Roman numerals

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Roman numerals
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{{For|a description of numeric words in Latin|Latin numerals}}{{Use dmy dates|date=August 2018}}{{Short description|Numbers in the Roman numeral system}}{{Contains special characters}}File:CuttySarkRomNum.jpg|thumb|upright=1.05|Roman numerals on stern of the ship {{ship||Cutty Sark}} showing draught in feet. The numbers range from 13 to 22, from bottom to top.]]{{numeral systems}}Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:BOOK, Illustrated Introduction to Latin Epigraphy, Gordon, Arthur E., University of California Press, 1982, 0-520-05079-7, Berkeley, Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.,
{| class="wikitable"! Symbol
! Value| 1| 5| 10| 50| 100| 500| 1,000
The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:
{{rn|I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII}}
The notations {{rn|IV}} and {{rn|IX}} can be read as "one less than five" (4) and "one less than ten" (9), although there is a strong tradition favouring representation of "4" as "{{rn|IIII}}" on Roman numeral clocks.WEB, Public clocks do a number on Roman numeralss,weblink Judkins, Maura, The Washington Post, 13 August 2019, Most clocks using Roman numerals traditionally use IIII instead of IV... One of the rare prominent clocks that uses the IV instead of IIII is Big Ben in London., 4 November 2011, Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. {{rn|MCM}}, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written {{rn|MCMXII}}. For this century, {{rn|MM}} indicates 2000. Thus the current year is {{rn|{{#time:xrY}}}} (2019).


There is not, and never has been, an "official", "binding", or universally accepted standard for Roman numerals.{{efn|An exception to this is where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law - an incorrect or ambiguous numeral for a copyright date may invalidate a copyright claim, or affect the termination date of the copyright period.WEB, Hayes, David P.,weblink Guide to Roman Numerals, Copyright Registration and Renewal Information Chart and Web Site, }}Usage in ancient Rome varied greatly and remained somewhat inconsistent in medieval times and later.WEB, Adams, Cecil, What is the proper way to style Roman numerals for the 1990s?, 23 February 1990,weblink The Straight Dope, The "rules" of the system as it is now applied have been established only by general usage over the centuries.

