The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BCE[1] until the early first millennium CE. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a place-valued system such as the decimal system.[2] The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.[citation needed]
Multiples of these values were expressed by repeating the symbol as many times as needed. For instance, a stone carving from Karnak shows the number 4,622 as:
Egyptian hieroglyphs could be written in both directions (and even vertically). In this example the symbols decrease in value from top to bottom and from left to right. On the original stone carving, it is right-to-left, and the signs are thus reversed.[citation needed]
Zero and negative numbers
nfr
heart with trachea beautiful, pleasant, good
By 1740 BCE, the Egyptians had a symbol for zero in accounting texts. The symbol nfr (𓄤), meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line.[4]
Rational numbers could also be expressed, but only as sums of unit fractions, i.e., sums of reciprocals of positive integers, except for 2⁄3 and 3⁄4. The hieroglyph indicating a fraction looked like a mouth, which meant "part":
Fractions were written with this fractional solidus, i.e., the numerator 1, and the positive denominator below. Thus, 1⁄3 was written as:
Special symbols were used for 1⁄2 and for the non-unit fractions 2⁄3 and, less frequently, 3⁄4:
If the denominator became too large, the "mouth" was just placed over the beginning of the "denominator":
(D54, D55) were used: if the feet pointed into the direction of writing, it signified addition, otherwise subtraction.[5]
Written numbers
As with most modern day languages, the ancient Egyptian language could also write out numerals as words phonetically, just like one can write thirty instead of "30" in English. The word (thirty), for instance, was written as
while the numeral (30) was
This was, however, uncommon for most numbers other than one and two and the signs were used most of the time.[citation needed]
Hieratic numerals
As administrative and accounting texts were written on papyrus or ostraca, rather than being carved into hard stone (as were hieroglyphic texts), the vast majority of texts employing the Egyptian numeral system utilize the hieratic script. Instances of numerals written in hieratic can be found as far back as the Early Dynastic Period. The Old Kingdom Abusir Papyri are a particularly important corpus of texts that utilize hieratic numerals.[citation needed]
A comparative chart of Egyptian numerals, including hieratic and demotic
Boyer proved 50 years ago[when?] that hieratic script used a different numeral system, using individual signs for the numbers 1 to 9, multiples of 10 from 10 to 90, the hundreds from 100 to 900, and the thousands from 1000 to 9000. A large number like 9999 could thus be written with only four signs—combining the signs for 9000, 900, 90, and 9—as opposed to 36 hieroglyphs. Boyer saw the new hieratic numerals as ciphered, mapping one number onto one Egyptian letter for the first time in human history. Greeks adopted the new system, mapping their counting numbers onto two of their alphabets, the Doric and Ionian.[citation needed]
In the oldest hieratic texts the individual numerals were clearly written in a ciphered relationship to the Egyptian alphabet. But during the Old Kingdom a series of standardized writings had developed for sign-groups containing more than one numeral, repeated as Roman numerals practiced. However, repetition of the same numeral for each place-value was not allowed in the hieratic script. As the hieratic writing system developed over time, these sign-groups were further simplified for quick writing; this process continued into Demotic, as well.[citation needed]
The following table shows the reconstructed Middle Egyptian forms of the numerals (which are indicated by a preceding asterisk), the transliteration of the hieroglyphs used to write them, and finally the Coptic numerals which descended from them and which give Egyptologists clues as to the vocalism of the original Egyptian numbers. A breve (˘) in some reconstructed forms indicates a short vowel whose quality remains uncertain; the letter 'e' represents a vowel that was originally u or i (exact quality uncertain) but became e by Late Egyptian.[citation needed]
^Loprieno, Antonio (1995) Ancient Egyptian: A Linguistic Introduction, Cambridge: Cambridge University Press, p. 71, 255
Bibliography
Allen, James Paul (2000). Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphs. Cambridge: Cambridge University Press. Numerals discussed in §§9.1–9.6.
Gardiner, Alan Henderson (1957). Egyptian Grammar; Being an Introduction to the Study of Hieroglyphs. 3rd ed. Oxford: Griffith Institute. For numerals, see §§259–266.
Goedicke, Hans (1988). Old Hieratic Paleography. Baltimore: Halgo, Inc.
Möller, Georg (1927). Hieratische Paläographie: Die Ägyptische Buchschrift in ihrer Entwicklung von der Fünften Dynastie bis zur römischen Kaiserzeit. 3 vols. 2nd ed. Leipzig: J. C. Hinrichs Schen Buchhandlungen. (Reprinted Osnabrück: Otto Zeller Verlag, 1965)
External links
Wikimedia Commons has media related to Hieroglyphs of Egypt: Numerals.
