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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

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

ADVENT 962 ADVENT

 

 

THE TRANSMIGRATION OF SOULS
THE, QUESTION, IS, AM, I, RIGHT,
DEAD, RIGHT, AM, I
THE, JOURNEY, OF, ATTEMPT
CROSSING, THE, GREAT, DIVIDE
ACROSS, THE, GREAT, DIVIDE
DIONYSUS
HUNG, SPREAD, EAGLED, ACROSS, A,
CROSSED, DIAGONAL
HUNG, SPREAD, EAGLED, UPON, THE,
CROSS, OF, CROSSES
THE, HORIZONTAL, DIAGONAL
THE, SECOND, COMING
THE SECOND COMING
EIGHTEEN, EIGHT, TEEN
EIGHTY, ONE
EIGHTY ONE
ONE, ZERO, EIGHT
ONE, OUGHT, EIGHT
ONE, NOUGHT, EIGHT
KALEIDOSCOPE x 2
WHEEL, OF, THE, LAW
ROUND, WHEELS
WHEELS, OF, THE, LAW
THE, LAW, OF, CAUSE, AND, EFFECT
THE LAW OF CAUSE AND EFFECT
MERRY, CHRIST, MASS
MERRY, CHRISTMAS
MARRIAGE, MA, R, R, I, AGE
MARRIAGE, OF, OPPOSITES
DEAD, ADD, E
AND, DEAD, IS
BETWEEN, A, ROCK, AND, A, HARD,
PLACE
RENEW, INTER, CONECTED, NESS
A, DOOR, AGAINST, A, DOOR
SPIRIT, S, PIRIT
SPIRIT, I, TRIPS
MILLIONAIRE
NINE, SEVEN, THREE, EHT, NAMUH,
NINE, SEVEN, THREE, DOT, COM
NINE, SEVEN, THREE, EHT, NAMUH,
NINE, SEVEN, THREE . COM
DOT, COM
MISH MASH, MISH, MASH
JAI, HO
HINDI, PHRASE, SIGNIFYING
THE, JOY, OF, VICTORY
THE JOY OF VICTORY
RISHI, PERSAD
LIFE, OR, DEATH
FIRST, OR, LAST
THERE, IS, A, TIME, FOR, EVERY,
PURPOSE, UNDER, HEAVEN
PARADOXICAL
PARADOX
PARADOX, P, ARADOX
THOUGHT, THROUGH, THOUGH
THOUGHT THROUGH THOUGH
THIS, AND, THAT
EXPERIENCE

 

 

T
=
2
-
3
THE
33
15
6
T
=
2
-
14
TRANSMIGRATION
178
70
7
O
=
6
-
2
OF
21
12
3
S
=
1
-
5
SOULS
86
14
5
-
-
11
4
24
Add to Reduce
318
111
21
-
-
1+1
1
2+4
Reduce to Deduce
1+2
1+1+1
2+1
-
-
2
-
6
Essence of Number
3
3
3

 

 

T
=
2
-
3
THE
33
15
6
Q
=
8
-
8
QUESTION
120
39
3
I
=
9
-
2
IS
19
10
1
A
=
1
-
2
AM
14
5
5
I
=
9
-
1
I
9
9
9
R
=
9
-
5
RIGHT
62
35
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
D
=
4
-
4
DEAD
14
14
5
R
=
9
-
5
RIGHT
62
35
8
A
=
1
-
2
AM
14
5
5
1
=
9
-
1
I
9
9
9
-
-
61
4
33
First Total
356
176
59
-
-
6+1
1
3+3
Add to Reduce
3+5+6
1+7+6
5+9
-
-
7
-
6
Second Total
14
14
14
-
-
-
4
-
Reduce to Deduce
1+4
1+4
1+4
-
-
7
5
6
Essence of Number
5
5
5

 

 

3
THE
33
15
6
7
JOURNEY
108
36
9
2
OF
21
12
3
7
ATTEMPT
95
32
5
19
First Total
257
95
23
1+9
Add to Reduce
2+5+7
9+5
2+3
10
Second Total
14
14
5
1+0
Reduce to Deduce
1+4
1+4
-
1
Essence of Number
5
5
5