A "base 10" system

Roman numerals are essentially a decimal or "base 10" number system. Powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order. In the absence of "place keeping" zeros, different symbols are used for each power of ten, but a common pattern is used for each of them.The underlying form of this pattern employs the symbols {{rn|I}} and {{rn|V}} (representing 1 and 5) as simple tally marks, to build the numbers from 1 to 9. Each marker for 1 ({{rn|I}}) adds a unit value up to 5 ({{rn|V}}), and is then added to ({{rn|V}}) to make the numbers from 6 to 9. Finally the unit symbol for the next power completes a "finger count" sequence:
{{rn|I, II, III, IIII, V, VI, VII, VIII, VIIII, X}}.
At some early time the Romans started to use the abbreviated forms {{rn|IV}} ("one less than 5") for {{rn|IIII}} and {{rn|IX}} ("one less than 10") for {{rn|VIIII}} - a convention that has been widely, although not universally, used ever since.{{efn|Without theorising about causation, it may be noted that "{{rn|IV}}" uses 25% fewer strokes than "{{rn|IIII}}", and takes up 25% less space. For the other forms ({{rn|IX}}, {{rn|XL}}, {{rn|XC}}, {{rn|CD}}, and {{rn|CM}}), the savings on either or both counts are 50% or more. "{{rn|IX}}" is also more distinctive than "{{rn|VIIII}}" and less likely to be confused with "{{rn|VIII}}". This equally applies to {{rn|XC}}, {{rn|CD}}, and {{rn|CM}}.}} This convention is called "subtractive" notation,Stanislas Dehaene (1997): The Number Sense : How the Mind Creates Mathematics. Oxford University Press; 288 pages. {{isbn|9780199723096}} as opposed to the purely "additive" notation of {{rn|IIII}} and {{rn|VIIII}}.Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990): Encyclopaedia of Mathematics, Volume 10, page 502. Springer; 546 pages. {{isbn|9781556080050}} Thus the numbers from 1 to 10 are generally written as
{{rn|I, II, III, IV, V, VI, VII, VIII, IX, X}}.BOOK, Reddy, Indra K., Khan, Mansoor A., Essential Math and Calculations for Pharmacy Technicians, CRC Press, 2003,weblink 978-0-203-49534-6
, The multiples of 10, from 10 to 100, are written according to the same pattern, with {{rn|X}}, {{rn|L}}, and {{rn|C}} taking the place of {{rn|I}}, {{rn|V}}, and {{rn|X}}
{{rn|X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C}}.
Note that 40 is usually written {{rn|XL}} ("10 less than 50") rather than {{rn|XXXX}}, and 90 as {{rn|XC}} ("10 less than 100") rather than {{rn|LXXXX}}.Similarly, the multiples of 100, 100 to 1000, are written as
{{rn|C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M}}.
where {{rn|CD}} is to be read as "100 less than 500" (that is, 400), and {{rn|CM}} as "100 less than 1000" (that is, 900).Since the system has no standard symbols for 5,000 and 10,000, the full pattern cannot be extended to the multiples of 1000 – restricting the "thousands" range of "normal" Roman numerals to 1,000, 2,000 and 3,000:
'''{{rn|M, MM, MMM}}.
A number containing several decimal places is represented, as in the Arabic system, by writing its power-of-ten parts — thousands, hundreds, tens and units — in sequence, from left to right, in descending order of value. For example:
  • 39 = 30 + 9 = {{rn|XXX}} + {{rn|IX}} = {{rn|XXXIX}}.
  • 246 = 200 + 40 + 6 = {{rn|CC}} + {{rn|XL}} + {{rn|VI}} = {{rn|CCXLVI}}.
  • 789 = 700 + 80 + 9 = {{rn|DCC}} + {{rn|LXXX}} + {{rn|IX}} = {{rn|DCCLXXXIX}}.
  • 2,421 = 2000 + 400 + 20 + 1 = {{rn|MM}} + {{rn|CD}} + {{rn|XX}} + {{rn|I}} = {{rn|MMCDXXI}}.
Any missing place (represented by a zero in the Arabic equivalent) is omitted, as in Latin (and English) speech:
  • 160 = 100 + 60 = {{rn|C}} + {{rn|LX}} = {{rn|CLX}}
  • 207 = 200 + 7 = {{rn|CC}} + {{rn|VII}} = {{rn|CCVII}}
  • 1,009 = 1,000 + 9 = {{rn|M}} + {{rn|IX}} = {{rn|MIX}}
  • 1,066 = 1,000 + 60 + 6 = {{rn|M}} + {{rn|LX}} + {{rn|VI}} = {{rn|MLXVI}}BOOK, Dela Cruz, M. L. P., Torres, H. D., Number Smart Quest for Mastery: Teacher's Edition, 2009, Rex Bookstore, Inc.,weblink 9789712352164
, BOOK, Python Cookbook, Martelli, Alex, Ascher, David, O'Reilly Media Inc., 2002,weblink 978-0-596-00167-4, Roman numerals for large numbers are nowadays seen mainly in the form of year numbers, as in these examples:
  • 1776 = 1,000 + 700 + 70 + 6 = {{rn|M}} + {{rn|DCC}} + {{rn|LXX}} + {{rn|VI}} = {{rn|MDCCLXXVI}} (the date written on the book held by the Statue of Liberty).WEB, What book is the Statue of Liberty holding? What is its significance?,weblink Quora
  • 1954 = 1,000 + 900 + 50 + 4 = {{rn|M}} + {{rn|CM}} + {{rn|L}} + {{rn|IV}} = {{rn|MCMLIV}} (as in the trailer for the movie The Last Time I Saw Paris)
  • 2014 = 2,000 + 10 + 4 = {{rn|MM}} + {{rn|X}} + {{rn|IV}} = {{rn|MMXIV}} (the year of the games of the {{rn|XXII}} (22nd) Olympic Winter Games (in Sochi)
  • The current year (2019) is {{rn|{{time:xrY}}}}.
The largest number that can be represented in this notation is 3,999 (3,000 + 900 + 90 + 9 = {{rn|MMM}} + {{rn|CM}} + {{rn|XC}} + {{rn|IX}} = {{rn|MMMCMXCIX}}).{{efn|Since the largest Roman numerals likely to be used today are year numbers up to the present there is normally no need to use Roman numerals for numbers beyond this limit. In the unlikely case a larger number might be needed there is really no reason why more "M"s, as required, could not be added, cumbersome as this might prove. Through the centuries during which Roman numerals remained the standard way of writing numbers throughout Europe there were various extensions to the system designed to indicate larger numbers, see the final sections of this article.}}

Variant forms

Forms exist that vary in one way or another from the general "standard" described above.

