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Evokation
  
 
Index
  

 

 

 


 

 

 

 

 

 


ADVENT 2249 ADVENT

 

TABLE, ARRIVE, A, R, R, I, VE, ARRIVE
TABLE, MASCULINITY, MASC, UL, I, N, I, TY, MASCULINITY
TABLE, FEMININITY, F, EM, I, N, I, TY, FEMININITY
TABLE, RESURRECTION, R, ESU, R, R, ECT, I, ON, RESURRECTION
TABLE, RESURRECTION, R, ESU, R, R, ECTION, RESURRECTION
TABLE, RESURRECTED, R, ESU, R, R, ECT, ED, RESURRECTED
TABLE, CRUCIFIED, CRUC, I, F, I, ED, CRUCIFIED
TABLE, CRUCIFIXION, CRUC, I, F, I, X, I, ON, CRUCIFIXION
TABLE, HALLELUJAH, HA, LLELUJ, AH, HALLELUJAH
TABLE, HALLELUJAH
TABLE, POW WOW, POW, WOW, POW WOW
TABLE, CADUCEUS, CADUC, EUS, CADUCEUS
TABLE, CADUCEUS, WAND, STAFF, STICK, HAND
TABLE, CADUCEUS

 

 

K
=
2
-
8
KAMIKAZE
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
-
8
KAMIKAZE
77
32
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
1
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
M
=
4
3
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
K
=
2
5
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Z
=
8
7
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
32
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
8
KAMIKAZE
77
32
5
-
2
4
3
4
5
6
7
8
9
-
-
5
-
-
-
7+7
3+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
8
KAMIKAZE
14
5
5
-
2
4
3
4
5
6
7
8
9
4
-
5
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
8
KAMIKAZE
5
5
5
-
2
4
3
4
5
6
7
8
9

 

 

K
=
2
-
8
KAMIKAZE
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
-
8
KAMIKAZE
77
32
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
1
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
A
=
1
2
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
M
=
4
3
1
M
13
4
4
-
-
-
3
4
-
6
7
-
-
I
=
9
4
1
I
9
9
9
-
-
-
3
-
-
6
7
-
9
K
=
2
5
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
A
=
1
6
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
Z
=
8
7
1
Z
26
8
8
-
-
-
3
-
-
6
7
8
-
E
=
5
8
1
E
5
5
5
-
-
-
3
-
5
6
7
-
-
-
-
32
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
8
KAMIKAZE
77
32
5
-
2
4
3
4
5
6
7
8
9
-
-
5
-
-
-
7+7
3+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
8
KAMIKAZE
14
5
5
-
2
4
3
4
5
6
7
8
9
4
-
5
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
8
KAMIKAZE
5
5
5
-
2
4
3
4
5
6
7
8
9

 

 

K
=
2
-
8
KAMIKAZE
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
-
8
KAMIKAZE
77
32
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
1
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
A
=
1
2
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
M
=
4
3
1
M
13
4
4
-
-
-
3
4
-
6
7
-
-
I
=
9
4
1
I
9
9
9
-
-
-
3
-
-
6
7
-
9
K
=
2
5
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
A
=
1
6
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
Z
=
8
7
1
Z
26
8
8
-
-
-
3
-
-
6
7
8
-
E
=
5
8
1
E
5
5
5
-
-
-
3
-
5
6
7
-
-
-
-
32
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
8
KAMIKAZE
77
32
5
-
2
4
3
4
5
6
7
8
9
-
-
5
-
-
-
7+7
3+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
8
KAMIKAZE
14
5
5
-
2
4
3
4
5
6
7
8
9
4
-
5
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
8
KAMIKAZE
5
5
5
-
2
4
3
4
5
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

K
=
2
-
8
KAMIKAZE
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
-
8
KAMIKAZE
77
32
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
A
=
1
6
1
A
1
1
1
-
1
-
3
-
-
6
7
-
-
K
=
2
1
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
K
=
2
5
1
K
11
2
2
-
-
2
3
-
-
6
7
-
-
M
=
4
3
1
M
13
4
4
-
-
-
3
4
-
6
7
-
-
E
=
5
8
1
E
5
5
5
-
-
-
3
-
5
6
7
-
-
Z
=
8
7
1
Z
26
8
8
-
-
-
3
-
-
6
7
8
-
I
=
9
4
1
I
9
9
9
-
-
-
3
-
-
6
7
-
9
-
-
32
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
8
KAMIKAZE
77
32
5
-
2
4
3
4
5
6
7
8
9
-
-
5
-
-
-
7+7
3+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
8
KAMIKAZE
14
5
5
-
2
4
3
4
5
6
7
8
9
4
-
5
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
8
KAMIKAZE
5
5
5
-
2
4
3
4
5
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

K
=
2
-
8
KAMIKAZE
-
-
-
-
1
2
4
5
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
-
8
KAMIKAZE
77
32
5
-
1
2
4
5
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
-
K
=
2
1
1
K
11
2
2
-
-
2
-
-
-
-
K
=
2
5
1
K
11
2
2
-
-
2
-
-
-
-
M
=
4
3
1
M
13
4
4
-
-
-
4
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
5
-
-
Z
=
8
7
1
Z
26
8
8
-
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
9
-
-
32
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
8
KAMIKAZE
77
32
5
-
2
4
4
5
8
9
-
-
5
-
-
-
7+7
3+2
-
-
-
-
-
-
-
-
-
4
-
4
8
KAMIKAZE
14
5
5
-
2
4
4
5
8
9
4
-
5
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
4
7
4
8
KAMIKAZE
5
5
5
-
2
4
4
5
8
9

 

 

 

-
T
I
M
E
L
E
S
S
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
1
5
-
1
1
+
=
18
1+8
=
9
-
-
9
-
-
9
-
-
-
-
19
19
14
-
19
19
+
=
99
9+9
=
18
1+8
=
9
12
T
I
M
E
L
E
S
S
N
E
S
S
-
-
-
-
-
-
-
-
-
-
20
9
13
5
12
5
19
19
14
5
19
19
+
=
159
1+5+9
=
15
1+5
=
6
-
2
9
4
5
3
5
1
1
5
5
1
1
+
=
42
4+2
=
6
-
-
6
12
T
I
M
E
L
E
S
S
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
1
+
=
4
-
-
4
-
-
4
-
2
-
-
-
-
-
-
-
-
-
-
-
+
=
2
-
-
2
-
-
2
-
-
--
-
-
3
-
-
-
-
-
-
-
+
=
3
-
-
3
-
-
3
-
-
-
4
-
-
-
-
-
-
-
-
-
+
=
4
-
-
4
-
-
4
-
-
-
-
5
-
5
-
-
5
5
-
-
+
=
20
2+0
=
2
-
-
2
-
-
9
-
-
-
-
-
-
-
-
-
-
+
=
9
-
-
9
-
-
9
12
T
I
M
E
L
E
S
S
N
E
S
S
-
-
-
-
-
-
-
-
-

 

 

6
ARRIVE
-
-
-
-
A
1
1
1
-
R
18
9
9
-
R
18
9
9
-
I
9
9
9
-
V+E
27
9
9
6
ARRIVE
73
37
37
1+1
-
7+3
3+7
3+7
6
ARRIVE
10
10
10
-
-
1+0
1+0
1+0
6
ARRIVE
1
1
1

 

 

11
MASCULINITY
-
-
-
-
M+A+S+C
36
18
9
-
U+L
33
6
6
-
I
9
9
9
-
N
14
5
5
-
I
9
9
9
-
T+Y
45
9
9
11
MASCULINITY
-
-
-

 

 

10
FEMININITY
-
-
-
-
F
6
6
6
-
E+M
18
9
9
-
I
9
9
9
-
N
14
5
5
-
I
9
9
9
-
T+Y
45
9
9
10
FEMININITY
-
-
-

 

 

12
RESURRECTION
-
-
-
-
R
18
9
9
-
E+S+U
45
18
9
-
R
18
9
9
-
R
18
9
9
-
E+C+T
28
10
1
-
I
9
9
9
-
O+N
29
11
2
12
RESURRECTION
-
-
-

 

 

12
RESURRECTION
-
-
-
-
R
18
9
9
-
E+S+U
45
18
9
-
R
18
9
9
-
R
18
9
9
-
E+C+T+I+O+N
66
30
3
12
RESURRECTION
-
-
-

 

 

11
RESURRECTED
-
-
-
-
R
18
9
9
-
E+S+U
45
18
9
-
R
18
9
9
-
R
18
9
9
-
E+C+T
28
10
1
-
E+D
9
9
9
11
RESURRECTED
136
64
46
1+1
-
1+3+6
6+4
4+6
2
RESURRECTED
10
10
10
-
-
1+0
1+0
1+0
2
RESURRECTED
1
1
1

 

 

