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SpringerReference
Hans Barnard
Surveying in Egypt
3 Feb 2012 23:30http://www.springerreference.com/index/chapterdbid/78364
© Springer-Verlag Berlin Heidelberg 2012
Surveying in Egypt
The English verb "to survey" refers to a variety of activities, two of which will be discussed here with an emphasis on the
way in which these were practiced in Ancient Egypt. The first can be provisionally defined as the techniques to reduce
reality to fit onto a map or a model, the second as the techniques to transfer the information and ideas reflected on a plan
or a model to the real world. Up until very recently a surveyor would go into the field with two instruments, one to measure
angles, such as a transit or a theodolite; and one to measure distances, such as a measuring tape or an electronic
distance‐measuring device . Modern technology has combined these two instruments into one, therefore referred(EDM)
to as a "total station," which can perform both functions. The underlying principles of surveying, and the fact that these are
based on the accurate measurement of angles and distances, were already mostly understood in Ancient Egypt. It must
be kept in mind that the Ancient Egyptian civilization lasted for more than 3,000 years and did change slowly but
continuously. The technology and methodology of surveying will have been different during the various periods of
Egyptian history (Table 1). From the available evidence it is not possible to determine an exact chronology of the
discipline of surveying in Ancient Egypt and the following discussion will be thematic rather than sequential.
Table 1 The chronology of Ancient Egyptian civilization following Baines and Malek ( : 36-37)2000
Period Dynasties Date
Early Dynastic Period 1st-3rd Dynasties 2950-2575 BCE
Old Kingdom 4th-8th Dynasties 2575-2150 BCE
First Intermediate Period 9th-11th Dynasties 2125-1975 BCE
Middle Kingdom 11th-14th Dynasties 1975-1640 BCE
Second Intermediate Period 15th-17th Dynasties 1630-1520 BCE
New Kingdom 18th-20th Dynasties 1539-1075 BCE
Third Intermediate Period 21st-25th Dynasties 1075-715 BCE
Late Period 25th-30th Dynasties 715-332 BCE
Greco‐Roman Period Macedonian and Roman rulers 332 BCE-395 CE
This evidence comprises a number of tools used for surveying, several plans and maps, inferences from marks and
modern measurements in extant structures and a few surviving texts on the subject. The Moscow (or Golenischev)
Mathematical Papyrus, probably written during the eleventh Dynasty (unknown provenance, now in the Pushkin State
Museum of Fine Arts in Moscow), discusses a series of problems of the area and volume of complex shapes, including a
curved surface (problem 10) and a truncated pyramid (problem 14). The Rhind (or Ahmes) Mathematical Papyrus, written
around 1550 BCE but claiming to be a copy of a twelfth Dynasty text (found in Luxor, now in the British Museum in
London) deals with a series of problems of area and volume, including the area of a triangle (problems 4 and 51), a
rectangle (problems 6 and 49) and a circle (problems 38 and 50) as well as the volume of a cylinder (problems 41 and
43).
Surveying would have been needed in Ancient Egypt, from the Old Kingdom onward, for at least two important
applications. First was the construction of the famous tombs, temples and pyramids, some of which still stand today and
testify to the accuracy of the measurements. Second, and with a larger impact on daily life, were the measurements to
restore the outlines of the agricultural fields after the yearly inundation of the Nile in July and August. The maximum
height of the inundation, measured in Nilometers at several places, differed from year to year and with that the area of
arable land. The available land needed to be redistributed each year and taxes were levied accordingly. This can be
illustrated by the following remarks of the Greek historian , who traveled through Egypt in the fifth century BCE.Herodotus
The King would send men to inspect and measure the loss of cultivated land in order that from then on
some of the tax, proportionate to the report of the loss, might be remitted. I attribute the ofinvention
geometry to this cause and from Egypt it spread to Greece (Herodotus, , translation Shore History 2.109
: 125).1987
Measuring distances in Ancient Egypt was done in the same way as it is still done today: by comparing an unknown with
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SpringerReference
Hans Barnard
Surveying in Egypt
3 Feb 2012 23:30http://www.springerreference.com/index/chapterdbid/78364
© Springer-Verlag Berlin Heidelberg 2012
a known distance indicated on a tape measure or a ruler. Several ancient measuring rods have been preserved, most of
them dating to the New Kingdom or later. Two were found in the tomb of Kha, the architect of the Pharaoh Amenhotep II
(eighteenth Dynasty), in Deir al‐Medina (near Luxor) and are now kept by the Museo Egizio in Turin. One was gilded and
probably a gift not meant for daily use; the other is hinged and was most likely used by its owner during his work (Arnold
). Longer distances were measured with a that had knots at regular distances, an activity known as "stretching1991 rope
the cord" (Shore ). This rope, reminiscent of "Gunter's chain" used by 17th-19th century surveyors, is often depicted1987
ending in the ram's head of the god Khnum, indicating the importance attached to the measurements and their accuracy.