 

 

8
CROSSING
104
41
5
3
THE
33
15
6
5
GREAT
51
24
6
6
DIVIDE
53
35
8
22
Add to Reduce
241
115
25
2+2
Reduce to Deduce
2+4+1
1+1+5
2+5
4
Essence of Number
7
7
7

 

 

5
ACROSS
75
21
3
3
THE
33
15
6
5
GREAT
51
24
6
6
DIVIDE
53
35
8
19
First Total
212
95
23
1+9
Add to Reduce
2+1+2
9+5
2+3
10
Second Total
5
14
5
1+0
Reduce to Deduce
-
1+4
-
1
Essence of Number
5
5
5

 

 

8
DIONYSUS
126
36
9

 

 

4
HUNG
50
23
5
6
SPREAD
63
27
9
6
EAGLED
34
25
7
6
ACROSS
75
21
3
1
A
1
1
1
7
CROSSED
83
29
2
8
DIAGONAL
63
36
9
38
First Total
369
162
36
3+8
Add to Reduce
3+6+9
1+6+2
3+6
11
Second Total
18
9
9
1+1
Reduce to Deduce
1+8
-
-
2
Essence of Number
9
9
9

 

 

4
HUNG
50
23
5
6
SPREAD
63
27
9
6
EAGLED
34
25
7
4
UPON
66
21
3
3
THE
33
15
6
5
CROSS
74
20
2
2
OF
21
12
3
7
CROSSES
98
26
8
37
First Total
439
169
43
3+7
Add to Reduce
4+3+9
1+6+9
4+3
10
Second Total
16
16
7
1+0
Reduce to Deduce
1+6
1+6
-
1
Essence of Number
7
7
7

 

 

3
THE
33
15
6
10
HORIZONTAL
138
57
3
8
DIAGONAL
63
36
9
21
Add to Reduce
234
108
18
2+1
Reduce to Deduce
2+3+4
1+0+8
1+8
3
Essence of Number
9
9
9

 

 

T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SECOND
60
24
6
C
=
3
-
6
COMING
61
34
7
-
-
6
4
15
First Total
154
73
19
-
-
-
-
1+5
Add to Reduce
1+5+4
7+3
1+9
-
-
6
-
6
Second Total
10
10
10
-
-
-
4
-
Reduce to Deduce
1+0
1+0
1+0
-
-
6
5
6
Essence of Number
1
1
1

 

 

-
15
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
-
-
-
-
-
-
-
-
40
-
-
8
-
-
1
-
-
6
5
-
-
-
6
-
9
5
-
+
=
40
4+0
=
4
=
4
=
4
94
-
-
8
-
-
19
-
-
15
14
-
-
-
15
-
9
14
-
+
=
94
9+4
=
13
1+3
4
=
4
-
15
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
-
-
-
--
-
-
-
-
33
-
2
-
5
-
-
5
3
-
-
4
-
3
-
4
-
-
7
+
=
33
3+3
=
6
=
6
=
6
60
-
20
-
5
-
-
5
3
-
-
4
-
3
-
13
-
-
7
+
=
60
6+0
=
6
=
6
=
6
-
15
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
-
-
-
--
-
-
-
-
154
-
20
8
5
-
19
5
3
15
14
4
-
3
15
13
9
14
7
+
=
154
1+5+4
=
10
1+0
1
=
1
73
-
2
8
5
-
1
5
3
6
5
4
-
3
6
4
9
5
7
+
=
73
7+3
=
10
1+0
1
=
1
-
15
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
3
--
-
-
-
3
--
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
5
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
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
15
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
45
-
-
15
-
73
-
46
4+5
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
4+5
-
-
1+5
-
7+3
-
4+6
9
6
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
9
-
-
6
-
10
-
10
1+6
2
8
5
-
1
5
3
6
5
4
-
3
6
4
9
5
7
-
-
-
-
-
1+0
-
1+4
9
7
T
H
E
-
S
E
C
O
N
D
-
C
O
M
I
N
G
-
-
9
-
-
6
-
1
-
1

