Previous Page
   Next Page
 
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

 

 

T
=
2
8
TRIANGLE
86
41
5
P
=
7
7
PYRAMID
86
41
5

 

 

TRIANGLE

 

 

-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
9
-
14
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
2
9
-
1
-
7
3
5
+
=
27
2+7
=
9
=
9
=
9
-
-
20
18
-
1
-
7
12
5
+
=
63
6+3
=
9
=
9
=
9
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
20
18
9
1
14
7
12
5
+
=
86
8+6
=
14
1+4
5
=
5
-
-
2
9
9
1
5
7
3
5
+
=
41
4+1
=
5
=
5
=
5
-
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
8
T
R
I
A
N
G
L
E
-
-
27
-
-
8
-
41
-
23
1+8
-
-
9
9
-
-
-
-
-
-
-
2+7
-
-
-
-
4+1
-
2+3
9
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5
-
-
2
9
9
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
9
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5

 

 

8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
9
-
14
-
-
-
+
=
23
2+3
=
5
=
5
=
5
8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
2
9
-
1
-
7
3
5
+
=
27
2+7
=
9
=
9
=
9
-
20
18
-
1
-
7
12
5
+
=
63
6+3
=
9
=
9
=
9
8
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
20
18
9
1
14
7
12
5
+
=
86
8+6
=
14
1+4
5
=
5
-
2
9
9
1
5
7
3
5
+
=
41
4+1
=
5
=
5
=
5
8
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
T
R
I
A
N
G
L
E
-
-
27
-
-
8
-
41
-
23
-
-
9
9
-
-
-
-
-
-
-
2+7
-
-
-
-
4+1
-
2+3
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5
-
2
9
9
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
8
T
R
I
A
N
G
L
E
-
-
9
-
-
8
-
5
-
5

 

 

T
=
2
-
8
TRIANGLE
86
41
5
P
=
7
-
7
PYRAMID
86
41
5

 

 

A
=
1
-
5
ANGLE
39
21
3
-
-
-
-
-
-
-
-
-
A
=
1
-
5
ANGEL
39
21
3

 

 

-
5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
7
3
5
+
=
16
1+6
=
7
=
7
=
7
-
-
1
-
7
12
5
+
=
25
2+5
=
7
=
7
=
7
-
5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
1
14
7
12
5
+
=
39
3+9
=
12
1+2
3
=
3
-
-
1
5
7
3
5
+
=
21
2+1
=
3
=
3
=
3
-
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
29
5
A
N
G
L
E
-
-
16
-
-
5
-
21
-
12
2+0
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3
-
-
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3

 

 

5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
1
-
7
3
5
+
=
16
1+6
=
7
=
7
=
7
-
1
-
7
12
5
+
=
25
2+5
=
7
=
7
=
7
5
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
1
14
7
12
5
+
=
39
3+9
=
12
1+2
3
=
3
-
1
5
7
3
5
+
=
21
2+1
=
3
=
3
=
3
5
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
5
A
N
G
L
E
-
-
16
-
-
5
-
21
-
12
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3
-
1
5
7
3
5
-
-
-
-
-
-
-
-
-
-
5
A
N
G
L
E
-
-
7
-
-
5
-
3
-
3

 

 

A
=
1
-
5
ANGLE
39
21
3
-
-
-
-
-
-
-
-
-
A
=
1
-
5
ANGEL
39
21
3

 

ANGEL AND ANGLE AND ANGLE AND ANGEL

 

-
5
A
N
G
E
L
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
5
A
N
G
E
L
-
-
-
-
-
--
-
-
-
-
-
-
1
-
7
5
3
+
=
16
1+6
=
7
=
7
=
7
-
-
1
-
7
5
12
+
=
25
2+5
=
7
=
7
=
7
-
5
A
N
G
E
L
-
-
-
-
-
--
-
-
-
-
-
-
1
14
7
5
12
+
=
39
3+9
=
12
1+2
3
=
3
-
-
1
5
7
5
3
+
=
21
2+1
=
3
=
3
=
3
-
5
A
N
G
E
L
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
29
5
A
N
G
E
L
-
-
16
-
-
5
-
21
-
12
2+0
-
-
-
-
-
-
-
-
1+6
-
-
-
-
2+1
-
1+2
2
5
A
N
G
E
L
-
-
7
-
-
5
-
3
-
3
-
-
1
5
7
5
3
-
-
-
-
-
-
-
-
-
-
2
5
A
N
G
E
L
-
-
7
-
-
5
-
3
-
3

 

 

ANGELS AND ANGLES ANGLES AND ANGELS

 

 

A
=
1
-
6
ANGELS
58
22
4
A
=
1
-
3
AND
19
10
1
A
=
1
-
6
ANGLES
58
22
4
-
-
3
-
15
Add to Reduce
135
54
9
-
-
-
-
1+5
Reduce to Deduce
1+3+5
5+4
-
Q
-
3
-
6
Essence of Number
9
9
9

 

 

