Fox News – Breaking News Updates

latest news and breaking news today

Roman numerals

source : wikipedia.org

Roman numerals

Jump to navigation
Jump to search

For a description of numeric words in Latin, see Latin numerals.

Roman numerals on stern of the ship Cutty Sark showing draught in feet. The numbers range from 13 to 22, from bottom to top.Numeral systems
Hindu–Arabic numeral system

Western Arabic
Eastern ArabicBengali
Devanagari
Gujarati
Gurmukhi
Odia
Sinhala
Tamil
Malayalam
Telugu
Kannada
DzongkhaTibetan
Balinese
Burmese
Javanese
Khmer
Lao
Mongolian
Thai

East Asian
Chinese
Suzhou
Hokkien
Japanese
Korean
Vietnamese
TangutCounting rods

American
Cherokee
Kaktovik (Iñupiaq)

Alphabetic
Abjad
Armenian
Āryabhaṭa
Cyrillic
Geʽez
Georgian
Greek
Hebrew
Roman

Former
Aegean
Attic
Babylonian
Brahmi
Chuvash
Cistercian
Egyptian
Etruscan
Glagolitic
Kharosthi
Mayan
Muisca
Pentimal
RumiPrehistoric counting
Tally marks
Quipu

Positional systems by base
2
3
4
5
6
8
10
12
16
20
60

Non-standard positional numeral systems
Bijective numeration (1)
Signed-digit representation (Balanced ternary)
mixed (factorial)
negative
Complex-base system (2i)
Non-integer base of numeration (φ)
Asymmetric numeral systems

List of numeral systemsvte

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:[1]

Symbol

I

V

X

L

C

D

M
Value

1

5

10

50

100

500

1000

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 by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some 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:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as “one less than five” (4) and “one less than ten” (9), although there is a tradition favouring representation of “4” as “IIII” on Roman numeral clocks.[2]

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying “a thousand, and a hundred less than another thousand”, means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000. The current year is MMXXI (2021).

Description

Roman numerals are essentially a decimal or “base 10” number system, but instead of place value notation (in which place-keeping zeros enable a digit to represent different powers of ten) it uses a set of symbols with fixed values. Tally-like combinations of these fixed symbols correspond to the digits of Arabic numerals. This structure allows for significant flexibility in notation, and many variant forms are attested.

In fact, there has never been an officially binding, or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and became thoroughly chaotic in medieval times. Even the post-renaissance restoration of a largely “classical” notation has failed to produce total consistency: variant forms are even defended by some modern writers as offering improved “flexibility”.[3] On the other hand, especially where a Roman numeral is considered a legally binding expression of a number, as in U.S. Copyright law (where an “incorrect” or ambiguous numeral may invalidate a copyright claim, or affect the termination date of the copyright period)[4] it is desirable to strictly follow the usual style described below.

Standard form

The following table displays how Roman Numerals are usually written:[5]

Individual decimal places

Thousands
Hundreds
Tens
Units
1
M
C
X
I
2
MM
CC
XX
II
3
MMM
CCC
XXX
III
4

CD
XL
IV
5

D
L
V
6

DC
LX
VI
7

DCC
LXX
VII
8

DCCC
LXXX
VIII
9

CM
XC
IX

The numerals for 4 (IV) and 9 (IX) are written using “subtractive notation”,[6] where the first symbol (I) is subtracted from the larger one (V, or X), thus avoiding the clumsier (IIII, and VIIII).[a] Subtractive notation is also used for 40 (XL) and 90 (XC), as well as 400 (CD) and 900 (CM).[7] These are the only subtractive forms in standard use.

A number containing several decimal digits is built by appending the Roman numeral equivalent for each, from highest to lowest, as in the following examples:

   39 = XXX + IX = XXXIX.
  246 = CC + XL + VI = CCXLVI.
  789 = DCC + LXXX + IX = DCCLXXXIX.
2,421 = MM + CD + XX + I = MMCDXXI.

Any missing place (represented by a zero in the place-value equivalent) is omitted, as in Latin (and English) speech:

  160 = C + LX = CLX
  207 = CC + VII = CCVII
1,009 = M + IX = MIX
1,066 = M + LX + VI = MLXVI[8][9]

Roman numerals for large numbers are seen in the form of year numbers, as in these examples:

1776 = M + DCC + LXX + VI = MDCCLXXVI (the date written on the book held by the Statue of Liberty).
1918 = M + CM + X + VIII = MCMXVIII (the first year of the Spanish flu pandemic)
1954 = M + CM + L + IV = MCMLIV (as in the trailer for the movie The Last Time I Saw Paris)[4]
2014 = MM + X + IV = MMXIV (the year of the games of the XXII (22nd) Olympic Winter Games (in Sochi, Russia))

The largest number that can be represented in this notation is 3,999 (MMMCMXCIX), but since the largest Roman numeral likely to be required today is MMXXI (the current year) there is no practical need for larger Roman numerals. Prior to the introduction of Arabic numerals in the West, ancient and medieval users of the system used various means to write larger numbers; see Large numbers below.

Variant forms

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

Use of additive notation
A typical clock face with Roman numerals in Bad Salzdetfurth, Germany

While subtractive notation for 4, 40 and 400 (IV, XL and CD) has been the usual form since Roman times, additive notation (IIII, XXXX and CCCC)[10] continued to be used, including in compound numbers like XXIIII,[11]LXXIIII,[12] and CCCCLXXXX.[13] The additive forms for 9, 90, and 900 (VIIII,[10]LXXXX,[14] and DCCCC[15]) 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, IIII is systematically used instead of IV, but subtractive notation is used for other digits; so that gate 44 is labelled XLIIII.[16]

Modern clock faces that use Roman numerals still usually employ IIII for four o’clock but 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.[17][18][19] However, this is far from universal: for example, the clock on the Palace of Westminster tower, Big Ben, uses a subtractive IV for 4 o’clock.[18]

Isaac Asimov theorises that the use of IV, as the initial letters of IVPITTER (a classical Latin spelling of the name of the Roman god Jupiter), may have been felt to have been impious in this context.[20] Although this, like several other theories, seems to be pure speculation.

The year number on Admiralty Arch, London. The year 1910 is rendered as MDCCCCX, rather than the more usual MCMX

Several monumental inscriptions created in the early 20th century use variant forms for “1900” (usually written MCM). These vary from MDCCCCX for 1910 as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for 1903, on the north entrance to the Saint Louis Art Museum.[21]

Especially on tombstones and other funerary inscriptions 5 and 50 have been occasionally written IIIII and XXXXX instead of V and L, and there are instances such as IIIIII and XXXXXX rather than VI or LX.[22][23]

Irregular subtractive notation

There is a common belief that any smaller digit placed to the left of a larger digit is subtracted from the total, and that by clever choices a long Roman numeral can be “compressed”. The best known example of this is the ROMAN() function in Microsoft Excel, which can turn 499 into CDXCIX, LDVLIV, XDIX, VDIV, or ID depending on the “

Form” setting.[24] There is no indication this is anything other than an invention by the programmer, and the universal-subtraction belief may be a result of modern users trying to rationalize the syntax of Roman numerals.

Epitaph of centurion Marcus Caelius, showing “XIIX”

There is however some historic use of subtractive notation other than that described in the above “standard”: in particular IIIXX for 17,[25]IIXX for 18,[26]IIIC for 97,[27]IIC for 98,[28][29] and IC for 99.[30] A possible explanation is that the word for 18 in Latin is duodeviginti, literally “two from twenty”, 98 is duodecentum (two from hundred), and 99 is undecentum (one from hundred).[31] However, the explanation does not seem to apply to IIIXX and IIIC, since the Latin words for 17 and 97 were septendecim (seven ten) and nonaginta septem (ninety seven), respectively.

