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Attic numerals

January 13, 2023

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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.

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 generic 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?.
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 โ€œThe Governor erected this orphanage in the year 1828โ€. The year is shown as ฮง๐……ฮ—ฮ—ฮ—ฮ”ฮ”ฮ ฮ™ฮ™ฮ™.

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 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]

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 ย  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: ฮตฮบฮฑฯ„ฯŒ ๐ŒŸ C
500 ย  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 ย  ๐…Ž "ฮง" in "ฮ ": 1000 ร— 5 = 5000 ? V
10000 ฮœ ๐…• Old Greek: ฮœฮฅฮกฮ™ฮŸฮ™ [myrioi] Modern: ฮผฯฯฮนฮฟฮน ? X
50000 ย  ๐…– "ฮœ" in "ฮ ": 10000 ร— 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, 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.[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 แผ‘ฮบฮฑฯ„ฯŒฮฝ.[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:

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 ฮ™ฮ™ฮ™ = ๐…‡ฮœฮงฮง๐……ฮ—ฮ—ฮ ฮ™ฮ™ฮ™.

Unicode

Main article: Ancient Greek Numbers (Unicode block)
Ancient Greek Numbers[1][2]
Official Unicode Consortium code chart (PDF)
ย  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+1014x ๐…€ ๐… ๐…‚ ๐…ƒ ๐…„ ๐…… ๐…† ๐…‡ ๐…ˆ ๐…‰ ๐…Š ๐…‹ ๐…Œ ๐… ๐…Ž ๐…
U+1015x ๐… ๐…‘ ๐…’ ๐…“ ๐…” ๐…• ๐…– ๐…— ๐…˜ ๐…™ ๐…š ๐…› ๐…œ ๐… ๐…ž ๐…Ÿ
U+1016x ๐…  ๐…ก ๐…ข ๐…ฃ ๐…ค ๐…ฅ ๐…ฆ ๐…ง ๐…จ ๐…ฉ ๐…ช ๐…ซ ๐…ฌ ๐…ญ ๐…ฎ ๐…ฏ
U+1017x ๐…ฐ ๐…ฑ ๐…ฒ ๐…ณ ๐…ด ๐…ต ๐…ถ ๐…ท ๐…ธ ๐…น ๐…บ ๐…ป ๐…ผ ๐…ฝ ๐…พ ๐…ฟ
U+1018x ๐†€ ๐† ๐†‚ ๐†ƒ ๐†„ ๐†… ๐†† ๐†‡ ๐†ˆ ๐†‰ ๐†Š ๐†‹ ๐†Œ ๐† ๐†Ž
Notes
1.^ As of Unicode version 15.0
2.^ Grey area indicates non-assigned code point

See also

Notes and references

  1. ^ a b Gow, James (1883). "The Greek numerical alphabet". The Journal of Philology. Cambridge. XXII: 278โ€“9.
  2. ^ a b Smith, David Eugene (1958). "Reading and writing numbers: Greek numerals". History of Mathematics. Vol.ย 2. New York: Dover Publications. pp.ย 49โ€“51. ISBNย 9780486204307.
  3. ^ Woodhead, Arthur Geoffrey (1981). The Study of Greek Inscriptions (Secondย ed.). Cambridge: Cambridge University Press. p.ย 18. ISBNย 0-521-23188-4.
  4. ^ Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. "ยง14". Greek Grammar (Revisedย ed.). Cambridge, MA: Harvard University Press. p.ย 10. ISBNย 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 ฮตฮบฮฑฯ„ฯŒ.

January 13, 2023
attic, numerals, this, article, contains, special, characters, without, proper, rendering, support, question, marks, boxes, other, symbols, symbolic, number, notation, used, ancient, greeks, they, were, also, known, herodianic, numerals, because, they, were, f. This article contains special characters Without proper rendering support you may see question marks boxes or other symbols 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 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 HHH 300 HHH 800 DDD 33 X 1000 and X D 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 X HHHDDPIII 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 Contents 1 The system 1 1 Symbols 1 1 1 Special symbols 1 1 2 The symbol for 100 1 2 Simple multiples of powers of ten 1 3 General numbers 2 Unicode 3 See also 4 Notes and referencesThe systemSymbols The Attic numerals used the following main symbols with the given values 1 2 Value Symbol Talents Staters Notes Etruscan Roman1 I Tally mark I5 P Old Greek PENTE pษ›ntษ› Modern pente V10 D Old Greek DEKA deka Modern deka X50 D in P 10 5 50 L100 H Old Greek HEKATON hษ›katon Modern ekato ๐ŒŸ C500 H in P 100 5 500 D1000 X Old Greek XILIOI kสฐilioi Modern xilioi M5000 X in P 1000 5 5000 V10000 M Old Greek MYRIOI myrioi Modern myrioi X50000 M in P 10000 5 50000 LThe 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 was five times one thousand Special symbols The fractions one half and one quarter were written and respectively The symbols were slightly modified when used to encode amounts in talents with a small capital tau T or in staters with a small capital sigma S Specific numeral symbols were used to represent one drachma and ten minas The symbol for 100 The use of H 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 HEKATON because H 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 แผ‘katon 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 Units I II III IIII P PI PII PIII PIIII1 2 3 4 5 6 7 8 9Tens D DD DDD DDDD D DD DDD DDDD10 20 30 40 50 60 70 80 90Hundreds H HH HHH HHHH H HH HHH HHHH100 200 300 400 500 600 700 800 900Thousands X XX XXX XXXX X XX XXX XXXX1000 2000 3000 4000 5000 6000 7000 8000 9000Tens of thousands M MM MMM MMMM M MM MMM MMMM10000 20000 30000 40000 50000 60000 70000 80000 90000Unlike the more familiar Roman numeral system the Attic system used only the so called additive notation Thus the numbers 4 and 9 were written IIII and PIIII not IP and ID 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 DDDD PIIII DDDDPIIII 2001 2000 1 XX I XXI 1982 1000 900 80 2 X HHHH DDD II X HHHH DDDII 62708 60000 2000 700 8 M XX HH PIII MXX HHPIII UnicodeMain article Ancient Greek Numbers Unicode block Ancient Greek Numbers 1 2 Official Unicode Consortium code chart PDF 0 1 2 3 4 5 6 7 8 9 A B C D E FU 1014x U 1015x U 1016x U 1017x U 1018x Notes 1 As of Unicode version 15 0 2 Grey area indicates non assigned code pointSee alsoEtruscan numerals Greek mathematics Mathematics of Ancient Greeks Greek numerals System of writing numbers History of ancient numeral systems Symbols representing numbers List of numeral system topics List of numeral systems List of numeral systemsNotes and references a b Gow James 1883 The Greek numerical alphabet The Journal of Philology Cambridge XXII 278 9 a b Smith David Eugene 1958 Reading and writing numbers Greek numerals History of Mathematics Vol 2 New York Dover Publications pp 49 51 ISBN 9780486204307 Woodhead Arthur Geoffrey 1981 The Study of Greek Inscriptions Second ed Cambridge Cambridge University Press p 18 ISBN 0 521 23188 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 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 ekato Retrieved from https en wikipedia org w index php title Attic numerals amp oldid 1127456675, wikipedia, wiki, book, books, library,

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