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Evokation
  
 
Index
  

 

 

THE NUCLEAR FAMILY 1969

 

 

 

 

 

 

 

 

 

 

 

 

 

A
=
1
9
ASTROLOGY
132
42
6
T
=
2
3
THE
33
15
6
S
=
1
6
STARRY
101
29
2
L
=
3
4
LOGO
49
22
4
-
-
7
22
Add to Reduce
315
108
18
-
=
-
2+2
Reduce to Deduce
3+1+5
1+0+8
1+8
-
-
7
4
Essence of Number
9
9
9

 

 

-
22
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
6
-
6
-
-
-
-
8
-
-
1
-
-
-
-
-
-
-
6
-
6
+
=
34
3+4
=
7
-
7
-
7
-
-
-
19
-
-
15
-
15
-
-
-
-
8
-
-
19
-
-
-
-
-
-
-
15
-
15
+
=
106
1+0+6
=
7
-
7
-
7
-
22
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
9
-
3
-
7
7
-
2
-
5
-
-
2
1
9
9
7
-
3
-
7
-
+
=
74
7+4
=
11
1+1
2
-
2
-
-
1
-
20
18
-
12
-
7
25
-
20
-
5
-
-
20
1
18
18
25
-
12
-
7
-
+
=
209
2+0+9
=
11
1+1
2
-
2
-
22
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
-
-
-
-
-
-
-
-
-
-
1
19
20
18
15
12
15
7
25
-
20
8
5
-
19
20
1
18
18
25
-
12
15
7
15
+
=
315
3+1+5
=
9
-
9
-
9
-
-
1
1
2
9
6
3
6
7
7
-
2
8
5
-
1
2
1
9
9
7
-
3
6
7
6
+
=
108
1+0+8
=
9
-
9
-
9
-
22
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
6
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
-
7
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
4
=
28
10
1
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
9
-
-
-
9
9
-
-
-
-
-
-
-
-
9
9
9
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
4
22
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
41
-
-
22
-
108
-
45
-
2+2
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
9
9
-
9
-
-
-
-
-
-
4+1
-
-
2+2
-
1+0+8
-
4+5
4
4
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
5
-
-
4
-
9
-
9
-
-
1
1
2
9
6
3
6
7
7
-
2
8
5
-
1
2
1
9
9
7
-
3
6
7
6
-
-
-
-
-
-
-
-
-
-
4
4
A
S
T
R
O
L
O
G
Y
-
T
H
E
-
S
T
A
R
R
Y
-
L
O
G
O
-
-
5
-
-
4
-
9
-
9

 

 

-
4
S
T
A
R
-
-
-
-
-
--
-
-
-
-
1
-
-
-
+
=
1
-
=
1
-
1
-
-
19
-
-
-
+
=
19
1+9
=
10
1+0
1
-
4
S
T
A
R
-
-
-
-
-
--
-
-
-
-
-
2
1
9
+
=
12
1+2
=
3
-
3
-
-
-
20
1
18
+
=
39
3+9
=
12
1+2
3
-
4
S
T
A
R
-
-
-
-
-
--
-
-
-
-
19
20
1
18
+
=
58
5+8
=
13
1+3
4
-
-
1
2
1
9
+
=
13
1+3
=
4
-
4
-
4
S
T
A
R
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
6
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
33
4
S
T
A
R
-
-
12
-
-
4
-
13
3+3
-
-
-
-
9
-
-
1+2
-
-
-
-
1+3
6
4
S
T
A
R
-
-
3
-
-
4
-
4
-
-
1
2
1
9
-
-
-
-
-
-
-
-
6
4
S
T
A
R
-
-
3
-
-
4
-
4

 

 

4
S
T
A
R
-
-
-
-
-
--
-
-
-
1
-
-
-
+
=
1
-
=
1
-
1
-
19
-
-
-
+
=
19
1+9
=
10
1+0
1
4
S
T
A
R
-
-
-
-
-
--
-
-
-
-
2
1
9
+
=
12
1+2
=
3
-
3
-
-
20
1
18
+
=
39
3+9
=
12
1+2
3
4
S
T
A
R
-
-
-
-
-
--
-
-
-
19
20
1
18
+
=
58
5+8
=
13
1+3
4
-
1
2
1
9
+
=
13
1+3
=
4
-
4
4
S
T
A
R
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
9
-
-
9
occurs
x
1
=
9
4
S
T
A
R
-
-
12
-
-
4
-
13
-
-
-
-
9
-
-
1+2
-
-
-
-
1+3
4
S
T
A
R
-
-
3
-
-
4
-
4
-
1
2
1
9
-
-
-
-
-
-
-
-
4
S
T
A
R
-
-
3
-
-
4
-
4

 

 

-
5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
-
1
-
-
-
1
+
=
2
-
=
2
-
2
-
-
19
-
-
-
19
+
=
38
3+8
=
11
1+1
2
-
5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
-
-
2
1
9
-
+
=
12
1+2
=
3
-
3
-
-
-
20
1
18
-
+
=
39
3+9
=
12
1+2
3
-
5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
-
19
20
1
18
19
+
=
77
7+7
=
14
1+4
5
-
-
1
2
1
9
1
+
=
14
1+4
=
5
-
5
-
5
S
T
A
R
S
-
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
1
occurs
x
3
=
3
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
33
5
S
T
A
R
S
-
-
12
-
-
5
-
14
3+3
-
-
-
-
9
-
-
-
1+2
-
-
-
-
1+4
6
5
S
T
A
R
S
-
-
3
-
-
5
-
5
-
-
1
2
1
9
1
-
-
-
-
-
-
-
-
6
5
S
T
A
R
S
-
-
3
-
-
5
-
5

 

 

5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
1
-
-
-
1
+
=
2
-
=
2
-
2
-
19
-
-
-
19
+
=
38
3+8
=
11
1+1
2
5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
-
2
1
9
-
+
=
12
1+2
=
3
-
3
-
-
20
1
18
-
+
=
39
3+9
=
12
1+2
3
5
S
T
A
R
S
-
-
-
-
-
--
-
-
-
19
20
1
18
19
+
=
77
7+7
=
14
1+4
5
-
1
2
1
9
1
+
=
14
1+4
=
5
-
5
5
S
T
A
R
S
-
-
-
-
-
-
-
-
-
1
-
1
-
1
-
-
1
occurs
x
3
=
3
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
5
S
T
A
R
S
-
-
12
-
-
5
-
14
-
-
-
-
9
-
-
-
1+2
-
-
-
-
1+4
5
S
T
A
R
S
-
-
3
-
-
5
-
5
-
1
2
1
9
1
-
-
-
-
-
-
-
-
5
S
T
A
R
S
-
-
3
-
-
5
-
5

 

 

9
FIRMAMENT
-
-
-
-
F+I+R+M
46
28
1
1
A
1
1
1
-
M+E+N+T
52
16
7
9
FIRMAMENT
99
45
9
-
-
9+9
4+5
-
9
FIRMAMENT
18
9
9
-
-
1+8
-
-
9
FIRMAMENT
9
9
9

 

 

