+0
-
-
7
-
6
Deduce
10
10
10
-
1
-
-
-
-
-
Produce
1+0
1+0
1+0
-
-
-
-
7
-
6
Essence
1
1
1
-
1

 

 

N
=
14
-
4
NINE
42
24
6
-
9
E
=
5
-
5
EIGHT
49
31
4
-
8
S
=
19
-
5
SEVEN
65
20
2
-
7
S
=
19
-
3
SIX
52
16
7
-
6
-
-
57
-
17
Add
208
91
19
-
30
-
-
5+7
-
1+7
Reduce
2+0+8
9+1
1+9
-
3+0
-
-
12
-
8
Deduce
10
10
10
-
3
-
-
1+2
-
-
Produce
1+0
1+0
1+0
-
-
-
-
3
-
8
Essence
1
1
1
-
3

 

 

4
FIVE
42
24
6

 

1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1

 

15
ONE TWO THREE FOUR
208
82
1
4
FIVE
42
24
6
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

3
ONE
34
16
7
-
3
SIX
52
16
7
3
TWO
58
13
4
-
5
SEVEN
65
20
2
5
THREE
56
29
2
-
5
EIGHT
49
31
4
4
FOUR
60
24
6
-
4
NINE
42
24
6
15
Add
208
82
19
-
17
Add
208
91
19
1+5
Reduce
2+0+8
8+2
1+9
-
1+7
Reduce
2+0+8
9+1
1+9
6
Deduce
10
10
10
-
8
Deduce
10
10
10
-
Produce
1+0
1+0
1+0
-
-
Produce
1+0
1+0
1+0
6
Essence
1
1
1
-
8
Essence
1
1
1

 

 

ENTERS THE NETERS

 

 

THE ELEMENTS OF EGYPTIAN WISDOM

Naomi Ozaniec 1994

THE SACRED SCRIPT - THE MEDU NETERS

Page 80 / The logical mind begins to reel / Page 81 / Language as evocation is immensely powerful. Word play is not finished; Neith can also be written by spelling the 't' with the sign for land, ta, in combination with the sign for water, 'n'. This particular hieroglyph represents ruffled water. By spelling the same name in a different way, we are presented with a different set of ideas. Here is Neith as 'the primeval water which gave birth to the land,' a theologically familiar concept. Once again a brief word encapsulates both divine name and divine function.

Hieroglyphic omitted

Schwaller de Lubicz reminds us repeatedly that we do need to look for a convoluted symbolism. The Medu Neters were chosen in such a way as to really signify all the qualities and functions implicit in the image. We are of course removed from the direct observation of vulture and ibis, crocodile and falcon, It is hard for us to understand the subtleties of movement, habit or life cycle which prompted a recognition deep in the Egyptian mind. It is well known that the humble dung beetle was raised to a sacred status from its simple egg-laying habit. The young emerged from the ball of dung as new life unbegotten. It is less well known that the scarab resembles the human skull, its two wing cases being reminiscent of the two halves of the human skull.

The ability to find the cosmic In the mundane through a correspondence is the hallmark of a mind sensitized through symbolic training. Any contemporary Qabalist recognizes this function for what it is, the inner workings of an esoteric system. These brief examples serve to illustrate the workings of both the Egyptian mind and the Egyptian tradition. Each letter had its own secret; all sacred alphabets are constructed in this way. Moreover a sacred language always serves a double purpose, a written double entendre. To the uninitiated there is no secret to hide. The language functions perfectly well at a purely practical level. To the initiated there exists another level of inner meaning as opposed to the apparent meaning. The inner meaning requires no elaborate subterfuge. It is there all the time, open and blatant. 'It / Page 82 / is hidden from view only because it represents a higher non-cerebral consciousness which simply evades the logical mind.

The Egyptians preserved this double function with astonishing brilliance and clarity over an immensely long period of time. Hebrew still functions as a sacred alphabet.. Each of its letters signifies ideas, numbers and cosmic principles.. A word becomes a code for an abstraction, a metaphysical concept, an esoteric teaching. An outsider cannot penetrate into the labyrinthine maze of meanings without becoming lost in ideas and distracted by elusive possibilities. A guide is always required in such matters - scribal training took place through an apprenticeship system. It is a mistake to think that we might uncover how the scribes viewed individual hieroglyphs by simply applying any meaning that springs to our mind. It is Clear that individual signs and arrangements carried a precise range of corresponding symbols.

Isha Schwaller de Lubicz acts as our guide into the intricacies of an individual hieroglyph in the book Her-Bak.

The letter r is written.in the lenticular shape of a half open mouth. Now look. for the ideas, qualities and functions this . sign represents. First, its nature. The mouth, ra, is the upper opening of the body, an entrance that communicates by two channels with the lungs and stomach; that is why this hiereglyph is. also the generic word for an entrance, ra. The mouth opens and shuts to eat, breathe and speak, as the eye, ar.t, opens and shuts to receive or refuse light. The mouth's function is dual, passive and active, it receives air and food, emits breath and voice. The eye's function is dual, likewise 'the reception of light and expression of organic and emotional response. The mouth's shape changes by the separation of the lips for the performance of its function. Opening, it widens or narrows like the shadow thrown on a disc by another disc which gradually eclipses it. In the partially occulteddisc, . the lentil or dark mouth is the complement of the crescent still visible. This gradual change of shape produces portions of different size that represents parts of the occulted disc. The characteristic has given the name ra to parts of a whole such as numerical fractions, chapters and so forth.

Page 83

These profound thoughts revolve around a single letter majestic insights might we discover if only someone would serve as our guide through all the hieroglyphic combinations! Here is a way of thinking quite unlike our own, a mind set removed from our utilitarian use of language. This totally symbolic thinking produced completely practical applications, as we see through Egypt's many lasting achievements there is no grounds whatsoever for thinking that this symbolic system produced woolly mindedness. On the contrary it gave rise to a mind that was both extensive and focused, deep and creative, tradittonal yet original.

 

 

 

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wiki.answers.com/.../What_are_the_most_popular_letters_in_the_alphabet - Cached - Similar

 

What is the frequency of the letters of the alphabet in English ... The world's most trusted dictionaries ... Dictionary; Other language resources. Help. US English; World English ... However, this gives the frequency of letters in English text, which is dominated by a relatively small ... The third column represents proportions, taking the least common letter (q) as equal to 1. ...
www.oxforddictionaries.com/page/frequencyalphabet - Cachedmost commonly used letters - Scott Bryce The most common first letter in a word in order of frequency ... The most commonly used words in the English language in order of frequency ...
scottbryce.com/cryptograms/stats.htm - Cached - Similar

 

Thousands of Lists - ListAfterList.com - Most Common Letters in ... According to a study done by AskOxford, using thier Concise English Dictionary, these are the most common letters in the English language. The letter "E" is ...
www.listafterlist.com › Fun & Games - CachedTrivia - What's the most popular letter? - ArcaMax Publishing 22 Apr 2007 ... "E" is the most frequently used letter in the English alphabet, "Q" is the least . ... Which is the world's most common language? ...
www.arcamax.com › ... › Knowledge › Trivia - Cached - Similar

 

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What is the most common letter? | Answerbag What is the most common letter? the bills they keep sending me. ... Im Alec. The most common letters in the English language are, in order, ETAOINSHRDLU. ...
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Letter frequency - Wikipedia, the free encyclopedia1 Relative frequencies of letters in the English language .... the frequency distributions of the 26 most common Latin letters across some languages. ...

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Show more results from wikipedia.orgWhat is the Most Commonly Used Letter in English? 25 Oct 2010 ... The most commonly used letter in the English language is the letter “e”. This is the case in the general language, in fiction and ...
www.wisegeek.com/what-is-the-most-commonly-used-letter-in-english.htm - Cached - Similar

 

Show more results from wikipedia.orgWhat is the Most Commonly Used Letter in English? 25 Oct 2010 ... The most commonly used letter in the English language is the letter “e”. This is the case in the general language, in fiction and ...
www.wisegeek.com/what-is-the-most-commonly-used-letter-in-english.htm -

 

 

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

TH5 MOST COMMONLY US5D L5TT5R IN TH5 5NGLISH LANGUAG5 IS THE L5TT5R "5"

 

 

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

285 4612 36446537 3154 352259 95 285 5573918 31573175 91 285 352259 "5"

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

 

 

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

285 4612 36446537 3154 352259 95 285 5573918 31573175 91 285 352259 "5"

THE MOST COMMONLY USED LETTER IN THE ENGLISH LANGUAGE IS THE LETTER "E"

 

Herbert S. Zim, in his classic introductory cryptography text "Codes and Secret Writing", gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKXJQ Z", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC".[1]

"ETAON RISHD LFCMU GYPWB VKXJQ Z"

 

 

THEN WE ALL STARTED SINGING LOOK AT THE FIVES LOOK AT THE FIVES LOOKAT

THE FIVES THE FIVES THE FIVES

AND

THEN LO AND BEHOLD YOU GOT THE MESSAGE

AND

YOU STARTED TO LAUGH AND SING

AND

SUDDENLY

OUT

OF

NOTHINGNESS

WOWEEWOW

WE WERE ALL LAUGHING SINGING AND DANCING

NOW WE KNOW WOW O WOW KNOW WE NOW

 

 

 

G
=
7
-
7
GRAHAMS
67
31
4
N
=
5
-
6
NUMBER
73
28
1
-
-
12
Q
13
First Total
140
59
5
-
-
1+2
-
1+3
Add to Reduce
1+4+0
5+9
-
-
-
3
-
4
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
3
-
4
Essence of Number
5
5
5

 

 

-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
-
8
-
-
19
-
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
-
7
18
1
-
1
13
-
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
-
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
-
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
6
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
-
1+3
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
6
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
6
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
8
-
-
19
-
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
7
18
1
-
1
13
-
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
-
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
13
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
1+3
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
7
9
1
8
1
4
1
-
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
4
G
R
A
H
A
M
S
-
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
5
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
8
-
-
19
14
-
-
-
-
-
+
=
41
4+1
=
5
=
5
=
5
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
9
1
-
1
4
-
-
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
7
18
1
-
1
13
-
-
21
13
2
5
18
+
=
99
9+9
=
18
1+8
9
=
9
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
7
18
1
8
1
13
19
14
21
13
2
5
18
+
=
140
1+4+0
=
5
=
5
=
5
-
7
9
1
8
1
4
1
5
3
4
2
5
9
+
=
59
5+9
=
14
1+4
5
=
5
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
13
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
39
-
-
12
-
59
-
41
1+3
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
3+9
-
-
1+2
-
5+9
-
4+1
4
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
12
-
-
3
-
14
-
5
-
7
9
1
8
1
4
1
5
3
4
2
5
9
-
-
1+2
-
-
-
-
1+4
-
-
4
G
R
A
H
A
M
S
N
U
M
B
E
R
-
-
3
-
-
3
-
5
-
5

 

 

THE

SWORD OF WORDS

 

 

