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Evokation
  
 
Index
  

 

 

 

 

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

 

 

ADVENT 779 ADVENT

 

 

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

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
-
189
90
18
1+8
-
1+8+9
9+0
1+8
9
-
18
9
9
-
-
1+8
-
-
9
-
9
9
9

 

 

5
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
10
1
-
-
1+0
-
-
5
THE SOLAR SYSTEM
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
6+2
14
Second Total
17
8
8
1+4
Reduce to Deduce
1+7
-
-
5
Essence of Number
8
8
8

 

 

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
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
7
7
7

 

 

-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
9
-
-
-
19
-
+
=
42
4+2
=
6
=
6
=
6
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
21
-
-
22
5
18
-
5
+
=
71
7+1
=
8
=
8
=
8
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
5
+
=
113
1+1+3
=
5
=
5
=
5
-
-
3
5
9
4
5
9
1
5
+
=
41
4+1
=
5
=
5
=
5
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
8
U
N
I
V
E
R
S
E
-
-
22
-
-
9
-
41
-
23
2+3
-
-
-
9
-
-
9
-
-
-
-
2+2
-
-
-
-
4+1
-
2+3
5
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5
-
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
5
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5

 

 

8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
+
=
15
1+5
=
6
=
6
=
6
-
-
14
9
-
-
-
19
-
+
=
42
4+2
=
6
=
6
=
6
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
5
+
=
26
2+6
=
8
=
8
=
8
-
21
-
-
22
5
18
-
5
+
=
71
7+1
=
8
=
8
=
8
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
5
+
=
113
1+1+3
=
5
=
5
=
5
-
3
5
9
4
5
9
1
5
+
=
41
4+1
=
5
=
5
=
5
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
U
N
I
V
E
R
S
E
-
-
22
-
-
9
-
41
-
23
-
-
-
9
-
-
9
-
-
-
-
2+2
-
-
-
-
4+1
-
2+3
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5

 

 

-
-
-
-
-
THE UNIVERSE
-
-
-
T
=
2
-
3
THE
33
15
6
U
=
3
-
8
UNIVERSE
113
41
5
-
-
5
-
11
THE UNIVERSE
146
56
11
-
-
-
-
1+1
-
1+4+6
5+6
1+1
-
-
5
-
2
THE UNIVERSE
11
11
2
-
-
-
-
-
-
1+1
1+0
-
-
-
5
-
2
THE UNIVERSE
2
2
2

 

 

-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
-
20
-
5
-
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
-
2
8
5
-
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
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
-
-
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
2
=
18
1+8
9
13
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+3
1+1
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
4
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
-
2
8
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
4
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

 

11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
20
-
5
-
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
2
8
5
-
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
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
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+1
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
2
8
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

 

11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
20
-
5
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
2
8
5
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
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
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
T
H
E
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+1
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
2
T
H
E
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
2
8
5
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
2
T
H
E
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

-
-
-
-
-
THE SOLAR SYSTEM
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
5
SOLAR
65
20
2
S
=
1
-
6
SYSTEM
101
20
2
-
-
4
-
14
THE SOLAR SYSTEM
199
55
10
-
-
-
-
1+4
-
1+9+9
5+5
1+0
-
-
5
-
5
THE SOLAR SYSTEM
19
10
1
-
-
-
-
-
-
1+9
1+0
-
-
-
5
-
5
THE SOLAR SYSTEM
10
1
1
-
-
-
-
-
-
1+0
-
-
-
-
5
-
5
THE SOLAR SYSTEM
1
1
1

 

 

-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
6
-
-
-
-
1
-
1
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
8
-
-
19
15
-
-
-
-
19
-
19
-
-
-
+
=
80
8+0
=
8
=
8
=
8
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
-
3
1
9
-
-
7
-
2
5
4
+
=
38
3+8
=
11
1+1
2
=
2
-
-
20
-
5
-
-
-
12
1
18
-
-
25
-
20
5
13
+
=
119
1+1+9
=
11
1+1
2
=
2
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
19
15
12
1
18
-
19
25
19
20
5
13
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
2
8
5
-
1
6
3
1
9
-
1
7
1
2
5
4
+
=
55
5+5
=
10
1+0
1
=
1
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
-
-
1
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
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
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
45
-
-
14
-
55
-
46
4+5
1+4
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
4+5
-
-
1+4
-
5+5
-
4+6
9
5
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
9
-
-
5
-
10
-
10
-
-
2
8
5
-
1
6
3
1
9
-
1
7
1
2
5
4
-
-
-
-
-
-
-
1+0
-
1+0
9
5
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
9
-
-
5
-
1
-
1

 

 

-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
6
-
-
-
1
-
1
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
8
-
19
15
-
-
-
19
-
19
-
-
-
+
=
80
8+0
=
8
=
8
=
8
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
3
1
9
-
7
-
2
5
4
+
=
38
3+8
=
11
1+1
2
=
2
-
-
20
-
5
-
-
12
1
18
-
25
-
20
5
13
+
=
119
1+1+9
=
11
1+1
2
=
2
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
19
15
12
1
18
19
25
19
20
5
13
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
2
8
5
1
6
3
1
9
1
7
1
2
5
4
+
=
55
5+5
=
10
1+0
1
=
1
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
-
1
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
--
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
-
-
-
-
-
-
-
-
-
5
-
-
-
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
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
45
-
-
14
-
55
-
46
4+5
1+4
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
4+5
-
-
1+4
-
5+5
-
4+6
9
5
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
9
-
-
5
-
10
-
10
-
-
2
8
5
1
6
3
1
9
1
7
1
2
5
4
-
-
-
-
-
-
-
1+0
-
1+0
9
5
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
9
-
-
5
-
1
-
1

 

 

-
-
-
-
-
THE CONSTELLATIONS
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
14
CONSTELLATIONS
65
52
7
-
-
5
-
17
THE CONSTELLATIONS
211
67
13
-
-
-
-
1+7
-
2+1+1
6+7
1+3
-
-
5
-
8
THE CONSTELLATIONS
4
13
4
-
-
-
-
-
-
-
1+3
-
-
-
5
-
8
THE CONSTELLATIONS
4
4
4
-
-
-
-
-
-
-
-
-
-
-
5
-
8
THE CONSTELLATIONS
4
1
4

 

 

-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+1
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
2
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
2
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
8
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
20
-
5
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
20
8
5
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
5
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
8
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
8
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

-
ORION
-
-
-
1
O
15
6
6
1
R
18
9
9
1
I
9
9
9
1
O
15
6
6
1
N
14
5
5
5
ORION
71
35
35
-
-
7+1
3+5
3+5
5
ORION
8
8
8

 

 

5
ORION
71
35
8
-
-
-
-
-
-
-
-
-
-
2
OR
33
15
6
4
IRON
56
29
2
2
IS
28
10
1
-
-
-
-
-
-
-
-
-
-
7
ORIONIS
99
54
9

 

 

5
ORION
71
35
8
-
-
-
-
-
-
-
-
-
-
-
ORIONIS
-
-
-
1
ORI
42
24
6
1
O
15
6
6
1
NIS
42
15
6
7
ORIONIS
99
54
18
-
-
9+9
5+4
1+8
7
ORIONIS
18
9
9
-
-
1+8
-
-
7
ORIONIS
9
9
9

 

 

5
ORION
71
35
8
-
-
-
-
-
-
-
-
-
-
-
ORIONIS
-
-
-
1
O
15
6
6
1
R
18
9
9
1
I
9
9
9
1
O
15
6
6
1
NIS
42
15
6
7
ORIONIS
99
54
36
-
-
9+9
5+4
3+6
7
ORIONIS
18
9
9
-
-
1+8
-
-
7
ORIONIS
9
9
9

 

ORION IS IS ORION

 

5
ORION
71
35
8
-
-
-
-
-
-
-
-
-
-
-
ORIONIS
-
-
-
1
O
15
6
6
1
R
18
9
9
1
I
9
9
9
1
O
15
6
6
1
N
14
5
5
1
I
9
9
9
1
S
19
10
1
7
ORIONIS
99
54
45
-
-
9+9
5+4
4+5
7
ORIONIS
18
9
9
-
-
1+8
-
-
7
ORIONIS
9
9
9

 

ORION IS IS ORION

 

-
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
-
6
-
-
6
-
9
6
5
+
=
72
7+2
=
9
=
9
=
9
-
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
-
15
-
-
15
-
9
15
14
+
=
162
1+6+2
=
9
=
9
=
9
-
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
-
6
-
-
9
-
-
-
+
=
41
4+1
=
5
=
5
=
5
-
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
-
6
-
-
18
-
-
-
+
=
122
1+2+2
=
5
=
5
=
5
-
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
-
15
6
-
15
18
9
15
14
+
=
284
2+8+4
=
9
=
9
=
9
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
-
6
6
-
6
9
9
6
5
+
=
113
1+1+3
=
9
=
9
=
9
-
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
3
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
6
6
-
6
-
-
6
-
-
-
6
occurs
x
6
=
36
3+6
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
3
=
27
1+8
9
11
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
34
-
-
23
-
113
-
50
1+1
2+3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
9
-
-
-
-
3+4
-
-
2+3
-
1+1+3
-
5+0
2
5
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
-
6
6
-
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
2
5
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5

 

 

23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
-
6
-
-
6
-
9
6
5
+
=
72
7+2
=
9
=
9
=
9
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
-
15
-
-
15
-
9
15
14
+
=
162
1+6+2
=
9
=
9
=
9
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
-
6
-
-
9
-
-
-
+
=
41
4+1
=
5
=
5
=
5
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
-
6
-
-
18
-
-
-
+
=
122
1+2+2
=
5
=
5
=
5
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
-
15
6
-
15
18
9
15
14
+
=
284
2+8+4
=
9
=
9
=
9
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
-
6
6
-
6
9
9
6
5
+
=
113
1+1+3
=
9
=
9
=
9
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
2
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
3
--
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
6
6
-
6
-
-
6
-
-
-
6
occurs
x
6
=
36
3+6
9
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
3
=
27
1+8
9
23
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
34
-
-
23
-
113
-
50
2+3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
9
-
-
-
-
3+4
-
-
2+3
-
1+1+3
-
5+0
5
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
-
6
6
-
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
5
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
-
O
F
-
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5