-
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
5
-
+
=
14
1+4
=
5
-
5
=
5
-
-
-
9
-
-
-
-
-
14
-
+
=
23
2+3
=
5
=
5
=
5
-
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
6
9
18
13
1
13
5
-
2
+
=
31
3+1
=
4
=
4
=
4
-
-
6
9
9
4
1
4
5
-
20
+
=
76
7+6
=
13
1+3
4
=
4
-
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
6
9
18
13
1
13
5
14
20
+
=
99
9+9
=
18
1+8
9
=
9
-
-
6
9
9
4
1
4
5
5
2
+
=
45
4+5
=
9
-
9
=
9
-
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
-`-
-
-
-
2
-
-
2
occurs
x
1
=
2
-
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
9
F
I
R
M
A
M
E
N
T
-
-
35
-``
-
9
-
45
-
27
1+0
-
-
9
9
-
-
-
-
-
-
-
-
3+5
-
-
-
-
4+5
-
2+7
1
9
F
I
R
M
A
M
E
N
T
-
-
8
-``
-
9
-
9
-
9
-
-
6
9
9
4
1
4
5
5
2
-
-
-
-
-
-
-
-
-
-
1
9
F
I
R
M
A
M
E
N
T
-
-
8
-``
-
9
-
9
-
9

 

 

9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
5
-
+
=
14
1+4
=
5
-
5
=
5
-
-
9
-
-
-
-
-
14
-
+
=
23
2+3
=
5
=
5
=
5
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
6
9
18
13
1
13
5
-
2
+
=
31
3+1
=
4
=
4
=
4
-
6
9
9
4
1
4
5
-
20
+
=
76
7+6
=
13
1+3
4
=
4
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
6
9
18
13
1
13
5
14
20
+
=
99
9+9
=
18
1+8
9
=
9
-
6
9
9
4
1
4
5
5
2
+
=
45
4+5
=
9
-
9
=
9
9
F
I
R
M
A
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-`-
-
-
-
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
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
9
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
F
I
R
M
A
M
E
N
T
-
-
35
-``
-
9
-
45
-
27
-
-
9
9
-
-
-
-
-
-
-
-
3+5
-
-
-
-
4+5
-
2+7
9
F
I
R
M
A
M
E
N
T
-
-
8
-``
-
9
-
9
-
9
-
6
9
9
4
1
4
5
5
2
-
-
-
-
-
-
-
-
-
-
9
F
I
R
M
A
M
E
N
T
-
-
8
-``
-
9
-
9
-
9

 

 

 

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

 

 

 

 

-
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
9
-
5
1
+
=
17
1+7
=
8
=
8
=
8
-
-
19
-
-
-
-
19
9
-
14
19
+
=
71
7+1
=
8
=
8
=
8
-
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
2
1
9
-
-
-
7
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
-
20
1
18
-
-
-
7
-
-
+
=
46
4+6
=
10
1+0
1
-
1
-
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
-
19
20
1
18
-
19
9
7
14
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
1
2
1
9
-
1
9
7
5
1
+
=
36
3+6
=
9
=
9
=
9
-
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
1
-
-
1
occurs
x
4
-
4
-
4
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
--
-
-
-
-
-
-
-
-
-
-
-
3
-
-
--
--
--
-
-
4
-
-
--
--
--
-
-
--
--
--
-
-
-
4
-
-
--
--
--
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
5
6
-
-
--
--
--
-
-
--
--
--
-
-
-
6
-
-
--
--
--
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
--
7
8
-
-
--
--
--
-
-
--
--
--
-
-
-
8
-
-
--
--
--
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
21
9
S
T
A
R
-
S
I
G
N
S
-
-
24
-
-
9
-
36
-
27
2+1
  
-
-
-
9
-
-
9
-
-
-
-
-
2+4
-
-
-
-
3+6
-
2+7
3
9
S
T
A
R
-
S
I
G
N
S
-
-
6
-
-
9
-
9
-
9
-
-
1
3
1
9
-
1
9
7
5
1
-
-
-
-
-
-
-
-
-
-
3
9
S
T
A
R
-
S
I
G
N
S
-
-
6
-
-
9
-
9
-
9

 

 

9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
9
-
5
1
+
=
17
1+7
=
8
=
8
=
8
-
19
-
-
-
-
19
9
-
14
19
+
=
71
7+1
=
8
=
8
=
8
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
-
2
1
9
-
-
-
7
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
20
1
18
-
-
-
7
-
-
+
=
46
4+6
=
10
1+0
1
-
1
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
19
20
1
18
-
19
9
7
14
19
+
=
126
1+2+6
=
9
=
9
=
9
-
1
2
1
9
-
1
9
7
5
1
+
=
36
3+6
=
9
=
9
=
9
9
S
T
A
R
-
S
I
G
N
S
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
1
-
-
1
occurs
x
4
-
4
-
4
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
--
7
-
-
-
-
9
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
S
T
A
R
-
S
I
G
N
S
-
-
24
-
-
9
-
36
-
27
 
-
-
-
9
-
-
9
-
-
-
-
-
2+4
-
-
-
-
3+6
-
2+7
9
S
T
A
R
-
S
I
G
N
S
-
-
6
-
-
9
-
9
-
9
-
1
3
1
9
-
1
9
7
5
1
-
-
-
-
-
-
-
-
-
-
9
S
T
A
R
-
S
I
G
N
S
-
-
6
-
-
9
-
9
-
9

 

 

-
9
T
H
E
-
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
6
-
9
-
-
+
=
31
3+1
=
4
-
4
-
4
-
-
-
8
-
-
26
15
-
9
-
-
+
=
58
5+8
=
13
1+3
4
-
4
-
9
T
H
E
-
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
-
4
-
1
3
+
=
15
1+5
=
6
-
6
-
6
-
-
20
-
5
-
-
-
4
-
1
3
+
=
33
3+3
=
6
-
6
-
6
-
9
T
H
E
-
Z
O
D
I
A
C
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
26
15
4
9
1
3
+
=
91
9+1
=
10
1+0
1
-
1
-
-
2
8
5
-
8
6
4
9
1
3
+
=
46
4+6
=
10
1+0
1
-
1
-
9
T
H
E
-
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
5
-
5
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
-
9
7
9
T
H
E
-
Z
O
D
I
A
C
-
-
38
-
-
9
-
46
-
37
-
-
-
-
-
-
-
-
-
9
-
-
-
-
3+8
-
-
-
-
4+6
-
3+7
7
9
T
H
E
-
Z
O
D
I
A
C
-
-
11
-
-
9
-
10
-
10
-
-
2
8
5
-
8
6
4
9
1
3
-
-
1+1
-
-
-
-
1+0
-
1+0
7
9
T
H
E
-
Z
O
D
I
A
C
-
-
2
-
-
9
-
1
-
1

 

 

-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
8
6
-
9
-
-
+
=
23
2+3
=
5
-
5
-
-
26
15
-
9
-
-
+
=
50
5+0
=
5
-
5
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
3
+
=
8
=
=
8
-
8
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
26
15
4
9
1
3
+
=
58
5+8
=
13
1+3
4
-
-
8
6
4
9
1
3
+
=
31
3+1
=
4
-
4
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
14
6
Z
O
D
I
A
C
-
-
31
-
-
6
-
31
1+4
-
-
-
-
9
-
-
-
-
3+1
-
-
-
-
3+1
5
6
Z
O
D
I
A
C
-
-
4
-
-
6
-
4
-
-
8
6
4
9
1
3
-
-
-
-
-
-
-
-
5
6
Z
O
D
I
A
C
-
-
4
-
-
6
-
4

 

 