There are multiple examples of IIX being used for 8. There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than VIII. XIIX was used by officers of the XVIII Roman Legion to write their number.[32][33] The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (c. 45 BC – AD 9). On the publicly displayed official Roman calendars known as Fasti, XIIX is used for the 18 days to the next Kalends, and XXIIX for the 28 days in February. The latter can be seen on the sole extant pre-Julian calendar, the Fasti Antiates Maiores.[34]

Rare variants

While irregular subtractive and additive notation has been used at least occasionally throughout history, some Roman numerals have been observed in documents and inscriptions 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.

Padlock used on the north gate of the Irish town of Athlone. “1613” in the date is rendered XVIXIII, (literally “16, 13”) instead of MDCXIII
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 (twenty second).[35] Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of “22nd Legion” stood for 18, and “corrected” it to XVIII.[35] Excerpt from Bibliothèque nationale de France.[36] The Roman numeral for 500 is rendered as VC, instead of D
There are some examples of year numbers after 1000 written as two Roman numerals 1–99, e.g. 1613 as XVIXIII, corresponding to the common reading “sixteen thirteen” of such year numbers in English, or 1519 as XVCXIX as in French quinze-cent-dix-neuf (fifteen-hundred and nineteen), and similar readings in other languages.[37]
In some French texts from the 15th century and later one finds constructions like IIIIXXXIX for 99, reflecting the French reading of that number as quatre-vingt-dix-neuf (four-score and nineteen).[37] Similarly, in some English documents one finds, for example, 77 written as “iiixxxvii” (which could be read “three-score and seventeen”).[38]
Another medieval accounting text from 1301 renders numbers like 13,573 as “XIII. M. V. C. III. XX. XIII”, that is, “13×1000 + 5×100 + 3×20 + 13”.[39]
Other numerals that do not fit the usual patterns – such as VXL for 45, instead of the usual 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.

Zero

“Place-keeping” zeros are alien to the system of Roman numerals – however the actual number zero (what remains after 1 is subtracted from 1) was also missing from the classical Roman numeral system. The word nulla (the Latin word meaning “none”) was used to represent 0, although the earliest attested instances are medieval. For instance Dionysius Exiguus used nulla alongside Roman numerals in a manuscript from A.D.525.[40][41] About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for “nothing”) for 0, in a table of epacts, all written in Roman numerals.[42]

The use of N to indicate “none” long survived in the historic apothecaries’ system of measurement: used well into the 20th century to designate quantities in pharmaceutical prescriptions.[43]

Fractions
A triens coin (​1⁄3 or ​4⁄12 of an as). Note the four dots (····) indicating its value.
A semis coin (​1⁄2 or ​6⁄12 of an as). Note the S indicating its value.

The base “Roman fraction” is S, indicating ​1⁄2.
The use of S (as in VIIS to indicate 7​1⁄2) is attested in some ancient inscriptions[44]
and also in the now rare apothecaries’ system (usually in the form SS):[43] but while Roman numerals for whole numbers are essentially decimal S does not correspond to ​5⁄10, as one might expect, but ​6⁄12.

The Romans used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 22 × 3) makes it easier to handle the common fractions of ​1⁄3 and ​1⁄4 than does a system based on ten (10 = 2 × 5).. Notation for fractions other than ​1⁄2 is mainly found on surviving Roman coins, many of which had values that were duodecimal fractions of the unit as. Fractions less than ​1⁄2 are indicated by a dot (·) for each uncia “twelfth”, the source of the English words inch and ounce; dots are repeated for fractions up to five twelfths. Six twelfths (one half), is S for semis “half”. Uncia dots were added to S for fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine.[45] The arrangement of the dots was variable and not necessarily linear. Five dots arranged like (⁙) (as on the face of a die) are known as a quincunx, from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.

Each fraction from ​1⁄12 to ​12⁄12 had a name in Roman times; these corresponded to the names of the related coins:

Fraction

Roman numeral

Name (nominative and genitive)

Meaning
​1⁄12

·

Uncia, unciae

“Ounce”
​2⁄12 = ​1⁄6

·· or :

Sextans, sextantis

“Sixth”
​3⁄12 = ​1⁄4

··· or ∴

Quadrans, quadrantis

“Quarter”
​4⁄12 = ​1⁄3

···· or ∷

Triens, trientis

“Third”
​5⁄12

····· or ⁙

Quincunx, quincuncis

“Five-ounce” (quinque unciae → quincunx)
​6⁄12 = ​1⁄2

S

Semis, semissis

“Half”
​7⁄12

Septunx, septuncis

“Seven-ounce” (septem unciae → septunx)
​8⁄12 = ​2⁄3

S·· or S:

Bes, bessis

“Twice” (as in “twice a third”)
​9⁄12 = ​3⁄4

S··· or S∴

Dodrans, dodrantisor nonuncium, nonuncii

“Less a quarter” (de-quadrans → dodrans)or “ninth ounce” (nona uncia → nonuncium)
​10⁄12 = ​5⁄6

S···· or S∷

Dextans, dextantisor decunx, decuncis

“Less a sixth” (de-sextans → dextans)or “ten ounces” (decem unciae → decunx)
​11⁄12

S····· or S⁙

Deunx, deuncis

“Less an ounce” (de-uncia → deunx)
​12⁄12 = 1

I

As, assis

“Unit”

Other Roman fractional notations included the following:

Fraction

Roman numeral

Name (nominative and genitive)

Meaning
​1⁄1728=12−3
𐆕

Siliqua, siliquae

​1⁄288

Scripulum, scripuli

“scruple”
​1⁄144=12−2
𐆔

Dimidia sextula, dimidiae sextulae

“half a sextula”
​1⁄72

𐆓

Sextula, sextulae

“​1⁄6 of an uncia”
​1⁄48

Ɔ

Sicilicus, sicilici

​1⁄36

𐆓𐆓

Binae sextulae, binarum sextularum

“two sextulas” (duella, duellae)
​1⁄24

Σ or 𐆒 or Є

Semuncia, semunciae

“​1⁄2 uncia” (semi- + uncia)
​1⁄8

Σ· or 𐆒· or Є·

Sescuncia, sescunciae

“​1.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap} 1⁄2 uncias” (sesqui- + uncia)
Large numbers

During the centuries that Roman numerals remained the standard way of writing numbers throughout Europe, there were various extensions to the system designed to indicate larger numbers, none of which were ever standardised.

Apostrophus
“1630” on the Westerkerk in Amsterdam. “M” and “D” are given archaic “apostrophus” form.

One of these was the apostrophus,[46] in which 500 was written as IↃ, while 1,000 was written as CIↃ.[20] This is a system of encasing numbers to denote thousands (imagine the Cs and Ↄs as parentheses), which has its origins in Etruscan numeral usage. The IↃ and CIↃ used to represent 500 and 1,000 most likely preceded, and subsequently influenced, the adoption of “D” and “M” in conventional Roman numerals.

In this system, an extra Ↄ denoted 500, and multiple extra Ↄs are used to denote 5,000, 50,000, etc. For example:

Base number

 

CIↃ = 1,000

CCIↃↃ = 10,000

CCCIↃↃↃ = 100,000
1 extra Ↄ

IↃ = 500

CIↃↃ = 1,500

CCIↃↃↃ = 10,500

CCCIↃↃↃↃ = 100,500
2 extra Ↄs

IↃↃ = 5,000

 

CCIↃↃↃↃ = 15,000

CCCIↃↃↃↃↃ = 105,000
3 extra Ↄs

IↃↃↃ = 50,000

 

 

CCCIↃↃↃↃↃↃ = 150,000
Page from a 16th-century manual, showing a mixture of apostrophus and vinculum numbers (see in particular the ways of writing 10,000).