Use of additive notation

File:BadSalzdetfurthBadenburgerStr060529.jpg|thumb|A typical clock face with Roman numerals in Bad SalzdetfurthBad SalzdetfurthWhile subtractive notation for multiples of 4 ({{rn|IV}}, {{rn|XL}} and {{rn|CD}}) has been the usual form since Roman times, additive notation ({{rn|IIII}}, {{rn|XXXX}},Julius Caesar (52-49 BC): Commentarii de Bello Gallico. Book II, Section 4: "... XV milia Atrebates, Ambianos X milia, Morinos XXV milia, Menapios VII milia, Caletos X milia, Veliocasses et Viromanduos totidem, Atuatucos XVIIII milia; ..." Section 8: "... ab utroque latere eius collis transversam fossam obduxit circiter passuum CCCC et ad extremas fossas castella constituit..." Book IV, Section 15: "Nostri ad unum omnes incolumes, perpaucis vulneratis, ex tanti belli timore, cum hostium numerus capitum CCCCXXX milium fuisset, se in castra receperunt." Book VII, Section 4: " hiberna remissis ipse se recipit die XXXX Bibracte." and {{rn|CCCC}}) continued to be used, including in compound numbers like {{rn|XXIIII}},Angelo Rocca (1612) De campanis commentarius. Published by Guillelmo Faciotti, Rome. (:File:Campana a XXIIII hominibus pulsata.jpg|Title of a Plate): "Campana a XXIIII hominibus pulsata" ("Bell to be sounded by 24 men") {{rn|LXXIIII}},Gerard Ter Borch (1673): (:File:Cornelis de Graeff (1650-1678).png|Portrait of Cornelis de Graef). Date on painting: "Out. XXIIII Jaer. M. DC. LXXIIII". and {{rn|CCCCLXXXX}}.Pliny the Elder (77-79 AD): [ Naturalis Historia], Book III: "Saturni vocatur, Caesaream Mauretaniae urbem CCLXXXXVII p[assum]. traiectus. reliqua in ora flumen Tader ... ortus in Cantabris haut procul oppido Iuliobrica, per CCCCL p. fluens ..." Book IV: "Epiri, Achaiae, Atticae, Thessalia in porrectum longitudo CCCCLXXXX traditur, latitudo CCLXXXXVII." Book VI: "tam vicinum Arsaniae fluere eum in regione Arrhene Claudius Caesar auctor est, ut, cum intumuere, confluant nec tamen misceantur leviorque Arsanias innatet MMMM ferme spatio, mox divisus in Euphraten mergatur." The additive forms for 9, 90, and 900 ({{rn|VIIII}},{{rn|LXXXX}},Thomas Bennet (1731): Grammatica Hebræa, cum uberrima praxi in usum tironum ... Editio tertia. Published by T. Astley, copy in the British Library; 149 pages. Page 24: "PRÆFIXA duo sunt viz. He emphaticum vel relativum (de quo Cap VI Reg. LXXXX.) & Shin cum Segal sequente Dagesh, quod denotat pronomen relativum..." and {{rn|DCCCC}}Pico Della Mirandola (1486)`Conclusiones sive Theses DCCCC ("Conclusions, or 900 Theses").) have also been used, although less frequently.The two conventions could be mixed in the same document or inscription, even in the same numeral. On the numbered gates to the Colosseum, for instance, {{rn|IIII}} is systematically used instead of {{rn|IV}}, but subtractive notation is used for other digits; so that gate 44 is labelled {{rn|XLIIII}}.WEB,weblink 360:12 tables, 24 chairs, and plenty of chalk, Roman Numerals…not quite so simple, 2 January 2011, Isaac Asimov speculates that the use of {{rn|IV}}, as the initial letters of "IVPITER" (a classical Latin spelling of the name of the Roman god Jupiter) may have been felt to have been impious in this context.BOOK, Isaac, Asimov, Asimov On Numbers,weblink Pocket Books, a division of Simon & Schuster, Inc, 1966, 12, Modern clock faces that use Roman numerals still usually employ {{rn|IIII}} for four o'clock but {{rn|IX}} for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century.BOOK, Time & Timekeepers, Milham, W.I., 1947, Macmillan, New York, 196, {{citation| title = Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning| first = Clifford A.| last = Pickover| authorlink = Clifford A. Pickover| publisher = Oxford University Press| year = 2003| isbn = 978-0-19-534800-2| page = 282 id = 52N0JJBspM0C plainurl = yes }}}}.BOOK, More of the straight dope, Adams, Cecil, Zotti, Ed, Ballantine Books, 1988, 978-0-345-35145-6, 154,weblink . However, this is far from universal: for example, the clock on the Palace of Westminster tower, "Big Ben", uses a subtractive {{rn|IV}} for 4 o'clock.File:AdmiraltyArchLondonCloseup.jpg|thumb|The year number on MDCCCCX}}, rather than the more usual {{rn|MCMX}}|alt=Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written {{rn|MCM}}). These vary from {{rn|MDCCCCX}} - a classical use of additive notation for {{rn|MCMX}} (1910), as seen on Admiralty Arch, London, to the more unusual, if not unique {{rn|MDCDIII}} for {{rn|MCMIII}} (1903), on the north entrance to the Saint Louis Art Museum.WEB, Gallery: Museum's North Entrance (1910),weblink Saint Louis Art Museum, 10 January 2014, The inscription over the North Entrance to the Museum reads: "Dedicated to Art and Free to All MDCDIII." These roman numerals translate to 1903, indicating that the engraving was part of the original building designed for the 1904 World's Fair., dead,weblink" title="">weblink 4 December 2010, Sometimes 5 and 50 have been written {{rn|IIIII}} and {{rn|XXXXX}} instead of {{rn|V}} and {{rn|L}}, and there are instances such as {{rn|IIIIII}} and {{rn|XXXXXX}} rather than {{rn|VI}} or {{rn|LX}}.ENCYCLOPEDIA, Joyce Maire, Reynolds, Anthony J. S., Spawforth, numbers, Roman, Oxford Classical Dictionary, 3rd, Simon, Hornblower, Anthony, Spawforth, Oxford University Press, 1996, 0-19-866172-X, BOOK, Kennedy, Benjamin Hall, The Revised Latin Primer, 1923, Longmans, Green & Co, London,