-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
8
6
-
9
-
-
+
=
23
2+3
=
5
-
5
-
-
26
15
-
9
-
-
+
=
50
5+0
=
5
-
5
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
3
+
=
8
=
=
8
-
8
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
26
15
4
9
1
3
+
=
58
5+8
=
13
1+3
4
-
-
8
6
4
9
1
3
+
=
31
3+1
=
4
-
4
-
6
Z
O
D
I
A
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
14
6
Z
O
D
I
A
C
-
-
31
-
-
6
-
31
1+4
-
-
-
-
9
-
-
-
-
3+1
-
-
-
-
3+1
5
6
Z
O
D
I
A
C
-
-
4
-
-
6
-
4
-
-
8
6
4
9
1
3
-
-
-
-
-
-
-
-
5
6
Z
O
D
I
A
C
-
-
4
-
-
6
-
4

 

 

 

 

-
THE SOLAR SYSTEM
-
-
-
3
THE
33
15
6
5
SOLAR
65
29
2
6
SYSTEM
101
38
2
14
THE SOLAR SYSTEM
199
82
10
1+4
-
1+9+9
8+2
1+0
5
THE SOLAR SYSTEM
19
10
1
-
-
1+9
1+0
-
5
THE SOLAR SYSTEM
10
1
1
-
-
1+0
-
-
5
THE SOLAR SYSTEM
1
1
1

 

 

3

SUN
54
9
9
5

EARTH
52
25
7
4

MOON
57
21
3
12

First Total
163
55
19
1+2

Add to Reduce
1+6+3
5+5
1+9
3

Second Total
10
10
10

-

Add to deduce
1+0
1+0
1+0
3

Final Total
1
1
1

 

 

3

SUN
54
9
9
7

MERCURY
103
40
4
5

VENUS
81
18
9
5

EARTH
52
25
7
4

MOON
57
21
3
4

MARS
51
15
6
7

JUPITER
99
36
9
6

SATURN
93
21
3
6

URANUS
94
22
4
7

NEPTUNE
95
32
5
5

PLUTO
84
21
3
59

First Total
863
260
62
5+9

Add to Reduce
8+6+3
2+6+0
6+2
16

Second Total
17
8
8
1+6

Add to Deduce
1+7

-

-
7

Final Total
8
8
8

 

 

3

SUN
54
9
9
7

MERCURY
103
40
4
5

VENUS
81
18
9
5

EARTH
52
25
7
4

MOON
57
21
3
4

MARS
51
15
6
7

JUPITER
99
36
9
6

SATURN
93
21
3
6

URANUS
94
22
4
7

NEPTUNE
95
32
5
5

PLUTO
84
21
3
6

NIBURU
73
37
1
65

First Total
936
297
63
6+5

Add to Reduce
9+3+6
2+9+7
6+3
11

Second Total
18
18
9
1+1

Add to Deduce
1+8
1+8
-
2

Final Total
9
9
9

 

 

S
=
1
3

SUN
54
9
9
E
=
5
5

EARTH
52
25
7
M
=
4
4

MOON
57
21
3
M
=
4
7

MERCURY
103
40
4
M
=
4
4

MARS
51
15
6
V
=
4
5

VENUS
81
18
9
S
=
1
6

SATURN
93
21
3
U
=
3
6

URANUS
94
22
4
N
=
5
7

NEPTUNE
95
32
5
P
=
7
5

PLUTO
84
21
3
J
=
1
7

JUPITER
99
36
9
N
=
5
6

NIBURU
73
37
1
-
-
44
65

First Total
936
297
63
-
-
4+4
6+5

Add to Reduce
9+3+6
2+9+7
6+3
-
-
8
11

Second Total
18
18
9
-
-
-
1+1

Add to Deduce
1+8
1+8
-
-
-
8
2

Final Total
9
9
9

 

 

6
NIBIRU
-
-
-
-
N
14
5
5
-
I
9
9
9
-
B
2
2
2
-
I
9
9
9
-
R
18
9
9
-
U
21
3
3
6
NIBIRU
73
37
37
-
-
7+3
3+7
3+7
6
NIBIRU
10
10
10
-
-
1+0
1+0
1+0
4
NIBIRU
1
1
1

 

 

6
NIBIRU
-
-
-
-
N+I+B
25
16
7
-
I+R
27
18
9
-
U
21
3
3
6
NIBIRU
73
37
19
-
-
7+3
3+7
1+9
6
NIBIRU
10
10
10
-
-
1+0
1+0
1+0
4
NIBIRU
1
1
1

 

 

3

SUN
54
9
9
5

VENUS
81
18
9
7

JUPITER
99
36
9
15

Add to Reduce
234
63
27
1+5

Reduce to Deduce
2+3+4
6+3
2+7
6

Essence of Number
9
9
9

 

 

1

-

 7

MERCURY

 103 40 4
2

-

 5

VENUS

 81 18 9
3

-

 4

MARS

 51 15 6
4

-

 7

JUPITER

 99 36 9
5

-

 6

SATURN

 93 21 3
15 - 29 First Total 427 130 31
1+5 - 2+9 Add to Reduce 4+2+7
1+3+0
 3+1
6 - 11 Second Total 13 4 4
- - 1+1 Reduce to Deduce 3+1 - -
6 - 2 Final Total 4 4 4

 

 

1

-

 7

MERCURY

 103 40 4
2

-

 5

VENUS

 81 18 9
3

-

 4

MARS

 51 15 6
4

-

 7

JUPITER

 99 36 9
5

-

 6

SATURN

 93 21 3
6

-

 3

SUN

 54 9 9
7

-

 4

MOON

 57 21 3
28 - 36 First Total 538 160 43
2+8 - 3+6 Add to Reduce 5+3+8 1+6+0 4+3
10 - 9 Second Total 16 7 7
1+0 - - Reduce to Deduce 1+6 - -
1 - 9 Final Total 7 7 7

 

 

1

-

 7

MERCURY

 103 40 4
2

-

 5

VENUS

 81 18 9
3

-

 4

MARS

 51 15 6
4

-

 7

JUPITER

 99 36 9
5

-

 6

SATURN

 93 21 3
6

-

 3

SUN

 54 9 9
7

-

 4

MOON

 57 21 3
8 - 5

EARTH

 52 25 7
9 - 6

URANUS

 94 22 4
10 - 7

NEPTUNE

 95 32 5
11 - 5

PLUTO

 84 21 3
66 - 59 First Total 863 260 62

6+6

-

5+9

 Add to Reduce 8+6+3 2+6+0

6+2
12

-

 14 Second Total 17 8 8
1+2

-

1+4

 Reduce to Deduce 1+7

-

-
3

-

 5 Final Total 8 8 8

 

 

3

TAO

 36 9 9
4

GAIA

 18 9 9
5

WORLD

 72 27 9
-
-
 - - -

-

-

-

-

-
3

SUN

 54 9 9
5

EARTH

 52 25 7
4

MOON

 57 21 3

 

 

3

SUN

 54 9 9
5

EARTH

 52 25 7
4

MOON

 57 21 3

 

 

3

SUN

 54 9 9
5

EARTH

 52 25 7
4

MOON

 57 21 3
12 First Total 163 55 19
1+2 Add to Reduce 1+6+3 5+5 1+9
3 Second Total 10 10 10

-

 Reduce to Deduce 1+0

1+0

1+0
3 Final Total 1 1 1

 

 

3
S
U
N
-
-
-
-
-
--
-
-
-
19
21
14
+
=
54
5+4
=
9
=
9
-
1
3
5
+
=
9
-
=
9
=
9
3
S
U
N
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
3
-
-
-
3
occurs
x
1
=
3
-
 -
-
5
-
-
5
occurs
x
1
=
5
3
S
U
N
-
-
9
-
-
3
-
9

 

 

