Attic numerals

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Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "" instead of the generic unit sign "I". Some amounts are "" = 50, "EEE" = 300, "EEE" = 800, "DDD" = 33, "Kh" = 1000, and "KhD"? = 1562?. EPMA-IGI-3-259-272-Tribute-list-3-crop1-cbadj.png
Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "𐅂" instead of the generic unit sign "Ι". Some amounts are "𐅄" = 50, "ΗΗΗ" = 300, "𐅅ΗΗΗ" = 800, "ΔΔΔ𐅂𐅂𐅂" = 33, "Χ" = 1000, and "Χ𐅅𐅄Δ𐅂𐅂"? = 1562?.
Plaque above the main entrance to the orphanage, which later became a prison, on the Greek island of Aegina. The ancient Greek inscription translates as "The Governor erected this orphanage in the year 1828". The year is shown as KhEEEDDPIII. Aegina Prison Attic Numerals.jpg
Plaque above the main entrance to the orphanage, which later became a prison, on the Greek island of Aegina. The ancient Greek inscription translates as “The Governor erected this orphanage in the year 1828”. The year is shown as Χ𐅅ΗΗΗΔΔΠΙΙΙ.

The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals (from acrophony) because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.

Contents

The Attic numerals were a decimal (base 10) system, like the older Egyptian and the later Etruscan, Roman, 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 is known to have been used on Attic inscriptions before the Common Era. [1] [2] 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. [ citation needed ]

The system

Symbols

The Attic numerals used the following main symbols, with the given values: [1] [2]

ValueSymbolTalentsStatersNotesEtruscanRoman
1ΙTally mark?𐌠I
5Π𐅈𐅏Old Greek: ΠΕΝΤΕ [pɛntɛ] Modern: πέντε𐌡V
10Δ𐅉𐅐Old Greek: ΔΕΚΑ [deka] Modern: δέκα𐌢X
50 Attic 00050.svg 𐅊𐅑"Δ" in "Π": 10 × 5 = 50𐌣L
100Η𐅋𐅒Old Greek: ΗΕΚΑΤΟΝ [hɛkaton] Modern: εκατό𐌟C
500 Attic 00500.svg 𐅌𐅓"Η" in "Π": 100 × 5 = 500 ?D
1000Χ𐅍𐅔Old Greek: ΧΙΛΙΟΙ [kʰilioi] Modern: χίλιοι ?M
5000 Attic 05000.svg 𐅎"Χ" in "Π": 1000 × 5 = 5000 ?V
10000Μ𐅕Old Greek: ΜΥΡΙΟΙ [myrioi] Modern: μύριοι ?X
50000 Attic 50000.svg 𐅖"Μ" in "Π": 10000 × 5 = 50000 ?L

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, "Τ") or in staters (with a small capital sigma, "Σ"). Specific numeral symbols were used to represent one drachma ("𐅂") and ten minas "𐅗".

The symbol for 100

The use of "Η" (capital eta) 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 [hɛkaton] (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. [3] [4] It was not until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/, resulting in the spelling ἑκατόν. [5]

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:

UnitsΙIIIIIIIIIΠΠIΠIIΠIIIΠIIII
123456789
TensΔΔΔΔΔΔΔΔΔΔ𐅄𐅄Δ𐅄ΔΔ𐅄ΔΔΔ𐅄ΔΔΔΔ
102030405060708090
HundredsΗΗΗΗΗΗΗΗΗΗ𐅅𐅅Η𐅅ΗΗ𐅅ΗΗΗ𐅅ΗΗΗΗ
100200300400500600700800900
ThousandsΧΧΧΧΧΧΧΧΧΧ𐅆𐅆Χ𐅆ΧΧ𐅆ΧΧΧ𐅆ΧΧΧΧ
100020003000400050006000700080009000
Tens of thousandsΜΜΜΜΜΜΜΜΜΜ𐅇𐅇Μ𐅇ΜΜ𐅇ΜΜΜ𐅇ΜΜΜΜ
100002000030000400005000060000700008000090000

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:

Unicode

Ancient Greek Numbers [1] [2]
Official Unicode Consortium code chart (PDF)
 0123456789ABCDEF
U+1014x𐅀𐅁𐅂𐅃𐅄𐅅𐅆𐅇𐅈𐅉𐅊𐅋𐅌𐅍𐅎𐅏
U+1015x𐅐𐅑𐅒𐅓𐅔𐅕𐅖𐅗𐅘𐅙𐅚𐅛𐅜𐅝𐅞𐅟
U+1016x𐅠𐅡𐅢𐅣𐅤𐅥𐅦𐅧𐅨𐅩𐅪𐅫𐅬𐅭𐅮𐅯
U+1017x𐅰𐅱𐅲𐅳𐅴𐅵𐅶𐅷𐅸𐅹𐅺𐅻𐅼𐅽𐅾𐅿
U+1018x𐆀𐆁𐆂𐆃𐆄𐆅𐆆𐆇𐆈𐆉𐆊𐆋𐆌𐆍𐆎
Notes
1. ^ As of Unicode version 15.0
2. ^ Grey area indicates non-assigned code point

See also

Notes and references

  1. 1 2 Gow, James (1883). "The Greek numerical alphabet". The Journal of Philology. Cambridge. XXII: 278–9.
  2. 1 2 Smith, David Eugene (1958). "Reading and writing numbers: Greek numerals". History of Mathematics. Vol. 2. New York: Dover Publications. pp. 49–51. ISBN   9780486204307.
  3. Woodhead, Arthur Geoffrey (1981). The Study of Greek Inscriptions (Second ed.). Cambridge: Cambridge University Press. p. 18. ISBN   0-521-23188-4.
  4. Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. "§14". Greek Grammar (Revised ed.). Cambridge, MA: Harvard University Press. p. 10. ISBN   0-674-36250-0.
  5. As found in Katharevousa, polytonic 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 εκατό.

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