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A

MAZE

IN

ZAZAZA ENTERS AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

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26
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=
115
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BEYOND THE VEIL ANOTHER VEIL ANOTHER VEIL BEYOND

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

"Perhaps the most famous of the early Jewish mystical texts is the fifth century Sefer Yezirah (The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."

 

Page 250

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY THE ACCOUNT

IS UNASHAMEDLY SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE AS

THOUGH HE WERE WRITING A BOOK. BUT LANGUAGE HAS BEEN ENTIRELY TRANSFORMED AND THE

MESSAGE OF CREATION IS NO LONGER CLEAR EACH LETTER OF THE HEBREW ALPHABET IS GIVEN

A NUMERICAL VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS REARRANGING

THEM IN ENDLESS CONFIGURATIONS THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL

CONNOTATIONS OF WORDS

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

....

 

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ME
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1

 

 

 

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LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

"By writing the 26 letters of the alphabet in a certain order one may put down almost any message (this book 'is written with the same letters' as the Encyclopaedia Britannica and Winnie the Pooh, only the order of the letters differs). In the same way Nature is able to convey with her language how a cell and a whole organism is to be constructed and how it is to function. Nature has succeeded better than we humans; for the genetic code there is only one universal language which is the same in a man, a bean plant and a bacterium."

"FOR THE GENETIC CODE THERE IS ONLY ONE UNIVERSAL LANGUAGE"

 

DNA AND DNA DNA AND DNA DNA AND DNA

DNA AND DNA DNA AND DNA DNA AND DNA

 

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

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THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

....

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly. too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the / Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry In the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 36in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus. Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillana adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

The Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656 years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, multiply this by 2 and again we have the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as-the interesting number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes difficult to escape the suspicion that many signs (number and otherwise) - indicate that early man observed the results of the movement of Precession and that the - transmission of this information was considered of prime importance.

With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would have constituted the construction-of a 'Unified Field Theory' for nothing less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced, that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two, four. Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radius ekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up his piece of stripped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

....

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 466

"Had not the normal, since time was, lived on the achievements of the abnormal? Men consciously and voluntarily descended into disease and madness, in search of knowledge which, acquired by fanaticism, would lead back to health; after the possession and use of it had ceased to be conditioned by that heroic and abnormal act of sacrifice. That was the true death on the cross, the true Atonement."

 

THE TRUE DEATH ON THE CROSS THE TRUE AT ONE MENT

 

 

ATONEMENT

 

-
-
-
-
A
-
-
-
-
-
-
-
-
T
-
-
-
-
-
-
-
-
O
-
-
-
-
-
-
-
-
N
-
-
-
-
A
T
O
N
E
M
E
N
T
-
-
-
-
M
-
-
-
-
-
-
-
-
E
-
-
-
-
-
-
-
-
N
-
-
-
-
-
-
-
-
T
-
-
-
-

 

 

ADVENT 490 ADVENT

 

EUCLID
EUCLID
THE ELEMENTS
THE ELEMENTS
GEO
GEODE
GEOMETRY
GEOMETRICAL
GEOCENTRIC
GEO, GEOMETRY, GEOMETRICAL, GEOCENTRIC
GEOGRAPHY
FRACTALS
OMPHALOS
ORACLE
ACE
DICE
IMAN
CABBALA
KABBALA
GREAT GREEN, GREAT, GREEN
TURN, TURNS, TURNED, TURNING
ASEKHA, ASEK, HA
RACE
JEWISH, NEW, YEAR
NEBUCHADNEZZAR
NEW, OLD
I, AM, NEUTRAL
VRIL, VIRILITY
VRIL, VIRILE
MAGNETIC, THOUGHT, GODS, DIVINE, REALITY

 

 

CITY OF REVELATION

John Michell 1972

Page 77

CHAPTER SEVEN

3168, The Perimeter of the Temple

"If the numbers of the sacred principles, mentioned by St John in connection with the New Jerusalem, are obtained from the Greek text by the cabalistic method of gematria, it is found that they correspond to the dimensions of the city, set out in Fig 16. (Figure omitted) For example, the perimeter of a hexagon contained within the circle representing the earth, 7920 feet in diameter, measures 2376 feet, and 2376 is the number of (Greek text omitted), the twelve apostles of the Lamb (Revelation 21.14). 2376 x 2 feet is equal to 1746 MY, and 1745 = (Greek text omitted), the twelve apostles. The names of the apostles are said to be in the twelve foundations of the wall of the city. The wall is the circle of diameter 7920 feet and 14,400 cubits in circumference, and the foundations are the twelve corners of the double hexagon inscribed within it, fonowing the customary pattern of an astrological chart. The position of the twelve apostles in the scheme is thus clearly defined.
Of all the canonical numbers the most notable is 3168. The New Jerusalem measures 48,000 furlongs or 31,680,000 feet round the perimeter of its four sides; the mean perimeter of the Stonehenge sarsen circle is 316.8 feet; the perimeter of the square 12 hides of Glastonbury is 31,680 feet; the significance of 31,680 in the canon of cosmology is illustrated in Fig.11, and we shall also find this number set round the border of Plato's mystical city, described in Laws.
Obviously the number 3168 had an important symbolic meaning, the Christian interpretation of which is provided in New Testament
gematria. The most sacred name of Christianity is (Greek text omitted);
(Greek text omitted), Lord Jesus Christ, and the number of these three words together is 3168. (Greek text omitted) is an astrological term meaning the ruler or dominant influence.
Another sacred phrase from the New Testament, (Greek text omitted) the Power of Christ (2 Corinthians 12.9) has the value 3168 if the alternative spelling of Christos, (Greek text omitted) is adopted.