-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
1
-
5
-
-
-
-
-
8
-
-
6
6
5
+
=
31
3+1
=
4
-
4
=
4
-
-
19
-
14
-
-
-
-
-
8
-
-
15
15
14
+
=
85
8+5
=
13
1+3
4
=
4
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
3
-
-
5
1
9
2
-
-
4
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
`-
-
21
-
-
5
1
18
20
-
-
13
-
-
-
+
=
78
7+8
=
15
1+5
6
=
6
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
19
21
14
-
5
1
18
20
8
-
13
15
15
14
+
=
163
1+6+3
=
10
1+0
1
=
1
-
-
1
3
5
-
5
1
9
2
8
-
4
6
6
5
+
=
55
5+5
=
10
1+0
1
=
1
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
38
-
-
12
-
55
-
37
-
 1+2
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+8
-
-
1+2
-
5+5
-
3+7
7
3
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
11
-
-
3
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
--
-
--
-
-
-
1+1
-
-
-
-
1+0
-
1+0
7
3
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
2
-
-
3
-
1
-
1

 

 

-
3
S
U
N
-
-
-
-
-
--
-
-
-
-
1
-
5
+
=
6
-
=
6
-
6
-
-
19
-
14
+
=
33
3+3
=
6
-
6
-
3
S
U
N
-
-
-
-
-
--
-
-
-
-
=
3
-
+
=
3
-
=
3
=
3
-
`-
-
21
-
+
=
21
2+1
=
3
=
3
-
3
S
U
N
-
-
-
-
-
--
-
-
-
`-
19
21
14
+
=
54
5+4
=
9
=
9
-
-
1
3
5
+
=
9
-
=
9
=
9
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
36
3
S
U
N
-
-
9
-
-
3
-
9

 

 

3
S
U
N
-
-
-
-
-
--
-
-
-
1
-
5
+
=
6
-
=
6
-
6
-
19
-
14
+
=
33
3+3
=
6
-
6
3
S
U
N
-
-
-
-
-
--
-
-
-
=
3
-
+
=
3
-
=
3
=
3
`-
-
21
-
+
=
21
2+1
=
3
=
3
3
S
U
N
-
-
-
-
-
--
-
-
`-
19
21
14
+
=
54
5+4
=
9
=
9
-
1
3
5
+
=
9
-
=
9
=
9
3
S
U
N
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
5
occurs
x
1
=
5
3
S
U
N
-
-
9
-
-
3
-
9

 

 

-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
6
6
5
+
=
17
1+7
=
8
-
8
=
8
-
-
-
15
15
14
+
=
44
4+4
=
8
=
8
=
8
-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
-
+
=
4
-
=
4
=
4
=
4
-
`-
13
-
-
-
+
=
13
1+3
=
4
=
4
=
4
-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
13
15
15
14
+
=
57
5+7
=
12
1+2
3
=
3
-
-
4
6
6
5
+
=
21
2+1
=
3
=
3
=
3
-
4
M
O
O
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
30
4
M
O
O
N
-
-
15
-
-
4
-
21
-
12
3+0
 -
-
-
-
-
-
-
1+5
-
-
-
-
2+1
-
1+2
3
4
M
O
O
N
-
-
6
-
-
4
-
3
-
3

 

 

4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
6
6
5
+
=
17
1+7
=
8
-
8
=
8
-
-
15
15
14
+
=
44
4+4
=
8
=
8
=
8
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
4
-
-
-
+
=
4
-
=
4
=
4
=
4
`-
13
-
-
-
+
=
13
1+3
=
4
=
4
=
4
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
`-
13
15
15
14
+
=
57
5+7
=
12
1+2
3
=
3
-
4
6
6
5
+
=
21
2+1
=
3
=
3
=
3
4
M
O
O
N
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
4
M
O
O
N
-
-
15
-
-
4
-
21
-
12
-
-
-
-
-
-
-
1+5
-
-
-
-
2+1
-
1+2
4
M
O
O
N
-
-
6
-
-
4
-
3
-
3

 

 

-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
+
=
8
-
=
8
=
8
-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
5
1
9
2
-
+
=
17
1+7
=
8
=
8
-
`-
5
1
18
20
-
+
=
44
4+4
=
8
=
8
-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
`-
5
1
18
20
8
+
=
52
5+2
=
7
=
7
-
-
5
1
9
2
8
+
=
25
2+5
=
7
=
7
-
5
E
A
R
T
H
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
20
5
E
A
R
T
H
-
-
25
-
-
5
-
25
2+0
 -
-
-
9
-
-
-
-
2+5
-
-
-
-
2+5
2
5
E
A
R
T
H
-
-
7
-
-
5
-
7

 

 

5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
-
-
-
8
+
=
8
-
=
8
=
8
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
5
1
9
2
-
+
=
17
1+7
=
8
=
8
`-
5
1
18
20
-
+
=
44
4+4
=
8
=
8
5
E
A
R
T
H
-
-
-
-
-
--
-
-
`-
5
1
18
20
8
+
=
52
5+2
=
7
=
7
-
5
1
9
2
8
+
=
25
2+5
=
7
=
7
5
E
A
R
T
H
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
5
E
A
R
T
H
-
-
25
-
-
5
-
25
-
-
-
9
-
-
-
-
2+5
-
-
-
-
2+5
5
E
A
R
T
H
-
-
7
-
-
5
-
7

 

 

-
5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
-
7
3
3
2
-
+
=
15
1+5
=
6
=
6
-
-
16
12
21
20
-
+
=
69
6+9
=
15
1+5
6
-
5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
-
16
12
21
20
15
+
=
84
8+4
=
12
1+2
3
-
-
7
3
3
2
6
+
=
21
2+1
=
3
=
3
-
5
P
L
U
T
O
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
-
3
3
-
-
-
-
3
occurs
x
2
=
9
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
27
5
P
L
U
T
O
-
-
18
-
-
5
-
21
2+7
-
 -
-
-
-
-
-
-
1+8
-
-
-
-
2+1
9
5
P
L
U
T
O
-
-
9
-
-
5
-
3

 

 

5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
7
3
3
2
-
+
=
15
1+5
=
6
=
6
-
16
12
21
20
-
+
=
69
6+9
=
15
1+5
6
5
P
L
U
T
O
-
-
-
-
-
--
-
-
-
16
12
21
20
15
+
=
84
8+4
=
12
1+2
3
-
7
3
3
2
6
+
=
21
2+1
=
3
=
3
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
3
3
-
-
-
-
3
occurs
x
2
=
9
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
5
P
L
U
T
O
-
-
18
-
-
5
-
21
-
 -
-
-
-
-
-
-
1+8
-
-
-
-
2+1
5
P
L
U
T
O
-
-
9
-
-
5
-
3

 

 

-
7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
-
5
-
+
=
10
1+0
=
1
=
1
=
1
-
`-
14
-
-
-
-
14
-
+
=
28
2+8
=
10
1+0
1
=
1
-
7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
7
2
3
-
5
+
=
22
2+2
=
4
=
4
=
4
-
`-
-
5
16
20
21
-
5
+
=
67
6+7
=
13
1+3
4
=
4
-
7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
-
`-
14
5
16
20
21
14
5
+
=
95
9+5
=
14
1+4
5
1+4
5
-
-
5
5
7
2
3
5
5
+
=
32
3+2
=
5
=
5
=
5
-
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
28
7
N
E
P
T
U
N
E
-
-
17
-
-
7
-
32
-
14
10
 -
-
-
-
-
-
-
-
-
-
1+7
-
-
-
-
3+2
-
1+4
1
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5

 

 

