Editing Roman numerals (section)

===Large numbers===

The modern form can only write numbers up to 3999, and without M in early Roman times only numbers up to 899 could be written. Various schemes have been used over time to write larger numbers.

====Apostrophus====
[[File:Westerkerk MDCXXX.jpg|thumb|upright=0.9| "1630" on the [[Westerkerk]] in Amsterdam. "{{rn|M}}" and "{{rn|D}}" are given archaic {{lang|la|apostrophus}} form.]]

Using the {{lang|la|apostrophus}} method,<ref name="merriam-webster">{{Cite web |url=https://www.merriam-webster.com/dictionary/apostrophus |title=Definition of Apostrophus |website=www.merriam-webster.com}}</ref> 500 is written as {{rn|IↃ}}, while 1,000 is written as {{rn|CIↃ}}.<ref name="asimov on numbers 12" /> This system of encasing numbers to denote thousands (imagine the {{rn|C}}s and {{rn|Ↄ}}s as parentheses) had its origins in Etruscan numeral usage.

Each additional set of {{rn|C}} and {{rn|Ↄ}} surrounding {{rn|CIↃ}} raises the value by a factor of ten: {{rn|CCIↃↃ}} represents 10,000 and {{rn|CCCIↃↃↃ}} represents 100,000. Similarly, each additional {{rn|Ↄ}} to the right of {{rn|IↃ}} raises the value by a factor of ten: {{rn|IↃↃ}} represents 5,000 and {{rn|IↃↃↃ}} represents 50,000. Numerals larger than {{rn|CCCIↃↃↃ}} do not occur.<ref name=PropN3218/>

[[File:Roman numerals Bungus 1584-1585.png|thumb|upright=0.9|Page from a 16th-century manual, showing a mixture of {{lang|la|apostrophus}} and {{lang|la|vinculum}} numbers (see in particular the ways of writing 10,000).]]
* '''{{rn|IↃ}}''' = 500 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''{{rn|CIↃ}}''' = 1,000
* '''{{rn|IↃↃ}}''' = 5,000 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;'''{{rn|CCIↃↃ}}''' = 10,000
* '''{{rn|IↃↃↃ}}''' = 50,000 &nbsp;&nbsp;&nbsp;'''{{rn|CCCIↃↃↃ}}''' = 100,000

Sometimes {{rn|CIↃ}} (1000) is reduced to {{rn|ↀ}}, {{rn|IↃↃ}} (5,000) to {{rn|ↁ}}; {{rn|CCIↃↃ}} (10,000) to {{rn|ↂ}}; {{rn|IↃↃↃ}} (50,000) to {{rn|ↇ}}; and {{rn|CCCIↃↃↃ}} (100,000) to {{rn|ↈ}}.<ref name="Ifrah2000">{{Cite book |last=Ifrah |first=Georges |title=The Universal History of Numbers: From Prehistory to the Invention of the Computer |date=2000 |publisher=John Wiley & Sons |others=Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk}}</ref> It is likely {{rn|IↃ}} (500) reduced to {{rn|D}} and {{rn|CIↃ}} (1000) influenced  the later {{rn|M}}.

[[John Wallis]] is often credited with introducing the symbol for [[infinity]] {{angbr|∞}}, and one conjecture is that he based it on {{rn|ↀ}}, since 1,000 was [[hyperbole|hyperbolically]] used to represent very large numbers.

====Vinculum====
Using the {{lang|la|[[Vinculum (symbol)|vinculum]]}}, conventional Roman numerals are multiplied by 1,000 by adding a "bar" or "overline", thus:<ref name="Ifrah2000" />
* '''{{rn|IV|border=t}}''' = 4,000
* '''{{rn|XXV|border=t}}''' = 25,000
The ''vinculum ''came into use in the [[Roman Republic|late Republic]],<ref name=Dilke>{{Cite book |last=Dilke |first=Oswald Ashton Wentworth |title=Mathematics and measurement |date=1987 |publisher=British Museum Publications |isbn=978-0-7141-8067-0 |series=Reading the past |location=London|page=15}}</ref> and it was a common alternative to the apostrophic ↀ during the Imperial era around the Roman world (M for '1000' was not in use until the Medieval period).<ref name="Chrisomalis01">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=102–109}}</ref><ref name="gordon01">{{Cite book |last=Gordon |first=Arthur E. |title=Illustrated Introduction to Latin Epigraphy |date=1982 |publisher=University of California Press |isbn=0-520-05079-7 |location=Berkeley |pages=122–123}}</ref> It continued in use in the Middle Ages, though it became known more commonly as {{lang|la|titulus}},<ref name="Chrisomalis02">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=119}}</ref> and it appears in modern editions of classical and medieval Latin texts.<ref>{{Cite book |last=Boethius |url=https://archive.org/download/aniciimanliitor00friegoog/aniciimanliitor00friegoog.pdf |title=De Institutione Arithmetica, libri duo |date=1867 |publisher=B.G.Teubner |pages=42 |author-link=Boethius |access-date=18 January 2023 |orig-date=6th century AD}}</ref><ref name="PlinyNH" />

