الأعداد المصرية

أنظمة الأرقام حسب الثقافة
الأرقام الهندية العربية
العربية المغربية; العربية المشرقية; الخمير	العائلة الهندية; البراهمية; التايلندية
أرقام شرق آسيا
الصينية; سوژو; عصي العد	اليابانية; الكورية
الأرقام الأبجدية
أبجد; الأرمنية; السيريلية; جعيز	العبرية; اليونانية (Ionian); أريابهاتا;
أنظمة أخرى
Attic; البابلية; المصرية; الإتروسكية	المايا; الرومانية; Urnfield
	قائمة مواضيع نظم الأرقام
Positional systems by base
	عشري (10)
	2, 4, 8, 16, 32, 64
	1, 3, 9, 12, 20, 24, 30, 36, 60, more…
	عرض • نقاش • تعديل

هذه المقالة تحتوي حروف خاصة. بدون دعم إظهار مناسب، فقد تشاهد علامات استفهام أو مربعات أو رموز أخرى.

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.^{[بحاجة لمصدر]}

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Digits and numbers

The following hieroglyphs were used to denote powers of ten:

Value

1

10

100

1,000

10,000

100,000

1 million, or
many

Hieroglyph

Gardiner's sign list ID

Z1

V20

V1

M12

D50

I8

C11

Description

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 4622 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.^{[بحاجة لمصدر]}

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]

Fractions

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:

={\frac {1}{3}}

Special symbols were used for ¹⁄₂ and for the non-unit fractions ²⁄₃ and, less frequently, ³⁄₄:

={\frac {1}{2}}

={\frac {2}{3}}

={\frac {3}{4}}

If the denominator became too large, the "mouth" was just placed over the beginning of the "denominator":

={\frac {1}{100}}

Addition and subtraction

For plus and minus signs, the hieroglyphs

and

(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.^{[بحاجة لمصدر]}

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.^{[بحاجة لمصدر]}

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.^{[بحاجة لمصدر]}

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.^{[بحاجة لمصدر]}

Two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus.^{[بحاجة لمصدر]}

Egyptian words for numbers

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.^{[بحاجة لمصدر]}

Egyptian transliteration	Reconstructed vocalization		English translation	Coptic (Sahidic dialect)
Egyptian transliteration	per Callender 1975^[6]	per Loprieno 1995^[7]	English translation	Coptic (Sahidic dialect)
wꜥ(w) (masc.) wꜥt (fem.)	wíꜥyaw (masc.) wiꜥī́yat (fem.)	*wúꜥꜥuw (masc.)	one	ⲟⲩⲁ (oua) (masc.) ⲟⲩⲉⲓ (ouei) (fem.)
snwj (masc.) sntj (fem.)	sínwaj (masc.) síntaj (fem.)	*sinúwwaj (masc.)	two	ⲥⲛⲁⲩ (snau) (masc.) ⲥⲛ̄ⲧⲉ (snte) (fem.)
ḫmtw (masc.) ḫmtt (fem.)	ḫámtaw (masc.) ḫámtat (fem.)	*ḫámtaw (masc.)	three	ϣⲟⲙⲛ̄ⲧ (šomnt) (masc.) ϣⲟⲙⲧⲉ (šomte) (fem.)
jfdw (masc.) jfdt (fem.)	j˘fdáw (masc.) j˘fdát (fem.)	*jifdáw (masc.)	four	ϥⲧⲟⲟⲩ (ftoou) (masc.) ϥⲧⲟ (fto) or ϥⲧⲟⲉ (ftoe) (fem.)
djw (masc.) djt (fem.)	dī́jaw (masc.) dī́jat (fem.)	*dī́jaw (masc.)	five	ϯⲟⲩ (tiou) (masc.) ϯ (ti) or ϯⲉ (tie) (fem.)
sjsw or jsw (?) (masc.) sjst or jst (?) (fem.)	j˘ssáw (masc.) j˘ssát (fem.)	*sáʾsaw (masc.)	six	ⲥⲟⲟⲩ (soou) (masc.) ⲥⲟ (so) or ⲥⲟⲉ (soe) (fem.)
sfḫw (masc.) sfḫt (fem.)	sáfḫaw (masc.) sáfḫat (fem.)	*sáfḫaw (masc.)	seven	ϣⲁϣϥ̄ (šašf) (masc.) ϣⲁϣϥⲉ (šašfe) (fem.)
ḫmnw (masc.) ḫmnt (fem.)	ḫ˘mā́naw (masc.) ḫ˘mā́nat (fem.)	*ḫamā́naw (masc.)	eight	ϣⲙⲟⲩⲛ (šmoun) (masc.) ϣⲙⲟⲩⲛⲉ (šmoune) (fem.)
psḏw (masc.) psḏt (fem.)	p˘sī́ḏaw (masc.) p˘sī́ḏat (fem.)	*pisī́ḏaw (masc.)	nine	ⲯⲓⲥ (psis) (masc.) ⲯⲓⲧⲉ (psite) (fem.)
mḏw (masc.) mḏt (fem.)	mū́ḏaw (masc.) mū́ḏat (fem.)	*mū́ḏaw (masc.)	ten	ⲙⲏⲧ (mēt) (masc.) ⲙⲏⲧⲉ (mēte) (fem.)
mḏwtj, ḏwtj, or ḏbꜥty (?) (masc.) mḏwtt, ḏwtt, or ḏbꜥtt (?) (fem.)	*ḏubā́ꜥataj (masc.)	*(mu)ḏawā́taj (masc.)	twenty	ϫⲟⲩⲱⲧ (jouōt) (masc.) ϫⲟⲩⲱⲧⲉ (jouōte) (fem.)
mꜥbꜣ (masc.) mꜥbꜣt (fem.)	*máꜥb˘ꜣ (masc.)	*máꜥb˘ꜣ (masc.)	thirty	ⲙⲁⲁⲃ (maab) (masc.) ⲙⲁⲁⲃⲉ (maabe) (fem.)
ḥmw	*ḥ˘mí (?)	*ḥ˘méw	forty	ϩⲙⲉ (hme)
dyw	*díjwu	*díjjaw	fifty	ⲧⲁⲉⲓⲟⲩ (taeiou)
sjsjw, sjsw, or jswjw (?)	*j˘ssáwju	*saʾséw	sixty	ⲥⲉ (se)
sfḫjw, sfḫw, or sfḫwjw (?)	*safḫáwju	*safḫéw	seventy	ϣϥⲉ (šfe)
ḫmnjw, ḫmnw, or ḫmnwjw (?)	*ḫamanáwju	*ḫamnéw	eighty	ϩⲙⲉⲛⲉ (hmene)
psḏjw or psḏwjw (?)	*p˘siḏáwju	*pisḏíjjaw	ninety	ⲡⲥⲧⲁⲓⲟⲩ (pstaiou)
št	*šúwat	*ší(nju)t	one hundred	ϣⲉ (še)
štj	*šū́taj	*šinjū́taj	two hundred	ϣⲏⲧ (šēt)
ḫꜣ	*ḫaꜣ	*ḫaꜣ	one thousand	ϣⲟ (šo)
ḏbꜥ	*ḏubáꜥ	*ḏ˘báꜥ	ten thousand	ⲧⲃⲁ (tba)
ḥfn			one hundred thousand
ḥḥ	*ḥaḥ	*ḥaḥ	one million	ϩⲁϩ (hah) "many"

References

^ "Egyptian numerals". Retrieved 2013-09-25.
^ "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, 255