 

 

23
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
5
1
-
-
-
-
-
-
9
6
5
6
-
6
-
9
6
5
+
=
72
7+2
=
9
=
9
=
9
-
-
8
-
-
15
14
19
-
-
-
-
-
-
9
15
14
15
-
15
-
9
15
14
+
=
162
1+6+2
=
9
=
9
=
9
23
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
-
-
2
5
3
3
1
2
-
-
-
-
6
-
9
-
-
-
+
=
41
4+1
=
5
=
5
=
5
-
20
-
5
3
-
-
-
20
5
12
12
1
20
-
-
-
-
6
-
18
-
-
-
+
=
122
1+2+2
=
5
=
5
=
5
23
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
20
8
5
3
15
14
19
20
5
12
12
1
20
9
15
14
15
6
15
18
9
15
14
+
=
284
2+8+4
=
9
=
9
=
9
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
6
6
6
9
9
6
5
+
=
113
1+1+3
=
9
=
9
=
9
23
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
3
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
2
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
3
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
5
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
6
6
6
-
-
6
-
-
-
6
occurs
x
6
=
36
3+6
9
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
-
9
occurs
x
3
=
27
1+8
9
23
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
34
-
-
23
-
113
-
50
2+3
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
-
-
3+4
-
-
2+3
-
1+1+3
-
5+0
5
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
6
6
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
5
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
O
F
O
R
I
O
N
-
-
7
-
-
5
-
5
-
5

 

 

the Alpha star of Orion we have to say “Alpha Orionis”, meaning “Alpha of Orion” – “Orionis” be-ing the genitive of Orion. Likewise, Eta of Carina is “Eta ... www.pretoria-astronomy.co.za/pdf/newsletters_august_2008

"If we want to talk about the Alpha star of Orion we have to say “Alpha Orionis”, meaning “Alpha of Orion” – “Orionis” being
the genitive of Orion."

 

[as genitive] (O·ri·o·nis / ˌôrēˈōnis/ ) used with a preceding letter or numeral to ... Orion is outlined by the prominent stars Betelgeuse (Alpha Orionis. ... www.encyclopedia.com/doc/1O999-orion.html

O·ri·on / əˈrīən/ 1. Greek Mythol. a giant and hunter who was changed into a constellation at his death. 2. Astron. a conspicuous constellation (the Hunter), said to represent a hunter holding a club and shield. It lies on the celestial equator and contains many bright stars, including Rigel, Betelgeuse, and a line of three that form Orion's belt. ∎  [as genitive] (O·ri·o·nis / ˌôrēˈōnis/ ) used with a preceding letter or numeral to designate a star in this constellation: the multiple star Theta Orionis.

 

 

RANKING STARS IN A CONSTELLATION

Or, for constellations not ending in "-us," add "-is" (e.g., Orion becomes Orionis). For your convenience, the genitive case is indicated at the top of the ... homepage.mac.com/kvmagruder/bcp/aster/constellations/alpha.htm

"Lift your eyes and look to the heavens: Who created all these?
He who brings out the starry host one by one, and calls them each by name.
Because of his great power and mighty strength, not one of them is missing."
Isaiah 40:25

Stars within a given constellation are usually ranked according to relative brightness by the Greek alphabet. The brightest star is alpha, the second-brightest beta, the third-brightest gamma, and so forth. There are some exceptions, when an especially common constellation (such as Ursa Major or Crux) is numbered according to its linear sequence, like a dot-to-dot diagram.

Star names have two parts; the first is the Greek letter indicating its brightness. The second part of a star name indicates its constellation. To obtain this constellation part of the star name, the letter of the Greek alphabet which indicates a star's brightness is conjoined with the Latin genitive case of the name of the constellation. For example, the brightest star of the constellation Centaurus is "alpha-Centauri," which happens to be the star nearest to our own Sun (though it is actually a multiple star system). "Centauri" is the Latin genitive case of "Centaurus." In general, the genitive case is obtained by changing the suffix "-us" to "-i," (e.g., Taurus becomes Tauri). Or, for constellations not ending in "-us," add "-is" (e.g., Orion becomes Orionis).

As to why it's Orionis rather than Orion, etc.—these are just the genitive (possessive) cases of the Latin names/words for the constellations. ... www.astro.cornell.edu/research/projects/CAS/faq.html

Cornell Astronomical Society

7) What do these names like "Delta Orionis" mean? Why is it "Orionis" and not "Orion?"

Some stars have their own proper names, like Rigel (in Orion), Vega (in Lyra), or Polaris (in Ursa Minor). These are either prominent, bright stars, or they occupy particular places in the constellations. (For example, two fun star names are Zubenelgenubi and Zubeneschamali, Arabic names meaning "The Southern Claw" and "The Northern Claw," respectively; the stars are in Libra, the Balance. Libra used to be part of Scorpius, the Scorpion; these stars were its two claws.)

Most stars, however, don't have special names. For those such stars visible to the eye, we use a system developed by Johann Bayer in the 17th century. He ranked stars in constellations in order from brightest to dimmest, using letters of the Greek alphabet: Alpha is the brightest star of a constellation, Beta the second brightest, etc. When the Greek alphabet has been exhausted, numbers are used. This latter system was devised by the 17th century British astronomer John Flamsteed, who assigned numbers even to stars that Bayer had given letter designations; most people only use the Flamsteed numbers for stars that do not have proper names or Greek letters.

As to why it's Orionis rather than Orion, etc.—these are just the genitive (possessive) cases of the Latin names/words for the constellations. Thus, "Delta Orionis" is "4th brightest star of the constellation Orion." While you need to learn Latin for the details (and it's very useful to know Latin, so you should consider it!), for nearly all the constellations the rules are: 1) if the name ends in "a" (Lyra, Andromeda,...), the genitive will end in "ae" (Lyrae, Andromedae,...); 2) if the name ends in "us" or "um" (Cygnus, Cepheus, Scutum,...), the genitive will end in "i" (Cygni, Cephei, Scuti,...); 3) anything else (Orion, Virgo,...) is likely a "3rd declension noun," which indicates a sort of kitchen-sink situation re whether/how the base portion of the noun changes—simple answer is, memorize the genitive versions.

 

 

9 Jun 2008 ... is designated R followed by the genitive of the constellation name (eg. ... At maximum light, FU Orionis stars are of spectral type A - G after which the spectral ... For more information, see: Orion variable stars ...
en.citizendium.org/wiki/Variable_star

 

Variable star - encyclopedia - Citezendium

FU Orionis stars

Named after the prototype of this class, FU Orionis (GCVS code: FU), these stars are characterized by a slow outburst in which the brightness of the star increases up to 6 magnitudes over a number of months and stays at maximum brightness for up to several years after which a slow decline sets in that dims the star by a couple of magnitudes. During an outburst the spectral type of the stars can change significantly and an emission spectrum develops as well. At maximum light, FU Orionis stars are of spectral type A - G after which the spectral type becomes later. All FU Orionis stars are associated with reflecting nebulae.[2][3]

FU Orionis stars are pre-main sequence stars somewhat similar to T Tauri stars. The prototype was first discovered in 1939 by A. Wachmann when the star increased some 100-fold in brightness. FU Orionis was studied in depth by George Herbig in the 1960s and 1970s.[2] There are some 10 stars known of this type.

 

ORION IS IS ORION

 

-
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
6
5
9
1
+
=
36
3+6
=
9
=
9
-
9
-
-
15
-
9
15
14
9
19
+
=
81
8+1
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
+
=
9
-
=
9
=
9
-
9
-
-
-
18
-
-
-
-
-
+
=
18
1+8
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
15
18
9
15
14
9
19
+
=
99
9+9
=
18
1+8
9
-
9
-
-
6
9
9
6
5
9
1
+
=
45
4+5
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
3
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
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
-
-
7
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
24
7
O
R
I
O
N
I
S
-
-
21
-
-
7
-
45
-
18
2+4
-
-
9
9
-
-
9
-
-
-
2+1
-
-
-
-
4+5
-
1+8
6
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9
-
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
6
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9

 

 

7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
6
-
9
6
5
9
1
+
=
36
3+6
=
9
=
9
-
9
-
15
-
9
15
14
9
19
+
=
81
8+1
=
9
=
9
-
9
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
+
=
9
-
=
9
=
9
-
9
-
-
18
-
-
-
-
-
+
=
18
1+8
=
9
=
9
-
9
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
15
18
9
15
14
9
19
+
=
99
9+9
=
18
1+8
9
-
9
-
6
9
9
6
5
9
1
+
=
45
4+5
=
9
=
9
-
9
7
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
5
-
6
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
O
R
I
O
N
I
S
-
-
21
-
-
7
-
45
-
18
-
-
9
9
-
-
9
-
-
-
2+1
-
-
-
-
4+5
-
1+8
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9

 

 

ORIONIS

ORIONIS OSIRION ORIONIS

OSIREION

 

 

Osireion - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Osireion

The Osirion or Osireon is located at Abydos at the rear of the temple of Seti I. It is an integral part of Seti I's funeral complex and is built to resemble an 18th ...