9
CRUCIFIED
-
-
-
-
C+R+U+C
45
18
9
-
I
9
9
9
-
F
6
6
6
-
I
9
9
9
-
E+D
9
9
9
9
CRUCIFIED
-
-
-

 

 

11
CRUCIFIXION
-
-
-
-
C+R+U+C
45
18
9
-
I
9
9
9
-
F
6
6
6
-
I
9
9
9
-
X
24
6
6
-
I
9
9
9
-
O+N
29
11
2
11
CRUCIFIXION
-
-
-

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SPIRIT
91
46
1
O
=
6
-
2
OF
21
12
3
G
=
7
-
3
GOD
26
17
8
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
37
-
6
-
91
46
37
-
-
-
-
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
-
-
12
-
2
-
21
12
12
-
-
-
-
-
-
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
17
-
3
-
26
17
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
3
-
-
6
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
3
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
3
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
3
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
3
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
3
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
1
2
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
81
18
-
1
2
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
6
-
-
-
F
=
6
11
1
F
6
6
6
-
-
-
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
6
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
4
4
5
18
14
8
27
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
1+8
1+4
-
2+7
O
=
6
-
2
OF
21
12
3
-
1
4
4
5
9
5
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
1
4
4
5
9
5
8
9
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
-
-
-
-
-
-
-
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9
-
1
4
4
5
9
5
8
9

 

 

-
-
-
-
14
THE SPIRIT OF GOD
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
G
=
7
-
3
GOD
26
17
8
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
-
-
16
-
14
THE SPIRIT OF GOD
171
90
18
-
-
1+6
-
1+4
-
1+7+1
9+0
1+8
-
-
7
-
5
THE SPIRIT OF GOD
9
9
9

 

 

-
-
-
-
15
GOD CHRIST SPIRIT
-
-
-
G
=
7
-
3
GOD
26
17
8
C
=
3
-
6
CHRIST
77
32
5
S
=
1
-
6
SPIRIT
91
46
1
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
-
1+1
-
1+5
-
1+9+4
9+5
1+4
-
-
2
-
6
GOD CHRIST SPIRIT
14
14
5
-
-
-
-
-
-
1+4
1+4
-
-
-
2
-
6
GOD CHRIST SPIRIT
5
5
5

 

 

-
-
-
-
14
GOD CHRIST SPIRIT
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CHRIST
77
32
5
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
17
-
3
GOD CHRIST SPIRIT
26
17
17
-
-
-
-
-
-
-
-
-
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
15
-
6
GOD CHRIST SPIRIT
77
41
32
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
17
-
3
-
91
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
15
GOD CHRIST SPIRIT
-
-
-
-
2
4
3
4
5
6
14
8
45
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
1+4
-
4+5
C
=
3
-
6
CHRIST
77
32
5
-
2
4
3
4
5
6
5
8
9
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
2
4
3
4
5
6
5
8
9
-
-
1+1
-
1+5
-
1+9+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
14
14
5
-
2
4
3
4
5
6
5
8
9
-
-
-
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
5
5
5
-
2
4
3
4
5
6
5
8
9

 

 

-
-
-
-
14
GOD CHRIST SPIRIT
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CHRIST
77
32
5
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
-
4
5
-
-
-
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
5
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
S
=
1
4
1
S
19
10
1
-
1
-
-
-
5
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
5
-
-
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
5
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
T
=
2
9
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
-
-
17
-
3
-
91
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
15
GOD CHRIST SPIRIT
-
-
-
-
2
4
3
4
5
6
14
8
45
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
1+4
-
4+5
C
=
3
-
6
CHRIST
77
32
5
-
2
4
3
4
5
6
5
8
9
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
2
4
3
4
5
6
5
8
9
-
-
1+1
-
1+5
-
1+9+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
14
14
5
-
2
4
3
4
5
6
5
8
9
-
-
-
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
5
5
5
-
2
4
3
4
5
6
5
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
14
GOD CHRIST SPIRIT
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CHRIST
77
32
5
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
5
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
5
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
5
-
-
-
-
D
=
4
14
1
D
4
4
4
-
-
-
-
4
5
-
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
P
=
7
5
1
P
16
7
7
-
-
-
-
-
5
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
-
-
17
-
3
-
91
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
15
GOD CHRIST SPIRIT
-
-
-
-
2
4
3
4
5
6
14
8
45
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
1+4
-
4+5
C
=
3
-
6
CHRIST
77
32
5
-
2
4
3
4
5
6
5
8
9
S
=
1
-
6
SPIRIT
91
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
15
GOD CHRIST SPIRIT
194
95
14
-
2
4
3
4
5
6
5
8
9
-
-
1+1
-
1+5
-
1+9+4
9+5
1+4
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
14
14
5
-
2
4
3
4
5
6
5
8
9
-
-
-
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
GOD CHRIST SPIRIT
5
5
5
-
2
4
3
4
5
6
5
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

10
HALLELUJAH
-
-
-
-
H+A
9
9
9
-
L+L+E+L+U+J
72
18
9
-
A+H
9
9
9
10
HALLELUJAH
90
36
27
1+0
-
9+0
3+6
2+7
1
HALLELUJAH
9
9
9

 

 

10
H
A
L
L
E
L
U
J
A
H
-
-
-
-
-
-
-
8
1
12
12
5
12
21
10
1
8
+
=
90
9+0
=
9
-
8
1
3
3
5
3
3
1
1
8
+
=
36
3+6
=
9
10
H
A
L
L
E
L
U
J
A
H
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
1
-
+
=
3
-
-
3
-
-
-
3
3
-
3
3
-
-
-
+
=
12
1+2
=
3
-
-
--
-
-
5
-
-
-
-
-
+
=
5
-
-
5
-
8
-
-
-
-
-
-
-
-
8
+
=
16
1+6
=
7
10
H
A
L
L
E
L
U
J
A
H
-
-
36
-
-
18
-
-
-
-
-
-
-
-
-
-
-
-
-
3+6
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9

 

 

6
POW WOW
-
-
-
-
POW
54
18
9
-
WOW
61
16
7
6
POW WOW
115
34
16
1+0
-
1+1+5
3+4
1+6
6
POW WOW
7
7
7

 

 

8
CADUCEUS
-
-
-
-
C+A+D+U+C
32
14
5
-
E+U+S
45
18
9
8
CADUCEUS
77
32
14
1+1
-
7+7
3+2
1+4
8
CADUCEUS
14
5
5
-
-
1+4
-
-
8
CADUCEUS
5
5
5

 

 

8
CADUCEUS
77
23
5
4
WAND
42
15
6
5
STAFF
52
16
7
5
STICK
62
17
8
4
HAND
27
18
9

 

 

 

RA OSIRIS 2 OSIRIS RA

 

-
RA OSIRIS
-
-
-
1
R
18
9
9
3
AOS
35
17
8
1
I
9
9
9
1
R
18
9
9
1
I
9
9
9
1
S
19
10
1
8
RA OSIRIS
108
45
36
-
1+0+8
4+6
3+6
8
RA OSIRIS
9
9
9

 

 

4
LORD
49
22
4
2
OF
21
12
3
5
DEATH
38
20
2
11
F
108
54
9
1+1
-
1+0+8
5+4
-
2
-
9
9
9

 

 

13
SETI-MER-EN-PTAH
-
-
-
-
SETI
53
26
8
-
MER
36
18
9
-
EN
19
10
1
-
PTAH
45
18
9
13
SETI-MER-EN-PTAH
153
72
27
1+3
-
1+5+3
7+2
2+7
4
SETI-MER-EN-PTAH
9
9
9

 

 

THE EGYPTIAN HEAVEN AND HELL

BOOK OF THE DEAD

E. A.Wallis Budge 1857 - 1934

Page 59/60

CHAPTER OF COMING FORTH BY DAY AND OF MAKING A WAY THROUGH AMMEHET.1

"Saith Osiris, the king, the lord of the two lands, MEN-MAAT-RA, whose word is maat, the son of the Sun, [procceeding] from his body loving him, the lord of crowns, SETI MER-EN-PTAH, whose word is maat, "Homage to "you, O ye lords of maat, who are free from iniquity, "who exist and live for ever and to the double henti "period of everlastingness, MEN-MAAT-, whose word is "maat, the son of the Sun, [proceeding] from his body, " loving him, the lord of diadems, SETI MER-EN-PTAH, / "whose word is maat, before you hath become a "khu (i.e., a spirit) in his attributes, he hath gained " the mastery through his words of power, and he "is laden with his splendours. O deliver ye the "Osiris, the king, the lord of the two lands, MEN-MAAT-RA, whose word is maat, the son of the Sun, lord of diadems, SETI MER-EN-PTAH, whose word is maat, from the crocodile of this Pool of "Matti. He hath his mouth, let him speak there-"with. Let there be granted unto him broad-handed- "ness in your presence, because I know you, and I "know your names. . ."

