ancient Egyptian units of measurement#Length

Egyptian units of length are attested from the Early Dynastic Period. Although it dates to the 5th dynasty, the Palermo stone recorded the level of the Nile River during the reign of the Early Dynastic pharaoh Djer, when the height of the Nile was recorded as 6 cubits and 1 palm{{sfn|Clagett|1999|p=3}} (about {{convert|3.217|m|ftin|abbr=on|sp=us|disp=or}}). A Third Dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found near the Step Pyramid of Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms, and digits in each of the sections.

{{cite book|last=Englebach|first=Clarke|title=Ancient Egyptian Construction and Architecture|year=1990|publisher=Dover|location=New York|isbn=0486264858}}

At some point, lengths were standardized by cubit rods. Examples have been found in the tombs of officials, noting lengths up to remen. Royal cubits were used for land measures such as roads and fields. Fourteen rods, including one double-cubit rod, were described and compared by Lepsius.{{sfnp|Lepsius|1865|pp=57 ff}} Two examples are known from the Saqqara tomb of Maya, the treasurer of Tutankhamun. Another was found in the tomb of Kha (TT8) in Thebes. These cubits are about {{convert|52.5|cm|sp=us|abbr=on}} long and are divided into palms and hands: each palm is divided into four fingers from left to right and the fingers are further subdivided into ro from right to left. The rulers are also divided into hands so that for example one foot is given as three hands and fifteen fingers and also as four palms and sixteen fingers.{{harvp|Clagett|1999}}.{{cite book|last=Gardiner|first=Allen|title=Egyptian Grammar 3rd Edition|year=1994|publisher=Griffith Institute|location=Oxford|isbn=0900416351}}{{cite book|last=Faulkner|first=Raymond|title=A Concise Dictionary of Middle Egyptian|publisher=Griffith Institute Asmolean Museum, Oxford|year=1991|isbn=0900416327}}{{cite book|last=Gillings|first=Richard|title=Mathematics in the Time of the Pharaohs|year=1972|publisher=MIT|isbn=0262070456|url-access=registration|url=https://archive.org/details/mathematicsintim0000gill_o9t9}}{{cite book|last=Loprieno|first=Antonio|title=Ancient Egyptian|publisher=CUP|location=New York|year=1996|isbn=0521448492}}

File:Coudée-turin.jpg

Surveying and itinerant measurement were undertaken using rods, poles, and knotted cords of rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots tied 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.Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2007

The digit was also subdivided into smaller fractions of {{1/2}}, {{1/3}}, {{1/4}}, and {{frac|1|16}}.{{harvp|Lepsius|1865|p=[https://archive.org/details/bub_gb_PRQGAAAAQAAJ/page/n48 44]}}. Minor units include the Middle Kingdom reed of 2 royal cubits,{{efn|The Egyptian reed was written N35:D58*M17-M3 or N35:D58-M17-Z7-T19 and pronounced nbi͗.}} the Ptolemaic xylon ({{langx|grc|ξύλον}}, {{abbr|lit|literally}}.{{nbsp}}"timber") of three royal cubits,{{citation |contribution-url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0063%3Aalphabetic+letter%3DM%3Aentry+group%3D2%3Aentry%3Dmensura-cn |contribution=Mensura |title=A Dictionary of Greek and Roman Antiquities |date=1890 |editor-last=Smith |editor-first=William |editor2=William Wayte |editor3=G.E. Marindin |display-editors=0 |last=Ridgeway |first=William |location=London |publisher=John Murray }}.{{citation |publisher=American Philological Association |date=1941 |title=Transactions and Proceedings |page=443 }}. the Ptolemaic fathom ({{langx|grc|ὀργυιά}}, orgyiá; {{langx|egy|ḥpt}}; {{langx|cop|ϩⲡⲟⲧ}}, hpot) of four lesser cubits,{{citation |url=https://books.google.com/books?id=3_wUAAAAIAAJ |contribution-url=https://books.google.com/books?id=3_wUAAAAIAAJ&pg=PA1312 |page=[https://books.google.com/books?id=3_wUAAAAIAAJ&pg=PA1313 1313] |contribution=3997: Iversen, Erik, Canon and Proportions in Egyptian Art |title=Annual Egyptological Bibliography 1955 |last=Janssen |first=Jozef M.A. |date=1956 |location=Leiden |publisher=E.J. Brill for the International Association of Egyptologists }}. and the kalamos of six royal cubits.