From Wikipedia, the free encyclopedia

The Osirion at the rear of the temple of Seti I at Abydos, the underground entry to the Osireion is at the top of the picture, see image below
The Osirion or Osireon is located at Abydos at the rear of the temple of Seti I. It is an integral part of Seti I's funeral complex and is built to resemble an 18th Dynasty Valley of the Kings tomb. [1] It was discovered by archaeologists Flinders Petrie and Margaret Murray who were excavating the site in 1902-3. The Osirion was originally built at a considerably lower level than the foundations of the temple of Seti, who ruled from 1294 - 1279 BC [2]. While there is disagreement as to its true age, despite the fact that it is situated at a lower depth than the structures nearby, that it features a very different architectural approach, and that it is frequently flooded with water which would have made carving it impossible had the water level been the same at the time of construction, Peter Brand says it "can be dated confidently to Seti's reign."[3]

 

-
OSIREION
-
-
-
1
O
15
6
6
1
S
19
10
1
1
I
9
9
9
1
R
18
9
9
1
E
5
5
5
1
I
9
9
9
1
O
15
6
6
1
N
14
5
5
8
OSIREION
104
59
50
-
-
1+0+4
5+9
4+5
8
OSIREION
5
14
9
-
-
-
1+4
-
8
OSIREION
5
5
9

 

 

-
OSIREION
-
-
-
2
S+O
25
16
7
1
I
9
9
9
1
R
18
9
9
1
E
5
5
5
1
I
9
9
9
2
O+N
29
11
2
8
OSIREION
104
59
50
-
-
1+0+4
5+9
4+5
8
OSIREION
5
14
9
-
-
-
1+4
-
8
OSIREION
5
5
9

 

 

-
OSIREION
-
-
-
4
O+S+I+R
61
25
7
4
E+I+O+N
43
25
7
8
OSIREION
104
50
14
-
-
1+0+4
5+0
1+4
8
OSIREION
5
5
5

 

 

-
OSIRION
-
-
-
1
O
15
6
6
1
S
19
10
1
1
I
9
9
9
1
R
18
9
9
1
I
9
9
9
1
O
15
6
6
1
N
14
5
5
7
OSIRION
99
54
45
-
-
9+9
5+4
4+5
7
OSIRION
18
9
9
-
-
1+8
-
-
7
OSIRION
9
9
9

 

 

-
OSIRION
-
-
-
2
S+O
34
16
7
1
I
9
9
9
1
R
18
9
9
1
I
9
9
9
2
O+N
29
11
2
7
OSIRION
99
54
45
-
-
9+9
5+4
4+5
7
OSIRION
18
9
9
-
-
1+8
-
-
7
OSIRION
9
9
9

 

 

O
=
6
-
8
OSIREION
104
50
5
O
=
6
-
7
OSIRION
99
54
9
-
-
3
-
6
-
203
104
14
-
-
1+2
-
1+5
-
2+0+3
1+1+3
9+5
-
-
3
-
6
-
5
5
14
-
-
-
-
-
-
1+8
-
-
-
-
3
-
6
-
9
9
9

 

 

Osireion - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Osireion

The Osirion or Osireon is located at Abydos at the rear of the temple of Seti I. It is an integral part of Seti I's funeral complex and is built to resemble an 18th ...

From Wikipedia, the free encyclopedia

The Osirion at the rear of the temple of Seti I at Abydos, the underground entry to the Osireion is at the top of the picture, see (image omitted) below

The Osirion or Osireon is located at Abydos at the rear of the temple of Seti I. It is an integral part of Seti I's funeral complex and is built to resemble an 18th Dynasty Valley of the Kings tomb. [1] It was discovered by archaeologists Flinders Petrie and Margaret Murray who were excavating the site in 1902-3. The Osirion was originally built at a considerably lower level than the foundations of the temple of Seti, who ruled from 1294 - 1279 BC [2]. While there is disagreement as to its true age, despite the fact that it is situated at a lower depth than the structures nearby, that it features a very different architectural approach, and that it is frequently flooded with water which would have made carving it impossible had the water level been the same at the time of construction, Peter Brand says it "can be dated confidently to Seti's reign."[3]

 

-
OSIRION
-
-
-
1
O
15
6
6
1
S
19
10
1
1
I
9
9
9
1
R
18
9
9
1
I
9
9
9
1
O
15
6
6
1
N
14
5
5
7
OSIRION
99
54
45
-
-
9+9
5+4
4+5
7
OSIRION
18
9
9
-
-
1+8
-
-
7
OSIRION
9
9
9

 

OSIRION

 

-
7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
6
1
9
-
9
6
5
+
=
36
3+6
=
9
=
9
=
9
-
-
15
19
9
-
9
15
14
+
=
81
8+1
=
9
=
9
=
9
-
7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
18
-
-
-
+
=
18
1+8
=
9
=
9
=
9
-
7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
15
19
9
18
9
15
14
+
=
99
9+9
=
9
1+8
9
=
9
-
-
6
1
9
9
9
6
5
+
=
45
4+5
=
9
=
9
=
9
-
7
O
S
I
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
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
EIGHT
8
-
-
-
-
-
-
-
-
-
9
9
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
24
7
O
S
I
R
I
O
N
-
-
21
-``
-
7
-
45
-
18
2+4
-
-
-
9
9
9
-
-
-
-
2+1
-
-
-
-
4+5
-
1+8
6
7
O
S
I
R
I
O
N
-
-
3
-``
-
7
-
9
-
9
-
-
6
1
9
9
9
6
5
-
-``
-
-
-
-
-
-
-
-
6
7
O
S
I
R
I
O
N
-
-
3
-``
-
7
-
9
-
9

 

 

7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
6
1
9
-
9
6
5
+
=
36
3+6
=
9
=
9
=
9
-
15
19
9
-
9
15
14
+
=
81
8+1
=
9
=
9
=
9
7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
18
-
-
-
+
=
18
1+8
=
9
=
9
=
9
7
O
S
I
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
15
19
9
18
9
15
14
+
=
99
9+9
=
9
1+8
9
=
9
-
6
1
9
9
9
6
5
+
=
45
4+5
=
9
=
9
=
9
7
O
S
I
R
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
--
--
-
-
-
-
--
5
-
-
5
occurs
x
1
=
5
=
5
-
6
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
9
9
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
7
O
S
I
R
I
O
N
-
-
21
-``
-
7
-
45
-
18
-
-
-
9
9
9
-
-
-
-
2+1
-
-
-
-
4+5
-
1+8
7
O
S
I
R
I
O
N
-
-
3
-``
-
7
-
9
-
9
-
6
1
9
9
9
6
5
-
-``
-
-
-
-
-
-
-
-
7
O
S
I
R
I
O
N
-
-
3
-``
-
7
-
9
-
9

 

 

ORION OSIRIS SIRIUS IRIS ISIS ISIS IRIS SIRIUS OSIRIS ORION

69965 619991 199931 9991 9191 9191 9991 199931 619991 69965

ORION OSIRIS SIRIUS IRIS ISIS ISIS IRIS SIRIUS OSIRIS ORION

 

 

Daily Mail

Monday February 23, 2009

ANSWERS TO CORRESPONDENTS

Compiled by Charles Legge

Page 57

QUESTION Are the three stars that make up Orion's belt a similar distance from the Earth or do they just appear that way?

ORION, the giant huntsman of Greek mythology whom Zeus placed among the stars as the constellation, has three stars of apparently similar brightness and colour (bluish-white) in his belt, given the Arabic names (from left to right) Alnitak, Alnilam and Mintaka.

In fact, Alnitak is 800 light years away from us, Alnilam 1,300 light years and Mintaka 900 light years. They appear in a straight line only in our line of sight.
Despite this, the three stars appear to be closely associated. Each is a luminous, hot supergiant having luminosities at least 100,000 times that of the Sun, and surface temperatures exceeding 25,000c (our Sun is 5,500c).

It's believed the three stars, and several other equally hot and luminous stars in the constellation Orion, were formed together as a close cluster. The passage of time has seen them drift apart.

Such luminous stars use up hydrogen at a prodigious rate so they're only a few million years old and have no more than a few million years to live before blowing themselves up in a supernova explosion.

These timescales are short in astronomical terms. Our Sun, with its far lower luminosity and lower fuel consumption, has shone for five billion years and is expected to shine steadily for the same amount of time before it, too, dies, in a much more sedate fashion than a supernova explosion.

The five billion years that our Sun has been around has meant that life has had time to develop on one of its planets — Earth.
It seems most unlikely that any hypopthetical planet around a star in Orion's belt could have developed sort of life when the history of the star, from birth to death, is only a few million years.

Norman Wallace, Sutton Coldfield, W Mids.

