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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 "๐…‚" instead of the geenric unit sign "ฮ™". Some amounts are "๐…„" = 50, "ฮ—ฮ—ฮ—" = 300, "๐……ฮ—ฮ—ฮ—" = 800, "ฮ”ฮ”ฮ”๐…‚๐…‚๐…‚" = 33, "ฮง" = 1000, and "ฮง๐……๐…„ฮ”๐…‚๐…‚"? = 1562?.

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.

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 โ€” 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 were eventually replaced by the classic Greek numerals 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]

Contents

The system

Symbols

The Attic numerals used the following main symbols, with the given values:

Value Symbol Talents Staters Notes Etruscan Roman
1 ฮ™ Tally mark? ๐Œ  I
5 ฮ  ๐…ˆ ๐… Old Greek: ฮ ฮ•ฮฮคฮ• [pษ›ntษ›] Modern: ฯ€ฮญฮฝฯ„ฮต ๐Œก V
10 ฮ” ๐…‰ ๐… Old Greek: ฮ”ฮ•ฮšฮ‘ [deka] Modern: ฮดฮญฮบฮฑ ๐Œข X
50 ๐…„ ๐…Š ๐…‘ "ฮ”" in "ฮ ": 10 ร— 5 = 50 ๐Œฃ L
100 ฮ— ๐…‹ ๐…’ Old Greek: ฮ—ฮ•ฮšฮ‘ฮคฮŸฮ [hษ›katon] Modern: แผ‘ฮบฮฑฯ„ฯŒฮฝ ๐ŒŸ C
500 ๐…… ๐…Œ ๐…“ "ฮ—" in "ฮ ": 100 ร— 5 = 500 ? D
1000 ฮง ๐… ๐…” Old Greek: ฮงฮ™ฮ›ฮ™ฮŸฮ™ [kสฐilioi] Modern: ฯ‡ฮฏฮปฮนฮฟฮน ? M
5000 ๐…† ๐…Ž "ฮง" in "ฮ ": 1000 ร— 5 = 5000 ? V
10000 ฮœ ๐…• Old Greek: ฮœฮฅฮกฮ™ฮŸฮ [myrion] Modern: ฮผฯฯฮนฮฟฮฝ ? X
50000 ๐…‡ ๐…– "ฮœ" in "ฮ ": 10000 ร— 5 = 50000 ? X

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, ๐…† was five times one thousand.

Special symbols

The fractions "one half" and "one quarter" were written "๐…" and "๐…€", respectively.

The symbols were slightly modified when used to encode amounts in talents (with a small capital tau, "ฮค") or in staters (with a small capital sigma, "ฮฃ"). Specific numeral symbols were used to represent one drachma ("๐…‚") and ten minas "๐…—".

The symbol for 100

The use of "ฮ—" (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 [hษ›katon] (with a "rough aspirated" sound /h/) and written "ฮ—ฮ•ฮšฮ‘ฮคฮŸฮ", because "ฮ—" 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.[1][2] 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 modern Greek spelling แผ‘ฮบฮฑฯ„ฯŒฮฝ. In modern Greek the /h/ phoneme has disappeared altogether, but the accent on the แผ‘ is retained in the standard 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:

Units ฮ™ II III IIII ฮ  ฮ I ฮ II ฮ III ฮ IIII
1 2 3 4 5 6 7 8 9
Tens ฮ” ฮ”ฮ” ฮ”ฮ”ฮ” ฮ”ฮ”ฮ”ฮ” ๐…„ ๐…„ฮ” ๐…„ฮ”ฮ” ๐…„ฮ”ฮ”ฮ” ๐…„ฮ”ฮ”ฮ”ฮ”
10 20 30 40 50 60 70 80 90
Hundreds ฮ— ฮ—ฮ— ฮ—ฮ—ฮ— ฮ—ฮ—ฮ—ฮ— ๐…… ๐……ฮ— ๐……ฮ—ฮ— ๐……ฮ—ฮ—ฮ— ๐……ฮ—ฮ—ฮ—ฮ—
100 200 300 400 500 600 700 800 900
Thousands ฮง ฮงฮง ฮงฮงฮง ฮงฮงฮงฮง ๐…† ๐…†ฮง ๐…†ฮงฮง ๐…†ฮงฮงฮง ๐…†ฮงฮงฮงฮง
1000 2000 3000 4000 5000 6000 7000 8000 9000
Tens of thousands ฮœ ฮœฮœ ฮœฮœฮœ ฮœฮœฮœฮœ ๐…‡ ๐…‡ฮœ ๐…‡ฮœฮœ ๐…‡ฮœฮœฮœ ๐…‡ฮœฮœฮœฮœ
10000 20000 30000 40000 50000 60000 70000 80000 90000

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 ฮ™ฮ™ฮ™ฮ™ and ฮ ฮ™ฮ™ฮ™ฮ™, not ฮ™ฮ  and ฮ™ฮ”.

General numbers

In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten โ€” units, tens, hundred, thousands, etc.. Then these parts would be written down in sequence, from largest to smallest value. For example:

  • 49 = 40 + 9 = ฮ”ฮ”ฮ”ฮ” + ฮ ฮ™ฮ™ฮ™ฮ™ = ฮ”ฮ”ฮ”ฮ”ฮ ฮ™ฮ™ฮ™ฮ™
  • 2001 = 2000 + 1 = ฮงฮง + I = ฮงฮงฮ™
  • 1982 = 1000 + 900 + 80 + 2 = ฮง + ๐…†ฮ—ฮ—ฮ—ฮ— + ๐…„ฮ”ฮ”ฮ” + ฮ™ฮ™ = ฮง๐…†ฮ—ฮ—ฮ—ฮ—๐…„ฮ”ฮ”ฮ”ฮ™ฮ™
  • 62708 = 60000 + 2000 + 700 + 8 = ๐…‡ฮœ + ฮงฮง + ๐……ฮ—ฮ— + ฮ III = ๐…‡ฮœฮงฮง๐……ฮ—ฮ—ฮ III.

Attic numerals are available in Unicode in the Ancient Greek Numbers block (U+10140 to U+1018F).

See also

Notes and references

  1. ^ Woodhead, A. G. (1981). The Study of Greek Inscriptions. Second Edition. Cambridge: Cambridge University Press. p. 18. ISBNย 0-521-23188-4.
  2. ^ Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. Greek Grammar. Revised Edition. Cambridge, MA: Harvard University Press. p. 10 (ยง14). ISBNย 0-674-36250-0.