(
or how to measure the Earth )
Egypt utilised two versions of the Cubit, the Sacred Cubit of 25 inches and the Royal, or Profane Cubit
of 20.6066 inches. The Egyptian
or Primitive or Pyramid inch (p.i.)was approximately one thousandth longer
than the standard modern British inch. The number of British inches in
the Royal cubit is therefore equal to 20.62" or 20.63", depending
on which source is used. I personally prefer 20.625",
a compromise between the two and the value used by Isaac Newton. The American
inch has a different value than the British and historically the value
of the inch has had discrepancies between every country that used it.
[ see
table ]
The value of the Egyptian inch has been extrapolated from the measures
in the Great Pyramid and from surviving measuring rods. It was a mathematical
entity that was used to measure the Earth based in Pi. The Egyptians measured
the Polar diameter as 500 million
inches or 20 million Sacred
Cubits and by consequence the number of inches in the circumference of
the Earth was Pi (3.1416) x 500,000,000 or 1,570,800,000"
. This obviously means that the measure in Sacred Cubits was 62,832,000 sc. or 2 Pi x 10 million. This
circle however is not the equatorial circle, the polar circle, because
of the equatorial bulge, only touches the surface at the Poles. (see diagram)
The equatorial circle has a different measure which can be computed closely
by a simple mnemonic encoded in the Great Pyramid. The height of the G.P.
is 280rc., which is the approximate degree of expansion of the Equator,
1/280th.
The equatorial radius is therefore 250,000,000" -:- 280 x 281 = 250,892,857"
This equation is reasonably accurate, it is within one mile of the stated
equatorial circumference of 24,901.55
miles, being approx. 24,902.8 miles. There is a more accurate computation
of the equatorial radius but first I need to demonstrate how the inch
and cubits work. [
see Megalithic Yard ]
As you have seen, the Sacred cubit and the inch measure circles related
to the Earth in round numbers based in Pi.The Royal Cubit is more related
to area measurement and time. For example ;
The sq.rt. of Pi (1.77245...)
x 20.6066 = 36.52424.. or the length of the year between Spring Equinoxes
divided by 10.
An area of 100 sq. rc., called a Setat by the Egyptians, has the same area
as a circle with a circumference in inches of the year x 10. This was
called by the Greeks an Aroura or year circle.
(20.6066 x 100) sqrd. -:- Pi =
1162.6025 sqrd. : 1162.6025 x Pi = 3652.424..
The diagonal of G2 also relates to this equation. It's diagonal is 581.3,
the diameter of a circle with a circumference equal to the length of the
year x 5.
One other calculation provides a close figure for the circumference of
the Earth. As you will see in the geometry section the inner pentagram
square has an area 18 times the base area of G1 and 20.6066 times the
base area of G2. Follow this simple trick.
(20.6066 x 100) sqrd. x 18 = 76,433,753
rc. x 20.6066 = 1,575,039,784" =
21,621.2 nautical miles.
There are 21,600 nautical miles in an AVERAGE Great Circle and I emphasise
average for a good reason. A nautical mile is the navigators equivalent
of one minute of arc of 360 degrees. (360 x 60 ) The Nautical
Mile has a modern value of 6076.103 ft. or 72,913.236 inches. Multiplied
by 21,600 that is 24,856.785 statute miles.The Equator circumference measures
24,901.55 statute miles or 21,638.9 n.m.!
Earth measure is a series of compromises to allow for the bulge
of the Equator.
The length of an Egyptian stadium was equal to 1/10th. of a minute of arc
and equalled approx. 354 rc., though it is known they had a more accurate
measure.(Stecchini / Tompkins). Therefore 354 x 10 x 21,600 = 76,464,000
rc.
Though it is known that they had a more accurate measure for the stadium
it does not appear to be a matter of record. However, it can be worked
out quite easily when the clues are looked at logically. The Nautical
Mile has a value in Royal Cubits of 3535.185 rc., making the stadium measure
equal to 353.5185rc. in modern estimates.