SECRET CHAMBERS

Robert Bauval

1

999

MAGICAL RELIGION

Page 120

"A century or so after the rediscovery of the Corpus Hermeticum, a strange regeneration of , Egyptian' mysticism was taking place in Western culture. The Hermetica was being circulated among scholars, the educated classes and even royalty.19 A new breed of 'Hermetic' philo- sophers, cabalists, alchemists, magicians, seers and wizards of all sorts began to emerge.20 In Chapter 2 we saw the bizarre involvement of the Papacy with Hermeticism and how some misguided scholars attempted to convince the Church not only that Hermes- Thoth was a prophet of Christianity, but also that his 'books' should be canonised and embraced as 'gospels' of the Roman Catholic Church. Others, more radical in their demands, went as far as to preach the return of the 'Egyptian' religion as the true religion of the world. Among the most forceful and influential of these new Hermetic activists was a mysterious Italian scholar from the Nolan region called Giordano Bruno.
Before the late 1960s very few people indeed, except within a tight academic circle, had even heard of Giordano Bruno.21 It was not until the British scholar Frances A. Yates took up the task of understanding Bruno's role and motives in the Italian Renaissance and, more importantly, his strange contacts in the French and English courts, that the true picture of Bruno's bizarre mission began to emerge. In her turning- point work, Giordano Bruno and the Hermetic Tradition (first published in 1962 in London), Yates performed a sort of intellectual archaeological feat by discovering the rudiments of a powerful esoteric tradition which had hitherto gone undetected. This tradition, as we shall see, almost certainly caused the formation of speculative Freemasonic and Rosicrucian movements and ultimately, as I shall also show, set up the conditions that were to lead seekers to look for the fabled 'Hall of Records' at Giza. To give a name to this mysterious 'tradition' Yates was to coin the phrase 'the Hermetic Tradition'.22
Giordano Bruno's mission began in 1581, when he set himself the task of persuading the monarchs of Europe to install, no less, the 'magical religion of the Egyptians' as the new religion of the world. That year, Bruno had arrived in the city of Paris after wandering out of Italy and through Europe for several months. In Paris he gave public lectures which eventually got him noticed by the French king, Henri III. Bruno, / Page 121 / by then, had developed an extremely high level of proficiency in the classical art of memory called mnemonics and had already published two books on the subject. Yates writes:
 This classical art, usually regarded as purely mnemotechnical, had a long history in the Middle Ages. .. In the Renaissance it became fashionable among Neoplatonists and Hermetists. It was now understood as a method of printing basic archetypal images on the memory. . . a kind of inner way of knowing the universe. The Hermetic experience of reflecting the universe in the mind is, I believe, at the root of Renaissance magic memory, in which the classic mnemonic with places and images is now understood, or applied, as a method of achieving this experience by imprinting archetypal, or magically activated, images on the memory. By using magical or talismanic images as memory- images, the Magus (magician) hoped to acquire universal knowledge, and also powers, obtained through the magical organisation of the imagination.- a magical powerful personality, tuned in, as it were, to the power of the cosmos. This amazing transformation, or adaptation, of the classical art of memory in the Renaissance has a history before Bruno, but in Bruno it reaches culmination. The De umbris idearum and the Cantus Circaeus . . . are his two first works on magic memory. This reveals him as a magician. . .23
The human memory has a natural system of selecting images, colours, scents or sounds in order to store vast amounts of information, moods, ideas, feelings and sensations. Imagine a day at the beach with friends and family, full of activities, full of fun and full of wonderful sensations. That day, however, something unusual happens. You are stung by a blue- bottle jellyfish. Years later you are visiting an aquarium somewhere else in the world, and in one of the displays floats a little blue-bottle jellyfish. Suddenly that 'image' unleashes the memories of that day on the beach. The blue-bottle is the 'icon' or 'archetypal image' in which was stored all the memories of that special day. Your mind will most certainly work out why the memory came to the surface by relating the jellyfish to the events remembered. It could have happened in a far more subtle way. You could have seen something totally unrelated, say, a postage stamp, whose colour very closely resembled that of the blue-bottle jellyfish. The unconscious mind makes the association, and the memories of that day will again flash in your mind. Except this time you may not be able to work out why this has happened, i.e. your conscious mind may not have registered what exactly it was that triggered the memory. This phenomenon is what the Hermetic scholars would have called the 'silent language' and what the ancient Egyptians would have called the 'language of the gods'.
Page122

..The classical art of mnemonics is to learn how to create such an icon yourself and store it in the mind; then, at a later date, unleash it at will to bring back the desired memory stored in it. A very simple example of this is when you tie a string on your finger in order to remind you of something later. on. This works so long as the item you wish to remember is simple and straightforward. What if the subject matter involved remembering a complex chain of events such as a Shakespeare play or a lecture on atomic physics? A far more sophisticated method would be needed, and that is where the art of mnemonics can be applied. One of the techniques is to imagine a house that you are familiar with, and allocate in chronological order the memory of each event to a room or item in this house. Later you can visualise yourself walking around the house along a predetermined route, entering the rooms and, as you encounter each item or 'icon', the memory that it 'stores' begins to unfold. It takes many years of practice to become a master of the art of memory, and those few who have the ability and intellect to become adepts will develop tremendous insight, which in turn can be converted into enormous power of influence and manipulation. Vast memory that can be controlled, like that of a powerful computer, translates into vast reservoirs of knowledge. Knowledge, as we all know, is power. The greater the memory and the more refined the means to store and control it, the greater the power of the magician.
Recognising such immense abilities in Giordano Bruno, Henri III appointed him as a spy to the French court, a sort of Renaissance version of James Bond, and dispatched him to the English court of Elizabeth I. The year was 1583. Commenting on this mission, Frances Yates writes that
. . . Henri III, who, by sending Bruno into England on some mission. . . changed the course of his life from a wandering magician into that of a very strange kind of missionary indeed. . .24
The 'strange kind' of mission that Bruno set out for himself was the extraordinary task of persuading the Elizabethan court, and through it eventually the whole of Europe, to adopt the 'true religion of the world'. That Bruno's intention was to attempt this is confirmed by a letter written by the English ambassador in Paris, Sir Henry Cobham, to Francis Walsingham in England to warn him of Bruno's hidden motives: 'Doctor Giordano Bruno Nolano, a professor in philosophy, intends to pass into England, whose religion I cannot commend. '25 This is a wonderful English understatement. For the religion that Cobham / Page123 / 'cannot commend' and which Bruno is bringing to England, as we shall see, is none other than the ancient Egyptian religion or, more precisely, that magical religion that he, Bruno, has discovered in the Hermetic texts.26 Bruno, in this ambitious and daring mission, is trying single- handed to seed the idea of a total general reformation of the world, a sort of intellectual and spiritual 'Second Coming' which he believes can be brought about by the revival of ancient Egypt's magical religion. To do this, Bruno is applying his own magical powers, that is the 'words of power' which are made the more devastating by linking them to talismans and archetypal images.27 Making use of a mixture of alchemical a1}d cabalistic techniques, Bruno's brand of magic using words and images is clearly 'Egyptian' in style. This is made evident when he wrote:
. . . the sacred letters used among the Egyptians were called hieroglyphs. . .
which were images. . . taken from things of nature, or their parts. By using such writings and voices, the Egyptians used to capture with marvellous skills the language of the gods (my italics). Afterwards when letters of the kind which we use now were invented. . . they brought about a great rift both in memory and in the divine and magical sciences.28
This statement alone demonstrates the amazing perceptive ability this sixteenth-century magician had. For we must remember that Bruno was writing these words more than three centuries before the Frenchman Champollion deciphered hieroglyphics.29 From the time he began his visit to England in 1583, Giordano Bruno went about proclaiming the imminent return of the magical religion of Egypt. As Frances Yates pointed out:
The works in the form of dialogues written in Italian which Bruno published in England are usually classified as moral and philosophical. . . both Bruno's proposed reform and his philosophy are related to his Hermetic religious mission . . . a mission [which] . . . becomes expanded into a projected full restoration of the magical religion of the pseudo-Egyptians of the Asclepius (a major tract on the Hermetica) . . .30 .
Yet Bruno was no New Age ranter. In Bruno we have the perfect example of how a powerful intuition can know what scientific minds have trouble perceiving. It was Bruno, for example, who introduced Copernicus's ideas of heliocentricity to the Oxford scholars by using his own intuitive vision of the planets and the sun.31 It was also Bruno who was among the very first to imagine a cosmos populated by innumerable / Page 124 / other worlds.32 We may thus wonder if his unusual intuition will not one day prove correct when he spoke of a revival of the 'magical Egyptian religion' in the Western world. In his major work Spaccio della Bestia Trionfante, which was written in England in 1584, Bruno's central theme is 'the glorification of the magical religion of the Egyptians,.33 In this work Bruno correctly detected in this ancient religious system that the worship of the Egyptians was the worship of 'God in things' and that communication with the divine could thus be achieved through all things in nature, by the application of a special magic which the Egyptian priests were the masters of:
. . for as the divinity descends in a certain manner inasmuch as it communicates itself to nature, so there is an ascent made to the divinity through nature. Thus through the light which shines in natural things one mounts up to the life which presides over them. . . And in truth I see how the wise men (of Egypt) by these means had power to make familiar, affable and domestic gods, which, through the voices which came out of the statues, gave counsels, doctrines, divinations and superhuman teachings. Whence with magical and divine rights they ascended to the height of the divinity by the same scale of nature by which the divinity descends to the smallest things by the communication of itself. . . Those wise men, then, in order to obtain certain benefits and gifts from gods, by means of profound magic, made use of certain natural things in which the divinity was latent, and through which the divinity was able and willing to communicate itself for certain effects. Whence those ceremonies were not vain fancies, but living voices which reached to the very ears of the gods. . .34
Bruno was living in a time of great expectation for some major religious reformation. A sort of 'Second Coming' frenzy was about to take hold of the European masses. Signs in the heavens were eagerly awaited. Rumours ran wild that soon a messianic-like child would be born and would unite Europe and the world under a fully reformed Christianity. Hermeticism, according to many, was the ideal tool in an attempt to activate this religious reform.35 As the Parisian scholar J. Dagens noted, 'the end of the sixteenth century and the start of the seventeenth century have been the golden age of the Religious Hermetism'.36 Using complex mathematical calculations, some astrono-mers and religious reformers worked out that the coming of such a messianic 'child' would take place at the end of the sixteenth century,37 and this would be made manifest with signs in the heavens. Amazingly, the heavens were to oblige with the sudden appearance of a supernova star in 1604.38
 This spectacular phenomenon took place in the constellation of / Page 125 / Cygnus."

 

 

G
=
7
-
8
GIORDANO
83
56
2
B
=
2
-
5
BRUNO
70
25
7
S
-
9
4
13
Add to Reduce
153
81
9
-
S
-
-
1+3
Reduce to Deduce
1+5+3
8+1
3+0
S
-
9
4
4
Add to Reduce
9
9
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
D
=
4
-
2
DE
9
9
9
U
=
3
-
6
UMBRIS
82
28
1
I
=
9
-
7
IDEARUM
71
35
8
S
-
16
4
15
Add to Reduce
162
72
30
-
-
1+6
-
1+5
Reduce to Deduce
1+6+2
7+2
3+0
S
-
7
4
6
Essence of Number
9
9
9

 

 

-
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
9
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
-
-
-
-
-
9
19
-
9
-
-
-
-
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
4
5
-
3
4
2
9
-
-
-
-
4
5
1
9
3
4
+
=
53
5+3
=
8
=
8
=
8
-
-
4
5
-
21
13
2
18
-
-
-
-
4
5
1
18
21
13
+
=
125
1+2+5
=
8
=
8
=
8
-
15
D
E
-
U
M
B
R
I
S
`
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
4
5
-
21
13
2
18
9
19
-
9
4
5
1
18
21
13
+
=
162
1+6+2
=
9
1+5
6
=
6
-
-
4
5
-
3
4
2
9
9
1
-
9
4
5
1
9
3
4
+
=
72
7+2
=
9
1+5
6
=
6
-
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
4
-
-
-
-
4
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
21
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
24
-
-
15
-
72
-
27
2+1
1+5
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
-
-
-
-
2+4
-
-
1+5
-
7+2
-
2+7
3
6
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9
-
-
4
5
-
3
4
2
9
9
1
-
9
4
5
1
9
3
4
-
-
-
-
-
-
-
-
-
-
3
6
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9

 

 

15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
9
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
-
-
-
-
9
19
-
9
-
-
-
-
-
-
+
=
37
3+7
=
10
1+0
1
=
1
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
4
5
-
3
4
2
9
-
-
-
-
4
5
1
9
3
4
+
=
53
5+3
=
8
=
8
=
8
-
4
5
-
21
13
2
18
-
-
-
-
4
5
1
18
21
13
+
=
125
1+2+5
=
8
=
8
=
8
15
D
E
-
U
M
B
R
I
S
`
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
4
5
-
21
13
2
18
9
19
-
9
4
5
1
18
21
13
+
=
162
1+6+2
=
9
1+5
6
=
6
-
4
5
-
3
4
2
9
9
1
-
9
4
5
1
9
3
4
+
=
72
7+2
=
9
1+5
6
=
6
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
-
4
-
-
-
-
4
-
-
4
occurs
x
4
=
16
1+6
7
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
24
-
-
15
-
72
-
27
1+5
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
-
-
-
-
2+4
-
-
1+5
-
7+2
-
2+7
6
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9
-
4
5
-
3
4
2
9
9
1
-
9
4
5
1
9
3
4
-
-
-
-
-
-
-
-
-
-
6
D
E
-
U
M
B
R
I
S
-
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9

 

 

15
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
9
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
-
-
-
9
19
9
-
-
-
-
-
-
+
=
37
3+7
=
10
1+0
1
=
1
15
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
4
5
3
4
2
9
-
-
-
4
5
1
9
3
4
+
=
53
5+3
=
8
=
8
=
8
-
4
5
21
13
2
18
-
-
-
4
5
1
18
21
13
+
=
125
1+2+5
=
8
=
8
=
8
15
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
4
5
21
13
2
18
9
19
9
4
5
1
18
21
13
+
=
162
1+6+2
=
9
1+5
6
=
6
-
4
5
3
4
2
9
9
1
9
4
5
1
9
3
4
+
=
72
7+2
=
9
1+5
6
=
6
15
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
-
4
-
-
-
-
4
-
-
4
occurs
x
4
=
16
1+6
7
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
9
9
-
9
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
24
-
-
15
-
72
-
27
1+5
-
-
-
-
-
9
9
-
9
-
-
-
9
-
-
-
-
2+4
-
-
1+5
-
7+2
-
2+7
6
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9
-
4
5
3
4
2
9
9
1
9
4
5
1
9
3
4
-
-
-
-
-
-
-
-
-
-
6
D
E
U
M
B
R
I
S
I
D
E
A
R
U
M
-
-
6
-
-
6
-
9
-
9