 

 

T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SECOND
60
24
6
C
=
3
-
6
COMING
61
34
7
O
=
6
-
2
OF
21
12
3
C
=
3
-
6
CHRIST
77
32
5
-
=
15
-
23
Add to Reduce
252
117
27
-
=
1+5
-
2+3
Reduce to Deduce
1+6+2
1+1+7
2+7
-
=
6
-
5
Essence of Number
9
9
9

 

 

-
EIGHTEEN
--
-
-
5
EIGHT
49
31
4
4
TEEN
24
15
6
9
EIGHTEEN
73
46
10
-
-
7+3
4+6
1+0
9
EIGHTEEN
10
10
1
-
-
1+0
1+0
-
9
EIGHTEEN
1
1
1

 

 

80
6
EIGHTY
74
38
2
1
3
ONE
34
16
7
81
9
Add to Reduce
108
54
9
8+1
-
Reduce to Deduce
1+0+8
5+4
-
9
9
Essence of Number
9
9
9

 

 

-
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
+
6
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
9
-
8
-
-
-
15
14
-
+
=
46
4+6
=
10
1+0
1
=
1
-
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
-
7
-
2
7
+
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
5
-
7
-
20
25
+
-
-
5
+
=
62
6+2
=
8
=
8
=
8
-
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
--
-
-
-
-
-
-
5
9
7
8
20
25
+
15
14
5
+
=
108
1+0+8
=
9
=
9
=
9
-
-
5
9
7
8
2
7
+
6
5
5
+
=
54
5+4
=
9
=
9
=
9
-
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
+
-
-
-
+
=
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
+
-
5
5
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
+
6
-
-
+
=
6
occurs
x
1
=
6
=
6
-
-
-
-
7
-
-
7
+
-
-
-
+
=
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
8
-
-
+
-
-
-
+
=
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
9
E
I
G
H
T
Y
+
O
N
E
+
+
37
-
-
9
-
54
-
36
-
-
5
-
-
-
-
-
+
-
5
5
-
-
3+7
-
-
-
-
5+4
-
3+6
8
-
E
I
G
H
T
Y
-
O
N
E
-
-
10
-
-
9
-
9
-
9
-
-
5
9
7
8
2
7
+
6
5
5
+
+
1+0
-
-
-
-
-
-
8
9
E
I
G
H
T
Y
+
O
N
E
+
+
2
-
-
9
-
9
-
9

 

 

9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
+
6
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
9
-
8
-
-
-
15
14
-
+
=
46
4+6
=
10
1+0
1
=
1
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
5
-
7
-
2
7
+
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
5
-
7
-
20
25
+
-
-
5
+
=
62
6+2
=
8
=
8
=
8
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
--
-
-
-
-
-
5
9
7
8
20
25
+
15
14
5
+
=
108
1+0+8
=
9
=
9
=
9
-
5
9
7
8
2
7
+
6
5
5
+
=
54
5+4
=
9
=
9
=
9
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
+
-
-
-
+
=
2
occurs
x
1
=
2
=
2
-
5
-
-
-
-
-
+
-
5
5
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
+
6
-
-
+
=
6
occurs
x
1
=
6
=
6
-
-
-
7
-
-
7
+
-
-
-
+
=
7
occurs
x
2
=
14
1+4
5
-
-
-
-
8
-
-
+
-
-
-
+
=
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
E
I
G
H
T
Y
+
O
N
E
+
+
37
-
-
9
-
54
-
36
-
5
-
-
-
-
-
+
-
5
5
-
-
3+7
-
-
-
-
5+4
-
3+6
-
E
I
G
H
T
Y
-
O
N
E
-
-
10
-
-
9
-
9
-
9
-
5
9
7
8
2
7
+
6
5
5
+
+
1+0
-
-
-
-
-
-
9
E
I
G
H
T
Y
+
O
N
E
+
+
2
-
-
9
-
9
-
9