 

 

HERA HERE HER RHEA RATHER RHEA RATHER RHEA HER HERE HERA

ZEUS SEE US I ME YOU SEE ZEUS ME I ME ZEUS SEE YOU ME I US SEE ZEUS

 

 

A

STAR LIGHT STAR

STORY

A

STARRY RIDE A RIDE STARRY

I AM ALL STARRY STARRY EYED AM I ME I AM ALL STARRY STARRY EYED AM I

I AM ALL STARRY STARRY I'D AM I ME I AM ALL STARRY STARRY I'D AM I

I AM ALL STARRY STARRY IDEA AM I ME I AM ALL STARRY STARRY IDEA AM I

I AM ALL STARRY STARRY LIGHT AM I ME I AM ALL STARRY STARRY LIGHT AM I

A

STAR STARE STAR

HELLO SAY I ME I SAY HELLO

 

 

W
=
5
-
4
WHEN
50
23
5
Y
=
7
-
3
YOU
61
16
7
W
=
5
-
4
WISH
59
23
5
U
=
3
-
4
UPON
66
21
3
A
=
1
-
1
A
1
1
1
S
=
1
-
4
STAR
58
13
4
-
-
22
4
20
First Total
295
97
25
-
-
2+2
-
2+0
Add to Reduce
2+9+5
9+7
2+5
Q
-
4
-
2
Second Total
16
16
7
-
-
-
-
-
Reduce to Deduce
1+6
1+6
-
-
-
4
-
2
Essence of Number
7
7
7

 

 

ALNI TAK ALNILAM MINTAKA

 

A
=
1
-
7
ALNITAK
68
23
5
A
=
1
-
7
ALNILAM
62
26
8
M
=
4
-
7
MINTAKA
69
24
6
-
-
6
4
21
First Total
199
73
19
-
-
-
-
2+1
Add to Reduce
1+9+9
7+3
1+9
Q
-
6
-
3
Second Total
19
10
10
-
-
-
-
-
Reduce to Deduce
1+9
1+0
1+0
Q
-
6
-
3
Third Totalr
10
1
1
-
-
-
-
-
Add to Reduce
1+0
-
-
Q
-
6
-
3
Essence of Number
1
1
1

 

ALNITAK ALNILAM MINTAKA

 

 

-
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
-
-
5
9
-
-
-
-
-
9
5
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
-
-
-
-
14
9
-
-
-
-
-
-
14
9
-
-
-
-
-
9
14
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
-
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
1
3
-
-
2
1
2
-
1
3
-
-
3
1
4
-
4
-
-
2
1
2
1
+
=
31
3+1
=
4
=
4
=
4
-
-
1
12
-
-
20
1
11
-
1
12
-
-
12
1
13
-
13
-
-
20
1
11
1
+
=
130
1+3+0
=
4
=
4
=
4
-
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
1
12
14
9
20
1
11
-
1
12
14
9
12
1
13
-
13
9
14
20
1
11
1
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
1
3
5
9
2
1
2
-
1
3
5
9
3
1
4
-
4
9
5
2
1
2
1
+
=
73
7+3
=
10
1+0
1
=
1
-
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
6
=
6
=
6
-
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
-
2
occurs
x
4
=
8
=
8
-
-
-
3
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
24
-
-
21
-
73
-
46
2+1
2+1
1
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
2+4
-
-
2+1
-
7+3
-
4+6
3
3
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
6
-
-
3
-
10
-
10
-
-
1
3
5
9
2
1
2
-
1
3
5
9
3
1
4
-
4
9
5
2
1
2
1
-
-
-
-
-
-
-
1+0
-
1+0
3
3
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
6
-
-
3
-
1
-
1

 

 

21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
-
-
5
9
-
-
-
-
-
9
5
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
-
-
-
14
9
-
-
-
-
-
-
14
9
-
-
-
-
-
9
14
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
1
3
-
-
2
1
2
-
1
3
-
-
3
1
4
-
4
-
-
2
1
2
1
+
=
31
3+1
=
4
=
4
=
4
-
1
12
-
-
20
1
11
-
1
12
-
-
12
1
13
-
13
-
-
20
1
11
1
+
=
130
1+3+0
=
4
=
4
=
4
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
1
12
14
9
20
1
11
-
1
12
14
9
12
1
13
-
13
9
14
20
1
11
1
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
1
3
5
9
2
1
2
-
1
3
5
9
3
1
4
-
4
9
5
2
1
2
1
+
=
73
7+3
=
10
1+0
1
=
1
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
6
=
6
=
6
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
-
2
occurs
x
4
=
8
=
8
-
-
3
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
24
-
-
21
-
73
-
46
2+1
1
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
2+4
-
-
2+1
-
7+3
-
4+6
3
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
6
-
-
3
-
10
-
10
-
1
3
5
9
2
1
2
-
1
3
5
9
3
1
4
-
4
9
5
2
1
2
1
-
-
-
-
-
-
-
1+0
-
1+0
3
A
L
N
I
T
A
K
-
A
L
N
I
L
A
M
-
M
I
N
T
A
K
A
-
-
6
-
-
3
-
1
-
1

 

 

7
ALNITAK
68
23
5
7
ALNILAM
62
26
8
7
MINTAKA
69
24
6
21
First Total
199
73
19
2+1
Add to Reduce
1+9+9
7+3
1+9
3
Second Total
19
10
10
-
Reduce to Deduce
1+9
1+0
1+0
3
Third Totalr
10
1
1
-
Reduce to Produce
1+0
-
-
3
Essence of Number
1
1
1

 

 

A
=
1
-
4
ALNI
36
18
9
A
=
1
-
4
ALNI
36
18
9
M
=
4
-
3
MIN
36
18
9
-
-
6
4
11
Add to Reduce
108
54
27
-
-
-
-
1+1
Reduce to Deduce
1+0+8
5+4
2+7
Q
-
6
-
2
Essence of Number
9
9
9

 

ALNI TAK ALNI LAM MIN TAKA

I

ME I ME

I

ALNI TAK ALNI LAM MIN TAKA

 

A
=
1
-
4
ALNI
36
18
9
A
=
1
-
4
ALNI
36
18
9
M
=
4
-
3
MIN
36
18
9
-
-
6
4
11
Add to Reduce
108
54
27
-
-
-
-
1+1
Reduce to Deduce
1+0+8
5+4
2+7
Q
-
6
-
2
Essence of Number
9
9
9

 

 

7
ALNITAK
68
23
5
7
ALNILAM
62
26
8
7
MINTAKA
69
24
6
21
First Total
199
73
19
2+1
Add to Reduce
1+9+9
7+3
1+9
3
Second Total
19
10
10
-
Reduce to Deduce
1+9
1+0
1+0
3
Third Totalr
10
1
1
-
Reduce to Produce
1+0
-
-
3
Essence of Number
1
1
1

 

 

T
=
2
-
3
TAK
32
5
5
L
=
3
-
3
LAM
26
8
8
T
=
2
-
4
TAKA
33
6
6
-
-
7
4
10
First Total
91
19
19
-
-
-
-
1+0
Add to Reduce
9+1
1+9
1+9
Q
-
7
-
1
Second Total
10
10
10
-
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
Q
-
7
-
1
Essence of Number
10
10
10

 

 

7
ALNITAK
68
23
5
7
ALNILAM
62
26
8
7
MINTAKA
69
24
6
21
First Total
199
73
19
2+1
Add to Reduce
1+9+9
7+3
1+9
3
Second Total
19
10
10
-
Reduce to Deduce
1+9
1+0
1+0
3
Third Totalr
10
1
1
-
Reduce to Produce
1+0
-
-
3
Essence of Number
1
1
1

 

 

ALNITAK ALNILAM MINTAKA

ALNI TAK ALNI LAM MIN TAKA

1+3+5+9 2+1+2 1+3+5+9 3+1+4 4+9+5 2+1+2+1

ALNI TAK ALNI LAM MIN TAKA

ALNITAK ALNILAM MINTAKA

 

 

ALNITAK (Zeta Orionis). With brilliant Betelgeuse and Rigel dominating great Orion, we pay little heed to the individual stars of the Hunter's belt except ... www.astro.uiuc.edu/~kaler/sow/alnitak.html

 

ALNITAK (Zeta Orionis). With brilliant Betelgeuse and Rigel dominating great Orion, we pay little heed to the individual stars of the Hunter's belt except as a group, the trio the Arabs called the "string of pearls." All second magnitude, Johannes Bayer seems to have named the stars Delta, Epsilon, and Zeta from right to left. The name of the left hand star, Alnitak (Zeta Orionis), stands in for the whole string, and comes from a phrase that means "the belt of al jauza," "al jauza" the Arabs female "central one." Separate Alnitak from the belt and it becomes a most remarkable star in its own right, the brightest class O star in the sky, a hot blue supergiant. Tucked right next to it is a companion, a blue class B hydrogen-fusing star about three seconds of arc away, the pair orbiting each other with a period estimated to be thousands of years long. The region around Alnitak is remarkable as well, containing several dusty clouds of interstellar gas, including the famed "Horsehead Nebula" to the south. Alnitak approaches first magnitude even though at a distance of 800 light years. To the eye (ignoring the companion), it is 10,000 times more luminous than the Sun. However, its 31,000 Kelvin surface radiates mostly in the ultraviolet where the eye cannot see, and when that it taken into account, Alnitak's luminosity climbs to 100,000 times solar. A planet like the Earth would have to be 300 times farther from Alnitak than Earth is from the Sun (8 times Pluto's distance) for life like ours to survive. Such brilliance can only come from a star of great mass, Alnitak's estimated to be about 20 times solar (its dimmer companion's about 14 times solar). Like all O stars, Alnitak is a source of X-rays that seem to come from a wind that blows from its surface at nearly 2000 kilometers per second, the X- rays produced when blobs of gas in the wind crash violently into one another. Massive stars use their fuel quickly and do not live very long. Alnitak is probably only about 6 million years old (as opposed to the Sun's 4.5 billion year age) and it has already begun to die, hydrogen fusion having ceased in its core. The star will eventually become a red supergiant somewhat like Betelgeuse and almost certainly will explode as a supernova, leaving its companion orbiting a hot, madly spinning neutron star. (Thanks to Monica Shaw, who helped research this star.)

Written by Jim Kaler. Return to STARS.