-
15
A
N
G
E
L
S
-
A
N
D
-
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
---
-
5
-
---
-
5
-
-
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
-
14
-
-
-
19
---
-
14
-
---
-
14
-
-
-
19
+
=
80
8+0
=
8
=
8
=
8
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
5
3
-
--
1
-
4
--
1
-
7
3
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
1
-
7
5
12
-
--
1
-
4
--
1
-
7
12
5
-
+
=
55
5+5
=
10
1+0
1
=
1
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
14
7
5
12
19
--
1
14
4
--
1
14
7
12
5
19
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
5
7
5
3
1
--
1
5
4
--
1
5
7
3
5
1
+
=
54
5+4
=
9
=
9
=
9
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
2
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
3
-
--
-
-
-
--
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
--
-
-
4
--
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
--
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
---
-
-
-
---
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
--
-
-
-
--
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
--
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
--
-
-
-
-
--
-
-
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
--
-
-
-
-
--
-
-
25
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
20
-
-
15
-
54
-
27
2+5
1+5
1
5
7
5
3
1
---
1
5
4
---
1
5
7
3
5
1
-
-
2+0
-
-
1+5
-
5+4
-
2+7
7
6
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
2
-
-
6
-
9
-
9

 

 

5
A
N
G
E
L
S
-
A
N
D
-
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
---
-
5
-
---
-
5
-
-
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
14
-
-
-
19
---
-
14
-
---
-
14
-
-
-
19
+
=
80
8+0
=
8
=
8
=
8
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
-
7
5
3
-
--
1
-
4
--
1
-
7
3
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
1
-
7
5
12
-
--
1
-
4
--
1
-
7
12
5
-
+
=
55
5+5
=
10
1+0
1
=
1
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
14
7
5
12
19
--
1
14
4
--
1
14
7
12
5
19
+
=
135
1+3+5
=
9
=
9
=
9
-
1
5
7
5
3
1
--
1
5
4
--
1
5
7
3
5
1
+
=
54
5+4
=
9
=
9
=
9
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
1
occurs
x
5
=
5
=
5
-
-
-
-
-
3
-
--
-
-
-
--
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
--
-
-
4
--
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
7
-
-
-
--
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
--
-
-
-
-
--
-
-
-
1
-
-
-
-
1
--
1
-
-
--
1
-
-
-
-
1
-
-
--
-
-
-
-
--
-
-
-
-
5
-
5
-
-
--
-
5
-
--
-
5
-
-
5
-
-
-
--
-
-
-
-
--
-
-
15
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
20
-
-
15
-
54
-
27
1+5
1
5
7
5
3
1
---
1
5
4
---
1
5
7
3
5
1
-
-
2+0
-
-
1+5
-
5+4
-
2+7
6
A
N
G
E
L
S
--
A
N
D
--
A
N
G
L
E
S
-
-
2
-
-
6
-
9
-
9

 

 

THREE ANGLES THREE ANGELS THREE ANGELS THREE ANGLES

TRY ANLES ANGELS O ANGELS TRY ANGLES

 

 

THREE FOUR FIVE FIVE FOUR THREE

 

 

EQUILATERAL TRIANGLE

 

19
EQUILATERAL TRIANGLE
207
90
9

 

 

19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
23
2+3
=
5
-
5
=
5
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
14
-
-
-
+
=
32
3+2
=
5
-
5
=
5
19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
`-
5
17
21
9
12
1
20
5
18
1
12
-
20
18
9
1
14
7
12
5
+
=
207
2+0+7
=
9
-
9
=
9
-
5
8
3
9
3
1
2
5
9
1
3
-
2
9
9
1
5
7
3
5
+
=
90
9+0
=
9
=
9
=
9
19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
4
=
36
=
9
19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
35
-
-
19
-
90
-
36
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
9
-
-
-
-
-
-
-
3+5
-
-
1+9
-
9+0
-
3+6
19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
8
-
-
10
-
9
-
9
-
5
8
3
9
3
1
2
5
9
1
3
-
2
9
9
1
5
7
3
5
-
-
-
-
-
1+0
-
-
-
-
19
E
Q
U
I
L
A
T
E
R
A
L
-
T
R
I
A
N
G
L
E
-
-
8
-
-
10
-
9
-
9

 

 

ISOSCELES TRIANGLE

 

17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
9
1
6
1
-
-
-
-
1
-
-
-
9
-
5
-
-
-
+
=
31
3+1
=
4
-
4
=
4
-
9
19
15
19
-
-
-
-
19
-
-
-
9
-
14
-
-
-
+
=
85
8+5
=
13
1+3
4
=
4
17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
`-
9
19
15
19
3
5
12
5
19
-
20
18
9
1
14
7
12
5
+
=
173
1+7+3
=
11
1+1
2
=
2
-
9
1
6
1
3
5
3
5
1
-
2
9
9
1
5
7
3
5
+
=
74
7+4
=
11
1+1
2
=
2
17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
4
=
20
=
2
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
=
9
17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
33
-
-
17
-
75
-
39
-
9
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
3+3
-
-
 1+7
-
7+5
-
3+9
17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
6
-
-
8
-
12
-
12
-
9
1
6
1
3
5
3
5
1
-
2
9
9
1
5
7
3
5
-
-
-
-
-
-
-
1+2
-
1+2
17
I
S
O
S
C
E
L
E
S
-
T
R
I
A
N
G
L
E
-
-
33
-
-
17
-
75
-
39

 

 