Irregular subtractive notation

File:Epitaph des Marcus Caelius.JPG|thumb|Epitaph of XIIX}}"The irregular use of subtractive notation, such as {{rn|IIIXX}} for 17,Michaele Gasp. Lvndorphio (1621): Acta publica inter invictissimos gloriosissimosque&c. ... et Ferdinandum II. Romanorum Imperatores.... Printed by Ian-Friderici Weissii. Page 123: "Sub Dato Pragæ IIIXX Decemb. A. C. M. DC. IIXX". Page 126, end of the same document: "Dabantur Pragæ 17 Decemb. M. DC. IIXX" {{rn|IIXX}} for 18,Raphael Sulpicius à Munscrod (1621): Vera Ac Germana Detecto Clandestinarvm Deliberationvm. Page 16, line 1: "repertum Originale Subdatum IIIXXX Aug. A. C. MDC.IIXX". Page 41, upper right corner: "Decemb. A. C. MDC.IIXX". Page 42, upper left corner: "Febr. A. C. MDC.XIX". Page 70: "IIXX. die Maij sequentia in consilio noua ex Bohemia allata....". Page 71: "XIX. Maij". {{rn|IIIC}} for 97,Wilhelm Ernst Tentzel (1699): Als Ihre Königl. Majestät in Pohlen und .... Page 39: "... und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC [1699]." {{rn|IIC}} for 98,Joh. Caspar Posner (1698): Mvndvs ante mvndvm sive De Chao Orbis Primordio, title page: "Ad diem jvlii A. O. R. M DC IIC".Wilhelm Ernst Tentzel (1700): Saxonia Nvmismatica: Das ist: Die Historie Des Durchlauchtigsten.... Page 26: "Die Revers hat eine feine Inscription: SERENISSIMO DN.DN... SENATUS.QVERNF. A. M DC IIC D. 18 OCT [year 1698 day 18 oct]." and {{rn|IC}} for 99Enea Silvio Piccolomini (1698): Opera Geographica et Historica. Helmstadt, J. M. Sustermann. Title page of first edition: "Bibliopolæ ibid. M DC IC" were occasionally used in more modern times. A possible explanation is that the word for 18 in Latin was duodeviginti, literally "two from twenty". Similarly, the words for 98 and 99 were duodecentum (two from hundred) and undecentum (one from hundred), respectively.BOOK, Benjamin H., Kennedy, Latin grammar, Longmans, Green, and Co., London, 1879, 150,weblink 9781177808293, These ways of saying 18, 98 and 99 have been attributed to influence from the Etruscans, who would say ciem zaθrum (three from twenty) for 17, eslem zaθrum (two from twenty) for 18 and θunem zaθrum (one from twenty) for 19.Giuliano Bonfante (1985): "Etruscan Words in Latin". Word, volume 36, issue 3, pages 203-210. {{doi|10.1080/00437956.1985.11435872}} However, the explanation does not seem to apply to {{rn|IIIXX}} and {{rn|IIIC}}, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.Another example of irregular subtractive notation is the use of {{rn|XIIX}} for 18. It was used by officers of the XVIII Roman Legion to write their number.BOOK, Handbook to life in ancient Rome, Lesley, Adkins, Roy A, Adkins, 2, 2004, 0-8160-5026-0, 270, BOOK, A manual of Roman coins, William, Boyne, 1968, 13, The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius ({{circa|45 BC|lk=no}} – AD 9). There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than {{rn|XVIII}}.