Page 78

The perimeter of the temple is 3168, Lord Jesus Christ, when the temple is measured by the foot, the most sacred unit of ancient metrology. In terms of the megalithic yard (2.72 feet), however, the perimeter measures 1164, because 3168 feet = 1164 MY. Yet this makes no difference to the symbolic interpretation by gematria, for 1164 is the number of another name of Christ, (Greek text omitted) Son of God.

As a geodetic or earth-measuring number, 3168 also demonstrates the antiquity and sacred origin of British metrology, for
31,680 inches = half a mile

31,680 ft. = 6 miles.

31,680 furlongs = 3960 miles = radius of the earth.

31,680 miles = perimeter of square containing the terrestrial sphere.

31,680 miles = circumference of circle drawn on the combined diameters of the earth and moon (10,080 miles)

Other cosmological correspondences of 3168 are given on page 109.

The Stonehenge sarsen circle with circumference of 316.8 feet
contains an area of 888 square yards, 888 being the number of Jesus, which is equal to 1080 square MY. The circle contained within a square of perimeter 316.8 feet, corresponding to the bluestone circle at Stonehenge, has an area of 666 square MY. Thus the two stone circles at Stonehenge have areas of 1080 and 666 square MY, these two numbers representing the opposite poles of lunar and solar or negative and positive energy.
The number 144 or 122 is characteristic of the New Jerusalem scheme, and 3168 demonstrates the value of (pi symbol 22/7 omitted) in terms of this number, for 144 x 7 = 1008 and 144 x 22 = 3168.

3168 in Plato's city
A remarkable use of the number 3168 occurs in Plato's account in Book V of.Laws of the mystical dimensions of the perfect city. Throughout his work Plato makes guarded reference to a secret canon of numbers that applies universally to every aspect of human life and activity, including government, astronomy, acoustics, kinetics, plane and solid geometry and divination. Linear measurements, areas and volumes are obviously incommensurable, but Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040. This is the ideal number of citizens in the state and serves other purposes in con­/ Page 79 / nection with the framing of laws and standards. The reason why it is most suitable for all matters of division is that for its size it has the greatest number of divisors, 60 in all, including the entire decad, the numbers 1 - 10. Another property of the number 5040 is that it is the radius of a circle with circumference 31,680. Further examina­tion of the numerical foundations of Plato's state shows that the scheme to which he refers is the ancient plan of the cosmic temple.
The lawgivers in Plato's state are reminded that the perfect human society would be one in which all possessions, wives, children, land and chattels were held in common, where all the citizens were of one mind and acted together so harmoniously that it were as if eyes, ears and hands were also common property. To keep this ideal alive is the function of the prophet. Human nature and conditioning, however, demand a more practical alternative, 'very near to the first in immortality and second to it in merit'. This is provided in Laws V.
Plato's state is arranged in a manner that can scarcely be under­stood literally, and is obviously intended, like the New Jerusalem, as a geometer's allegory. The land is all divided into twelve parts, each dedicated to one of the twelve gods and populated by one of the twelve tribes of the 5040 households. The city is similarly divided, forming a microcosm of the state as a whole. In the centre of the city is the acropolis and 'from this centre he must divide up the city itself and the whole country into twelve parts. The twelve parts must be equalised by making those of good land small and those of inferior land greater. He must mark off 5040 allotments, and each of these he must cut in two and join two pieces to form the allotments, so that each contains a near piece and a distant piece - joining the piece next to the city with the piece furthest off, the second nearest with the second furthest, and so on with the rest.'
The only way in which this division can be represented is by a circle of radius 5040, a hundred times larger than that of Stonehenge measured in feet; the perimeter of this circle is 31 ,680. In Fig. 24 (Figure 24 omitted) the radius of the circle should be divided equally into 5040 parts to produce 5040 concentric circles. These are bisected into 10,080 semi­circles by the diameter and positioned out in Plato's manner into 5040 double allotments, each of equal area.
In this scheme 31,680 is not only the circumference of the circular state, but also the area of each of its 2520 pairs of rings, proving Plato's assertion that linear and area pleasurements can be made / Page 80 / (Figure 24 omitted) commensurable by number. The entire circle is divided into two halves, each containing 39,916,800 square units of land. These numbers, which are inherent in the New Jerusalem scheme, have the following significance:
31,680 is divisible by all the numbers1-12 with the exception of 7

5040 = 1 x 2 x 3 x 4 x 5 x 6 x 7

39,916,800 = 1 x 2 x 3 x 4 x 5x 6 x 7 x 8 x 9 x.10 x 11

5040, the radius of the circular city, is the product of the numbers1 - 7; 7920, the side of the square city, is the product of numbers 8 - 11. In each case the perimeter of the city is 31,680. In Plato's Republic is the famous, cryptic reference to the 'marriage number', which should be consulted by the guardians of the state in all matters relating to the seasonal union of male and female. There appear to be two numbers involved, adding up to a third, but the riddle is so obscure that no firm solution has been reached despite the vast literature on the subject. For various reasons the number 12,960,000 or 36002 is most commonly proposed, and this would seem appropriate, for 12,960 = 5040 + 7920. 12,960 therefore represents the union of square and circle, symbol of the sacred marriage, and the gematria is also appropriate, for 1296 = (Greek text omitted) Mary mother of Jesus.

FIGURE 24 (Figure omitted) Plato's city divided into 5040 rings, Perimeter = 31,680, Areas: A + a = B + b = C + c = 31,680.