A depiction of land surveyors in action can be found on the top register of wall 5 in the tomb of Menna, an administrator
who lived during the reign of Pharaoh Tuthmosis IV or that of his successor Amenophis III (eighteenth Dynasty) (Fig. 1).
Fig. 1 Fragment of the top register of wall 5 of the 18th Dynasty tomb of Menna, showing land surveyors in action (photograph by
Robert L. Mond and Ernest J. Mackay, 1914-1916, used with the kind permission of the Griffith Institute, Oxford, UK).
No single Ancient Egyptian unit of length can be given, as this not only varied over time, but also by purpose and place.
Several systems existed simultaneously, as they did in Europe until very recently (the "Convention of the Metre" was
signed in 1875 and the "International System of Units" in 1954 but neither are implemented, or even adopted, by all
countries). The basis for the Ancient Egyptian unit of length was the cubit, the length from the elbow to the tip of the
middle finger (Arnold ; Gillings ; Skinner ). A cubit was divided into seven "palms" and 28 "fingers" (one1991 1982 1954
palm being four fingers). Two cubits seem to have been in use, the "royal cubit" and the "short cubit"; the former was
most often about 524 mm (20.6 in.), the latter 449 mm (17.7 in.). A finger was therefore either approximately 19 mm (0.74
in.), when taken from the royal cubit, or approximately 16 mm (0.63 in.), when taken from the short cubit (Gillings ). It1982
is possible that at times the short cubit was divided into only six palms, and 24 fingers (Skinner ). The royal cubit1954
would then be close to one short cubit plus four fingers (one palm) long. A hundred cubits, 52.4 m (171.9 ft) in length, was
called a , a or, in the Greco‐Roman period, a . An area of 100 × 100 cubits (a square hayr, khet orhayt khet schoenia
schoenia) was called a or, in the Greco‐Roman period, an .setat arura
A remarkable additional unit was the , defined as half the diameter of a square with sides of one royal cubit inremen
length. The length of this diameter is cubits, which can not be written as the sum of reciprocal fractions (such as
), the notation system used in Ancient Egypt, but only as an unending decimal
fraction (like ). A remen would be about 371 mm (14.6 in.) or, by coincidence, almost
exactly 19.5 fingers (Table 2). The advantage of the remen was that it allowed areas of land to be halved, or doubled,
while preserving the proportions simply by changing the unit. A square with sides of a cubit, for instance, has twice the
area of a square with sides of a remen and half the area of a square with sides of two remen (a "double‐remen"). To
calculate the area of a circle (pi) was approximated as (2 × (1 − 1/9)) = 16 /9 = 256/81, which equals 3.16049…π 2 2 2
(whereas the correct value of = 3.14159…).π
Table 2 Overview of the most important ancient egyptian units of length
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SpringerReference
Hans Barnard
Surveying in Egypt
3 Feb 2012 23:30http://www.springerreference.com/index/chapterdbid/78364
© Springer-Verlag Berlin Heidelberg 2012
Fingers Cubits mm Square (cubits )
2Square (mm )
2
Remen 19.5 1/2 ×½ 371 1/2 137,288
Cubit 28 1 524 1 274,576
Double‐remen 39 741 2 549,152
Less is known about how angles, the second basic element of surveying, were understood in Ancient Egypt. There is
ample evidence of the use of plumb bobs, often combined with a set‐square or another device that could have served as
a , which essentially create a 0° angle with the vertical (and a 90° angle with the horizontal). Some of thesesight
instruments were apparently used to establish levels (Arnold ; Lehner ). Marks representing different elevations1991 1997
are preserved in several structures amongst which are the fourth Dynasty Mastabet al‐Fara'un, the burial complex of
Pharaoh Shepseskaf, in Sakkara (near Cairo), the fifth Dynasty pyramid of Niuserra in Abusir (near Cairo) and the
eleventh Dynasty temple of Mentuhotep in Deir al‐Bahri (near Luxor). It has been suggested that water in channels cut for
this purpose was used to create a level plain (Edwards ), which can be considered a 0° angle with the horizontal1993
(and a 90° angle with the vertical).