 

 

9
MNEMOSYNE
-
-
-
-
M+N+E+M
45
18
9
-
O
15
6
6
-
S+Y+N+E
63
18
9
9
MNEMOSYNE
123
42
33
-
-
1+2+3
4+2
3+3
9
MNEMOSYNE
6
6
6

 

 

9
MNEMOSYNE
-
-
-
-
M+N
27
9
9
-
E+M
18
9
9
-
O
15
6
6
-
S+Y+N+E
63
18
9
9
MNEMOSYNE
123
42
33
-
-
1+2+3
4+2
3+3
9
MNEMOSYNE
6
6
6

 

 

-
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
6
1
-
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
14
-
-
15
19
-
14
-
+
=
62
6+2
=
8
=
8
=
8
-
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
4
-
-
7
-
5
+
=
25
2+5
=
7
=
7
=
7
-
-
13
-
5
13
-
-
25
-
5
+
=
61
6+1
=
7
=
7
=
7
-
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
-
13
14
5
13
15
19
25
14
5
+
=
123
1+2+3
=
6
=
6
=
6
-
-
4
5
5
4
6
1
7
5
5
+
=
42
4+2
=
6
=
6
=
6
-
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
1
-
-
-
-`
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-`
2
TWO
2
-
-
-
-
-
3
-
-
--
--
--
-
-
-
--
--
-
-
3
THREE
3
-
--
--
--
-
-
-
4
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
--
--
--
6
-
-
--
--
-
-
6
occurs
x
1
=
6
=
6
-
-
-
--
--
--
-
-
7
--
--
-
-
7
occurs
x
1
=
7
=
7
8
-
-
--
--
--
-
-
-
--
--
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
--
--
--
-
22
9
M
N
E
M
O
S
Y
N
E
-
-
23
-
-
10
-
42
-
24
2+2
-
-
-
-
-
-
-
-
-
-
-
-
2+3
-
-
1+0
-
4+2
-
2+4
4
9
M
N
E
M
O
S
Y
N
E
-
-
5
-
-
1
-
6
-
6
-
-
4
5
5
4
6
1
7
5
5
-
-
-
-
-
-
-
-
-
-
4
9
M
N
E
M
O
S
Y
N
E
-
-
5
-
-
1
-
6
-
6

 

 

9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
6
1
-
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
14
-
-
15
19
-
14
-
+
=
62
6+2
=
8
=
8
=
8
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
4
-
5
4
-
-
7
-
5
+
=
25
2+5
=
7
=
7
=
7
-
13
-
5
13
-
-
25
-
5
+
=
61
6+1
=
7
=
7
=
7
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-
13
14
5
13
15
19
25
14
5
+
=
123
1+2+3
=
6
=
6
=
6
-
4
5
5
4
6
1
7
5
5
+
=
42
4+2
=
6
=
6
=
6
9
M
N
E
M
O
S
Y
N
E
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
4
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
--
--
--
6
-
-
--
--
-
-
6
occurs
x
1
=
6
=
6
-
-
--
--
--
-
-
7
--
--
-
-
7
occurs
x
1
=
7
=
7
9
M
N
E
M
O
S
Y
N
E
-
-
23
-
-
10
-
42
-
24
-
-
-
-
-
-
-
-
-
-
-
-
2+3
-
-
1+0
-
4+2
-
2+4
9
M
N
E
M
O
S
Y
N
E
-
-
5
-
-
1
-
6
-
6
-
4
5
5
4
6
1
7
5
5
-
-
-
-
-
-
-
-
-
-
9
M
N
E
M
O
S
Y
N
E
-
-
5
-
-
1
-
6
-
6

 

 

A
=
1
-
2
AD
5
5
5
H
=
8
-
9
HERENNIUM
107
53
8
S
-
9
4
11
Add to Reduce
112
58
13
-
S
-
-
1+1
Reduce to Deduce
1+1+2
5+8
1+3
S
-
9
4
2
Add to Reduce
4
13
4
-
-
-
-
-
Reduce to Deduce
1+2
1+3
-
-
-
9
-
2
Essence of Number
4
4
4

 

 

-
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
5
9
-
-
+
=
27
2+7
=
9
=
9
=
9
-
-
-
-
-
8
-
-
-
14
14
9
-
-
+
=
45
4+5
=
9
=
9
=
9
-
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
4
-
-
5
9
5
-
-
-
3
4
+
=
31
3+1
=
4
=
4
=
4
-
-
1
4
-
-
5
18
5
-
-
-
21
13
+
=
67
6+7
=
13
1+3
4
=
4
-
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
4
-
8
5
18
5
14
14
9
21
13
+
=
112
1+1+2
=
4
=
4
=
4
-
-
1
4
-
8
5
9
5
5
5
9
3
4
+
=
58
5+8
=
13
1+3
4
=
4
-
11
A
D
-
H
E
R
E
N
N
I
U
M
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
4
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
5
5
5
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
1
=
18
1+8
9
15
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
30
-
1
11
-
58
-
31
1+5
1+1
-
-
-
-
-
9
-
-
-
9
-
-
-
-
3+0
-
-
1+1
-
5+8
-
3+1
6
2
A
D
-
H
E
R
E
N
N
I
U
M
-
-
3
-
1
2
-
13
-
4
-
-
1
4
-
8
5
9
5
5
5
9
3
4
-
-
-
-
-
-
-
1+3
-
-
6
2
A
D
-
H
E
R
E
N
N
I
U
M
-
-
3
-
-
2
-
4
-
4

 

 

1
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
5
9
-
-
+
=
27
2+7
=
9
=
9
=
9
-
-
-
-
8
-
-
-
14
14
9
-
-
+
=
45
4+5
=
9
=
9
=
9
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
1
4
-
-
5
9
5
-
-
-
3
4
+
=
31
3+1
=
4
=
4
=
4
-
1
4
-
-
5
18
5
-
-
-
21
13
+
=
67
6+7
=
13
1+3
4
=
4
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
1
4
-
8
5
18
5
14
14
9
21
13
+
=
112
1+1+2
=
4
=
4
=
4
-
1
4
-
8
5
9
5
5
5
9
3
4
+
=
58
5+8
=
13
1+3
4
=
4
11
A
D
-
H
E
R
E
N
N
I
U
M
-T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
-
5
5
5
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
1
=
18
1+8
9
11
A
D
-
H
E
R
E
N
N
I
U
M
-
-
30
-
1
11
-
58
-
31
1+1
-
-
-
-
-
9
-
-
-
9
-
-
-
-
3+0
-
-
1+1
-
5+8
-
3+1
2
A
D
-
H
E
R
E
N
N
I
U
M
-
-
3
-
1
2
-
13
-
4
-
1
4
-
8
5
9
5
5
5
9
3
4
-
-
-
-
-
-
-
1+3
-
-
2
A
D
-
H
E
R
E
N
N
I
U
M
-
-
3
-
-
2
-
4
-
4

 

 

1
A
D
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
5
9
-
-
+
=
27
2+7
=
9
=
9
=
9
-
-
-
8
-
-
-
14
14
9
-
-
+
=
45
4+5
=
9
=
9
=
9
11
A
D
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
1
4
-
5
9
5
-
-
-
3
4
+
=
31
3+1
=
4
=
4
=
4
-
1
4
-
5
18
5
-
-
-
21
13
+
=
67
6+7
=
13
1+3
4
=
4
11
A
D
H
E
R
E
N
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
1
4
8
5
18
5
14
14
9
21
13
+
=
112
1+1+2
=
4
=
4
=
4
-
1
4
8
5
9
5
5
5
9
3
4
+
=
58
5+8
=
13
1+3
4
=
4
11
A
D
H
E
R
E
N
N
I
U
M
-T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
5
5
5
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
1
=
18
1+8
9
11
A
D
H
E
R
E
N
N
I
U
M
-
-
30
-
1
11
-
58
-
31
1+1
-
-
-
-
9
-
-
-
9
-
-
-
-
3+0
-
-
1+1
-
5+8
-
3+1
2
A
D
H
E
R
E
N
N
I
U
M
-
-
3
-
1
2
-
13
-
4
-
1
4
8
5
9
5
5
5
9
3
4
-
-
-
-
-
-
-
1+3
-
-
2
A
D
H
E
R
E
N
N
I
U
M
-
-
3
-
-
2
-
4
-
4

 

 

Daily Mail, Thursday, November 17, 2011

ANSWERS TO CORRESPONDENTS

Compiled by Charles Legge

Page 70

QUESTION The W. B Yeats poem Mad As The Mists and snow name checks Homer, Horace, Cicero and and Tully ('and here is Tully's open page') Who was Tully?


TULLY and Cicero are one and the same person - the Roman statesman and philosopher whose full latin name was Marcus Tullius Cicero (106-43 BC).

David Bradbury, London.

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 21

"The Ad Herennium was a well known and much used text in the Middle Ages when it had an immense prestige because it was thought to be by Cicero. It was therefore believed that the precepts for the artificial memory which it expounded had been drawn up by Tullius himself"

Page 32

"Though the medieval tradition which assigned the authorship of Ad Herennium to 'Tullius' was wrong in fact, it was not wrong in its inference that the art of memory was practised and recommended by Tullius."

Page 282

"By the THE LADDER OF MINERVA we rise from the first to the last..."

 

 

APOCATASTASIS = 144 AND 36 3+6 = 9

 

CATHOLIC ENCYCLOPEDIA: Apocatastasis www.newadvent.org › Catholic Encyclopedia › ACached - SimilarNot helpful? You can block www.newadvent.org results when you're signed in to search.www.newadvent.org
A name given in the history of theology to the doctrine which teaches that a time will come when all free creatures will share in the grace of salvation; in a special ...

 

Apocatastasis

(Greek, apokatastasis; Latin, restitutio in pristinum statum, restoration to the original condition).