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This article contains special characters Without proper rendering support you may see question marks boxes or other symbols The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BCE 1 until the early first millennium CE It was a system of numeration based on multiples of ten often rounded off to the higher power written in hieroglyphs The Egyptians had no concept of a place valued system such as the decimal system 2 The hieratic form of numerals stressed an exact finite series notation ciphered one to one onto the Egyptian alphabet citation needed Contents 1 Digits and numbers 2 Zero and negative numbers 3 Fractions 4 Addition and subtraction 5 Written numbers 6 Hieratic numerals 7 Egyptian words for numbers 8 See also 9 References 10 Bibliography 11 External linksDigits and numbers EditThe following hieroglyphs were used to denote powers of ten Value 1 10 100 1 000 10 000 100 000 1 million ormanyHieroglyphGardiner s sign list ID Z1 V20 V1 M12 D50 I8 C11Description Single stroke Cattle hobble Coil of rope Water lily also called lotus Bent finger Tadpole Heh 3 Multiples of these values were expressed by repeating the symbol as many times as needed For instance a stone carving from Karnak shows the number 4 622 as Egyptian hieroglyphs could be written in both directions and even vertically In this example the symbols decrease in value from top to bottom and from left to right On the original stone carving it is right to left and the signs are thus reversed citation needed Zero and negative numbers Editnfr heart with tracheabeautiful pleasant goodBy 1740 BCE the Egyptians had a symbol for zero in accounting texts The symbol nfr 𓄤 meaning beautiful was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line 4 Fractions EditMain article Egyptian fraction Rational numbers could also be expressed but only as sums of unit fractions i e sums of reciprocals of positive integers except for 2 3 and 3 4 The hieroglyph indicating a fraction looked like a mouth which meant part Fractions were written with this fractional solidus i e the numerator 1 and the positive denominator below Thus 1 3 was written as 1 3 displaystyle frac 1 3 Special symbols were used for 1 2 and for the non unit fractions 2 3 and less frequently 3 4 1 2 displaystyle frac 1 2 2 3 displaystyle frac 2 3 3 4 displaystyle frac 3 4 If the denominator became too large the mouth was just placed over the beginning of the denominator 1 100 displaystyle frac 1 100 Addition and subtraction EditFor plus and minus signs the hieroglyphsand D54 D55 were used if the feet pointed into the direction of writing it signified addition otherwise subtraction 5 Written numbers EditAs with most modern day languages the ancient Egyptian language could also write out numerals as words phonetically just like one can write thirty instead of 30 in English The word thirty for instance was written as while the numeral 30 was This was however uncommon for most numbers other than one and two and the signs were used most of the time citation needed Hieratic numerals EditAs administrative and accounting texts were written on papyrus or ostraca rather than being carved into hard stone as were hieroglyphic texts the vast majority of texts employing the Egyptian numeral system utilize the hieratic script Instances of numerals written in hieratic can be found as far back as the Early Dynastic Period The Old Kingdom Abusir Papyri are a particularly important corpus of texts that utilize hieratic numerals citation needed A comparative chart of Egyptian numerals including hieratic and demotic Boyer proved 50 years ago when that hieratic script used a different numeral system using individual signs for the numbers 1 to 9 multiples of 10 from 10 to 90 the hundreds from 100 to 900 and the thousands from 1000 to 9000 A large number like 9999 could thus be written with only four signs combining the signs for 9000 900 90 and 9 as opposed to 36 hieroglyphs Boyer saw the new hieratic numerals as ciphered mapping one number onto one Egyptian letter for the first time in human history Greeks adopted the new system mapping their counting numbers onto two of their alphabets the Doric and Ionian citation needed In the oldest hieratic texts the individual numerals were clearly written in a ciphered relationship to the Egyptian alphabet But during the Old Kingdom a series of standardized writings had developed for sign groups containing more than one numeral repeated as Roman numerals