 

 

THE PERIODIC TABLE

 

Periodic table - Wikipedia

https://en.wikipedia.org › wiki › Periodic_table

The periodic table, also known as the periodic table of elements, is a tabular display of the chemical elements, which are arranged by atomic number, electron? ...

?Periodic trends · ?Extended periodic table · ?Alternative periodic tables · ?Block
chemical properties. The structure of the table shows periodic trends. The seven rows of the table, called periods, generally have metals on the left and nonmetals on the right. The columns, called groups, contain elements with similar chemical behaviours. Six groups have accepted names as well as assigned numbers: for example, group 17 elements are the halogens; and group 18 are the noble gases. Also displayed are four simple rectangular areas or blocks associated with the filling of different atomic orbitals.

The elements from atomic numbers 1 (hydrogen) to 118 (oganesson) have all been discovered or synthesized, completing seven full rows of the periodic table.[1][2] The first 94 elements, hydrogen to plutonium, all occur naturally, though some are found only in trace amounts and a few were discovered in nature only after having first been synthesized.[n 1] Elements 95 to 118 have only been synthesized in laboratories, nuclear reactors, or nuclear explosions.[3] The synthesis of elements having higher atomic numbers is currently being pursued: these elements would begin an eighth row, and theoretical work has been done to suggest possible candidates for this extension. Numerous synthetic radioisotopes of naturally occurring elements have also been produced in laboratories.

The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts soon proved to be correct, culminating with the discovery of gallium and germanium in 1875 and 1886 respectively, which corroborated his predictions.[4] Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences. Some discussion remains ongoing regarding the placement and categorisation of specific elements, the future extension and limits of the table, and whether there is an optimal form of the table.

Each chemical element has a unique atomic number (Z) representing the number of protons in its nucleus.[n 2] Most elements have differing numbers of neutrons among different atoms, with these variants being referred to as isotopes. For example, carbon has three naturally occurring isotopes: all of its atoms have six protons and most have six neutrons as well, but about one per cent have seven neutrons, and a very small fraction have eight neutrons. Isotopes are never separated in the periodic table; they are always grouped together under a single element. Elements with no stable isotopes have the atomic masses of their most stable isotopes, where such masses are shown, listed in parentheses.[8]

In the standard periodic table, the elements are listed in order of increasing atomic number Z. A new row (period) is started when a new electron shell has its first electron. Columns (groups) are determined by the electron configuration of the atom; elements with the same number of electrons in a particular subshell fall into the same columns (e.g. oxygen and selenium are in the same column because they both have four electrons in the outermost p-subshell). Elements with similar chemical properties generally fall into the same group in the periodic table, although in the f-block, and to some respect in the d-block, the elements in the same period tend to have similar properties, as well. Thus, it is relatively easy to predict the chemical properties of an element if one knows the properties of the elements around it.[9]

Since 2016, the periodic table has 118 confirmed elements, from element 1 (hydrogen) to 118 (oganesson). Elements 113, 115, 117 and 118, the most recent discoveries, were officially confirmed by the International Union of Pure and Applied Chemistry (IUPAC) in December 2015. Their proposed names, nihonium (Nh), moscovium (Mc), tennessine (Ts) and oganesson (Og) respectively, were made official in November 2016 by IUPAC.[10][11][12][13]

The first 94 elements occur naturally; the remaining 24, americium to oganesson (95–118), occur only when synthesized in laboratories. Of the 94 naturally occurring elements, 83 are primordial and 11 occur only in decay chains of primordial elements.[3] No element heavier than einsteinium (element 99) has ever been observed in macroscopic quantities in its pure form, nor has astatine (element 85); francium (element 87) has been only photographed in the form of light emitted from microscopic quantities (300,000 atoms).[14]

Sets of elements

In chronological order, this section discusses metals and nonmetals (and metalloids); categories of elements; groups and periods; and periodic table blocks. While the recognition of metals as solid, fusible and generally malleable substances dates from antiquity,[15][16] Antoine Lavoisier may have the first to formally distinguish between metals and nonmetals ('non-métalliques') in 1789 with the publication of his 'revolutionary'[17] Elementary Treatise on Chemistry.[18] In 1811, Berzelius referred to nonmetallic elements as metalloids,[19][20] in reference to their ability to form oxyanions.[21][22] In 1825, in a revised German edition of his Textbook of Chemistry,[23][24] he subdivided the metalloids into three classes. These were: constantly gaseous 'gazolyta' (hydrogen, nitrogen, oxygen); real metalloids (sulfur, phosphorus, carbon, boron, silicon); and salt-forming 'halogenia' (fluorine, chlorine, bromine, iodine).[25] Only recently, since the mid-20th century, has the term metalloid been widely used to refer to elements with intermediate or borderline properties between metals and nonmetals. Mendeleev published his periodic table in 1869, along with references to groups of families of elements, and rows or periods of his periodic table. At the same time, Hinrichs wrote that simple lines could be drawn on a periodic table in order to delimit properties of interest, such as elements having metallic lustre (in contrast to those not having such lustre).[26] Charles Janet, in 1928, appears to have been the first to refer to the periodic table's blocks.[27]

Metals, metalloids and nonmetals


Metals, metalloids, nonmetals, and elements with unknown chemical properties.
Classification may vary depending on author's focus.
According to their shared physical and chemical properties, the elements can be classified into the major categories of metals, metalloids and nonmetals. Metals are generally shiny, highly conducting solids that form alloys with one another and salt-like ionic compounds with nonmetals (other than noble gases). A majority of nonmetals are colored or colorless insulating gases; nonmetals that form compounds with other nonmetals feature covalent bonding. In between metals and nonmetals are metalloids, which have intermediate or mixed properties.[28]

Metal and nonmetals can be further classified into subcategories that show a gradation from metallic to non-metallic properties, when going left to right in the rows. The metals may be subdivided into the highly reactive alkali metals, through the less reactive alkaline earth metals, lanthanides and actinides, via the archetypal transition metals, and ending in the physically and chemically weak post-transition metals. Nonmetals may be simply subdivided into the polyatomic nonmetals, being nearer to the metalloids and show some incipient metallic character; the essentially nonmetallic diatomic nonmetals, nonmetallic and the almost completely inert, monatomic noble gases. Specialized groupings such as refractory metals and noble metals, are examples of subsets of transition metals, also known[29] and occasionally denoted.[30]

Placing elements into categories and subcategories based just on shared properties is imperfect. There is a large disparity of properties within each category with notable overlaps at the boundaries, as is the case with most classification schemes.[31] Beryllium, for example, is classified as an alkaline earth metal although its amphoteric chemistry and tendency to mostly form covalent compounds are both attributes of a chemically weak or post-transition metal. Radon is classified as a nonmetallic noble gas yet has some cationic chemistry that is characteristic of metals. Other classification schemes are possible such as the division of the elements into mineralogical occurrence categories, or crystalline structures. Categorizing the elements in this fashion dates back to at least 1869 when Hinrichs[32] wrote that simple boundary lines could be placed on the periodic table to show elements having shared properties, such as metals, nonmetals, or gaseous elements.

Categories
Categorisation as described here can vary among authors
The elements of the periodic table shown here are divided into nine categories; six for the metals, and two for nonmetals, and a metalloid category. The nine categories (or sets) correspond to those found in the literature for the applicable part of the periodic table. Different authors may use different categorisation schema depending on the properties of interest.

An individual category is not necessarily exclusive according to its name, boundary, or shared properties. For example, while beryllium in Group 2 is colored as an alkaline earth metal, it is amphoteric rather than alkaline in nature

 

118 Elements and Their Symbols and Atomic Numbers

The periodic table of elements is widely used in the field of Chemistry to look up chemical elements as they are arranged in a manner that displays periodic trends in the chemical properties of the elements. However, the Periodic table generally displays only the symbol of the element and not its entire name.