A name given in the history of theology to the doctrine which teaches that a time will come when all free creatures will share in the grace of salvation; in a special way, the devils and lost souls.
This doctrine was explicitly taught by St. Gregory of Nyssa, and in more than one passage. It first occurs in his "De animâ et resurrectione" (P.G., XLVI, cols. 100, 101) where, in speaking of the punishment by fire assigned to souls after death, he compares it to the process whereby gold is refined in a furnace, through being separated from the dross with which it is alloyed. The punishment by fire is not, therefore, an end in itself, but is ameliorative; the very reason of its infliction is to separate the good from the evil in the soul. The process, moreover, is a painful one; the sharpness and duration of the pain are in proportion to the evil of which each soul is guilty; the flame lasts so long as there is any evil left to destroy. A time, then, will come, when all evil shall cease to be since it has no existence of its own apart from the free will, in which it inheres; when every free will shall be turned to God, shall be in God, and evil shall have no more wherein to exist. Thus, St. Gregory of Nyssa continues, shall the word of St. Paul be fulfilled: Deus erit omnia in omnibus (1 Corinthians 15:28), which means that evil shall, ultimately, have an end, since, if God be all in all, there is no longer any place for evil (cols. 104, 105; cf. col. 152). St. Gregory recurs to the same thought of the final annihilation of evil, in his "Oratio catechetica", ch. xxvi; the same comparison of fire which purges gold of its impurities is to be found there; so also shall the power of God purge nature of that which is preternatural, namely, of evil. Such purification will be painful, as is a surgical operation, but the restoration will ultimately be complete. And, when this restoration shall have been accomplished (he eis to archaion apokatastasis ton nyn en kakia keimenon), all creation shall give thanks to God, both the souls which have had no need of purification, and those that shall have needed it. Not only man, however, shall be set free from evil, but the devil, also, by whom evil entered into the world (ton te anthropon tes kakias eleutheron kai auton ton tes kakias eyreten iomenos). The same teaching is to be found in the "De mortuis" (ibid., col. 536). Bardenhewer justly observes ("Patrologie", Freiburg, 1901, p. 266) that St. Gregory says elsewhere no less concerning the eternity of the fire, and of the punishment of the lost, but that the Saint himself understood this eternity as a period of very long duration, yet one which has a limit. Compare with this "Contra Usurarios" (XLVI, col. 436), where the suffering of the lost is spoken of as eternal, aionia, and "Orat. Catechet.", XXVI (XLV, col. 69), where evil is annihilated after a long period of time, makrais periodois. These verbal contradictions explain why the defenders of orthodoxy should have thought that St. Gregory of Nyssa's writings had been tampered with by heretics. St. Germanus of Constantinople, writing in the eighth century, went so far as to say that those who held that the devils and lost souls would one day be set free had dared "to instil into the pure and most healthful spring of his [Gregory's] writings the black and dangerous poison of the error of Origen, and to cunningly attribute this foolish heresy to a man famous alike for his virtue and his learning" (quoted by Photius, Bibl. Cod., 223; P.G. CIII, col. 1105). Tillemont, "Mémoires pour l'histoire ecclésiastique" (Paris, 1703), IX, p. 602, inclines to the opinion that St. Germanus had good grounds for what he said. We must, however, admit, with Bardenhewer (loc. cit.) that the explanation given by St. Germanus of Constantinople cannot hold. This was, also, the opinion of Petavius, "Theolog. dogmat." (Antwerp, 1700), III, "De Angelis", 109-111.
The doctrine of the apokatastasis is not, indeed, peculiar to St. Gregory of Nyssa, but is taken from Origen, who seems at times reluctant to decide concerning the question of the eternity of punishment. Tixeront has well said that in his De Principiis (I.6.3) Origen does not venture to assert that all the evil angels shall sooner or later return to God (P.G., XI, col. 168, 169); while in his "Comment. in Rom.", VIII, 9 (P.G., XIV, col. 1185), he states that Lucifer, unlike the Jews, will not be converted, even at the end of time. Elsewhere, on the other hand, and as a rule, Origen teaches the apokatastasis, the final restoration of all intelligent creatures to friendship with God. Tixeront writes thus concerning the matter: "Not all shall enjoy the same happiness, for in the Father's house there are many mansions, but all shall attain to it. If Scripture sometimes seems to speak of the punishment of the wicked as eternal, this is in order to terrify sinners, to lead them back into the right way, and it is always possible, with attention, to discover the true meaning of these texts. It must, however, always be accepted as a principle that God does not chasten except to amend, and that the sole end of His greatest anger is the amelioration of the guilty. As the doctor uses fire and steel in certain deep-seated diseases, so God does but use the fire of hell to heal the impenitent sinner. All souls, all impenitent beings that have gone astray, shall, therefore, be restored sooner or later to God's friendship. The evolution will be long, incalculably long in some cases, but a time will come when God shall be all in all. Death, the last enemy, shall be destroyed, the body shall be made spiritual, the world of matter shall be transformed, and there shall be, in the universe, only peace and unity" [Tixeront, Histoire des dogmes, (Paris, 1905), I, 304, 305]. The palmary text of Origen should be referred to De Principiis III.6.6. For Origen's teaching and the passages wherein it is expressed consult Huet, "Origeniana", II, qu. 11, n. 16 (republished in P.G., XVII, col. 1023-26); and Petavius, "Theol. dogmat., De Angelis", 107-109; also Harnack ["Dogmengeschichte" (Freiburg, 1894), I, 645, 646], who connects the teaching of Origen on this point with that of Clement of Alexandria. Tixeront also writes very aptly concerning this matter: "Clement allows that sinful souls shall be sanctified after death by a spiritual fire, and that the wicked shall, likewise, be punished by fire. Will their chastisement be eternal? It would not seem so. In the Stromata, VII, 2 (P.G., IX, col. 416), the punishment of which Clement speaks, and which succeeds the final judgment, constrains the wicked to repent. In chapter xvi (col. 541) the author lays down the principle that God does not punish, but corrects; that is to say that all chastisement on His part is remedial. If Origen be supposed to have started from this principle in order to arrive at the apokatastasis--and Gregory of Nyssa as well--it is extremely probable that Clement of Alexandria understood it in the same sense" (Histoire des dogmes, I, 277). Origen, however, does not seem to have regarded the doctrine of the apokatastasis as one meant to be preached to all, it being enough for the generality of the faithful to know that sinners will be punished. (Against Celsus VI.26)

The doctrine, then, was first taught by Origen, and by Clement of Alexandria, and was an influence in their Christianity due to Platonism, as Petavius has plainly shown (Theol. dogmat. De Angelis, 106), following St. Augustine City of God XXI.13. Compare Janet, "La philosophiede Platon" (Paris, 1869), I, 603. It is evident, moreover, that the doctrine involves a purely natural scheme of divine justice and of redemption. (Plato, Republic, X, 614b.)

It was through Origen that the Platonist doctrine of the apokatastasis passed to St. Gregory of Nyssa, and simultaneously to St. Jerome, at least during the time that St. Jerome was an Origenist. It is certain, however, that St. Jerome understands it only of the baptized: "In restitutione omnium, quando corpus totius ecclesiæ nunc dispersum atque laceratum, verus medicus Christus Jesus sanaturus advenerit, unusquisque secundum mensuram fidei et cognitionis Filii Dei . . . suum recipiet locum et incipiet id esse quod fuerat" (Comment. in Eph., iv, 16; P.G., XXVI, col. 503). Everywhere else St. Jerome teaches that the punishment of the devils and of the impious, that is of those who have not come to the Faith, shall be eternal. (See Petavius, Theol. dogmat. De Angelis, 111, 112.) The "Ambrosiaster" on the other hand seems to have extended the benefits of redemption to the devils, (In Eph., iii, 10; P.L., XVII, col. 382), yet the interpretation of the "Ambrosiaster" on this point is not devoid of difficulty. [See Petavius, p. 111; also, Turmel, Histoire de la théologie positive, depuis l'origine, etc. (Paris, 1904) 187.]

From the moment, however, that anti-Origenism prevailed, the doctrine of the apokatastasis was definitely abandoned. St. Augustine protests more strongly than any other writer against an error so contrary to the doctrine of the necessity of grace. See, especially, his "De gestis Pelagii", I: "In Origene dignissime detestatur Ecclesia, quod et iam illi quos Dominus dicit æterno supplicio puniendos, et ipse diabolus et angeli eius, post tempus licet prolixum purgati liberabuntur a poenis, et sanctis cum Deo regnantibus societate beatitudinis adhærebunt." Augustine here alludes to the sentence pronounced against Pelagius by the Council of Diospolis, in 415 (P.L., XLIV, col. 325). He moreover recurs to the subject in many passages of his writings, and in City of God XXI sets himself earnestly to prove the eternity of punishment as against the Platonist and Origenist error concerning its intrinsically purgatorial character. We note, further, that the doctrine of the apokatastasis was held in the East, not only by St. Gregory of Nyssa, but also by St. Gregory of Nazianzus as well; "De seipso", 566 (P.G., XXXVII, col. 1010), but the latter, though he asks the question, finally decides neither for nor against it, but rather leaves the answer to God. Köstlin, in the "Realencyklopädie für protestantische Theologie" (Leipzig, 1896), I, 617, art. "Apokatastasis", names Diodorus of Tarsus and Theodore of Mopsuestia as having also held the doctrine of apokatastasis, but cites no passage in support of his statement. In any case, the doctrine was formally condemned in the first of the famous anathemas pronounced at the Council of Constantinople in 543: Ei tis ten teratode apokatastasis presbeuei anathema esto [See, also, Justinian, Liber adversus Originem, anathemas 7 and 9.] The doctrine was thenceforth looked on as heterodox by the Church.

It was destined, nevertheless, to be revived in the works of ecclesiastical writers, and it would be interesting to verify Köstlin's and Bardenhewer's statement that it is to be traced in Bar Sudaili, Dionysius the Areopagite, Maximus the Confessor, Scotus Erigena, and Amalric of Bena. It reappears at the Reformation in the writings of Denk (d. 1527), and Harnack has not hesitated to assert that nearly all the Reformers were apocatastasists at heart, and that it accounts for their aversion to the traditional teaching concerning the sacraments (Dogmengeschichte, III, 661). The doctrine of apokatastasis viewed as a belief in a universal salvation is found among the Anabaptists, the Moravian Brethren, the Christadelphians, among rationalistic Protestants, and finally among the professed Universalists. It has been held, also, by such philosophic Protestants as Schleiermacher, and by a few theologians, Farrar, for instance, in England, Eckstein and Pfister in Germany, Matter in France. Consult Köstlin, art. cit., and Grétillut, "Exposé de théologie systématique" (Paris, 1890), IV, 603.

 

 

9
APOCATASTASIS
-
-
-
-
A+P
17
8
8
-
O+C
18
9
9
-
A+T+A+S+T+A+S
81
27
9
-
I
9
9
9
-
S
19
10
1
9
APOCATASTASIS
144
54
36
-
-
1+4+4
5+4
3+6
9
APOCATASTASIS
9
9
9

 

 

-
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
1
-
-
1
9
1
+
=
18
1+8
=
9
=
9
-
-
-
-
15
-
-
-
-
19
-
-
19
9
19
+
=
81
8+1
=
9
=
9
-
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
-
1
7
-
3
1
2
1
-
2
1
-
-
-
+
=
18
1+8
=
9
=
9
-
-
1
16
-
3
1
20
1
-
20
1
-
-
-
+
=
63
6+3
=
9
=
9
-
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
-
1
16
15
3
1
20
1
19
20
1
19
9
19
+
=
144
1+4+4
=
6
=
6
-
-
1
7
6
3
1
2
1
1
2
1
1
9
1
+
=
36
4+2
=
6
=
6
-
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
-`
1
-
-
-
1
-
1
1
-
1
1
-
1
-`
-
1
occurs
x
7
=
7
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-`
2
occurs
x
2
=
4
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
--
--
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
17
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
28
-
-
13
-
36
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
2+8
-
-
1+7
-
3+6
8
4
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
10
-
-
4
-
9
-
-
1
7
6
3
1
2
1
1
2
1
1
9
1
-
-
1+0
-
-
-
-
-
8
4
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
1
-
-
4
-
9

 

 

13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
1
-
-
1
9
1
+
=
18
1+8
=
9
=
9
-
-
-
15
-
-
-
-
19
-
-
19
9
19
+
=
81
8+1
=
9
=
9
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
1
7
-
3
1
2
1
-
2
1
-
-
-
+
=
18
1+8
=
9
=
9
-
1
16
-
3
1
20
1
-
20
1
-
-
-
+
=
63
6+3
=
9
=
9
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-
1
16
15
3
1
20
1
19
20
1
19
9
19
+
=
144
1+4+4
=
6
=
6
-
1
7
6
3
1
2
1
1
2
1
1
9
1
+
=
36
4+2
=
6
=
6
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
-
-
-
-
-
-
-`
1
-
-
-
1
-
1
1
-
1
1
-
1
-`
-
1
occurs
x
7
=
7
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-`
2
occurs
x
2
=
4
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
13
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
28
-
-
13
-
36
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
2+8
-
-
1+7
-
3+6
4
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
10
-
-
4
-
9
-
1
7
6
3
1
2
1
1
2
1
1
9
1
-
-
1+0
-
-
-
-
-
4
A
P
O
C
A
T
A
S
T
A
S
I
S
-
-
1
-
-
4
-
9

 

 

THE COSMIC MIND BOGGLING BOOK

Neil McAleer 1982

"The crater Giordano Bruno is believed to be one of the youngest craters on the moon..."

 

 

-
S
-
-
-
GIORDANO BRUNO
-
-
-
A
=
1
-
8
GIORDANO
83
47
2
H
=
8
-
5
BRUNO
70
25
7
S
-
9
4
13
GIORDANO BRUNO
153
72
9
-
S
-
S
1+3
-
1+5+3
7+2
-
S
-
9
4
4
GIORDANO BRUNO
9
9
9

 

 

-
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
-
9
6
-
-
-
5
6
-
-
-
-
5
6
+
=
37
3+7
=
10
1+0
1
=
1
-
-
-
9
15
-
-
-
14
15
-
-
-
-
14
15
+
=
82
8+2
=
10
1+0
1
=
1
-
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
9
4
1
-
-
-
2
9
3
-
-
+
=
35
3+5
=
8
=
8
=
8
-
-
7
-
-
18
4
1
-
-
-
2
18
3
-
-
+
=
71
7+1
=
8
=
8
=
8
-
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
7
9
15
18
4
1
14
15
-
2
18
21
14
15
+
=
153
1+5+3
=
9
=
9
=
9
-
-
7
9
6
9
4
1
5
6
-
2
9
3
5
6
+
=
72
7+2
=
9
=
9
=
9
-
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
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
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
37
-
-
13
-
72
-
36
-
1+3
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
3+7
-
-
1+3
-
7+2
-
3+6
8
4
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
10
-
-
4
-
9
-
9
-
-
7
9
6
9
4
1
5
6
-
2
9
3
5
6
-
-
1+0
-
-
-
-
-
-
-
8
4
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
1
-
-
4
-
9
-
9

 

 

