How the Ancient Egyptians had Calculated the Earth's Circumference between 3750-1500 BC:a revision of the method used by Eratosthenes Christian Irigaray
Eratosthenes (276-194 BC) is credited as "the first" person to have measured the circumference of the Earth in our modern history books, but a serious study of the circumstances shows that Eratosthenes did not actually measure anything, and that he simply copied an earlier method of the Egyptians. Eratosthenes was a Greco-Egyptian director of the Library of Alexandria at the time, and he had access to the ancient records of science collected during the Alexandrian era which contained not only Egyptian but Mesopotamian and Persian knowledge of a variety of kinds. Among these documents was one from which Eratosthenes copied a method of deriving the Earth’s circumference, but the method itself (as we will see) shows that the actual experiment and record of this in Egypt occurred as
early as 3750 BC, making “the first” to actually measure a portion of the Earth’s
circumference and calculating were most probably Predynastic Egyptians living up to 3500 years before Eratosthenes’ time.
History of Cartography "Around 350 BC Aristotle put forward six arguments to prove that the Earth was spherical and from that time on scholars generally accepted that indeed it was a sphere."
How Aristotle Proved the Earth is Spherical (explains the lunar eclipse observation too)
Aristotle's Astronomy by Thomas Fowler: "To prove that the earth is a sphere"
To prove that the earth is a sphere, he produced the argument that all
earthly substances move towards the center, and thus would eventually
have to form a sphere. He also used evidence based on observation. If
the earth were not spherical, lunar eclipses would not show segments
with a curved outline. Furthermore, when one travels northward or
southward, one does not see the same stars at night, nor do they
occupy the same positions in the sky. (De Caelo, Book II, chapter 14)
That the celestial bodies must also be spherical in shape, can be
determined by observation. In the case of the stars, Aristotle argued
that they would have to be spherical, as this shape, which is the most
perfect, allows them to retain their positions. (De Caelo, Book II,
chapter 11)
...
In Science before Socrates, Daniel Graham argues against the
prevalent belief that the Presocratic philosophers did not produce any
empirical science and that the first major Greek science, astronomy,
did not develop until at least the time of Plato. Instead, Graham
proposes that the advances made by Presocratic philosophers in the
study of astronomy deserve to be considered as scientific
contributions.
...
Virtually all philosophers came to accept Anaxagoras' theory of lunar
light and eclipses. Aristotle endorsed Anaxagoras' theory of eclipses
as a paradigm of scientific explanation. Anaxagoras' theories launched
a geometrical approach to astronomy and were accepted as foundational
principles by all mathematical astronomers from Aristarchus to Ptolemy
to Copernicus and Galileo-and to the present day.
...
Also D.R. Dicks in Early Greek Astronomy to Aristotle, says speculation about the spherical earth can be dated to at least the 6th century BC.
Supporting historical references found on the History Wiki: Spherical Earth
The earliest evidence for a spherical Earth came from an ancient
Phoenician expedition for ancient Egypt. The Egyptian pharaoh Necho
II, during his reign from 610 BCE to 595 BCE, employed Phoenician
sailors to circumnavigate around the entire African continent, then
known as "Libya". In The Histories (written c. 431 BCE - 425 BCE),
Herodotus described how the Phoenicians reported the sun being
observed shining from the north. ... With this expedition, the
Phoenicians and Egyptians were thus the first to discover evidence of
the Earth being curved and therefore spherical.
The ancient Egyptians ahead of Eratosthenes
Eratosthenes gets the credit for the first earth measure of any
accuracy. The Egyptians had the same knowledge some 2000 years
earlier. The height of the Great Pyramid x 43200 = Earth Polar Radius
The base perimeter of the Great Pyramid x 43200 = Earth
Circumference.
.
The Egyptian Heritage in the Ancient Measurements of the Earth, by Gyula Priskin, Published in Göttinger Miszellen, 208 (2006), pp. 75-88.
Abstract: The comparison of an Egyptian text recording the
north-south extent of the country with the descriptions of
Eratosthenes’ and Posidonius’ experiments to measure the earth’s
circumference reveals that early Hellenic mathematical geography
borrowed much information from Egyptian science. A further analysis of
all the figures circulated for the length of the meridian in antiquity
reinforces the case that Hellenic geographers were greatly influenced
by Egyptian ideas when they formed their opinions on the size of the
earth.
.
Egyptian Estimates of the Size and Shape of the Earth
From Stecchini's The Pyramids of Egypt.