Rare variants

While the subtractive and additive notations seem to have been used interchangeably through history, some other Roman numerals have been occasionally observed that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.File:Padlock,_Athlone.jpg|thumb|200px|Padlock used on the north gate of the Irish town of XVIXIII}}, (literally "16, 13") instead of {{rn|MDCXIII}}
  • {{rn|IIXX}} was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely duo et vice(n)sima (literally "two and twentieth") rather than the "regular" vice(n)sima secunda (twentieth second).Stephen James Malone, (2005) Legio XX Valeria Victrix.... PhD thesis. On page 396 it discusses many coins with "Leg. IIXX" and notes that it must be Legion 22. The footnote on that page says: "The form IIXX clearly reflecting the Latin duo et vicensima 'twenty-second': cf. X5398, legatus I[eg II] I et vicensim(ae) Pri[mi]g; VI 1551, legatus leg] IIXX Prj; III 14207.7, miles leg IIXX; and III 10471-3, a vexillation drawn from four German legions including 'XVIII PR' - surely here the stonecutter's hypercorrection for IIXX PR. Apparently, at least one ancient stonecutter mistakenly thought that the {{rn|IIXX}} of "22nd Legion" stood for 18, and "corrected" it to {{rn|XVIII}}.
File:Excerpt from BnF ms. 1433 fr., fol. 24r.png|thumb|300x300px|Excerpt from (Bibliothèque nationale de France]].BOOK,weblink L' Atre périlleux et Yvain, le chevalier au lion ., 1301-1350, EN, The Roman numeral for 500 is rendered as {{Rn|VC}}, instead of {{Rn|D}})
  • 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|XVCXIX}} as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.M. Gachard (1862): "II. Analectes historiques, neuvième série (nos CCLXI-CCLXXXIV)". Bulletin de la Commission royale d'Historie, volume 3, pages 345-554. Page 347: Lettre de Philippe le Beau aux échevins..., quote: "Escript en nostre ville de Gand, le XXIIIIme de febvrier, l'an IIIIXXXIX [quatre-vingt-dix-neuf = 99]." Page 356: Lettre de l'achiduchesse Marguerite au conseil de Brabant..., quote: "... Escript à Bruxelles, le dernier jour de juing anno XVcXIX [1519]." Page 374: Letters patentes de la rémission ... de la ville de Bruxelles, quote: "... Op heden, tweentwintich ['twenty-two'] daegen in decembri, anno vyfthien hondert tweendertich ['fifteen hundred thirty-two'] ... Gegeven op ten vyfsten dach in deser jegewoirdige maent van decembri anno XV tweendertich [1532] vorschreven." Page 419: Acte du duc de Parme portant approbation..., quote": "Faiet le XVme de juillet XVc huytante-six [1586]." {{doi|10.3406/bcrh.1862.3033}}
  • In some French texts from the 15th century and later one finds constructions like {{rn|IIIIXXXIX}} for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen). Similarly, in some English documents one finds, for example, 77 written as "{{rn|iiixxxvii}}" (which could be read "three-score and seventeen").Herbert Edward Salter (1923) Registrum Annalium Collegii Mertonensis 1483-1521 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 = iiixxxvii:vi:i, i.e. 10:3:4 + 21:8:8 + 45:14:1 = 77:6:1.
  • Another medieval accounting text from 1301 renders numbers like 13,573 as "{{rn|XIII. M. V. C. III. XX. XIII}}, that is, "(13 × 1000) + (5 × 100) + (3 × 20) + 13".Johannis de Sancto Justo (1301): "E Duo Codicibus Ceratis" ("From Two Texts in Wax"). In de Wailly, Delisle (1865): Contenant la deuxieme livraison des monumens des regnes de saint Louis,... Volume 22 of Recueil des historiens des Gaules et de la France. Page 530: "SUMMA totalis, XIII. M. V. C. III. XX. XIII. l. III s. XI d. [Sum total, 13 thousand 5 hundred 3 score 13 livres, 3 sous, 11 deniers].
  • Other numerals that do not fit the usual patterns — such as {{rn|VXL}} for 45, instead of the usual {{rn|XLV}} — may be due to scribal errors, or the writer's lack of familiarity with the system, rather than being genuine variant usage.

