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Evokation
  
 
Index
  

 

 

-
ALL IS NUMBER
-
-
-
3
ALL
25
7
7
2
IS
28
10
1
6
NUMBER
73
28
1
11
ALL IS NUMBER
126
45
9
1+1
-
1+2+6
4+5
-
2
ALL IS NUMBER
9
9
9

 

 

-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
-
-
-
-
5
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
14
9
-
-
-
19
-
-
-
-
-
14
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
1
3
-
3
1
-
7
3
1
7
5
+
=
52
5+2
=
7
=
7
=
7
-
-
21
-
-
22
5
18
-
1
12
-
12
1
-
7
21
1
7
5
+
=
133
1+3+3
=
7
=
7
=
7
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
1
12
-
12
1
14
7
21
1
7
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
+
=
72
7+2
=
9
=
9
=
9
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
1
-
-
-`
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
16
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
29
-
-
17
-
72
-
27
1+6
1+7
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
1+7
-
7+2
-
2+7
7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
11
-
-
8
-
9
-
9
-
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
-
-
1+1
-
-
-
-
-
-
-
7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
2
-
-
8
-
9
-
9

 

 

17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
-
-
-
-
5
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
14
9
-
-
-
19
-
-
-
-
-
14
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
1
3
-
3
1
-
7
3
1
7
5
+
=
52
5+2
=
7
=
7
=
7
-
21
-
-
22
5
18
-
1
12
-
12
1
-
7
21
1
7
5
+
=
133
1+3+3
=
7
=
7
=
7
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
1
12
-
12
1
14
7
21
1
7
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
+
=
72
7+2
=
9
=
9
=
9
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
1
-
-
-`
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
-
3
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
29
-
-
17
-
72
-
27
1+7
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
1+7
-
7+2
-
2+7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
11
-
-
8
-
9
-
9
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
-
-
1+1
-
-
-
-
-
-
-
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
2
-
-
8
-
9
-
9

 

 

-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
5
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
-
9
19
-
14
-
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
3
3
-
-
-
-
-
3
4
2
5
9
+
=
30
3+0
=
3
=
3
=
3
-
-
1
12
12
-
-
-
-
-
21
13
2
5
18
+
=
84
8+4
=
12
1+2
3
=
3
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
12
12
-
9
19
-
14
21
13
2
5
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
1
3
3
-
9
1
-
5
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
3
-
-
-
-
-`
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
21
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
24
-
-
11
-
45
-
27
2+1
1+1
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
2+4
-
-
1+1
-
4+5
-
2+7
3
2
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
6
-
-
2
-
9
-
9

 

 

11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
5
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
9
19
-
14
-
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
3
3
-
-
-
-
-
3
4
2
5
9
+
=
30
3+0
=
3
=
3
=
3
-
1
12
12
-
-
-
-
-
21
13
2
5
18
+
=
84
8+4
=
12
1+2
3
=
3
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
12
12
-
9
19
-
14
21
13
2
5
18
+
=
126
1+2+6
=
9
=
9
=
9
-
1
3
3
-
9
1
-
5
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
3
-
-
-
-
-`
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
24
-
-
11
-
45
-
27
1+1
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
2+4
-
-
1+1
-
4+5
-
2+7
2
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
6
-
-
2
-
9
-
9

 

 

-
ALL IS NUMBER
-
-
-
3
ALL
25
7
7
2
IS
28
10
1
6
NUMBER
73
28
1
11
ALL IS NUMBER
126
45
9
1+1
-
1+2+6
4+5
-
2
ALL IS NUMBER
9
9
9

 

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

"'Into the Comet' and 'The Nine Billion Names of God' both involve computers and the troubles they may cause us. While writing this preface, I had occasion to call upon my own HP 9100A computer, Hal Junior, to answer an interesting question. Looking at my records, I find that I have now written just about one hundred short stories. This volume contains eighteen of them: therefore, how many possible 18-story collections will I be able to put together? The answer ­as I am sure will be instantly obvious to you - is 100 x 99. . . x 84 x 83 divided by 18 x 17 x 16 ... x .2 x 1. This is an impressive number - Hal Junior tells me that it is approximately 20,772,733,124,605,000,000.

Page 15

The Nine Billion Names of God

 

3
THE
33
15
6
4
NINE
42
24
6
7
BILLION
73
37
1
5
NAMES
52
16
7
2
OF
21
12
3
3
GOD
26
17
8
24
-
247
121
31
2+4
-
2+4+7
1+2+1
3+1
6
-
13
4
4
-
-
1+3
-
-
6
-
4
4
4

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

The Nine Billion Names of God

Page 15 (number missing)
'This is a slightly unusual request,' said Dr Wagner, with what he hoped was commendable restraint. 'As far as I know, it's the first time anyone's been asked to supply a Tibetan monastery with an Automatic Sequence Computer. I don't wish to be inquisitive, but I should hardly have thought that your - ah - establishment had much use for such a machine. Could you explain just what you intend to do with it?'
'Gladly,' replied the lama, readjusting his silk robes and carefully putting away the slide rule he had been using far currency conversions. 'Your Mark V Computer can carry out any routine mathematical operation involving up to ten digits. However, for our work we are interested in letters, not numbers. As we wish you to modify the output circuits, the machine will be printing words, not columns of figures.'
'I don't quite understand. . .'
'This is a project on which we have been working for the last three centuries - since the lamasery was founded, in fact. It is somewhat alien to your way of thought, so I hope you will listen with an open mind while I explain it.'
'Naturally.'
'It is really quite simple. We have been compiling a list which shall contain all the possible names of God.'
'I beg your pardon?'

Page16

'We have reason to believe,' continued the lama imperturbably, 'that all such names can be written with not more than nine letters in an alphabet we have devised.'
'And you have been doing this for three centuries?'
'Yes: we expected it would take us about fifteen thousand years to complete the task.'
'Oh,' Dr Wagner looked a little dazed. 'Now I see why you wanted to hire one of our machines. But what exactly is the purpose of this project?'
The lama hesitated for a fraction of a second, and Wagner wondered if he had offended him. If so, there was no trace of annoyance in the reply.
'Call it ritual, if you like, but it's a fundamental part of our belief. All the many names of the Supreme Being - God Jehova, Allah, and so on - they are only man-made labels. There is a philosophical problem of some difficulty here, which I do not propose to discuss, but somewhere among all the possible combinations of letters that can occur are what one may call the real names of God. By systematic permutation of letters, we have been trying to list them all.'
'I see. You've been starting at AAAAAAA . . . and working up to ZZZZZZZZ . . .'
'Exactly - though we use a special alphabet of our own. Modifying the electromatic typewriters to deal with this is, of course, trivial. A rather more interesting problem is that of devising suitable circuits to eliminate ridiculous combinations. For example, no letter must occur more than three times in succession.'
,'Three? Surely you mean two.'
'Three is correct: I am afraid it would take too long to explain why, even if you understood our language.' "

 

I = 9 9 = I

R = 9 9 = R

 

OF

T9ME AND STA9S

A9thu9 C. Cla9ke,1972

Page 15

THE N9NE B9LL9ON NAMES OF GOD

'Th9s 9s a sl9ghtly unusual 9equest,'sa9d D9 Wagne9, w9th what he hoped was commendable 9est9a9nt.' As fa9 as 9 know, 9t's the f99st t9me anyone's been asked to supply a T9betan monaste9y with an Automat9c Sequence Compute9. 9 don't w9sh to be 9nqu9s9t9ve, but 9 should ha9dly have thought that you9- ah - establ9shment had much use for such a mach9ne.Could you expla9n just what you 9ntend to do w9th 9t?'

'Gladly,' 9epl9ed the lama, 9eadjust9ng h9s s9lk 9obes and ca9efully putting away the sl9de 9ule he had been us9ng fo9 cu99ency conve9s9ons. 'You9 Ma9k V Compute9 can ca99y out any 9out9ne mathemat9cal ope9at9on 9nvolv9ng up to ten d9g9ts. Howeve9, for ou9 work we are 9nte9ested 9n lette9s, not numbe9s. As we w9sh you to mod9fy the output c9rcu9ts,the mach9ne w9ll be p99nt9ng wo9ds not columns of f9gu9es.'

'9 dont qu9te unde9stand…'

'Th9s 9s a p9oject on wh9ch we have been work9ng fo9 the last th9ee centu99es - s9nce the lamase9y was founded, 9n fact.9t 9s somewhat al9en to you9 way of thought, so9 hope you w9ll l9sten with an open m9nd wh9le 9 expla9n 9t

'Natu9ally.'

'9t 9s 9eally qu9te s9mple.We have been comp9l9ng a l9st wh9ch shall conta9n all the poss9ble names of God'

'9 beg you9 pa9don?' / Page16 / 'We have 9eason to bel9eve' cont9nued the lama 9mpe9tu9bably, ' that all such names can be w99tten with not mo9e than n9ne lette9s 9n an alphabet we have dev9sed,'

'And you have been do9ng th9s for three centu99es?

'Yes: we expected9t would take us about f9fteen thousand years to complete the task.'

'Oh, Dr Wagne9 looked a l9ttle dazed. 'Now9 see why you wanted to h99e one of ou9 mach9nes. But what exactly9s the pu9pose of th9s p9oject ?

'The lama hes9tated fo9 a f9act9on of a second, and Wagne9 wonde9ed9f he had offended h9m.9f so the9e was no t9ace of annoyance9n the 9eply.

'Call9t 99tual, 9f you l9ke, but 9t's a fundamental pa9t of ou9 bel9ef. All the many names of the Sup9eme Be9ng - God , Jehova , Allah , and so on - they a9e only man made labels. The9e 9s a ph9losoph9cal p9oblem of some d9ff9culty he9e, wh9ch9 do not p9opose to d9scuss, but somewhe9e among all the poss9ble comb9nat9ons of lette9s that can occu9 a9e what one may call the 9eal names of God. By systemat9c pe9mutat9on of lette9s, we have been t9y9ng to l9st them all'

9 see. You've been sta9t9ng at AAAAAAA… and wo9k-9ng up to ZZZZZZZZ …'

'Exactly - though we use a spec9al alphabet of ou9 own. Mod9fy9ng the elect9omat9c typew99te9s to deal w9th th9s 9s of cou9se t99v9al. A 9athe9 mo9e 9nte9est9ng p9oblem 9s that of dev9s9ng su9table c99cu9ts to el9m9nate 9 9d9culous comb9nat9ons. Fo9 example, no lette9 must occu9 mo9e than th9ee t9mes 9n sucess9on.'