Sometimes CIↃ was reduced to ↀ for 1,000. John Wallis is often credited for introducing the symbol for infinity (modern ∞), and one conjecture is that he based it on this usage, since 1,000 was hyperbolically used to represent very large numbers. Similarly, IↃↃ for 5,000 was reduced to ↁ; CCIↃↃ for 10,000 to ↂ; IↃↃↃ for 50,000 to ↇ; and CCCIↃↃↃ for 100,000 to ↈ.
[47]

Vinculum

Another system was the vinculum, in which conventional Roman numerals were multiplied by 1,000 by adding a “bar” or “overline”.[47] It was a common alternative to the apostrophic ↀ during the Imperial era: both systems were in simultaneous use around the Roman world (M for ‘1000’ was not in use until the Medieval period).[48][49]
The use of vinculum for multiples of 1,000 can be observed, for example, on the milestones erected by Roman soldiers along the Antonine Wall in the mid-2nd century AD.[50]
There is some scope for confusion when an overline is meant to denote multiples of 1,000, and when not. The Greeks and Romans often overlined letters acting as numerals to highlight them from the general body of the text, without any numerical significance. This stylistic convention was, for example, also in use in the inscriptions of the Antonine Wall,[51] and the reader is required to decipher the intended meaning of the overline from the context. The vinculum for marking 1,000s continued in use in the Middle Ages, though it became known more commonly as titulus.[52]

Some modern sources describe Vinculum as if it were a part of the current “standard”:[53] however this is purely hypothetical – since no common modern usage requires numbers larger than the current year (MMXXI). Nonetheless, for reference: here are some examples, to give an idea of how it might be used::

IV = 4,000
IVDCXXVII = 4,627
XXV = 25,000
XXVCDLIX = 25,459

Another inconsistent medieval usage was the addition of vertical lines (or brackets) before and after the numeral to multiply it by 10 (or 100): thus M for 10,000 as an alternative form for X. In combination with the overline the bracketed forms might be used to raise the multiplier to (say) ten (or one hundred) thousand, thus:

VIII for 80,000 (or 800,000)
XX for 200,000 (or 2,000,000) Use of Roman numeral “I” (with exaggerated serifs) contrasting with the upper case letter “I”.

This use of lines is distinct from the custom, once very common, of adding both underline and overline (or very large serifs) to a Roman numeral, simply to make it clear that it is a number, e.g.
for 1967.

Origin of the system

The system is closely associated with the ancient city-state 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, all largely conjectural.

Etruscan numerals
Main article: 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.)[54]

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.[54]

Early Roman numerals

The early Roman numerals for 1, 10, and 100 were the Etruscan ones: “I”, “X”, and “Ж”. The symbols for 5 and 50 changed from Ʌ and “𐌣” to V and ↆ at some point. The latter had flattened to ⊥ (an inverted T) by the time of Augustus, and soon afterwards became identified with the graphically similar letter L.[55]

The symbol for 100 was written variously as >I< or ƆIC, was then abbreviated to Ɔ or C, with C (which matched a Latin letter) finally winning out. It may have helped that C is the initial of centum, Latin for “hundred”.

The numbers 500 and 1000 were denoted by V or X overlaid with a box or circle. Thus 500 was like a Ɔ superimposed on a Þ. It became D or Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified as the letter D; an alternative symbol for “thousand” was a CIƆ, and half of a thousand or “five hundred” is the right half of the symbol, IƆ, and this may have been converted into D.[20]

The notation for 1000 was a circled or boxed X: Ⓧ, ⊗, ⊕, and by Augustinian times was partially identified with the Greek letter Φ phi. Over time, the symbol changed to Ψ and ↀ. The latter symbol further evolved into ∞, then ⋈, and eventually changed to M under the influence of the Latin word mille “thousand”.[55]

According to Paul Kayser, the basic numerical symbols were I, X, C and Φ (or ⊕) and the intermediate ones were derived by taking half of those (half an X is V, half a C is L and half a Φ/⊕ is D).[56]

Entrance to section LII (52) of the Colosseum, with numerals still visible
Classical Roman numerals

The Colosseum was constructed in Rome in CE 72-80,[57] and while the original perimeter wall has largely disappeared, the numbered entrances from XXIII (23) to LIIII (54) survive,[58] to demonstrate that in Imperial times Roman numerals had already assumed their classical form: as largely standardised in current use. The most obvious anomaly (a common one that persisted for centuries) is the inconsistent use of subtractive notation – while XL is used for 40, IV is avoided in favour of IIII: in fact gate 44 is labelled XLIIII.

Use in the Middle Ages and Renaissance

Lower case, or minuscule, letters were developed in the Middle Ages, well after the demise of the Western Roman Empire, and since that time lower-case versions of Roman numbers have also been commonly used: i, ii, iii, iv, and so on.

13th century example of iiij.

Since the Middle Ages, a “j” has sometimes been substituted for the final “i” of a “lower-case” Roman numeral, such as “iij” for 3 or “vij” for 7. This “j” can be considered a swash variant of “i”. Into the early 20th century, the use of a final “j” was still sometimes used in medical prescriptions to prevent tampering with or misinterpretation of a number after it was written.[59]

Numerals in documents and inscriptions from the Middle Ages sometimes include additional symbols, which today are called “medieval Roman numerals”. Some simply substitute another letter for the standard one (such as “A” for “V”, or “Q” for “D”), while others serve as abbreviations for compound numerals (“O” for “XI”, or “F” for “XL”). Although they are still listed today in some dictionaries, they are long out of use.[60]

Number

Medievalabbreviation

Notes and etymology
5

A

Resembles an upside-down V. Also said to equal 500.
6

Either from a ligature of VI, or from digamma (ϛ), the Greek numeral 6 (sometimes conflated with the στ ligature).[55]7

S, Z

Presumed abbreviation of septem, Latin for 7.
9.5

Scribal abbreviation, an x with a slash through it. Likewise, IX̷ represented 8.5
11

O

Presumed abbreviation of onze, French for 11.
40

F

Presumed abbreviation of English forty.
70

S

Also could stand for 7, with the same derivation.
80

R

90

N

Presumed abbreviation of nonaginta, Latin for 90. (Ambiguous with N for “nothing” (nihil)).
150

Y

Possibly derived from the lowercase y’s shape.
151

K

Unusual, origin unknown; also said to stand for 250.[61]160

T

Possibly derived from Greek tetra, as 4 × 40 = 160.
200

H

Could also stand for 2 (see also 𐆙, the symbol for the dupondius). From a barring of two I’s.
250

E

300

B

400

P, G

500

Q

Redundant with D; abbreviates quingenti, Latin for 500. Also sometimes used for 500,000.[62]800

Ω

Borrowed from Gothic.
900

ϡ

Borrowed from Gothic.
2000

Z

Chronograms, messages with dates encoded into them, were popular during the Renaissance era. The chronogram would be a phrase containing the letters I, V, X, L, C, D, and M. By putting these letters together, the reader would obtain a number, usually indicating a particular year.