13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
9
6
-
-
-
5
6
-
-
-
-
5
6
+
=
37
3+7
=
10
1+0
1
=
1
-
-
9
15
-
-
-
14
15
-
-
-
-
14
15
+
=
82
8+2
=
10
1+0
1
=
1
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
7
-
-
9
4
1
-
-
-
2
9
3
-
-
+
=
35
3+5
=
8
=
8
=
8
-
7
-
-
18
4
1
-
-
-
2
18
3
-
-
+
=
71
7+1
=
8
=
8
=
8
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
7
9
15
18
4
1
14
15
-
2
18
21
14
15
+
=
153
1+5+3
=
9
=
9
=
9
-
7
9
6
9
4
1
5
6
-
2
9
3
5
6
+
=
72
7+2
=
9
=
9
=
9
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
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
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
37
-
-
13
-
72
-
36
1+3
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
3+7
-
-
1+3
-
7+2
-
3+6
4
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
10
-
-
4
-
9
-
9
-
7
9
6
9
4
1
5
6
-
2
9
3
5
6
-
-
1+0
-
-
-
-
-
-
-
4
G
I
O
R
D
A
N
O
-
B
R
U
N
O
-
-
1
-
-
4
-
9
-
9

 

 

13
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
9
6
-
-
-
5
6
-
-
-
5
6
+
=
37
3+7
=
10
1+0
1
=
1
-
-
9
15
-
-
-
14
15
-
-
-
14
15
+
=
82
8+2
=
10
1+0
1
=
1
13
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
7
-
-
9
4
1
-
-
2
9
3
-
-
+
=
35
3+5
=
8
=
8
=
8
-
7
-
-
18
4
1
-
-
2
18
3
-
-
+
=
71
7+1
=
8
=
8
=
8
13
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
7
9
15
18
4
1
14
15
2
18
21
14
15
+
=
153
1+5+3
=
9
=
9
=
9
-
7
9
6
9
4
1
5
6
2
9
3
5
6
+
=
72
7+2
=
9
=
9
=
9
13
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
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
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
6
-
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
37
-
-
13
-
72
-
36
1+3
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
3+7
-
-
1+3
-
7+2
-
3+6
4
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
10
-
-
4
-
9
-
9
-
7
9
6
9
4
1
5
6
2
9
3
5
6
-
-
1+0
-
-
-
-
-
-
-
4
G
I
O
R
D
A
N
O
B
R
U
N
O
-
-
1
-
-
4
-
9
-
9

 

 

BELOVED OF GOD OF GOD BELOVED

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 21

"The Ad Herennium was a well known and much used text in the Middle Ages when it had an immense prestige because it was thought to be by Cicero. It was therefore believed that the precepts for the artificial memory which it expounded had been drawn up by Tullius himself"

Page 32

"Though the medieval tradition which assigned the authorship of Ad Herennium to 'Tullius' was wrong in fact, it was not wrong in its inference that the art of memory was practised and recommended by Tullius."

Page 282

"By the THE LADDER OF MINERVA we rise from the first to the last..."

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 175

CHAPTER 8

LULLISM AS AN ART OF MEMORY

THOUGH we have now reached the Renaissance, with Camillo, we have to retrace our steps to the Middle Ages during this chapter. For there was another kind of art of memory which began in the Middle Ages, which continued into the Renaissance and beyond, and which it was the aim of many in the Renaissance to combine with the classical art in some new synthesis whereby memory should reach still further heights of insight and of power. This other art of memory was the Art of Ramon Lull.

Lullism and its history is a most difficult subject and one for the exploration of which the full materials have not yet been assembled; The enormous number of Lull's own writings, some of them still unpublished, the vast Lullist literature written by his followers, the extreme complexity of Lullism, make it impossible as yet to reach very definite conclusions about what is, undoubtedly.ra strand of major importance in the European tradition. And what I have to do now is to write one not very long chapter giving some idea of what the Art of Ramon Lullwas like, of why it was an art of memory, of how it differs from the classical art of memory, and of how Lullism became absorbed at the Renaissance into Renaissance forms of the classical art.

Obviously- I am attempting the impossible, yet the impossible must be attempted because it is essential for the later part of this book that there should be some sketch at this stage of Lullism itself. The chapter is based on my own two articles on the art of Ramon Lull:' it is orientated towards a comparison of Lullism as an art of memory with. the classical art; and it is not concerned solely with 'genuine' Lullism but also with the Renaissance interpretation of Lullism, for it is this. which is important for the next stages of our history.

 

ART AT R AT ART

 

 

-
LULL
-
-
-
1
L
12
3
3
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
4
LULL
57
12
12
-
-
5+7
1+2
1+2
4
LULL
12
3
3
-
-
1+2
-
-
4
LULL
3
3
3

 

 

-
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
-
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
-
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
-
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
-
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
-
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
-
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
1
-
-
--
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
--
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
3
3
3
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
--
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
--
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
--
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
--
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
--
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
--
-
-
-
-
9
NINE
9
-
-
-
-
-
42
4
L
U
L
L
-
-
3
-
-
4
-
12
-
3
4+2
-
3
3
3
3
-
-
-
-
-
-
-
1+2
-
-
6
4
L
U
L
L
-
-
3
-
-
4
-
3
-
3

 

 

4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
12
21
12
12
+
=
57
5+7
=
12
12
1+2
=
3
-
3
3
3
3
+
=
12
1+2
=
3
=
3
=
3
4
L
U
L
L
-
-
-
-
-
-
-
-
-
-
-
3
3
3
3
-
-
3
occurs
x
4
=
12
1+2
3
4
L
U
L
L
-
-
3
-
-
4
-
12
-
3
-
3
3
3
3
-
-
-
-
-
-
-
1+2
-
-
4
L
U
L
L
-
-
3
-
-
4
-
3
-
3

 

 

-
-
-
-
-
LULLABY
-
-
-
-
-
-
-
1
L
12
3
3
-
-
-
-
1
U
21
3
3
-
-
-
-
1
L
12
3
3
-
-
-
-
1
L
12
3
3
-
-
-
-
2
A+B
3
3
3
-
-
-
-
1
Y
25
7
7
L
=
3
-
7
LULLABY
85
22
22
-
-
-
-
-
-
8+5
2+2
2+2
L
=
3
-
7
LULLABY
13
4
4
-
-
-
-
-
-
1+3
-
-
L
=
3
-
7
LULLABY
4
4
4

 

 

C
=
3
-
6
CORPUS
92
29
2
H
=
8
-
10
HERMETICUM
115
52
7
S
-
11
4
16
Add to Reduce
207
81
9
-
S
1+1
S
1+6
Reduce to Deduce
2+0+7
8+1
-
S
-
2
4
7
Essence of Number
9
9
9

 

 

-
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
24
-
-
6
-
-
-
1
-
8
-
-
-
-
-
9
-
-
-
+
=
24
2+4
=
6
=
6
=
6
51
-
-
15
-
-
-
19
-
8
-
-
-
-
-
9
-
-
-
+
=
51
5+1
=
6
=
6
=
6
-
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
57
-
3
-
9
7
3
-
-
-
5
9
4
5
2
-
3
3
4
+
=
57
5+7
=
12
1+2
3
=
3
156
-
3
-
18
16
21
-
-
-
5
18
13
5
20
-
3
21
13
+
=
156
1+5+6
=
12
1+2
3
=
3
-
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
207
-
3
15
18
16
21
19
-
8
5
18
13
5
20
9
3
21
13
+
=
207
2+0+7
=
9
=
9
=
9
81
-
3
6
9
7
3
1
-
8
5
9
4
5
2
9
3
3
4
+
=
81
8+1
=
9
=
9
=
9
-
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
--
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-`-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
5
--
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-`-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
--
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
45
-
-
16
-
81
-
45
4+5
-
-
-
9
/
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
4+5
-
-
1+6
-
8+1
-
4+5
9
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
9
-
-
7
-
9
-
9
-
-
3
6
9
7
3
1
-
8
5
9
4
5
2
9
3
3
4
-T
-
-
-
-
-
-
-
-
-
9
16
C
O
R
P
U
S
-
H
E
R
M
E
T
I
C
U
M
-
-
9
-
-
7
-
9
-
9

 

 

-
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
24
-
-
6
-
-
-
1
8
-
-
-
-
-
9
-
-
-
+
=
24
2+4
=
6
=
6
=
6
51
-
-
15
-
-
-
19
8
-
-
-
-
-
9
-
-
-
+
=
51
5+1
=
6
=
6
=
6
-
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
57
-
3
-
9
7
3
-
-
5
9
4
5
2
-
3
3
4
+
=
57
5+7
=
12
1+2
3
=
3
156
-
3
-
18
16
21
-
-
5
18
13
5
20
-
3
21
13
+
=
156
1+5+6
=
12
1+2
3
=
3
-
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
-
-
-
-
-
-
-
-
207
-
3
15
18
16
21
19
8
5
18
13
5
20
9
3
21
13
+
=
207
2+0+7
=
9
=
9
=
9
81
-
3
6
9
7
3
1
8
5
9
4
5
2
9
3
3
4
+
=
81
8+1
=
9
=
9
=
9
-
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
--
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
3
-
-
-
3
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-`-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
5
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-`-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
--
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
45
-
-
16
-
81
-
45
4+5
-
-
-
9
/
-
-
-
-
9
-
-
-
9
-
-
-
-
-
4+5
-
-
1+6
-
8+1
-
4+5
9
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
9
-
-
7
-
9
-
9
-
-
3
6
9
7
3
1
8
5
9
4
5
2
9
3
3
4
-T
-
-
-
-
-
-
-
-
-
9
16
C
O
R
P
U
S
H
E
R
M
E
T
I
C
U
M
-
-
9
-
-
7
-
9
-
9

 

 

-
5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
-
8
6
8
-
-
+
=
22
2+2
=
4
=
4
=
4
-
-
26
15
8
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
9
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
-
1
18
+
=
19
1+9
=
10
1+0
1
=
1
-
5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
-
26
15
8
1
18
+
=
68
6+8
=
14
1+4
5
=
5
-
-
8
6
8
1
9
+
=
32
3+2
=
5
=
5
=
5
-
5
Z
O
H
A
R
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
8
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
21
5
Z
O
H
A
R
-
-
24
-
-
5
-
32
-
23
2+1
-
-
-
-
-
9
-
-
2+4
-
-
-
-
3+2
-
2+3
3
5
Z
O
H
A
R
-
-
6
-
-
5
-
5
-
5
-
-
8
6
8
1
9
-
-
-
-
-
-
-
-
-
-
3
5
Z
O
H
A
R
-
-
6
-
-
5
-
5
-
5

 

 

5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
8
6
8
-
-
+
=
22
2+2
=
4
=
4
=
4
-
26
15
8
-
-
+
=
49
4+9
=
13
1+3
4
=
4
5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
9
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
1
18
+
=
19
1+9
=
10
1+0
1
=
1
5
Z
O
H
A
R
-
-
-
-
-
-
-
-
-
-
-
26
15
8
1
18
+
=
68
6+8
=
14
1+4
5
=
5
-
8
6
8
1
9
+
=
32
3+2
=
5
=
5
=
5
5
Z
O
H
A
R
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
8
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
5
Z
O
H
A
R
-
-
24
-
-
5
-
32
-
23
-
-
-
-
-
9
-
-
2+4
-
-
-
-
3+2
-
2+3
5
Z
O
H
A
R
-
-
6
-
-
5
-
5
-
5
-
8
6
8
1
9
-
-
-
-
-
-
-
-
-
-
5
Z
O
H
A
R
-
-
6
-
-
5
-
5
-
5

 

 

-
ZOHAR
-
-
-
2
Z+O
41
14
5
2
H+A
9
9
9
1
R
18
9
9
5
ZOHAR
68
32
14
=
-
6+8
3+2
1+4
5
ZOHAR
14
5
5
=
-
1+4
-
-
5
ZOHAR
5
5
5

 

 

4
MAKE
30
12
3
7
BELIEVE
60
33
6
11
Add to Reduce
90
45
9
1+1
Reduce to Deduce
9+0
4+5
-
2
Essence of Number
9
9
9

 

 

-
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
4
1
2
5
-
2
5
3
-
5
4
5
+
=
45
4+5
=
9
=
9
=
9
-
-
13
1
11
5
-
2
5
12
-
5
22
5
+
=
81
8+1
=
9
=
9
=
9
-
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
13
1
11
5
-
2
5
12
9
5
22
5
+
=
90
9+0
=
9
=
9
=
9
-
-
4
1
2
5
-
2
5
3
9
5
4
5
+
=
45
4+5
=
9
=
9
=
9
-
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
-
-
5
-
-
5
-
5
-
-
5
occurs
x
4
=
20
=
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
21
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
24
-
-
11
-
45
-
27
2+1
1+1
-
-
-
5
-
-
5
-
-
5
-
5
-
-
2+4
-
-
1+1
-
4+5
-
2+7
3
2
M
A
K
E
-
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9
-
6
4
1
2
5
-
2
5
3
9
5
4
5
-
-
-
-
6
6
6
-
6
-
3
2
M
A
K
E
-
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9