Most of the symbols are similar to the name of the element but some symbols of elements have Latin roots. An example for this is silver which denoted by Ag from its Latin name “Argentum”. Another such example would be the symbol ‘Fe’ which is used to denote Iron and can be traced to the Latin word for iron, “Ferrum”. It could prove difficult for a beginner in chemistry to learn the names of all the elements in the periodic table because these symbols do not always correspond to the English names of the elements. Therefore, a list of 118 elements and their symbols and atomic numbers is provided below:

118 Elements and Their Symbols and Atomic Numbers

Name of the Element Symbol of the Element Atomic Number
Hydrogen H 1
Helium He 2
Lithium Li 3
Beryllium Be 4
Boron B 5
Carbon C 6
Nitrogen N 7
Oxygen O 8
Fluorine F 9
Neon Ne 10
Sodium Na 11
Magnesium Mg 12
Aluminium Al 13
Silicon Si 14
Phosphorus P 15
Sulfur S 16
Chlorine Cl 17
Argon Ar 18
Potassium K 19
Calcium Ca 20
Scandium Sc 21
Titanium Ti 22
Vanadium V 23
Chromium Cr 24
Manganese Mn 25
Iron Fe 26
Cobalt Co 27
Nickel Ni 28
Copper Cu 29
Zinc Zn 30
Gallium Ga 31
Germanium Ge 32
Arsenic As 33
Selenium Se 34
Bromine Br 35
Krypton Kr 36
Rubidium Rb 37
Strontium Sr 38
Yttrium Y 39
Zirconium Zr 40
Niobium Nb 41
Molybdenum Mo 42
Technetium Tc 43
Ruthenium Ru 44
Rhodium Rh 45
Palladium Pd 46
Silver Ag 47
Cadmium Cd 48
Indium In 49
Tin Sn 50
Antimony Sb 51
Tellurium Te 52
Iodine I 53
Xenon Xe 54
Cesium Cs 55
Barium Ba 56
Lanthanum La 57
Cerium Ce 58
Praseodymium Pr 59
Neodymium Nd 60
Promethium Pm 61
Samarium Sm 62
Europium Eu 63
Gadolinium Gd 64
Terbium Tb 65
Dysprosium Dy 66
Holmium Ho 67
Erbium Er 68
Thulium Tm 69
Ytterbium Yb 70
Lutetium Lu 71
Hafnium Hf 72
Tantalum Ta 73
Tungsten W 74
Rhenium Re 75
Osmium Os 76
Iridium Ir 77
Platinum Pt 78
Gold Au 79
Mercury Hg 80
Thallium Tl 81
Lead Pb 82
Bismuth Bi 83
Polonium Po 84
Astatine At 85
Radon Rn 86
Francium Fr 87
Radium Ra 88
Actinium Ac 89
Thorium Th 90
Protactinium Pa 91
Uranium U 92
Neptunium Np 93
Plutonium Pu 94
Americium Am 95
Curium Cm 96
Berkelium Bk 97
Californium Cf 98
Einsteinium Es 99
Fermium Fm 100
Mendelevium Md 101
Nobelium No 102
Lawrencium Lr 103
Rutherfordium Rf 104
Dubnium Db 105
Seaborgium Sg 106
Bohrium Bh 107
Hassium Hs 108
Meitnerium Mt 109
Darmstadtium Ds 110
Roentgenium Rg 111
Copernicium Cn 112
Nihonium Nh 113
Flerovium Fl 114
Moscovium Mc 115
Livermorium Lv 116
Tennessine Ts 117
Oganesson Og 118

 

 

PYTHAGORAS = 7728176911 = PYTHAGORAS

1112345677789

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1112345677789

PYTHAGORAS = 7728176911 = PYTHAGORAS

 

A BRIEF HISTORY OF INFINITY

"The Quest to Think the Unthinkable

Brian Clegg 2003

Page 66

"When dealing with such ratios, they would know that there was a clear relationship in terms of a full unit - so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4..."

 

The Theorem of Pythagoras 25 Nov 2001 ... Brief description and proof of the Pythagorean theorem by dissection, ... Ancient Egyptian builders may have known the (3,4,5) triangle and ... arc.iki.rssi.ru/mirrors/stern/stargaze/Spyth.htm - Cached - Similar -

 

Pythagorean Triangles and Triples Jump to The 3-4-5 Triangle‎: 3 4 5 on graph paper But all Pythagorean triangles are even easier to draw on squared paper because all their sides are ... www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html - Cached - Similar

 

-3:4:5 triangle definition - Math Open Reference - Sep 23
You could of course use any dimensions you like, and then use Pythagoras' theorem to see if it is a right triangle. But the numbers 3,4,5 are easy to ...
www.mathopenref.com/triangle345.html - Cached - Similar

 

-The Pythagorean Theorem and the Maya Long Count Various ancient cultures based some of their artwork on the 3-4-5 right triangle, frequently referred to by geometrists as a perfect triangle. Pythagoras is ... www.earthmatrix.com/pythagoras.html - Cached - Similar

 

-Our Ancient Friend and Brother, the Great Pythagoras The evidence that the particular triangle alluded to in the Monitor is the 3,4,5 right triangle can be derived from the odd comments about Pythagoras' ... www.sricf-ca.org/paper1.htm - Similar

 

-The 3-4-5 Rule is the Pythagorean Theorem: Set Control Lines for ... The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or ...
homerenorepair.suite101.com/.../the_345_rule_is_the_pythagorean_theorem - Cached - Similar

 

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The Babylonians were using Pythagoras' Theorem over 1,000 years before he was born. An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.4 Aug 2021

The Babylonians were using Pythagoras’ Theorem over 1,000 years before he was born Subscribe to BBC Science Focus Magazine and get 6 issues for just £9.99
An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.

By Sara Rigby

Published: 04th August, 2021 at 17:05

Students may not believe that Pythagoras’ Theorem has real-world uses, but a 3,700-year-old tablet proves that their maths teachers are right. The artifact, named Si.427, shows how ancient land surveyors used geometry to draw boundaries accurately.

Discovered in central Iraq in 1894, Si.427 sat in a museum in Istanbul for over a century. Now, mathematician Dr Daniel Mansfield from the University of New South Wales, Australia, has studied the clay tablet and uncovered its meaning.

“Si.427 dates from the Old Babylonian (OB) period – 1900 to 1600 BCE,” said Mansfield. “It’s the only known example of a cadastral document from the OB period,

which is a plan used by surveyors define land boundaries. In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off.


As many will remember from their school days, Pythagoras’ Theorem states that the sides of a right-angled triangle obey the formula a2 + b2 = c2, where a and b are the lengths of the short sides, and c is the length of the longest side. A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13. Any triangle with sides of these lengths must be a right-angled triangle.

This fact is useful for marking out accurate rectangles: constructing a triangle whose sides are a Pythagorean triple gives you a right angle every time. This makes Si.427 the earliest-known example of applied geometry.

Read more about ancient maths:
40,000-year-old yarn suggests Neanderthals had basic maths skills
Archimedes: inventor of war machines and calculus (almost)
“Nobody expected that the Babylonians were using Pythagorean triples in this way,” Mansfield said. “It is more akin to pure mathematics, inspired by the practical problems of the time.

“The discovery and analysis of the tablet have important implications for the history of mathematics,” he said. “For instance, this is over a thousand years before Pythagoras was born.

“This is from a period where land is starting to become private – people started thinking about land in terms of ‘my land and your land’, wanting to establish a proper boundary to have positive neighbourly relationships. And this is what this tablet immediately says. It’s a field being split, and new boundaries are made.”

However, this mathematics wasn’t always simple for the Babylonians. Their number system was different from the one we use now. Ours is in a system called base 10: numbers are written by breaking them down into hundreds, tens, units, and so on. The Babylonian number system, however, used the much more complex base 60, similar to how we keep time: 60 seconds make up one minute, and 60 minutes make up one hour.

“This raises a very particular issue – their unique base 60 number system means that only some Pythagorean shapes can be used,” said Mansfield.

In 2017, Mansfield studied another tablet from later in the same time period. This one, called Plimpton 322, contained what he calls ‘proto-trigonometry’: a table studying different types of triangle.

“It seems that the author of Plimpton 322 went through all these Pythagorean shapes to find these useful ones,” he said. “This deep and highly numerical understanding of the practical use of rectangles earns the name ‘proto-trigonometry’ but it is completely different to our modern trigonometry involving sin, cos, and tan.”

The issue of geometry and land ownership came up over and over for the ancient Babylonians, highlighting just how important this mathematics was.

“Another tablet refers to a dispute between Sin-bel-apli – a prominent individual mentioned on many tablets including Si.427 – and a wealthy female landowner,” Mansfield said.

“The dispute is over valuable date palms on the border between their two properties. The local administrator agrees to send out a surveyor to resolve the dispute. It is easy to see how accuracy was important in resolving disputes between such powerful individuals.”

 

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PYTHAGORAS THEOREM
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4
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PYTHAGORAS THEOREM
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7

 

The Babylonians were using Pythagoras’ Theorem over 1,000 years before he was bornSubscribe to BBC Science Focus Magazine and get 6 issues for just £9.99
An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.

By Sara Rigby

Published: 04th August, 2021 at 17:05


As many will remember from their school days, Pythagoras’ Theorem states that the sides of a right-angled triangle obey the formula a2 + b2 = c2, where a and b are the lengths of the short sides, and c is the length of the longest side.

A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13.

Any triangle with sides of these lengths must be a right-angled triangle.

This fact is useful for marking out accurate rectangles: constructing a triangle whose sides are a Pythagorean triple gives you a right angle every time. This makes Si.427 the earliest-known example of applied geometry.

 

A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13.

Any triangle with sides of these lengths must be a right-angled triangle.