Historical Metrology, a New Analysis of the Archaeological and the Historical Evidence Relating to Weights and Measures, by A. E. Berriman,...
The Acropolis Width and Ancient Geodesy Nicholas Kollerstrom
“Was the Earth measured in remote antiquity?” This was the stirring
question with which Berriman opened his book, Ancient Metrology. To
be sure, the question had earlier been tackled in Nicholson’s Men and
Measures, as to whether a knowledge of Earth’s dimension had afforded
the original basis for units of measure. Here we inquire,
specifically, as to whether the ancient Greek units of measure were
related to the circumference of the Earth. This hypothesis tends to be
related to the notion that a global, maritime civilization had once
existed in prehistory. Our inquiry is therefore in some degree related
to the thesis propounded by Francis Bacon, in his New Atlantis: “You
shall understand (that which you will scarce think credible) that
about three thousand years ago, or somewhat more, the navigation of
the world (especially for remote voyages) was greater than at this
day.” Could there have been a civilization of prehistory which
vanished, but left behind its geodetically-defined units? ....
The position here advocated could be described as Newtonian, insofar
as Isaac Newton believed, that one function of ancient temples was
that of expressing the proportions of the world ....
From his study of the Hermetic texts of the Egyptians, Newton stated in The System of the World what some controversial authors are trying to say today:
It was the ancient opinion of not a few, in the earliest ages of
philosophy, that the fixed stars stood immoveable in the highest parts
of the world; that, under the fixed stars the planets were carried
about the sun; that the earth, as one of the planets, described an
annual course about the sun, while by a diurnal motion it was in the
mean time revolved about its own axis;
As Steven Weinberg says in his latest book, To Explain the World: The Discovery of Modern Science, (the Dendera Zodiac is shown on the book cover) "At several points in this book I suggest that, as great as is the progress that has been made in the methods of science, we may today be repeating some of the errors of the past." Indeed, it seems as though some forgotten history is repeating itself in the controversy over early knowledge of precession, the spherical earth and what this means for modern science. For instance, in The Zodiac of Paris by Jed Z. Buchwald & Diane Greco Josefowicz "The Dendera zodiac--an ancient bas-relief temple ceiling adorned with mysterious symbols of the stars and planets--was first discovered by the French during Napoleon's campaign in Egypt, and quickly provoked a controversy between scientists and theologians."
This is a fascinating study of how politics, science, and religion
intersected in the heated debates over the meanings of the
hieroglyphics on a pair of stones brought from Egypt to Paris in 1821.
At the heart of the tale is the question of how we know the past. It
has the excitement of a real-life archeology mystery combined with a
clash between science and theology that has great resonance for
today. --Walter Isaacson, author of Einstein: His Life and Universe
See, Buchwald, J.Z. "Egyptian Stars under Paris Skies." Engineering and Science 66.4 (2003): 20-31. Notice of long standing errors on the Dendera Zodiac English Wiki talk page: "It might be that the Dendera Zodiac is academic hotstuff that not many academics dare touching, ... said Rursus." ...and to be compared with the Dendera Zodiac Google French translation:
Jean-Baptiste Biot, astronomer and Egyptologist, meanwhile, looks in
detail at the Egyptian circular zodiac.... and shows that the
celestial arrangement goes well beyond the Roman era. ... According to
Sylvie Cauville, Egyptologist, author of numerous books including The
Eye of Re, the founding charter of the Dendera temple is part of the
ancient writings of the library of Cheops.
The Temple of Hathor at Dendera:
The temple complex, as it stands today, was built on the site of an
older temple, and is a replica of the original. The present building
was first initiated by Ptolemy III, with numerous additions by
subsequent Ptolemaic and Roman rulers. The inscription on the present
temple states that the original building was erected in the far
pre-dynastic times, by the followers of Heru (Horus).
Michael Rice, in Egypt's Legacy, "the precession is fundamental to an understanding of what powered the development of Egypt" (p.10).
Update comment: One item in reference to the torus is the discovery of earth's magnetospheric lines having a dodecahedral vortex configuration. So from the etheric the earth is indeed something of a torus. Author John Michell's ancient metrology discusses the blueprint of megalithic monuments as being related to what he called the New Jerusalem or Cosmological Circle, which has the form of a dodecahedron in three dimensions!
Another update to connect some of the references: The Cosmological Circle is also known today as Plato's Wheel, drawn from his Timaeus. Ernest Pecci shows how the scalene triangles within Plato's Wheel are fundamental to the geometry of the Great Pyramid and that the builders knew the precise circumference of the planet. See The Sacred Geometry of the Great Pyramid: From the Drawing Board of Its Architects by Ernest F. Pecci.