'Th9ee? Su9ely you mean two.'

'Th9ee 9s co99ect; 9 am af9a9d 9t would take too long to expla9n why , even 9f you unde9stood ou9 language.'/ Page 17 / '9'm su9e 9t would,' sa9d Wagne9 hast9ly. 'Go on.'

'Luck9ly, 9t w9ll be a s9mple matte9 to adapt you9 Automat9c Sequence Compute9 fo9 th9s wo9k, s9nce once 9t has been p9og9ammed p9ope9ly 9t w9ll pe9mute each lette9 9n tu9n and p99nt the 9esult. What would have taken us f9fteen thousand years 9t w9ll be able to do 9n a hund9ed days.'

'Dr Wagne9 was sca9cely consc9ous of the fa9nt sounds f9om the Manhatten st9eets fa9 below. He was 9n a d9ffe9ent wo9ld, a wo9ld of natu9al, not man-made mounta9ns. H9gh up 9n the99 9emote ae99es these monks had been pat9ently at wo9k gene9at9on afte9 gene9at9on, comp9l9ng the99 l9sts of mean9ngless wo9ds. Was the9e any l9m9ts to the foll9es of mank9nd ? St9ll, he must g9ve no h9nt of h9s 9nne9 thoughts. The custome9 was always 99ght…"

Page 68

Into the Comet


"Pickett's fingers danced over the beads, sliding them up and down the wires with lightning speed. There were twelve wires in all, so that the abacus could handle numbers up to 999,999,999,999 - or could be divided into separate sections where several independent calculations could be carried out simultaneously.
'374072,' said Pickett, after an incredibly brief interval of time. 'Now see how long you take to do it, with pencil and paper.'
There was a much longer delay before Martens, who like most mathematicians was poor at arithmetic, called out '375072'. A hasty check soon confirmed that Martens had taken at least three times as long as Pickett to arrive at the wrong answer.
The atronomer's face was a study in mingled chagrin, astonishment, and curiosity.
'Where did you learn that trick?' he asked. 'I thought those things could only add and subtract.'
'Well - multiplication's only repeated addition, isn't it? All I did was to add 856 seven times in the unit column, three times in the tens column, and four times in the hundreds column. You do the same thing when you use pencil and paper. Of course, there are some short cuts, but if you think I'm fast, you should have seen my granduncle. He used to work in a Yokohama bank, and you couldn't see his fingers / Page 69 / when he was going at speed"

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

Abacus - Wikipedia
https://en.wikipedia.org/wiki/Abacus

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown.

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and ?3/4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.

 

A
=
1
-
1
A
1
1
1
C
=
3
-
8
COUNTING
103
40
4
T
=
2
-
5
TABLE
40
13
4
-
-
6
-
14
Add to Reduce
144
54
9
-
-
-
-
1+4
Reduce to Deduce
1+4+4
5+4
1+6
-
-
6
-
5
Essence of Number
9
9
9

 

 

 

 

 

10
PRIME NUMBERS
-
-
-
5
P+R+I+M+E
61
34
7
7
N+U+M+B+E+R+S
92
38
2
12
PRIME NUMBERS
153
72
9
1+2
-
1+5+3
7+2
-
3
PRIME NUMBERS
9
9
9

 

 

12
PRIME NUMBERS
153
72
9
3
ZERO
64
28
1

 

ATEN

A

TEN

 

12
PRIME NUMBERS
153
72
9
3
ZERO
64
28
1
15
Add to Reduce
217
100
10
1+5
Reduce to Deduce
2+1+7
 1+0+0
1+0
6
Essence of Number
TEN
1
1

 

 

5
PRIME
61
34
7
6
NUMBER
73
28
1
11
-
134
62
8
1+1
-
1+3+4
6+2
-
2
-
8
8
8

 

 

5
PRIME
61
34
7
7
NUMBERS
92
38
2
12
F
153
72
9
1+2
-
1+5+3
7+2
-
3
-
9
9
9

 

 

4
ZERO
64
28
1
6
NUMBER
73
28
1

 

4
ZERO
64
28
1
7
NUMBERS
92
38
2

 

 

11
NOTHINGNESS
144
54
9
4
ZERO
64
28
1

 

 

8
CALCULUS
-
-
-
1
C
3
3
3
1
A
1
1
1
1
L
12
3
3
1
C
3
3
3
1
U
21
3
3
1
L
12
3
3
1
U
21
3
3
1
S
19
10
1
8
CALCULUS
92
29
20
-
-
9+2
2+9
2+0
8
CALCULUS
11
11
2
-
-
1+1
1+1
-
5
CALCULUS
2
2
2

 

 

10
CALCULATES
97
34
7
7
NUMBERS
92
38
2
17
First Total
189
72
9
1+7
Add to Reduce
1+8=9
7+2
-
8
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
8
Essence of Number
9
9
9

 

 

10
PRECESSION
123
69
6
2
OF
21
12
3
3
THE
33
15
6
9
EQUINOXES
129
57
3
24
Add to Reduce
306
153
18
2+4
Reduce to Deduce
3+0+6
1+5+3
1+8
6
Essence of Number
9
9
9

 

 

15
THE PYRAMID TEXTS
19
10
1
N
THE
33
15
6
-
PYRAMID
86
41
5
-
TEXTS
88
25
7

15
THE PYRAMID TEXTS
207
81
18
-
-
2+0+7
8+1
1+8

15
THE PYRAMID TEXTS
9
9
9

 

THISISTHESCENEOFTHESEENUNSEENTHEUNSEENSEENOFTHESCENEUNSEENTHISISTHESCENE

 

3
THE
33
15
6
5
GREAT
51
24
6
7
PYRAMID
86
41
5
2
OF
21
12
3
4
GIZA
43
25
7
21
Add to Reduce
234
117
27
2+1
Reduce to Deduce
2+3+4
1+1+7
2+7
3
Essence of Number
9
9
9

 

 

-
PHARAOH + PYRAMID
19
10
-
7
PHARAOH
67
40
4
7
PYRAMID
86
41
5
14
PYRAMID + PHARAOH
153
81
9
1+4
-
1+7+1
8+1
-
5
PHARAOH + PYRAMID
9
9
9

 

 

-
OSIRIS ISIS SET
-
-
-
8
OSIRIS
89
44
8
4
ISIS
56
38
2
3
SET
44
17
8
15
SET ISIS OSIRIS
189
99
18
1+5
-
1+8+9
9+9
1+9
6
ISIS OSIRIS SET
18
18
9
-
-
1+8
1+8
-
6
OSIRIS SET ISIS
9
9
9
-
-
-
-
-
8
NAMES OF GOD
99
45
9

 

1 x 8 x 9 = 72 = 8 x 9 x 1

 

 

3
RED
27
18
9
6
SET
44
17
8

 

 

6
OSIRIS
89
35
9
-
8 x 9
72
-
-
6
OSIRIS
89
35
9

 

 

 

HOLY BIBLE

REVELATION

Chapter 21 V 1-7

Page 1351

A New Heaven and a New Earth

1And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea. 2And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. 3And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God. 4And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.

5And he that sat upon the throne said, Behold, I make all things new. And he said unto me, Write: for these words are true and faithful. 6And he said unto me, It is done. I am Alpha and Omega, the beginning and the end. I will give unto him that is athirst of the fountain of the water of life freely. 7He that overcometh shall inherit all things; and I will be his God, and he shall be my son.

FOR SON ALSO READ DAUGHTER FOR DAUGHTER ALSO READ SON.

 

GOD

ALMIGHTY

IS

 

-
-
-
-
-
AHAEL
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
18
-
5
AHAEL
27
18
18
-
2
2
3
4
5
6
7
8
9
-
-
1+8
-
-
-
2+7
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
AHAEL
9
9
9
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
AHAEL
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
18
-
5
AHAEL
27
18
18
-
2
2
3
4
5
6
7
8
9
-
-
1+8
-
-
-
2+7
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
AHAEL
9
9
9
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
AHAEL
-
-
-
-
1
3
5
8
A
=
1
-
1
A
1
1
1
-
1
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
L
=
3
-
1
L
12
3
3
-
-
3
-
-
E
=
5
-
1
E
5
5
5
-
-
-
5
-
H
=
8
-
1
H
8
8
8
-
-
-
-
8
-
-
18
-
5
AHAEL
27
18
18
-
2
3
5
8
-
-
1+8
-
-
-
2+7
1+8
1+8
-
-
-
-
-
-
-
9
-
5
AHAEL
9
9
9
-
2
3
5
8

 

 

RAPHAEL AHAEL RAPHAEL

 

The Mystery of The Seventh Seal - Sacred Texts
www.sacred-texts.com/grim/moses6/m607.htm

Seal of the Angels of the Seven Planets and Spirits. CONJURATION. I, N.N., a servant of God, call upon, desire, and conjure thee, Ahael, Banech, by the most holy words Agios, (Tetr.,) Eschiros, Adonai, Alpha et Omega, Raphael, Michael, Uriel, Schmaradiel, Zaday, and by all the known names of Almighty God, by whatever ...

 

 

6th and 7th Books of Moses | Aaron | Names Of God In ... - Scribd
https://es.scribd.com/document/96554895/6th-and-7th-Books-of-Moses

The Mystery of The Seventh Seal Sacred Texts Grimoires Index Previous THE MYSTERY OF THE SEVENTH SEAL.sacred-texts. ... Ahael. Germany [1849] See Also The Sixth Book of Moses Title Page The Twelve Tables of the Spirits THE FIRST TABLE OF THE SPIRITS OF THE AIR THE SECOND TABLE OF THE SPIRITS ...