Modern use

By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient “Arabic” equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:

Spanish Real using IIII instead of IV as regnal number of Charles IV of Spain
Names of monarchs and popes, e.g. Elizabeth II of the United Kingdom, Pope Benedict XVI. These are referred to as regnal numbers and are usually read as ordinals; e.g. II is pronounced “the second”. This tradition began in Europe sporadically in the Middle Ages, gaining widespread use in England during the reign of Henry VIII. Previously, the monarch was not known by numeral but by an epithet such as Edward the Confessor. Some monarchs (e.g. Charles IV of Spain and Louis XIV of France) seem to have preferred the use of IIII instead of IV on their coinage (see illustration).
Generational suffixes, particularly in the U.S., for people sharing the same name across generations, for example William Howard Taft IV.
In the French Republican Calendar, initiated during the French Revolution, years were numbered by Roman numerals – from the year I (1792) when this calendar was introduced to the year XIV (1805) when it was abandoned.
The year of production of films, television shows and other works of art within the work itself. It has been suggested – by BBC News, perhaps facetiously – that this was originally done “in an attempt to disguise the age of films or television programmes.”[63] Outside reference to the work will use regular Arabic numerals.
Hour marks on timepieces. In this context, 4 is often written IIII.
The year of construction on building faces and cornerstones.
Page numbering of prefaces and introductions of books, and sometimes of appendices and annexes, too.
Book volume and chapter numbers, as well as the several acts within a play (e.g. Act iii, Scene 2).
Sequels to some films, video games, and other works (as in Rocky II).
Outlines that use numbers to show hierarchical relationships.
Occurrences of a recurring grand event, for instance:
The Summer and Winter Olympic Games (e.g. the XXI Olympic Winter Games; the Games of the XXX Olympiad)
The Super Bowl, the annual championship game of the National Football League (e.g. Super Bowl XLII; Super Bowl 50 was a one-time exception[64])
WrestleMania, the annual professional wrestling event for the WWE (e.g. WrestleMania XXX). This usage has also been inconsistent.Specific disciplines

In astronomy, the natural satellites or “moons” of the planets are traditionally designated by capital Roman numerals appended to the planet’s name. For example, Titan’s designation is Saturn VI.

In chemistry, Roman numerals are often used to denote the groups of the periodic table.
They are also used in the IUPAC nomenclature of inorganic chemistry, for the oxidation number of cations which can take on several different positive charges. They are also used for naming phases of polymorphic crystals, such as ice.

In education, school grades (in the sense of year-groups rather than test scores) are sometimes referred to by a Roman numeral; for example, “grade IX” is sometimes seen for “grade 9”.

In entomology, the broods of the thirteen and seventeen year periodical cicadas are identified by Roman numerals.

Stylised “IX” represents “9” in unit emblem of 9th Aero Squadron AEF, 1918

In graphic design stylised Roman numerals may represent numeric values.

In law, Roman numerals are commonly used to help organize legal codes as part of an alphanumeric outline.

In advanced mathematics (including trigonometry, statistics, and calculus), when a graph includes negative numbers, its quadrants are named using I, II, III, and IV. These quadrant names signify positive numbers on both axes, negative numbers on the X axis, negative numbers on both axes, and negative numbers on the Y axis, respectively. The use of Roman numerals to designate quadrants avoids confusion, since Arabic numerals are used for the actual data represented in the graph.

In military unit designation, Roman numerals are often used to distinguish between units at different levels. This reduces possible confusion, especially when viewing operational or strategic level maps. In particular, army corps are often numbered using Roman numerals (for example the American XVIII Airborne Corps or the WW2-era German III Panzerkorps) with Arabic numerals being used for divisions and armies.

In music, Roman numerals are used in several contexts:

Movements are often numbered using Roman numerals.
In Roman Numeral Analysis, harmonic function is identified using Roman Numerals.
Individual strings of stringed instruments, such as the violin, are often denoted by Roman numerals, with higher numbers denoting lower strings.

In pharmacy, Roman numerals were used with the now largely obsolete apothecaries’ system of measurement: including SS to denote “one half” and N to denote “zero”.[43][65]

In photography, Roman numerals (with zero) are used to denote varying levels of brightness when using the Zone System.

In seismology, Roman numerals are used to designate degrees of the Mercalli intensity scale of earthquakes.

In sport the team containing the “top” players and representing a nation or province, a club or a school at the highest level in (say) rugby union is often called the “1st XV”, while a lower-ranking cricket or American football team might be the “3rd XI”.

In tarot, Roman numerals (with zero) are used to denote the cards of the Major Arcana.

In theology and biblical scholarship, the Septuagint is often referred to as LXX, as this translation of the Old Testament into Greek is named for the legendary number of its translators (septuaginta being Latin for “seventy”).

Modern use in European languages other than English

Some uses that are rare or never seen in English speaking countries may be relatively common in parts of continental Europe and in other regions (e.g. Latin America) that use a European language other than English. For instance:

Capital or small capital Roman numerals are widely used in Romance languages to denote centuries, e.g. the French .mw-parser-output span.smallcaps{font-variant:small-caps}.mw-parser-output span.smallcaps-smaller{font-size:85%}xviiie siècle[66] and the Spanish siglo XVIII mean “18th century”. Slavic languages in and adjacent to Russia similarly favor Roman numerals (xviii век). On the other hand, in Slavic languages in Central Europe, like most Germanic languages, one writes “18.” (with a period) before the local word for “century”.

Boris Yeltsin’s signature, dated 10 November 1988, rendered as 10.XI.1988.

Mixed Roman and Arabic numerals are sometimes used in numeric representations of dates (especially in formal letters and official documents, but also on tombstones). The month is written in Roman numerals, while the day is in Arabic numerals: “4.VI.1789” and “VI.4.1789” both refer unambiguously to 4 June 1789.

Business hours table on a shop window in Vilnius, Lithuania

Roman numerals are sometimes used to represent the days of the week in hours-of-operation signs displayed in windows or on doors of businesses,[67] and also sometimes in railway and bus timetables. Monday, taken as the first day of the week, is represented by I. Sunday is represented by VII. The hours of operation signs are tables composed of two columns where the left column is the day of the week in Roman numerals and the right column is a range of hours of operation from starting time to closing time. In the example case (left), the business opens from 10 AM to 7 PM on weekdays, 10 AM to 5 PM on Saturdays and is closed on Sundays. Note that the listing uses 24-hour time.

Sign at 17.9 km on route SS4 Salaria, north of Rome, Italy

Roman numerals may also be used for floor numbering.[68][69] For instance, apartments in central Amsterdam are indicated as 138-III, with both an Arabic numeral (number of the block or house) and a Roman numeral (floor number). The apartment on the ground floor is indicated as 138-huis.

In Italy, where roads outside built-up areas have kilometre signs, major roads and motorways also mark 100-metre subdivisionals, using Roman numerals from I to IX for the smaller intervals. The sign IX/17 thus marks 17.9 km.

Certain Spanish-speaking Latin American countries use Roman numerals to designate assemblies of their national legislatures. For instance, the composition of the Mexican Congress of the Union from 2018-2021 (elected in the 2018 Mexican general election) is called the LXIV Legislature of the Mexican Congress (or more commonly the “LXIV Legislature”).

A notable exception to the use of Roman numerals in Europe is in Greece, where Greek numerals (based on the Greek alphabet) are generally used in contexts where Roman numerals would be used elsewhere.

Unicode

The “Number Forms” block of the Unicode computer character set standard has a number of Roman numeral symbols in the range of code points from U+2160 to U+2188.[70] This range includes both upper- and lowercase numerals, as well as pre-combined characters for numbers up to 12 (Ⅻ or XII). One justification for the existence of pre-combined numbers is to facilitate the setting of multiple-letter numbers (such as VIII) on a single horizontal line in Asian vertical text. The Unicode standard, however, includes special Roman numeral code points for compatibility only, stating that “[f]or most purposes, it is preferable to compose the Roman numerals from sequences of the appropriate Latin letters”.[71]
The block also includes some apostrophus symbols for large numbers, an old variant of “L” (50) similar to the Etruscan character, the Claudian letter “reversed C”, etc.

