In considering the greater functions of the necropoli of the IVth and Vth Dynasties the place to start is with Pharoah Snefru, the initial surveyance as seen at Giza and Abusir can first be seen at Dashur..

Snefru 2613 BC – 2589 BC may probably be credited with developing the pyramid into its true form. He apparently began by build what was probably a step pyramid at Maidum (Madum)1, which was later converted into a true pyramid. But this effort met with disaster (though probably not a quick one), because of the pyramid's mass and steep slope. He also built the Red and Bent Pyramids at Dahshur. The Bent Pyramid was the first true pyramid planned from the outset, while the Red Pyramid is the first successful true pyramid built in Egypt. The Red and Bent Pyramids are, respectively, the third and fourth largest pyramids known to have been built in Egypt.

In many respects, including the combined scale of building projects and the evolutionary architectural achievements, Snefru must be ranked as one of Egypt's most renowned pyramid builders. In fact, the sheer volume of building work was greater than any other ruler in the Old Kingdom.

However, his achievements in pyramid building extended beyond the pyramid structure itself, and obviously incorporated evolving religious beliefs. During his reign, we see the first real elements of the sun worship that was to follow and reach a culmination over a thousand years later in the reign of Akhenaten.

 

For the first time in the orientation of the building plan the main axis was oriented from east to west rather than north to south, as were earlier pyramids. This was apparently a move away from the astronomical "star" oriented beliefs, toward the east-west passage of the sun and the worship of Ra. Now, with Snefru, the mortuary temple is on the east rather than than on the north side like in the Djoser Step Pyramid complex at Saqqara. Furthermore, we see the first of the small satellite pyramids placed near the southern face of the main pyramid, a structure that we still do not completely understand today. Furthermore, the pyramid and mortuary temple elements were now linked by a causeway to a valley temple located on the edge of the cultivation closer to the Nile. We believe that the valley temple operated as a monumental gateway to the whole of the pyramid complex.

http://www.touregypt.net/featurestories/snefru.htm

 

At Dashur a centre can be determined and the projection of the sub-division into ten, as well as concentric circles radiating from the centre, which would have been alongside the banks of the Nile, the spatial relationships are differant, the various elements are more widely spaced, and this aspect was considerably 'tightened' at Giza and Abusir to great effect What is also apparant at Dashur in terms of zonal banding, were from a given centre certain stars or constellations would be seen to set behind the pyramids, or to rise across from them through centre, such that could be taken as the horizon aspect of that pyramid, thus pyramids becoming associated with particular stars Thus whilst the Pyramid complex itself was representative of the Gods Re/Horus/Hathor in terms of aspects of the Sun (with Hathor and Horus as Eyes of Re personified by the planets Venus and Mercury which are often merged with the Sun), then also the pyramid in terms of it's relationship to the Horizon found association with particular stars.The map i have used for Dashur is from this site;

http://www.earlyworld.de/pyramiden.htm

 

 
   

What needs to be considered in terms of positing stars in fixed determinative positions relative to architectural surveyance and construct is the effects of precession, in the diagram above i have indicated Spica rising at 72*, and i'm sure that was the primary star for that alignment, yet in 2570 Bc whilst the other star positions are accurate, Spica was at more like 74*, having been at 72* several centuries earlier, though then Arcturus had been at more like 38*, the positions were variable and over time this would have been readily observed.

Looking at the zonal distribution of the Pyramids at Dahshur/Giza/Abusir it seems a zonal bandwith of four degrees was taken into account, this would cover discrepancies of movement over the historical period of the Old Kingdom of the key rising points of stars, the diagrams show this bandwidth, margin for change.

When Hipparchus determined his theory of Precession of the Equinoxes, it was a two degree discrepancy in the positioning of Spica that he observed...

 

Hipparchus was born in Nicaea (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 147 BC to 127 Bc
To get co-ordinates of stars, Hipparchus made observations during moon eclipses just as his predecessors did, and he compared his results with those of Timocharis about 150 years before concerning Spica, a bright star near the ecliptic. During moon eclipses, it was easy to measure the distance between Spica and the centre of the Moon, and then, as the Sun is at exactly 180° from the Moon, to get the difference of longitude between the Sun and Spica. Especially if the eclipse happened near the equinox, the position of the Sun was precisely known, and the longitude of Spica could so be deduced precisely. Timocharis had found for Spica a distance of 8° before the Autumn equinoctial point g. Hipparchus got 6°. The longitude of Spica had so increased of 2°.