Records of land area also date to the Early Dynastic Period. The Palermo stone records grants of land expressed in terms of kha and setat. Mathematical papyri also include units of land area in their problems. For example, several problems in the Moscow Mathematical Papyrus give the area of rectangular plots of land in terms of setat and the ratio of the sides and then require the scribe to solve for their exact lengths.

The setat was the basic unit of land measure and may originally have varied in size across Egypt's nomes. Later, it 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).[http://www.digitalegypt.ucl.ac.uk/weights/area.html Digital Egypt: Measuring area in Ancient Egypt]

During the Old Kingdom:

During the Middle and New Kingdom, the "eighth", "fourth", "half", and "thousand" units were taken to refer to the setat rather than the cubit strip:

During the Ptolemaic period, the cubit strip square was surveyed using a length of 96 cubits rather than 100, although the aroura was still figured to compose 2,756.25{{nbsp}}m². A 36{{nbsp}}square{{nbsp}}cubit area was known as a kalamos and a 144{{nbsp}}square{{nbsp}}cubit area as a hamma. The uncommon bikos may have been {{frac|1|1|2}}{{nbsp}}hammata or another name for the cubit strip. The Coptic shipa ({{lang|cop|ϣⲓⲡⲁ}}) was a land unit of uncertain value, possibly derived from Nubia.{{sfnp|Crum|1939|p=570}}

File:Bronze vessel used a capacity measure. Inscribed with the cartouches of the birth-name and throne name of Amenhotep III. 18th Dynasty. From Egypt. The Petrie Museum of Egyptian Archaeology, London.jpg of the birth and throne names of Amenhotep III of the 18th Dynasty]]

Units of volume appear in the mathematical papyri. For example, computing the volume of a circular granary in RMP{{nbsp}}42 involves cubic cubits, khar, heqats, and quadruple heqats. RMP{{nbsp}}80 divides heqats of grain into smaller henu.

File:RMP-80.jpg: 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 {{frac|2|1|2}}; etc.]]

The oipe was also formerly romanized as the apet.{{citation |title=Encyclopaedia Britannica, 9th ed. |contribution=Weights and Measures |volume=XXIV |date=1888 }}.

File:Green glazed faience weight, inscribed for the high Steward Aabeni. Late Middle Kingdom. From Abydos, Egypt. The Petrie Museum of Egyptian Archaeology, London.jpg, inscribed for the high steward Aabeni during the late Middle Kingdom]]

File:Serpentine weight of 10 daric. Inscribed for Taharqa in the midst of Sais. 25th Dynasty. From Egypt, probably from Nesaft. The Petrie Museum of Egyptian Archaeology, London.jpg]]

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 qedet ({{frac|1|10}} of a deben) and the shematy ({{frac|1|12}} of a deben) were used.

The qedet or kedet is also often known as the kite, from the Coptic form of the same name ({{lang|cop|ⲕⲓⲧⲉ}} or {{lang|cop|ⲕⲓϯ}}).{{sfnp|Weigall|1908|p=ix}} In 19th-century sources, the deben and qedet are often mistakenly transliterated as the uten and kat respectively, although this was corrected by the 20th century.{{sfnp|Weigall|1908|pp=iii & ix}}

{{main|Egyptian calendar|Alexandrian calendar}}

The former annual flooding of the Nile organized prehistoric and ancient Egypt into three seasons: Akhet ("Flood"), Peret ("Growth"), and Shemu or Shomu ("Low Water" or "Harvest").{{harvp|Tetley|2014|p=[http://www.egyptchronology.com/uploads/2/6/9/4/26943741/ch_3_investigating_ancient_egyptian_calendars.pdf 39]}}.{{sfnp|Winlock|1940|p=453}}{{sfnp|Clagett|1995|p=[https://archive.org/details/bub_gb_8c10QYoGa4UC/page/n84 4–5]}}