The measure for the stadium obtained by multiplying the number of square
inches in the Setat by 18, as in the previous equation, divided by 216,000
= ( 76,433,753 -:- 21,600 -:- 10) =
353.8599 rc.. It's an ugly number, and the Egyptians didn't particularly
like ugly numbers. The measure from the west side of G2 to the west side
of G3 is 353.5 rc., the measure from the G.P. centre to Covingtons Tomb,
which is due south, is 3535 rc.. It could be 3535.3535...rc., not an ugly
number and one that can lead us straight to the answer. Watch this ;
3535.3535 x 21,600 = 76,363,636. 3636. This is a very pretty number
. It is the product of (12 -:-
11) x 7 x 10 million. A really pretty equation ! This number can be
divided by all the numbers from 1 to 10 and each division produces more
pretty numbers as you will see in the following table ;
| 76,363,636. 3636 divided by; |
2 |
= |
38181818.18 |
| 76,363,636. 3636 divided by; |
3 |
= |
25454545.45 |
| 76,363,636. 3636 divided by; |
4 |
= |
19090909.09 |
| 76,363,636. 3636 divided by; |
5 |
= |
15272727.27 |
| 76,363,636. 3636 divided by; |
6 |
= |
12727272.72 |
| 76,363,636. 3636 divided by; |
7 |
= |
10909090.90 |
| 76,363,636. 3636 divided by; |
8 |
= |
9545454.545 |
| 76,363,636. 3636 divided by; |
9 |
= |
8484848.848 |
| 76,363,636. 3636 divided by; |
10 |
= |
7636363.636 |
| 76,363,636. 3636 divided by; |
12 |
= |
6363636.363 |
| 76,363,636. 3636 divided by; |
21 |
= |
3636363.636 |
| 76,363,636. 3636 divided by; |
42 |
= |
1818181.818 |
| 76,363,636. 3636 divided by; |
180 |
= |
424242.4242 |
| 76,363,636. 3636 divided by; |
360 |
= |
212121.2121 |
| 76,363,636. 3636 divided by; |
1260 |
= |
60606.06060 |
| 76,363,636. 3636 divided by; |
2520 |
= |
30303.03030 |
| 76,363,636. 3636 divided by; |
5040 |
= |
15151.51515 |
| 76,363,636. 3636 divided by; |
21,600 |
= |
3535.3535 |
12 -:- 11 x 7 = 7.63636363
Do you see what I mean by 'pretty'. They are all repetitive and can be
subdivided by simply moving the decimal point, and for those of you
not aware, the Egyptians had a fractional / decimal system as is found
in the Rhind/Ahmes mathmatical papyrus.
So we can begin to assume that a stadium measured 353.535..r.c. in the
Average Great Circle. Conclusive proof of this system can be found by
analysing the measures found at Giza and in the geometries. 353.535..
x 2 = 707.0707 the radius of the inner heptagon circle. Multiply by
two again and it is the diameter of that circle 1414.14, which is the
measure from G1's centre to the south side of G3's causeway and the length
of G1's causeway. 1.41414 is the mnemonic for the sq.rt. of
2 (1.414213..)
This rounding up of square roots and other equations was endemic to the
Egyptians system of mathematics, as in the 8 x 8 square having the same
area as a 9 diameter circle [ see main text
] and leads us straight into the rest of the Earth measuring system.
The ratio of the Royal cubit to the Sacred Cubit is 25 -:- 20.6066 =
1. 2132.....
If we do the same rounding up that would become 1.21212.... or 40 -:- 33
The Giza grid is 4000 x 4000 r.c., divide by 40 and multiply by 33 and
it becomes 3300 x 3300 sacred cubits. It's true measure would be 3297,
but we're moving to a much bigger level of measuring. Giza is a number
game in Royal Cubits, now we're looking at the Earth in Average Great
Circles and it's a different game altogether. One clue before we move
on. 76,363,636.3636.... -:- 360 x 33 =
7,000,000.