7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
-
5
-
-
-
-
5
-
+
=
10
1+0
=
1
=
1
=
1
`-
14
-
-
-
-
14
-
+
=
28
2+8
=
10
1+0
1
=
1
7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
7
2
3
-
5
+
=
22
2+2
=
4
=
4
=
4
`-
-
5
16
20
21
-
5
+
=
67
6+7
=
13
1+3
4
=
4
7
N
E
P
T
U
N
E
-
-
-
-
-
--
-
-
-
-
`-
14
5
16
20
21
14
5
+
=
95
9+5
=
14
1+4
5
1+4
5
-
5
5
7
2
3
5
5
+
=
32
3+2
=
5
=
5
=
5
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
5
5
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
7
N
E
P
T
U
N
E
-
-
17
-
-
7
-
32
-
14
-
-
-
-
-
-
-
-
-
-
1+7
-
-
-
-
3+2
-
1+4
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5

 

 

-
5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
1
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
9
-
19
+
=
28
2+8
=
10
1+0
1
=
1
-
5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
1
9
-
5
-
+
=
15
1+5
=
6
=
6
=
6
-
-
1
18
-
5
-
+
=
24
2+4
=
6
=
6
=
6
-
5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
1
18
9
5
19
+
=
52
5+2
=
7
=
7
=
7
-
-
1
9
9
5
1
+
=
25
2+5
=
7
=
7
=
7
-
5
A
R
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
30
5
A
R
I
E
S
-
-
15
-
1
6
-
25
-
16
3+0
-
-
-
-
-
-
-
-
1+5
-
-
-
-
2+5
-
1+6
3
5
A
R
I
E
S
-
-
6
-
-
6
-
7
-
7

 

 

5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
1
+
=
10
1+0
=
1
=
1
=
1
-
-
-
9
-
19
+
=
28
2+8
=
10
1+0
1
=
1
5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
1
9
-
5
-
+
=
15
1+5
=
6
=
6
=
6
-
1
18
-
5
-
+
=
24
2+4
=
6
=
6
=
6
5
A
R
I
E
S
-
-
-
-
-
--
-
-
-
-
-
1
18
9
5
19
+
=
52
5+2
=
7
=
7
=
7
-
1
9
9
5
1
+
=
25
2+5
=
7
=
7
=
7
5
A
R
I
E
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
5
A
R
I
E
S
-
-
15
-
1
6
-
25
-
16
-
-
 -
-
-
-
-
-
1+5
-
-
-
-
2+5
-
1+6
5
A
R
I
E
S
-
-
6
-
-
6
-
7
-
7

 

 

-
6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
1
+
=
6
-
=
6
-
6
-
-
-
-
-
-
-
19
+
=
33
3+3
=
6
=
6
-
6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
-
-
2
1
3
9
3
-
+
=
18
1+8
=
9
=
9
-
`-
20
1
21
18
21
-
+
=
81
8+1
=
9
=
9
-
6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
-
`-
20
1
21
18
21
19
+
=
100
1+0+0
=
1
=
1
-
-
2
1
3
9
3
1
+
=
19
1+9
=
10
1+0
1
-
6
T
A
U
R
U
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
3
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
30
6
T
A
U
R
U
S
-
-
15
-
-
6
-
19
3+0
-
-
-
-
9
-
-
-
-
1+5
-
-
-
-
1+9
3
6
T
A
U
R
U
S
-
-
6
-
-
6
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
3
6
T
A
U
R
U
S
-
-
6
-
-
6
-
1

 

 

6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
+
=
6
-
=
6
-
6
-
-
-
-
-
-
19
+
=
33
3+3
=
6
=
6
6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
-
2
1
3
9
3
-
+
=
18
1+8
=
9
=
9
`-
20
1
21
18
21
-
+
=
81
8+1
=
9
=
9
6
T
A
U
R
U
S
-
-
-
-
-
--
-
-
`-
20
1
21
18
21
19
+
=
100
1+0+0
=
1
=
1
-
2
1
3
9
3
1
+
=
19
1+9
=
10
1+0
1
6
T
A
U
R
U
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
6
T
A
U
R
U
S
-
-
15
-
-
6
-
19
-
-
-
-
9
-
-
-
-
1+5
-
-
-
-
1+9
6
T
A
U
R
U
S
-
-
6
-
-
6
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
6
T
A
U
R
U
S
-
-
6
-
-
6
-
1

 

 

-
6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
5
9
+
=
23
2+3
=
5
=
5
-
5
-
`-
-
-
-
9
14
9
+
=
32
3+2
=
5
=
5
-
5
-
6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
-
-
7
5
4
-
-
-
+
=
16
1+6
=
7
=
7
-
7
-
`-
7
5
13
-
-
-
+
=
25
2+5
=
7
=
7
-
7
-
6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
-
`-
7
5
13
9
14
9
+
=
57
5+7
=
12
1+2
3
-
3
-
-
7
5
4
9
5
9
+
=
39
3+9
=
12
1+2
3
-
3
-
6
G
E
M
I
N
I
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
--
-
-
4
-
-
-
 -
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
--
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
--
7
-
-
-
-
-
 -
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
9
occurs
x
2
=
18
1+8
9
20
6
G
E
M
I
N
I
-
-
25
-
-
6
-
39
-
21
2+0
-
-
-
-
9
-
9
-
-
2+5
-
-
-
-
3+9
-
2+1
2
6
G
E
M
I
N
I
-
-
7
-
-
6
-
12
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+2
-
-
2
6
G
E
M
I
N
I
-
-
7
-
-
6
-
3
-
3

 

 

6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
5
9
+
=
23
2+3
=
5
=
5
-
5
`-
-
-
-
9
14
9
+
=
32
3+2
=
5
=
5
-
5
6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
-
7
5
4
-
-
-
+
=
16
1+6
=
7
=
7
-
7
`-
7
5
13
-
-
-
+
=
25
2+5
=
7
=
7
-
7
6
G
E
M
I
N
I
-
-
-
-
-
--
-
-
-
-
`-
7
5
13
9
14
9
+
=
57
5+7
=
12
1+2
3
-
3
-
7
5
4
9
5
9
+
=
39
3+9
=
12
1+2
3
-
3
6
G
E
M
I
N
I
-T
-
-
-
-
-
-
-
-
-
--
-
-
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
6
G
E
M
I
N
I
-
-
25
-
-
6
-
39
-
21
-
-
-
-
9
-
9
-
-
2+5
-
-
-
-
3+9
-
2+1
6
G
E
M
I
N
I
-
-
7
-
-
6
-
12
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+2
-
-
6
G
E
M
I
N
I
-
-
7
-
-
6
-
3
-
3

 

 

-
6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
=
=
5
-
5
=
5
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
-
-
3
1
-
3
5
9
+
=
21
2+1
=
3
=
3
=
3
-
`-
3
1
-
3
5
18
+
=
30
3+0
=
3
=
3
=
3
-
6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
-
`-
3
1
14
3
5
18
+
=
44
4+4
=
8
=
8
=
8
-
-
3
1
5
3
5
9
+
=
26
2+6
=
8
=
8
=
8
-
6
C
A
N
C
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
27
6
C
A
N
C
E
R
-
-
18
-
-
6
-
26
-
17
2+7
-
-
-
-
-
-
-
-
-
1+8
-
-
-
-
2+6
-
1+7
9
6
C
A
N
C
E
R
-
-
9
-
-
6
-
8
-
8

 

 