 

 

11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
4
1
2
5
-
2
5
3
-
5
4
5
+
=
45
4+5
=
9
=
9
=
9
-
13
1
11
5
-
2
5
12
-
5
22
5
+
=
81
8+1
=
9
=
9
=
9
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
13
1
11
5
-
2
5
12
9
5
22
5
+
=
90
9+0
=
9
=
9
=
9
-
4
1
2
5
-
2
5
3
9
5
4
5
+
=
45
4+5
=
9
=
9
=
9
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
5
-
-
5
-
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
M
A
K
E
-
B
E
L
I
E
V
E
-
-
24
-
-
11
-
45
-
27
1+1
-
-
-
5
-
-
5
-
-
5
-
5
-
-
2+4
-
-
1+1
-
4+5
-
2+7
2
M
A
K
E
-
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9
6
4
1
2
5
-
2
5
3
9
5
4
5
-
-
-
-
6
6
6
-
6
-
2
M
A
K
E
-
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9

 

 

11
M
A
K
E
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
11
M
A
K
E
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
4
1
2
5
2
5
3
-
5
4
5
+
=
45
4+5
=
9
=
9
=
9
-
13
1
11
5
2
5
12
-
5
22
5
+
=
81
8+1
=
9
=
9
=
9
11
M
A
K
E
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
13
1
11
5
2
5
12
9
5
22
5
+
=
90
9+0
=
9
=
9
=
9
-
4
1
2
5
2
5
3
9
5
4
5
+
=
45
4+5
=
9
=
9
=
9
11
M
A
K
E
B
E
L
I
E
V
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
2
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
5
-
-
5
-
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
M
A
K
E
B
E
L
I
E
V
E
-
-
24
-
-
11
-
45
-
27
1+1
-
-
-
5
-
5
-
-
5
-
5
-
-
2+4
-
-
1+1
-
4+5
-
2+7
2
M
A
K
E
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9
6
4
1
2
5
2
5
3
9
5
4
5
-
-
-
-
6
6
6
-
6
-
2
M
A
K
E
B
E
L
I
E
V
E
-
-
6
-
-
2
-
9
-
9

 

 

11
IMAGINATIVE
-
-
-
-
I
9
9
9
-
M+A+G
21
12
3
-
I
9
9
9
-
N+A+T
35
8
8
-
I
9
9
9
-
V+E
27
9
9
11
IMAGINATIVE
-
-
-

 

 

-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
9
5
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
-
9
-
-
-
9
14
-
-
9
-
-
+
=
41
4+1
=
5
=
5
=
5
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
1
2
-
4
5
+
=
24
2+4
=
6
=
6
=
6
-
-
-
13
1
7
-
-
1
20
-
22
5
+
=
69
6+9
=
15
6
=
6
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
1
20
9
22
5
+
=
110
1+1+0
=
2
=
2
=
2
-
-
9
4
1
7
9
5
1
2
9
4
5
+
=
56
5+6
=
11
1+1
2
=
2
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
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
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
11
I
M
A
G
I
N
A
T
I
V
E
-
-
28
-
-
11
-
56
-
29
1+7
-
9
-
-
-
9
-
-
-
9
-
-
-
-
2+8
-
-
1+1
-
5+6
-
2+9
8
11
I
M
A
G
I
N
A
T
I
V
E
-
-
10
-
-
2
-
11
-
11
-
-
9
4
1
7
9
5
1
2
9
4
5
-
-
1+0
-
-
-
-
1+1
-
1+1
8
11
I
M
A
G
I
N
A
T
I
V
E
-
-
1
-
-
2
-
2
-
2

 

 

11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
9
-
-
-
9
14
-
-
9
-
-
+
=
41
4+1
=
5
=
5
=
5
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
1
2
-
4
5
+
=
24
2+4
=
6
=
6
=
6
-
-
13
1
7
-
-
1
20
-
22
5
+
=
69
6+9
=
15
6
=
6
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
1
20
9
22
5
+
=
110
1+1+0
=
2
=
2
=
2
-
9
4
1
7
9
5
1
2
9
4
5
+
=
56
5+6
=
11
1+1
2
=
2
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
9
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
I
M
A
G
I
N
A
T
I
V
E
-
-
28
-
-
11
-
56
-
29
-
9
-
-
-
9
-
-
-
9
-
-
-
-
2+8
-
-
1+1
-
5+6
-
2+9
11
I
M
A
G
I
N
A
T
I
V
E
-
-
10
-
-
2
-
11
-
11
-
9
4
1
7
9
5
1
2
9
4
5
-
-
1+0
-
-
-
-
1+1
-
1+1
11
I
M
A
G
I
N
A
T
I
V
E
-
-
1
-
-
2
-
2
-
2

 

 

-
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
-
9
6
5
+
=
43
4+3
=
7
=
7
=
7
-
-
9
-
-
-
9
14
-
-
9
15
14
+
=
70
7+0
=
7
=
7
=
7
-
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
1
2
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
13
1
7
-
-
1
20
-
-
-
+
=
42
4+2
=
6
=
6
=
6
-
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
1
20
9
15
14
+
=
112
1+1+2
=
4
=
4
=
4
-
-
9
4
1
7
9
5
1
2
9
6
5
+
=
58
5+8
=
13
1+3
4
=
4
-
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
8
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
6
-6
-
-
6
occurs
x
1
=
6
=
6
--
--
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
9
-
-
--
-
9
occurs
x
3
=
27
2+7
9
11
11
I
M
A
G
I
N
A
T
I
O
N
-
-
34
-
-
11
-
58
-
31
1+1
1+1
9
-
-
-
9
-
-
-
9
-
-
-
-
3+4
-
-
1+1
-
5+8
-
3+1
2
2
I
M
A
G
I
N
A
T
I
O
N
-
-
7
-
-
2
-
13
-
4
-
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
-
-
-
-
1+3
-
-
2
2
I
M
A
G
I
N
A
T
I
O
N
--
-
7
-
-
2
-
4
-
4

 

 

11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
-
9
6
5
+
=
43
4+3
=
7
=
7
=
7
-
9
-
-
-
9
14
-
-
9
15
14
+
=
70
7+0
=
7
=
7
=
7
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
1
2
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
13
1
7
-
-
1
20
-
-
-
+
=
42
4+2
=
6
=
6
=
6
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
1
20
9
15
14
+
=
112
1+1+2
=
4
=
4
=
4
-
9
4
1
7
9
5
1
2
9
6
5
+
=
58
5+8
=
13
1+3
4
=
4
11
I
M
A
G
I
N
A
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
6
-6
-
-
6
occurs
x
1
=
6
=
6
--
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
9
-
-
-
9
-
-
-
9
-
-
--
-
9
occurs
x
3
=
27
2+7
9
11
I
M
A
G
I
N
A
T
I
O
N
-
-
34
-
-
11
-
58
-
31
1+1
9
-
-
-
9
-
-
-
9
-
-
-
-
3+4
-
-
1+1
-
5+8
-
3+1
2
I
M
A
G
I
N
A
T
I
O
N
-
-
7
-
-
2
-
13
-
4
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
-
-
-
-
1+3
-
-
2
I
M
A
G
I
N
A
T
I
O
N
--
-
7
-
-
2
-
4
-
4

 

 

-
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
-
-
9
14
-
+
=
32
3+2
=
5
=
5
=
5
-
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
5
+
=
17
1+7
=
8
=
8
=
8
-
-
-
13
1
7
-
-
5
+
=
26
2+6
=
8
8
=
8
-
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
5
+
=
58
5+8
=
13
1+3
4
=
4
-
-
9
4
1
7
9
5
5
+
=
40
4+0
=
4
=
4
=
4
-
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
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
19
7
I
M
A
G
I
N
E
-
-
26
-
-
11
-
40
-
22
1+9
-
9
-
-
-
9
-
-
-
-
2+6
-
-
1+1
-
4+0
-
2+2
10
7
I
M
A
G
I
N
E
-
-
8
-
-
2
-
4
-
4
1+0
-
9
4
1
7
9
5
5
-
-
-
-
-
-
-
-
-
-
1
7
I
M
A
G
I
N
E
-
-
8
-
-
2
-
4
-
4

 

 

7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
+
=
23
2+3
=
5
=
5
=
5
-
9
-
-
-
9
14
-
+
=
32
3+2
=
5
=
5
=
5
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
5
+
=
17
1+7
=
8
=
8
=
8
-
-
13
1
7
-
-
5
+
=
26
2+6
=
8
8
=
8
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
5
+
=
58
5+8
=
13
1+3
4
=
4
-
9
4
1
7
9
5
5
+
=
40
4+0
=
4
=
4
=
4
7
I
M
A
G
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
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
7
I
M
A
G
I
N
E
-
-
26
-
-
11
-
40
-
22
-
9
-
-
-
9
-
-
-
-
2+6
-
-
1+1
-
4+0
-
2+2
7
I
M
A
G
I
N
E
-
-
8
-
-
2
-
4
-
4
-
9
4
1
7
9
5
5
-
-
-
-
-
-
-
-
-
-
7
I
M
A
G
I
N
E
-
-
8
-
-
2
-
4
-
4

 

 

-
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
9
-
-
-
9
14
-
19
+
=
51
5+1
=
6
=
6
=
6
-
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
13
1
7
-
-
5
-
+
=
26
2+6
=
8
8
=
8
-
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
5
19
+
=
77
7+7
=
14
1+4
5
=
5
-
-
9
4
1
7
9
5
5
1
+
=
41
4+1
=
5
=
5
=
5
-
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
--
--
--
--
--
--
-
--
--
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
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
19
8
I
M
A
G
I
N
E
S
-
-
26
-
-
8
-
41
-
23
1+9
-
9
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
4+1
-
2+3
10
8
I
M
A
G
I
N
E
S
-
-
8
-
-
8
-
5
-
5
1+0
-
9
4
1
7
9
5
5
1
-
-
-
-
-
-
-
-
-
-
1
8
I
M
A
G
I
N
E
S
-
-
8
-
-
8
-
5
-
5

 

 

8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
5
-
1
+
=
24
2+4
=
6
=
6
=
6
-
9
-
-
-
9
14
-
19
+
=
51
5+1
=
6
=
6
=
6
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
-
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
13
1
7
-
-
5
-
+
=
26
2+6
=
8
8
=
8
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
9
13
1
7
9
14
5
19
+
=
77
7+7
=
14
1+4
5
=
5
-
9
4
1
7
9
5
5
1
+
=
41
4+1
=
5
=
5
=
5
8
I
M
A
G
I
N
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
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
I
M
A
G
I
N
E
S
-
-
26
-
-
8
-
41
-
23
-
9
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
4+1
-
2+3
8
I
M
A
G
I
N
E
S
-
-
8
-
-
8
-
5
-
5
-
9
4
1
7
9
5
5
1
-
-
-
-
-
-
-
-
-
-
8
I
M
A
G
I
N
E
S
-
-
8
-
-
8
-
5
-
5

 

 

10
REVOLUTION
151
52
7
1
R
18
9
9
9
EVOLUTION
133
43
7

 

 

8
REVOLVER
117
45
9

 

 

-
REVOLVER
-
-
-
1
R
18
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
1
R
18
9
9
8
REVOLVER
117
45
45
-
-
1+1+7
4+5
4+5
8
REVOLVER
9
9
9

 

 

-
REVOLVE
-
-
-
1
R
18
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
7
REVOLVE
99
36
36
-
-
1+1+7
3+6
3+6
7
REVOLVE
9
9
9

 

 

7
REVOLVE
99
36
9
6
EVOLVE
81
27
9
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
4
LOVE
54
18
18
-
-
5+4
1+8
1+8
4
LOVE
9
9
6

 

 

7
REVOLVE
99
36
9
6
EVOLVE
81
27
9
-
-
-
27
9
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
4
LOVE
135
45
45
-
-
5+4
4+5
4+5
4
LOVE
9
9
6

 

 

7
REVOLVE
99
36
9
1
R
18
9
9
7
EVOLVER
99
36
9
-
-
-
-
-
-
-
-
-
-
-
REVOLVE
-
-
-
1
R
18
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
-
-
-
-
1
R
18
9
9
-
-
-
-
-
-
EVOLVER
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
-
-
15
ADD
216
81
81
1+5
REDUCE
2+1+6
8+1
8+1
6
DEDUCE
9
9
9

 

 

REVOLVER EVOLVER LOVER

 