 

 

INCLUDE EUCLID INCLUDE

 

 

-
-
-
-
-
EUCLID
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
5
5
5
-
E
-
-
5
-
E
5
E
-
-
-
-
-
U
21
3
3
-
U
3
-
-
-
U
3
U
-
-
-
-
-
C
3
3
3
-
C
3
-
-
-
C
3
C
-
-
-
-
-
L
12
3
3
-
L
3
-
-
-
L
3
L
-
-
-
-
-
I
9
9
9
-
I
-
-
-
9
I
9
I
-
-
-
-
-
D
4
4
4
-
D
-
4
-
-
D
4
D
E
=
5
-
6
EUCLID
54
27
27
-
-
9
4
-
9
-
27
-
-
-
-
-
-
-
5+4
2+7
2+7
-
-
-
-
-
-
-
2+7
-
-
-
5
-
6
EUCLID
9
9
9
-
-
9
4
-
9
-
9
-

 

 

-
6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
-
6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
-
6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
-
6
E
U
C
L
I
D
-
-
-
-
-
-
-
-
1
-
-
-
-
-
--
-
-
--
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
5
-
-
-
-
-
-
--
5
occurs
x
1
=
5
6
-
-
--
-
--
--
-
-
-
6
-
-
-
-
--
7
-
-
--
-
--
--
-
-
--
7
-
-
-
-
--
8
-
-
--
-
--
--
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
24
6
E
U
C
L
I
D
-
-
21
-
-
6
-
27
2+4
-
-
3
3
3
-
-
-
-
2+1
-
-
-
-
2+7
6
6
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
6
6
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
6
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
6
E
U
C
L
I
D
-
-
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
6
E
U
C
L
I
D
-
-
21
-
-
6
-
27
-
-
3
3
3
-
-
-
-
2+1
-
-
-
-
2+7
6
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
6
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

T
=
2
3
THE
33
15
6
E
=
5
8
ELEMENTS
93
30
3
-
-
7
11
Add to Reduce
126
45
9
-
-
-
1+1
Reduce to Deduce
1+2+6
4+5
-
Q
-
7
2
Essence of Number
9
9
9

 

 

-
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
5
-
1
+
=
14
1+4
=
5
-
5
-
5
-
-
-
8
-
-
-
-
-
-
-
14
-
19
+
=
41
4+1
=
5
-
5
-
5
-
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
5
3
5
4
5
-
2
-
+
=
31
3+1
=
4
-
4
-
4
-
-
20
-
5
-
5
12
5
13
5
-
20
-
+
=
85
8+5
=
13
1+3
4
-
4
-
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
5
12
5
13
5
14
20
19
+
=
126
1+2+6
=
9
-
9
-
9
-
-
2
8
5
-
5
3
5
4
5
5
2
1
+
=
45
4+5
=
9
-
9
-
9
-
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
--
3
--
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
5
-
5
-
5
-
5
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
22
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
23
-
-
11
-
45
-
27
2+2
1+1
-
-
5
-
5
-
5
-
5
5
-
-
-
-
2+3
-
-
1+1
-
4+5
-
2+7
4
2
T
H
E
-
E
L
E
M
E
N
T
S
-
-
5
-
-
2
-
9
-
9
-
-
2
8
5
-
5
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
4
2
T
H
E
-
E
L
E
M
E
N
T
S
-
-
5
-
-
2
-
1
-
1

 

 

11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
-
-
5
-
1
+
=
14
1+4
=
5
-
5
-
5
-
-
8
-
-
-
-
-
-
-
14
-
19
+
=
41
4+1
=
5
-
5
-
5
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
5
3
5
4
5
-
2
-
+
=
31
3+1
=
4
-
4
-
4
-
20
-
5
-
5
12
5
13
5
-
20
-
+
=
85
8+5
=
13
1+3
4
-
4
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
5
12
5
13
5
14
20
19
+
=
126
1+2+6
=
9
-
9
-
9
-
2
8
5
-
5
3
5
4
5
5
2
1
+
=
45
4+5
=
9
-
9
-
9
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
1
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
--
3
--
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
5
-
5
-
5
-
5
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
11
T
H
E
-
E
L
E
M
E
N
T
S
-
-
23
-
-
11
-
45
-
27
1+1
-
-
5
-
5
-
5
-
5
5
-
-
-
-
2+3
-
-
1+1
-
4+5
-
2+7
2
T
H
E
-
E
L
E
M
E
N
T
S
-
-
5
-
-
2
-
9
-
9
-
2
8
5
-
5
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
2
T
H
E
-
E
L
E
M
E
N
T
S
-
-
5
-
-
2
-
1
-
1

 

 

G
=
7
3
GEO
27
18
9
G
=
7
5
GEODE
27
18
9
G
=
7
8
GEOMETRY
108
45
9
G
=
7
11
GEOMETRICAL
108
54
9
G
=
7
10
GEOCENTRIC
99
54
9

 

 

-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
7
5
-
+
=
12
1+2
=
3
=
3
-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
7
5
15
+
=
27
2+7
=
9
=
9
-
-
7
5
6
+
=
18
1+8
=
9
=
9
-
3
G
E
O
-
-
-
-
-
--
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
27
3
G
E
O
-
-
18
-
-
3
-
18
2+7
-
-
-
-
-
-
1+8
-
-
-
-
1+8
9
3
G
E
O
-
-
9
-
-
3
-
9
-
-
7
5
6
-
-
-
-
-
-
-
-
9
3
G
E
O
-
-
9
-
-
3
-
9

 

 

3
G
E
O
-
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
G
E
O
-
-
-
-
-
--
-
-
-
7
5
-
+
=
12
1+2
=
3
=
3
3
G
E
O
-
-
-
-
-
--
-
-
-
7
5
15
+
=
27
2+7
=
9
=
9
-
7
5
6
+
=
18
1+8
=
9
=
9
3
G
E
O
-
-
-
-
-
--
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
7
occurs
x
1
=
7
3
G
E
O
-
-
18
-
-
3
-
18
-
-
-
-
-
-
1+8
-
-
-
-
1+8
3
G
E
O
-
-
9
-
-
3
-
9
-
7
5
6
-
-
-
-
-
-
-
-
3
G
E
O
-
-
9
-
-
3
-
9