6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
=
=
5
-
5
=
5
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
-
3
1
-
3
5
9
+
=
21
2+1
=
3
=
3
=
3
`-
3
1
-
3
5
18
+
=
30
3+0
=
3
=
3
=
3
6
C
A
N
C
E
R
-
-
-
-
-
--
-
-
-
-
`-
3
1
14
3
5
18
+
=
44
4+4
=
8
=
8
=
8
-
3
1
5
3
5
9
+
=
26
2+6
=
8
=
8
=
8
6
C
A
N
C
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
3
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
6
C
A
N
C
E
R
-
-
18
-
-
6
-
26
-
17
-
-
-
-
-
-
-
-
-
1+8
-
-
-
-
2+6
-
1+7
6
C
A
N
C
E
R
-
-
9
-
-
6
-
8
-
8

 

 

-
3
L
E
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
`-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
L
E
O
-
-
-
-
-
--
-
-
-
-
3
5
-
+
=
8
-
=
8
=
8
-
`-
12
5
-
+
=
17
1+7
=
8
=
8
-
3
L
E
O
-
-
-
-
-
--
-
-
-
`-
12
5
15
+
=
32
3+2
=
5
=
5
-
-
3
5
6
+
=
14
1+4
=
5
=
5
-
3
L
E
O
T
-
-
-
-
-
-
-
1
-
3
-
3
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
-
-
-
-
-
---
-
-
5
-
-
-
5
occurs
x
1
=
5
---
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
3
-
3
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
31
3
L
E
O
-
-
14
-
-
3
-
14
3+1
-
-
-
-
-
-
1+4
-
-
-
-
1+4
4
3
L
E
O
-
-
5
-
-
3
-
5

 

 

3
L
E
O
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
`-
-
-
15
+
=
15
1+5
=
6
=
6
3
L
E
O
-
-
-
-
--
-
-
-
3
5
-
+
=
8
-
=
8
=
8
`-
12
5
-
+
=
17
1+7
=
8
=
8
3
L
E
O
-
-
-
-
--
-
-
`-
12
5
15
+
=
32
3+2
=
5
=
5
-
3
5
6
+
=
14
1+4
=
5
=
5
3
L
E
O
T
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
6
occurs
x
1
=
6
3
L
E
O
-
-
14
-
-
3
-
14
-
-
-
-
-
-
1+4
-
-
-
-
1+4
3
L
E
O
-
-
5
-
-
3
-
5

 

 

-
5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
6
+
=
15
1+5
=
6
=
6
=
6
-
-
-
9
-
-
15
+
=
24
2+4
=
6
=
6
=
6
-
5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
-
4
-
9
7
-
+
=
20
2+0
=
2
=
2
=
2
-
-
22
-
18
7
-
+
=
47
4+7
=
11
1+1
2
=
2
-
5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
-
22
9
18
7
15
+
=
71
7+1
=
8
=
8
=
8
-
-
4
9
9
7
6
+
=
35
3+5
=
8
=
8
=
8
-
5
V
I
R
G
O
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
19
5
V
I
R
G
O
-
-
26
-
-
5
-
35
-
26
10
-
-
9
9
-
-
-
-
2+6
-
-
-
-
3+5
-
2+6
1
5
V
I
R
G
O
-
-
8
-
-
5
-
8
-
8

 

 

5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
6
+
=
15
1+5
=
6
=
6
=
6
-
-
9
-
-
15
+
=
24
2+4
=
6
=
6
=
6
5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
4
-
9
7
-
+
=
20
2+0
=
2
=
2
=
2
-
22
-
18
7
-
+
=
47
4+7
=
11
1+1
2
=
2
5
V
I
R
G
O
-
-
-
-
-
--
-
-
-
-
-
22
9
18
7
15
+
=
71
7+1
=
8
=
8
=
8
-
4
9
9
7
6
+
=
35
3+5
=
8
=
8
=
8
5
V
I
R
G
O
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
5
V
I
R
G
O
-
-
26
-
-
5
-
35
-
26
-
-
9
9
-
-
-
-
2+6
-
-
-
-
3+5
-
2+6
5
V
I
R
G
O
-
-
8
-
-
5
-
8
-
8

 

 

-
5
L
I
B
R
A
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
5
L
I
B
R
A
-
-
-
-
-
--
-
-
-
-
-
-
3
-
2
9
1
+
=
15
1+5
=
6
=
6
=
6
-
`-
12
-
2
18
1
+
=
33
3+3
=
6
=
6
=
6
-
5
L
I
B
R
A
-
-
-
-
-
--
-
-
-
-
-
`-
12
9
2
18
1
+
=
42
4+2
=
6
=
6
=
6
-
-
3
9
2
9
1
+
=
24
2+4
=
6
=
6
=
6
-
5
L
I
B
R
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
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-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
30
5
L
I
B
R
A
-
-
15
-
-
5
-
24
-
15
3+0
 -
-
9
-
9
-
-
-
1+5
-
-
-
-
2+4
-
1+5
3
5
L
I
B
R
A
-
-
6
-
-
5
-
6
-
6

 

 

5
L
I
B
R
A
-
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-
-
-
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-
-
-
-
-
-
9
-
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9
-
=
9
=
9
=
9
5
L
I
B
R
A
-
-
-
-
-
--
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3
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2
9
1
+
=
15
1+5
=
6
=
6
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6
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12
-
2
18
1
+
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33
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=
6
=
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5
L
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-
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-
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9
2
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42
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=
6
=
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9
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24
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=
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=
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5
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I
B
R
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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1
-
-
1
occurs
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1
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1
=
1
-
-
-
2
-
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occurs
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2
=
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-
3
-
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3
occurs
x
1
=
3
=
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-
9
-
9
-
-
-
9
occurs
x
2
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1+8
9
5
L
I
B
R
A
-
-
15
-
-
5
-
24
-
15
-
-
9
-
9
-
-
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1+5
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-
-
-
2+4
-
1+5
5
L
I
B
R
A
-
-
6
-
-
5
-
6
-
6

 

 
SAGITTARIUS
3
SAG
27
18
9
1
I
9
9
9
3
TTA
41
5
5
1
R
18
9
9
1
I
9
9
9
2
US
40
13
4
11
SAGITTARIUS
144
63
45
1+1
-
1+4+4
6+3
4+5
1
SAGITTARIUS
9
9
9

 

 

11
-
S
A
G
I
T
T
A
R
I
U
S
-
-
-
-
-
--
-
-
-
-
-
-
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-
-
9
-
-
-
-
9
-
1
+
=
20
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=
2
-
2
-
2
TWO
2
19
-
9
-
-
9
-
19
+
=
56
5+6
=
11
1+1
2
-
2
TWO
2
11
-
S
A
G
I
T
T
A
R
I
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-
-
-
-
-
--
-
-
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-
-
`-
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19
1
7
9
20
20
1
18
9
21
19
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=
144
1+4+4
=
9
-
9
-
9
NINE
9
-
-
1
1
7
9
2
2
1
9
9
3
1
+
=
45
4+5
=
9
-
9
-
9
NINE
9
11
-
S
A
G
I
T
T
A
R
I
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
4
=
4
-
4
FOUR
4
-
-
-
-
-
-
2
2
-
-
-
-
2
-
-
2
occurs
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2
=
4
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
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3
-
3
THREE
3
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
-
-
6
-
6
-
-
-
-
6
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
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-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
SEVEN
7
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
NINE
9
11
23
S
A
G
I
T
T
A
R
I
U
S
-
-
22
-
-
11
-
45
-
27
-
-
-
2+3
-
-
-
9
-
-
-
9
9
-
-
-
-
2+2
-
-
1+1
-
4+5
-
2+7
-
2+7
11
5
S
A
G
I
T
T
A
R
I
U
S
-
-
4
-
-
2
-
9
-
9
-
9

