Andrew Bourmistroff

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Articles submitted by Andrew Bourmistroff
Copyright 20002002 Andrew Bourmistroff.
All rights reserved.
Reprinted with Permission.
Parameter A and the Egyptian Decans
by Andrew Bourmistroff
Editorial correction by Gilles &
Margaret Nullens ( UK )
Abstract
 Why ancient Egyptians
built up Pyramids ?
 Was Pyramid symbol of the
Sun ?
 Why ancient Egyptians
divided the ecliptic on the 36 Decans only ?
I. Parameter A
In Part I " Hermetic geometry
" from my work " Numbers of Thoth
" , I described how some of my results refer to new
properties of Pyramid considered as geometrical figure.
The most important new property of
any Pyramid is the maximum difference ( β  α ) :
α  it is the angle of the
lateral edge of the pyramid in relation to its base
; β  it is the angle of the lateral side of the
pyramid in relation to its base ;
The maximum difference ( β 
α ) is equal to 9.879 degrees in any Pyramid.
Later I named the
maximum difference ( β  α )
the universal Parameter
A.
2. The Egyptian Year and the
Decans
It is known that ancient Egyptians
used their own calendar.
" The ancient Egyptians
originally employed a calendar based upon the Moon , and , like many peoples
throughout the world , they regulated their lunar calendar by means of the
guidance of a sidereal calendar. They used the seasonal appearance of the star
Sirius ( Sothis ); this corresponded closely to the true solar year , being only
12 minutes shorter. Certain difficulties arose , however , because of the
inherent incompatibility of lunar and solar years. To solve this problem the
Egyptians invented a schematized civil year of 365 days divided into three
seasons , each of which consisted of four months of 30 days each. To
complete the year , five intercalary days were added at its end , so that the 12
months were equal to 360 days plus five extra days. This civil calendar was
derived from the lunar calendar ( using months ) and the agricultural , or Nile
, fluctuations ( using seasons ); it was , however , no longer directly
connected to either and thus was not controlled by them. The civil calendar
served government and administration , while the lunar calendar continued to
regulate religious affairs and everyday life.
In time , the
discrepancy between the civil calendar and the older lunar structure became
obvious. Because the lunar calendar was controlled by the rising of Sirius , its
months would correspond to the same season each year , while the civil calendar
would move through the seasons because the civil year was about onefourth day
shorter than the solar year. Hence , every four years it would fall behind the
solar year by one day , and after 1,460 years it would again agree with the
lunisolar calendar. Such a period of time is called a Sothic cycle." [ 1 ]
The 3 seasons are
:
 Aakhet
, which
correspond to the Nile over flow
 Pert
, which
correspond to seedtime
 Shemu , which
correspond to harvest
Aakhet's
season consist of next 4 months :
 Thoth
 Paophi
 Hathor
 Khoiak
Pert's season
consist of next 4 months :
 Tybi
 Mekhir
 Phamenoth
 Pharmuthi
Shemu's season
consist of next 4 months :
 Pakhons
 Pauni
 Epiphi
 Mesore
The Epagomenes
consist of 5 special days :
 the first day –
Osiris’ day
 the second day –
Horus’ day
 the third day –
Seth’s day
 the fourth day –
Isis’ day
 the fifth day – Nephthys' day
The ancient Egyptians also used an
unusual system of time intervals known as the Decans. The Decans were 36
special bright groups of stars from the sky along the ecliptic. These Decans
were used as a special calendar  each decan would rise above the dawn horizon
for ten days every year.
" HERMETICA : EXCERPT VI :
From the Discourses of Hermes to Tat.
Tat. In your former
General Discourses you promised to explain about the thirtysix Decans; I
therefore ask you to tell me about them now, and to explain their
working.
Hermes. I am quite
willing, Tat; and of all my teachings, this will be of supreme importance, and
will stand highest among them. I bid you mark it well. I have told you before
about the zodiacal circle, which is also called the animalbearing circle, and
about the five planetstars and the sun and the moon, and the several circles of
these seven bodies.