17
ISOSCELES TRIANGLE
-
-
-
-
I
9
9
9
-
S+O
34
16
7
-
S+C+E
27
18
9
-
L+E+S
36
18
9
-
T
20
2
2
-
R
18
9
9
-
I
9
9
9
-
A+N+G+L+E
39
21
3
17
ISOSCELES TRIANGE
-
-
-

 

 

17
ISOSCELES TRIANGLE
192
74
2
12
ISOSCELES TRI
153
81
9
5
ANGLE
39
21
3

 

 

9
ISOSCELES
106
61
7
8
TRIANGLE
86
41
5
17
-
192
102
12
1+7
-
1+9+2
1+0+2
1+2
8
-
12
3
3
-
-
1+2
-
-
8
-
3
3
3

 

 

-
ISOSCELES TRIANGLE
-
-
-
12
I+S+O+S+C+E+L+E+S+T+R+I
153
81
9
5
A+N+G+L+E
39
21
3
17
ISOSCELES TRIANGLE
81
102
12
1+7
Add to Reduce
8+1
1+0+2
1+2
8
Reduce to Deuce
9
9
3

 

 

17
ISOSCELES TRIANGLE
192
102
3
19
EQUILATERAL TRIANGLE
207
90
9
19
RIGHT ANGLED TRIANGLE
191
101
2
55
First Total
590
293
14
5+5
Add to Reduce
5+9+0
2+9+3
1+4
10
Second Total
14
14
5
1+0
Reduce to Deuce
1+4
1+4
-
1
Essence of Number
5
5
5

 

 

17
ISOSCELES TRIANGLE
192
102
3
19
RIGHT ANGLED TRIANGLE
191
101
2

 

 

RIGHT ANGLED TRIANGLE

 

5
RIGHT
62
35
8
6
ANGLED
43
25
7
8
TRIANGLE
86
41
5
19
F
191
101
20
1+9
-
1+9+1
1+0+1
2+0
10
  
11
2
2
1+0
-
1+1
-
-
1
-
2
2
2

 

 

19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
8
-
-
-
5
-
-
-
-
-
-
-
9
-
5
-
-
-
+
=
36
3+6
=
9
-
9
=
9
-
-
9
-
8
-
-
-
14
-
-
-
-
-
-
-
9
-
14
-
-
-
+
=
54
5+4
=
9
-
9
=
9
19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
-
-
-
--
-
-
-
-
`-
18
9
7
8
20
-
1
14
7
12
5
4
-
20
18
9
1
14
7
12
5
+
=
191
1+9+1
=
11
1+1
2
=
2
-
9
9
7
8
2
-
1
5
7
3
5
4
-
2
9
9
1
5
7
3
5
+
=
101
1+0+1
=
2
=
2
=
2
19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
9
occurs
x
4
=
36
=
9
19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
39
-
-
19
-
101
-
38
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+9
-
1+0+1
-
3+8
19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
12
-
-
10
-
2
-
11
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
1+2
-
-
1+0
-
-
-
1+1
19
R
I
G
H
T
-
A
N
G
L
E
D
-
T
R
I
A
N
G
L
E
-
-
3
-
-
1
-
2
-
2

 

 

I

ME

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OUROBOROS 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..."

 

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

 

-pythagoras For integers m and n, {n2-m2, 2mn, n2+m2}is a pythagorean triangle. For m=1, n=2, you'll get {3, 4, 5}. I'll add a diagram so that this isn't completely ... www.mathpuzzle.com/pythagoras.html - Cached - Similar

 

-The Pythagorean Theorem First described by the Greek mathematician Pythagoras 2500 years ago, the Pythagorean ... For example: 3,4,5 or 6,8,10 or 9,12,15 or 12,16,20 ... etc ... www.worsleyschool.net/.../pythagoras/pythagoreantheorem.html - Cached - Similar

 

-pythagoras Pythagoras the 3-4-5 fallacy. ... Traditionally the example used to illustrate the Pythagorean theorem is the 3-4-5 diagram. This is a fallacy, ... www.marques.co.za/duke/pythagoras.htm - Cached - Similar -

 

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 -

 

 

I

ME

NUMBERS

EGYPTPYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OUROBOROS PYTHAGORAS

 

Pythagoras theorem states that

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

 

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
9
1+2
-
1+3
Add to Reduce
1+5+8
7+7
2+3
3
-
4
Second Total
14
14
5
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
12
-
-
-
14
-
13
First Total
158
77
9
1+2
-
-
-
1+4
-
1+3
Add to Reduce
1+5+8
7+7
2+3
12
-
-
-
5
-
4
Second Total
14
14
5
-
-
-
-
-
-
-
Reduce to Deduce
1+4
1+4
--
3
-
-
-
5
-
4
Essence of Number
5
5
5

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 38

"In the sphere of the natural sciences and of mathematics there have been endless disputes as to how much the Greeks borrowed from their neighbours, and the disputes are likely to continue, for the evidence is scanty and unreliable. It is safe to assume that the Greeks (noted then as now for commercial enterprise) took all they could get. Their own writers say as much, for they attribute the origin of very many useful inventions to other peoples. But this one thing, the scientific outlook and method, was not there to take; they had to invent it themselves. It is well to be clear on this point, for European civilization rests on three legs. They are Greek science, Jewish religion and Roman law. / Page 39 / Roman law may well be considered the Roman development of Greek scientific method. I will therefore deal with two examples in some little detail. These are taken from the sphere of mathematics and astronomy, for it was in these two sciences that the Greeks had their most outstanding success, doing about as much as could possibly be done under the conditions of their day and laying the foundations on which all subsequent work has been based.