 

 

11
S
A
G
I
T
T
A
R
I
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
9
-
-
-
-
9
-
1
+
=
20
2+0
=
2
-
2
-
2
TWO
2
19
-
9
-
-
9
-
19
+
=
56
5+6
=
11
1+1
2
-
2
TWO
2
11
S
A
G
I
T
T
A
R
I
U
S
-
-
-
-
-
--
-
-
-
-
-
-
`-
19
1
7
9
20
20
1
18
9
21
19
+
=
144
1+4+4
=
9
-
9
-
9
NINE
9
-
1
1
7
9
2
2
1
9
9
3
1
+
=
45
4+5
=
9
-
9
-
9
NINE
9
11
S
A
G
I
T
T
A
R
I
U
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
4
=
4
-
4
FOUR
4
-
-
-
-
-
2
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
3
THREE
3
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
SEVEN
7
-
-
-
-
9
-
-
-
9
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
NINE
9
11
S
A
G
I
T
T
A
R
I
U
S
-
-
22
-
-
11
-
45
-
27
-
27
1+1
-
-
-
9
-
-
-
9
9
-
-
-
-
2+2
-
-
1+1
-
4+5
-
2+7
-
2+7
2
S
A
G
I
T
T
A
R
I
U
S
-
-
4
-
-
2
-
9
-
9
-
9

 

 

Zodiac | Symbols, Dates, Facts, & Signs

Encyclopedia Britannica
https://www.britannica.com › Science › Astronomy

zodiac ; ? Aries (Ram): March 21–April 19 ; ? Taurus (Bull): April 20–May 20 ; ? Gemini (Twins): May 21–June 21 ; ? Cancer (Crab): June 22–July 22 ; ? Leo (Lion): ...
?Constellations of the Zodiac... · ?Zodiac Sign Quiz · ?Uncover the history of the zodiac

zodiac
astronomy and astrology

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Related Topics: astrology ecliptic triplicity
zodiac, in astronomy and astrology, a belt around the heavens extending 9° on either side of the ecliptic, the plane of Earth’s orbit and of the Sun’s apparent annual path. The orbits of the Moon and of the principal planets also lie entirely within the zodiac. The 12 astrological signs of the zodiac are each considered to occupy 1/12 (or 30°) of its great circle. These signs no longer correspond to the astronomical constellations in which the Sun actually appears. The constellations are irregular in size and shape, and the Sun regularly passes through one constellation (Ophiuchus) that is not considered a member of the zodiac.

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Because most of the constellations through which the ecliptic passes represent animals, the ancient Greeks called its zone zodiakos kyklos, “circle of animals,” or ta zodia, “the little animals.” The size and number of zodiacal constellations varied in antiquity and became fixed only with the development of mathematical astronomy. The list below gives the constellations of the zodiac, with the dates of the Sun’s passage through them in the era when their boundaries were fixed. These dates are still used for the astrological signs, though precession of the equinoxes has shifted the constellations eastward; e.g., on January 1 the direction of the sun is now in Sagittarius instead of Capricornus. The history of the symbols is unknown; they seem to appear first in Greek manuscripts of the late Middle Ages.

Astrology horoscope circle. Wheel with zodiac signs, constellations horoscope with titles, geometric representation
Britannica Quiz
Zodiac Sign Quiz
? Aries (Ram): March 21–April 19

? Taurus (Bull): April 20–May 20

? Gemini (Twins): May 21–June 21

? Cancer (Crab): June 22–July 22

? Leo (Lion): July 23–August 22

? Virgo (Virgin): August 23–September 22

? Libra (Balance): September 23–October 23

? Scorpius (Scorpion): October 24–November 21

? Sagittarius (Archer): November 22–December 21

? Capricornus (Goat): December 22–January 19

? Aquarius (Water Bearer): January 20–February 18

? Pisces (Fish): February 19–March 20

The Editors of Encyclopaedia Britannica
This article was most recently revised and updated by Adam Augustyn.

Key People: Hipparchus al-Battani

Related Topics: Sun zodiac celestial sphere
ecliptic, in astronomy, the great circle that is the apparent path of the Sun among the constellations in the course of a year; from another viewpoint, the projection on the celestial sphere of the orbit of Earth around the Sun. The constellations of the zodiac are arranged along the ecliptic. The ecliptic is inclined at 23.44° to the plane of the celestial equator; this inclination is called the obliquity of the ecliptic. The two points of intersection of the ecliptic and the plane mark the vernal and autumnal equinoxes.

In the ecliptic system of astronomical coordinates, celestial longitude is measured in degrees east from the vernal equinox along the ecliptic. Celestial latitude is measured in degrees north (positive) or south (negative) from the ecliptic to the ecliptic poles. Each ecliptic pole is 23.44° from the corresponding celestial pole.

Star trails over banksia trees, in Gippsland, Vic., Austl. The south celestial pole, located in the constellation Octans, is at the centre of the trails.


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Henry Gillard Glindoni: John Dee Performing an Experiment Before Queen Elizabeth I
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Key People: Zarathushtra J.F.C. Fuller Robert Fludd Heinrich Cornelius Agrippa von Nettesheim Aleister Crowley
Related Topics: witchcraft magic alchemy divination astrology
occultism, various theories and practices involving a belief in and knowledge or use of supernatural forces or beings. Such beliefs and practices—principally magical or divinatory—have occurred in all human societies throughout recorded history, with considerable variations both in their nature and in the attitude of societies toward them. In the West the term occultism has acquired intellectually and morally pejorative overtones that do not obtain in other societies where the practices and beliefs concerned do not run counter to the prevailing worldview.

Occult practices centre on the presumed ability of the practitioner to manipulate natural laws for personal benefit or on behalf of another; such practices tend to be regarded as evil only when they also involve the breaking of moral laws. Some anthropologists have argued that it is not possible to make a clear-cut distinction between magic—a principal component of occultism—and religion, and this may well be true of the religious systems of some nonliterate societies. The argument does not hold, however, for any of the major religions, which regard both natural and moral law as immutable.

The Western tradition of occultism, as popularly conceived, is of an ancient “secret philosophy” underlying all occult practices. This secret philosophy derives ultimately from Hellenistic magic and alchemy on the one hand and from Jewish mysticism on the other. The principal Hellenistic source is the Corpus Hermeticum, the texts associated with Hermes Trismegistos, which are concerned with astrology and other occult sciences and with spiritual regeneration.

Kabbala
Kabbala
The Jewish element is supplied by the Kabbala (the doctrine of a secret mystical interpretation of the Torah), which had been familiar to scholars in Europe since the Middle Ages and which was linked with the Hermetic texts during the Renaissance. The resulting Hermetic-Kabbalistic tradition, known as Hermetism, incorporated both theory and magical practice, with the latter presented as natural, and thus good, magic, in contrast to the evil magic of sorcery or witchcraft.

Alchemy was also absorbed into the body of Hermetism, and this link was strengthened in the early 17th century with the appearance of Rosicrucianism, an alleged secret brotherhood that utilized alchemical symbolism and taught secret wisdom to its followers, creating a spiritual alchemy that survived the rise of empirical science and enabled Hermetism to pass unscathed into the period of the Enlightenment.

Freemasons
Freemasons
During the 18th century the tradition was taken up by esoterically inclined Freemasons who could not find an occult philosophy within Freemasonry. These enthusiasts persisted, both as individual students of Hermetism and, in continental Europe, as groups of occult practitioners, into the 19th century, when the growth of religious skepticism led to an increased rejection of orthodox religion by the educated and a consequent search for salvation by other means—including occultism.