 

 

7
ALNITAK
68
23
5

 

 

-
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
14
9
-
-
-
+
=
23
2+3
=
5
=
5
-
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
-
1
3
-
-
2
1
2
+
=
9
3+1
=
9
=
9
-
-
1
12
-
-
20
1
11
+
=
45
4+5
=
9
=
9
-
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
-
1
12
14
9
20
1
11
+
=
68
6+8
=
14
=
5
-
-
1
3
5
9
2
1
2
+
=
23
2+3
=
5
=
5
-
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
25
7
A
L
N
I
T
A
K
-
-
20
-
-
7
-
23
2+5
-
-
-
-
9
-
-
-
-
-
2+0
-
-
-
-
2+3
7
7
A
L
N
I
T
A
K
-
-
2
-
-
7
-
5
-
-
1
3
5
9
2
1
2
-
-
-
-
-
-
-
-
7
7
A
L
N
I
T
A
K
-
-
2
-
-
7
-
5

 

 

7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
+
=
14
1+4
=
5
=
5
-
-
-
14
9
-
-
-
+
=
23
2+3
=
5
=
5
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
1
3
-
-
2
1
2
+
=
9
3+1
=
9
=
9
-
1
12
-
-
20
1
11
+
=
45
4+5
=
9
=
9
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
1
12
14
9
20
1
11
+
=
68
6+8
=
14
=
5
-
1
3
5
9
2
1
2
+
=
23
2+3
=
5
=
5
7
A
L
N
I
T
A
K
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
2
-
2
-
-
2
occurs
x
2
=
4
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
7
A
L
N
I
T
A
K
-
-
20
-
-
7
-
23
-
-
-
-
9
-
-
-
-
-
2+0
-
-
-
-
2+3
7
A
L
N
I
T
A
K
-
-
2
-
-
7
-
5
-
1
3
5
9
2
1
2
-
-
-
-
-
-
-
-
7
A
L
N
I
T
A
K
-
-
2
-
-
7
-
5

 

 

ALNILAM (Epsilon Orionis). Three brilliant stars mark the belt of Orion the Hunter, from right to left (west to east) Mintaka, Alnilam, and Alnitak. ... www.astro.uiuc.edu/~kaler/sow/alnilam.html

 

ALNILAM (Epsilon Orionis). Three brilliant stars mark the belt of Orion the Hunter, from right to left (west to east) Mintaka, Alnilam, and Alnitak. The names of all three refer to the whole set. The outer two are named after the "belt" of the Arabs "Central One (a mysterious feminine figure), while Alnilam comes from an Arabic word that aptly means "the String of Pearls," which the trio so well represents. The brightest of the Belt stars (which Bayer lettered in alphabetic order, again from right to left, Delta, Epsilon, and Zeta), and ranking fourth in the whole constellation, Alnilam shines at bright second magnitude (1.70). Though all three stars have similar colors, classes, and temperatures, Alnilam, a hot B (B0) bright supergiant, is notably the most luminous: it is brightest even though farthest away, half again farther than the other two (which lie at nearly the same distance, about 870 light years). From Alnilam's measured (though rather uncertain) distance of 1340 light years, it spectacularly radiates (after correction for its great amount of ultraviolet light) 375,000 solar luminosities from its 25,000 Kelvin surface, and is so hot that it illuminates its own (faint) nebulous cloud from the surrounding interstellar gases. Alnilam has served for many years as a "standard star" against which to compare others. Its brilliant blue and relatively simple spectrum also provides a fine background against which to study the gases of the intervening interstellar space. Like most supergiants, Alnilam is losing mass. A powerful wind blows from the star's surface at speeds up to 2000 kilometers per second, the flow rate two millionths of a solar mass per year (20 million times that from the Sun). Though seemingly single, which disallows direct measure of mass by means of a double-star orbit, the luminosity tells of an evolving star with a mass some 40 times solar. Currently only 4 or so million years old, its internal hydrogen fusion is shutting down, if it has not done so already. The star will shortly turn into a magnificent red supergiant far more luminous than nearby (on the sky) Betelgeuse, its only fate someday to explode.

Written by Jim Kaler. Return to STARS.

 

 

7
ALNILAM
62
26
8

 

 

-
7
A
L
N
I
L
A
M
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
14
9
-
-
-
+
=
23
2+3
=
5
=
5
-
7
A
L
N
I
L
A
M
-
-
-
-
-
-
-
-
-
-
1
3
-
-
3
1
4
+
=
12
1+2
=
3
=
3
-
-
1
12
-
-
12
1
13
+
=
39
3+9
=
1+2
=
3
-
7
A
L
N
I
L
A
M
-
-
-
-
-
-
-
-
-
-
1
12
14
9
12
1
13
+
=
62
6+2
=
8
=
8
-
-
1
3
5
9
3
1
4
+
=
26
2+6
=
8
=
8
-
7
A
L
N
I
L
A
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
23
7
A
L
N
I
L
A
M
-
-
22
-
-
21
-
73
2+3
-
1
-
-
-
-
1
-
-
-
2+2
-
-
2+1
-
7+3
5
7
A
L
N
I
L
A
M
-
-
4
-
-
3
-
10
-
-
1
3
5
9
3
1
4
-
-
-
-
-
-
-
1+0
5
7
A
L
N
I
L
A
M
-
-
4
-
-
3
-
1

 

 

7
EPSILON
-
-
-
-
E+P+S
40
13
4
-
L+I+O+N
50
23
5
7
EPSILON
90
36
9
-
-
9+0
3+6
-
7
EPSILON
9
9
9

 

 

-
7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
9
-
6
5
+
=
21
2+1
=
3
=
3
=
3
-
-
-
-
19
9
-
15
14
+
=
57
5+7
=
12
1+2
3
=
3
-
7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
-
5
7
-
-
3
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
5
16
-
-
12
-
-
+
=
33
3+3
=
6
=
6
=
6
-
7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
-
5
16
19
9
12
15
14
+
=
90
9+0
=
9
=
9
=
9
-
-
5
7
1
9
3
6
5
+
=
36
3+6
=
9
=
9
=
9
-
7
E
P
S
I
L
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
--
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
14
7
E
P
S
I
L
O
N
-
-
31
-
-
7
-
36
-
27
1+4
-
-
-
-
9
-
-
-
-
-
3+1
-
-
-
-
3+6
-
2+7
5
7
E
P
S
I
L
O
N
-
-
2
-
-
7
-
9
-
9

 

 

7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
1
9
-
6
5
+
=
21
2+1
=
3
=
3
=
3
-
-
-
19
9
-
15
14
+
=
57
5+7
=
12
1+2
3
=
3
7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
5
7
-
-
3
-
-
+
=
15
1+5
=
6
=
6
=
6
-
5
16
-
-
12
-
-
+
=
33
3+3
=
6
=
6
=
6
7
E
P
S
I
L
O
N
-
-
-
-
-
--
-
-
-
-
-
5
16
19
9
12
15
14
+
=
90
9+0
=
9
=
9
=
9
-
5
7
1
9
3
6
5
+
=
36
3+6
=
9
=
9
=
9
7
E
P
S
I
L
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
5
-
--
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
E
P
S
I
L
O
N
-
-
31
-
-
7
-
36
-
27
-
-
-
-
9
-
-
-
-
-
3+1
-
-
-
-
3+6
-
2+7
7
E
P
S
I
L
O
N
-
-
2
-
-
7
-
9
-
9

 

 

-
7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
6
5
9
1
+
=
36
3+6
=
9
=
9
-
9
-
`-
15
-
9
15
14
9
19
+
=
81
8+1
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
+
=
9
-
=
9
=
9
-
9
-
`-
-
18
-
-
-
-
-
+
=
18
1+8
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
`-
15
18
9
15
14
9
19
+
=
99
9+9
=
18
1+8
9
-
9
-
-
6
9
9
6
5
9
1
+
=
45
4+5
=
9
=
9
-
9
-
7
O
R
I
O
N
I
S
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
3
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
--
-
-
-
-
-
-
4
-
-
-
-
-
-
-
--
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
5
--
-
6
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
7
-
-
7
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
24
7
O
R
I
O
N
I
S
-
-
21
-
-
7
-
45
-
18
2+4
-
-
9
9
-
-
9
-
-
-
2+1
-
-
-
-
4+5
-
1+8
6
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9
-
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
6
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9

 

 

7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
6
-
9
6
5
9
1
+
=
36
3+6
=
9
=
9
-
9
`-
15
-
9
15
14
9
19
+
=
81
8+1
=
9
=
9
-
9
7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
-
-
+
=
9
-
=
9
=
9
-
9
`-
-
18
-
-
-
-
-
+
=
18
1+8
=
9
=
9
-
9
7
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
`-
15
18
9
15
14
9
19
+
=
99
9+9
=
18
1+8
9
-
9
-
6
9
9
6
5
9
1
+
=
45
4+5
=
9
=
9
-
9
7
O
R
I
O
N
I
S
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
5
-
6
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
O
R
I
O
N
I
S
-
-
21
-
-
7
-
45
-
18
-
-
9
9
-
-
9
-
-
-
2+1
-
-
-
-
4+5
-
1+8
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
7
O
R
I
O
N
I
S
-
-
3
-
-
7
-
9
-
9

 

 

E
=
5
-
7
EPSILON
90
36
9
O
=
6
-
7
ORIONIS
99
45
9
-
-
11
4
14
First Total
189
81
18
-
-
1+1
-
1+4
Add to Reduce
1+8+9
8+1
1+8
Q
-
2
-
5
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
Q
-
2
-
5
Essence of Number
9
9
9

 

 

-
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
9
-
6
5
-
6
-
9
6
5
9
1
+
=
57
5+7
=
12
1+2
3
=
3
-
-
-
-
19
9
-
15
14
-
15
-
9
15
14
9
19
+
=
138
1+3+8
=
12
1+2
3
=
3
-
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
5
7
-
-
3
-
-
-
-
9
-
-
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
-
5
16
-
-
12
-
-
-
-
18
-
-
-
-
-
+
=
51
5+1
=
6
=
6
=
6
-
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
5
16
19
9
12
15
14
-
15
18
9
15
14
9
19
+
=
189
1+8+9
=
9
=
9
=
9
-
-
5
7
1
9
3
6
5
-
6
9
9
6
5
9
1
+
=
81
8+1
=
9
=
9
=
9
-
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
--
-
-
-
5
-
-
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
-
-
6
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
7
-
-
-
-
-
-
7
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
14
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
31
-
-
14
-
81
-
36
1+4
1+4
-
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
3+1
-
-
1+4
-
8+1
-
3+6
5
5
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
4
-
-
5
-
9
-
9
-
-
5
7
1
9
3
6
5
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
5
5
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
4
-
-
5
-
9
-
9

 

 