Tat. You have,
thricegreatest one.
Hermes. I desire you
then, in your thoughts about the thirtysix Decans also, to bear in mind what I
have told you, that so my teaching about the Decans also maybe intelligible to
you.
Tat. I bear in mind what
you have told me, father.
Hermes. I told you, my
son, that there is a body which encloses all things. You must conceive the shape
of that body as circular; for such is the shape of the universe.
Tat. I conceive its
shape as circular, even as you bid me, father.
Hermes. And you must
understand that below the circle of this body are placed the thirtysix Decans,
between the circle of the universe and that of the zodiac, separating the one
circle from the other; they bear up, as it were, the circle of the universe, and
look down on the circle of the zodiac. They retard the allenclosing
body,—for that body would move with extreme velocity if it were left to
itself,—but they urge on the seven other circles, because these circles move
with a slower movement than the circle of the universe. And subject to the
Decans is the constellation called the Bear, which is centrally situated with
regard to the zodiac. The Bear is composed of seven stars, and has overhead
another Bear to match it. The function of the Bear resembles that of the axle of
a wheel; it never sets nor rises, but abides in one place, revolving about a
fixed point, and making the zodiacal circle revolve, transmitting the world from
night to day, and from day to night. Let us understand then that both the ...
of the seven planets and all... ;or rather, that the Decans stand round about
all things in the Cosmos as guardians, holding all things together, and watching
over the good order of all things.
Tat. Even so I conceive
them, father, according to your words.
Hermes. And further, my
son, you must understand that the Decans are exempt from the things that befall
the other stars. They are not checked in their course and brought to a
standstill, nor hindered and made to move backwards, as the planets are; nor yet
are they as are the other stars. They are free, and exalted above all things;
and as careful guardians and overseers of the universe, they go round it in the
space of a night and a day.
Tat. Tell me then,
father, do the Decans act on us men also?
Hermes. Yes, my son,
they act on us most potently. If they act on the heavenly bodies, how could it
be that they should not act on us also, both on individual men and on
communities The force which works in all events that befall men collectively
comes from the Decans; for instance, overthrows of kingdoms, revolts of cities,
famines, pestilences, overflowings of the sea, earthquakes,— none of these
things, my son, take place without the working of the Decans.For if the Decans
rule over the seven planets, and we are subject to the planets, do you not see
that the force set in action by the Decans reaches us also, whether it is worked
by the Decans themselves or by means of the planets? And besides this, my
son, you must know that there is yet another sort of work which the Decans do;
they sow upon the earth the seed of certain forces, some salutary and others
most pernicious, which the many call daemons.
Tat. And what is the
bodily form of these beings, father?
Hermes. They do not
possess bodies made of some special kind of matter, nor are they moved by soul,
as we are; for there is no such thing as a race of daemons distinct from other
beings; but they are forces put in action by these six and thirty gods.
" [ 2 ]
3. 36 Pyramids in the
Sky
Taking into consideration that a
circle is divided in 360 degrees and that the Egyptian year has 365 days ,
we can say that the Earth rotates , in average :
360 / 365 = 0.9863
degrees each day.
Or , in other words , the Sun has
an average shift in the sky along the ecliptic as 0.9863 degrees per
day.
By the way , the movement of
the Earth in its orbit around the Sun, does not proceed at a constant rate
because of the eccentricity of the orbit of the Earth. The maximum rate
is 1.0020 degrees per day ( on 4 January ) while the minimum rate is
0.9701 degrees per day ( on 4 July)  with modern value of
eccentricity ( 0.0167 ) .
From my previous data we saw that
the Sun has average shift in the sky of 9.863 degrees per ten days or per one
Egyptian Decan.