The Egyptians knew of many useful methods of -geo- metrical calculation, for finding the area of a field, the volume of a barrel and so on. The Babylonians and earlier Mesopotamians had made accurate observations of sun, moon and stars over long periods and developed ingenious methods for calculating their future positions in the sky. In these arts of calculation these people had nothing to learn from the Greeks; it was the other way about. But there is no evidence that they ever dreamt of turning the art of calculation into the science of mathematics. Solving particular problems, however ingeniously, is not necessarily science any more than is playing chess (though all chess problems are geometrical) or keeping accounts (though all money reckoning is arithmetical). Mathematical science in the proper sense of the word attains its end by two means : (1) generalizing as far as is possible all problems and their solutions, so that one solution solves any number of particular cases; (2) finding proofs that solutions are correct as opposed to finding solutions which might be right by chance, not by necessity. The method used is the method of discussion in its specifically mathematical form.

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. They adjusted three pegs to make a triangle with the knots at the pegs when the cord was stretched tight round them. The Greeks, seeing this trick, generalized the problem and looked for a proof of the solution. The final result, after two centuries of effort, is the First Book of Euclid's Elements, leading up to Proposition 47—that the square on the hypotenuse of a right-angled triangle equals the sum of / Page 40 / the squares on the other sides, and that this must be so, granted the assumptions made at the beginning. (The proposition is further generalized in, Euclid VI, 31.) In this way a technical dodge of the land surveyor, depending upon the fact that 32+42= 52, was turned into science.

Page 38 Notes

1 Thucydides IV, 104—V, 26.
2 Hippocrates, Vol. ii, pp. 138 seq. Loeb Classical Library.

 

 

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

 

-pythagoras Pythagoras the 3-4-5 fallacy. ... Traditionally the example used to illustrate the Pythagorean theorem is the 3-4-5 diagram. This is a fallacy, ... www.marques.co.za/duke/pythagoras.htm - Cached - Similar -

 

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 -

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

 

 

-
-
-
-
-
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

 

PYTHAGORAS

7728176911

THE MISSING NUMBERS

3 - 4 - 5

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
A
=
1
-
1
A
1
1
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

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

3 AND 4 AND 5

 

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

 

 

 

PRECESSION OF THE EQUINOXES

 

24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
-
-
-
-
-
-
-
-
24
-
-
-
-
-
-
1
1
9
6
5
-
6
-
-
-
8
-
-
-
-
-
9
5
6
6
-
1
+
=
63
6+3
=
9
-
-
-
-
9
-
-
-
-
-
-
19
19
9
15
14
-
15
-
-
-
8
-
-
-
-
-
9
14
15
24
-
19
+
=
180
1+8+0
=
9
-
-
-
-
9
24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
-
-
-
-
-
-
-
-
-
-
16
18
5
3
5
-
-
-
-
-
-
-
6
-
20
-
5
-
5
17
 21
-
-
-
-
5
-
+
=
126
1+2+6
=
9
-
-
-
-
5
-
7
9
5
3
5
-
-
-
-
-
-
-
6
-
2
-
5
-
5
8
3
-
-
-
-
5
-
+
=
63
6+3
=
9
-
-
-
-
5
24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
-
-
-
-
-
-
-
-
-
`-
16
18
5
3
5
19
19
9
15
14
-
15
6
-
20
8
5
-
5
17
21
9
14
15
24
5
19
+
=
306
3+0+6
=
9
-
-
-
-
9
-
7
9
5
3
5
1
1
9
6
5
-
6
6
-
2
8
5
-
5
8
3
9
5
6
6
5
1
+
=
126
1+2+6
=
9
-
-
-
-
9
24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
2
-
-
-
3
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
5
-
-
-
5
-
-
5
-
-
-
5
occurs
x
7
=
35
3+5
=
8
-
-
-
-
-
-
-
-
-
6
-
-
6
6
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
6
occurs
-
5
-
30
3+0
=
3
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
7
-
  
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
=
7
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
=
9
24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
41
-
-
24
-
126
-
-
45
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
4+1
-
-
2+4
-
1+2+6
-
-
4+5
24
P
R
E
C
E
S
S
I
O
N
-
O
F
-
T
H
E
-
E
Q
U
I
N
O
X
E
S
-
-
5
-
-
6
-
9
-
-
9

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT

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'

 

The Abbe Sieyes author of the pamphlet What is the third estate? intrigued with Napoleon Bonaparte and became a Consul of the French Republic.
www.age-of-the-sage.org/historical/biography/abbe_sieyes.html

 

Qu'est-ce que le tiers état? ( What is the third estate? ).

The Abbé Sieyès "... it was in Paris that he spent his last days in 1836."