In an extension of the {{lang|la|vinculum}}, a three-sided box (now sometimes printed as two vertical lines and a {{lang|la|vinculum}}) is used to multiply by 100,000,<ref name="Chrisomalis03">{{Cite book |last=Chrisomalis |first=Stephen |title=Numerical Notation: A Comparative History |title-link=Numerical Notation: A Comparative History |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87818-0 |pages=402–403}}</ref><ref name=Dilke /> thus:
* '''{{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} p.''' = 1,332,000 paces (1,332 [[Mile#Roman|Roman miles]]).{{efn|1={{rn|XIII|border=vt}} = 13 × 100,000 = 1,300,000 and {{rn|XXXII|border=t}} = 32 × 1000 = 32,000, so '{{rn|XIII|border=vt}}{{nbsp}}{{rn|XXXII|border=t}} = 1,332,000. '''p.''' is a common abbreviation for {{lang|la|passus}}, paces, the Romans counting a pace as two steps.}}<ref name="PlinyNH">{{Cite book |last=Pliny |url=https://archive.org/details/L352PlinyNaturalHistoryII37/page/n429/mode/2up |title=Natural History |date=1961 |publisher=Harvard University Press |series=Loeb Classical Library |volume=L352 |at=Book VI, XXVI, 100 (pp 414-415) |orig-date=1st century AD}}</ref>

{{lang|la|Vinculum}} notation is distinct from the custom of adding an overline to a numeral simply to indicate that it is a number. Both usages can be seen on Roman inscriptions of the same period and general location, such as on the [[Antonine Wall]].<ref>{{Cite web |title=RIB 2208. Distance Slab of the Twentieth Legion |url=https://romaninscriptionsofbritain.org/inscriptions/2208 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}</ref><ref>{{Cite web |title=RIB 2171. Building Inscription of the Second and Twentieth Legions |url=https://romaninscriptionsofbritain.org/inscriptions/2171 |access-date=9 November 2020 |website=Roman Inscriptions in Britain}}</ref>

==== Other ====

* There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as {{rn|XVIXIII}}, corresponding to the common reading "sixteen thirteen" of such year numbers in English, or 1519 as {{rn|X{{Overset|C|V}}XIX}} as in [[French language|French]] ''quinze-cent-dix-neuf'' (fifteen-hundred and nineteen), and similar readings in other languages.<ref name="gach1862">{{Cite journal |last=Gachard |first=M. |date=1862 |title=II. Analectes historiques, neuvième série (n<sup>os</sup> CCLXI-CCLXXXIV) |url=https://www.persee.fr/doc/bcrh_0770-6707_1862_num_31_3_3033 |journal=Bulletin de la Commission royale d'Historie |volume=31 |issue=3 |pages=345–554 |doi=10.3406/bcrh.1862.3033}} <br />Page 347: {{lang|fr|Lettre de Philippe le Beau aux échevins..., quote: "Escript en nostre ville de Gand, le XXIIII<sup>me</sup> de febvrier, l'an IIII<sup>XX</sup>XIX [quatre-vingt-dix-neuf {{=}} 99].}}" <br />Page 356: {{lang|fr|Lettre de l'achiduchesse Marguerite au conseil de Brabant..., quote: "... Escript à Bruxelles, le dernier jour de juing anno XV<sup>c</sup>XIX [1519].}}" <br />Page 374: {{lang|fr|Letters patentes de la rémission ... de la ville de Bruxelles, quote}}: "{{lang|nl|... Op heden, tweentwintich ['twenty-two'] daegen in decembri, anno vyfthien hondert tweendertich}} ['fifteen hundred thirty-two'] {{lang|nl|... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich [1532] vorschreven.}}" <br />Page 419: {{lang|fr|Acte du duc de Parme portant approbation..., quote: "Faiet le XV<sup>me</sup> de juillet XV<sup>c</sup> huytante-six [1586].}}".</ref>

* In some French texts from the 15th century and later, one finds constructions like {{rn|IIII<sup>XX</sup>XIX}} for 99, reflecting the French reading of that number as {{lang|fr|quatre-vingt-dix-neuf}} (four-score and nineteen).<ref name=gach1862/> Similarly, in some English documents one finds, for example, 77 written as "{{rn|iii<sup>xx</sup>xvii}}" (which could be read "three-score and seventeen").<ref name=salt1923>{{Cite book |last=Salter |first=Herbert Edward |url=https://books.google.com/books?id=dfNAAAAAYAAJ&q=iiixx |title=Registrum Annalium Collegii Mertonensis 1483–1521 |date=1923 |publisher=Oxford Historical Society |volume=76}} 544 pages. Page 184 has the computation in pounds:shillings:pence (li:s:d) x:iii:iiii + xxi:viii:viii + xlv:xiiii:i = iii<sup>xx</sup>xvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.</ref>

* A medieval accounting text from 1301 renders numbers like 13,573 as "{{rn|{{sc|XIII. M. V. C. III. XX. XIII}}}}", that is, "13×1000 + 5×100 + 3×20 + 13".<ref name="wade1865">{{Cite encyclopedia |chapter=E Duo Codicibus Ceratis Johannis de Sancto Justo |url=https://books.google.com/books?id=NrxuEwPNWD4C&pg=PA530 |date=1865 |orig-date=1301 |last1=de Wailly |last2=Delisle | title=Recueil des historiens des Gaules et de la France. Par Martin Bouquet: Contenant la deuxieme livraison des monumens des regnes de saint Louis, de Philippe le Hardi, de Philippe le bel, de Louis X, de Philippe V et de Charles IV ... Jusqu'en MCCCXXVIII. Tome Vingt-Deuxième |trans-chapter=From Two Texts in Wax by John of St Just |encyclopedia=Recueil des Historiens des Gaules et de la France |lang=la |volume=22 |quote-page=530 |quote= SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. |trans-quote=Sum total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers.}}</ref>