Symbol


Value

1,000

5,000

10,000

6

50

50,000

100,000

See also

Egyptian numerals
Etruscan numerals
Greek numerals
Hebrew numerals
Kharosthi numerals
Maya numerals
Roman abacus
Proto-writing
Roman numerals in Unicode
Pentimal system

References

Notes

^ Without theorising about causation, it may be noted that IV and IX not only have fewer characters than IIII and VIIII, but are less likely to be confused (especially at a quick glance) with III and VIII.

Citations

^ .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:”\”””\”””‘””‘”}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg”)right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. ISBN 0-520-05079-7. Alphabetic symbols for larger numbers, such as Q for 500,000, have also been used to various degrees of standardization.

^ Judkins, Maura (4 November 2011). “Public clocks do a number on Roman numerals”. The Washington Post. Retrieved 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.

^ Adams, Cecil (23 February 1990). “What is the proper way to style Roman numerals for the 1990s?”. The Straight Dope.

^ a b Hayes, David P. “Guide to Roman Numerals”. Copyright Registration and Renewal Information Chart and Web Site.

^ Reddy, Indra K.; Khan, Mansoor A. (2003). “1 (Working with Arabic and Roman numerals)”. Essential Math and Calculations for Pharmacy Technicians. CRC Press. p. 3. ISBN 978-0-203-49534-6. Table 1-1 Roman and Arabic numerals (table very similar to the table here, apart from inclusion of Vinculum notation.

^ Stanislas Dehaene (1997): The Number Sense : How the Mind Creates Mathematics. Oxford University Press; 288 pages. ISBN 9780199723096

^ Ûrij Vasilʹevič Prokhorov and Michiel Hazewinkel, editors (1990): Encyclopaedia of Mathematics, Volume 10, page 502. Springer; 546 pages. ISBN 9781556080050

^ Dela Cruz, M. L. P.; Torres, H. D. (2009). Number Smart Quest for Mastery: Teacher’s Edition. Rex Bookstore, Inc. ISBN 9789712352164.

^ Martelli, Alex; Ascher, David (2002). Python Cookbook. O’Reilly Media Inc. ISBN 978-0-596-00167-4.

^ a b 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: “…in hiberna remissis ipse se recipit die XXXX Bibracte.”

^ Angelo Rocca (1612) De campanis commentarius. Published by Guillelmo Faciotti, Rome. Title of a Plate: “Campana a XXIIII hominibus pulsata” (“Bell to be sounded by 24 men”)

^ Gerard Ter Borch (1673): Portrait of Cornelis de Graef. Date on painting: “Out. XXIIII Jaer. // M. DC. LXXIIII”.

^ 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.”

^ 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…”

^ Pico Della Mirandola (1486) Conclusiones sive Theses DCCCC (“Conclusions, or 900 Theses”).

^ “360:12 tables, 24 chairs, and plenty of chalk”. Roman Numerals…not quite so simple. 2 January 2011.

^ Milham, W.I. (1947). Time & Timekeepers. New York: Macmillan. p. 196.

^ a b Pickover, Clifford A. (2003), Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford University Press, p. 282, ISBN 978-0-19-534800-2.

^ Adams, Cecil; Zotti, Ed (1988). More of the straight dope. Ballantine Books. p. 154. ISBN 978-0-345-35145-6..

^ a b c Asimov, Isaac (1966). Asimov on Numbers (PDF). Pocket Books, a division of Simon & Schuster, Inc. p. 12.

^ “Gallery: Museum’s North Entrance (1910)”. Saint Louis Art Museum. Archived from the original on 4 December 2010. Retrieved 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.

^ Reynolds, Joyce Maire; Spawforth, Anthony J. S. (1996). “numbers, Roman”. In Hornblower, Simon; Spawforth, Anthony (eds.). Oxford Classical Dictionary (3rd ed.). Oxford University Press. ISBN 0-19-866172-X.

^ Kennedy, Benjamin Hall (1923). The Revised Latin Primer. London: Longmans, Green & Co.

^ “ROMAN function”. support.microsoft.com.

^ 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”

^ 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”.

^ Wilhelm Ernst Tentzel (1699): Als Ihre Königl. Majestät in Pohlen und …. Page 39: “… und der Umschrifft: LITHUANIA ASSERTA M. DC. IIIC [1699].”

^ 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].”

^ Enea Silvio Piccolomini (1698): Opera Geographica et Historica. Helmstadt, J. M. Sustermann. Title page of first edition: “Bibliopolæ ibid. M DC IC”

^ Kennedy, Benjamin H. (1879). Latin grammar. London: Longmans, Green, and Co. p. 150. ISBN 9781177808293.

^ Adkins, Lesley; Adkins, Roy A (2004). Handbook to life in ancient Rome (2 ed.). p. 270. ISBN 0-8160-5026-0.

^ Boyne, William (1968). A manual of Roman coins. p. 13.

^ Degrassi, Atilius, ed. (1963), Inscriptiones Italiae, 13: Fasti et Elogia, Rome: Istituto Poligrafico dello Stato, Fasciculus 2: Fasti anni Numani et Iuliani

^ a b 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.

^ L’ Atre périlleux et Yvain, le chevalier au lion . 1301–1350.

^ a b 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

^ 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.

^ 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].

^ Faith Wallis, trans. Bede: The Reckoning of Time (725), Liverpool, Liverpool Univ. Pr., 2004. ISBN 0-85323-693-3.

^ Byrhtferth’s Enchiridion (1016). Edited by Peter S. Baker and Michael Lapidge. Early English Text Society 1995. ISBN 978-0-19-722416-8.

^ C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina.

^ a b c Bachenheimer, Bonnie S. (2010). Manual for Pharmacy Technicians. ISBN 978-1-58528-307-1.

^ “RIB 2208. Distance Slab of the Sixth Legion”. Roman Inscriptions in Britain. Retrieved 11 November 2020.

^ Maher, David W.; Makowski, John F., “Literary Evidence for Roman Arithmetic with Fractions Archived 27 August 2013 at the Wayback Machine”, Classical Philology 96 (2011): 376–399.

^ “Merriam-Webster Unabridged Dictionary”.

^ a b Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley & Sons.

^ Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. pp. 102–109. ISBN 978-0-521-87818-0.

^ Gordon, Arthur E. (1982). Illustrated Introduction to Latin Epigraphy. Berkeley: University of California Press. pp. 122–123. ISBN 0-520-05079-7.

^ “RIB 2208. Distance Slab of the Twentieth Legion”. Roman Inscriptions in Britain. Retrieved 9 November 2020.

^ “RIB 2171. Building Inscription of the Second and Twentieth Legions”. Roman Inscriptions in Britain. Retrieved 9 November 2020.

^ Chrisomalis, Stephen (2010). Numerical Notation: A Comparative History. Cambridge University Press. p. 119. ISBN 978-0-521-87818-0.

^ “What is Vinculum Notation?”. Numerals Converter. Retrieved 9 November 2020.

^ a b 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 LXXXIII (83), issue 1, pages 103–130. ISSN 0035-1652

^ a b c Perry, David J. Proposal to Add Additional Ancient Roman Characters to UCS Archived 22 June 2011 at the Wayback Machine.

^ Keyser, Paul (1988). “The Origin of the Latin Numerals 1 to 1000”. American Journal of Archaeology. 92 (4): 529–546. doi:10.2307/505248. JSTOR 505248.

^ Hopkins, Keith (2005). The Colosseum. Cambridge, MA: Harvard University Press. ISBN 978-0-674-01895-2.

^ Claridge, Amanda (1998). Rome: An Oxford Archaeological Guide (First ed.). Oxford: Oxford University Press. ISBN 978-0-19-288003-1.