More conservative references show the "Pythagoreans were the first ... to say the earth is round." - George Sarton (noted founder of the academic discipline of the History of Science) Ancient Science Through the Golden Age of Greece. Pythagoras was an Egyptian initiate and some of his knowledge was directly attributed to the Egyptians. Both Kepler and Newton were also privy to some of the secret oral tradition. Kepler acknowledged his debt to the Egyptians. Newton went to great lengths in a paper trying to figure out the Sacred Cubit.
Another "source": Ancient Wisdom Discovery that the Earth is spherical -
The first (official) measurement of the radius of the earth was made
by Erasthenes (b. 275 B.C.), who was the head of the great library of
Alexandria. He was born in Cyrene, now Libya. It seems likely that the
ancient Egyptians, much before Egypt's conquest by Alexander the
great, had already grasped the idea of a spherical Earth, and it was
from them that this doctrine was adopted by Pythagoras, who, as we
know, spent many years of study in Egypt.
The Egyptian Pyramid and the Archytas Doubling of the Cube by Pierre Beaudry
... the Great Pyramid included in its very construction frame the idea
of doubling the cube. ... Now, as you all know, the geometric problem
that Archytas had to resolve was formulated as follows: {find two mean
proportionals between two extremes in the ratio of two to one}. In
order to find those two mean proportionals, the Archytas construction
for the doubling of the cube required a {cone, a torus, and a
cylinder}. ... However, this Greek discovery was based on the more
ancient Egyptian discovery as its {necessary predecessor}.
Thus, the Egyptian doubling of the cube is simply a derivative of two
astrophysical observations that had to be made at the site of the
Great Pyramid in order to establish its architectural design. Those
two conic projections, from the North Pole and from the Ecliptic,
generate the frame-shadow of the Great Pyramid whose triangular
meridian angle, PAM, shows that the two proportional segments, AM and
AP, respectively represent the sides of two cubes whose volumes are in
the ratio of 2/1. So, it becomes clear that this {is} where the
Archytas construction took its origins. ... Ironically, this Great
Pyramid triangular frame-shadow of 90°, 52°, and 38° degrees, with its
harmonically conjugated segments, AB, AM, and AP, not only reflects
the power of successively doubling the cube, but also reflects the
golden section, the Great Pyramid paradox of squaring the circle, and
the 256 series behind the well tempered musical system.
The Constructive Geometry of Pythagorean Sphaerics: Part I by Pierre Beaudry
Pythagoras had established his Astronomy on the original
accomplishments of the Egyptians, who, themselves had received their
legacy from Atlas, the original Trans-Atlanticist founder of ancient
Astronomy, and the first inventor of the celestial sphere, which,
according to Jean Sylvain Bailly, can be dated at about 4,000 BC.
The discovery of Precession Astronomy can be traced back, in an
architectural documented form, to the construction of the Step Pyramid
of Zoser at Saqqara (circa 3400 B.C.).... Between the years 495 and
491 B.C.,... Khnum-Ab-R'a, who was chief minister of works in Egypt,
had left an inscription on a public monument of the valley of Wadi
Hammamat, which put on record his 24 architect predecessors, leading
back to Imhotep .
...
For more on the Torus and Sphere of the Earth, with animations and illustrations:
Archytas from the Standpoint of Cusa, Gauss, and Riemann & Hyperbolic Functions -- A Fugue Across 25 Centuries & On Principles and Powers by Bruce Director
...
Thales Theorem and the Archytas Model by Pierre Beaudry
Prehistoric Egyptian Geodesy: "Giza (Heliopolis) to the Equator = 1/12th the circumference of the earth. (360°/12 = 30° 00’)."
Precession and the Pyramid Astronomical Knowledge in Ancient Egypt by
Jim Fournier
There is one point about ancient Egypt which stands out above all
others, an insight critical not only to our understanding of Egypt,
but also to our overall understanding of history. The ancient
Egyptians observed, and to an important degree understood, the
precession of the equinoxes. This point is really a subsidiary
correlate to the realization that at least circa 2500 BC the Egyptians
knew the size of the earth very precisely. Precise geodetic knowledge
is contingent upon precise astronomical observations, and both taken
together imply an advanced understanding of geometry, as well as
precession. It follows that the ancient Greeks should be taken at
their word when they claim that their knowledge is of great antiquity
and was derived from Egyptian sources. Indeed it is nothing if not
bizarre that modern scholars of the Greek world should go to great
lengths to dismiss such claims on the part of the authors of the
primary texts themselves, to instead rely on the advice of modern
Egyptologists that the ancient Egyptians had no such knowledge.