 

 

8
QUO VADIS
108
36
9
6
VOX POP
108
36
9
8
INSTINCT
108
36
9
8
STARTING
108
36
9
9
COMPLETES
108
36
9
7
JOURNEY
108
36
9

 

 

HOLY BIBLE

Scofield References

C 1 V 16

THE ACTS OF THE APOSTLES

Page 1148 (Part quoted)

"MEN AND BRETHREN THIS SCRIPTURE MUST NEEDS HAVE BEEN FULFILLED

WHICH THE HOLY GHOST BY THE MOUTH OF DAVID SPAKE"

 

 

THE ENGLISH ANGEL

Peter Burton & Harland Walshaw

Angles & Angels

The Venerable Bede tells the story of the slave boys from Northumbria in the Forum at Rome. St Gregory, struck by their fair hair and blue eyes, asks their nationality. When told that they are Angles, he replies, with one of those rare puns that work in two languages, 'Non Angli, sed angeli.' Not Angles, but angels.
Even so, we would not consider ourselves to be the most angelic of nations. Yet when you begin to look closely at our buildings and our monuments, our pubs and our cemeteries, our churches, lamp posts and theatres, you realise that we are a country infested by angels, in almost plague-like proportion: lurking in the hammer-beams, squatting on the gravestones, cherubim and seraphim floating in the vaulting. On ships' prows and shop fronts, on inn signs and organ cases, on floor tiles and roof bosses, winged figures decorate our world, haunting this godless age with the image of a spiritual past: heralds of God, their message now unheeded.
The profusion of angel carving, in church architecture, civic monument, and folk art, constitutes a decorative tradition which, if not exclusively English, has no parallel for its range and invention in any other country. There are famous foreign angels, such as those of Giselbertus in Autun, or the smiling angel of Reims; and Italian painting swarms with the creatures. But in England, no cathedral is complete without its celestial host, no graveyard without its guardians of the dead; and Anglo-angels playa secular role that leads them into places where you think they would fear to tread.
Nor are angels confined to the distant past. Some of the most powerful images in this book come from the twentieth century, and the piece of modern sculpture that has caught the public imagination is Anthony Gormley's Angel of the North, its glinting wings embracing the motorway traffic

Angels have also inhabited the imagination of English writers down the centuries. 'iVlost men know the make of angels and archangels: wrote Lord Byron, 'since there's scarce a scribbler has not one to show.' Most twentieth century scribblers, more surprisingly, had an angel to show from Robert Bridges to Ted Hughes, the poets laureate met their angels and relayed their messages. After all, the beginnings of English literature were angelically inspired. Caedmon, the first English poet, was a herdsman at Whitby Abbey when he was visited by an angel in a dream, who instructed him to write songs in his native tongue. Few poets who followed in his footsteps quite forgot their debt to Caedmon's angel.

Page 6

England is a country where angel footsteps have often trod. A pilgrimage to angelic sites would take us to the shrine of Our Lady of Walsingham, repositioned by angels on firmer foundations while the builders slept; to Glastonbury Tor, where St Joseph and his community of hermits were guided by the Archangel Gabriel to build the first Christian church in Britain; to St Michael's Mount off the Cornish coast, where in AD 495 some fishermen saw the blessed Archangel on a rocky ledge, and where miraculous cures for the toothache were reported after his divine intercession; and to the tomb of the first English historian, Bede himself, recorder of others' angelic experiences, whose epitaph was completed by an angel while the stone carver paused, searching for a suitable adjective: it was the angel who gave to Bede the posthumous title, 'Venerable'.
The history of angels in England is rich, varied and long, lasting from before the time of Bede, and unfinished yet.
.

Page 5

'Non Angli, sed angeli.' Not Angles, but angels.

 

NON ANGLI SED ANGELI

NOT ANGLES BUT ANGELS

 

N
=
5
-
3
NON
43
16
7
A
=
1
-
5
ANGLI
43
25
7
-
-
6
-
8
First Total
86
41
14
-
-
-
-
-
Add to Reduce
8+6
4+1
1+4
-
-
6
-
8
Second Total
14
5
5
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
6
-
8
Essence of Number
5
5
5

 

 

S
=
1
-
3
SED
28
10
1
A
=
1
-
6
ANGELI
48
30
3
-
-
2
-
9
First Total
76
40
4
-
-
-
-
-
Add to Reduce
7+6
4+0
-
-
-
2
-
9
Second Total
13
4
4
-
-
-
-
-
Reduce to Deduce
1+3
-
-
-
-
2
-
9
Essence of Number
4
4
4

 

 

N
=
5
-
8
NON ANGLI
86
41
5
S
=
1
-
9
SED ANGELI
76
40
4
-
-
6
-
17
Add to Reduce
162
81
4
-
-
-
-
1+7
Reduce to Deduce
1+6+2
8+1
-
-
-
6
-
8
Essence of Number
9
9
9

 

 

N
=
5
-
3
NOT
49
13
4
A
=
1
-
6
ANGLES
58
22
4
B
=
2
-
3
BUT
43
7
7
A
=
1
-
6
ANGELS
58
22
4
-
-
9
-
18
First Total
208
64
10
-
-
-
-
1+8
Add to Reduce
2+0+8
6+4
1+0
-
-
9
-
9
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
9
-
9
Essence of Number
1
1
1

 

 

8
NON ANGLI
86
41
5
9
SED ANGELI
76
40
4
17
Add to Reduce
162
81
4
1+7
Reduce to Deduce
1+6+2
8+1
-
8
Essence of Number
9
9
9

 

 