^ Bastedo, Walter A. Materia Medica: Pharmacology, Therapeutics and Prescription Writing for Students and Practitioners, 2nd ed. (Philadelphia, PA: W.B. Saunders, 1919) p582. Retrieved 15 March 2010.

^ Capelli, A. Dictionary of Latin Abbreviations. 1912.

^ Bang, Jørgen. Fremmedordbog, Berlingske Ordbøger, 1962 (Danish)

^ Gordon, Arthur E. (1983). Illustrated Introduction to Latin Epigraphy. University of California Press. pp. 44. ISBN 9780520038981. Retrieved 3 October 2015. roman numerals.

^ Owen, Rob (13 January 2012). “TV Q&A: ABC News, ‘Storage Wars’ and ‘The Big Bang Theory'”. Pittsburgh Post-Gazette. Retrieved 13 January 2012.

^ NFL won’t use Roman numerals for Super Bowl 50 Archived 1 December 2015 at the Wayback Machine, National Football League. Retrieved 5 November 2014

^ Reddy, Indra K.; Khan, Mansoor A. (2003). Essential Math and Calculations for Pharmacy Technicians. CRC Press. ISBN 978-0-203-49534-6.

^ Lexique des règles typographiques en usage à l’imprimerie nationale (in French) (6th ed.). Paris: Imprimerie nationale. March 2011. p. 126. ISBN 978-2-7433-0482-9. On composera en chiffres romains petites capitales les nombres concernant : ↲ 1. Les siècles.

^ Beginners latin Archived 3 December 2013 at the Wayback Machine, Government of the United Kingdom. Retrieved 1 December 2013

^ Roman Arithmetic Archived 22 November 2013 at the Wayback Machine, Southwestern Adventist University. Retrieved 1 December 2013

^ Roman Numerals History Archived 3 December 2013 at the Wayback Machine. Retrieved 1 December 2013

^ “Unicode Number Forms” (PDF).

^ The Unicode Standard, Version 6.0 – Electronic edition (PDF), Unicode, Inc., 2011, p. 486

Sources

Menninger, Karl (1992). Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications. ISBN 978-0-486-27096-8.

Further reading

Aczel, Amir D. 2015. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. 1st edition. New York: Palgrave Macmillan.
Goines, David Lance. A Constructed Roman Alphabet: A Geometric Analysis of the Greek and Roman Capitals and of the Arabic Numerals. Boston: D.R. Godine, 1982.
Houston, Stephen D. 2012. The Shape of Script: How and Why Writing Systems Change. Santa Fe, NM: School for Advanced Research Press.
Taisbak, Christian M. 1965. “Roman numerals and the abacus.” Classica et medievalia 26: 147–60.

External links

Look up Appendix:Roman numerals in Wiktionary, the free dictionary.
Wikimedia Commons has media related to Roman numerals.Library resources about Roman numerals
Online books
Resources in your library
Resources in other libraries
“Roman Numerals (Totally Epic Guide)”. Know The Romans.vteLatin script
History
Spread
Romanization
Roman numeralsAlphabets (list)
Classical Latin alphabet
ISO basic Latin alphabet
Phonetic alphabets
International Phonetic Alphabet
X-SAMPA
Spelling alphabetLetters (list)
Letters of the ISO basic Latin alphabet
Aa