 

 

9
E
I
G
H
T
Y
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
6
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
9
-
8
-
-
15
14
-
+
=
46
4+6
=
10
1+0
1
=
1
9
E
I
G
H
T
Y
O
N
E
-
-
-
-
-
--
-
-
-
-
-
5
-
7
-
2
7
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
5
-
7
-
20
25
-
-
5
+
=
62
6+2
=
8
=
8
=
8
9
E
I
G
H
T
Y
O
N
E
-
-
-
-
--
-
-
-
-
-
5
9
7
8
20
25
15
14
5
+
=
108
1+0+8
=
9
=
9
=
9
-
5
9
7
8
2
7
6
5
5
+
=
54
5+4
=
9
=
9
=
9
9
E
I
G
H
T
Y
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
+
=
2
occurs
x
1
=
2
=
2
-
5
-
-
-
-
-
-
5
5
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
1
=
6
=
6
-
-
-
7
-
-
7
-
-
-
+
=
7
occurs
x
2
=
14
1+4
5
-
-
-
-
8
-
-
-
-
-
+
=
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
E
I
G
H
T
Y
O
N
E
+
+
37
-
-
9
-
54
-
36
-
5
-
-
-
-
-
-
5
5
-
-
3+7
-
-
-
-
5+4
-
3+6
-
E
I
G
H
T
Y
O
N
E
-
-
10
-
-
9
-
9
-
9
-
5
9
7
8
2
7
6
5
5
+
+
1+0
-
-
-
-
-
-
9
E
I
G
H
T
Y
O
N
E
+
+
2
-
-
9
-
9
-
9

 

 

1
3
ONE
34
16
7
8
5
EIGHT
49
31
4
9
8
First Total
83
47
11
-
-
Add to Reduce
8+3
4+7
1+1
9
8
Second Total
11
11
2
-
-
Reduce to Deduce
1+1
1+1
-
9
8
Essence of Number
2
2
2

 

 

O
=
6
-
3
ONE
34
16
7
Z
=
8
-
4
ZERO
64
28
1
E
=
5
-
5
EIGHT
49
31
4
-
-
19
4
12
First Total
147
75
12
-
-
1+9
1
1+2
Add to Reduce
1+4+7
7+5
1+2
-
-
10
-
3
Second Total
12
12
3
-
-
1+0
4
-
Reduce to Deduce
1+2
1+2
-
-
-
1
5
3
Essence of Number
3
3
3

 

 

1
O
=
6
-
3
ONE
34
16
7
0
O
=
6
-
5
OUGHT
71
26
8
8
E
=
5
-
5
EIGHT
49
31
4
9
-
-
17
4
13
First Total
154
73
19
-
-
-
1+7
1
1+3
Add to Reduce
1+5+4
7+3
1+9
9
-
-
8
-
4
Second Total
10
10
10
-
-
-
-
4
-
Reduce to Deduce
1+0
1+0
1+0
9
-
-
8
5
4
Essence of Number
1
1
1

 

 

3
ONE
34
16
7
6
NOUGHT
85
31
4
5
EIGHT
49
31
4
14
First Total
168
78
15
1+4
Add to Reduce
1+6+8
7+8
1+5
5
Second Total
15
15
6
-
Reduce to Deduce
1+5
1+5
-
5
Essence of Number
6
6
6

 

 

Kaleidoscope - Wikipedia, the free encyclopedia
A kaleidoscope is a tube of mirrors containing loose colored beads, pebbles or other small colored objects. The viewer looks in one end and light enters the ... en.wikipedia.org/wiki/Kaleidoscope