 

 

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PYTHAGORAS THEOREM
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PYTHAGORAS
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11
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PYTHAGORAS THEOREM
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=
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2
1
Y
25
7
7
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7
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T
=
2
3
1
T
20
2
2
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2
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H
=
8
4
1
H
8
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8
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8
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A
=
1
5
1
A
1
1
1
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1
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G
=
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6
1
G
7
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6
6
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18
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A
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9
1
A
1
1
1
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1
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10
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S
19
10
1
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1
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PYTHAGORAS THEOREM-
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11
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20
2
2
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12
1
H
8
8
8
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=
5
13
1
E
5
5
5
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6
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18
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5
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5
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5
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13
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PYTHAGORAS THEOREM
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PYTHAGORAS THEOREM
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LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

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5
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18
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9
1
A
1
1
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=
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10
1
S
19
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11
1
T
20
2
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=
5
13
1
E
5
5
5
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O
15
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-
-
-
-
-
-
-
-
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
1+7
-
2+1+4
9+7
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7
-
3
4
3
4
1
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PYTHAGORAS
130
58
4
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
17
PYTHAGORAS THEOREM
214
97
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
3
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
3
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
3
-
-
-
-
-
-
M
=
4
17
1
M
13
4
4
-
-
-
3
4
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
3
-
5
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
O
=
6
14
1
O
15
6
6
-
-
-
3
-
-
6
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
3
-
-
-
7
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
3
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
H
=
8
12
1
H
8
8
8
-
-
-
3
-
-
-
-
8
-
R
=
9
8
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
R
=
9
15
1
R
18
9
9
-
-
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
3
4
3
4
10
12
21
16
18
-
-
-
-
-
PYTHAGORAS THEOREM
-
-
-
-
-
-
-
-
1+0
1+2
2+1
1+6
1+8
P
=
7
-
10
PYTHAGORAS
130
58
4
-
3
4
3
4
1
3
3
7
9
T
=
2
4
7
THEOREM
84
39
3
-
-
-
-
-
-
-
-
-
-
-
-
9
-
17
PYTHAGORAS THEOREM
214
97
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
1+7
-
2+1+4
9+7
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
16
7
-
3
4
3
4
1
3
3
7
9
4
-
4
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
PYTHAGORAS THEOREM
7
7
7
-
3
4
3
4
1
3
3
7
9

 

 

THE PYTHAGOREAN EQUATION

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
T
=
2
-
3
THE
33
15
6
P
=
7
-
11
PYTHAGOREAN
130
58
4
E
=
5
-
8
EQUATION
102
39
3
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
4
-
4
-
-
-
1+3
-
-
-
4
9
4
4
THE PYTHAGOREAN EQUATION
4
4
4

 

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
20
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
21
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
4
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
4
-
-
7
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
4
-
-
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
4
-
-
-
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
4
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
I
=
9
20
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
O
=
6
21
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
U
=
3
17
1
U
21
3
3
-
-
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
O
=
6
21
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
P
=
7
4
1
P
16
7
7
-
-
-
-
4
-
-
7
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
4
-
-
7
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
4
-
-
7
-
-
H
=
8
7
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
H
=
8
2
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
Q
=
8
16
1
Q
8
8
8
-
-
-
-
4
-
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
4
-
-
-
-
9
I
=
9
20
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE PYTHAGOREAN EQUATION
-
-
-
-
3
6
3
4
25
12
21
24
18
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
2+5
3+0
2+1
2+4
1+8
P
=
7
-
11
PYTHAGOREAN
130
58
4
-
3
6
3
4
7
3
3
6
9
E
=
5
-
8
EQUATION
102
39
3
-
-
-
-
-
-
-
-
-
-
-
-
13
-
22
THE PYTHAGOREAN EQUATION
265
112
13
-
3
6
3
4
7
3
3
7
9
4
-
1+3
-
2+2
-
2+6+5
1+1+2
1+3
-
-
-
-
-
-
-
-
-
-
-
4
4
4
4
THE PYTHAGOREAN EQUATION
13
4
4
-
3
6
3
4
7
3
3
7
9
4
-
4
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
9
4
8
THE PYTHAGOREAN EQUATION
4
4
4
-
3
6
3
4
6
3
3
7
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

THE MISSING NUMBERS FROM THE NAME PYTHAGORAS ARE 3 4 5

so, for instance, in the famous right angled triangle of Pythagoras' theorem, they would think of of the longest side being 5 units long when the other side were 3 and 4."

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

THE GROWTH OF SCIENCE

A.P.Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

POPE INNOCENT

From Wikipedia, the free encyclopedia

Pope Innocent may refer to:
Pope Innocent I (401–417)
Pope Innocent II (1130–1143)
Pope Innocent III (1198–1216)
Pope Innocent IV (1243–1254)
Blessed Pope Innocent V (1276)
Pope Innocent VI (1352–1362)
Pope Innocent VII (1404–1406)
Pope Innocent VIII (1484–1492)
Pope Innocent IX (1591)
Pope Innocent X (1644–1655)
Blessed Pope Innocent XI (1676–1689)
Pope Innocent XII (1691–1700)
Pope Innocent XIII (1721–1724)

Additionally, one antipope has chosen the name Innocent:
Antipope Innocent III (1179–1180)

POPE INNOCENT

 

-
-
-
-
-
POPE INNOCENT
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
4
POPE
52
25
7
-
-
-
-
-
-
-
-
-
-
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
3
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
POPE INNOCENT
-
-
-
-
-
-
-
-
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
25
12
14
8
9
-
-
-
-
-
POPE INNOCENT
-
-
-
-
-
-
-
-
2+5
3+0
1+4
-
-
P
=
7
-
4
POPE
52
25
7
-
1
2
3
4
7
3
5
8
9
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
7
3
5
8
9
4
-
1+6
-
1+2
-
1+4+6
6+5
1+1
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
11
11
2
-
1
2
3
4
7
3
5
8
9
4
-
4
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
2
2
2
-
1
2
3
4
7
3
5
8
9

 

 

-
-
-
-
-
POPE INNOCENT
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
4
POPE
52
25
7
-
-
-
-
-
-
-
-
-
-
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
O
=
6
2
1
O
15
6
6
-
1
-
-
4
-
6
-
8
-
P
=
7
3
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
E
=
5
4
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
I
=
9
5
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
N
=
5
6
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
7
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
O
=
6
8
1
O
15
6
6
-
1
-
-
4
-
6
-
8
-
C
=
3
9
1
C
3
3
3
-
1
-
3
4
-
-
-
8
-
E
=
5
10
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
11
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
T
=
2
12
1
T
20
2
2
-
1
2
-
4
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
25
12
14
8
9
-
-
-
-
-
POPE INNOCENT
-
-
-
-
-
-
-
-
2+5
3+0
1+4
-
-
P
=
7
-
4
POPE
52
25
7
-
1
2
3
4
7
3
5
8
9
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
7
3
5
8
9
4
-
1+6
-
1+2
-
1+4+6
6+5
1+1
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
11
11
2
-
1
2
3
4
7
3
5
8
9
4
-
4
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
2
2
2
-
1
2
3
4
7
3
5
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 5 = 25

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 5 = 25

 

-
-
-
-
-
POPE INNOCENT
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
4
POPE
52
25
7
-
-
-
-
-
-
-
-
-
-
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
1
2
-
4
-
-
-
8
-
C
=
3
9
1
C
3
3
3
-
1
-
3
4
-
-
-
8
-
E
=
5
4
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
6
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
7
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
E
=
5
10
1
E
5
5
5
-
1
-
-
4
5
-
-
8
-
N
=
5
11
1
N
14
5
5
-
1
-
-
4
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
1
-
-
4
-
6
-
8
-
O
=
6
8
1
O
15
6
6
-
1
-
-
4
-
6
-
8
-
P
=
7
1
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
P
=
7
3
1
P
16
7
7
-
1
-
-
4
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
1
-
-
4
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
25
12
14
8
9
-
-
-
-
-
POPE INNOCENT
-
-
-
-
-
-
-
-
2+5
3+0
1+4
-
-
P
=
7
-
4
POPE
52
25
7
-
1
2
3
4
7
3
5
8
9
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
1
2
3
4
7
3
5
8
9
4
-
1+6
-
1+2
-
1+4+6
6+5
1+1
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
11
11
2
-
1
2
3
4
7
3
5
8
9
4
-
4
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
2
2
2
-
1
2
3
4
7
3
5
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
POPE INNOCENT
-
-
-
-
2
3
5
6
7
9
P
=
7
-
4
POPE
52
25
7
-
-
-
-
-
-
-
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
2
3
5
6
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
2
-
-
-
-
-
C
=
3
9
1
C
3
3
3
-
-
3
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
5
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
5
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
6
-
-
O
=
6
8
1
O
15
6
6
-
-
-
-
6
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
7
-
P
=
7
3
1
P
16
7
7
-
-
-
-
-
7
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
3
25
12
14
9
-
-
-
-
-
POPE INNOCENT
-
-
-
-
-
-
2+5
3+0
1+4
-
P
=
7
-
4
POPE
52
25
7
-
2
3
7
3
5
9
I
=
9
-
8
INNOCENT
94
40
4
-
-
-
-
-
-
-
-
-
16
-
12
POPE INNOCENT
146
65
11
-
2
3
7
3
5
9
4
-
1+6
-
1+2
-
1+4+6
6+5
1+1
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
11
11
2
-
2
3
7
3
5
9
4
-
4
-
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
4
7
4
3
POPE INNOCENT
2
2
2
-
2
3
7
3
5
9