 

What does the name AHAEL mean? - Namemeaningsdictionary
namemeaningsdictionary.com/meaning-of-the.../ahael/what-does-the-name-ahael-mea...

The Horoscope and Astrology meaning of the name AHAEL. AHAEL means: With a Life Path 9, your numbers are (9, 18/9, 27/9, 36/9). Considered to be feminine and introvert, number nine stands for universal love, eternity and faith, creative abilities, loyalty. It relates to wisdom and creativity. Nine has qualities of leadership, ...

 

HOLY BIBLE

THE REVELATION OF SAINT JOHN THE DIVINE

1The Revelation of Jesus Christ, which God gave unto him, to shew unto his servants things which must shortly come to pass; and he sent and signified it by his angel unto his servant John: 2Who bare record of the word of God, and of the testimony of Jesus Christ, and of all things that he saw. 3Blessed is he that readeth, and they that hear the words of this prophecy, and keep those things which are written therein: for the time is at hand.

John Greets the Seven Churches
4John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne; 5And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood, 6And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen. 7Behold, he cometh with clouds; and every eye shall see him, and they also which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.
8I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty.
9I John, who also am your brother, and companion in tribulation, and in the kingdom and patience of Jesus Christ, was in the isle that is called Patmos, for the word of God, and for the testimony of Jesus Christ. 10I was in the Spirit on the Lord's day, and heard behind me a great voice, as of a trumpet, 11Saying, I am Alpha and Omega, the first and the last: and, What thou seest, write in a book, and send it unto the seven churches which are in Asia; unto Ephesus, and unto Smyrna, and unto Pergamos, and unto Thyatira, and unto Sardis, and unto Philadelphia, and unto Laodicea.
12And I turned to see the voice that spake with me. And being turned, I saw seven golden candlesticks; 13And in the midst of the seven candlesticks one like unto the Son of man, clothed with a garment down to the foot, and girt about the paps with a golden girdle. 14His head and his hairs were white like wool, as white as snow; and his eyes were as a flame of fire; 15And his feet like unto fine brass, as if they burned in a furnace; and his voice as the sound of many waters. 16And he had in his right hand seven stars: and out of his mouth went a sharp twoedged sword: and his countenance was as the sun shineth in his strength.
17And when I saw him, I fell at his feet as dead. And he laid his right hand upon me, saying unto me, Fear not; I am the first and the last: 18I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death. 19Write the things which thou hast seen, and the things which are, and the things which shall be hereafter; 20The mystery of the seven stars which thou sawest in my right hand, and the seven golden candlesticks. The seven stars are the angels of the seven churches: and the seven candlesticks which thou sawest are the seven churches.

 

Revelation 5
The Book with Seven Seals

1And I saw in the right hand of him that sat on the throne a book written within and on the backside, sealed with seven seals. 2And I saw a strong angel proclaiming with a loud voice, Who is worthy to open the book, and to loose the seals thereof? 3And no man in heaven, nor in earth, neither under the earth, was able to open the book, neither to look thereon. 4And I wept much, because no man was found worthy to open and to read the book, neither to look thereon.
The Lamb is Worthy5And one of the elders saith unto me, Weep not: behold, the Lion of the tribe of Juda, the Root of David, hath prevailed to open the book, and to loose the seven seals thereof.
6And I beheld, and, lo, in the midst of the throne and of the four beasts, and in the midst of the elders, stood a Lamb as it had been slain, having seven horns and seven eyes, which are the seven Spirits of God sent forth into all the earth. 7And he came and took the book out of the right hand of him that sat upon the throne. 8And when he had taken the book, the four beasts and four and twenty elders fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints. 9And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation.

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
3
GOD
26
17
8
-
-
-
-
-
-
-
-
8
-
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
2
US
40
4
4
-
-
-
-
4
-
-
-
-
-
-
-
15
-
9
Add to Reduce
126
45
18
-
1
2
3
4
5
6
7
8
9
-
-
1+5
-
-
Reduce to Deduce
1+2+6
4+5
1+8
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
Essence of Number
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
GOD WITH US
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
45
-
9
GOD WITH US
126
54
45
-
1
2
3
4
5
6
7
8
9
-
-
4+5
-
-
-
1+2+6
5+4
4+5
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
GOD WITH US
9
9
9
-
3
-
3
4
5
6
7
8
9

 

 

SUNURANUSVENUS

SUNURASUNVESUN

 

-
-
-
-
-
SUN
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
9
-
3
SUN
54
18
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
5+4
4+5
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
SUN
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
VENUS
-
-
-
-
1
2
3
4
5
6
7
8
9
V
=
4
-
2
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
2
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
9
-
5
VENUS
81
27
18
-
1
2
3
4
10
6
7
8
9
-
-
-
-
-
-
8+1
2+7
1+8
-
-
-
-
-
1+0
-
-
-
-
-
-
9
-
5
VENUS
9
9
9
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
VENUS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
9
-
5
VENUS
81
27
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+1
2+7
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
VENUS
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
VENUS
-
-
-
-
1
2
3
4
5
6
7
8
9
V
=
4
-
2
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
2
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
9
-
5
VENUS
81
27
18
-
1
2
3
4
10
6
7
8
9
-
-
-
-
-
-
8+1
2+7
1+8
-
-
-
-
-
1+0
-
-
-
-
-
-
9
-
5
VENUS
9
9
9
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
URANUS
-
-
-
-
1
2
3
4
5
6
7
8
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
22
-
5
URANUS
94
31
22
-
2
2
6
4
5
6
7
8
9
-
-
2+2
-
-
-
9+4
3+1
2+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
URANUS
13
2
4
-
2
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+3
3+1
2+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
URANUS
9
2
4
-
2
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
URANUS
-
-
-
-
1
2
3
4
5
6
7
8
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
22
-
5
URANUS
94
31
22
-
2
2
6
4
5
6
7
8
9
-
-
2+2
-
-
-
9+4
3+1
2+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
URANUS
13
2
4
-
2
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+3
3+1
2+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
5
URANUS
9
2
4
-
2
2
6
4
5
6
7
8
9

 

 

-
ALL IS NUMBER
-
-
-
3
ALL
25
7
7
2
IS
28
10
1
6
NUMBER
73
28
1
11
ALL IS NUMBER
126
45
9
1+1
-
1+2+6
4+5
-
2
ALL IS NUMBER
9
9
9

 

 

JOSEPH AND HIS BROTHERS

Thomas Mann

1875 - 1955

JOSEPH THE PROVIDER

Page 967

ALL TOO BLISSFUL

"But I am King, and teacher; I may not think what I cannot teach. Whereas such a one very soon learns not even to think the unteachable."
Here Tiy, his mother, cleared her throat, rattled her ornaments, and said, looking ahead of her into space:
"Pharaoh is to be praised when he practises statesmanship in matters of religious belief and spares the simplicity of the many. That is why I warned him not to wound the popular attachment to Usir, king of the lower regions. There is no contradiction between knowing and sparing, in this connection; and the office of teacher need not darken knowledge. Never have priests taught the multitude all they themselves know. They have told them what was wholesome, and wisely left in the realm of the mysteries what was not beneficial. Thus knowledge and wisdom are together in the world, truth and forbearance. The mother recommends that it so remain."
"Thank you, Mama," said Amenhotep, with a deprecating bow. "Thank you for the contribution. It is very valuable and will for / Page 968 / eternal ages be held in honour. But we are speaking of two different things. My Majesty speaks of the fetters which the teaching puts upon the thoughts of God; yours refers to priestly statecraft, which divides teaching and knowledge. But Pharaoh would not be arrogant, and there is no greater arrogance than such a division. No, there
is no arrogance in the world greater than that of dividing the children of our Father into initiate and uninitiate and teaching double words: all-knowingly for the masses, knowingly in the inner circle. No, we must speak what we know, and witness what we have seen. Pharaoh wants to do nothing but improve the teaching, even though it be made hard for him by the teaching.

 

 

JESUS AND THE GODDESS

THE SECRET TEACHINGS OF THE ORIGINAL CHRISTIANS

Page 203

The one moving surface of /page 204/ the water represents universal psyche. Individual psyches are the individual waves. We are unique movements on the shared still depths of Consciousness.

THE EVOLVING COSMOS

To know itself the Mystery arises as the primal syzygy subject and object - which results in partial Gnosis and partial ignorance. As subjective Consciousness it knows its Self, but as psyche it mistakes its self for its many objective self-images.47 As a continuation of the initial impulse towards self-knowledge, that part of Consciousness which has become identified with each psyche-body is in the process of completing the journey of Gnosis by progressively awakening to its true nature.
We can understand this fundamental duality by seeing how it manifests in each of us. We appear to be an evolving psyche-body on a journey of awakening, but our essential nature is ineffable Consciousness. Knowing our essential nature is the realization of Gnosis, because as Consciousness we already exist permanently in the state of Gnosis. Whilst we identify with the psyche-body, however, we experience only relative states of ignorance.
Plato describes these two states as 'being' and 'becoming'.48 Consciousness is being. We experience this as the sense of I AM. It is unchanging, quality less presence, It is what we area Psyche, on the other is- what we experience. It is an unfolding succession of changing appearances. It is impermanence. It is perpetually in the process of becoming something else. The Mystery as Consciousness is being what it is. Consciousness witnesses itself as a psyche-body in the process of becoming /page 204/ aware of what is. We are witnessing becoming.

 

 

-
-
-
-
-
MEA CULPA
-
-
-
M
=
4
-
3
MEA
19
10
1
C
=
3
-
5
CULPA
53
26
8
-
-
7
-
8
-MEA CULPA
72
36
9
-
-
-
-
-
-
7+2
3+6
-
-
-
7
-
8
MEA CULPA-
9
9
9

 

 

Mea culpa - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Mea_culpa

Mea culpa is a Latin phrase that translates into English as "through my fault". It is repeated three times in the prayer of confession at the Catholic Mass:

Mea culpa

From Wikipedia, the free encyclopedia

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2014)

Mea culpa is a Latin phrase that translates into English as "through my fault". It is repeated three times in the prayer of confession at the Catholic Mass: mea culpa, mea culpa, mea maxima culpa — "through my fault, through my fault, through my most grievous fault". The three phrases are in the ablative case, which gives the instrumental meaning "through"

 

M
=
4
-
8
-MEA CULPA
72
36
9
M
=
4
-
8
-MEA CULPA
72
36
9
M
=
4
-
8
-MEA CULPA
72
36
9
-
-
7
-
24
-
216
108
27
-
-
-
-
2+4
-
2+1+6
1+0+8
2+7
-
-
7
-
6
-
9
9
9

 

mea culpa, mea culpa, mea maxima culpa through my fault, through my fault, through my most grievous fault.