-
-
-
-
-
REVOLVER
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
2
E+V
27
9
9
-
-
-
-
2
O+L
27
9
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
R
18
9
9
L
=
3
-
8
REVOLVER
117
45
45
-
-
-
-
-
EVOLVER
-
-
-
-
-
-
-
2
E+V
27
9
9
-
-
-
-
2
O+L
27
9
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
R
18
9
9
R
=
9
-
7
EVOLVER
99
36
36
-
-
-
-
-
LOVER
-
-
-
-
5
-
-
2
L+O
27
9
9
-
1
-
-
2
V+E
27
9
9
-
1
-
-
1
R
18
9
9
L
=
3
-
5
LOVER
72
27
27
-
-
-
-
-
-
-
-
-
-
-
15
-
20
288
108
108
-
-
1+5
-
2+0
-
2+7+0
9+0
9+0
-
-
6
-
2
9
9
9

 

REVOLVER EVOLVER LOVER

 

 

THE

SWORD OF WORDS

 

 

WORKS WELL WHEN WATCHED

 

-
-
-
-
-
WORKS
-
-
-
-
-
-
-
1
W
23
5
5
-
-
-
-
1
O
15
6
6
-
-
-
-
1
R
18
9
9
-
-
-
-
1
K
11
2
2
-
-
-
-
1
S
19
10
1
W
=
5
-
5
WORKS
86
32
23
-
-
-
-
-
WELL
-
-
-
-
-
-
-
1
W
23
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
L
12
3
3
-
-
-
-
1
L
12
3
3
W
=
5
-
4
WELL
52
16
16
-
-
-
-
-
WHEN
-
-
-
-
-
-
-
1
W
23
5
5
-
-
-
-
1
H
8
8
8
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
W
=
5
-
4
WHEN
50
23
23
-
-
-
-
-
WATCHED
-
-
-
-
-
-
-
1
W
23
5
5
-
-
-
-
1
A
1
1
1
-
-
-
-
1
T
20
2
2
-
-
-
-
1
C
3
3
3
-
-
-
-
1
H
8
8
8
-
-
-
-
1
E
5
5
5
-
-
-
-
1
D
4
4
4
W
=
5
-
7
WATCHED
64
28
28
-
-
-
-
-
-
-
-
-
-
-
20
-
20
252
99
90
-
-
2+0
-
2+0
-
2+7+0
9+9
9+0
-
-
2
-
2
9
9
9

 

WORKS WELL WHEN WATCHED

 

 

-
EXPOUNDED
-
-
-
3
E+X+P
45
18
9
2
O+U
36
9
9
2
N+D
18
9
9
2
E+D
9
9
9
9
EXPOUNDED
108
45
36
=
-
1+0+8
4+5
3+6
9
EXPOUNDED
9
9
9

 

 

EVOLVE LOVE LOVE EVOLVE

 

-
EVOLVE LOVE LOVE EVOLVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
20
EVOLVE LOVE LOVE EVOLVE
270
90
45
2+0
-
2+7+0
9+0
4+5
2
EVOLVE LOVE LOVE EVOLVE
9
9
9
-
-
-
-
-
2
EVOLVE LOVE LOVE EVOLVE
9
9
9

 

 

-
6
S
P
I
R
I
T
-
-
-
-
3
-
-
-
-
-
-
-
1
-
9
-
9
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
19
-
9
-
9
-
+
=
37
3+7
=
10
1+0
1
=
1
-
6
S
P
I
R
I
T
-
-
-
-
3
-
-
-
-
-
-
-
-
7
-
9
-
2
+
=
18
1+8
=
9
=
9
=
9
-
-
-
16
-
18
-
20
+
=
54
5+4
=
9
=
9
=
9
-
6
S
P
I
R
I
T
-
-
-
-
3
-
-
-
-
-
-
-
19
16
9
18
9
20
+
=
91
9+1
=
10
1+0
1
=
1
-
-
1
7
9
9
9
2
+
=
37
3+7
=
10
1+0
1
=
1
-
6
S
P
I
R
I
T
-
-
-
-
3
-
-
-
-
-
---
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
---
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
3
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
3
-
3
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
3
-
3
-
-
-
-
6
SIX
6
-
-
-
-
-
---
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
9
9
--
-
-
9
occurs
x
3
=
27
2+7
9
26
6
S
P
I
R
I
T
-
-
19
-
-
6
-
37
-
19
2+6
-
-
-
9
9
9
-
-
-
1+0
-
-
-
-
3+7
-
1+9
8
6
S
P
I
R
I
T
-
-
1
-
-
6
-
10
-
10
-
-
1
7
9
9
9
2
-
-
-
-
-
-
-
1+0
-
1+0
8
6
S
P
I
R
I
T
-
-
1
-
-
6
-
1
-
1

 

 

6
S
P
I
R
I
T
-
-
-
-
-
-
-
-
1
-
9
-
9
-
+
=
19
1+9
=
10
1+0
1
=
1
-
19
-
9
-
9
-
+
=
37
3+7
=
10
1+0
1
=
1
6
S
P
I
R
I
T
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
-
2
+
=
18
1+8
=
9
=
9
=
9
-
-
16
-
18
-
20
+
=
54
5+4
=
9
=
9
=
9
6
S
P
I
R
I
T
-
-
-
-
-
-
-
-
-
-
-
19
16
9
18
9
20
+
=
91
9+1
=
10
1+0
1
=
1
-
1
7
9
9
9
2
+
=
37
3+7
=
10
1+0
1
=
1
6
S
P
I
R
I
T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
9
9
-
-
-
9
occurs
x
3
=
27
2+7
9
6
S
P
I
R
I
T
-
-
19
-
-
6
-
37
-
19
-
-
-
9
9
9
-
-
-
1+0
-
-
-
-
3+7
-
1+9
6
S
P
I
R
I
T
-
-
1
-
-
6
-
10
-
10
-
1
7
9
9
9
2
-
-
-
-
-
-
-
1+0
-
1+0
6
S
P
I
R
I
T
-
-
1
-
-
6
-
1
-
1

 

 

T
=
1
-
2
TO
35
8
8
B
=
2
-
2
BE
7
7
7
O
=
6
-
2
OR
33
15
6
N
=
1
-
3
NOT
49
13
4
T
=
1
-
2
TO
35
8
8
B
=
2
-
2
BE
7
7
7
T
=
2
-
4
THAT
49
13
4
I
=
9
-
2
IS
28
10
1
T
=
3
-
3
THE
33
15
6
Q
=
8
-
8
QUESTION
120
39
3
-
-
36
-
30
-
396
135
54
-
-
3+6
-
3+0
-
3+9+6
1+3+5
5+4
Q
-
9
Q
3
Q
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
9
-
3
-
9
9
9

 

 

G
=
7
4
GOOD
41
23
5
A
=
1
3
AND
19
10
1
E
=
4
4
EVIL
48
21
3
-
-
12
11
Add to Reduce
108
54
9
-
-
1+2
1+1
Reduce to Deduce
1+0+8
5+4
-
-
-
3
2
Essence of Number
9
9
9

 

 

-
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
5
-
-
-
-
9
-
+
=
26
2+6
=
8
=
8
=
8
-
-
-
15
15
-
-
-
14
-
-
-
-
9
-
+
=
53
5+3
=
8
=
8
=
8
-
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
4
-
1
-
4
-
5
22
-
12
+
=
55
5+5
=
10
1+0
1
=
1
-
-
7
-
-
4
-
1
-
4
-
5
4
-
3
+
=
28
2+8
=
10
1+0
1
=
1
-
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
7
15
15
4
-
1
14
4
-
5
22
9
12
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
6
6
4
-
1
5
4
-
5
4
9
3
+
=
54
5+4
=
9
=
9
=
9
-
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
10
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
35
-
-
11
-
54
-
27
1+0
1+1
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
3+5
-
-
1+1
-
5+4
-
2+7
1
2
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
8
-
-
2
-
9
-
9
-
-
7
6
6
4
-
1
5
4
-
5
4
9
3
-
-
-
-
-
-
-
-
-
-
1
2
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
8
-
-
2
-
9
-
9

 

 

11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
5
-
-
-
-
9
-
+
=
26
2+6
=
8
=
8
=
8
-
-
15
15
-
-
-
14
-
-
-
-
9
-
+
=
53
5+3
=
8
=
8
=
8
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
7
-
-
4
-
1
-
4
-
5
22
-
12
+
=
55
5+5
=
10
1+0
1
=
1
-
7
-
-
4
-
1
-
4
-
5
4
-
3
+
=
28
2+8
=
10
1+0
1
=
1
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
7
15
15
4
-
1
14
4
-
5
22
9
12
+
=
108
1+0+8
=
9
=
9
=
9
-
7
6
6
4
-
1
5
4
-
5
4
9
3
+
=
54
5+4
=
9
=
9
=
9
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
11
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
35
-
-
11
-
54
-
27
1+1
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
3+5
-
-
1+1
-
5+4
-
2+7
2
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
8
-
-
2
-
9
-
9
-
7
6
6
4
-
1
5
4
-
5
4
9
3
-
-
-
-
-
-
-
-
-
-
2
G
O
O
D
-
A
N
D
-
E
V
I
L
-
-
8
-
-
2
-
9
-
9

 

 

11
G
O
O
D
N
D
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
5
-
-
-
9
-
+
=
26
2+6
=
8
=
8
=
8
-
-
15
15
-
-
14
-
-
-
9
-
+
=
53
5+3
=
8
=
8
=
8
11
G
O
O
D
A
N
D
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
7
-
-
4
1
-
4
5
22
-
12
+
=
55
5+5
=
10
1+0
1
=
1
-
7
-
-
4
1
-
4
5
4
-
3
+
=
28
2+8
=
10
1+0
1
=
1
11
G
O
O
D
A
N
D
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
7
15
15
4
1
14
4
5
22
9
12
+
=
108
1+0+8
=
9
=
9
=
9
-
7
6
6
4
1
5
4
5
4
9
3
+
=
54
5+4
=
9
=
9
=
9
11
G
O
O
D
A
N
D
E
V
I
L
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
4
-
4
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
5
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
11
G
O
O
D
A
N
D
E
V
I
L
-
-
35
-
-
11
-
54
-
27
1+1
-
-
-
-
-
-
-
-
-
9
-
-
-
3+5
-
-
1+1
-
5+4
-
2+7
2
G
O
O
D
A
N
D
E
V
I
L
-
-
8
-
-
2
-
9
-
9
-
7
6
6
4
1
5
4
5
4
9
3
-
-
-
-
-
-
-
-
-
-
2
G
O
O
D
A
N
D
E
V
I
L
-
-
8
-
-
2
-
9
-
9

 

 

S
=
1
-
6
SEARCH
54
27
9
F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EXTRA
68
23
5
T
=
2
-
11
TERRESTRIAL
145
55
1
I
=
9
-
12
INTELLIGENCE
115
61
7
S
-
23
4
37
First Total
421
187
25
-
-
2+3
-
3+7
Add to Reduce
4+2+1
1+8+7
2+5
-
-
5
-
10
Second Total
7
16
7
-
-
-
-
1+0
Reduce to Deduce
-
1+6
-
-
-
5
-
1
Essence of Number
7
7
7

 

 

S
=
1
-
6
SEARCH
54
27
9
F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EXTRA
68
23
5
T
=
2
-
11
TERRESTRIAL
145
55
1
L
=
3
-
4
LIFE
32
23
5
S
-
17
4
29
First Total
338
149
23
-
-
1+7
-
2+9
Add to Reduce
3+8+8
1+4+9
2+3
-
-
8
-
11
Second Total
14
14
5
-
-
-
-
1+1
Reduce to Deduce
1+4
1+4
-
-
-
8
-
2
Essence of Number
5
5
5

 

 

4
S.E.T.I.
53
17
8

 

 

-
4
S
E
T
I
-
-
-
-
-
-
-
-
-
-
1
-
2
9
+
=
10
1+0
-
1
=
1
`-
-
19
-
-
9
+
=
28
2+8
=
10
1+0
1
-
4
S
E
T
I
-
-
-
=
-
-
-
-
-
-
2
5
2
-
+
=
7
=
=
7
=
7
-
-
-
5
20
-
+
=
25
2+5
=
7
=
7
-
4
S
E
T
I
-
-
-
-
-
-
-
-
`-
-
19
5
20
9
+
=
53
5+3
=
8
=
8
-
-
1
5
2
9
+
=
17
1+7
=
8
1+0
8
-
4
S
E
T
I
T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
28
4
S
E
T
I
-
-
17
-
-
3
-
17
2+8
-
-
-
-
9
T
-
1+7
-
-
-
-
1+7
10
4
S
E
T
I
-
-
8
-
-
3
-
8
1+0
-
-
5
2
9
T
T
-
-
-
-
-
-
1
4
S
E
T
I
-
-
8
-
-
3
-
8

 

 

4
S
E
T
I
-
-
-
-
-
-
-
-
-
1
-
2
9
+
=
10
1+0
-
1
=
1
-
19
-
-
9
+
=
28
2+8
=
10
1+0
1
4
S
E
T
I
-
-
-
=
-
-
-
-
-
2
5
2
-
+
=
7
=
=
7
=
7
-
-
5
20
-
+
=
25
2+5
=
7
=
7
4
S
E
T
I
-
-
-
-
-
-
-
-
-
19
5
20
9
+
=
53
5+3
=
8
=
8
-
1
5
2
9
+
=
17
1+7
=
8
1+0
8
4
S
E
T
I
T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
9
-
-
9
occurs
x
1
=
9
4
S
E
T
I
-
-
17
-
-
3
-
17
-
-
-
-
9
T
-
1+7
-
-
-
-
1+7
4
S
E
T
I
-
-
8
-
-
3
-
8
-
-
5
2
9
T
T
-
-
-
-
-
-
4
S
E
T
I
-
-
8
-
-
3
-
8

 

 

QUO VADIS

 

Quo vadis - Wikipedia, the free encyclopedia Quo vadis? is a Latin phrase meaning "Where are you going?" or "Whither goest thou?". The modern usage of the phrase refers to a legend in Christian ... en.wikipedia.org/wiki/Quo_vadis

Quo vadis? is a Latin phrase meaning "Where are you going?" or "Whither goest thou?". The modern usage of the phrase refers to a legend in Christian tradition, related in the apocryphal Acts of Peter (Vercelli Acts XXXV), in which Saint Peter meets Jesus as Peter is fleeing from likely crucifixion in Rome. Peter asks Jesus the question; Jesus' answer, "I am going to Rome to be crucified again" (Eo Romam iterum crucifigi), prompts Peter to gain the courage to continue his ministry and eventually become a martyr.