 


Pope Innocent I (401–417)
Pope Innocent II (1130–1143)
Pope Innocent III (1198–1216)
Pope Innocent IV (1243–1254)
Blessed Pope Innocent V (1276)
Pope Innocent VI (1352–1362)
Pope Innocent VII (1404–1406)
Pope Innocent VIII (1484–1492)
Pope Innocent IX (1591)
Pope InnocentX (1644–1655)
Blessed Pope Innocent XI (1676–1689)
Pope Innocent XII (1691–1700)
Pope Innocent XIII (1721–1724)

 

 

3
THE
33
15
6
6
DIVINE
63
36
9
8
FEMININE
75
48
3
17
First Total
171
99
18
1+7
Add to Reduce
1+7+1
9+9
1+8
8
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
8
Essence of Number
9
9
9

 

 

 

 

 

 

 

THE DIVINE FEMININE

 

-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
=
-
3
THE
33
15
6
4
-
-
-
-
-
-
-
-
-
D
=
4
=
-
6
DIVINE
63
36
9
4
-
-
-
-
-
-
-
-
-
F
=
6
=
-
8
FEMININE
75
48
3
4
1
2
3
4
5
6
7
8
9
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
4
4
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
D
=
4
-
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
6
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
36
4
4
6
-
63
36
36
-
-
-
-
-
-
-
-
-
-
F
=
6
-
10
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
E
=
5
-
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
-
12
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
48
4
4
8
-
75
48
48
-
-
-
-
-
-
-
-
-
-
-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
12
35
6
7
8
36
T
=
2
=
-
3
THE
33
15
6
-
-
-
-
1+2
3+5
-
-
-
3+6
D
=
4
=
-
6
DIVINE
63
36
9
4
1
2
3
3
8
6
7
8
9
F
=
6
=
-
8
FEMININE
75
48
3
4
-
-
-
-
-
-
-
-
-
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
1
2
3
3
8
6
7
8
9
-
-
1+2
-
-
1+7
-
1+7+1
9+9
1+8
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
18
9
4
1
2
3
3
8
6
7
8
9
-
-
-
-
-
-
-
-
1+8
-
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
9
9
4
1
2
3
3
8
6
7
8
9

 

 

-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
=
-
3
THE
33
15
6
4
-
-
-
-
-
-
-
-
-
D
=
4
=
-
6
DIVINE
63
36
9
4
-
-
-
-
-
-
-
-
-
F
=
6
=
-
8
FEMININE
75
48
3
4
1
2
3
4
5
6
7
8
9
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
H
=
8
-
2
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
E
=
5
-
3
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
D
=
4
-
4
1
D
4
4
4
-
1
-
3
4
-
-
7
-
-
I
=
9
-
5
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
V
=
4
-
6
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
I
=
9
-
7
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
N
=
5
-
8
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
-
9
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
F
=
6
-
10
1
F
6
6
6
-
1
-
3
-
-
6
7
-
-
E
=
5
-
11
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
M
=
4
-
12
1
M
13
4
4
-
1
-
3
4
-
-
7
-
-
I
=
9
-
13
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
N
=
5
-
14
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
I
=
9
-
15
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
N
=
5
-
16
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
-
17
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
12
35
6
7
8
36
T
=
2
=
-
3
THE
33
15
6
-
-
-
-
1+2
3+5
-
-
-
3+6
D
=
4
=
-
6
DIVINE
63
36
9
4
1
2
3
3
8
6
7
8
9
F
=
6
=
-
8
FEMININE
75
48
3
4
-
-
-
-
-
-
-
-
-
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
1
2
3
3
8
6
7
8
9
-
-
1+2
-
-
1+7
-
1+7+1
9+9
1+8
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
18
9
4
1
2
3
3
8
6
7
8
9
-
-
-
-
-
-
-
-
1+8
-
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
9
9
4
1
2
3
3
8
6
7
8
9

 

ADDED TO ALL MINUS NONE SHARED BY EVERYTHING MULTIPLIED IN ABUNDANCE

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 7 = 35

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 7 = 35

 

-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
=
-
3
THE
33
15
6
4
-
-
-
-
-
-
-
-
-
D
=
4
=
-
6
DIVINE
63
36
9
4
-
-
-
-
-
-
-
-
-
F
=
6
=
-
8
FEMININE
75
48
3
4
1
2
3
4
5
6
7
8
9
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
1
T
20
2
2
-
1
2
3
-
-
-
7
-
-
D
=
4
-
4
1
D
4
4
4
-
1
-
3
4
-
-
7
-
-
V
=
4
-
6
1
V
22
4
4
-
1
-
3
4
-
-
7
-
-
M
=
4
-
12
1
M
13
4
4
-
1
-
3
4
-
-
7
-
-
E
=
5
-
3
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
-
8
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
-
9
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
-
11
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
-
14
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
N
=
5
-
16
1
N
14
5
5
-
1
-
3
-
5
-
7
-
-
E
=
5
-
17
1
E
5
5
5
-
1
-
3
-
5
-
7
-
-
F
=
6
-
10
1
F
6
6
6
-
1
-
3
-
-
6
7
-
-
H
=
8
-
2
1
H
8
8
8
-
1
-
3
-
-
-
7
8
-
I
=
9
-
5
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
-
7
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
-
13
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
I
=
9
-
15
1
I
9
9
9
-
1
-
3
-
-
-
7
-
9
-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
1
2
3
12
35
6
7
8
36
T
=
2
=
-
3
THE
33
15
6
-
-
-
-
1+2
3+5
-
-
-
3+6
D
=
4
=
-
6
DIVINE
63
36
9
4
1
2
3
3
8
6
7
8
9
F
=
6
=
-
8
FEMININE
75
48
3
4
-
-
-
-
-
-
-
-
-
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
1
2
3
3
8
6
7
8
9
-
-
1+2
-
-
1+7
-
1+7+1
9+9
1+8
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
18
9
4
1
2
3
3
8
6
7
8
9
-
-
-
-
-
-
-
-
1+8
-
4
-
-
-
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
9
9
4
1
2
3
3
8
6
7
8
9

 

 

-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
2
4
5
6
8
9
T
=
2
=
-
3
THE
33
15
6
4
-
-
-
-
-
-
D
=
4
=
-
6
DIVINE
63
36
9
4
-
-
-
-
-
-
F
=
6
=
-
8
FEMININE
75
48
3
4
2
4
5
6
8
9
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
4
5
6
8
9
T
=
2
-
1
1
T
20
2
2
-
2
-
-
-
-
-
D
=
4
-
4
1
D
4
4
4
-
-
4
-
-
-
-
V
=
4
-
6
1
V
22
4
4
-
-
4
-
-
-
-
M
=
4
-
12
1
M
13
4
4
-
-
4
-
-
-
-
E
=
5
-
3
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
-
8
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
-
9
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
-
11
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
-
14
1
N
14
5
5
-
-
-
5
-
-
-
N
=
5
-
16
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
-
17
1
E
5
5
5
-
-
-
5
-
-
-
F
=
6
-
10
1
F
6
6
6
-
-
-
-
6
-
-
H
=
8
-
2
1
H
8
8
8
-
-
-
-
-
8
-
I
=
9
-
5
1
I
9
9
9
-
-
-
-
-
-
9
I
=
9
-
7
1
I
9
9
9
-
-
-
-
-
-
9
I
=
9
-
13
1
I
9
9
9
-
-
-
-
-
-
9
I
=
9
-
15
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
=
-
17
THE DIVINE FEMININE
-
-
-
-
2
12
35
6
8
36
T
=
2
=
-
3
THE
33
15
6
-
-
1+2
3+5
-
-
3+6
D
=
4
=
-
6
DIVINE
63
36
9
4
2
3
8
6
8
9
F
=
6
=
-
8
FEMININE
75
48
3
4
-
-
-
-
-
-
-
-
12
-
-
17
THE DIVINE FEMININE
171
99
18
4
2
3
8
6
8
9
-
-
1+2
-
-
1+7
-
1+7+1
9+9
1+8
4
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
18
9
4
2
3
8
6
8
9
-
-
-
-
-
-
-
-
1+8
-
4
-
-
-
-
-
-
Q
-
3
-
-
8
THE DIVINE FEMININE
9
9
9
4
2
3
8
6
8
9

 

 

 

 

3
THE
33
15
6
6
DIVINE
63
36
9
9
DIMENSION
102
48
3
18
First Total
198
99
18
1+8
Add to Reduce
1+9+8
9+9
1+8
9
Second Total
18
18
9
-
Reduce to Deduce
1+8
1+8
-
9
Essence of Number
9
9
9

 

GODS HOST

?