14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
9
-
6
5
-
6
-
9
6
5
9
1
+
=
57
5+7
=
12
1+2
3
=
3
-
-
-
19
9
-
15
14
-
15
-
9
15
14
9
19
+
=
138
1+3+8
=
12
1+2
3
=
3
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
5
7
-
-
3
-
-
-
-
9
-
-
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
5
16
-
-
12
-
-
-
-
18
-
-
-
-
-
+
=
51
5+1
=
6
=
6
=
6
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
--
-
-
-
-
-
5
16
19
9
12
15
14
-
15
18
9
15
14
9
19
+
=
189
1+8+9
=
9
=
9
=
9
-
5
7
1
9
3
6
5
-
6
9
9
6
5
9
1
+
=
81
8+1
=
9
=
9
=
9
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
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
1
=
7
=
7
-
-
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
14
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
31
-
-
14
-
81
-
36
1+4
-
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
3+1
-
-
1+4
-
8+1
-
3+6
5
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
4
-
-
5
-
9
-
9
-
5
7
1
9
3
6
5
-
6
9
9
6
5
9
1
-
-
-
-
-
-
-
-
-
-
5
E
P
S
I
L
O
N
-
O
R
I
O
N
I
S
-
-
4
-
-
5
-
9
-
9

 

 

MINTAKA (Delta Orionis). Orion is defined by his great belt, three bright second magnitude stars in a row that the ancient Arabs called "the string of ... www.astro.uiuc.edu/~kaler/sow/mintaka.html

 

MINTAKA (Delta Orionis). Orion is defined by his great belt, three bright second magnitude stars in a row that the ancient Arabs called "the string of pearls," which is the meaning of the name of the middle star, Alnilam. The two flanking stars, eastern Alnitak and western Mintaka, both come from Arabic phrases that mean "the belt of the Central One," the Central One the Arabic personification of our Orion, a woman lost to history. Though (at magnitude 2.21) Mintaka is the seventh brightest star in Orion, and the faintest of the three belt stars, it still received the Delta designation from Bayer, who lettered the belt stars in order from west to east before dropping down to Orion's lower half to continue the process. Of the sky's brightest stars, first through third magnitude, Mintaka is closest to the celestial equator, only a quarter of a degree to the south, the star rising and setting almost exactly east and west. The star is wonderfully complex. A small telescope shows a seventh magnitude companion separated by almost a minute of arc. At Mintaka's distance of 915 light years (very nearly the same as Alnitak at the eastern end of the belt), the faint companion orbits at least a quarter of a light year from the bright one. In between is a vastly dimmer 14th magnitude component. The bright star we call Mintaka (whose solo magnitude is 2.23) is ALSO double, and consists of a hot (30,000 Kelvin) class B, slightly evolved, giant star and a somewhat hotter class O star, each radiating near 90,000 times the solar luminosity (after correction for a bit of interstellar dust absorption), each having masses somewhat over 20 times the solar mass. This pair is too close to be separated directly. The duplicity is known through the star's spectrum (its rainbow of light), which detects two stars orbiting each other every 5.73 days, and also because the stars slightly eclipse each other, causing a dip of about 0.2 magnitudes. Mintaka is most famed. however, as a background against which the thin gas of interstellar space was first detected, when the German astronomer Johannes Hartmann in 1904 discovered absorptions in the star's spectrum that could not be produced by the orbiting pair. From this discovery, and others that followed, we now know that all of the Galaxy's interstellar space contains an enormously complex medium of gas and dust that is the birthplace of new stars. Mintaka will also, to some distant generation of astronomers, be famed in death, as each of its components is so massive that their only fate is to explode violently as supernovae.

Written by Jim Kaler. Return to STARS.

 

 

7
MINTAKA
69
24
6

 

 

-
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
-
+
=
14
1+4
=
5
=
5
-
-
-
9
14
-
-
-
-
+
=
23
2+3
=
5
=
5
-
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
4
-
-
2
1
2
1
+
=
10
1+0
=
1
=
1
-
-
13
-
-
20
1
11
1
+
=
46
4+6
=
10
1+0
1
-
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
13
9
14
20
1
11
1
+
=
69
6+9
=
15
1+5
6
-
-
4
9
5
2
1
2
1
+
=
24
2+4
=
6
=
6
-
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
-
-
-
-
-
2
-
2
-
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
24
7
M
I
N
T
A
K
A
-
-
21
-
-
7
-
24
2+4
-
-
9
-
-
-
-
-
-
-
2+1
-
-
-
-
2+4
6
7
M
I
N
T
A
K
A
-
-
3
-
-
7
-
6
-
-
4
9
5
2
1
2
1
-
-
-
-
-
-
-
-
6
7
M
I
N
T
A
K
A
-
-
3
-
-
7
-
6

 

 

7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
-
+
=
14
1+4
=
5
=
5
-
-
9
14
-
-
-
-
+
=
23
2+3
=
5
=
5
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
4
-
-
2
1
2
1
+
=
10
1+0
=
1
=
1
-
13
-
-
20
1
11
1
+
=
46
4+6
=
10
1+0
1
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
13
9
14
20
1
11
1
+
=
69
6+9
=
15
1+5
6
-
4
9
5
2
1
2
1
+
=
24
2+4
=
6
=
6
7
M
I
N
T
A
K
A
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
-
-
-
-
2
-
2
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
7
M
I
N
T
A
K
A
-
-
21
-
-
7
-
24
-
-
9
-
-
-
-
-
-
-
2+1
-
-
-
-
2+4
7
M
I
N
T
A
K
A
-
-
3
-
-
7
-
6
-
4
9
5
2
1
2
1
-
-
-
-
-
-
-
-
7
M
I
N
T
A
K
A
-
-
3
-
-
7
-
6

 

 

O
=
6
-
6
OSIRIS
89
35
8
I
=
9
-
4
ISIS
56
20
2
O
=
6
-
5
ORION
71
35
8
-
-
21
4
15
Add to Reduce
216
90
18
-
-
2+1
-
1+5
Reduce to Deduce
2+1+6
9+0
1+8
Q
-
3
-
6
Essence of Number
9
9
9

 

 

-
15
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
-
-
-
--
-
-
-
-
-
-
6
1
9
-
9
1
-
9
1
9
1
-
6
-
9
6
5
-
+
=
72
7+2
=
9
=
9
=
9
-
`-
15
19
9
-
9
19
-
9
19
9
19
-
15
-
9
15
14
-
+
=
180
1+8+0
=
9
=
9
=
9
-
15
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
-
-
18
-
-
-
-
-
-
-
-
-
18
-
-
-
-
+
=
36
3+6
=
9
=
9
=
9
-
15
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
-
-
-
--
-
-
-
-
-
`-
15
19
9
18
9
19
-
9
19
9
19
-
15
18
9
15
14
-
+
=
216
2+1+6
=
9
=
9
=
9
-
-
6
1
9
9
9
1
-
9
1
9
1
-
6
9
9
6
5
-
+
=
90
9+0
=
9
=
9
=
9
-
15
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
-
-
-
3
-
-
-`
-
-
-
-
-`
-
3
-
-
-
-`
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
-
4
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
--
-
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
9
9
-
-
9
-
9
-
-
-
9
9
-
-
-
-
-
9
occurs
x
7
=
63
6+3
9
24
15
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
21
-
-
15
-
90
-
27
2+4
1+5
-
-
9
9
9
-
-
9
-
9
-
-
-
9
9
-
-
-
-
-
2+1
-
-
1+5
-
9+0
-
2+7
6
6
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
3
-
-
6
-
9
-
9
-
-
6
1
9
9
9
1
-
9
1
9
1
-
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
-
6
6
O
S
I
R
I
S
-
I
S
I
S
-
O
R
I
O
N
-
-
-
3
-
-
6
-
9
-
9

 

 

O
=
6
-
6
OSIRIS
89
35
8
O
=
6
-
5
ORION
71
35
8
-
-
12
4
11
Add to Reduce
160
70
16
-
-
1+2
-
1+1
Reduce to Deduce
1+6+0
7+0
1+6
Q
-
3
-
2
Essence of Number
7
7
7

 

 

-
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
6
1
9
-
9
1
-
6
-
9
6
5
+
=
52
5+2
=
7
=
7
=
7
-
`-
15
19
9
-
9
19
-
15
-
9
15
14
+
=
124
1+2+4
=
7
=
7
=
7
-
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
-
-
18
-
-
-
-
18
-
-
-
+
=
36
3+6
=
9
=
9
=
9
-
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
15
19
9
18
9
19
-
15
18
9
15
14
+
=
160
1+6+0
=
7
=
7
=
7
-
-
6
1
9
9
9
1
-
6
9
9
6
5
+
=
70
7+0
=
7
=
7
=
7
-
11
O
S
I
R
I
S
-
O
R
I
O
N
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
3
-
-
-`
-
3
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
4
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
--
-
6
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
7
-
-
-
-
-
-
7
-
-
7
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
9
9
-
-
-
9
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
24
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
21
-
-
15
-
70
-
27
2+4
1+1
-
-
9
9
9
-
-
-
9
9
-
-
-
-
2+1
-
-
1+5
-
7+0
-
2+7
6
2
O
S
I
R
I
S
-
O
R
I
O
N
-
-
3
-
-
6
-
7
-
9
-
-
6
1
9
9
9
1
-
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
6
2
O
S
I
R
I
S
-
O
R
I
O
N
-
-
3
-
-
6
-
7
-
9

 

 