The phrase also occurs a few times in the Vulgate translation of the Bible, notably including the occurrence in John 13:36 in which Peter also asks the question of Jesus, after the latter announces he is going to where his followers cannot come.

 

 

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

 

 

Quo Vadis. I fled by night and in the grey of dawn met on the lonely way a man I knew but could not name. He said “Good morning”, I the same .. rtnl.org.uk/now_and_then/html/242.html

 

Quo Vadis
I fled by night and in the grey
of dawn met on the lonely way
a man I knew but could not name.
He said “Good morning”, I the same
and asked if he was going far.
He said “As far as Golgotha.”
And then I knew and the cock crew.

 

Quo vadis is a Latin phrase meaning "Where are you going?" It is used as a proverbial phrase from the Bible (John 13:36, 16:5). ... en.wikipedia.org/wiki/Quo_Vadis -

 

 

HOLY BIBLE

Scofield References

C 1 V 16

THE ACTS OF THE APOSTLES

Page 1148 (Part quoted)

"MEN AND BRETHREN THIS SCRIPTURE MUST NEEDS HAVE BEEN FULFILLED

WHICH THE HOLY GHOST BY THE MOUTH OF DAVID SPAKE"

 

 

T
=
2
-
3
THE
33
15
6
S
=
1
-
4
STAR
58
13
4
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DAVID
40
22
4
B
-
13
Q
14
Add to Reduce
152
62
17
-
-
1+3
-
1+4
Reduce to Deduce
1+5+2
6+2
1+7
-
-
4
-
5
Essence of Number
8
8
8

 

 

T
=
2
-
3
THE
33
15
6
S
=
1
-
4
SONG
55
10
1
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DAVID
40
22
4
B
-
13
Q
14
First Total
149
59
14
-
-
1+3
-
1+4
Add to Reduce
1+4+9
5+9
1+4
-
-
4
-
5
Second Total
14
14
5
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
4
-
5
Essence of Number
5
5
5

 

 

I
=
9
-
1
I
9
9
9
A
=
1
-
2
AM
14
5
5
T
=
2
-
3
THE
33
15
6
R
=
9
-
4
ROOT
68
23
5
A
=
1
-
3
AND
19
10
1
T
=
2
-
3
THE
33
15
6
O
=
6
-
9
OFFSPRING
110
56
2
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DAVID
40
22
4
A
=
1
-
3
AND
19
10
1
T
=
2
-
3
THE
33
15
6
B
=
2
-
6
BRIGHT
64
37
1
A
=
1
-
3
AND
19
10
1
M
=
4
-
7
MORNING
90
45
9
S
=
1
-
4
STAR
58
13
4
-
-
51
-
58
First Total
630
297
63
-
-
5+1
-
5+8
Add to Reduce
6+3+0
2+9+7
6+3
Q
-
6
Q
13
Second Total
9
18
9
-
-
-
-
1+3
Reduce to Deduce
-
1+8
-
-
-
6
-
4
Essence of Number
9
9
9

 

 

 

CHEIRO'S BOOK OF NUMBERS

Circa 1926

Page106
"Shakespeare, that Prince of Philosophers, whose thoughts will adorn English literature for all time, laid down the well-known axiom: There is a tide in the affairs of men which if taken at the flood, leads on to fortune." The question has been asked again and again, Is there some means of knowing when the moment has come to take the tide at the flood?
My answer to this question is that the Great Architect of the Universe in His Infinite Wisdom so created all things in such harmony of design that He endowed the human mind with some part of that omnipotent knowledge which is the attribute of the Divine Mind as the Creator of all.

The question has been asked again and again, Is there some means of knowing when the moment has come to take the tide at the flood?

 

 

 THE

QUESTION

HAS BEEN ASKED AGAIN AND AGAIN

IS THERE SOME MEANS OF KNOWING WHEN THE MOMENT HAS COME TO TAKE

THE TIDE AT THE

FLOOD

 

 

T
=
2
-
3
THE
33
15
6
Q
=
8
-
8
QUESTION
120
39
3
H
=
8
-
3
HAS
28
10
1
B
=
2
-
4
BEEN
26
17
8
A
=
1
-
5
ASKED
40
13
4
A
=
1
-
5
AGAIN
32
23
5
A
=
1
-
3
AND
19
10
1
A
=
1
-
5
AGAIN
32
23
5
I
=
9
-
2
IS
28
10
1
T
=
2
-
5
THERE
56
29
2
S
=
1
-
4
SOME
52
16
7
M
=
4
-
5
MEANS
52
16
7
O
=
6
-
2
OF
21
12
3
K
=
2
-
7
KNOWING
93
39
3
W
=
5
-
4
WHEN
50
23
5
T
=
2
-
3
THE
33
15
6
M
=
4
-
6
MOMENT
80
26
8
H
=
8
-
3
HAS
28
10
1
C
=
3
-
4
COME
36
18
9
T
=
2
-
2
TO
35
8
8
T
=
2
-
4
TAKE
37
10
1
T
=
2
-
3
THE
33
15
6
T
=
2
-
4
TIDE
38
20
2
A
=
1
-
2
AT
21
3
3
T
=
2
-
3
THE
33
15
6
F
=
6
-
5
FLOOD
52
25
7
B
-
87
Q
104
First Total
1108
460
118
-
-
8+7
-
1+0+4
Add to Reduce
1+1+0+8
4+6+0
1+1+8
-
-
15
-
5
Second Total
10
10
10
-
-
1+5
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
6
-
5
Essence of Number
1
1
1

 

 

YOU ARE GOING ON A JOURNEY A VERY SPECIAL JOURNEY DO HAVE A PLEASANT JOURNEY DO

 

 

8
QUO VADIS
108
36
9
6
VOX POP
108
36
9
11
SORROW
108
36
9
8
INSTINCT
108
36
9
11
DESCENDANTS
108
36
9
8
STARTING
108
36
9
9
NARRATIVE
108
36
9
9
SEQUENCES
108
36
9
9
COMPLETES
108
36
9
9
AMBIGUOUS
108
36
9
7
JOURNEY
108
36
9

 

 

KEEPER OF GENESIS

A QUEST FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock 1996

Page 254

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

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

That common language is science and mathematics.

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

 

 

THE LURE AND ROMANCE OF ALCHEMY.

A history of the secret link between magic and science

1990
C. J. S.Thompson

Page# 31 / 32

note 1 Julius Ruska ,Tabula Smaragdini 1926

"THE EMERALD TABLE OF HERMES: "

"True it is, without falsehood certain most true.That which is
above is like to that which is below, and that which is below is like
to that which is above, to accomplish the miracles of one thing.
And as in all things whereby contemplation of one, so in all things
arose from this one thing by a single act of adoption.
The father thereof is the Sun the mother the Moon.
The wind carried it in its womb,the earth is the source thereof.
It is the father of all works throughout the world.
The power thereof is perfect.
If it be cast on to earth, it will separate the element of earth
from that of fire, the subtle from the gross.
With great sagacity it doth ascend gently from earth to heaven.
Again it doth descend to earth and uniteth in itself from
things superior and things inferior.
Thus thou wilt possess the brightness of the world, and all
obscurity will fly far from thee.
This thing is the strong fortitude of all strength, for it over-
cometh every subtle thing and doth penetrate every solid substance.
Thus was this world created.
Hence will there be marvellous adaptations achieved of which
the manner is this.
For this reason I am called Hermes Trismegistus because I hold
three parts of the wisdom of the whole world.
That which I had to say about the operation of Sol is completed."

 

 

Freiheit - Keeping The Dream Alive lyrics. From the Original Motion Picture ... In my fantasy I remember their faces The hopes we had were much too high ... www.lyricsmode.com/lyrics/f/freiheit/keeping_the_dream_alive.html


Tonight the rain is falling
Full of memories of people and places
And while the past is calling
In my fantasy I remember their faces

The hopes we had were much too high
Way out of reach but we have to try
The game will never be over
Because we're keeping the dream alive

I hear myself recalling
Things you said to me
The night it all started
And still the rain is falling
Makes me feel the way
I felt when we parted

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one
The game will never be over
Because we're keeping the dream alive

I need you
I love you

The game will never be over
Because we're keeping the dream alive

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one

The game will never be over
Because we're keeping the dream alive

The game will never be over
Because we're keeping the dream alive

The game will never be over

Mmm mmm mmm mmm mmm mmm mmm mmm mmm.

 

 

I

SAY

IS THIS THE OTHER SIDE OF THE GREAT DIVIDE

?

NO ITS OVER THERE

I

HAVE JUST BEEN OVER THERE AND THEY SAID ITS OVER HERE

 

 

Did Spacemen Colonise the Earth?

Robin Collyns 1974

Page 206

"FINIS"

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1924

THE THUNDERBOLT

Page 715

"There is our friend, there is Hans Castorp! We recognize him at a distance, by the little beard he assumed 'while sitting at the " bad" Russian table. Like all the others, he is wet through and glowing. He is running, his feet heavy with mould, the bayonet swinging in his, hand. Look! He treads on the hand of a fallen comrade; with his hobnailed boot he treads the hand deep into the slimy, branch-strewn ground. But it is he. What, singing? As one sings, unaware, staring stark ahead, yes, thus. he spends his hurrying breath, to sing half soundlessly:

"And loving words I've carven
Upon its branches fair-"

He stumbles, No, he has flung himself down, a hell-hound is coming howling, a huge explosive shell, a disgusting sugar-loaf from the infernal regions. He lies with his face in the cool mire, legs. sprawled out, feet twisted, heels turned down. The product of a perverted science, laden with death, slopes earthward thirty paces in front of him and buries its nose in the ground; explodes inside there, with hideous expense of power, and raises up a fountain high as a house, of mud, fire, iron, molten metal, scattered fragments of humanity. Where it fell, two youths had lain, friends who in their need flung themselves down together - now they are scattered, commingled and gone.
Shame of our shadow-safety! Away! No more!-But our friend? Was he hit? He thought so, for the moment. A great clod of earth struck him on the shin, it hurt, but he smiles at it. Up he gets, and staggers on, limping on his earth-bound feet, all unconsciously singing:

"Its waving branches whiispered
A message in my ear -"

and thus, in the tumult, in the rain, in the dusk, vanishes out of our sight.
Farewell, honest Hans Castorp, farewell, Life's delicate child!
Your tale is told. We have told it to the end, and it was neither short nor long, but hermetic. We have told it for its own sake, not for yours, for you were simple. But after all, it was your story, it befell you, you must have more in you than we thought; we will not disclaim the pedagogic weakness we conceived for / Page 716 / you in the telling; which could even lead us to press a finger delicately to our eyes at the thought that we shall see you no more, hear you no more for ever.
Farewell - and if thou livest or diest! Thy prospects are poor. The desperate dance, in which thy fortunes are caught up, will last yet many a sinful year; we should not care to set a high stake on thy life by the time it ends. We even confess that it is without great concern we leave the question open. Adventures of the flesh and in the spirit, while enhancing thy simplicity, granted thee to know in the spirit what in the flesh thou scarcely couldst have done. Moments there were, when out of death, and the rebellion of the flesh, there came to thee, as thou tookest stock of thyself, a dream of love. Out of this universal feast of death, out of this extremity of fever, kindling. the rain-washed evening sky to a fiery glow, may it be that Love one day shall mount?

FINIS OPERIS

 
 
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