We have an Egyptian version in Royal Cubits of our nautical mile system
accurate to within one mile of the modern system, but it revolves around
7 and 11. Our system of measure excludes those numbers, and yet they
are stamped all over Giza. If we now look for a harmonious system of
a.g.c. in Sacred Cubits all is revealed
.
12 -:- 11 x 7 = 7.636363.... -:-
1.212121... = 6.3
6.3 is 2Pi of 3.15. An average Pi, one that operates between the polar
circle circumference and the equatorial circle circumference. [ see
diagram ]
Polar
Pi is true Pi of 3.1416, Equatorial Pi is 3.1416 -:- 280 x 281 = 3.15282
3.15 gives an a.g.c. of 63,000,000 sacred cubits and it too is divisable
by all the numbers from 1 - 10, only this time these are solid round
numbers.
| 63,000,000 divided by ; |
2 |
= |
31,500,000
|
| 63,000,000 divided by ; |
3 |
= |
21,000,000
|
| 63,000,000 divided by ; |
4 |
= |
15,750,000
|
| 63,000,000 divided by ; |
5 |
= |
12,600,000
|
| 63,000,000 divided by ; |
6 |
= |
10,500,000
|
| 63,000,000 divided by ; |
7 |
= |
9,000,000
|
| 63,000,000 divided by ; |
8 |
= |
7,875,000
|
| 63,000,000 divided by ; |
9 |
= |
7,000,000
|
| 63,000,000 divided by ; |
10 |
= |
6,300,000
|
| 63,000,000 divided by ; |
12 |
= |
5,250,000
|
| 63,000,000 divided by ; |
21 |
= |
3,000,000
|
| 63,000,000 divided by ; |
42 |
= |
1,500,000
|
| 63,000,000 divided by ; |
180 |
= |
350,000 |
| 63,000,000 divided by ; |
360 |
= |
175,000
|
| 63,000,000 divided by ; |
1260 |
= |
50,000 |
| 63,000,000 divided by ; |
2520 |
= |
25,000 |
| 63,000,000 divided by ; |
5040 |
= |
12,50 |
| 63,000,000 divided by ; |
12,600 |
= |
5,000 |
12 -:-
11 x 7 -:- 1.21212... = 6.3
There is
a very interesting development in this as it pertains to the British
inch. We began by looking for average great circles that were commensurate
with the known value of an Egyptian stadium. We have utilised the harmonics
and mnemonics of the Giza geometries and standard Egyptian mathematical
practice and found two overlapping systems of measure of the average
great circle, one in Sacred Cubits which measures 63,000,000 s.c. or
1,575,000,000" and another in Royal Cubits which measures 76,363,636.63
rc or 1,573,594,909". The difference between these two AVERAGE circles
is about 22 miles on the size of the planet, about 1 in 1,130. I stress
that these are average circles used for navigating over long distances
and this will become relevant as we elaborate that theme elsewhere.
All that I need to point out at the moment are three unique features
of this system. 33 degrees of the a.g.c. in Royal Cubits equals 7 million
rc.. 33 degrees of the a.g.c. along the 30th. parallel (Giza) equals
6,060,606.06.. rc. or 5 million s.c. (cos. 0.8660 ), and most important
of all, using the same number of inches for both systems ( 1,575,000,000
) the ratio of Royal to Sacred cubits becomes 25 -:- 40 x 33 = 20.625,
the number of British inches in the Royal Cubit. The inch we inherited
from antiquity is the average inch between the two average systems of
great circle.
Stonehenge
and Avebury circle are exactly 33 degrees west of the Great Pyramid
. Stonehenge is 1/17th.( lat.51* 10.88' ) of a great circle north of
Giza which is 1/12th north of the Equator ( lat.30 degrees). Avebury
is 1/7th of a great circle north of the Equator (lat. 51* 25.714' )
. Subtract the latitude of Stonehenge from the latitude of Avebury and
Silbury Hill and the result is a fraction of a great circle. It is 1/1428th.
1428 x 22 = 31416
1428
x 44 =62832
That's
Pi for now folks.
Copyright
2001 ã
David Alan Ritchie
|