 

 

-
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
+
=
15
1+5
=
6
=
6
=
6
-
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
5
+
=
21
2+1
=
3
=
3
=
3
-
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
4
5
+
=
36
3+6
=
9
=
9
=
9
-
-
7
5
6
4
5
+
=
27
2+7
=
9
=
9
=
9
-
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
27
5
G
E
O
D
E
-
-
22
-
-
5
-
27
-
18
2+7
-
-
-
-
-
-
-
-
2+2
-
-
-
-
2+7
-
1+8
9
5
G
E
O
D
E
-
-
4
-
-
5
-
9
-
9
-
-
7
5
6
4
5
-
-
-
-
-
-
-
-
-
-
9
5
G
E
O
D
E
-
-
4
-
-
5
-
9
-
9

 

 

5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
+
=
15
1+5
=
6
=
6
=
6
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
7
5
-
4
5
+
=
21
2+1
=
3
=
3
=
3
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
-
7
5
15
4
5
+
=
36
3+6
=
9
=
9
=
9
-
7
5
6
4
5
+
=
27
2+7
=
9
=
9
=
9
5
G
E
O
D
E
-
-
-
-
-
--
-
-
-
-
 
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
5
G
E
O
D
E
-
-
22
-
-
5
-
27
-
18
-
-
-
-
-
-
-
-
2+2
-
-
-
-
2+7
-
1+8
5
G
E
O
D
E
-
-
4
-
-
5
-
9
-
9
-
7
5
6
4
5
-
-
-
-
-
-
-
-
-
-
5
G
E
O
D
E
-
-
4
-
-
5
-
9
-
9

 

 

-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
5
2
9
25
+
=
39
3+9
=
12
1+2
3
=
3
-
-
7
5
-
13
5
20
18
7
+
=
93
9+3
=
12
1+2
3
=
3
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
13
5
20
18
25
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
5
6
4
5
2
9
7
+
=
45
4+5
=
9
=
9
=
9
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
12
8
G
E
O
M
E
T
R
Y
-
-
33
-
-
8
-
45
-
27
1+2
-
-
-
-
-
-
-
9
-
-
-
3+3
-
-
-
-
4+5
-
2+7
3
8
G
E
O
M
E
T
R
Y
-
-
9
-
-
8
-
9
-
9

 

 

8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
7
5
-
4
5
2
9
25
+
=
39
3+9
=
12
1+2
3
=
3
-
7
5
-
13
5
20
18
7
+
=
93
9+3
=
12
1+2
3
=
3
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
7
5
15
13
5
20
18
25
+
=
108
1+0+8
=
9
=
9
=
9
-
7
5
6
4
5
2
9
7
+
=
45
4+5
=
9
=
9
=
9
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
8
G
E
O
M
E
T
R
Y
-
-
33
-
-
8
-
45
-
27
-
-
-
-
-
-
-
9
-
-
-
3+3
-
-
-
-
4+5
-
2+7
8
G
E
O
M
E
T
R
Y
-
-
9
-
-
8
-
9
-
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
45
-
8
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
-
-
-
9
-
8
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
45
-
8
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
-
-
-
9
-
8
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
2
4
5
6
7
9
T
=
2
-
1
T
20
2
2
-
2
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
4
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
6
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
7
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
45
-
8
GEOMETRY
108
45
45
-
2
4
10
6
14
9
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
1+0
-
1+4
-
-
-
9
-
8
GEOMETRY
9
9
9
-
2
4
1
6
5
9

 

 

-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
9
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
9
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
5
2
9
-
3
1
3
+
=
39
3+9
=
12
1+2
3
=
3
-
-
7
5
-
13
5
20
18
-
3
1
12
+
=
84
8+4
=
12
1+2
3
=
3
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
13
5
20
18
9
3
1
12
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
5
6
4
5
2
9
9
3
1
3
+
=
54
5+4
=
9
=
9
=
9
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
11
G
E
O
M
E
T
R
I
C
A
L
-
-
37
-
-
11
-
54
-
36
-
1+1
-
-
-
-
-
-
9
9
-
-
-
-
-
10
-
-
1+1
-
5+4
-
3+6
8
2
G
E
O
M
E
T
R
I
C
A
L
-
-
1
-
-
2
-
9
-
9

 

 

-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
3
5
-
2
9
-
3
+
=
34
3+4
=
7
=
7
=
7
-
-
7
5
-
3
5
-
20
18
-
3
+
=
61
6+1
=
7
=
7
=
7
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
3
5
14
20
18
9
3
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
5
6
3
5
5
2
9
9
3
+
=
54
5+4
=
9
=
9
=
9
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
13
10
G
E
O
C
E
N
T
R
I
C
-
-
32
-
-
10
-
54
-
36
1+3
1+0
-
-
-
-
-
-
-
9
9
-
-
-
3+2
-
-
1+0
-
5+4
-
3+6
4
1
G
E
O
C
E
N
T
R
I
C
-
-
5
-
-
1
-
9
-
9

 

 