Bb

Cc

Dd

Ee

Ff

Gg

Hh

Ii

Jj

Kk

Ll

Mm

Nn

Oo

Pp

Qq

Rr

Ss

Tt

Uu

Vv

Ww

Xx

Yy

Zz

MultigraphsDigraphs
ch

dz
gh
ij
ll
ly
nh
ny
sh
sz
thTrigraphs
dzs
eauTetragraphs
ough
tschPentagraphstzschKeyboard layouts (list)
QWERTY
QWERTZ
AZERTY
Dvorak
Colemak
BÉPO
NeoStandards
ISO/IEC 646
Unicode
Western Latin character setsLists
Precomposed Latin characters in Unicode
Letters used in mathematics
List of typographical symbols and punctuation marks
Diacritics
Palaeography
vteAncient Rome topics
Outline
TimelineHistory
Foundation
Kingdom
overthrow
RepublicEmpire
History
Pax Romana
Principate
Dominate
Western Empire
fall
historiography of the fall
Byzantine Empire
decline
fallConstitution
History
Kingdom
Republic
Empire
Late Empire
Senate
Legislative assemblies
Curiate
Centuriate
Tribal
Plebeian
Executive magistrates
SPQRLaw
Twelve Tables
Mos maiorum
Citizenship
Auctoritas
Imperium
Status
LitigationGovernment
Curia
Forum
Cursus honorum
Collegiality
Emperor
Legatus
Dux
Officium
Prefect
Vicarius
Vigintisexviri
Lictor
Magister militum
Imperator
Princeps senatus
Pontifex Maximus
Augustus
Caesar
Tetrarch
Optimates
Populares
ProvinceMagistratesOrdinary
Consul
Censor
Praetor
Tribune
Tribune of the plebs
Military tribune
Quaestor
Aedile
Promagistrate
GovernorExtraordinary
Rex
Interrex
Dictator
Magister equitum
Decemviri
Consular tribune
TriumvirMilitary
History
Borders
Establishment
Structure
Campaigns
Political control
Strategy
Engineering
Frontiers and fortifications
castra
Technology
Army
Legion
Infantry tactics
Personal equipment
Siege engines
Navy
Auxiliaries
Decorations and punishments
Hippika gymnasiaEconomy
Agriculture
Deforestation
Commerce
Finance
Currency
Republican currency
Imperial currencyCulture
Architecture
Art
Bathing
Calendar
Clothing
Cosmetics
Cuisine
Hairstyles
Education
Literature
Music
Mythology
Religion
Deities
Romanization
Romans
Sexuality
Theatre
WineSociety
Patricians
Plebs
Conflict of the Orders
Secessio plebis
Equites
Gens
Tribes
Assembly
Naming conventions
Demography
Women
Marriage
Adoption
Slavery
BagaudaeTechnology
Amphitheatres
Aqueducts
Bridges
Circuses
Civil engineering
Concrete
Domes
Metallurgy
Numerals
Roads
Temples
Theatres
Sanitation
ThermaeLatin
History
Alphabet
Versions
Old
Classical
Vulgar
Late
Medieval
Renaissance
New
Contemporary
Ecclesiastical
Romance languagesWritersLatin
Aelius Donatus
Ammianus Marcellinus
Appuleius
Asconius Pedianus
Augustine
Aurelius Victor
Ausonius
Boëthius
Caesar
Catullus
Cassiodorus
Censorinus
Cicero
Claudian
Columella
Cornelius Nepos
Ennius
Eutropius
Fabius Pictor
Sextus Pompeius Festus
Rufus Festus
Florus
Frontinus
Fronto
Fulgentius
Gellius
Horace
Hydatius
Hyginus
Jerome
Jordanes
Julius Paulus
Justin
Juvenal
Lactantius
Livy
Lucan
Lucretius
Macrobius
Marcellus Empiricus
Marcus Aurelius
Manilius
Martial
Nicolaus Damascenus
Nonius Marcellus
Obsequens
Orosius
Ovid
Petronius
Phaedrus
Plautus
Pliny the Elder
Pliny the Younger
Pomponius Mela
Priscian
Propertius
Quadrigarius
Quintilian
Quintus Curtius Rufus
Sallust
Seneca the Elder
Seneca the Younger
Servius
Sidonius Apollinaris
Silius Italicus
Statius
Suetonius
Symmachus
Tacitus
Terence
Tertullian
Tibullus
Valerius Antias
Valerius Maximus
Varro
Velleius Paterculus
Verrius Flaccus
Vergil
VitruviusGreek
Aelian
Aëtius of Amida
Appian
Arrian
Cassius Dio
Diodorus Siculus
Diogenes Laërtius
Dionysius of Halicarnassus
Dioscorides
Eusebius of Caesaria
Galen
Herodian
Josephus
Julian
Libanius
Lucian
Pausanias
Philostratus
Phlegon of Tralles
Photius
Plutarch
Polyaenus
Polybius
Porphyrius
Priscus
Procopius
Simplicius of Cilicia
Sozomen
Stephanus Byzantinus
Strabo
Themistius
Theodoret
Zonaras
ZosimusMajor cities
Alexandria
Antioch
Aquileia
Berytus
Bononia
Carthage
Constantinopolis
Eboracum
Leptis Magna
Londinium
Lugdunum
Lutetia
Mediolanum
Pompeii
Ravenna
Roma
Smyrna
Vindobona
VolubilisLists and othertopics
Cities and towns
Climate
Consuls
Dictators
Distinguished women
Dynasties
Emperors
Generals
Gentes
Geographers
Institutions
Laws
Legacy
Legions
Magistri equitum
Nomina
Pontifices Maximi
Praetors
Quaestors
Tribunes
Roman–Iranian relations
Wars and battles
Civil wars and revoltsFiction
Films
vteTypes of writing systemsOverview
History of writing
GraphemeLists
Writing systems
undeciphered
inventors
constructed
Languages by writing system / by first written accountsTypesAbjads
NumeralsAramaic
Hatran
Arabic
Egyptian hieroglyphs
Hebrew
Ashuri
Cursive
Rashi
Solitreo
Tifinagh
Manichaean
Nabataean
Old North Arabian
Pahlavi
Pegon
Phoenician
Paleo-Hebrew
Pitman shorthand
Proto-Sinaitic
Psalter Pahlavi
Punic
Samaritan
South Arabian
Zabur
Musnad
Sogdian
Syriac
ʾEsṭrangēlā
Serṭā
Maḏnḥāyā
Teeline Shorthand
UgariticAbugidasBrahmicNorthern
Assamese
Bengali
Bhaiksuki
Bhujimol
Brāhmī
Devanāgarī
Dogri
Gujarati
Gupta
Gurmukhī
Kaithi
Kalinga
Khojki
Khudabadi
Laṇḍā
Lepcha
Limbu
Mahajani
Meitei
Modi
Multani
Nagari
Nandinagari
Odia
Karani
ʼPhags-pa
Pracalit (Newar)
Ranjana
Sharada
Siddhaṃ
Soyombo
Sylheti Nagari
Takri
Tibetan
Uchen
Umê
Tirhuta
Tocharian
Zanabazar Square
Marchen
Marchung
Pungs-chen
Pungs-chung
DrushaSouthern
Ahom
Balinese
Batak
Baybayin
Bhattiprolu
Buda
Buhid
Burmese
Chakma
Cham
Fakkham
Grantha
Goykanadi
Hanunuo (Hanunó’o)
Javanese
Kadamba
Kannada
Karen
Kawi
Khmer
Kulitan
Lanna
Lao
Leke
Lontara (Bilang-bilang)
Makasar
Malayalam
Old Maldivian
Dhives Akuru
Eveyla Akuru
Mon (Old Mon)
New Tai Lue
Pallava
Pyu
Rejang
Rencong
Saurashtra
Shan
Sinhala
Sundanese (Old Sundanese)
Tagbanwa
Tai Le
Tai Noi
Tai Tham
Tai Viet
Tamil
Tamil-Brahmi
Telugu
Thai
Tigalari
Vatteluttu
Kolezhuthu
MalayanmaOthers
Boyd’s syllabic shorthand
Canadian syllabics
Blackfoot
Déné syllabics
Fox I
Geʽez
Gunjala Gondi
Japanese Braille
Jenticha
Kharosthi
Mandombe
Masaram Gondi
Meroitic
Miao
Mwangwego
Pahawh Hmong
Sorang Sompeng
Thaana
Thomas Natural Shorthand
Warang CitiAlphabetsLinear
A-Chik Tok’birim
Abkhaz
Adlam
Armenian
Avestan
Avoiuli
Bassa Vah
Borama
Carian
Caucasian Albanian
Coelbren
Coorgi–Cox alphabet
Coptic
Cyrillic
Deseret
Duployan shorthand
Chinook writing
Early Cyrillic
Eclectic shorthand
Elbasan
Etruscan
Evenki
Fox II
Fraser
Gabelsberger shorthand
Garay
Georgian
Asomtavruli
Nuskhuri
Mkhedruli
Glagolitic
Gothic
Gregg shorthand
Greek
Greco-Iberian alphabet
Hangul
Hanifi
IPA
Jenticha
Kaddare
Kayah Li
Klingon
Latin
Beneventan
Blackletter
Carolingian minuscule
Fraktur
Gaelic
Insular
Kurrent
Merovingian
Sigla
Sütterlin
Tironian notes
Visigothic
Luo
Lycian
Lydian
Manchu
Mandaic
Medefaidrin
Molodtsov
Mongolian
Mru
Neo-Tifinagh
N’Ko
Ogham
Oirat
Ol Chiki
Old Hungarian
Old Italic
Old Permic
Orkhon
Old Uyghur
Osage
Osmanya
Pau Cin Hau
Runic
Anglo-Saxon
Cipher
Dalecarlian
Elder Futhark
Younger Futhark
Gothic
Marcomannic
Medieval
Staveless
Sidetic
Shavian
Somali
Sorang Sompeng
Tifinagh
Tolong Siki
Vagindra
Vietnamese
Visible Speech
Vithkuqi
Wancho
Warang Citi
ZaghawaNon-linear
Braille
Maritime flags
Telegraph code
New York Point
Flag semaphore
Moon typeIdeograms and pictograms
Adinkra
Aztec
Blissymbol
Dongba
Ersu Shaba
Emoji
IConji
Isotype
Kaidā
Míkmaq
Mixtec
New Epoch Notation Painting
Nsibidi
Ojibwe Hieroglyphs
Siglas poveiras
Testerian
Yerkish
ZapotecLogogramsChinese family of scriptsChinese Characters
Simplified
Traditional
Oracle bone script
Bronze Script
Seal Script
large
small
bird-worm
Hanja
Idu
Kanji
Chữ Nôm
ZhuangChinese-influenced
Jurchen
Khitan large script
Sui
TangutCuneiform
Akkadian
Assyrian
Elamite
Hittite
Luwian
SumerianOther logo-syllabic
Anatolian
Bagam
Cretan
Isthmian
Maya
Proto-Elamite
Yi (Classical)Logo-consonantal
Demotic
Hieratic
HieroglyphsNumerals
Hindu-Arabic
Abjad
Attic (Greek)
Muisca
RomanSemi-syllabariesFull
Celtiberian
Northeastern Iberian
Southeastern Iberian
KhomRedundant
Espanca
Pahawh Hmong
Khitan small script
Southwest Paleohispanic
Zhuyin fuhaoSomacheirograms
ASLwrite
SignWriting
si5s
Stokoe NotationSyllabaries
Afaka
Bamum
Bété
Byblos
Canadian Aboriginal
Cherokee
Cypriot
Cypro-Minoan
Ditema tsa Dinoko
Eskayan
Geba
Great Lakes Algonquian
Iban
Idu
Japanese
Hiragana
Katakana
Man’yōgana
Hentaigana
Sogana
Jindai moji
Kikakui
Kpelle
Linear B
Linear Elamite
Lisu
Loma
Nüshu
Nwagu Aneke script
Old Persian Cuneiform
Sumerian
Vai
Woleai
Yi (Modern)
YugtunvteBraille ⠃⠗⠁⠊⠇⠇⠑Braille cell
1829 braille
International uniformity
ASCII braille
Unicode braille patternsBraille scriptsFrench-ordered
Albanian
Azerbaijani
Cantonese
Catalan
Chinese (mainland Mandarin) (largely reassigned)
Czech
Dutch
English (Unified English)
Esperanto
French
German
Ghanaian
Guarani
Hawaiian
Hungarian
Iñupiaq
IPA
Irish
Italian
Latvian
Lithuanian
Luxembourgish (extended to 8-dots)
Maltese
Māori
Navajo
Nigerian
Philippine
Polish
Portuguese
Romanian
Samoan
Slovak
South African
Spanish
Taiwanese Mandarin (largely reassigned)
Turkish
Vietnamese
Welsh
Yugoslav
ZambianNordic family
Estonian
Faroese
Icelandic
Northern Sami
Scandinavian
Danish
Finnish
Greenlandic
Norwegian
SwedishRussian lineage familyi.e. Cyrillic-mediated scripts
Belarusian
Bulgarian
Kazakh
Kyrgyz
Mongolian
Russian
Tatar
UkrainianEgyptian lineage familyi.e. Arabic-mediated scripts
Arabic
Persian
Urdu (Pakistan)Indian lineage familyi.e. Bharati Braille
Devanagari (Hindi / Marathi / Nepali)
Bengali (Bangla / Assamese)
Gujarati
Kannada
Malayalam
Odia
Punjabi
Sinhala
Tamil
Telugu
Urdu (India)Other scripts
Amharic
Armenian
Burmese
Cambodian
Dzongkha (Bhutanese)
Georgian
Greek
Hebrew
Inuktitut (reassigned vowels)
Thai and Lao (Japanese vowels)
Tibetan
Reordered
Algerian Braille (obsolete)Frequency-based
American Braille (obsolete)Independent
Chinese semi-syllabaries
Cantonese
Mainland Chinese Mandarin
Taiwanese Mandarin
Two-Cell Chinese (Shuangpin)
Japanese
KoreanEight-dot
Luxembourgish
Kanji
Gardner–Salinas braille codes (GS8)Symbols in braille
Braille music
Canadian currency marks
Computer Braille Code
Gardner–Salinas braille codes (science; GS8/GS6)
International Phonetic Alphabet (IPA)
Nemeth braille codeBraille technology
Braille e-book
Braille embosser
Braille translator
Braille watch
Mountbatten Brailler
Optical braille recognition
Perforation
Perkins Brailler
Refreshable braille display
Slate and stylus
BraigoPersons
Louis Braille
Charles Barbier
Valentin Haüy
Thakur Vishva Narain Singh
Sabriye Tenberken
William Bell WaitOrganisations
Braille Institute of America
Braille Without Borders
Japan Braille Library
National Braille Association
Blindness organizations
Schools for the blind
American Printing House for the BlindOther tactile alphabets
Decapoint
Moon type
New York Point
Night writing
VibrateseRelated topics
Accessible publishing
Braille literacy
RoboBraillevteElectronic writing systems
Emoticons
Emoji
Kaomoji
iConji
Leet
UnicodevteInternet slang variants
3arabizi
Alay (Indonesia)
Denglisch
Doge
DoggoLingo
Fingilish (Persian)
Greeklish
Gyaru-moji (Japan)
Jejemon (Philippines)
Leet (“1337”)
Lolspeak / LOLspeak / Kitteh
Martian language (Chinese)
Miguxês (Portuguese)
O RLY?
Padonkaffsky jargon (Russian)
Pseudo-Chinese
Translit
Volapuk
See also English internet slang (at Wiktionary)
SMS language