Giant kaleidoscope, San Diego harbor. A kaleidoscope is a tube of mirrors containing loose colored beads, pebbles or other small colored objects. The viewer looks in one end and light enters the other end, reflecting off the mirrors. Typically there are two rectangular lengthwise mirrors. Setting of the mirrors at 45° creates eight duplicate images of the objects, four at 60°, and four at 90°. As the tube is rotated, the tumbling of the colored objects presents the viewer with varying colors and patterns. Any arbitrary pattern of objects shows up as a beautiful symmetric pattern because of the reflections in the mirrors. A two-mirror model yields a pattern or patterns isolated against a solid black background, while a three-mirror (closed triangle) model yields a pattern that fills the entire field. For a 2D symmetry group, a kaleidoscopic point is a point of intersection of two or more lines of reflection symmetry. In the case of a discrete group the angle between consecutive lines is 180°/n for an integer n≥2. At this point there are n lines of reflection symmetry, and the point is a center of n-fold rotational symmetry. See also symmetry combinations. Modern kaleidoscope are made of brass tubes, stained glass, wood, steel, gourds and most any other material an artist can sculpt or manipulate. The part of the kaleidoscope which holds objects to be viewed is called an object chamber or cell. Object cells may contain almost any material. Sometimes the object cell is filled with liquid so the items float and move through the object cell with slight movement from the person viewing.

Contents [hide]
1 Etymology
2 History
3 Background
4 See also
5 References
6 External links

[edit] Etymology

A toy kaleidoscope tube. First attested 1817 in English, the word "kaleidoscope" derives from the Greek καλός (kalos), "beautiful"[1] + είδος (eidos), "shape"[2] + σκοπέω (scopeο), "to look at, to examine"[3][4].

More informatively: "looking at beautiful forms" (PB May 2009)

[edit] History

Patterns as seen through a kaleidoscope tube. Known to the ancient Greeks, it was reinvented by Sir David Brewster in 1816 while conducting experiments on light polarization; Brewster patented it in 1817. His initial design was a tube with pairs of mirrors at one end, and pairs of translucent disks at the other, and beads between the two. Initially intended as a science tool, the kaleidoscope was quickly copied as a toy. Brewster believed he would make money from his popular invention; however, a fault in the wording of his patent allowed others to copy his invention.[citation needed]

In America, Charles Bush popularized the kaleidoscope. Today, these early products often sell for over $1,000. Cozy Baker collected kaleidoscopes and wrote books about a few of the artists who were making them in the 1970s through 2000. Baker is credited with energizing a renaissance in kaleidoscope-making in America. In 1999 a short lived magazine dedicated to kaleidoscopes called Kaleidoscope Review was published covering artists, collectors, dealers, events, and how-to articles. This magazine was created and edited by Brett Bensley, at that time a well known kaleidoscope artist and resource on kaleidoscope information.

Craft galleries often carry a few, while others specialize in them and carry dozens of different types from different artists and craftspeople.

Kaleidoscopes are related to hyperbolic geometry.

[edit] Background
For some background on the geometry of the kaleidoscope, see Reflection group.

[edit] See also
Teleidoscope
Kaleidoplex
Fractals

[edit] References
1.^ Kalos, Henry George Liddell, Robert Scott, "A Greek-English Lexicon", at Perseus
2.^ Eidos, Henry George Liddell, Robert Scott, "A Greek-English Lexicon", at Perseus
3.^ Skopeo, Henry George Liddell, Robert Scott, "A Greek-English Lexicon", at Perseus
4.^ Online Etymology Dictionary

[edit] External links
Media related to Kaleidoscopes at Wikimedia Commons
[1] spectacular kaleidoscope on youtube
[2] another spectacular kaleidoscope on youtube (links to more)
12 in HU, moving interactive kaleidoscope
Literary and Philosophical Remarks.
Kaleidoscope History
How to make a Kaleidoscope
Kaleidoscope Mirror Designs
Infography about Kaleidoscopes
Digital kaleidoscope gallery
Customizable interactive animated Kaleidoscope application for iPhone

 

 