 

-
-
-
-
14
MEA MAXIMA CULPA
-
-
-
M
=
4
-
3
MEA
19
10
1
M
=
4
-
6
MAXIMA
61
25
7
C
=
3
-
5
CULPA
53
26
8
-
-
7
-
16
MEA MAXIMA CULPA
133
61
16
-
-
-
-
1+6
-
1+3+3
6+1
1+6
-
-
7
-
7
MEA MAXIMA CULPA
7
7
7

 

 

HOLY BIBLE
Genesis 1:27.

“So God created mankind in his own image, in the image of God he created them; male and female he created them.”

 

-
-
-
-
-
MARRIED
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
41
-
7
MARRIED
68
41
41
-
1
2
3
8
5
6
7
8
27
-
-
4+1
-
-
-
6+8
4+1
4+1
-
-
-
-
-
-
-
-
-
2+7
-
-
5
-
7
MARRIED
14
5
5
-
1
2
3
8
5
6
7
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
MARRIED
5
5
5
-
1
2
3
8
5
6
7
8
9

 

 

-
-
-
-
-
MARRIED
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
2
M+A
13
4
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
2
E+D
15
5
5
-
-
-
-
-
-
-
-
-
9
-
-
-
-
7
MARRIED
68
41
41
-
1
2
3
8
5
6
7
8
36
-
-
-
-
-
-
6+8
4+1
4+1
-
-
-
-
-
-
-
-
-
3+6
-
-
-
-
7
MARRIED
14
5
5
-
1
2
3
8
5
6
7
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
MARRIED
5
5
5
-
1
2
3
8
5
6
7
8
9

 

 

en.wikipedia.org/wiki/Measure_for_Measure

Measure for Measure is a play by William Shakespeare, believed to have been written in 1603 or 1604. It was (and continues to be) classified as comedy, but its ...

Measure for Measure

From Wikipedia, the free encyclopedia
Facsimile of the title page of Measure for Measure from the First Folio, published in 1623
Measure for Measure is a play by William Shakespeare, believed to have been written in 1603 or 1604. It was (and continues to be) classified as comedy, but its mood defies those expectations. As a result and for a variety of reasons, some critics have labelled it as one of Shakespeare's problem plays. Originally published in the First Folio of 1623 (where it was first labelled as a comedy), the play's first recorded performance was in 1604. The play deals with the issues of mercy, justice, and truth and their relationship to pride and humility: "Some rise by sin, and some by virtue fall".

 

M
=
4
-
7
MEASURE
82
28
1
F
=
6
-
3
FOR
39
21
3
M
=
4
-
7
MEASURE
82
28
1
-
-
14
-
17
First Total
203
77
5
-
-
1+4
-
1+7
Add to Reduce
2+0+3
7+7
-
-
-
5
-
8
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
5
-
8
Essence of Number
5
5
5

 

 

To Kill a Mockingbird - Wikipedia
https://en.wikipedia.org/wiki/To_Kill_a_Mockingbird
To Kill a Mockingbird is a novel by Harper Lee published in 1960. It was immediately successful, winning the Pulitzer Prize, and has become a classic of modern American literature. The plot and characters are loosely based on Lee's observations of her family, her neighbors and an event that occurred near her hometown ...

To Kill a Mockingbird by Harper Lee. The unforgettable novel of a childhood in a sleepy Southern town and the crisis of conscience that rocked it, To Kill A Mockingbird became both an instant bestseller and a critical success when it was first published in 1960

 

TO KILL A MOCKINGBIRD

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
K
=
2
-
4
KILL
44
17
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
M
=
4
-
7
MOCKING
72
36
9
-
-
-
-
-
-
-
-
-
9
B
=
2
-
4
BIRD
33
24
6
-
-
-
-
-
-
6
-
-
-
-
-
11
-
18
First Total
185
86
32
-
1
2
3
4
5
6
7
16
9
-
-
1+1
-
1+8
Add to Reduce
1+8+5
8+6
3+2
-
-
-
-
-
-
-
-
1+6
-
-
-
2
-
9
Second Total
14
14
5
-
1
2
3
4
5
6
7
7
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
9
Essence of Number
5
5
5
-
1
2
3
4
5
6
7
7
9

 

 

-
-
-
-
7
MOCKING
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
K
=
2
4
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
36
-
7
MOCKING
72
36
36
-
1
2
3
4
5
6
7
8
9
-
-
3+6
-
-
-
7+2
3+6
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
MOCKING
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
MOCKING
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
C
=
3
3
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
K
=
2
4
1
K
11
2
2
-
1
2
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
N
=
5
6
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
G
=
7
7
1
G
7
7
7
-
1
-
-
-
-
-
7
8
-
-
-
36
-
7
MOCKING
72
36
36
-
1
2
3
4
5
6
7
8
9
-
-
3+6
-
-
-
7+2
3+6
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
MOCKING
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
MOCKING
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
4
1
K
11
2
2
-
1
2
-
-
-
-
-
8
-
C
=
3
3
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
M
=
4
1
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
N
=
5
6
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
G
=
7
7
1
G
7
7
7
-
1
-
-
-
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
-
-
36
-
7
MOCKING
72
36
36
-
1
2
3
4
5
6
7
8
9
-
-
3+6
-
-
-
7+2
3+6
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
7
MOCKING
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
MOCKING
-
-
-
-
2
3
4
5
6
7
9
K
=
2
4
1
K
11
2
2
-
2
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
3
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
4
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
5
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
6
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
7
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
36
-
7
MOCKING
72
36
36
-
2
3
4
5
6
7
9
-
-
3+6
-
-
-
7+2
3+6
3+6
-
-
-
-
-
-
-
-
-
-
9
-
7
MOCKING
9
9
9
-
2
3
4
5
6
7
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
7
ANOTHER
81
36
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
B
=
2
-
5
BITES
55
19
1
-
1
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
D
=
4
-
4
DUST
64
10
1
-
1
-
-
-
-
-
-
-
-
-
-
15
-
22
First Total
267
96
24
-
2
2
3
4
5
6
7
8
9
-
-
1+5
-
2+2
Add to Reduce
2+6+7
9+6
2+4
-
-
-
-
-
-
-
-
-
-
-
-
6
-
4
Second Total
15
15
6
-
2
2
3
4
5
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+5
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
4
Essence of Number
6
6
6
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
N
=
5
-
9
NUMERICAL
96
42
6
-
-
-
-
-
-
6
-
-
-
B
=
2
-
4
BIAS
31
13
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
F
=
6
-
6
FAVOUR
83
29
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
3
THE
33
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
-
-
36
-
30
First Total
329
149
32
-
1
2
3
4
5
18
7
8
9
-
-
3+6
-
1+8
Add to Reduce
3+2+9
1+4+9
3+2
-
-
-
-
-
-
1+8
-
-
-
-
-
9
-
9
Second Total
14
14
5
-
1
2
3
4
5
9
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
Essence of Number
5
5
5
-
1
2
3
4
5
9
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
F
=
6
-
6
FAVOUR
83
29
2
-
1
2
-
-
-
-
7
8
9
O
=
6
-
2
OF
21
12
3
-
1
-
3
-
-
-
7
8
9
B
=
2
-
4
BIAS
31
13
4
-
1
-
-
4
-
-
7
8
9
I
=
9
-
2
IN
23
14
5
-
1
-
-
-
5
-
7
8
9
N
=
5
-
9
NUMERICAL
96
42
6
-
1
-
-
-
-
6
7
8
9
T
=
2
-
3
THE
33
6
6
-
1
-
-
-
-
6
7
8
9
F
=
6
-
4
FIVE
42
24
6
-
1
-
-
-
-
6
7
8
9
-
-
36
-
30
First Total
329
149
32
-
1
2
3
4
5
18
7
8
9
-
-
3+6
-
1+8
Add to Reduce
3+2+9
1+4+9
3+2
-
-
-
-
-
-
1+8
-
-
-
-
-
9
-
9
Second Total
14
14
5
-
1
2
3
4
5
9
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
Essence of Number
5
5
5
-
1
2
3
4
5
9
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
2
3
4
5
6
F
=
6
-
6
FAVOUR
83
29
2
-
2
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
3
-
-
-
B
=
2
-
4
BIAS
31
13
4
-
-
-
4
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
5
-
N
=
5
-
9
NUMERICAL
96
42
6
-
-
-
-
-
6
T
=
2
-
3
THE
33
6
6
-
-
-
-
-
6
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
6
-
-
36
-
30
First Total
329
149
32
-
2
3
4
5
18
-
-
3+6
-
1+8
Add to Reduce
3+2+9
1+4+9
3+2
-
-
-
-
-
1+8
-
-
9
-
9
Second Total
14
14
5
-
2
3
4
5
9
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
-
-
-
-
-
-
9
-
9
Essence of Number
5
5
5
-
2
3
4
5
9

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 82

The Sacred Fifty

"We must return to the treatise 'The Virgin of the World'. This treatise is quite explicit in saying that Isis and Osiris were sent to help the Earth by giving primitive mankind the arts of civilization:
And Horus thereon said:

'How was it, mother, then, that Earth received God's Efflux?' And Isis said:

'I may not tell the story of (this) birth; for it is not permitted to describe the origin of thy descent, O Horus (son) of mighty power, lest afterwards the way-of-birth of the immortal gods should be known unto men - except so far that God the Monarch, the universal Orderer and Architect, sent for a little while thy mighty sire Osiris, and the mightiest goddess Isis, that they might help the world, for all things needed them.
'Tis they who filled life full of life. 'Tis they who caused the savagery of mutual slaughtering of men to cease. 'Tis they who hallowed precincts to the Gods their ancestors and spots for holy rites. 'Tis they who gave to men laws, food and shelter.'