10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
15
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
7
5
-
3
5
-
2
9
-
3
+
=
34
3+4
=
7
=
7
=
7
-
7
5
-
3
5
-
20
18
-
3
+
=
61
6+1
=
7
=
7
=
7
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
7
5
15
3
5
14
20
18
9
3
+
=
99
9+9
=
18
1+8
9
=
9
-
7
5
6
3
5
5
2
9
9
3
+
=
54
5+4
=
9
=
9
=
9
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
5
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
10
G
E
O
C
E
N
T
R
I
C
-
-
32
-
-
10
-
54
-
36
1+0
-
-
-
-
-
-
-
9
9
-
-
-
3+2
-
-
1+0
-
5+4
-
3+6
1
G
E
O
C
E
N
T
R
I
C
-
-
5
-
-
1
-
9
-
9

 

 

-
-
-
-
-
GEOGRAPHY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
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
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
57
-
9
GEOGRAPHY
102
57
57
-
1
2
3
4
5
6
28
8
9
-
-
5+7
-
-
-
1+0+2
5+7
5+7
-
-
-
-
-
-
-
2+8
-
-
-
-
12
-
9
GEOGRAPHY
3
12
12
-
1
2
3
4
5
6
10
8
9
-
-
1+2
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
1+0
-
-
-
-
3
-
9
GEOGRAPHYY
3
3
3
-
1
2
3
4
5
6
1
8
9

 

 

-
-
-
-
-
GEOGRAPHY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
1
G
7
7
7
-
-
2
3
4
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
2
3
4
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
2
3
4
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
2
3
4
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
2
3
4
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
2
3
4
-
-
-
8
-
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
-
-
7
-
-
-
-
57
-
9
GEOGRAPHY
102
57
57
-
1
2
3
4
5
6
28
8
9
-
-
5+7
-
-
-
1+0+2
5+7
5+7
-
-
-
-
-
-
-
2+8
-
-
-
-
12
-
9
GEOGRAPHY
3
12
12
-
1
2
3
4
5
6
10
8
9
-
-
1+2
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
1+0
-
-
-
-
3
-
9
GEOGRAPHY
3
3
3
-
1
2
3
4
5
6
1
8
9

 

 

-
-
-
-
-
GEOGRAPHY
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
2
3
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
2
3
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
2
3
4
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
2
3
4
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
2
3
4
-
-
7
-
-
P
=
7
-
1
P
16
7
7
-
-
2
3
4
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
2
3
4
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
2
3
4
-
-
-
-
9
-
-
57
-
9
GEOGRAPHY
102
57
57
-
1
2
3
4
5
6
28
8
9
-
-
5+7
-
-
-
1+0+2
5+7
5+7
-
-
-
-
-
-
-
2+8
-
-
-
-
12
-
9
GEOGRAPHY
3
12
12
-
1
2
3
4
5
6
10
8
9
-
-
1+2
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
1+0
-
-
-
-
3
-
9
GEOGRAPHY
3
3
3
-
1
2
3
4
5
6
1
8
9

 

 

-
-
-
-
-
GEOGRAPHY
-
-
-
-
1
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
7
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
57
-
9
GEOGRAPHY
102
57
57
-
1
5
6
28
8
9
-
-
5+7
-
-
-
1+0+2
5+7
5+7
-
-
-
-
2+8
-
-
-
-
12
-
9
GEOGRAPHY
3
12
12
-
1
5
6
10
8
9
-
-
1+2
-
-
-
-
1+2
1+2
-
-
-
-
1+0
-
-
-
-
3
-
9
GEOGRAPHY
3
3
3
-
1
5
6
1
8
9

 

 

-
-
-
-
-
FRACTALS
-
-
-
-
1
2
3
4
5
6
7
8
9
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
26
-
8
FRACTALS
80
35
26
-
3
2
6
4
5
6
7
8
9
-
-
2+6
-
-
-
8+0
3+5
2+6
-
-
-
-
-
-
-
-
-
-
-
-
8
-
8
FRACTALS
8
8
8
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
FRACTALS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
4
5
-
7
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
4
5
-
7
8
-
S
=
1
-
1
S
19
10
1
-
1
-
-
4
5
-
7
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
4
5
-
7
8
-
C
=
3
-
1
C
3
3
3
-
-
-
3
4
5
-
7
8
-
L
=
3
-
1
L
12
3
3
-
-
-
3
4
5
-
7
8
-
F
=
6
-
1
F
6
6
6
-
-
-
-
4
5
6
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
4
5
-
7
8
9
-
-
26
-
8
FRACTALS
80
35
26
-
3
2
6
4
5
6
7
8
9
-
-
2+6
-
-
-
8+0
3+5
2+6
-
-
-
-
-
-
-
-
-
-
-
-
8
-
8
FRACTALS
8
8
8
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
FRACTALS
-
-
-
-
1
2
3
6
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
6
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
9
-
-
26
-
8
FRACTALS
80
35
26
-
3
2
6
6
9
-
-
2+6
-
-
-
8+0
3+5
2+6
-
-
-
-
-
-
-
-
8
-
8
FRACTALS
8
8
8
-
3
2
6
6
9

 

 

-
8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
8
-
-
6
1
+
=
21
2+1
=
3
=
3
=
3
-
-
15
-
-
8
-
-
15
19
+
=
57
5+7
=
12
1+2
3
=
3
-
8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-``
-
-
-
-
4
7
-
1
3
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
13
16
-
1
12
-
-
+
=
42
4+2
=
6
=
6
=
6
-
8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-
-
-
-
15
13
16
8
1
12
15
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
6
4
7
8
1
3
6
1
+
=
36
3+6
=
9
=
9
=
9
-
8
O
M
P
H
A
L
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
--
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
7
--
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
16
8
O
M
P
H
A
L
O
S
-
-
29
-
-
8
-
36
-
27
1+6
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
3+6
-
2+7
7
8
O
M
P
H
A
L
O
S
-
-
11
-
-
-
-
9
-
9
-
-
6
4
7
8
1
3
6
1
-
-
1+1
-
-
-
-
-
-
-
7
8
O
M
P
H
A
L
O
S
-
-
2
-
-
8
-
9
-
9