-
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
9
-
6
1
-
6
-
-
+
=
22
2+2
=
4
-
4
=
4
-
-
-
-
-
-
9
-
15
19
-
15
-
-
+
=
58
5+8
=
13
1+3
4
=
4
-
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
-
2
1
3
5
-
4
-
-
3
-
7
5
+
=
30
3+9
=
12
1+2
3
=
3
-
-
11
1
12
5
-
4
-
-
3
-
16
5
+
=
57
5+7
=
12
1+2
3
=
3
-
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
11
1
12
5
9
4
15
19
3
15
16
5
+
=
115
1+1+5
=
7
-
7
=
7
-
-
2
1
3
5
9
4
6
1
3
6
7
5
+
=
52
5+2
=
7
-
7
=
7
-
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
37
-
-
12
-
52
-
34
-
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+2
-
5+2
-
3+4
8
3
K
A
L
E
I
D
O
S
C
O
P
E
-
-
10
-
-
3
-
7
-
7
-
-
2
1
3
5
9
4
6
1
3
6
7
5
-
-
1+0
-
-
-
-
-
-
-
8
3
K
A
L
E
I
D
O
S
C
O
P
E
-
-
1
-
-
3
-
7
-
7

 

 

12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
-
6
1
-
6
-
-
+
=
22
2+2
=
4
-
4
=
4
-
-
-
-
-
9
-
15
19
-
15
-
-
+
=
58
5+8
=
13
1+3
4
=
4
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
2
1
3
5
-
4
-
-
3
-
7
5
+
=
30
3+9
=
12
1+2
3
=
3
-
11
1
12
5
-
4
-
-
3
-
16
5
+
=
57
5+7
=
12
1+2
3
=
3
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
11
1
12
5
9
4
15
19
3
15
16
5
+
=
115
1+1+5
=
7
-
7
=
7
-
2
1
3
5
9
4
6
1
3
6
7
5
+
=
52
5+2
=
7
-
7
=
7
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
K
A
L
E
I
D
O
S
C
O
P
E
-
-
37
-
-
12
-
52
-
34
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+2
-
5+2
-
3+4
3
K
A
L
E
I
D
O
S
C
O
P
E
-
-
10
-
-
3
-
7
-
7
-
2
1
3
5
9
4
6
1
3
6
7
5
-
-
1+0
-
-
-
-
-
-
-
3
K
A
L
E
I
D
O
S
C
O
P
E
-
-
1
-
-
3
-
7
-
7

 

 

5
WHEEL
53
26
8
2
OF
21
12
3
3
THE
33
15
6
3
LAW
36
9
9
13
Add to Reduce
143
62
26
1+3
Reduce to Deduce
1+4+3
6+2
2+6
4
Essence of Number
8
8
8

 

 

5
ROUND
72
27
9
6
WHEELS
72
27
9
11
Add to Reduce
144
54
18
1+1
Reduce to Deduce
1+4+4
5+4
1+8
2
Essence of Number
9
9
9

 

 

6
WHEELS
72
27
9
2
OF
21
12
3
3
THE
33
15
6
3
LAW
36
9
9
14
Add to Reduce
162
63
27
1+4
Reduce to Deduce
1+6+2
6+3
2+7
5
Essence of Number
9
9
9

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
3
LAW
36
9
9
O
=
6
-
2
OF
21
12
3
C
=
3
-
5
CAUSE
49
13
4
A
=
1
-
3
AND
19
10
1
E
=
5
-
6
EFFECT
45
27
9
-
-
20
4
22
First Total
203
86
32
-
-
2+0
1
2+2
Add to Reduce
2+0+3
8+6
3+2
-
-
2
-
4
Second Total
5
14
5
-
-
-
4
-
Reduce to Deduce
-
1+4
-
-
-
2
5
4
Essence of Number
5
5
5

 

 

21-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
-
6
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
8
-
-
-
-
-
-
15
-
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
1
5
-
-
6
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
66
6+6
=
12
1+2
3
=
3
-
-
20
-
5
-
12
1
23
-
-
6
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
147
1+4+7
=
12
1+2
3
=
3
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
12
1
23
-
15
6
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
203
2+0+3
=
5
=
5
=
5
-
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
86
8+6
=
14
1+4
5
=
5
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
``-
2
-
-
-`
-
-
-
-`
-
-
-`
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
16
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
29
-
-
22
-
86
-
32
1+6
2+2
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+9
-
-
2+2
-
8+6
-
3+2
7
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
11
-
-
4
-
14
-
5
-
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
1+1
-
-
-
-
1+4
-
-
7
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
2
-
-
4
-
5
-
5