"Page 73

A Fairy Tale

'I INVOKE THEE, LADY ISIS, WITH WHOM THE GOOD DAIMON DOTH UNITE,

HE WHO IS LORD IN THE PERFECT BLACK.'

 

 

THE SIRIUS MYSTERY

Robert K.G.Temple 1976

Page 74

"Mead quotes an Egyptian magic papyrus, this being an uncontested Egyptian document which he compares to a passage in the Trismegistic literature: 'I invoke thee, Lady Isis, with whom the Good Daimon doth unite, He who is Lord in the perfect black. '37
We know that Isis is identified with Sirius A, and here we may have a / Page 74 / description of her star-companion 'who is Lord in the perfect black', namely the invisible companion with whom she is united, Sirius B.
Mead, of course, had no inkling of the Sirius question. But he cited this magic papyrus in order to shed comparative light on some extraordinary passages in a Trismegistic treatise he translated which has the title 'The Virgin of the World'. In his comments on the magic papyrus Mead says: 'It is natural to make the Agathodaimon ("the Good Daimon") of the Papyrus refer to Osiris; for indeed it is one of his most frequent designations. Moreover, it is precisely Osiris who is pre-eminently connected with the so-called "under­world", the unseen world, the "mysterious dark". He is lord there. . . and indeed one of the ancient mystery-sayings was precisely, "Osiris is a dark God." ,
'The Virgin of the World' is an extraordinary Trismegistic treatise in the form of a dialogue between the hierophant (high priest) as spokesman for Isis and the neophyte who represents Horus. Thus the priest instructing the initiate is portrayed as Isis instructing her son Horus.
The treatise begins by claiming it is 'her holiest discourse' which 'so speaking Isis doth pour forth'. There is, throughout, a strong emphasis on the hierarchical principle of lower and higher beings in the universe - that earthly mortals are presided over at intervals by other, higher, beings who interfere in Earth's affairs when things here become hopeless, etc. Isis says in the treatise: 'It needs must, therefore, be the less should give place to the greater mysteries.' What she is to disclose to Horus is a great mystery. Mead describes it as the mystery practised by the arch-hierophant. It was the degree (here 'degree' is in the sense of 'degree' in the Masonic 'mysteries', which are hopelessly garbled and watered-down versions of genuine mysteries of earlier times) 'called the "Dark Mystery" or "Black Rite". It was a rite performed only for those who were judged worthy of it after long probation in lower degrees, something of a far more sacred character, apparently, than the instruction in the mysteries enacted in the light.'
Mead adds: 'I would suggest, therefore, that we have here a reference to the most esoteric institution of the Isiac tradition. . .', Isiac meaning of course 'Isis-tradition', and not to be confused with the Book of Isaiah in the Bible (so that perhaps it is best for us not to use the word-form 'Isiac').
It is in attempting to explain the mysterious 'Black Rite' of Isis at the highest degree of the Egyptian mysteries that Mead cited the magic papyrus which I have already quoted. He explains the 'Black Rite' as being connected with Osiris being a 'dark god' who is 'Lord of the perfect black' which is 'the unseen world, the mysterious black'.
This treatise 'The Virgin of the World' describes a personage called Hermes who seems to represent a race of beings who taught earthly mankind the arts of civilization after which: 'And thus, with charge unto his kinsmen of the Gods to keep sure watch, he mounted to the Stars'.
According to this treatise mankind have been a troublesome lot requiring scrutiny and, at rare intervals of crisis, intervention.
After Hermes left Earth to return to the stars there was or were in Egypt someone or some people designated as 'Tat' (Thoth) who were initiates into the celestial mysteries."

Page 77

"Bearing these books in mind (and I am sure they are there waiting under­ground like a time bomb for us), it is interesting to read this passage in 'The Virgin of the World' following shortly upon that previously quoted:
The sacred symbols of the cosmic elements were hid away hard by the secrets of Osiris. Hermes, ere he returned to Heaven, invoked a spell on them, and spake these words: . . . 'O holy books, who have been made by my immortal hands, by incorruption's magic spells. . . (at this point there is a lacuna as the text is hopeless) . . . free from decay throughout eternity remain and incorrupt from time! Become unseeable, unfindable, for every one whose foot shall tread the plains of this land, until old Heaven doth bring forth meet instruments for you, whom the Creator shall call souls.'
Thus spake he; and, laying spells on them by means of his own works, he shut them safe away in their own zones. And long enough the time has been since they were hid away.
In the treatise the highest objective of ignorant men searching for the truth
is described as: '(Men) will seek out. . . the inner nature of the holy spaces which no foot may tread, and will chase after them into the height, desiring to observe the nature of the motion of the Heaven.
'These are as yet moderate things. For nothing more remains than Earth's remotest realms; nay, in their daring they will track out Night, the farthest Night of all.'..."

Page 82

"We must note Stecchini's remarks about Delphi as follows :38
The god of Delphi, Apollo, whose name means 'the stone', was identified with an object, the omphalos, 'navel', which has been found. It consisted of an ovoidal stone. . . . The omphalos of Delphi was similar to the object which represented the god Amon in Thebes, the 'navel' of Egypt. In 1966 I presented to the annual meeting of the Archaeological Institute of America a paper in which I maintained that historical accounts, myths, and legends, and some monuments of Delphi, indicate that the oracle was established there by the Pharaohs of the Ethiopian Dynasty.

 

DELPHI = 9 = DELPHI

OMPHALOS = 9 = OMPHALOS

NAVEL = 9 = NAVEL

 

 

IN

THE

BEGINNING

WAS THE WORD AND THE WORD WAS

WITH

GOD AND THE WORD WAS GOD

THE

SAME WAS IN THE BEGINNING WITH

GOD ALL THINGS WERE MADE BY GOD AND WITHOUT GOD

WAS

NOT

ANYTHING

MADE THAT WAS MADE

IN

GOD

WAS LIFE AND THE LIFE WAS

THE

LIGHT

OF

HUMANKIND

AND THE

LIGHT

SHINETH IN THE DARKNESS AND THE DARKNESS COMPREHENDED IT NOT

 

 

I

AM

ALPHA AND OMEGA

THE BEGINNING AND THE END THE FIRST AND THE LAST

I

AM

THE ROOT AND THE OFFSPRING

OF

DAVID

AND

THE BRIGHT AND MORNING STAR

AND

THE SPIRIT AND THE BRIDE SAY COME

AND

LET THEM THAT HEARETH SAY COME

AND

LET THEM THAT IS ATHIRST COME

AND

WHOSOEVER WILL LET THEM TAKE THE WATER OF LIFE FREELY

 

 

THE CHRISTOS THE

CHRIST

 

CHRISTOS SEE HERE IS THE CHRISTOS

 

OSIRIS

 

 

THE HERMETICA

THE LOST WISDOM OF THE PHARAOHS

Timothy Freke & Peter Gandy

To the Memory of Giordano Bruno 1548 - 1600

Mundus Nihil Pulcherrimum

The World is a Beautiful Nothing

Page 23

"Although we have used the familiar term 'God' in the explanatory notes which accompany each chapter, we have avoided this term in the text itself. Instead we have used 'Atum - one of the ancient Egyptian names for the Supreme One God."

 

Page 45

The Being of Atum

"Atum is Primal Mind."

Page 45

The Being of Atum

Give me your whole awareness, and concentrate your thoughts, for Knowledge of Atum's Being requires deep insight, which comes only as a gift of grace.

It is like a plunging torrent of water whose swiftness outstrips any man who strives to follow it, leaving behind not only the hearer, but even the teacher himself.

To conceive of Atum is difficult.

To define him is impossible.

The imperfect and impermanent cannot easily apprehend the eternally perfected.

Atum is whole and conconstant.

In himself he is motionless, yet he is self-moving.

He is immaculate, incorruptible and ever-lasting.

He is the Supreme Absolute Reality. He is filled with ideas which are imperceptible to the senses, and with all-embracing Knowledge.

Atum is Primal Mind.

Page 46

He is too great to be called by the name 'Atum'. He is hidden, yet obvious everywhere.

His Being is known through thought alone, yet we see his form before our eyes.

He is bodiless, yet embodied in everything. There is nothing which he is not. He has no name, because all names are his name. He is the unity in all things, so we must know him by all names and call everything 'Atum'.

He is the root and source of all. Everything has a source, except this source itself, which springs from nothing.

Atum is complete like the number one, which remains itself whether multiplied or divided, and yet generates all numbers.

Atum is the Whole which contains everything. He is One, not two.

He is All, not many.

The All is not many separate things, but the Oneness that subsumes the parts.

The All and the One are identical.

You think that things are many when you view them as separate, but when you see they all hang on the One, /Page 47/ and flow from the One, you will realise they are united­linked together, and connected by a chain of Being from the highest to the lowest, all subject to the will of Atum.

The Cosmos is one as the sun is one, the moon is one and the Earth is one.

Do you think there are many Gods? That's absurd - God is one.

Atum alone is the Creator of all that is immortal, and all that is mutable.

If that seems incredible, just consider yourself. You see, speak, hear, touch, taste, walk, think and breathe.

It is not a different you who does these various things, but one being who does them all.

To understand how Atum makes all things, consider a farmer sowing seeds; here wheat - there barley,
now planting a vine - then an apple tree.

Just as the same man plants all these seeds, so Atum sows immortality in heaven and change on Earth.

Throughout the Cosmos he disseminates Life and movement­the two great elements that comprise Atum and his creation, and so everything that is.

Page 48

Atum is called 'Father' because he begets all things, and, from his example, the wise hold begetting children the most sacred pursuit of human life. Atum works with Nature, within the laws of Necessity, causing extinction and renewal, constantly creating creation to display his wisdom.

Yet, the things that the eye can see are mere phantoms and illusions.

Only those things invisible to the eye are real. Above all are the ideas of Beauty and Goodness.

Just as the eye cannot see the Being of Atum, so it cannot see these great ideas.