 

 

8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-
-
-
6
-
-
8
-
-
6
1
+
=
21
2+1
=
3
=
3
=
3
-
15
-
-
8
-
-
15
19
+
=
57
5+7
=
12
1+2
3
=
3
8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-``
-
-
-
4
7
-
1
3
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
13
16
-
1
12
-
-
+
=
42
4+2
=
6
=
6
=
6
8
O
M
P
H
A
L
O
S
-
-
-
-
-
--
-
-
-
-
-
15
13
16
8
1
12
15
19
+
=
99
9+9
=
18
1+8
9
=
9
-
6
4
7
8
1
3
6
1
+
=
36
3+6
=
9
=
9
=
9
8
O
M
P
H
A
L
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
--
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
6
-
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
--
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
8
O
M
P
H
A
L
O
S
-
-
29
-
-
8
-
36
-
27
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
3+6
-
2+7
8
O
M
P
H
A
L
O
S
-
-
11
-
-
-
-
9
-
9
-
6
4
7
8
1
3
6
1
-
-
1+1
-
-
-
-
-
-
-
8
O
M
P
H
A
L
O
S
-
-
2
-
-
8
-
9
-
9

 

 

-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
-
9
1
3
3
5
+
=
21
2+1
=
3
=
3
-
-
-
18
1
3
12
5
+
=
39
3+9
=
12
1+2
3
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
15
18
1
3
12
5
+
=
54
5+4
=
9
=
9
-
-
6
9
1
3
3
5
+
=
27
2+7
=
9
=
9
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
21
6
O
R
A
C
L
E
-
-
24
-
-
6
-
27
2+1
-
-
9
-
-
-
-
-
-
2+4
-
-
-
-
2+7
3
6
O
R
A
C
L
E
-
-
6
-
-
6
-
9

 

 

-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
-
9
1
3
3
5
+
=
21
2+1
=
3
=
3
-
-
-
18
1
3
12
5
+
=
39
3+9
=
12
1+2
3
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
15
18
1
3
12
5
+
=
54
5+4
=
9
=
9
-
-
6
9
1
3
3
5
+
=
27
2+7
=
9
=
9
-
6
O
R
A
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
21
6
O
R
A
C
L
E
-
-
24
-
-
6
-
27
2+1
-
-
9
-
-
-
-
-
-
2+4
-
-
-
-
2+7
3
6
O
R
A
C
L
E
-
-
6
-
-
6
-
9

 

 

-
3
A
C
E
-
-
-
-
-
--
-
-
-
-
1
3
5
+
=
9
-
=
9
=
9
-
3
A
C
E
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
36
3
A
C
E
-
-
9
-
-
3
-
9
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
3
A
C
E
-
-
9
-
-
3
-
9

 

 

3
A
C
E
-
-
-
-
-
--
-
-
-
1
3
5
+
=
9
-
=
9
=
9
3
A
C
E
-
-
-
-
-
--
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
5
occurs
x
1
=
5
3
A
C
E
-
-
9
-
-
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
3
A
C
E
-
-
9
-
-
3
-
9

 

 

-
4
D
I
C
E
-
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
-
4
D
I
C
E
-
-
-
-
-
-
-
-
-
-
4
-
3
5
+
=
12
1+2
=
3
=
3
-
4
D
I
C
E
-
-
-
-
-
-
-
-
-
-
4
9
3
5
+
=
21
2+1
=
3
=
3
-
4
D
I
C
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
24
4
D
I
C
E
-
-
21
-
-
4
-
21
2+4
-
-
9
-
-
-
-
2+1
-
-
-
-
2+1
6
4
D
I
C
E
-
-
3
-
-
4
-
3

 

 

4
D
I
C
E
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
4
D
I
C
E
-
-
-
-
-
-
-
-
-
4
-
3
5
+
=
12
1+2
=
3
=
3
4
D
I
C
E
-
-
-
-
-
-
-
-
-
4
9
3
5
+
=
21
2+1
=
3
=
3
4
D
I
C
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
9
-
-
-
-
9
occurs
x
1
=
9
4
D
I
C
E
-
-
21
-
-
4
-
21
-
-
9
-
-
-
-
2+1
-
-
-
-
2+1
4
D
I
C
E
-
-
3
-
-
4
-
3

 

 

 

 

Imam Reza shrine - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Imam_Reza_shrine
Imām Reza shrine (Persian: حرم امام رضا) in Mashhad, Iran is a complex which contains the mausoleum of Imām Reza, the eighth Imām of Twelver Shi'ites. ...

Mashhad - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Mashhad

Mashhad (Persian: مشهد Mashhad, Arabic: مشهد Mašhad‎, English: The Place of Martyrdom), is the second largest city in Iran and one of the holiest cities in the ...

Mashhad International Airport - Payam Mashhad FC - Takhti Stadium (Mashhad)

 

 

I
=
9
-
4
IMAM
36
18
9
R
=
9
-
4
REZA
50
23
5
S
-
18
4
8
First Total
86
41
14
-
S
1+8
-
-
Add to Reduce
8+6
4+1
1+4
S
-
9
4
5
Second Total
14
5
5
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
9
-
5
Essence of Number
5
5
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
-
7
MASHHAD
54
27
9
I
=
9
-
4
IRAN
42
24
6

 

 