-
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
-
-
5
6
5
-
-
5
-
-
9
-
1
-
-
-
-
5
-
-
-
9
+
=
45
4+5
=
9
=
9
=
9
`-
`-
14
15
14
-
-
14
-
-
9
-
19
-
-
-
-
14
-
-
-
9
+
=
108
8+1
=
9
=
9
=
9
-
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
1
-
7
3
-
-
-
5
4
-
1
-
7
5
3
-
+
=
36
3+6
=
9
=
9
=
9
`-
`-
-
-
-
-
1
-
7
12
-
-
-
5
4
-
1
-
7
5
12
-
+
=
54
5+4
=
9
=
9
=
9
-
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
`-
`-
14
15
14
-
1
14
7
12
9
-
19
5
4
-
1
14
7
5
12
9
+
=
162
1+6+2
=
9
=
9
=
9
-
-
5
6
5
-
1
5
7
3
9
-
1
5
4
-
1
5
7
5
3
9
+
=
81
8+1
=
9
=
9
=
9
-
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
-
5
-
-
-
-
-
5
-
-
-
5
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
35
-
-
12
-
81
-
36
1+0
1+7
5
-
5
-
-
5
-
-
-
-
-
5
-
-
-
5
-
5
-
9
-
-
3+5
-
-
1+2
-
8+1
-
3+6
1
8
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
8
-
-
3
-
9
-
9
-
-
5
6
5
-
1
5
7
3
9
-
1
5
4
-
1
5
7
5
3
9
-
-
-
-
-
-
-
-
-
-
1
8
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
8
-
-
3
-
9
-
9

 

 

7
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
-
5
6
5
-
-
5
-
-
9
-
1
-
-
-
-
5
-
-
-
9
+
=
45
4+5
=
9
=
9
=
9
`-
14
15
14
-
-
14
-
-
9
-
19
-
-
-
-
14
-
-
-
9
+
=
108
8+1
=
9
=
9
=
9
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
1
-
7
3
-
-
-
5
4
-
1
-
7
5
3
-
+
=
36
3+6
=
9
=
9
=
9
`-
-
-
-
-
1
-
7
12
-
-
-
5
4
-
1
-
7
5
12
-
+
=
54
5+4
=
9
=
9
=
9
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
--
-
-
-
-
`-
14
15
14
-
1
14
7
12
9
-
19
5
4
-
1
14
7
5
12
9
+
=
162
1+6+2
=
9
=
9
=
9
-
5
6
5
-
1
5
7
3
9
-
1
5
4
-
1
5
7
5
3
9
+
=
81
8+1
=
9
=
9
=
9
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
5
-
-
5
-
-
-
-
-
5
-
-
-
5
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
17
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
35
-
-
12
-
81
-
36
1+7
5
-
5
-
-
5
-
-
-
-
-
5
-
-
-
5
-
5
-
9
-
-
3+5
-
-
1+2
-
8+1
-
3+6
8
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
8
-
-
3
-
9
-
9
-
5
6
5
-
1
5
7
3
9
-
1
5
4
-
1
5
7
5
3
9
-
-
-
-
-
-
-
-
-
-
8
N
O
N
-
A
N
G
L
I
-
S
E
D
-
A
N
G
E
L
I
-
-
8
-
-
3
-
9
-
9

 

 

N
=
5
-
3
NOT
49
13
4
A
=
1
-
6
ANGLES
58
22
4
B
=
2
-
3
BUT
43
7
7
A
=
1
-
6
ANGELS
58
22
4
-
-
9
-
18
First Total
208
64
10
-
-
-
-
1+8
Add to Reduce
2+0+8
6+4
1+0
-
-
9
-
9
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
9
-
9
Essence of Number
1
1
1

 

 

9
NOT ANGLES
107
35
8
9
BUT ANGELS
101
29
2
18
First Total
208
64
10
1+8
Add to Reduce
2+0+8
6+4
1+0
9
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
9
Essence of Number
1
1
1

 

 

-
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
-
-
5
6
-
-
-
5
-
-
-
1
-
-
-
-
-
-
5
-
-
-
1
+
=
23
2+3
=
5
=
5
=
5
`-
`-
14
15
-
-
-
14
-
-
-
19
-
-
-
-
-
-
14
-
-
-
19
+
=
95
9+5
=
14
=
5
=
5
-
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
2
-
1
-
7
3
5
-
-
2
3
2
-
1
-
7
5
3
-
+
=
41
4+1
=
5
=
5
=
5
`-
`-
-
-
20
-
1
-
7
12
5
-
-
2
21
20
-
1
-
7
5
12
-
+
=
113
1+1+3
=
5
=
5
=
5
-
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
`-
`-
14
15
20
-
1
14
7
12
5
19
-
2
21
20
-
1
14
7
5
12
19
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
5
6
2
-
1
5
7
3
5
1
-
2
3
2
-
1
5
7
5
3
1
+
=
64
6+4
=
10
1+0
1
=
1
-
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
2
-
-
-
-
-
21
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
24
-
-
18
-
64
-
37
2+1
1+8
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
5
-
-
-
-
2+4
-
-
1+8
-
6+4
-
3+7
3
9
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
6
-
-
9
-
10
-
10
-
-
5
6
2
-
1
5
7
3
5
1
-
2
3
2
-
1
5
7
5
3
1
-
-
-
-
-
-
-
1+0
-
1+0
3
9
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
6
-
-
9
-
1
-
1