They are attributes of Atum alone, and are inseparable from him.

They are so perfectly without blemish that Atum himself is in love with them.

There is nothing which Atum lacks, so nothing that he desires.

There is nothing that Atum can lose, so nothing can cause him grief. Atum is everything.

Atum makes everything, and everything is a part of Atum.

Atum, therefore, makes himself.

This is Atum's glory - he is all-creative, and this creating is his very Being.

It is impossible for him ever to stop creating­for Atum can never cease to be.

Page 49

Atum is everywhere.

Mind cannot be enclosed, because everything exists within Mind.

Nothing is so quick and powerful.

Just look at your own experience. Imagine yourself in any foreign land, and quick as your intention you will be there!

Think of the ocean - and there you are.

You have not moved as things move, but you have travelled, nevertheless.

Fly up into the heavens - you won't need wings!

Nothing can obstruct you - not the burning heat of the sun, or the swirling planets.

Pass on to the limits of creation. Do you want to break out beyond the boundaries of the Cosmos?

For your mind, even that is possible.

Can you sense what power you possess? If you can do all this, then what about your Creator?

Try and understand that Atum is Mind.

This is how he contains the Cosmos. All things are thoughts which the Creator thinks."

 

 

Daily Mail, Thursday, November 17, 2011

ANSWERS TO CORRESPONDENTS

Compiled by Charles Legge

Page 70

QUESTION The W. B Yeats poem Mad As The Mists and snow name checks Homer, Horace, Cicero and and Tully ('and here is Tully's open page') Who was Tully?


TULLY and Cicero are one and the same person - the Roman statesman and philosopher whose full latin name was Marcus Tullius Cicero (106-43 BC).

David Bradbury, London.

 

-
TULLIUS
-
-
-
1
T
20
2
2
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
1
I
9
9
9
1
U
21
3
3
1
S
19
10
1
7
TULLIUS
114
33
24
-
-
1+1+4
3+3
2+4
7
TULLIUS
6
6
6

 

 

-
-
-
-
-
TULLIUS
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
24
12
7
TULLIUS
114
33
24
-
1
2
12
-
-
-
-
-
9
-
-
2+4
1+2
-
-
1+1+4
3+3
2+4
-
-
-
1+2
-
-
-
-
-
-
-
-
6
3
7
TULLIUS
6
6
6
-
1
2
3
-
-
-
-
-
9

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 21

"The Ad Herennium was a well known and much used text in the Middle Ages when it had an immense prestige because it was thought to be by Cicero. It was therefore believed that the precepts for the artificial memory which it expounded had been drawn up by Tullius himself"

Page 32

"Though the medieval tradition which assigned the authorship of Ad Herennium to 'Tullius' was wrong in fact, it was not wrong in its inference that the art of memory was practised and recommended by Tullius."

Page 282

"By THE LADDER OF MINERVA we rise from the first to the last..."

 

 

B
=
2
-
2
BY
27
9
9
T
=
2
-
3
THE
33
15
6
L
=
3
-
6
LADDER
44
26
8
O
=
6
-
2
OF
21
12
3
M
=
4
-
7
MINERVA
82
37
1
W
=
5
-
2
WE
28
10
1
R
=
9
-
4
RISE
51
24
6
F
=
6
-
4
FROM
52
25
7
T
=
2
-
3
THE
33
15
6
F
=
6
-
5
FIRST
72
27
9
T
=
2
-
2
TO
35
8
8
T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAST
52
7
7
-
-
52
-
47
-
563
230
77
-
-
5+2
-
4+7
-
5+6+3
2+3+0
7+7
-
-
7
-
11
-
14
5
14
-
-
-
-
1+1
-
1+4
-
1+4
-
-
7
-
2
-
5
5
5

 

 

Daily Mail, Thursday, November 17, 2011

ANSWERS TO CORRESPONDENTS

Compiled by Charles Legge

Page 70

QUESTION The W. B Yeats poem Mad As The Mists and snow name checks Homer, Horace, Cicero and and Tully ('and here is Tully's open page') Who was Tully?


TULLY and Cicero are one and the same person - the Roman statesman and philosopher whose full latin name was Marcus Tullius Cicero (106-43 BC).

Male Roman citizens typically had three names, their praenomen (given name), their nomen (clan name) and their' cognomen (nickname or family name), but in English classical Latin authors are generally known by a single name, often Anglicised. These sometimes derive from the nomen (for example, Horace's full name was Quintus Horatius Flaccus) and sometimes from the cognomen (as with Gaius Julius Caesar).

In Cicero's case, he's today known by his cognomen, but has sometimes in the past been called Tully from his nomen.

Despite coming from humble stock, Cicero's skill as an orator saw him rise to the supreme position of state in the Republic, the consulship, in 63BC and he played a key role in the defeat of the Catiline conspiracy.

As a result of the rise to power of Julius Caesar, he took a lesser role in his later years, devoting himself to literature Instead.

After Caesar's assassination in 44BC, Cicero returned to politics and took a key role in the senatorial opposition to Mark Antony.

He was murdered on Antony's orders when he took power. Cicero's surviving letters form a key source for the history of the fall of the Roman Republic and its replacement by the rule of the emperors.

David Bradbury, London.

 

TULLY and Cicero are one and the same person -

the Roman statesman and philosopher whose full latin name was Marcus Tullius Cicero (106-43 BC).

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
6
MARCUS
75
30
3
-
-
-
-
-
-
-
-
-
-
T
=
2
2
7
TULLIUS
114
33
6
-
-
-
-
-
-
-
-
-
-
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
19
-
242
98
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
-
-
21
-
6
-
75
30
21
-
-
-
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
I
=
9
11
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
24
-
7
-
114
33
24
-
-
-
-
-
-
-
-
-
-
C
=
3
14
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
16
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
O
=
6
19
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
-
-
35
-
6
-
53
35
35
-
3
2
24
4
5
6
7
8
36
-
-
-
-
-
-
-
-
-
-
-
-
2+4
-
-
-
-
-
3+6
-
-
-
-
6
MARCUS
75
30
3
-
3
2
6
4
5
6
7
8
9
-
-
-
-
7
TULLIUS
114
33
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
CICERO
53
35
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
19
First Total
242
98
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
10
Second Total
8
17
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
Essence of Number
8
8
8
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
6
MARCUS
75
30
3
-
-
-
-
-
-
-
-
-
-
T
=
2
2
7
TULLIUS
114
33
6
-
-
-
-
-
-
-
-
-
-
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
19
-
242
98
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
I
=
9
11
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
C
=
3
14
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
16
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
O
=
6
19
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
-
-
80
-
19
-
242
98
80
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
MARCUS
75
30
3
-
3
2
24
4
5
6
7
8
36
-
-
-
-
7
TULLIUS
114
33
6
-
-
-
2+4
-
-
-
-
-
3+6
-
-
-
-
6
CICERO
53
35
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
19
First Total
242
98
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
10
Second Total
8
17
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
Essence of Number
8
8
8
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
6
MARCUS
75
30
3
-
-
-
-
-
-
-
-
-
-
T
=
2
2
7
TULLIUS
114
33
6
-
-
-
-
-
-
-
-
-
-
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
19
-
242
98
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
C
=
3
14
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
C
=
3
16
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
O
=
6
19
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
I
=
9
11
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
7
8
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
-
-
80
-
19
-
242
98
80
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
MARCUS
75
30
3
-
3
2
24
4
5
6
7
8
36
-
-
-
-
7
TULLIUS
114
33
6
-
-
-
2+4
-
-
-
-
-
3+6
-
-
-
-
6
CICERO
53
35
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
19
First Total
242
98
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
10
Second Total
8
17
8
-
3
2
6
4
5
6
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
Essence of Number
8
8
8
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
9
M
=
4
1
6
MARCUS
75
30
3
-
-
-
-
-
-
-
-
T
=
2
2
7
TULLIUS
114
33
6
-
-
-
-
-
-
-
-
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
-
-
-
-
-
-
9
-
19
-
242
98
17
-
1
2
3
4
5
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
-
C
=
3
14
1
C
3
3
3
-
-
-
3
-
-
-
-
C
=
3
16
1
C
3
3
3
-
-
-
3
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
O
=
6
19
1
O
15
6
6
-
-
-
-
-
-
6
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
9
I
=
9
11
1
I
9
9
9
-
-
-
-
-
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
80
-
19
-
242
98
80
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
MARCUS
75
30
3
-
3
2
24
4
5
6
36
-
-
-
-
7
TULLIUS
114
33
6
-
-
-
2+4
-
-
-
3+6
-
-
-
-
6
CICERO
53
35
8
-
3
2
6
4
5
6
9
-
-
-
-
19
First Total
242
98
17
-
-
-
-
-
-
-
-
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
-
-
-
-
-
-
-
-
10
Second Total
8
17
8
-
3
2
6
4
5
6
9
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
1
Essence of Number
8
8
8
-
3
2
6
4
5
6
9

 

 

M
=
4
1
6
MARCUS
75
30
3
T
=
2
2
7
TULLIUS
114
33
6
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
19
First Total
242
98
17
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
10
Second Total
8
17
8
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
1
Essence of Number
8
8
8

 