....
After reviewing the opinions and work of the best of the Egyptian
astronomical tradition: Sir Issac Newton, Sir John Herschel, and Sir
Norman Lockyer, Neugebauer & Parker, Livio Catullo Stecchini, Robert
Bauval, and even Schwaller de Lubicz, and finally, visiting the key
sites myself, I believe the situation we are faced with is one in
which it can be demonstrated that c2500 BC someone designed and
oversaw the construction of an object, the Great Pyramid, which
encoded exceedingly accurate geodetic information along with profound
geometric insight and subtly. While it is disorienting to recognize
that so early in the chronology of human civilization there stands
such a discontinuous alpha point, it exists, and attempting to dismiss
its implications is no substitute for grappling honestly with them.
_
The Culture of Astronomy by Thomas Karl Dietrich: "The Great Pyramid at Giza demonstrates that it is a scale model of the Earth in the proportion of 43,200 Great Pyramids equal to one Earth."
Also, from Cosmo Myth, Thomas Karl Dietrich discovered
Substantiating evidence that Eratosthenes did not discover the size of
the Earth, but only read about it in the Library of Alexandria
(Culture of Astronomy). John Michell already discusses this fallacy in
some detail in his famous The New View over Atlantis (p.135-6). Thomas
G. Brophy in The Origin Map (p.110-11) actually states that
Eratosthenes used data from the latitude and longitude of the ancient
Nabta Playa which was also used in the Piri Re'is Map from Istanbul
noticed by Charles Hapgood in Maps of the Ancient Sea Kings.
And ... though a mathematical explanation was asked for, Richard Grossinger says in The Night Sky: The Science and Anthropology of the Stars and Planets- "History changes everything, and we must struggle to regain primary experience, whether visionary or scientific." (p.100) The shape of the earth was commonly known in the ancient practice of shamanism (including the Egyptians). Also, E. C. Krupp, Skywatchers, Shamans & Kings: Astronomy and the Archaeology of Power.
OK ... a little math :-) ... The approximate diameter of the earth in miles: 7920 = 8 x 9 x 10 x 11. These numbers are encoded in the geometry of the Cosmological Circle. Michael Schneider, Constructing the Cosmological Circle:
The Cosmological Circle is a geometric diagram that has appeared in
the arts, crafts, architecture, religion and literature of cultures
around the world, and is associated with their golden ages. Because
it's the visual representation of the harmony naturally inherent in
the structure of the numbers 1 through 12, it encodes the ideal
patterns and proportions toward which nature's forms strive. ... Its
dimensions are described as the Heavenly City described in The Book of
Revelation, seen in the plan of the Buddhist Brobodur temple,
Stonehenge, Glastonbury, and described as Plato's ideal city Magnesia.
Also, 7920 = 55 x 144. Notice the Fibonacci numbers and that 144/55 is approximately equal to the Golden Number squared. Half the value of the the Golden Number squared is equal to the midradius of the dodecahedron. Schneider says the geometry is just a mask for the Number Canon. Now, the question is how did they discover the Number Canon?
The Number Canon removes the geometric mask and looks into the numbers
at the heart of the Cosmological Circle. The way the twelve numbers
combine and organize into an all-encompassing whole was the model for
most of the ancient world as a microcosmic representation of the
harmonious universe. It was used as a standard for defining
relationships among weights, measures, music and the proportions of
sacred art and architecture.
According to WolframAlpha, ... this answer requested by AnubhaV ... is mathematically correct.
Supporting references -- Thoth: Architect of the Universe, by Ralph Ellis, in a review by Elliot Malach he says:
The author ties the measurements and mathematics of the pyramids,
Stonehenge and Avebury with the myth of Thoth, who educated mankind in
math and the mysteries of the heavens, leaving repositories of
knowledge throughout the Earth. Those repositories may not be "inside"
these megalithic structures, but instead the fundamental mathematics
encoded in the architecture of these structures themselves.
From Wikipedia Thoth:
The Egyptians credited him as the author of all works of science,
religion, philosophy, and magic. The Greeks further declared him the
inventor of astronomy, astrology, the science of numbers, mathematics,
geometry, land surveying, medicine, botany, theology, civilized
government, the alphabet, reading, writing, and oratory. They further
claimed he was the true author of every work of every branch of
knowledge, human and divine.