-
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
-
-
9
-
-
-
+
=
9
-
=
9
=
9
-
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
-
4
1
4
+
=
9
-
=
9
=
9
-
-
-
13
1
13
+
=
27
2+7
=
9
=
9
-
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
9
13
1
13
+
=
36
3+6
=
9
=
9
-
-
9
4
1
4
+
=
18
1+8
=
9
=
9
-
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
4
-
4
-
-
4
occurs
x
2
=
8
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
31
4
I
M
A
M
-
-
14
-
-
4
-
18
3+1
-
9
-
-
-
-
-
1+4
-
-
-
-
1+8
4
4
I
M
A
M
-
-
5
-
-
4
-
9
-
-
9
4
1
4
-
-
-
-
-
-
-
-
4
4
I
M
A
M
-
-
5
-
-
4
-
9

 

 

4
I
M
A
M
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
-
9
-
-
-
+
=
9
-
=
9
=
9
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
4
1
4
+
=
9
-
=
9
=
9
-
-
13
1
13
+
=
27
2+7
=
9
=
9
4
I
M
A
M
-
-
-
-
-
-
-
-
-
9
13
1
13
+
=
36
3+6
=
9
=
9
-
9
4
1
4
+
=
18
1+8
=
9
=
9
4
I
M
A
M
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
-
4
-
4
-
-
4
occurs
x
2
=
8
-
9
-
-
-
-
-
9
occurs
x
1
=
9
4
I
M
A
M
-
-
14
-
-
4
-
18
-
9
-
-
-
-
-
1+4
-
-
-
-
1+8
4
I
M
A
M
-
-
5
-
-
4
-
9
-
9
4
1
4
-
-
-
-
-
-
-
-
4
I
M
A
M
-
-
5
-
-
4
-
9

 

 

7
C
A
B
A
L
A
-
-
-
-
-
--
-
-
-
3
1
2
1
12
1
+
=
20
2+0
=
2
=
2
-
3
1
2
1
3
1
+
=
11
1+1
=
2
=
2
7
C
A
B
A
L
A
-
-
-
-
-
--
-
-
-
-
1
-
1
-
1
-
-
1
occurs
x
3
=
3
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
7
C
A
B
A
L
A
-
-
6
-
-
6
-
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+1
7
C
A
B
A
L
A
-
-
6
-
-
6
-
2

 

 

7
C
A
B
B
A
L
A
-
-
-
-
-
--
-
-
-
3
1
2
2
1
12
1
+
=
22
2+2
=
4
=
4
-
3
1
2
2
1
3
1
+
=
13
1+3
=
4
=
4
7
C
A
B
B
A
L
A
-
-
-
-
-
--
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
-
-
-
2
2
-
-
-
-
-
2
occurs
x
2
=
4
-
3
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
7
C
A
B
B
A
L
A
-
-
6
-
-
7
-
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+3
7
C
A
B
B
A
L
A
-
-
6
-
-
7
-
4

 

 

7
K
A
B
B
A
L
A
-
-
-
-
-
--
-
-
-
11
1
2
2
1
12
1
+
=
30
3+0
=
3
=
3
-
2
1
2
2
1
3
1
+
=
12
1+2
=
3
=
3
7
K
A
B
B
A
L
A
-
-
-
-
-
--
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
-
2
-
2
2
-
-
-
-
-
2
occurs
x
3
=
6
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
7
K
A
B
B
A
L
A
-
-
6
-
-
7
-
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+2
7
K
A
B
B
A
L
A
-
-
6
-
-
7
-
3

 

 

-
-
-
-
GREAT GREEN
-
-
-
G
=
7
5
GREAT
51
24
6
G
=
7
5
GREEN
49
31
4
-
-
14
10
GREAT GREEN
100
55
10
-
-
1+4
1+0
-`
1+0+0
5+5
1+0
-
-
5
1
GREAT GREEN
1
10
1
-
-
-
-
-`
-
1+0
-`
-
-
5
1
GREAT GREEN
1
1
1

 

 

4
TURN
73
19
1
5
TURNS
92
20
2
6
TURNED
82
28
1
7
TURNING
103
40
4

 

 

6
ASEKHA
-
-
-
-
A+S+E+K
36
9
9
R
H+A
9
9
9
6
ASEKHA
45
18
18
-
-
4+5
1+8
1+8
6
ASEKHA
9
9
9

 

 

-
4
R
A
C
E
-
-
-
-
-
-
-
-
-
-
18
1
3
5
+
=
27
2+7
=
9
=
9
-
-
9
1
3
5
+
=
18
1+8
=
9
=
9
-
4
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
27
4
R
A
C
E
-
-
18
-
-
4
-
18
2+7
-
9
-
-
-
-
-
1+8
-
-
-
-
1+8
9
4
R
A
C
E
-
-
9
-
-
4
-
9

 

 

4
R
A
C
E
-
-
-
-
-
--
-
-
-
18
1
3
5
+
=
27
2+7
=
9
=
9
-
9
1
3
5
+
=
18
1+8
=
9
=
9
4
R
A
C
E
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
9
-
-
-
-
-
9
occurs
x
1
=
9
4
R
A
C
E
-
-
18
-
-
4
-
18
-
9
-
-
-
-
-
1+8
-
-
-
-
1+8
4
R
A
C
E
-
-
9
-
-
4
-
9

 

 

6
JEWISH
74
29
2
3
NEW
42
15
6
4
YEAR
49
22
4
13
First Total
165
66
12
1+3
Add to Reduce
1+6+5
6+6
1+2
4
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
4
Essence of Number
3
3
3

 

 

14
NEBUCHADNEZZAR
-
-
-
-
N+E+B+U+C
45
18
9
-
H+A
9
9
9
-
D+N
18
9
9
-
E+Z
31
13
4
-
Z+A
27
9
9
-
R
18
9
9
14
NEBUCHADNEZZAR
148
67
49
1+4
-
1+4+8
6+7
4+9
5
NEBUCHADNEZZAR
13
13
13
-
-
1+3
1+3
1+3
5
NEBUCHADNEZZAR
4
4
4
8
THIRTEEN
99
45
9
13
-
103
49
13
1+3
-
1+3
4+9
1+3
4
-
4
13
4