 
-
-
-
-
-
-
-
-
-
3
-
5
9
M
=
4
1
6
MARCUS
75
30
3
-
-
-
-
-
T
=
2
2
7
TULLIUS
114
33
6
-
-
-
-
-
C
=
3
3
6
CICERO
53
35
8
-
-
-
-
-
9
-
19
-
242
98
17
-
3
-
5
9
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A+S+S
39
21
3
-
3
1
-
-
T
=
2
7
1
T+M+O
48
12
3
-
3
2
-
-
C
=
3
4
1
C
3
3
3
-
3
3
-
-
U
=
3
5
1
U
21
3
3
-
3
4
-
-
U
=
3
8
1
U
21
3
3
-
3
5
-
-
L
=
3
9
1
L
12
3
3
-
3
6
-
-
L
=
3
10
1
L
12
3
3
-
3
7
-
-
U
=
3
12
1
U
21
3
3
-
3
8
-
-
C
=
3
14
1
C
3
3
3
-
3
9
-
-
C
=
3
16
1
C
3
3
3
-
3
10
-
-
E
=
5
17
1
E
5
5
5
-
-
-
5
-
R
=
9
3
1
R
18
9
9
-
-
-
-
9
I
=
9
11
1
I
9
9
9
-
-
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
9
-
80
-
19
-
242
98
80
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
MARCUS
75
30
3
-
30
-
5
36
-
-
-
-
7
TULLIUS
114
33
6
-
3+0
-
-
3+6
-
-
-
-
6
CICERO
53
35
8
-
3
-
5
9
-
-
-
-
19
First Total
242
98
17
-
-
-
-
-
-
-
-
-
1+9
Add to Reduce
2+4+2
9+8
1+7
-
-
-
-
-
-
-
-
-
10
Second Total
8
17
8
-
3
-
5
9
-
-
-
-
1+0
Reduce to Deduce
-
1+7
-
-
-
-
-
-
-
-
-
-
1
Essence of Number
8
8
8
-
3
-
5
9

 

 

-
TULLIUS
-
-
-
1
T
20
2
2
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
1
I
9
9
9
1
U
21
3
3
1
S
19
10
1
7
TULLIUS
114
33
24
-
-
1+1+4
3+3
2+4
7
TULLIUS
6
6
6

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 21

"The Ad Herennium was a well known and much used text in the Middle Ages when it had an immense prestige because it was thought to be by Cicero. It was therefore believed that the precepts for the artificial memory which it expounded had been drawn up by Tullius himself"

Page 32

"Though the medieval tradition which assigned the authorship of Ad Herennium to 'Tullius' was wrong in fact, it was not wrong in its inference that the art of memory was practised and recommended by Tullius."

 

-
TULLIUS
-
-
-
1
T
20
2
2
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
1
I
9
9
9
1
U
21
3
3
1
S
19
10
1
7
TULLIUS
114
24
12
-
-
1+1+4
2+4
1+2
7
TULLIUS
6
6
6

 

 

THE ART OF MEMORY

FRANCIS A. YATES 1966

THREE LATIN SOURCES FOR THE CLASSICAL ART OF MEMORY

Page 111

MEDIEVAL MEMORY AND THE FORMATION OF IMAGES

"Petrarch makes his allusions to the art by introducing examples of men of antiquity famed for good memories and associating these with the classical art. His paragraph on the memories of Lucullus and Hortensius begins thus: - 'Memory is of two kinds, one for things, one for words.' 57

LUCULLUS 33333331 LUCULLUS

 

-
LUCULLUS
-
-
-
1
L
12
3
3
1
U
21
3
3
1
C
3
3
3
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
1
U
21
3
3
1
S
19
10
1
8
LUCULLUS
121
31
22
-
-
1+2+1
3+1
2+2
8
LUCULLUS
4
4
4

 

 

-
LULL
-
-
-
1
L
12
3
3
1
U
21
3
3
1
L
12
3
3
1
L
12
3
3
4
LULL
57
12
12
-
-
5+7
1+2
1+2
4
LULL
12
3
3
-
-
1+2
-
-
4
LULL
3
3
3

 

 

ART AT R AT ART

 

 

https://en.wikipedia.org/wiki/The_Morrígan

The Morrígan ("phantom queen") or Mórrígan ("great queen"), also known as Morrígu, is a figure from Irish mythology. The name is spelled Morríghan or Mór-Ríoghain in Modern Irish. The Morrígan is mainly associated with war and fate, especially with foretelling doom and death in battle. In this role she often appears as a ...
The Morrígan ("phantom queen") or Mórrígan ("great queen"), also known as Morrígu, is a figure from Irish mythology. The name is spelled Morríghan or Mór-Ríoghain in Modern Irish.
The Morrígan is mainly associated with war and fate, especially with foretelling doom and death in battle. In this role she often appears as a crow, the badb.[1] She is also associated with sovereignty, the land and livestock. She is believed to be a manifestation of the earth- and sovereignty-goddess,[2][3] chiefly representing the goddess's role as guardian of the territory and its people.[4][5]
The Morrígan is often described as a trio of individuals, all sisters, called 'the three Morrígna'.[2][6][7] Membership of the triad varies; sometimes it is given as Badb, Macha and Nemain[8] while elsewhere it is given as Badb, Macha and Anand (the latter is given as another name for the Morrígan).[9] It is believed that these were all names for the same goddess.[2][10] The three Morrígna are also named as sisters of the three land goddesses Ériu, Banba and Fódla.
She is associated with the banshee of later folklore.

Etymology
There is some disagreement over the meaning of the Morrígan's name. Mor may derive from an Indo-European root connoting terror or monstrousness, cognate with the Old English maere (which survives in the modern English word "nightmare") and the Scandinavian mara and the Old East Slavic "mara" ("nightmare");[11] while rígan translates as 'queen'.[12] This can be reconstructed in the Proto-Celtic language as *Moro-rigani-s.[13] Accordingly, Morrígan is often translated as "Phantom Queen". This is the derivation generally favoured in current scholarship.[14]
In the Middle Irish period the name is often spelled Mórrígan with a lengthening diacritic over the o, seemingly intended to mean "Great Queen" (Old Irish mór, 'great';[11] this would derive from a hypothetical Proto-Celtic *Mara Rigani-s).[15] Whitley Stokes believed this latter spelling was due to a false etymology popular at the time.[16] There have also been attempts by modern writers to link the Morrígan with the Welsh literary figure Morgan le Fay from the Matter of Britain, in whose name mor may derive from Welsh word for "sea", but the names are derived from different cultures and branches of the Celtic linguistic tree.[11]

 

 

-
-
-
-
-
MORRIGAN
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
50
-
8
MORRIGAN
95
50
50
-
1
2
3
4
5
6
7
8
27
-
-
5+0
-
-
-
9+5
5+0
5+0
-
-
-
-
-
-
-
-
-
2+7
-
-
5
-
8
MORRIGAN
14
5
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
MORRIGAN
5
5
5
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
MORRIGAN
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
50
-
8
MORRIGAN
95
50
50
-
1
2
3
4
5
6
7
8
27
-
-
5+0
-
-
-
9+5
5+0
5+0
-
-
-
-
-
-
-
-
-
2+7
-
-
5
-
8
MORRIGAN
14
5
5
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
MORRIGAN
5
5
5
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
MORRIGAN
-
-
-
-
1
4
5
6
7
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
4
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
7
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
9
-
-
50
-
8
MORRIGAN
95
50
50
-
1
4
5
6
7
27
-
-
5+0
-
-
-
9+5
5+0
5+0
-
-
-
-
-
-
2+7
-
-
5
-
8
MORRIGAN
14
5
5
-
1
4
5
6
7
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
5
-
8
MORRIGAN
5
5
5
-
1
4
5
6
7
9

 

 

-
MINERAL
-
-
-
3
MIN
36
18
9
4
REAL
36
18
9
7
MINERAL
72
36
18
-
-
7+2
3+6
1+8
7
MINERAL
9
9
9

 

MERLIN MINERAL MERLIN

 

-
MERLIN
-
-
-
1
M
13
4
4
1
E
5
5
5
1
R
18
9
9
1
L
12
3
3
1
I
9
9
9
1
N
14
5
5
6
MERLIN
71
35
35
-
-
7+1
3+5
3+5
6
MERLIN
8
8
8

 

 

-
MINERAL
1
1
1
1
A
-
-
-
-
-
-
-
-
1
M
13
4
4
1
E
5
5
5
1
R
18
9
9
1
L
12
3
3
1
I
9
9
9
1
N
14
5
5
7
MINERAL
72
36
18
-
-
7+2
3+6
1+8
7
MINERAL
9
9
9

 

 

MINING FOR MINERALS

TINTAGEL

 

https://en.wikipedia.org/wiki/Merlin

Merlin (Welsh: Myrddin) is a legendary figure best known as the wizard featured in Arthurian legend and medieval Welsh poetry. The standard depiction of the character first appears in Geoffrey of Monmouth's Historia Regum Britanniae, written c. 1136, and is based on an amalgamation of previous historical and legendary ...
Significant other(s)?: ?Lady of the Lake?, ?Morgan le Fay
Created by?: ?Geoffrey of Monmouth
First appearance?: ?Prophetiae Merlini

Merlin (Welsh: Myrddin) is a legendary figure best known as the wizard featured in Arthurian legend and medieval Welsh poetry. The standard depiction of the character first appears in Geoffrey of Monmouth's Historia Regum Britanniae, written c. 1136, and is based on an amalgamation of previous historical and legendary figures. Geoffrey combined existing stories of Myrddin Wyllt (Merlinus Caledonensis), a North Brythonic prophet and madman with no connection to King Arthur, with tales of the Romano-British war leader Ambrosius Aurelianus to form the composite figure he called Merlin Ambrosius (Welsh: Myrddin Emrys). He is allegedly buried in the Broceliande forest, near Paimpont in Brittany.
Geoffrey's rendering of the character was immediately popular, especially in Wales.[1] Later writers expanded the account to produce a fuller image of the wizard. Merlin's traditional biography casts him as a cambion: born of a mortal woman, sired by an incubus, the non-human from whom he inherits his supernatural powers and abilities.[2] Merlin matures to an ascendant sagehood and engineers the birth of Arthur through magic and intrigue.[3] Later authors have Merlin serve as the king's advisor and mentor to the knights until he is bewitched and imprisoned by the Lady of the Lake.[3]

Name and etymology[edit]
The name "Merlin" is derived from the Welsh Myrddin, the name of the bard Myrddin Wyllt, one of the chief sources for the later legendary figure. Geoffrey of Monmouth Latinised the name to Merlinus in his works. Medievalist Gaston Paris suggests that Geoffrey chose the form Merlinus rather than the regular Merdinus to avoid a resemblance to the Anglo-Norman word merde (from Latin merda) for feces.[4]

Clas Myrddin or Merlin's Enclosure is an early name for Great Britain stated in the Third Series of Welsh Triads.[5] Celticist A. O. H. Jarman suggests that the Welsh name Myrddin (Welsh pronunciation: ['m?rð?n]) was derived from the toponym Caerfyrddin, the Welsh name for the town known in English as Carmarthen.[6] This contrasts with the popular folk etymology that the town was named for the bard. The name Carmarthen is derived from the town's previous Roman name Moridunum,[4][6] in turn derived from Celtic Brittonic moridunon, "sea fortress".[7]

 

www.english-heritage.org.uk/visit/places/tintagel-castle/

Immerse yourself in history, myths and stunning scenery at Tintagel Castle, set high on Cornwall's rugged north coast between Padstow and Bude. Inextricably linked with the legend of King Arthur, for centuries this dramatic castle and coastline has fired the imaginations of writers, artists and even the brother of a king.
?History of Tintagel Castle · ?Explore Tintagel Castle · ?Description of Tintagel Castle

Into Cornwall, Mining in Cornwall, Mine sites in Cornwall, Cornish ...
https://www.intocornwall.com/features/geology-and-mining.asp
Mineralogists will find a fine collection of Cornish minerals extracted from mines around Cornwall housed in the Royal Institution of Cornwall Museum in Truro, including: cassiterite (tin oxide); chalcopyrite (copper and iron sulphide); chalcocite (copper sulphide); galena (lead sulphide); native copper (pure copper metal in ...