 

 

22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
-
6
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
8
-
-
-
-
-
-
15
-
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
1
5
-
-
6
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
66
6+6
=
12
1+2
3
=
3
-
20
-
5
-
12
1
23
-
-
6
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
147
1+4+7
=
12
1+2
3
=
3
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
12
1
23
-
15
6
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
203
2+0+3
=
5
=
5
=
5
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
86
8+6
=
14
1+4
5
=
5
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
``-
2
-
-
-`
-
-
-
-`
-
-
-`
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
29
-
-
22
-
86
-
32
2+2
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+9
-
-
2+2
-
8+6
-
3+2
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
11
-
-
4
-
14
-
5
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
1+1
-
-
-
-
1+4
-
-
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
2
-
-
4
-
5
-
5

 

 

5
MERRY
79
34
7
6
CHRIST
77
32
5
4
MASS
52
7
7
15
First Total
208
73
19
1+5
Add to Reduce
2+0+8
7+3
1+9
6
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
6
Essence of Number
1
1
1

 

 

5
MERRY
79
34
7
9
CHRISTMAS
110
38
2
14
First Total
189
72
9
1+4
Add to Reduce
1+8+9
7+2
-
5
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
5
Essence of Number
9
9
9

 

 

-
MARRIAGE
--
-
-
2
M+A
14
5
5
1
R
18
9
9
1
R
18
9
9
1
I
9
9
9
3
A+G+E
13
13
4
8
MARRIAGE
72
45
36
-
-
7+2
4+5
3+6
8
MARRIAGE
9
9
9

 

 

8
MARRIAGE
72
45
9
2
OF
21
12
3
9
OPPOSITES
134
44
8
19
First Total
227
101
20
1+9
Add to Reduce
2+2+7
1+0+1
2+0
10
Second Total
11
2
2
1+0
Reduce to Deduce
1+1
-
-
1
Essence of Number
2
2
2

 

 

-
DEAD
--
-
-
3
ADD
9
9
9
1
E
5
5
5
4
DEAD
14
14
14
-
-
1+4
1+4
1+4
4
DEAD
5
5
5

 

 

3
AND
19
10
1
4
DEAD
14
14
5
2
IS
28
10
1
9
Add to Reduce
61
34
7
-
Reduce to Deduce
6+1
3+4
-
9
Essence of Number
7
7
7

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
7
Add to Reduce
72
27
18
-
Reduce to Deduce
7+2
2+7
1+8
7
Essence of Number
9
9
9

 

 

7
BETWEEN
74
29
2
1
A
1
1
1
4
ROCK
47
20
2
3
AND
19
10
1
1
A
1
1
1
4
HARD
31
22
4
5
PLACE
37
19
1
25
Add to Reduce
210
102
12
2+5
Reduce to Deduce
2+1+0
1+0+2
1+2
7
Essence of Number
3
3
3

 

 

5
RENEW
65
29
2
5
INTER
66
30
3
7
CONNECT
74
29
2
2
ED
9
9
9
4
NESS
57
12
3
23
First Total
271
109
19
2+3
Add to Reduce
2+7+1
1+0+9
1+9
5
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
5
Essence of Number
1
1
1

 

 

A
=
1
-
1
A
1
1
1
D
=
4
-
4
DOOR
52
25
7
A
=
1
-
7
AGAINST
71
26
8
A
=
1
-
1
A
1
1
1
D
=
4
-
4
DOOR
52
25
7
-
-
11
4
17
First Total
177
78
24
-
-
1+1
1
1+7
Add to Reduce
1+7+7
7+8
2+4
-
-
2
-
8
Second Total
15
15
6
-
-
-
4
-
Reduce to Deduce
1+5
1+5
-
-
-
2
5
8
Essence of N