Retrieved from “https://en.wikipedia.org/w/index.php?title=Roman_numerals&oldid=1016620696”

enumerate - How to list items like this: (i), (ii), (iii

enumerate – How to list items like this: (i), (ii), (iii – (ii) Second conclusion here (iii) Third conclusion here. effectively? I do it manually but it doesn't look good. Enumerate doesn't work either. lists enumerate. Share. Improve this question. Follow edited Jan 9 '15 at 17:09. lockstep. 227k 62 62 gold badges 664 664 silver badges 761 761 bronze badges.TYPE IV – These buildings have masonry walls like type III buildings but the interior wood consists of heavy timber. In a heavy-timber building, a wood column cannot be less than 8″ thick in any dimension and a wood girder cannot be less than 6″ thick. The floor and roof are plank board.D = ii E = iii F = IV G = V A = vi Roman numeral I refers to the chord built on the first note of the C major scale. Roman numeral II refers to the chord built on the second note of the C major scale, and so on. If you notice, some of the Roman numerals are capitalized while others are not. Uppercase Roman numerals pertain to a major chord

PDF Types of Construction Type I Type Ii Type Iv Type V – i, ii, iii, iv, v, vi, vii, viii, ix, x, xi, xii The notations IV and IX can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as " IIII " on Roman numeral clocks.III/IV is the 12th studio album by alt-country singer-songwriter Ryan Adams, released on December 14, 2010 through PAX AM.The album is his fifth with backing band The Cardinals, and was recorded in 2006 during the same sessions that yielded Easy Tiger.A double album, III/IV was recorded prior to bassist Catherine Popper's departure, and also marks guitarist and backing vocalist Neal Casal'sDrug Schedule IV Controlled Substances. The medicines in drug classification Schedule IV /Schedule 4 can and are abused and can be addictive or create a dependency, but less than those of Schedules 1, 2 and 3. Examples of Schedule IV substances include: Tramadol, Xanax (alprazolam), carisoprodol (Soma), Klonopin (clonazepam), Valium (diazepam

PDF  Types of Construction Type I Type Ii Type Iv Type V

How to Decipher the I – IV – V Chord Pattern – MONTHLY REPORT• March 2021 • Volume IV • Chapter III Great Awakening Team March 4, 2021 MONTHLY REPORT • February 2021 • Volume IV • Chapter IIName the Operators Listed Below Are (I) < (Ii) + + (Iii) andand (Iv) ? : CISCE ICSE Class 10. Question Papers 301. Textbook Solutions 25526. Important Solutions 2865. Question Bank Solutions 25576. Concept Notes & Videos 237. Time Tables 15. Syllabus. Advertisement Remove all ads.(ii) by substitution at the 3-position with an acyclic alkyl substituent; (iii) by substitution at the 2-amino nitrogen atom with alkyl, dialkyl, benzyl, or methoxybenzyl groups; or (iv) by inclusion of the 2-amino nitrogen atom in a cyclic structure. (h) Marijuana, tetrahydrocannabinols, and synthetic cannabinoids.

Apartamentos Topacio Unitursa (I, II, III, IV), Calpe ...
Characteristics of study populations. I II III IV V ...
Borrowed Chords - How To Spot & Play Over Them
1 Jauge niveau huile moteur 701457 pour renault clio 1 2 3 ...
Überschrift 1: Nummerierung I, II, III, 1, 2, 3, 4, IV V ...
1: Mecanismos de la reacciones de hipersensibilidad I, II ...
Hypersensitivity : Introduction and Classification (Types ...
Star Wars: Episode I, II, III, IV, V, VI, VII, VIII ...
Graph Quadrants. I, II, III, IV Quadrants (graphquadrants ...
Leather Holster Ruger MK Mark I II III IV with 5 1/2 inch ...
Buy Collagen Peptides Powder Type I, II, III, IV, V, X 1 ...

Rocky I II III IV V – .

Roman Numerals – 1 through 100 – Roman numerals numbers 1 through 100.
1 2
3 4 5 6 7 8 h 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
97 98 99 100 .

Anglian Dances – I, II, III, IV – .