 

 

-
-
-
-
9
CORRECTED
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
-
1
C
3
3
3
-
1
-
3
-
-
-
7
8
-
O
=
6
-
1
O
15
6
6
-
1
-
-
-
-
6
7
8
-
R
=
9
-
1
R
18
9
9
-
1
-
-
-
-
-
7
8
9
R
=
9
-
1
R
18
9
9
-
1
-
-
-
-
-
7
8
9
E
=
5
-
1
E
5
5
5
-
1
-
-
-
5
-
7
8
-
C
=
3
-
1
C
3
3
3
-
1
-
3
-
-
-
7
8
-
T
=
2
-
1
T
20
2
2
-
1
2
-
-
-
-
7
8
-
E
=
5
-
1
E
5
5
5
-
1
-
-
-
5
-
7
8
-
D
=
4
-
1
D
4
4
4
-
1
-
-
4
-
-
7
8
-
-
-
46
-
9
CORRECTED
91
46
46
-
1
2
6
4
10
6
7
8
18
-
-
4+6
-
-
-
9+1
4+6
4+6
-
-
-
-
-
1+0
-
-
-
1+8
-
-
10
-
9
CORRECTED
10
10
10
-
1
2
6
4
1
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
9
CORRECTED
1
1
1
-
1
2
6
4
1
6
7
8
9

 

 

-
-
-
-
9
CORRECTED
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
T
20
2
2
-
1
2
-
-
-
-
7
8
-
C
=
3
-
1
C
3
3
3
-
1
-
3
-
-
-
7
8
-
C
=
3
-
1
C
3
3
3
-
1
-
3
-
-
-
7
8
-
D
=
4
-
1
D
4
4
4
-
1
-
-
4
-
-
7
8
-
E
=
5
-
1
E
5
5
5
-
1
-
-
-
5
-
7
8
-
E
=
5
-
1
E
5
5
5
-
1
-
-
-
5
-
7
8
-
O
=
6
-
1
O
15
6
6
-
1
-
-
-
-
6
7
8
-
R
=
9
-
1
R
18
9
9
-
1
-
-
-
-
-
7
8
9
R
=
9
-
1
R
18
9
9
-
1
-
-
-
-
-
7
8
9
-
-
46
-
9
CORRECTED
91
46
46
-
1
2
6
4
10
6
7
8
18
-
-
4+6
-
-
-
9+1
4+6
4+6
-
-
-
-
-
1+0
-
-
-
1+8
-
-
10
-
9
CORRECTED
10
10
10
-
1
2
6
4
1
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
9
CORRECTED
1
1
1
-
1
2
6
4
1
6
7
8
9

 

 

9
CORRECTED
-
-
-
-
1
2
3
4
5
6
7
8
9
1
C+O
18
9
9
-
1
2
3
4
-
6
7
8
9
1
R
18
9
9
-
1
2
3
4
-
6
7
8
9
1
R
18
9
9
-
1
2
3
4
-
6
7
8
9
1
E
5
5
5
-
1
2
3
4
5
6
7
8
-
1
C+T
23
5
5
-
1
2
3
4
5
6
7
8
-
1
E+D
9
9
9
-
1
2
3
4
-
6
7
8
9
9
CORRECTED
91
46
46
-
1
2
3
4
10
6
7
8
36
-
-
9+1
4+6
4+6
-
-
-
-
-
1+0
-
-
-
3+6
9
CORRECTED
10
10
10
-
1
2
3
4
1
6
7
8
9
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
9
CORRECTED
1
1
1
-
1
2
3
4
1
6
7
8
9

 

 

9
CORRECTED
-
-
-
-
5
9
1
C+O
18
9
9
-
-
9
1
R
18
9
9
-
-
9
1
R
18
9
9
-
-
9
1
E
5
5
5
-
5
-
1
C+T
23
5
5
-
5
-
1
E+D
9
9
9
-
-
9
9
CORRECTED
91
46
46
-
10
36
-
-
9+1
4+6
4+6
-
1+0
3+6
9
CORRECTED
10
10
10
-
1
9
-
-
1+0
1+0
1+0
-
-
-
9
CORRECTED
1
1
1
-
1
9

 

 

ALGEBRA

 

-
-
-
-
7
ALGEBRA
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
28
-
7
ALGEBRA
46
28
28
-
2
2
3
4
5
6
7
8
9
-
-
2+8
-
-
-
4+6
2+8
2+8
-
-
-
-
-
-
-
-
-
-
-
-
10
-
7
ALGEBRA
10
10
10
-
2
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
ALGEBRA
1
1
1
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
ALGEBRA
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
L
=
3
2
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
G
=
7
3
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
B
=
2
5
1
B
2
2
2
-
-
2
-
4
-
6
-
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
-
-
28
-
7
ALGEBRA
46
28
28
-
2
2
3
4
5
6
7
8
9
-
-
2+8
-
-
-
4+6
2+8
2+8
-
-
-
-
-
-
-
-
-
-
-
-
10
-
7
ALGEBRA
10
10
10
-
2
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
ALGEBRA
1
1
1
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
ALGEBRA
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
A
=
1
7
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
B
=
2
5
1
B
2
2
2
-
-
2
-
4
-
6
-
8
-
L
=
3
2
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
G
=
7
3
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
-
-
28
-
7
ALGEBRA
46
28
28
-
2
2
3
4
5
6
7
8
9
-
-
2+8
-
-
-
4+6
2+8
2+8
-
-
-
-
-
-
-
-
-
-
-
-
10
-
7
ALGEBRA
10
10
10
-
2
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
7
ALGEBRA
1
1
1
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
7
ALGEBRA
-
-
-
-
1
2
3
5
7
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
B
=
2
5
1
B
2
2
2
-
-
2
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
5
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
7
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
9
-
-
28
-
7
ALGEBRA
46
28
28
-
2
2
3
5
7
9
-
-
2+8
-
-
-
4+6
2+8
2+8
-
-
-
-
-
-
-
-
-
10
-
7
ALGEBRA
10
10
10
-
2
2
3
5
7
9
-
-
1+0
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
1
-
7
ALGEBRA
1
1
1
-
2
2
3
5
7
9

 

 

-
-
-
-
9
EQUATIONS
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Q
=
7
2
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
3
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
7
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
28
-
9
EQUATIONS
121
49
40
-
2
2
3
4
10
6
7
8
9
-
-
2+8
-
-
-
1+2+1
4+9
4+0
-
-
-
-
-
1+0
-
-
-
-
-
-
10
-
9
EQUATIONS
4
13
4
-
2
2
3
4
1
6
7
8
9
-
-
1+0
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
9
EQUATIONS
4
4
4
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
9
EQUATIONS
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
4
5
-
7
-
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
4
-
-
7
8
-
U
=
3
3
1
U
21
3
3
-
-
-
3
4
-
-
7
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
4
-
-
7
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
4
-
-
7
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
4
-
-
7
-
9
O
=
6
7
1
O
15
6
6
-
-
-
-
4
-
6
7
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
4
5
-
7
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
4
-
-
7
-
-
-
-
40
-
9
EQUATIONS
121
49
40
-
2
2
3
4
10
6
7
8
9
-
-
4+0
-
-
-
1+2+1
4+9
4+0
-
-
-
-
-
1+0
-
-
-
-
-
-
4
-
9
EQUATIONS
4
13
4
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
EQUATIONS
4
4
4
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
9
EQUATIONS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
4
1
A
1
1
1
-
1
-
-
4
-
-
7
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
4
-
-
7
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
4
-
-
7
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
4
-
-
7
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
4
5
-
7
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
4
5
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
4
-
6
7
-
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
4
-
-
7
8
-
I
=
9
6
1
I
9
9
9
-
-
-
-
4
-
-
7
-
9
-
-
40
-
9
EQUATIONS
121
49
40
-
2
2
3
4
10
6
7
8
9
-
-
4+0
-
-
-
1+2+1
4+9
4+0
-
-
-
-
-
1+0
-
-
-
-
-
-
4
-
9
EQUATIONS
4
13
4
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
EQUATIONS
4
4
4
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
9
EQUATIONS
-
-
-
-
1
2
3
5
6
8
9
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
5
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
6
-
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
40
-
9
EQUATIONS
121
49
40
-
2
2
3
10
6
8
9
-
-
4+0
-
-
-
1+2+1
4+9
4+0
-
-
-
-
1+0
-
-
-
-
-
4
-
9
EQUATIONS
4
13
4
-
2
2
3
1
6
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
9
EQUATIONS
4
4
4
-
2
2
3
1
6
8
9

 

 

T
=
2
6
1
THE
33
15
6
E
=
5
-
1
EQUATION
102
39
3
-
-
4
-
9
Add to Reduce
135
54
9
-
-
-
-
-
Reduce to Deduce
1+3+5
5+4
-
-
-
-
-
9
Essence of Number
9
9
9

 

 
 
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