It is unclear how a right angle on a given base line, essential for many surveying tasks, was constructed. There is no
evidence that the special case of the theorem of , which proves that a triangle with sides of 3, 4 and 5 units willPythagoras
have one right angle, was employed (Gillings ). Over short distances a right angle could have been constructed by1982
sighting over a set‐square (Arnold ; Edwards ). The accuracy of this method could be improved by several1991 1993
techniques, but probably not sufficiently to account for the results evident from the surviving structures. Another way to
construct a right angle is by establishing two large equilateral triangles with one side, and two corners, in common. The
diagonals of the resulting rhomboid, one of which would correspond with the base line, will be at a right angle (Arnold
). What techniques were used to achieve the observed level of accuracy with the tools available at the time remains1991
enigmatic, but the ancient surveyors could draw on generations of experience with the layout of agricultural fields and
canals.
There is some archaeological and textual evidence about angles other than 0° and 90°, relating to the inclination of
pyramids, pylons and the walls of buildings. This includes a set of preserved marks in the foundation trenches of Old
Kingdom mastaba number 17 in Maidum (Arnold ) and problems 56-60 of Rhind Mathematical Papyrus (Gillings 1991
). The angle of the face of a structure was described using the , which can be defined as the length of the1982 seqet
setback of the building from the vertical at a height of one cubit or, in modern terms, as the cotangent of the angle of the
wall with the horizontal (Gillings ). A vertical wall has a seqet of zero and a wall with an inclination of 45° has a seqet1982
of one cubit. The Great Pyramid in Giza, built by Pharaoh Khufu (Cheops) of the fourth Dynasty, rises at an angle of
51°52′ with the horizon and consequently has a seqet of 0.79 cubit (about five palms, two fingers). The measurements by
the ancient surveyors were sometimes transferred to the structures under construction by elaborate means, such as the
mud‐brick walls under the outer court of the twelfth Dynasty pyramid of Senwosret in Lisht, believed to indicate the
desired level to which the court had to be built up, or the lines of rock‐cut postholes surrounding the Great Pyramid
(Arnold ).1991
Measurements were not only needed to ensure a practical and secure structure, but often also to make it correspond to
religious beliefs or cultic necessities. Despite a dearth of concrete information, the latter has become subject of much
. Many proportions of structures and angles of shafts are assumed to have had a special meaning, but thesespeculation
are rarely fully understood. The orientation of the pyramids according to the cardinal points is generally thought to have
been motivated by stellar elements in the Ancient Egyptian religion. This orientation was most likely achieved by
astro‐surveying, performed by priests rather than surveyors. One instrument that was probably used for this is the ,bay
part of a palm rib with a slit at its base through which stars, or the sun, could be observed. A bay was used in combination
with a merkhet, which doubled as a plumb bob and a sundial. A set of these instruments (now in the Staatliche Museum
Charlottenburg in Berlin, found in Abydos?) once belonged to Hor, a priest of the twenty‐sixth Dynasty. According to the
inscription on the merkhet it "… knows the motion of the two discs (sun and moon) and every star…" (translation Wells
: 37). An inscription on the bay indicates that it is "… for indicating the commencement of a feast…" (translation1999
Wells : 37). With these relatively simple instruments it is possible to observe, through the slit in the bay, the passing1999
of a star across a vertical line, established by the plumb bob attached to the merkhet. In the day, the bay would cast a
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SpringerReference
Hans Barnard
Surveying in Egypt
3 Feb 2012 23:30http://www.springerreference.com/index/chapterdbid/78364
© Springer-Verlag Berlin Heidelberg 2012
shadow that could be aligned rather accurately because of the slit in the top. Either could be used to find true North, for
instance by bisecting the angle of the rising and setting of a celestial body over a horizontal plane (Edwards ; Lehner1993
), or by observing the alignment of a pair of selected stars (Spence ). Surveyors would then again be needed to1997 2000
transfer the observations to the actual building under construction.