 

 

18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
-
5
6
-
-
-
5
-
-
-
1
-
-
-
-
-
-
5
-
-
-
1
+
=
23
2+3
=
5
=
5
=
5
`-
14
15
-
-
-
14
-
-
-
19
-
-
-
-
-
-
14
-
-
-
19
+
=
95
9+5
=
14
=
5
=
5
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
2
-
1
-
7
3
5
-
-
2
3
2
-
1
-
7
5
3
-
+
=
41
4+1
=
5
=
5
=
5
`-
-
-
20
-
1
-
7
12
5
-
-
2
21
20
-
1
-
7
5
12
-
+
=
113
1+1+3
=
5
=
5
=
5
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
--
-
-
-
-
`-
14
15
20
-
1
14
7
12
5
19
-
2
21
20
-
1
14
7
5
12
19
+
=
208
2+0+8
=
10
1+0
1
=
1
-
5
6
2
-
1
5
7
3
5
1
-
2
3
2
-
1
5
7
5
3
1
+
=
64
6+4
=
10
1+0
1
=
1
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
2
-
-
-
-
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
18
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
24
-
-
18
-
64
-
37
1+8
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
5
-
-
-
-
2+4
-
-
1+8
-
6+4
-
3+7
9
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
6
-
-
9
-
10
-
10
-
5
6
2
-
1
5
7
3
5
1
-
2
3
2
-
1
5
7
5
3
1
-
-
-
-
-
-
-
1+0
-
1+0
9
N
O
T
-
A
N
G
L
E
S
-
B
U
T
-
A
N
G
E
L
S
-
-
6
-
-
9
-
1
-
1

 

 

CONCERNING THE SAPTARSHI

IMAGINE HOW WOULD SUCH A ONE AS THAT ARRIVE ON PLANET EARTH

A

STARSHIP

?

 

 

-
QUO VADIS
-
-
-
1
Q
17
8
8
1
U
21
3
3
1
O
15
6
6
5
VADIS
55
19
1
9
QUO VADIS
108
36
18
-
-
1+0+8
3+6
1+8
9
QUO VADIS
9
9
9

 

 

-
QUO VADIS
-
-
-
5
VADIS
55
19
1
1
Q
17
8
8
1
U
21
3
3
1
O
15
6
6
9
QUO VADIS
108
36
18
-
-
1+0+8
3+6
1+8
9
QUO VADIS
9
9
9

 

 

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

 

 

THE ANANGA RANGA OF KALYANA MALLA

Translated By Sir Richard Burton and F. F. Arbuthnot

and

THE SYMPOSIUM OF PLATO

Translated By Benjamin Jowett

Edition 1963

Page 9

THE PLATONIC AND HINDU ATTITUDES TO LOVE AND SEX

by

Kenneth Walker


"PLATO, who was born in 428-7 B.C., devoted four of his dialogues mainly to the questions of love and sexual pleasure, the Lysis, the Symposium, the Phaedrus and the Philebus, qf which the Symposium and the Phaedrus are by far the most important. The opening words of the Philebus state in the clearest possible form the opposing points of view of the popular pursuit of pleasure and the sterner Platonic attitude:

"Philebus was saying that enjoyment and pleasure and delight, and the class of feelings akin to them, are a good to every living being, whereas I contend, that not these, but wisdom and intelligence and memory, and their kindred, right opinion and true reasoning, are better and more desirable than pleasure for all who are able to partake of them, and that to all such who are or ever will be they are the most advantageous of all things. Have I not given, Philebus, a fair statement of the two sides of the argument? "
Although in the Lysis and the Symposium the treatment is poetical and romantic, in the latter dialogue the inferiority of physical love is considerably stressed. /Page 10/ The seeker for truth is advised to proceed step by step, from the love of human forms to the virtually mystical contemplation of the abstract ideal of beauty itself. This is summarised at the conclusion of Socrates' famous speech:

"He who has been instructed thus far in the things of love, and who has learned to see the beautiful in due order and succession, when he comes toward the end will suddenly perceive a nature of wondrous beauty-a nature which in the first place is ever­lasting, not growing and decaying, or waxing and waning; secondly, not fair in one point of view and foul in another, or at one time or in one relation or at one place fair, at another time or in another relation or at another place foul, as if fair to some and foul to others, or in the likeness of a face or hands or any other part of the bodily frame, or in any form of speech or knowledge, or existing in any other being, as for example, in an animal, or in heaven, or in earth, or in any other place; but beauty absolute separate simple and everlasting, which without diminution and without increase, or any change, is imparted to the ever-growing and perishing beauties of all other things. He who from these ascending under the influence of true love, begins to perceive that beauty, is not far from the end. And the true order of going, or being led by another, to the things of love, is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps only, and from one going on to two, and from two to all fair forms, and from fair arms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the /Page 11/ absolute beauty, and at last knows what the essence of beauty is ... In that communion only, beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality), and bringing forth and nourishing true virtue to become the friend of god and be immortal, if mortal man may."

