Editing Greek numerals (section)

==History==
The [[Minoans|Minoan]] and [[Mycenaean civilization]]s' [[Linear A]] and [[Linear B]] alphabets used a different system, called [[Aegean numerals]], which included number-only symbols for powers of ten: {{lang|gmy|𐄇}}&nbsp;=&nbsp;1, {{lang|gmy|𐄐}}&nbsp;=&nbsp;10, {{lang|gmy|𐄙}}&nbsp;=&nbsp;100, {{lang|gmy|𐄢}}&nbsp;=&nbsp;1000, and {{lang|gmy|𐄫}}&nbsp;=&nbsp;10000.<ref name=Verdun-2007-03-20>{{cite web |last=Verdan |first=Samuel |date=20 March 2007 |title=Systèmes numéraux en Grèce ancienne: Description et mise en perspective historique |lang=fr |url=http://www.dma.ens.fr/culturemath/histoire%20des%20maths/htm/Verdan/Verdan.htm |access-date=2 March 2011 |archive-date=2 February 2010 |archive-url=https://web.archive.org/web/20100202054101/http://www.dma.ens.fr/culturemath/histoire%20des%20maths/htm/Verdan/Verdan.htm |url-status=dead }}</ref>

[[Attic numerals]] composed another system that came into use perhaps in the 7th&nbsp;century&nbsp;BC. They were [[acrophonic]], derived (after the initial one) from the first letters of the names of the numbers represented. They ran {{GrGl|Zeta archaic}}&nbsp;=&nbsp;1, {{GrGl|Pi archaic}}&nbsp;=&nbsp;5, {{GrGl|Delta 04}}&nbsp;=&nbsp;10, {{GrGl|Eta classical}}&nbsp;=&nbsp;100, {{GrGl|Chi normal}}&nbsp;=&nbsp;1,000, and {{GrGl|Mu classical}}&nbsp;=&nbsp;10,000. The numbers 50, 500, 5,000, and 50,000 were represented by the letter {{GrGl|Pi archaic}} with minuscule powers of ten written in the top-right corner: [[File:Attic_00050.svg|x16px]], [[File:Attic_00500.svg|x16px]], [[File:Attic_05000.svg|x16px]], and [[File:Attic_50000.svg|x16px]].<ref name=Verdun-2007-03-20/> One-half was represented by {{script|Grek|𐅁}}<!-- can also use {{big|<math>\boldsymbol\mathsf\subset</math>}}, not browser-font dependent; really should be sans-serif, capital Lunate sigma Ϲ, or non-existant TeX <math>\boldsymbol\mathsf\Varsigma</math> (vs. l.c. \varsigma) --> (left half of a full circle) and one-quarter by   ɔ (right side of a full circle). The same system was used outside of [[Attica]], but the symbols varied with the [[Archaic Greek alphabets|local alphabets]]; for example, 1,000 was {{GrGl|Psi_V-shaped}} in [[Boeotia]].<ref name=Heath-2003>{{cite book |last=Heath |first=Thomas L. |orig-year=1931 |year=2003 |title=A Manual of Greek Mathematics |edition={{small|[2003]}} reprint |publisher=Oxford University Press{{sup|[1931]}}; Dover Books{{sup|[2003]}} |location=Oxford, UK |pages=[https://books.google.com/books?id=_HZNr_mGFzQC&pg=PA14 14]&nbsp;ff |isbn=9780486154442 |url=https://books.google.com/books?id=_HZNr_mGFzQC&pg=PA14 |access-date=1 November 2013 |via=Google Books}}</ref>

The present system probably developed around [[Miletus]] in [[Ionia]]. 19th&nbsp;century classicists placed its development in the 3rd&nbsp;century&nbsp;BC, the occasion of its first widespread use.<ref>{{cite book |last=Thompson |first=Edward M. |year=1893 |title=Handbook of Greek and Latin Palaeography |page=114 |place=New York, NY |publisher=D. Appleton}}</ref> More thorough [[modern archaeology]] has caused the date to be pushed back at least to the 5th&nbsp;century&nbsp;BC,<ref>{{cite book |department=The Packard Humanities Institute |publisher=[[Cornell University]] & [[Ohio State University]] |title=Searchable Greek Inscriptions |article=IG I³ 1387 |id={{nobreak|IG I³ 1387}}&nbsp; ''also known as'' &nbsp;{{nobreak|IG I² 760}} |article-url=http://epigraphy.packhum.org/inscriptions/oi?ikey=1592&bookid=4&region=1 |access-date=1 November 2013}}</ref> a little before [[Athens (city-state)|Athens]] abandoned its [[Archaic Greek alphabets|pre-Eucleidean alphabet]] in favour of [[Ionic alphabet|Miletus]]'s in 402&nbsp;BC, and it may predate that by a century or two.<ref>{{cite book |last=Jeffery |first=Lilian H. |year=1961 |title=The Local Scripts of Archaic Greece |pages=38&nbsp;ff |place=Oxford, UK |publisher=Clarendon Press}}</ref> The present system uses the 24&nbsp;letters adopted under [[Eucleides]], as well as three [[Phoenician alphabet|Phoenician]] and Ionic ones that had not been dropped from the Athenian alphabet (although kept for numbers): [[digamma (letter)|digamma]], [[koppa (letter)|koppa]], and [[sampi (letter)|sampi]]. The position of those characters within the numbering system imply that the first two were still in use (or at least remembered as letters) while the third was not. The exact dating, particularly for [[sampi]], is problematic since its uncommon value means the first attested representative near Miletus does not appear until the 2nd&nbsp;century&nbsp;BC,<ref>{{cite book |department=The Packard Humanities Institute |publisher=[[Cornell University]] & [[Ohio State University]] |title=Searchable Greek Inscriptions |article=Magnesia&nbsp;4 |id=Magnesia&nbsp;4&nbsp; ''also known as'' &nbsp;{{nobreak|Syll³ 695.b}} |article-url=http://epigraphy.packhum.org/inscriptions/oi?ikey=260445&bookid=509&region=8&subregion=27 |access-date=1 November 2013}}</ref> and its use is unattested in Athens until the 2nd&nbsp;century&nbsp;CE.<ref>{{cite book |department=The Packard Humanities Institute |publisher=[[Cornell University]] & [[Ohio State University]] |title=Searchable Greek Inscriptions |article=IG II² 2776 |article-url=http://epigraphy.packhum.org/inscriptions/oi?ikey=5028&bookid=5&region=1 |access-date=1 November 2013}}</ref> (In general, Athenians resisted using the new numerals for the longest of any Greek state, but had fully adopted them by {{circa|50&nbsp;CE}}.<ref name=Heath-2003/>)