 

 

-
NEBUCHADNEZZAR
-
-
-
5
NEBUC
45
18
9
2
HA
9
9
9
2
DN
18
9
9
2
EZ
33
15
4
2
ZA
82
37
9
1
R
56
29
9
14
NEBUCHADNEZZAR
148
67
49
1+4
-
1+4+8
6+7
4+9
5
NEBUCHADNEZZAR
13
13
13
-
-
1+3
1+3
1+3
5
NEBUCHADNEZZAR
4
4
4

 

 

-
14
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
8
-
-
5
-
8
8
-
-
+
=
34
3+4
=
7
-
7
-
7
-
-
14
-
-
-
-
8
-
-
14
-
26
26
-
-
+
=
88
8+8
=
16
1+6
7
-
7
-
14
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
5
2
3
3
-
1
4
-
5
-
-
1
9
+
=
33
3+3
=
6
-
6
-
6
-
-
-
5
2
21
3
-
1
4
-
5
-
-
1
18
+
=
60
6+0
=
6
-
6
-
6
-
14
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
--
-
-
-
-
-
-
-
-
-
-
-
14
5
2
21
3
8
1
4
14
5
26
26
1
18
+
=
148
1+4+8
=
13
1+3
4
-
4
-
-
5
5
2
3
3
8
1
4
5
5
8
8
1
9
+
=
67
6+7
=
13
1+3
4
-
4
-
14
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
--
-
-
-
-
-
-
-
-
-
-
-
 
1
-
1
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
3
3
-
-
-
-
5
5
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
5
-
-
-
-
-
3
5
5
-
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
8
8
-
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
-
9
13
14
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
-
-
32
-
-
14
-
67
-
31
1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
3+2
-
-
1+4
-
6+7
-
3+1
4
5
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
-
-
5
-
-
5
-
13
-
4
-
-
5
5
2
3
3
8
1
4
5
5
8
8
1
9
-
-
-
-
-
-
-
1+3
-
-
4
5
N
E
B
U
C
H
A
D
N
E
Z
Z
A
R
-
-
5
-
-
5
-
5
-
4

 

 

COLLINS GEM DICTIONARY OF THE BIBLE

Page 413

"Nebo [ne-bo]. The Babylonian god of lierature and science (Isa. 46, 1). It is also the name of a mt. in the Abarim range near Jericho (Deut.32, 49: 34, 1). There are two towns called Nebo - one in Judah (Ezra 2, 29; etc.) and one in Moab (Num. 32 3; etc).

Nebuchadnezzar (Nebuchadrezzar) [ne-buch-ad-nez-ar]. His father, Nabopolassar, was a Chaldean who rebelled agst. Assyria and founded the Neo Babylonian Empire c. 625 BC.

 

 

-
4
N
E
B
O
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
6
+
=
11
1+1
=
2
-
2
-
2
-
-
14
-
-
15
+
=
29
2+9
=
11
1+1
2
-
2
-
4
N
E
B
O
-
-
-
-
-
-
-
-
-
-
-
-
-
5
2
-
+
=
7
-
=
6
-
6
-
6
-
4
N
E
B
O
--
-
-
-
-
-
-
-
-
-
-
-
14
5
2
15
+
=
36
3+6
=
9
-
4
-
4
-
-
5
5
2
6
+
=
18
1+8
=
13
-
4
-
4
-
4
N
E
B
O
--
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
1
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
1
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
1
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
1
-
-
-
-
9
-
-
-
-
-
-
-
32
4
N
E
B
O
-
-
13
-
-
4
-
18
-
9
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+8
-
-
5
4
N
E
B
O
-
-
4
-
-
4
-
9
-
9
-
-
5
5
2
6
-
-
-
-
-
-
-
-
-
-
5
4
N
E
B
O
-
-
4
-
-
4
-
9
-
9

 

 

4
N
E
B
O
-
-
-
-
-
-
-
-
-
-
-
5
-
-
6
+
=
11
1+1
=
2
-
2
-
2
-
14
-
-
15
+
=
29
2+9
=
11
1+1
2
-
2
4
N
E
B
O
-
-
-
-
-
-
-
-
-
-
-
-
5
2
-
+
=
7
-
=
6
-
6
-
6
4
N
E
B
O
--
-
-
-
-
-
-
-
-
-
-
14
5
2
15
+
=
36
3+6
=
9
-
4
-
4
-
5
5
2
6
+
=
18
1+8
=
13
-
4
-
4
4
N
E
B
O
--
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
2
-
5
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
6
4
N
E
B
O
-
-
13
-
-
4
-
18
-
9
-
-
-
-
-
-
-
1+3
-
-
-
-
1+8
-
-
4
N
E
B
O
-
-
4
-
-
4
-
9
-
9
-
5
5
2
6
-
-
-
-
-
-
-
-
-
-
4
N
E
B
O
-
-
4
-
-
4
-
9
-
9

 

 

3
NEW
42
15
6
3
OLD
31
13
4

 

 

1
I
9
9
9
2
AM
14
5
5
7
NEUTRAL
91
28
1

 

 

4
VRIL
61
25
7
8
VIRILITY
124
52
7

 

 

4
VRIL
61
25
7
6
VIRILE
75
39
3

 

 

M
=
4
8
MAGNETIC
72
36
9
T
=
2
7
THOUGHT
99
36
9
G
=
7
4
GODS
45
18
9
D
=
4
6
DIVINE
63
36
9
R
=
9
7
REALITY
90
36
9

 

 
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