.Further inquiry showed that, in spite of the roughness of the observations, there was an evidence of a general increase in the longitude of the stars (measured from West to East) unaccompanied by any change of latitude. The agreement between the motions of different stars was enough to justify him in trusting his predecessors and concluding that the changes did not come from a movement of the stars, but from a change in the position of the equinoctial points (from which longitudes were measured) ; one of the two circles who define these points must have moved, and the fact that the latitudes did not change showed that the ecliptic must have retained its position and that the change must have been caused by a motion of the equator. Again, Hipparchus measured the obliquity of the ecliptic, as several of his predecessors had done before, and found no appreciable change. He inferred that the equator was slowly sliding from East to West, keeping a constant inclination to the ecliptic.

http://skolor.nacka.se/samskolan/eaae/summerschools/PrecessGB.html

   

In terms of determining whether Precession has been a consideration of the ancient Egypptians in their conceptualization of these necropoli, then first one should consider the calculation of the five extra days was in terms of 1/72 nd of 360, the inverse of this gives 1/5th of 360 is 72 portions of one sector in terms of the sub-division of the Heavens into five.

Given that Precession advances 1 degree every 72 years, this presents the simplest of formulae that 72 x72=5,184 years, which if multiplied by five gives the approximation for the cycle at 25,920 years.

There appears however to be a vital qualification to this, in the sense that the ten sectors also each have incorporate in their geometric design a Pentagon, which has a given value of eight years, in terms of the Earth/Venus cycle, thus in a 72 degree section there are two of these, so;

 

72* x 72 ( +16)=5,200 years.

to give a rounded symbolic cycle of 26,000 years.

In terms of a single sector, then;

36* x 72 (+8)=2,600 years.

The schemata only really concerns itself with sectors of 36*, such as Arcturus rising at 36* and being at it's highest point due North, traversing 72* in total, ( in terms of identification with Osiris, probably accounting for the numer of conspirators determining his inevitable end), and sectors of 72* such as Orion rising at 108* and being due South at 180*, thus if seen in terms of Precession the concern would be with greater epochs of 5,200 years, which in comparative terms would be a period from the time of the First Dynasty circa 3,200 Bc until around the present time. Below is the necropolis of Abusir, showing the projection from centre, very close to the edge of Abusir lake, and the basic ten sub-divisions, more information on Abusir from here;

http://egyptphoto.ncf.ca/Abusir.htm

http://guardians.net/egypt/cj98/abusir/abusir1.htm

 
   
     

Essentialy then the ten Pentagons conceptualized within the ten sectors qualify 25,920 years to 26,000, and the numerics involved in ten such cycles need to be considered;

 

Cycles = Earth years =Venus orbits = (Earth+Venus) =(Venus-Earth)

1..............8...................13.......................21...................5

5..............40..................65.....................105..................25

10.............80................130.....................210........ .........50

 

The above emboldened figures are the critical numeric aspects of ten cycles of Venus, and to find corroborative evidence that these were of considerable importance then it needs to realised that these figures represent the key numeric symbolism of the Great Pyramid, in terms of the positionings upon the course layers. There were overall 210 courses of Sandstone masonry blocks to create the core, with the 'Queens Chamber' being on the 25th course and the 'Kings Chamber' on the 50th, these the differentials of 5 and 10 Earth/Venus cycles respectively.

In a Precession cycle of 26,000 years there would be 3,250 such cycles

 

Cycles.................8(Earth years)............x13(Venus orbits).......Differential

3,240.................25,920.......................42,120...................16,200

3,250.................26,000.......................42,250...................16,250

The final differential here agrees with the Earth/Venus orbital period ratio of 365.25/224.7=1.625

The sum of the Venus orbits at 42,250 is 650x65.0, and it can be noted Sirius rises and sets 65* from due South, traversing 130*


Those figures can be found to have a very intriguing relationship with the sum of intergers of 20 when set out four square, the sum value of which is 210, a figure which relates to 10 cycles of the Earth/Venus pentagonal ideagram, the 80 Earth orbits of such a cycle being added to the 130 equivalent orbits of Venus to make the composite sum.