Look again on this data
:
Parameter A of any
Pyramid = 9. 879 degrees
One Egyptian Decan ( in angular
meaning ) = 9. 863 degrees
Conclusion
On this base I conclude that
:
 Pyramids were sacred symbols
of the Sun ( Re ) for ancient Egyptians
 Pyramids were sacred symbols
of the Egyptian Decan as general time interval
in Egyptian year
 Ancient Egyptians believed
that the ecliptic ( The Path of the Sun ) consisted of 36 Decans (Pyramids)
plus 5 additional days
 Ancient Egyptians knew the
meaning of the Parameter A of Pyramids and that a circle was divided in
360 degrees
Enclosure # 1 : Definition of
Year [ 3 ]
 A Year
is time
required for the Earth to travel once around the Sun, about 365 1/4 days. This
fractional number makes necessary the periodic intercalation of days in any
calendar that is to be kept in step with the seasons. In the Gregorian
calendar a common year contains 365 days, and every fourth year (with a few
exceptions) is a leap year of 366 days.
 The Solar Year
is
year (365 days 5 hours 48 minutes 46 seconds), also called Tropical
Year, or year of the seasons, is the time between two successive
occurrences of the vernal equinox (the moment when the Sun apparently crosses
the celestial equator moving north). Because of the precession of the
equinoxes (an effect of a slow wobble in the Earth's rotation), the solar year
is shorter than the Sidereal Year (365 days 6 hours 9 minutes 10
seconds), which is the time taken by the Sun to return to the same place in
its annual apparent journey against the background of the
stars.
 The Anomalistic Year
(365 days 6 hours 13 minutes 53 seconds) is the time between two passages
of the Earth through perihelion, the point in its orbit nearest the
Sun.
 A Lunar Year
(used in some calendars) of 12 synodic months (12 cycles of lunar phases) is
about 354 days long.
 A Cosmic Year is
the time (about 225 million years) needed for the solar system to revolve once
around the centre of the Milky Way Galaxy.
Enclosure # 2 : Definition of
the Decans [ 4 ]

The Decans are
36 star configurations circling the sky somewhat to the south of the ecliptic.
They make their appearance in drawings and texts inside coffin lids of the
10th dynasty (around 2100 BC) and are shown on the tomb ceilings of Seti I
(131804 BC) and of some of the Rameses in Thebes. The decans appear to have
provided the basis for the division of the day into 24 hours.
Besides
representing star configurations as decans, the Egyptians marked out about 25
constellations, such as crocodile, hippopotamus, lion, and a falconheaded
god. Their constellations can be divided into northern and southern
groups, but the various representations are so discordant that only three
constellations have been identified with certainty: Orion (depicted as Osiris), Sirius (a recumbent cow), and Ursa Major (foreleg or front part of a
bull). The most famous Egyptian star map is a 1stcenturyBC stone chart found
in the temple at Dandarah and now in the Louvre.
References
[ 1 ] Encyclopaedia Britannica ,
1996.
[ 2 ] Hermetica , p.158 
160 , Solos Press , 1997.
[ 3 ] Encyclopaedia Britannica ,
1996.
[ 4 ] Ibid.
Copyright 2003 by Andrew Bourmistroff
[email protected]
All rights reserved.
Reprinted with Permission.
Has the Great Pyramid shifted by 9.85 degrees
?
By Andrew
Bourmistroff
[email protected]
Editorial correction by Graham Russell (UK)
The important fact to any
researcher is the availability of precise & true geodesic information
which refers to interesting object.
Doubtlessly such information is in the works by W.M.F.Petrie [1] & J.H.Cole
[2] it refers to the Complex Giza and the Great Pyramid.