Celestial observation were also used for the first known attempt to calculate the circumference of the earth, by
Eratosthenes during the reign of Ptolemy III Euergetes (246-221 BCE). Eratosthenes was born in Cyrene and(Libya)
brought to Egypt as a tutor for the son of Ptolemy III and a librarian of the library of Alexandria (with about 500,000
'books'). Alexandria was the capital of Egypt during the Greco-Roman period and, at the time, the most powerful and
influential city in the region. Thanks to the patronage of the Ptolemaic rulers and the renowned library, scholarly and
scientific knowledge advanced greatly. Basing his calculations on the difference, on the same day, in the height of the sun
in Alexandria and in Aswan, Eratosthenes came surprisingly close to the actual figure (Berthon and Robinson 1991).
See also: , , Nilometer Maps in Egypt Mathematics
References
Arnold, D. . New York: Oxford University Press, 1991.Building in Egypt. Pharaonic Stone Masonry
Baines, J. and J. Malek. . Oxford: Andromeda, 2000 (revised edition).Cultural Atlas of Ancient Egypt. 1980
Berthon, S. and A. Robinson. . London-New York-Sydney-Toronto: Guild Publishing,The Shape of the World
1991.
Edwards, I. E. S. . Harmondsworth: Penguin Books, 1993 (revised edition).Pyramids of Egypt. 1947
Gillings, R. J. . New York: Dover Publications, Inc., 1982Mathematics in the Time of the Pharaohs. 1972
(corrected edition).
Harrell, J. A. Cartography. . Ed. D. B. Redford. Cairo: TheThe Oxford Encyclopaedia of Ancient Egypt. Volume I
American University in Cairo Press, 2001. 239-41.
Lehner, M. . New York: Thames and Hudson, 1997.The Complete Pyramids
Neugebauer, O. Ancient Mathematics and Astronomy. . Ed. Ch. Singer, E. J.A History of Technology. Volume I
Holmyard, and A. R. Hall. Oxford: Clarendon Press, 1954. 784-803.
Shaw, I. N. and P. T. Nicholson. . London: British Museum Press,British Museum Dictionary of Ancient Egypt
1995.
Shore, A. F. Egyptian Cartography. . Ed. J. B. Harley, D. Woodward.The History of Cartography. Volume I
Chicago: University of Chicago Press, 1987. 117-29.
Skinner, F. G. Measures and Weights. . Oxford: Clarendon Press, 1954.A History of Technology. Volume I
774-84.
Spence, K. Ancient Egyptian Chronology and the Astronomical Orientation of Pyramids. 408 (2000): 320-4.Nature
Wells, R. A. Astronomy in Egypt. . Ed. Ch. Walker. London: British MuseumAstronomy Before the Telescope
Press, 1999. 28-41. 1996.
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SpringerReference
Hans Barnard
Surveying in Egypt
3 Feb 2012 23:30http://www.springerreference.com/index/chapterdbid/78364
© Springer-Verlag Berlin Heidelberg 2012
Surveying in Egypt
Hans Barnard
DOI: 10.1007/SpringerReference_78364
URL: http://www.springerreference.com/index/chapterdbid/78364
Part of: Encyclopaedia of the History of Science, Technology, and Medicine in
Non-Western Cultures
Editor: Helaine Selin
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