The Phaedrus was written in Athens in the fourth century B.C. and probably in Plato's middle years. The opening theme of the work is the art of rhetoric and this leads to a discussion of love. There follows the memorable allegory of the charioteer, Reason, and his two horses, representing the moral and con­cupiscent elements in human nature. This formulation of the tripartite nature. of the soul has been fundamental to Western philosophy. Here is the distinction which is reflected in the warring of the flesh and the spirit, of which St. Paul and so many later Christian teachers speak. Plato, it is true, did not make an absolute separation of these two aspects of the soul, aware as he was of the ease with which the higher passes into the lower or the lower can be "tamed and humbled, and follow the will of the charioteer". Such concepts are common in the strains of Christian mysticism. St. Francis would gladly have echoed th sentiment of the great final prayer of this work: "Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul: and may the outward and the inward man be at one". But it is undoubted that from the denigration of the senses, cleaHy laid down in Plato's last work, the Laws, and which is certainly implicit in the Phaedrus, 'stems the tenacious tradition in the /Page 12/ West that the body and its desires should be treated with severe discipline, as unworthy of the higher nature of man and tending to deprive him of true happiness and harmony."

 

"BELOVED PAN AND ALL YE OTHER GODS WHO HAUNT THIS PLACE,

GIVE ME BEAUTY IN THE INWARD SOUL: AND MAY THE OUTWARD AND THE INWARD MAN BE AT ONE".

 

 

Humanitites Institute Colloquium: Redefining Nature's Boundaries ... - 10:37pm
Plato wrote of his teacher Socrates invoking a prayer in a grove of Attica to Pan, god of nature: “Beloved Pan, and all ye other gods who haunt this place, ...
www.bucknell.edu/x31103.xml - Cached - Similar

Plato wrote of his teacher Socrates invoking a prayer in a grove of Attica to Pan, god of nature: “Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul; and may the outward and inward man be at one.” A few centuries later, the writer Plutarch described the announcement of the death of Pan in the heyday of the Roman Empire. Thamus, an Egyptian pilot called by a mysterious voice while at sea, is told to announce the death of the god. “Looking toward the land, he said the words as he had heard them: ‘Great Pan is dead.’ Even before he had finished there was a great cry of lamentation, not of one person, but of many, mingled with exclamations of amazement.”

 

Pan (mythology) - Wikipedia, the free encyclopedia
The god, still infatuated, took some of the reeds, because he could not identify ... When you reach Palodes, take care to proclaim that the great god Pan is dead. .... Vinci, Leo (1993), Pan: Great God Of Nature, Neptune Press, London ... en.wikipedia.org/wiki/Pan_(mythology)

 

The Death of Pan

Pan, Mikhail Vrubel 1900.If one were to believe the Greek historian Plutarch (in "The Obsolescence of Oracles" (Moralia, Book 5:17)), Pan is the only Greek god who is dead. During the reign of Tiberius (A.D. 14-37), the news of Pan's death came to one Thamus, a sailor on his way to Italy by way of the island of Paxi. A divine voice hailed him across the salt water, "Thamus, are you there? When you reach Palodes,[17] take care to proclaim that the great god Pan is dead." Which Thamus did, and the news was greeted from shore with groans and laments.

Robert Graves (The Greek Myths) suggested that the Egyptian Thamus apparently misheard Thamus Pan-megas Tethnece 'the all-great Tammuz is dead' for 'Thamus, Great Pan is dead!' Certainly, when Pausanias toured Greece about a century after Plutarch, he found Pan's shrines, sacred caves and sacred mountains still very much frequented.

 

 

GREAT PAN IS NOT DEAD

 

Shakespeare Quotes - Such Stuff as Dreams Are Made on.
www.enotes.com/shakespeare-quotes/we-such-stuff-dreams-made

The Tempest Act 4, scene 1, William Shakespeare

 

Prospero:
Our revels now are ended. These our actors,
As I foretold you, were all spirits, and
Are melted into air, into thin air:
And like the baseless fabric of this vision,
The cloud-capp'd tow'rs, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep.

 

 

2
WE
28
10
1
3
ARE
24
15
6
4
SUCH
51
15
6
5
STUFF
72
18
9
2
AS
20
2
2
6
DREAMS
60
24
6
3
ARE
24
15
6
4
MADE
23
14
5
2
ON
29
11
2
3
AND
19
10
1
3
OUR
54
18
9
4
LITTLE
78
24
6
4
LIFE
32
23
5
2
IS
28
10
1
7
ROUNDED
81
36
9
4
WITH
60
24
6
1
A
1
1
1
5
SLEEP
57
21
3
66
First Total
741
291
84
6+6
Add to Reduce
7+4+1
2+9+1
8+4
12
Second Total
12
12
12
1+2
Reduce to Deduce
1+2
1+2
1+2
3
Essence of Number
3
3
3

 

 

G
=
7
-
3
GOD
26
17
8
I
=
9
-
2
IS
28
10
1
E
=
5
-
10
EVERYWHERE
134
62
8
I
=
9
-
2
IS
28
10
1
E
=
5
-
10
EVERYTHING
133
61
7
I
=
9
-
2
IS
28
10
1
P
=
7
-
7
PERFECT
73
37
1
-
-
51
-
36
Add to Reduce
450
207
27
-
-
5+1
-
3+6
Reduce to Deduce
4+5+0
2+0+7
2+7
-
-
6
-
9
Essence of Number
9
9
9

 

 
 
Top
  
 
Evokation
  
Previous Page
Index
 Next Page