11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
6
1
9
-
9
1
-
6
-
9
6
5
+
=
52
5+2
=
7
=
7
=
7
`-
15
19
9
-
9
19
-
15
-
9
15
14
+
=
124
1+2+4
=
7
=
7
=
7
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
+
=
18
1+8
=
9
=
9
=
9
`-
-
-
-
18
-
-
-
-
18
-
-
-
+
=
36
3+6
=
9
=
9
=
9
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
-
-
-
--
-
-
-
-
`-
15
19
9
18
9
19
-
15
18
9
15
14
+
=
160
1+6+0
=
7
=
7
=
7
-
6
1
9
9
9
1
-
6
9
9
6
5
+
=
70
7+0
=
7
=
7
=
7
11
O
S
I
R
I
S
-
O
R
I
O
N
T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
6
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
9
9
9
-
-
-
9
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
11
O
S
I
R
I
S
-
O
R
I
O
N
-
-
21
-
-
15
-
70
-
27
1+1
-
-
9
9
9
-
-
-
9
9
-
-
-
-
2+1
-
-
1+5
-
7+0
-
2+7
2
O
S
I
R
I
S
-
O
R
I
O
N
-
-
3
-
-
6
-
7
-
9
-
6
1
9
9
9
1
-
6
9
9
6
5
-
-
-
-
-
-
-
-
-
-
2
O
S
I
R
I
S
-
O
R
I
O
N
-
-
3
-
-
6
-
7
-
9

 

 

O
=
6
-
6
ORION OSIRIS
160
70
7
S
=
1
-
-
NOSIS
76
22
4
S
=
1
-
-
SON IS
76
22
4
S
=
1
-
-
IS SON
76
22
4
S
=
1
-
-
NOSIS
76
22
4
O
=
6
-
6
ORION OSIRIS
160
70
7

 

GNOSIS GOD KNOWS THIS THAT THIS KNOWS GOD GNOSIS

 

 

3
THE
33
15
6
6
GOLDEN
57
30
3
6
GIRDLE
55
37
1
15
First Total
145
82
10
1+5
Add to Reduce
1+4+5
8+2
1+0
6
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
6
Essence of Number
1
1
1

 

 

6
ORIONS
90
36
9
4
BELT
39
12
3
10
First Total
129
48
12
1+0
Add to Reduce
1+2+9
4+8
1+2
1
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
1
Essence of Number
3
3
3

 

 

6
OSIRIS
89
35
8
2
IS
28
10
1
4
LORD
49
22
4
2
OF
21
12
3
4
TIME
47
20
2
18
First Total
234
99
9
1+8
Add to Reduce
2+3+4
9+9
-
9
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
9
Essence of Number
9
9
9

 

 

-
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
9
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
-
15
-
-
-
15
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
3
-
9
4
-
-
6
-
2
-
4
5
+
=
33
3+3
=
6
=
6
=
6
-
-
12
-
18
4
-
-
6
-
20
-
13
5
+
=
78
7+8
=
15
1+5
6
=
6
-
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
12
15
18
4
-
15
6
-
20
9
13
5
+
=
117
1+1+7
=
9
=
9
=
9
-
-
3
6
9
4
-
6
6
-
2
9
4
5
+
=
54
5+4
=
9
=
9
=
9
-
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
16
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
29
-
-
10
-
54
Q
36
1+6
1+0
-
6
-
-
-
6
6
-
-
-
-
-
-
-
2+9
-
-
1+0
-
5+4
-
3+6
7
1
L
O
R
D
-
O
F
-
T
I
M
E
-
-
11
-
-
1
-
9
Q
9
-
-
3
6
9
4
-
6
6
-
2
9
4
5
-
-
1+1
-
-
-
-
-
-
-
7
1
L
O
R
D
-
O
F
-
T
I
M
E
-
-
1
-
-
1
-
9
-
9

 

 

10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
6
-
-
-
9
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
15
-
-
-
15
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
3
-
9
4
-
-
6
-
2
-
4
5
+
=
33
3+3
=
6
=
6
=
6
-
12
-
18
4
-
-
6
-
20
-
13
5
+
=
78
7+8
=
15
1+5
6
=
6
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
12
15
18
4
-
15
6
-
20
9
13
5
+
=
117
1+1+7
=
9
=
9
=
9
-
3
6
9
4
-
6
6
-
2
9
4
5
+
=
54
5+4
=
9
=
9
=
9
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
L
O
R
D
-
O
F
-
T
I
M
E
-
-
29
-
-
10
-
54
Q
36
1+0
-
6
-
-
-
6
6
-
-
-
-
-
-
-
2+9
-
-
1+0
-
5+4
-
3+6
1
L
O
R
D
-
O
F
-
T
I
M
E
-
-
11
-
-
1
-
9
Q
9
-
3
6
9
4
-
6
6
-
2
9
4
5
-
-
1+1
-
-
-
-
-
-
-
1
L
O
R
D
-
O
F
-
T
I
M
E
-
-
1
-
-
1
-
9
-
9

 

 

3
LEO
32
14
5
7
REGULUS
103
31
4
10
Add to Reduce
162
45
9
1+0
Reduce to Deduce
1+6+2
4+5
-
1
Essence of Number
9
9
9

 

 

3
THE
33
15
6
13
CONSTELLATION
159
51
6
2
OF
21
12
3
3
LEO
32
14
5
21
First Total
245
92
20
2+1
Add to Reduce
2+4+5
9+2
2+0
3
Second Total
11
11
2
-
Reduce to Deduce
1+1
1+1
-
3
Essence of Number
2
2
2

 

 

L
=
3
4
LION
50
23
5
K
=
2
4
KING
41
23
5
-
-
5
8
First Total
91
46
10
-
-
-
-
Add to Reduce
9+1
4+6
1+0
Q
-
5
8
Second Total
10
10
1
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
5
8
Essence of Number
1
1
1

 

 

5
HORUS
81
27
9

 

 

7
GODSEND
68
32
5

 

 

3
THE
33
15
6
3
GOD
26
17
8
7
PATTERN
94
31
4
13
Add to Reduce
153
63
18
1+3
Reduce to Deduce
1+5+3
6+3
1+8
4
Essence of Number
9
9
9

 

 

-
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
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
6+2
16
Second Total
17
8
8
1+6
Reduce to Deduce
1+7
-
-
7
Essence of Number
8
8
8

 

 

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
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
7
7
7

 

 

4
GODS
45
18
9
6
SPIRIT
91
37
1
4
ISIS
89
35
8
6
OSIRIS
89
35
8
6
VISHNU
93
30
3
5
SHIVA
59
59
4
7
KRISHNA
80
35
3
7
SHRISTI
102
39
3
5
RISHI
63
36
9
4
ISHI
45
27
9
6
CHRIST
77
32
5

 

 

GODS SPIRIT GODS

ISIS OSIRIS VISHNU SHIVA SHRI KRISHNA SHRISTI RISHI ISHI CHRIST

SING A SONG OF NINES OF NINES A SONG SING

 

 

THE

HALLELUJA CHORUS CHORUS HALLELUJAH

HALLELUJA SEE HORUS HORUS SEE HALLELUJAH

HALLELUJA HOURS OF HORUS HORUS OF HOURS HALLELUJAH

 

 

T
=
2
-
3
THE
33
15
6
A
=
1
-
4
AMEN
33
15
6
N
=
5
-
4
NAME
33
15
6
N
=
5
-
5
NAMES
52
16
7
N
=
5
-
7
NAMASTE
73
19
1

 

 

-
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
-
-
5
-
-
-
1
-
-
+
=
6
-
=
6
=
6
=
6
-
`-
14
-
-
-
19
-
-
+
=
33
3+3
=
6
=
6
=
6
-
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
-
-
-
1
4
1
-
2
5
+
=
13
1+3
=
4
=
4
=
4
-
`-
-
1
13
1
-
20
5
+
=
40
4+0
=
4
=
4
=
4
-
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
-
`-
14
1
13
1
19
20
5
+
=
73
7+3
=
10
1+0
1
=
1
-
-
5
1
4
1
1
2
5
+
=
19
1+9
=
10
1+0
1
=
1
-
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
1
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
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
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
33
7
N
A
M
A
S
T
E
-
-
12
-
-
7
-
19
-
10
3+3
-
-
-
-
-
-
-
-
-
-
1+2
-
-
-
-
1+9
-
1+0
6
7
N
A
M
A
S
T
E
-
-
3
-
-
7
-
10
-
1
-
-
5
1
4
1
1
2
5
-
-
-
-
-
-
-
1+0
-
-
6
7
N
A
M
A
S
T
E
-
-
3
-
-
7
-
1
-
1

 

 

7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
-
5
-
-
-
1
-
-
+
=
6
-
=
6
=
6
=
6
`-
14
-
-
-
19
-
-
+
=
33
3+3
=
6
=
6
=
6
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
-
-
1
4
1
-
2
5
+
=
13
1+3
=
4
=
4
=
4
`-
-
1
13
1
-
20
5
+
=
40
4+0
=
4
=
4
=
4
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
=
`-
14
1
13
1
19
20
5
+
=
73
7+3
=
10
1+0
1
=
1
-
5
1
4
1
1
2
5
+
=
19
1+9
=
10
1+0
1
=
1
7
N
A
M
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
1
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
7
N
A
M
A
S
T
E
-
-
12
-
-
7
-
19
-
10
-
-
-
-
-
-
-
-
-
-
1+2
-
-
-
-
1+9
-
1+0
7
N
A
M
A
S
T
E
-
-
3
-
-
7
-
10
-
1
-
5
1
4
1
1
2
5
-
-
-
-
-
-
-
1+0
-
-
7
N
A
M
A
S
T
E
-
-
3
-
-
7
-
1
-
1

 

 

O
=
6
-
6
ORION OSIRIS
160
70
7
S
=
1
-
-
NOSIS
76
22
4
S
=
1
-
-
SON IS
76
22
4
S
=
1
-
-
IS SON
76
22
4
S
=
1
-
-
NOSIS
76
22
4
O
=
6
-
6
ORION OSIRIS
160
70
7

 

GNOSIS GOD KNOWS THIS THAT THIS KNOWS GOD GNOSIS

 

 

