The Attic
numerals are a
symbolic number notation used by the
ancient Greeks
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...
. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by
Herodian
Herodian or Herodianus ( el, Ἡρωδιανός) of Syria, sometimes referred to as "Herodian of Antioch" (c. 170 – c. 240), was a minor Roman civil servant who wrote a colourful history in Greek titled ''History of the Empire from the Death o ...
; or as acrophonic numerals (from
acrophony) because the basic symbols derive from the first letters of the
(ancient) Greek words that the symbols represented.
The Attic numerals were a decimal (base 10) system, like the older
Egyptian
Egyptian describes something of, from, or related to Egypt.
Egyptian or Egyptians may refer to:
Nations and ethnic groups
* Egyptians, a national group in North Africa
** Egyptian culture, a complex and stable culture with thousands of years of ...
and the later
Etruscan __NOTOC__
Etruscan may refer to:
Ancient civilization
*The Etruscan language, an extinct language in ancient Italy
*Something derived from or related to the Etruscan civilization
**Etruscan architecture
**Etruscan art
**Etruscan cities
** Etrusca ...
,
Roman
Roman or Romans most often refers to:
*Rome, the capital city of Italy
*Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*'' Epistle to the Romans'', shortened to ''Romans'', a lette ...
, and
Hindu-Arabic systems. Namely, the number to be represented was broken down into simple multiples (1 to 9) of
powers of ten — units, tens, hundred, thousands, etc.. Then these parts were written down in sequence, in order of decreasing value. As in the basic Roman system, each part was written down using a combination of two symbols, representing one and five times that power of ten.
Attic numerals were adopted possibly starting in the 7th century BCE and although presently called Attic, they or variations thereof were universally used by the Greeks. No other
numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The same sequence of symbo ...
is known to have been used on
Attic inscriptions
before the Common Era
Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the or ...
.
Their replacement by the
classic Greek numerals started in other parts of the Greek World around the 3rd century BCE. They are believed to have served as model for the Etruscan number system, although the two were nearly contemporary and the symbols are not obviously related.
The system
Symbols
The Attic numerals used the following main symbols, with the given values:
The symbols representing 50, 500, 5000, and 50000 were composites of an old form of the capital letter
pi (with a short right leg) and a tiny version of the applicable power of ten. For example, 𐅆 was five times one thousand.
Special symbols
The fractions "one half" and "one quarter" were written "𐅁" and "𐅀", respectively.
The symbols were slightly modified when used to encode amounts in
talents (with a small capital
tau
Tau (uppercase Τ, lowercase τ, or \boldsymbol\tau; el, ταυ ) is the 19th letter of the Greek alphabet, representing the voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300.
The name in English ...
, "Τ") or in
stater
The stater (; grc, , , statḗr, weight) was an ancient coin used in various regions of Greece. The term is also used for similar coins, imitating Greek staters, minted elsewhere in ancient Europe.
History
The stater, as a Greek silver curre ...
s (with a small capital
sigma, "Σ"). Specific numeral symbols were used to represent one
drachma
The drachma ( el, δραχμή , ; pl. ''drachmae'' or ''drachmas'') was the currency used in Greece during several periods in its history:
# An ancient Greek currency unit issued by many Greek city states during a period of ten centuries, fr ...
("𐅂") and ten
minas
Minas or MINAS may refer to:
People with the given name Minas
* Menas of Ethiopia (died 1563)
* Saint Menas (Minas, 285–309)
* Minias of Florence (Minas, Miniato, died 250)
* Minas Alozidis (born 1984), Greek hurdler
* Minas Avetisyan (1928 ...
"𐅗".
The symbol for 100
The use of "Η" (capital
eta
Eta (uppercase , lowercase ; grc, ἦτα ''ē̂ta'' or ell, ήτα ''ita'' ) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel . Originally denoting the voiceless glottal fricative in most dialects, ...
) for 100 reflects the early date of this numbering system. In the Greek language of the time, the word for a hundred would be pronounced (with a "rough aspirated" sound /h/) and written "ΗΕΚΑΤΟΝ", because "Η" represented the sound /h/ in the Attic alphabet. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked. It was not until
Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the
spiritus asper
In the polytonic orthography of Ancient Greek, the rough breathing ( grc, δασὺ πνεῦμα, dasỳ pneûma or ''daseîa''; la, spīritus asper) character is a diacritical mark used to indicate the presence of an sound before a vowel, d ...
began to represent /h/, resulting in the spelling .
[As found in ]Katharevousa
Katharevousa ( el, Καθαρεύουσα, , literally "purifying anguage) is a conservative form of the Modern Greek language conceived in the late 18th century as both a literary language and a compromise between Ancient Greek and the contempor ...
, polytonic
Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography ( el, πολυτονικό σύστημα γραφής, translit=polytonikó sýstīma grafī́s), which includes fiv ...
Greek in general and Modern Greek in particular before the 1982 official adoption of the monotonic system; however, neither the /h/ phoneme nor the spiritus asper, or "rough breathing mark", are present in monotonic Standard Modern Greek, resulting in the standard modern spelling .
Simple multiples of powers of ten
Multiples 1 to 9 of each power of ten were written by combining the two corresponding "1" and "5" digits, namely:
Unlike the more familiar Roman numeral system, the Attic system used only the so-called "additive" notation. Thus, the numbers 4 and 9 were written ΙΙΙΙ and ΠΙΙΙΙ, not ΙΠ and ΙΔ.
General numbers
In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts would be written down in sequence, from largest to smallest value. For example:
* 49 = 40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = ΔΔΔΔΠΙΙΙΙ
* 2001 = 2000 + 1 = ΧΧ + I = ΧΧΙ
* 1982 = 1000 + 900 + 80 + 2 = Χ + 𐅅ΗΗΗΗ + 𐅄ΔΔΔ + ΙΙ = Χ𐅅ΗΗΗΗ𐅄ΔΔΔΙΙ
* 62708 = 60000 + 2000 + 700 + 8 = 𐅇Μ + ΧΧ + 𐅅ΗΗ + ΠΙΙΙ = 𐅇ΜΧΧ𐅅ΗΗΠΙΙΙ.
Unicode
See also
*
*
*
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Notes and references
{{Ancient Greek mathematics
Numerals
Ancient Athens
Numerals
A numeral is a figure, symbol, or group of figures or symbols denoting a number. It may refer to:
* Numeral system used in mathematics
* Numeral (linguistics), a part of speech denoting numbers (e.g. ''one'' and ''first'' in English)
* Numerical d ...
Society of ancient Greece
de:Griechische Zahlen