GODS HOST IS THE HOLY GHOST

 

-
-
-
-
-
GODS HOST IS THE HOLY GHOST
-
-
-
G
=
7
-
4
GODS
45
27
9
H
=
8
-
4
HOST
62
26
8
G
=
7
-
2
IS
28
19
1
4
-
22
-
10
-
135
72
18
4
4
-
4
-
4
4
-
4
T
=
2
-
3
THE
33
18
6
H
=
8
-
4
HOLY
60
24
6
G
=
7
-
5
GHOST
69
33
6
4
-
17
-
12
-
162
72
18
4
-
1+8
4
-
4
4
-
4
-
-
8
-
22
GODS HOST IS THE HOLY GHOST
297
144
36
4
-
4
-
2+2
-
2+9+7
1+4+4
3+6
-
4
8
4
4
GODS HOST IS THE HOLY GHOST
18
9
9
4
-
4
-
-
-
1+8
-
-
-
4
8
4
4
GODS HOST IS THE HOLY GHOST
9
9
9

 

 

Wednesday 11 September 2013

THE MYSTERIES OF THE SNOWFLAKE

Pages 14/15/17/18

Mysteries of the snowflake: The curious world of ... - The Independent

› News › Environment › Nature‎

5 Jan 2013 - Mysteries of the snowflake: The curious world of the ice-crystal experts ... The ice crystals, nestling in the ice clouds as unborn snowflakes, ...

Everybody loves snow, right? But not many of us are obsessed, like the scientists who study these icy enigmas. Nicola Gill enters the curious world of 'dendrites' and 'plates'

Mathematician and philosopher René Descartes is one of many fine minds through the ages to be fascinated by snowflakes and to ponder how such perfection could be created.

While every flake really is a law unto itself, other supposed snow ‘facts’ are not quite so true. The oft-quoted idea that it’s ‘too cold to snow’ is nonsense (it snows at the South Pole where it’s rarely above -40C), and even the apparent truism that snow is white turns out to be slushy logic. Ice crystals are clear, like glass, but when they form a large pile, light is reflected off the surface, bounces around and eventually scatters back out. Since all colours are scattered roughly equally, snow only appears to be white.

These, and many other reasons, are why world-renowned snowflake obsessive, California-based Ken Libbrecht, has made it his life’s work to study, photograph and ‘grow’ snowflakes. The author of several beautiful books showcasing his favourite flakes out of the 7,000 he has photographed, he lives and breathes dendrites, rosettes and plates. “There is something magical about snowflakes,” he says from his laboratory in Pasadena. “You don’t often see such complex symmetry in nature and that makes them extraordinary. The whole intriguing structure of a snow crystal simply arises quite literally out of thin air, as it tumbles through the clouds. The way the crystal grows depends on the temperature it is shaped in – a simple enough idea to grasp – but the underlying physics is fiendishly complicated and has remained a puzzle. I spend a lot, and I mean a lot, of time thinking about this.”

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,

 

Letter frequency - Wikipedia, the free encyclopedia
"The most common letter in the English alphabet is E."

 

LOOK AT THE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

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

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

 

THE INDEPENDENT MAGAZINE

Wednesday 11 September 2013

Mysteries of the snowflake: The curious world of the ice-crystal experts.

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

"The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,"

 

SORT OUT THE WHEAT FROM THE CHAFF

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

Why is the Letter E the Most Common Letter in the English ...
https://englishlanguagethoughts.com › 2018/04/08 › w...

 

LETTER NUMBER FREQUENCIES

 

L
=
3
-
6
LETTER
80
26
8
-
1
2
3
4
5
6
7
8
9
N
=
5
-
6
NUMBER
73
28
1
-
-
-
-
-
-
-
-
-
-
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
 -14
-
23
First Total
275
122
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
26
-
6
-
80
26
26
-
-
-
-
-
-
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
28
-
6
-
73
28
28
-
-
-
-
-
-
-
-
-
-
F
=
6
13
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Q
=
8
16
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
20
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
21
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
23
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
59
-
11
-
122
68
59
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
6
12
4
40
6
7
8
36
L
=
3
-
6
LETTER
80
26
8
-
-
-
1+2
-
4+0
-
-
-
3+6
N
=
5
-
6
NUMBER
73
28
1
-
1
6
3
4
4
6
7
8
9
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
14
-
23
First Total
275
122
14
-
1
6
3
4
4
6
7
8
9
-
-
1+4
-
2+3
Add to Reduce
2+7+5
1+2+2
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Second Total
14
5
5
-
1
6
3
4
4
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Essence of Number
5
5
5
-
1
6
3
4
4
6
7
8
9

 

 

L
=
3
-
6
LETTER
80
26
8
-
1
2
3
4
5
6
7
8
9
N
=
5
-
6
NUMBER
73
28
1
-
-
-
-
-
-
-
-
-
-
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
 -14
-
23
First Total
275
122
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
F
=
6
13
1
F
6
6
6
-
-
-
-
-
-
6
7
-
-
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
Q
=
8
16
1
Q
17
8
8
-
-
-
-
-
-
-
7
8
-
U
=
3
17
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
C
=
3
20
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
I
=
9
21
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
S
=
1
23
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
1
6
12
4
40
6
7
8
36
L
=
3
-
6
LETTER
80
26
8
-
-
-
1+2
-
4+0
-
-
-
3+6
N
=
5
-
6
NUMBER
73
28
1
-
1
6
3
4
4
6
7
8
9
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
14
-
23
First Total
275
122
14
-
1
6
3
4
4
6
7
8
9
-
-
1+4
-
2+3
Add to Reduce
2+7+5
1+2+2
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Second Total
14
5
5
-
1
6
3
4
4
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Essence of Number
5
5
5
-
1
6
3
4
4
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 8 = 40

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 8 = 40

 

L
=
3
-
6
LETTER
80
26
8
-
1
2
3
4
5
6
7
8
9
N
=
5
-
6
NUMBER
73
28
1
-
-
-
-
-
-
-
-
-
-
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
 -14
-
23
First Total
275
122
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
23
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
7
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
U
=
3
17
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
C
=
3
20
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
19
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
F
=
6
13
1
F
6
6
6
-
-
-
-
-
-
6
7
-
-
Q
=
8
16
1
Q
17
8
8
-
-
-
-
-
-
-
7
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
I
=
9
21
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
1
6
12
4
40
6
7
8
36
L
=
3
-
6
LETTER
80
26
8
-
-
-
1+2
-
4+0
-
-
-
3+6
N
=
5
-
6
NUMBER
73
28
1
-
1
6
3
4
4
6
7
8
9
F
=
6
-
11
FREQUENCIES
122
68
5
-
-
-
-
-
-
-
-
-
-
-
-
14
-
23
First Total
275
122
14
-
1
6
3
4
4
6
7
8
9
-
-
1+4
-
2+3
Add to Reduce
2+7+5
1+2+2
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Second Total
14
5
5
-
1
6
3
4
4
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
Essence of Number
5
5
5
-
1
6
3
4
4
6
7
8
9

 

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

Why is the Letter E the Most Common Letter in the English ...
https://englishlanguagethoughts.com › 2018/04/08 › w...

8 Apr 2018 — The letter makes up 12.702% of the letters in an average text, and is the most commonly-used letter in English. The next most frequently-used ...This is a question I’ve been asking myself ruefully these last few days. The E on my keyboard hasn’t been very coöperative, insisting that I bang it at least a few times for it to make the letter E appear on the screen. This has made me really… appreciate, for wont of a better word, just how often we have to use the letter E.