Non-numeric combinations

As Roman numerals are composed of ordinary alphabetic characters, there may sometimes be confusion with other uses of the same letters. For example, "XXX" and "XL" have other connotations in addition to their values as Roman numerals, while "IXL" more often than not is a gramogram of "I excel", and is in any case not an unambiguous Roman numeral.

Origin of the system

The system as we use today is closely associated with the city of Rome and the Empire that it created. However, due to the scarcity of surviving examples, the origins of the system are obscure and there are several competing theories, largely conjectural.

Etruscan numerals

Rome was founded sometime between 850 and 750 BC. At the time, the region was inhabited by diverse populations of which the Etruscans were the most advanced. The ancient Romans themselves admitted that the basis of much of their civilization was Etruscan. Rome itself was located next to the southern edge of the Etruscan domain, which covered a large part of north-central Italy.The Roman numerals, in particular, are directly derived from the Etruscan number symbols: "𐌠", "𐌡", "𐌢", "𐌣", and "𐌟" for 1, 5, 10, 50, and 100 (They had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired number, from higher to lower value. Thus the number 87, for example, would be written 50 + 10 + 10 + 10 + 5 + 1 + 1 = 𐌣𐌢𐌢𐌢𐌡𐌠𐌠 (this would appear as 𐌠𐌠𐌡𐌢𐌢𐌢𐌣 since Etruscan was written from right to left.)Gilles Van Heems (2009)> "Nombre, chiffre, lettre : Formes et réformes. Des notations chiffrées de l'étrusque" ("Between Numbers and Letters: About Etruscan Notations of Numeral Sequences"). Revue de philologie, de littérature et d'histoire anciennes, volume {{rn|LXXXIII}} (83), issue 1, pages 103-130. {{issn|0035-1652}}The symbols "𐌠" and "𐌡" resembled letters of the Etruscan alphabet, but "𐌢", "𐌣", and "𐌟" did not. The Etruscans used the subtractive notation, too, but not like the Romans. They wrote 17, 18, and 19 as "𐌠𐌠𐌠𐌢𐌢", "𐌠𐌠𐌢𐌢", and 𐌠𐌢𐌢, mirroring the way they spoke those numbers ("three from twenty", etc.); and similarly for 27, 28, 29, 37, 38, etc. However they did not write "𐌠𐌡" for 4 (or "𐌢𐌣" for 40), and wrote "𐌡𐌠𐌠", "𐌡𐌠𐌠𐌠" and "𐌡𐌠𐌠𐌠𐌠" for 7, 8, and 9, respectively.

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: "{{rn|I}}", "{{rn|X}}", and "{{rn|Ж}}". The symbols for 5 and 50 changed from {{rn|Ʌ}} and "𐌣" to {{rn|V}} and ↆ at some point. The latter had flattened to {{rn|⊥}} (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter {{rn|L}}.The symbol for 100 was written variously as {{rn|>I

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