For instance, we have next Cole's data :
Table I 
The Great Pyramid :
The length
of the sides 
Side 
North 
East 
South 
West 
Average 
meters 
230,253 
230,391 
230,454 
230,357 
230,364 
Table II 
The Great Pyramid :
The errors
of the 90 ° corners 
Corner 
North
 West 
South
 West 
South
 East 
North
 East 
error 

0 ' 2 " 
+
0 ' 33 " 

3 ' 33 " 
+
3 ' 2 " 
Table III 
The Great Pyramid :
The
direction of the sides 
Side 
North 
East 
South 
West 
direction 
0°2'30"
W. of true N. 
0°1'57"
N. of true E. 
0°5'30"
W. of true N. 
0°2'28"
N. of true E. 
Concerning to geometry of the
Great Pyramid my attention was attracted by fresh work "The
Pyramid Paper" by Terrans Nevin (USA).
He used his own mathematical software for the analysis of the geometry of the
Great Pyramid on basis of Cole's data.
In May 1995 he found the socalled special "Four
Circles".
Then in March 1997 a
mysterious line was found by Dave Seymour and Terrans Nevin. No
satisfactory explaination has yet be found for its line.
Four corners of the base and the apex of the Great Pyramid have a geometrical
and constructive shift from each other.
The Great Pyramid has a hidden azimuth of
350.15 degrees (or 9.85 degrees West of true North).
At once I saw that the value 9.85 degrees is very close to my Parameter A of
9.879
degrees.
As you remember, the maximum difference (β  α) or Parameter A is equal to 9.879 degrees of
any Pyramid, where :
α  it is an angle of an inclination of a lateral edge of the pyramid
and it's base ;
β  it is an angle of an inclination of a lateral side of the pyramid
and it's base ;
But is it possible to aggregate together these two meanings ?
Because the speech goes about only idealized meaning of 9.879 degrees and about
the meaning of 9.85 degrees obtained after due consideration of the
practical geometry of Cole's measurements.
It is known from
plane analytic geometry that the equation of a straight line is called a linear
equation with variable parameters ( x ) and ( y ) to which the coordinates at any
point of this straight line may be found .
The general equation of this type is defined as ax + by + c = 0 ( 1 ) and is
called as a general equation of a straight line .
The equation of straight line, allowing for a variable ( y ) , i.e. equation of
type y = kx + b ( 2 ) is called as an equation with an angular factor . Parameter
( k ) is called an angular factor and it is proportional to the tangent of
the angle of the slope of the straight line to the axis ( ox ) .
k = tan φ ( 3 )
Parameter ( b ) is the value of a section cut by a straight line ( 2 ) . It is
considered from the origin of the coordinates on the axis ( oy ) .
The equation of type x / a + y / b = 1 ( 4 ) where ( a ) and
( b ) are values
of sections cut by a straight line on axes of the coordinates ( Figure 1 ) is
known as a form of the equation of a straight line in sections .
Figure 1
The angle ( Φ ) between two straight lines y = kx + b
( 5 ) and y1 = k1x
+ b1 ( 6 ) is the angle on which it is necessary to turn the first straight line (with an
angular factor ( k ) ) to coincide it with the second straight line (with an angular factor
( k1 ) ) counter clockwise ( Figure 2 ) .
Figure 2
This angle is calculated under using the next formula :
tan Φ = (k1  k) / (1 + k1 k ) ( 7 )
Now we shall consider the formula as a
function of an angular difference
in
trigonometry :
tan (β  α) = (tan β  tan α) / (1 + tan β tan
α) ( 8 )
The conformity between two formulas is certain :
Φ =
(β  α) = Parameter A
k1 = tan β
k = tan α
Hence we can confirm the connection between the hidden azimuth 9.85 degrees
(West of true North)
and the universal Parameter A
of the Pyramid equal
9.879 degrees (Figure 3).
Figure 3
References:
1. W.M.F. Petrie , The Pyramids and
Temples of Gizeh , London , Field & Tuer , 1883.
2. J. H. Cole , Determination of the Exact
Size and Orientation of the Great Pyramid of Giza , Cairo , Government Press ,
1925.
Copyright 2003 by Andrew Bourmistroff
[email protected]
All rights reserved.
Reprinted with Permission.