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

 

 

10
CODE DE CODE
67
13
4
6
C+O
18
9
9
4
D+E
9
9
9
4
D+E
9
9
9
6
C+O
18
9
9
4
D+E
9
9
9
10
CODE DE CODE
63
36
36
1+0
-
6+3
3+6
3+6
1
CODE DE CODE
9
9
9

 

 

1
I
9
9
9
3
SAY
45
9
9
7
DECODER
54
36
9
6
DECODE
36
27
9
4
CODE
27
18
9
-
-
-
-
-
-
-
-
-
-
5
CODED
31
22
4
5
CODES
46
19
1

 

 

-
CODE
--
-
-
2
C+O
18
9
9
2
D+E
9
9
9
-
DECODE
--
-
-
2
D+E
9
9
9
2
C+O
18
9
9
2
D+E
9
9
9
-
DECODER
--
-
-
2
D+E
9
9
9
2
C+O
18
9
9
2
D+E
9
9
9
1
R
18
9
9

 

CODE DE CODE

C+O D+E D+E C+O D+E

9+9+9+9+9

C+O D+E D+E C+O D+E

CODE DE CODE

 

 

SACRED NUMBER

THE SECRET QUALITIES OF QUANTITIES

Miranda Lundy 2009

 

-
-
-
-
24
THE QUALITIES OF QUANTITIES
-
-
-
T
=
2
-
3
THE
33
15
6
Q
=
8
-
9
QUALITIES
113
41
5
O
=
6
-
2
OF
21
12
3
Q
=
8
-
10
QUANTITIES
135
45
9
-
-
24
-
24
THE QUALITIES OF QUANTITIES
302
113
23
-
-
2+4
-
2+4
-
3+0+2
1+1+3
2+3
-
-
6
-
6
THE QUALITIES OF QUANTITIES
5
5
9

 

 

SACRED NUMBER

THE SECRET QUALITIES OF QUANTITIES

Miranda Lundy 2009

 

-
-
-
-
24
THE SECRET QUALITIES OF QUANTITIES
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SECRET
70
25
7
Q
=
8
-
9
QUALITIES
113
41
5
O
=
6
-
2
OF
21
12
3
Q
=
8
-
10
QUANTITIES
135
45
9
-
-
25
-
30
THE SECRET QUALITIES OF QUANTITIES
372
138
30
-
-
2+5
-
3+0
-
3+7+2
1+3+8
3+0
-
-
7
-
3
THE SECRET QUALITIES OF QUANTITIES
12
12
3
-
-
-
-
-
-
1+2
1+2
-
-
-
7
-
3
THE SECRET QUALITIES OF QUANTITIES
3
3
3

 

 

-
-
-
-
24
THE ESOTERIC QUALITIES OF QUANTITIES
-
-
-
T
=
2
-
3
THE
33
15
6
E
=
5
-
8
ESOTERIC
94
40
8
Q
=
8
-
9
QUALITIES
113
41
5
O
=
6
-
2
OF
21
12
3
Q
=
8
-
10
QUANTITIES
135
45
9
-
-
29
-
32
THE ESOTERIC QUALITIES OF QUANTITIES
396
153
27
-
-
2+9
-
3+2
-
3+9+6
1+5+3
2+7
-
-
11
-
5
THE ESOTERIC QUALITIES OF QUANTITIES
18
9
9
-
-
1+1
-
-
-
1+8
-
-
-
-
2
-
5
THE ESOTERIC QUALITIES OF QUANTITIES
9
9
9

 

 

-
EXOTERIC
-
-
-
5
EXOTE
69
24
6
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
EXOTERIC
99
45
27
-
-
9+9
4+5
2+7
8
EXOTERIC
18
9
9
-
-
1+8
5+4
2+7
8
EXOTERIC
9
9
9

 

 

8
EXOTERIC
99
45
9
8
ESOTERIC
94
40
4

 

 

8
EXOTERIC
99
45
9
8
ESOTERIC
94
40
4
16
First Total
193
85
13
1+6
Add to Reduce
1+9+3
8+5
1+3
7
Second Total
13
13
4
8
Reduce to Deduce
1+3
1+3
-
7
Essence of Number
4
4
4

 

 

-
ESOTERIC
-
-
-
5
ESOTE
64
19
1
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ESOTERIC
94
40
22
-
-
9+4
4+0
2+2
8
ESOTERIC
13
4
4
-
-
1+3
-
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
1
E
5
5
5
1
S
19
10
1
1
O
15
6
6
1
T
20
2
2
1
E
5
5
5
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ESOTERIC
94
49
40
-
-
9+4
4+9
4+0
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
1
E
5
5
5
3
SOT
54
18
9
1
E
5
5
5
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ESOTERIC
94
49
40
-
-
9+4
4+9
4+0
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
5
ESOTE
64
28
1
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ESOTERIC
94
49
40
-
-
9+4
4+9
4+0
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
1
I
9
9
9
6
SECRET
70
34
7
1
O
15
6
6
8
ESOTERIC
94
49
22
-
-
9+4
4+9
2+2
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
1
O
15
6
6
6
SECRET
70
34
7
1
I
9
9
9
8
ESOTERIC
94
49
22
-
-
9+4
4+9
2+2
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
EGYPT
-
-
-
-
-
-
1
E
5
5
5
--
-
5
1
G
7
7
7
-
7
-
1
Y
25
7
7
-
7
-
1
P
16
7
7
-
7
-
1
T
20
2
2
--
-
2
5
EGYPT
73
28
28
-
21
7
-
-
7+3
2+8
2+8
-
2+1
-
5
EGYPT
10
10
10
--
3
7
-
-
1+0
1+0
1+0
-
-
-
5
EGYPT
1
7
7
--
3
7

 

 

EGYPT 57772 EGYPT

EGYPT

777

EGYPT

5+2 = 7 7 = 5+2

EGYPT

EGYPT 57772 EGYPT

EGYPT

EGYPT 57772 EGYPT

 

 

J
=
1
-
6
JOSEPH
73
28
1
J
=
1
-
5
JESUS
74
11
2
M
=
4
-
4
MARY
57
21
3
-
-
6
-
15
-
204
60
6
-
-
-
-
1+5
-
2+0+4
6+0
-
-
-
-
-
6
-
6
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
JOSEPH
1
6+1
7
-
-
-
-
5
JESUS
2
5+2
7
-
-
-
-
4
MARY
3
4+3
7

 

RE THE HOLY FAMILY
REMEMBER THE HOLY SEVEN
THE ROOT NUMBER OF THE 6 LETTERED JOSEPH = 1 (6+1) = 7
THE ROOT NUMBER OF THE 5 LETTERED JESUS = 2 (2+5) = 7
THE ROOT NUMBER OF THE 4 LETTERED MARY = 3 (4+3) = 7

 

J
=
1
-
6
JOSEPH
73
28
1
J
=
1
-
5
JESUS
74
11
2
M
=
4
-
4
MARY
57
21
3
-
-
6
-
15
-
204
60
6
-
-
-
-
1+5
-
2+0+4
6+0
-
-
-
-
-
6
-
6
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
JOSEPH
1
6+1
7
-
-
-
-
5
JESUS
2
5+2
7
-
-
-
-
4
MARY
3
4+3
7

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

THE BULL OF MINOS

Leonard Cottrell 1953

Chapter VII

Page 90

THE QUEST CONTINUES

"OUT IN THE DARK BLUE SEA THERE LIES A LAND CALLED CRETE, A RICH AND LOVELY LAND,

WASHED BY THE WAVES ON EVERY SIDE, DENSELY PEOPLED AND BOASTING NINETY CITIES. . .

ONE OF THE NINETY TOWNS IS A GREAT CITY CALLED KNOSSOS, AND THERE FOR NINE YEARS,

KING MINOS RULED AND ENJOYED THE FRIENDSHIP OF ALMIGHTY ZEUS

SUN 9 9 SUN

EARTH 7 7 EARTH

MOON 3 3 MOON

JUPITER 99 99 JUPITER

 

WHO SHALL I SAY SENT ME UNTO THEM

TELL THEM THAT I AM HATH SENT ME UNTO YOU

 

 

 

HARMONIC 288

Bruce Cathie

1977

THE MEASURE OF LIGHT

Page 95

"The search for this particular value was a lengthy one and the clue that led me finally to a possible solution was a study of the construction of the Grand Gallery. The height of the Gallery was the first indication that it was not just an elaborate access passage. Previous measurements made by scientific investigators pointed to some interesting possibilities."

Page 95

"The value that I calculated for length was extremely close to that of the one published in Davidson and Aldersmith's book, their value being

1836 inches,"

Page 95/97

"A search of my physics books revealed that 1836 was the closest approximation the scientists have calculated to the mass / ratio of the positive hydrogen ion, i.e. the proton, to the electron."

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT

I

PLANETS STARS AND LIFE

Page 24

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "

Page 24 / 25
"A manifestly artificial signal- even if it were as boring as lists of prime numbers, or the digits of 'pi' - would imply that 'intelli- gence' wasn't unique to the Earth and had evolved elsewhere. The nearest potential sites are so far away that signals would take many years in transit. For this reason alone, transmission would be primarily one-way. There would be time to send a measured response, but no scope for quick repartee!
Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.)
Clearly, alien beings wouldn't use metres, kilograms or seconds. But we could exchange information about the ratios of two masses (such as thc ratio of proton and electron masses) or of two lengths, which are 'pure numbers' that don't depend on what units are used: the statement that one rod is ten times as long as another is true (or false) whether we measure lengths / in feet or metres or some alien units"

 

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence'"

 

 

 

 
 
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