The Egyptian civil calendar in place by Dynasty V{{sfnp|Clagett|1995|p=[https://archive.org/details/bub_gb_8c10QYoGa4UC/page/n36 28]}} followed regnal eras resetting with the ascension of each new pharaoh.{{harvp|Clagett|1995|p=[https://archive.org/details/bub_gb_8c10QYoGa4UC/page/n187 5]}}. It was based on the solar year and apparently initiated during a heliacal rising of Sirius following a recognition of its rough correlation with the onset of the Nile flood.{{sfnp|Parker|1950|p=23}} It followed none of these consistently, however. Its year was divided into 3 seasons, 12 months, 36 decans, or 360 days with another 5 epagomenal days{{sfnp|Parker|1950|p=7}}—celebrated as the birthdays of five major gods{{sfnp|Spalinger|1995|p=33}} but feared for their ill luck{{sfnp|Spalinger|1995|p=35}}—added "upon the year". The Egyptian months were originally simply numbered within each season{{sfnp|Parker|1950|pp=43–5}} but, in later sources, they acquired names from the year's major festivals{{sfnp|Clagett|1995|p=14–15}} and the three decans of each one were distinguished as "first", "middle", and "last".{{sfnp|Clagett|1995|p=[https://archive.org/details/bub_gb_8c10QYoGa4UC/page/n84 4]}} It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work.{{sfnp|Jauhiainen|2009|p=39}} This scheme lacked any provision for leap year intercalation until the introduction of the Alexandrian calendar by Augustus in the 20s{{nbsp}}BC, causing it to slowly move through the Sothic cycle against the solar, Sothic, and Julian years.Marshall Clagett, Ancient Egyptian Science: Calendars, clocks, and astronomy, 1989 Dates were typically given in a YMD format.

The civil calendar was apparently preceded by an observational lunar calendar which was eventually made lunisolar{{efn|Parker extensively developed the thesis that the predynastic lunar calendar was already lunisolar, using intercalary months every 2 or 3 years to maintain Sirius's return to the night sky in its twelfth month,{{sfnp|Parker|1950|pp=30–2}} but no evidence of such intercalation exists predating the schematic lunisolar calendar developed in {{nowrap|4th century BC.{{sfnp|Tetley|2014|p=[http://www.egyptchronology.com/uploads/2/6/9/4/26943741/ch_10_resolving_the_eponymous_month_conflict.pdf 153]}}}}}} and fixed to the civil calendar, probably in 357{{nbsp}}BC.{{sfnp|Clagett|1995|p=[https://archive.org/details/bub_gb_8c10QYoGa4UC/page/n34 26]}} The months of these calendars were known as "temple months"{{sfnp|Parker|1950|p=17}} and used for liturgical purposes until the closing of Egypt's pagan temples under Theodosius ITheodosian Code 16.10.12 in the AD{{nbsp}}390s and the subsequent suppression of individual worship by his successors.{{sfn|Høyrup|p=13}}

Smaller units of time were vague approximations for most of Egyptian history. Hours—known by a variant of the word for "stars"{{sfnp|Vygus|2015|p=409}}—were initially only demarcated at night and varied in length. They were measured using decan stars and by water clocks. Equal 24-part divisions of the day were only introduced in 127{{nbsp}}BC. Division of these hours into 60 equal minutes is attested in Ptolemy's 2nd-century works.

• Egyptian hieroglyphics and Transliteration of Ancient Egyptian
• Ancient Egyptian mathematics and technology
• Egyptian calendar and astronomy
• Ancient Mesopotamian, Hebrew, Persian, Greek, Roman, and Byzantine units of measurement
• Modern Egyptian units of measurement & Metric system

{{Noteslist}}

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• [https://web.archive.org/web/20070928120047/http://www.celticnz.org/images/Octart/image059.JPG Egyptian ceremonial ruler showing fingers, palms, hands, fists, feet, remen]
• [http://www.mathorigins.com/image%20grid/CUBIT_003.htm Cubit divided into fingers and hands]
• [https://web.archive.org/web/20050405181242/http://hbar.phys.msu.su/gorm/ahist/arnold/arnold.htm Modern replica of Egyptian ruler]
• [http://www.digitalegypt.ucl.ac.uk/weights/lenght.html Measuring length in Ancient Egypt] Page by Digitalegypt (University College London).
• [http://www.hallofmaat.com/modules.php?name=Articles&file=article&sid=39 Irrational numbers and pyramids] {{Webarchive|url=https://web.archive.org/web/20150924024654/http://www.hallofmaat.com/modules.php?name=Articles&file=article&sid=39 |date=2015-09-24 }} Article by Gay Robins and C. C. D. Shute
• [https://web.archive.org/web/20110720051944/http://mathcs.slu.edu/history-of-math/index.php/Egyptian_Mathematics:_Introduction Introduction to Egyptian Mathematics], with photographs of Maya's cubit rod from the Louvre and land surveying scenes from the tomb of Menna.

{{systems of measurement}}

{{DEFAULTSORT:Egyptian Units Of Measurement}}

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