4
GODS
45
18
9
6
SPIRIT
91
37
1
4
ISIS
89
35
8
6
OSIRIS
89
35
8
6
VISHNU
93
30
3
5
SHIVA
59
59
4
7
KRISHNA
80
35
3
7
SHRISTI
102
39
3
5
RISHI
63
36
9
4
ISHI
45
27
9
6
CHRIST
77
32
5

 

 

GODS SPIRIT GODS

ISIS OSIRIS VISHNU SHIVA SHRI KRISHNA SHRISTI RISHI ISHI CHRIST

SING A SONG OF NINES OF NINES A SONG SING

 

 

THE

HALLELUJA CHORUS CHORUS HALLELUJAH

HALLELUJA SEE HORUS HORUS SEE HALLELUJAH

HALLELUJA HOURS OF HORUS HORUS OF HOURS HALLELUJAH

 

 

SCHRODINGERS CAT SCHRODINGERS

 

S
=
1
-
12
SCHRODINGERS
139
67
4
C
=
3
-
3
CAT
24
6
6
D
=
4
-
3
DID
17
17
8
C
=
3
-
10
CURIOUSITY
160
52
7
K
=
2
-
4
KILL
44
17
6
T
=
2
-
3
THE
33
15
6
C
=
3
-
3
CAT
24
6
6
-
-
18
4
38
First Total
441
180
19
-
-
1+8
-
3+8
Add to Reduce
4+4+1
1+8+0
6+2
-
-
9
-
11
Second Total
9
10
10
4
4
-
4
1+1
Reduce to Deduce
-
1+0
1+0
Q
-
9
5
2
Essence of Number
9
7
7

 

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

GODIS EVERYTHING EVERYTHING ISGOD

THEREFORE I QUESTION I QUESTION I THEREFORE

?

R U GODS I ME I ME I GODS U R

 

 

0
4
ZERO
64
28
1
1
6
ONE
34
16
7
2
2
TWO
58
13
4
3
2
THREE
56
29
2
4
6
FOUR
60
24
6
5
6
FIVE
42
24
6
6
1
SIX
52
16
7
7
1
SEVEN
65
20
2
8
5
EIGHT
49
31
4
9
5
NINE
42
24
6
45
38
Add
522
225
45
4+5
3+8
Reduce
5+2+2
2+2+5
4+5
9
11
Deduce
9
9
9
4+5
3+8
Produce
5+2+2
2+2+5
4+5
9
11
Essence
9
9
9

 

 

0
4
ZERO
64
28
1
1
6
ONE
34
16
7
2
2
TWO
58
13
4
3
2
THREE
56
29
2
4
6
FOUR
60
24
6
5
6
FIVE
42
24
6
6
1
SIX
52
16
7
7
1
SEVEN
65
20
2
8
5
EIGHT
49
31
4
9
5
NINE
42
24
6
45
38
Add
522
225
45
4+5
3+8
Reduce
5+2+2
2+2+5
4+5
9
11
Deduce
9
9
9
4+5
3+8
Produce
5+2+2
2+2+5
4+5
9
11
Essence
9
9
9

 

 

3
THE
33
15
6
3
GOD
26
17
8
7
PATTERN
94
31
4
13
Add to Reduce
153
63
18
1+3
Reduce to Deduce
1+5+3
6+3
1+8
4
Essence of Number
9
9
9

 

 

ARE ARHATS STARS STARS ARHATS ARE

R RATS STARS STARS RATS R

HARD IS THE WAY THE WAY IS HARD

 

 

THE

PATH OF PTAH

THAT ISISIS ISISIS THAT

THAT

THOUGHT

THINKING KINGS KIN ALWAYS DRINKING

THE

WATERS OF LIFE IN ENDLESS CYCLE

THAT

IS

THE WAY THE ONLY WAY

THE

RIVER OF LIFE AND DEATH

THAT THAT THAT

THAT ISISIS ISISIS THAT

NEVER ENDING CYCLE OF CREATIVE LIFE

BORN OUT OF AWARENESS INTO OBLIVION OUT OF OBLIVION INTO AWARENESS

ACTION IN ACTION IN ACTION IN ACTION

CREATORS THOUGHT DIVINE LAW GODS LAW DIVINE THOUGHT CREATORS

 

 

I

ME

A

SELF OF KNOWLEDGE AKNOWLEDGE KNOWLEDGE OF SELF

THAT

I ME I SELF I ME I

IS

KNOWLEDGE

OF NO SELF AT ALL

 

 

-
6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
-
5
-
+
=
20
2+0
=
2
=
2
-
2
-
`-
15
-
9
-
14
-
+
=
38
3+8
=
11
1+1
2
-
2
-
6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
5
-
2
+
=
16
1+6
=
7
=
7
-
7
-
`-
-
18
-
5
-
20
+
=
43
4+3
=
7
=
7
-
7
-
6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
-
`-
15
18
9
5
14
20
+
=
81
8+1
=
9
=
9
-
9
-
-
6
9
9
5
5
2
+
=
36
3+6
=
9
=
9
-
9
-
6
O
R
I
E
N
T
T
-
-
-
-
-
-
-
-
-
1
-
-
3
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
3
-
-
-
2
-
-
2
occurs
x
1
=
2
-
2
3
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
--
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
6
O
R
I
E
N
T
-
-
22
-
-
6
-
36
-
187
2+3
-
-
9
9
-
-
-
-
-
2+2
-
-
-
-
3+6
-
1+8
5
6
O
R
I
E
N
T
-
-
4
-
-
6
-
9
-
9
-
-
6
9
9
5
5
2
-
-
-
-
-
-
-
-
-
-
5
6
O
R
I
E
N
T
-
-
4
-
-
6
-
9
-
9

 

 

6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
-
6
-
9
-
5
-
+
=
20
2+0
=
2
=
2
-
2
`-
15
-
9
-
14
-
+
=
38
3+8
=
11
1+1
2
-
2
6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
9
-
5
-
2
+
=
16
1+6
=
7
=
7
-
7
`-
-
18
-
5
-
20
+
=
43
4+3
=
7
=
7
-
7
6
O
R
I
E
N
T
-
-
-
-
-
--
-
-
-
-
`-
15
18
9
5
14
20
+
=
81
8+1
=
9
=
9
-
9
-
6
9
9
5
5
2
+
=
36
3+6
=
9
=
9
-
9
6
O
R
I
E
N
T
T
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
2
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
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
6
O
R
I
E
N
T
-
-
22
-
-
6
-
36
-
187
-
-
9
9
-
-
-
-
-
2+2
-
-
-
-
3+6
-
1+8
6
O
R
I
E
N
T
-
-
4
-
-
6
-
9
-
9
-
6
9
9
5
5
2
-
-
-
-
-
-
-
-
-
-
6
O
R
I
E
N
T
-
-
4
-
-
6
-
9
-
9

 

 

-
11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
-
5
-
-
-
9
6
5
+
=
40
4+0
=
4
-
4
-
4
-
`-
15
-
9
-
14
-
-
-
9
15
14
+
=
76
7+6
=
13
1+3
4
-
4
-
11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
5
-
2
1
2
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
`-
-
18
-
5
-
20
1
20
-
-
-
+
=
64
6+4
=
10
1+0
1
-
1
-
11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
15
18
9
5
14
20
1
20
9
15
14
+
=
140
1+4+0
=
5
-
5
-
5
-
-
6
9
9
5
5
2
1
2
9
6
5
+
=
59
5+9
=
14
1+4
5
-
5
-
11
O
R
I
E
N
T
A
T
I
O
N
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
3
-
-
-
2
-
2
-
-
-
-
-
2
occurs
x
2
=
4
-
4
3
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
--
-
-
-
-
-
--
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
7
-
-
-
-
-
-
-
-
7
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
22
11
O
R
I
E
N
T
A
T
I
O
N
-
-
23
-
-
11
-
59
-
23
2+2
1+1
-
9
9
-
-
-
-
-
9
-
-
-
-
2+3
-
-
1+1
-
5+9
-
2+3
4
2
O
R
I
E
N
T
A
T
I
O
N
-
-
5
-
-
2
-
14
-
5
-
-
6
9
9
5
5
2
2
2
9
6
5
-
-
-
-
-
-
-
1+4
-
-
4
2
O
R
I
E
N
T
A
T
I
O
N
-
-
5
-
-
2
-
5
-
5

 

 

11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
6
-
9
-
5
-
-
-
9
6
5
+
=
40
4+0
=
4
-
4
-
4
`-
15
-
9
-
14
-
-
-
9
15
14
+
=
76
7+6
=
13
1+3
4
-
4
11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
9
-
5
-
2
1
2
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
`-
-
18
-
5
-
20
1
20
-
-
-
+
=
64
6+4
=
10
1+0
1
-
1
11
O
R
I
E
N
T
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
`-
15
18
9
5
14
20
1
20
9
15
14
+
=
140
1+4+0
=
5
-
5
-
5
-
6
9
9
5
5
2
1
2
9
6
5
+
=
59
5+9
=
14
1+4
5
-
5
11
O
R
I
E
N
T
A
T
I
O
N
T
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
3
-
-
-
2
-
2
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
5
5
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
6
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
O
R
I
E
N
T
A
T
I
O
N
-
-
23
-
-
11
-
59
-
23
1+1
-
9
9
-
-
-
-
-
9
-
-
-
-
2+3
-
-
1+1
-
5+9
-
2+3
2
O
R
I
E
N
T
A
T
I
O
N
-
-
5
-
-
2
-
14
-
5
-
6
9
9
5
5
2
2
2
9
6
5
-
-
-
-
-
-
-
1+4
-
-
2
O
R
I
E
N
T
A
T
I
O
N
-
-
5
-
-
2
-
5
-
5

 

 

6
ORIENT
81
36
9
11
ORIENTATION
140
59
5

 

 
 
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