 

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But those interested turned to new forms of occultism rather than to the Hermetic tradition: on the one hand to spiritualism, the practice of alleged regular communication between the living and the spirits of the dead through a living “medium,” and on the other hand to theosophy, a blend of Western occultism and Eastern mysticism that proved to be a most effective propagator of occultism but whose influence had declined markedly by the late 20th century.

Indeed, despite the 19th-century revival, occult ideas have failed to gain acceptance in academic circles, although they have occasionally influenced the work of major artists, such as the poet William Butler Yeats and the painter Wassily Kandinsky, and occultism in Europe and North America seems destined to remain the province of popular culture.

Robert Andrew Gilbert


Scorpio

Scorpius, (Latin: “Scorpion”) also called Scorpio, in astronomy, zodiacal constellation lying in the southern sky between Libra and Sagittarius, at about 16 hours 30 minutes right ascension and 30° south declination. Its brightest star, Antares (Alpha Scorpii), the 15th brightest star in the sky, has a magnitude of 1.1. Its name comes from the Greek for “rival of Ares” (i.e., rival of the planet Mars) and was probably given because of the star’s red colour and brightness. The brightest X-ray source in the sky, Scorpius X-1, is found in this constellation.


Scorpius

In astrology, Scorpius (or Scorpio) is the eighth sign of the zodiac, considered as governing the period from about October 24 to about November 21. Its representation as a scorpion is related to the Greek legend of the scorpion that stung Orion to death (said to be why Orion sets as Scorpius rises in the sky). Another Greek myth relates that a scorpion caused the horses of the Sun to bolt when they were being driven for a day by the inexperienced youth Phaeton.

 

T
=
2
-
3
THE
33
15
6
S
=
1
-
4
STAR
58
13
4
C
=
3
-
6
CHART
50
23
5
-
-
6
-
13
Add to Reduce
141
51
15
-
-
-
-
1+3
Reduce to Deduce
1+4+1
5+1
1+5
Q
-
6
-
4
Essence of Number
6
6
6

 

 

A
=
1
-
5
ARIES
52
25
7
T
=
2
-
6
TAURUS
100
19
1
G
=
7
-
6
GEMINI
57
39
3
C
=
3
-
6
CANCER
44
26
8
L
=
3
-
3
LEO
32
14
5
V
=
4
-
5
VIRGO
71
35
8
L
=
3
-
5
LIBRA
42
24
6
S
=
1
-
7
SCORPIO
95
41
5
S
=
1
-
11
SAGITTARIUS
144
45
9
C
=
3
-
9
CAPRICORN
97
52
7
A
=
1
-
8
AQUARIUS
107
26
8
P
=
7
-
6
PISCES
71
26
8
-
-
36
4
77
First Total
912
372
75
-
-
3+6
-
7+7
Add to Reduce
9+1+2
3+7+2
7+5
-
-
9
-
14
Second Total
12
12
12
-
-
-
-
1+4
Reduce to Deduce
1+2
1+2
1+2
-
-
9
-
5
Essence of Number
3
3
3

 

 

-
-
-
-
-
A STARRY LOG IS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
4
STAR
58
13
4
-
-
-
-
4
-
-
-
-
-
C
=
3
-
6
CHART
50
23
5
-
-
-
-
-
5
-
-
-
-
-
-
6
-
13
-
141
51
15
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
5
ARIES
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
6
TAURUS
100
19
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
6
GEMINI
57
39
3
-
-
-
3
-
-
-
-
-
-
C
=
3
-
6
CANCER
44
26
8
-
-
-
-
-
-
-
-
8
-
L
=
3
-
3
LEO
32
14
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
5
VIRGO
71
35
8
-
-
-
-
-
-
-
-
8
-
L
=
3
-
5
LIBRA
42
24
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
7
SCORPIO
95
41
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
11
SAGITTARIUS
144
45
9
-
-
-
-
-
-
-
-
-
9
C
=
3
-
9
CAPRICORN
97
52
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
8
AQUARIUS
107
26
8
-
-
-
-
-
-
-
-
8
-
P
=
7
-
6
PISCES
71
26
8
-
-
-
-
-
-
-
-
8
-
-
-
36
-
77
-
912
372
75
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
42
4
90
Add to Reduce
1053
423
90
-
1
2
3
4
15
12
14
32
9
-
-
4+2
-
9+0
Reduce to Deduce
1+0+5+3
4+2+3
9+0
-
-
-
-
-
1+5
1+2
1+4
3+2
-
-
-
6
-
9
Essence of Number
9
9
9
-
1
2
3
4
6
3
5
5
9

 

 

T
=
2
-
3
THE
33
15
6
Z
=
8
-
6
ZODIAC
58
31
4
-
-
10
4
9
First Total
91
46
10
-
-
1+0
-
-
Add to Reduce
9+1
4+6
1+0
-
-
1
-
9
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
1
-
9
Essence of Number
1
1
1

 

 

S
=
1
-
9
STAR-OLOGY
132
42
6
A
=
1
-
9
ASTROLOGY
132
42
6
A
=
1
-
12
ASTROLOGICAL
132
51
6

 

A
=
1
5

ARIES
52
25
7
T
=
2
6

TAURUS
100
19
1
G
=
7
6

GEMINI
57
39
3
C
=
3
6

CANCER
44
26
8
L
=
3
3

LEO
32
14
5
V
=
4
5

VIRGO
71
35
8
L
=
3
5

LIBRA
42
24
6
S
=
1
7

SCORPIO
95
41
5
S
=
1
11

SAGITTARIUS
144
45
9
C
=
3
9

CAPRICORN
97
52
7
A
=
1
8

AQUARIUS
107
35
8
P
=
7
6

PISCES
71
26
8
-
-
36
77

First Total
912
381
75
-
-
3+5
7+7

Add to Reduce
9+1+2
3+8+1
7+5
-
-
8
14

Second Total
12
12
12
-
-
-
1+4

Add to Deduce
1+2
1+2
1+2
-
-
8
5

Final Total
3
3
3

 

 

3+3
=
6
THE RAM
65
29
2
3+4
=
7
THE BULL
80
26
8
3+5
=
8
THE TWINS
118
37
1
3+4
=
7
THE CRAB
57
30
3
3+4
=
7
THE LION
83
38
2
3+6
=
9
THE VIRGIN
112
58
4
3+6
=
9
THE SCALES
92
29
2
3+8
=
11
THE SCORPION
109
46
1
3+6
=
9
THE ARCHER
86
50
5
3+4
=
7
THE GOAT
76
31
4
3+12
=
15
THE WATER CARRIER
172
82
1
3+6
=
9
THE FISHES
99
45
9
104

First Total
1149
501
42
1+0+4

Add to Reduce
1+1+4+9
5+0+1
4+2
5

Second Total
15
6
6
-

Add to Deduce
1+5
-
-
5

Final Total
6
6
6

 

 

A
=
1
3

AIR
28
19
1
F
=
6
4

FIRE
38
29
2
E
=
5
5

EARTH
52
25
7
W
=
5
5

WATER
67
22
4
H
=
8
5

HUMAN
57
21
3
S
=
1
6

SPIRIT
91
37
1
-
-
26
28

-
333
153
18
-
-
2+6
10

-
3+3+3
1+5+3
1+8
-
-
8
1

-
9
9
9

 

 

1
I
9
9
9
2
ME
18
9
9
5
BEING
37
28
1

 

 
 
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