Article snapshot taken from Wikipedia with creative commons attribution-sharealike license.
Give it a read and then ask your questions in the chat.
We can research this topic together.
A ] diagram shows how to construct an elliptical vault using simple measures along an arc. The ] depicting this diagram was found in the area of the ] in ]. A curve is divided into five sections and the height of the curve is given in cubits, palms and fingers in each of the sections.<ref name="CR"/>
A ] diagram shows how to construct an elliptical vault using simple measures along an arc. The ] depicting this diagram was found in the area of the ] in ]. A curve is divided into five sections and the height of the curve is given in cubits, palms and fingers in each of the sections.<ref name="CR"/>
Lengths could be measured by ] rods, examples of which have been found in the tombs of officials. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865.<ref name=lepsius>{{cite book|last=Lepsius|first=Richard|title=Die altaegyptische Elle und ihre Eintheilung|year=1865|publisher=Dümmler|location=Berlin|url=http://books.google.com/books?id=PRQGAAAAQAAJ|language=German}}</ref> Two examples are known from the tomb of ] – the treasurer of ] – in ]. Another was found in the tomb of Kha (]) in ]. These cubits are ca 52,5 cm long and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided.<ref name="MC">{{cite book|last=Clagett|first=Marshall|title=Ancient Egyptian science, a Source Book. Volume Three: Ancient Egyptian Mathematics.|year=1999|publisher=American Philosophical Society| location=Philadelphia| isbn=978-0-87169-232-0| url=http://books.google.com/books?id=8c10QYoGa4UC}}</ref>
Lengths could be measured by ] rods, examples of which have been found in the tombs of officials. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865.<ref name=lepsius>{{cite book|last=Lepsius|first=Richard|title=Die altaegyptische Elle und ihre Eintheilung|year=1865|publisher=Dümmler|location=Berlin|url=http://books.google.com/books?id=PRQGAAAAQAAJ|language=German}}</ref> Two examples are known from the tomb of ] – the treasurer of ] – in ]. Another was found in the tomb of Kha (]) in ]. These cubits are ca 52,5 cm long and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided. '''1 Royal cubit = 7 palms x 4 fingers = 28 fingers''' <ref name="MC">{{cite book|last=Clagett|first=Marshall|title=Ancient Egyptian science, a Source Book. Volume Three: Ancient Egyptian Mathematics.|year=1999|publisher=American Philosophical Society| location=Philadelphia| isbn=978-0-87169-232-0| url=http://books.google.com/books?id=8c10QYoGa4UC}}</ref>
]
]
Revision as of 19:33, 27 September 2012
Ancient Egyptian units of measure include units for length, area and volume.
Length
Units of length date back to at least the early dynastic period. In the Palermo stone, for instance, the level of the Nile river is recorded. During the reign of PharaohDjer the height of the river Nile was given as measuring 6 cubits and 1 palm. This is equivalent to approximately 320 cm (roughly 10 feet 6 inches).
A third dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found in the area of the Step Pyramid in Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms and fingers in each of the sections.
Lengths could be measured by cubit rods, examples of which have been found in the tombs of officials. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865. Two examples are known from the tomb of Maya – the treasurer of Tutankhamun – in Saqqara. Another was found in the tomb of Kha (TT8) in Thebes. These cubits are ca 52,5 cm long and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided. 1 Royal cubit = 7 palms x 4 fingers = 28 fingers
Cubit rod from the Turin Museum.
For longer distances, such as land measurements, the Ancient Egyptians used rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots ties at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer and Penanhor.