practiced However repetition of the same numeral for each place value was not allowed in the hieratic script As the hieratic writing system developed over time these sign groups were further simplified for quick writing this process continued into Demotic as well citation needed Two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus citation needed Egyptian words for numbers EditThe following table shows the reconstructed Middle Egyptian forms of the numerals which are indicated by a preceding asterisk the transliteration of the hieroglyphs used to write them and finally the Coptic numerals which descended from them and which give Egyptologists clues as to the vocalism of the original Egyptian numbers A breve in some reconstructed forms indicates a short vowel whose quality remains uncertain the letter e represents a vowel that was originally u or i exact quality uncertain but became e by Late Egyptian citation needed Egyptian transliteration Reconstructed vocalization English translation Coptic Sahidic dialect perCalendarr 1975 6 per Loprieno 1995 7 wꜥ w masc wꜥt fem wiꜥyaw masc wiꜥi yat fem wuꜥꜥuw masc one ⲟⲩⲁ oua masc ⲟⲩⲉⲓ ouei fem snwj masc sntj fem sinwaj masc sintaj fem sinuwwaj masc two ⲥⲛⲁⲩ snau masc ⲥⲛ ⲧⲉ snte fem ḫmtw masc ḫmtt fem ḫamtaw masc ḫamtat fem ḫamtaw masc three ϣⲟⲙⲛ ⲧ somnt masc ϣⲟⲙⲧⲉ somte fem jfdw masc jfdt fem j fdaw masc j fdat fem jifdaw masc four ϥⲧⲟⲟⲩ ftoou masc ϥⲧⲟ fto or ϥⲧⲟⲉ ftoe fem djw masc djt fem di jaw masc di jat fem di jaw masc five ϯⲟⲩ tiou masc ϯ ti or ϯⲉ tie fem sjsw or jsw masc sjst or jst fem j ssaw masc j ssat fem saʾsaw masc six ⲥⲟⲟⲩ soou masc ⲥⲟ so or ⲥⲟⲉ soe fem sfḫw masc sfḫt fem safḫaw masc safḫat fem safḫaw masc seven ϣⲁϣϥ sasf masc ϣⲁϣϥⲉ sasfe fem ḫmnw masc ḫmnt fem ḫ ma naw masc ḫ ma nat fem ḫama naw masc eight ϣⲙⲟⲩⲛ smoun masc ϣⲙⲟⲩⲛⲉ smoune fem psḏw masc psḏt fem p si ḏaw masc p si ḏat fem pisi ḏaw masc nine ⲯⲓⲥ psis masc ⲯⲓⲧⲉ psite fem mḏw masc mḏt fem mu ḏaw masc mu ḏat fem mu ḏaw masc ten ⲙⲏⲧ met masc ⲙⲏⲧⲉ mete fem mḏwtj ḏwtj or ḏbꜥty masc mḏwtt ḏwtt or ḏbꜥtt fem ḏuba ꜥataj masc mu ḏawa taj masc twenty ϫⲟⲩⲱⲧ jouōt masc ϫⲟⲩⲱⲧⲉ jouōte fem mꜥbꜣ masc mꜥbꜣt fem maꜥb ꜣ masc maꜥb ꜣ masc thirty ⲙⲁⲁⲃ maab masc ⲙⲁⲁⲃⲉ maabe fem ḥmw ḥ mi ḥ mew forty ϩⲙⲉ hme dyw dijwu dijjaw fifty ⲧⲁⲉⲓⲟⲩ taeiou sjsjw sjsw or jswjw j ssawju saʾsew sixty ⲥⲉ se sfḫjw sfḫw or sfḫwjw safḫawju safḫew seventy ϣϥⲉ sfe ḫmnjw ḫmnw or ḫmnwjw ḫamanawju ḫamnew eighty ϩⲙⲉⲛⲉ hmene psḏjw or psḏwjw p siḏawju pisḏijjaw ninety ⲡⲥⲧⲁⲓⲟⲩ pstaiou st suwat si nju t one hundred ϣⲉ se stj su taj sinju taj two hundred ϣⲏⲧ set ḫꜣ ḫaꜣ ḫaꜣ one thousand ϣⲟ so ḏbꜥ ḏubaꜥ ḏ baꜥ ten thousand ⲧⲃⲁ tba ḥfn one hundred thousandḥḥ ḥaḥ ḥaḥ one million ϩⲁϩ hah many See also EditEgyptian language Egyptian mathematicsReferences Edit Egyptian numerals MacTutor School of Mathematics and Statistics University of St Andrews Retrieved January 12 2023 The Story of Numbers by John McLeish Merzbach Uta C and Carl B Boyer A History of Mathematics Hoboken NJ John Wiley 2011 p 10 George Gheverghese Joseph 2011 The Crest of the Peacock Non European Roots of Mathematics Third ed Princeton p 86 ISBN 978 0 691 13526 7 Cajori Florian 1993 1929 A History of Mathematical Notations Dover Publications pp pp 229 230 ISBN 0 486 67766 4 Callender John B 1975 Middle Egyptian 1975 Loprieno Antonio 1995 Ancient Egyptian A Linguistic Introduction Cambridge Cambridge University Press p 71 255Bibliography EditAllen James Paul 2000 Middle Egyptian An Introduction to the Language and Culture of Hieroglyphs Cambridge Cambridge University Press Numerals discussed in 9 1 9 6 Gardiner Alan Henderson 1957 Egyptian Grammar Being an Introduction to the Study of Hieroglyphs 3rd ed Oxford Griffith Institute For numerals see 259 266 Goedicke Hans 1988 Old Hieratic Paleography Baltimore Halgo Inc Moller Georg 1927 Hieratische Palaographie Die Agyptische Buchschrift in ihrer Entwicklung von der Funften Dynastie bis zur romischen Kaiserzeit 3 vols 2nd ed Leipzig J C Hinrichs Schen Buchhandlungen Reprinted Osnabruck Otto Zeller Verlag 1965 External links Edit Wikimedia Commons has media related to Hieroglyphs of Egypt Numerals Introduction to Hieroglyphs Numbers and Fractions at the Wayback Machine archived September 29 2007 Numbers and dates at the Wayback Machine archived March 4 2001 Egyptian Numbers at the Wayback Machine archived January 12 2004 Egyptian Math History Retrieved from https en wikipedia org w index php title Egyptian numerals amp oldid 1133985144, wikipedia, wiki, book, books, library,