(B=40) & (C=65)

40 Earth orbits=65 orbits of Venus.

Sum=105

(B+C=105)(A+D=105)

Differential=25

(B-A=25) & (D-C=25)

(AC=80)& (BD=130)

80 Earth orbits =130 orbits of Venus.

Sum=210

(A+B+C+D=210)

Differential=50

(C-A=50) & (D-B=50)

 

It can be seen therefore how the sum of intergers of 20 set thus relates well to the key figures of the Earth/Venus cycle, and also therefore to the design of the Great Pyramid, as this is 210 sandstone masonry courses in height (ABCD), has shafts leading toward the 90th level (D) from the 'Queens Chamber' and shafts leading toward the 105th level (B+C)&(A+D) from the 'Kings Chamber' the respective chambers are set on the 25th course (D-C) and (B-A) and upon the 50th course (C-A) & (D-B).

Also the Kings chamber shafts leading to the 105th course have a differential of 15 with those leading to the 90th level from the Queens chamber, ie 105-90=15, one of the numbers of the 15,40,65,90 sequance.

. To say: Osiris (N)., thou hast encircled every god in thine arms, . their lands, all their possessions. Osiris (N)., thou art great, thou art bent around like the circle which encircles the nb.wt. the apertures of the (heavenly) windows are open for thee;the steps of light are revealed for thee.Greetings to thee, sole one, of whom it is said, he will live always!Horus comes, he with the long stride comes;he comes, he who wins power over the horizon, who wins power over the gods.
To say: A Great One is awake beside his ka, after this Great One had fallen asleep by his ka;. (N). is awake beside his ka, after this (N). had fallen asleep by his ka;. this Great One is awake; (N). is awake;the gods are awake, awakened are the mighty ones.., raise thyself up, stand up.The Great Ennead, who are in Heliopolis, have assigned thee to thy great position,. that thou mayest sit, (N)., at the head of the Ennead,. like Geb, the hereditary prince of the gods, like Osiris at the head of the mighty ones, as Horus lord of men and gods.
 

In terms of the Egyptians formulating an epoch of 5,200 years, then interestingly the Mayan came up with the same figure by these means;

1 kin = 1 day
uinal (1 uinal = 20 kin = 20 days)
tun (1 tun = 18 uinal = 360 days = approx. 1 year)
katun (1 katun = 20 tun = 7,200 days = approx. 20 years)
baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years)

The baktun are numbered from 1 to 13.

http://webexhibits.org/calendars/calendar-mayan.html

 

Ostensibly then that's 13 (Baktun) x 394=5,122 'years'

However it can be noted that was formulated using a Tun of 360 days rather than 365, so to qualify this in terms of 365 day years,then it needs to be qualified in terms of the five Uayeb, Haab was the civil calendar of the Mayas. It consisted of 18 "months/Uinal" of 20 days each, followed by 5 extra days, known as Uayeb. This gives a year length of 365 days.

thus, 20 (Haab) x 365=7,300 days

20(Katun) x 7,300=146,000 days or 400 years

13 x 400=5,200

(13 x 2,000=26,000)

According to the Popol Vuh, a sacred book of the Maya, they were living in the fourth world. The Popol Vuh describes the first three worlds that the gods failed in making and the creation of the successful fourth world where men were placed. The Maya believed that the fourth world would end in catastrophe and the fifth and final world would be created that would signal the end of mankind

 

The Egyptian numerics suggest they would have seen things more in terms of;

8 x 650=5,200

(8 x 3,250=26,000)

 

What is in effect apparant is that the Maya usage of 13 is relative to the number of orbits of Venus in the 8/13 Earth/Venus cycle, whilst the Egyptians are using the multipar 8, relative to the Earth orbits/years, in other words two sides of the same coin, the Maya are noted for their observations of Venus and calendars and numerics based upon multipars of 13.

 

As noted however both the Maya and the Aztecs essentialy broke down the Great Age into the concept of 'Five Suns', each of 5.200 years , and below is a recent find from the Temple precinct of Sekhemt at Karnak showing the birthing of five consecutive 'Suns', as personified by the prefection of the Atum in the Morning (Nefertum).

 
   
 

 

 

Part One- Preliminary study of Pentagonal geometry and associated Phi ratio in terms of the cult of Osiris.

Part Two-Furthur consideration of the geometry as regards architectural projections upon the Giza Plateau.

Part Three-Considering the contextual implications of a subdivision of Giza into ten sectors.

Part Four-Examaning the central area of the projections around the Sphinx and associated cults.

Part Five-Determination of the central cultic role of Sokar~Osiris in terms of the Giza Necropolis.

Part Six-The Birthing of Nefertem through the Sacred Centre.by the waters.

Part Eight-The Sah~Sopdet~Sopdu relationship

 
     

 

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