Units of Length
Name
Egyptian name
Equivalent Egyptian values
Metric Equivalent
Royal cubit
meh niswt
1 royal cubit = 7 palms = 28 fingers
c. 52.5 cm
Standard cubit
meh nedjes
1 standard cubit = 6 palms = 24 fingers
c. 45 cm
Remen
remen
1 remen = 5 palms = 20 fingers
c. 37.5 cm
Djeser
djeser
1 djeser = 4 palms = 16 fingers
c. 30 cm
Span (large)
pedj-aa
1 large span = 3.5 palms = 14 fingers
c. 25 cm
Span (small)
pedj-sheser
1 small span = 3 palms = 12 fingers
c. 22.5 cm
Fist
1 fist = 6 fingers
c. 10.75 cm
Hand
1 hand = 5 fingers
c. 9.38 cm
Palm
shesep
1 palm = 4 fingers
c. 7.5 cm
Finger
djeba
1 finger = 1/4 palm
c. 1.88 cm
Khet (rod)
khet
1 khet = 100 cubits
c. 52.5 m
River measure
iteru
1 iteru = 20,000 cubits
c. 10.5 km
Area
The records of areas of land date back to the early dynastic period. Gifts of land recorded in the Palermo stone are expressed in terms of kha, setat, etc. Further examples of units of area come from the mathematical papyri. Several problems in the Moscow Mathematical Papyrus for instance give the area of a rectangular plot of land (measured in setjats) and given a ratio for the lengths of the sides of the rectangles one is asked to compute the lengths of the sides.
The setat was equal to one square khet, where a khet measured 100 cubits. The setat could be divided into strips one khet long and ten cubit wide (a Kha).
Units of Area
Name
Egyptian name
Equivalent Egyptian values
Metric Equivalent
Kha-ta
kha-ta
100,000 sq cubits
27,565 square meters
Setat (setjat)
setat
1 square khet = 10,000 square cubits
2,756½ square meters
Kha
kha
1000 square cubits = 1/10 setat
275.65 square meters
Ta
ta
100 square cubits = 1/100 setat
27.565 square meters
Shoulder (Remen)
remen
1/2 ta = 50 square cubits
13.7 square meters
Heseb
heseb
1/2 remen = 25 square cubits
6.8 square meters
Sa
sa
1/2 heseb = 12.5 square cubits
3.4 square meters
Volume, Capacity and Weight
Several problems in the mathematical papyri deal with volume questions. For example in RMP 42 the volume of a circular granary is computed as part of the problem and units of cubic cubits, khar, quadruple heqats and heqats are used.
Problem 80 on the Rhind Mathematical Papyrus recorded how to divide grain (measured in heqats), a topic included in RMP 42 into smaller units called henu:
Problem 80 on the Rhind Mathematical Papyrus
The text states: As for vessels (debeh) used in measuring grain by the functionaries of the granary, done into henu : 1 hekat makes 10 ; 1/2 makes 5 ; 1/4 makes 2½ etc.
Weights were measured in terms of deben. This unit would have been equivalent to 13.6 grams in the Old Kingdom and Middle Kingdom. During the New Kingdom however it was equivalent to 91 grams. For smaller amounts the kite (1/10 of a deben) and the shematy (1/12 of a deben) were used.
The Egyptians divided their year (rnpt) into 365 days (hrw). The Egyptian calendar had 12 months (abd) of 30 days each, plus 5 epagomenal days.
They divided their year into 3 seasons, named Akhet, Peret and Shemu. Akhet was the season of inundation. Peret was the season which saw the emergence of life after the inundation. The season of Shemu was named after the low water and included harvest time.
Units of time
Name
Egyptian name
Equivalent Egyptian values
hour
unut
1 day = 24 hours
day
hrw
1 day = 1/30 month = 24 hours
month
abd
1 month = 30 days
Inundation season
akhet
Akhet = 4 months = 120 days
Emergence season
peret
Peret = 4 months = 120 days
Harvest season
shemu
Shemu = 4 months = 120 days
year
renpet
1 year = 365 days
The introduction of equal length hours occurred in 127 BC. The Alexandrian scholar Claudius Ptolemaeus introduced the division of the hour into 60 minutes in the second century AD.
^ Katz, Victor J. (editor),Imhausen, Annette et.al. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press. 2007, p 17, ISBN 978-0-691-11485-9
T. Pommerening, Altagyptische Rezepturen metrologisch neu onterpretiert, Berichte zur Wissenschaftgeschichte 26 (2003) p. 1 - 16
Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989
