Roman Numerals

Roman numerals are a numeral system used by the ancient Romans for, after only seven letters, write whole numbers (but not zero , they were not aware, or more precisely, they considered not as a number).

The numbering has been standardized in current use and is based on four principles:

• Any letter placed on the right of another set a value greater than or equal to his own addition to it.
• Any drive letter placed immediately to the left of a letter higher than it shows that the number that corresponds to it must be subtracted the number that follows.
• The values are grouped in descending order, except for values to be dropped by the previous rule.
• The same letter can not be used four times consecutively except Mr.

Drive Letter: I is a unit for V and X, X is a unit for L and C, C is a unit for D and M.

Origin

Contrary to popular belief, the Roman numerals are not acronymic : for example, C is not initially stands for centum (written CENTVM). The figures, attested in other languages and scripts of Italy , were originally separate symbols, then combined with the letters. Thus, in Etruscan count (which the alphabet was also borrowed and adapted by the Romans ) we find the symbols I, , X, , 8 and for I, V, X, L, M and C .

These figures are derived from the use of notched sticks and the need to include benchmarks: The shepherd who wants to count his animals without knowing list is just a stick on which notches are, moving his herd before him , and shifts her nail a notch each time an animal passes in front of him the final slot is the number of animals, and it suffices to identify its position to keep the number. With this system, initial figures are always simple notches subsequently transcribed by "I".

The identification is not easy when the number of slots exceeds a handful, because the eye does not see clearly beyond the collections of three or four things: to read IIIIIIII is virtually impossible (as compared to VIII, many simpler). The shepherd is naturally led to intersperse regular notches of different shape, to serve as a visual cue, and the natural groupings (for a shepherd counting on his fingers) is in groups of five ( 10 for the Etruscans ). Such a combination is still used today on rules to be measured.

The mark "five" may be a natural slot longer (used on rules), or bias (used on sizes), but these two brands do not differ much from simple notches when it comes to transcribe them. The trademarks used are simple finally formed by a double notch (V-shaped or when we read in the other direction). Reunion next ten notches, is almost always a notch cross X. Benchmarks Subsequent more elaborate forms, three slots: 50 corresponds to V plus a notch, to give initially forms N, Z or E, and a hundred matches "X plus a notch, giving forms type star (). These forms were less stable, and have subsequently evolved toward forms two lines, L for fifty, and C per cent.

With a stick and scored, the shepherd can easily locate the notch on which stopped the countdown. If thirteen animals, for example, the nail stops on the third slot after the first ten, which is simply transcribed XIII. If he has twenty-nine, his nail is a notch before the third decade, which is denoted XXIX. If he has fifty-nine, his finger has spent the first fifty, and is a notch before the next decade: LIX.

This identification can lead to original scripts very atypical example, one step before the note down to ten before fifty IXL (for thirty nine). He was subsequently adjusted to form the system known today.

Scoring basic classical

This system, which simplified the old Greek and Phoenician counts, you can write all the numbers from 1 to 4999, using the Latin alphabet most similar to former unary systems. However this system has not totally replaced because it was too simple and insufficient to express all the numbers (especially the larger numbers, which gave rise to all sorts of extensions).

The complexity of the basic Roman system (without the numbers above 4999) already appears in the following examples:

Also its complex design, combining additions and subtractions was also difficult to understand even for the Romans themselves, who continued to use systems that are based purely additive forms "simplistic" (including calculations). He persisted in many variants do not respect the rules imposed above, and using the true origins of this purely additive numeration system.

Some numbers can be written several ways: 99 or IC can be written XCIX ^Procedure

To know the value of a number written in Roman numerals, the number must be read from right to left, just add the digit, unless it is lower than the former, in this case, it is subtracted. Thus:

• XVI = 1 + 5 + 10 = 16;
• XIV = 5 to 1 + 10 = 14, because I is less than V;
• TEN = 10 to 1 + 500 = 509, because I is less than X;
• MMMMCMXCIX = 10-1 + 100-10 + 1000 - 100 + 1000 * 4 = 4999;
• MMMMDCCCLXXXVIII = 4888, is the Roman numeral in the longest amount of symbols.

Examples of Roman numerals in the base system

• 888 = DCCCLXXXVIII;
• 1000 = M;
• MDXV = 1515 = 1 000 + 500 + 10 + 5.
• MCMLXXV = 1975 = 1000 + (1000 - 100) + 50 + 10 2 + 5.
• MMII = 2002 = 1000 2 + 1 2.

Once these writing conventions were asked, we can write integers to Roman numerals. But the mathematicians of the time did not use this notation to make additions or multiplications, they were using charts. They used what makes a positional numeration , but be aware that this positional numeration could be used to write larger numbers permanently.

Extensions

Medieval Variants

Clock with a four Watchmaker

In the Middle Ages , the writing of Roman numerals is sometimes debased.

4 is written IIII instead of IV (which in fact is an old variant - in practice among the Etruscans ). This custom was revived in watchmaking , where the number 4 written IIII, mainly for reasons of readability on a round face, especially when the (engravings figures) are inclined. This is what earned him his name four watchmaker .

60 to 400, and include one written by the score, the number twenty (xx) as superscript: either IIII ^xx for 80 ^{Variants of the inclusion of Roman numerals in text}

In the Middle Ages, when the Latin alphabet was monumental replaced by the uncial , easier to draw with the pen, the numbers being written in small letters like the rest of the text. The use of capital was rare (not even the beginning of the sentence) and rather reserved for decorative initials at the beginning of paragraph (which were merely enlarged versions of the letters of the alphabet).

Also, to allow insertion of numbers in a text, they were framed midpoints in order to more easily distinguish the words. For example, XXVII representing the number 27 in medieval manuscripts (the lowercase did not have yet developed suscrit , appeared much later in Gothic script for easy reading of the text to better distinguish the and the whose legs were very close).

The position of these points varied according to the authors (the use of punctuation, particularly the distinction between point and point, had been well controlled until much later), and sometimes indistinguishable in the text normal punctuation mark (this is especially true for manuscripts in Catalan , former Occitan and Old French , but also medieval manuscripts in England and the Holy Roman Empire ). We also found that use of the midpoint (which often took the shape of small indents) on monumental inscriptions in Latin, which combine text with numbers, such as monuments and religious buildings.

The use of midpoints has now lost because Roman numerals are no longer used as adjectives determinants numerals (to indicate quantities used today decimal digit Indo-European, often called Arabic numerals in French ), but mostly as adjectives ordinal context whose poses fewer problems of interpretation (after the name of a sovereign, or accompanied by an ordinal suffix) and normally in uppercase (or small caps) in a sentence.

Later, when the letter J was differentiated from the letter the official records started using the instead of at the end of a number (such as marking the end though the number can not be longer extend). Since this time there was no difference upper / lower case in the uncial script, so we wrote vii instead VIII or even (note: above, the letter also spelled lowercase no point suscrit, appeared much later on the new consonant only similarity with the vowel with which it could still freely be confused in spelling, choice of form used is often very long remained a matter of style-independent vocal or consonantal value of the letter for details, see Item suscrit ).

Extensions Classic

Different forms above have often been diverted and were sometimes mutually incompatible, as the accountants used a scoring system more logical and simple, from the disposition of their design charts, and in connection with the original system, purely additive, where a bar is added to each unit. They have taken this principle:

Beyond 4999, it employs a macron (horizontal bar, comma in Latin) suscrit above number to indicate a factor of 1000 and two macrons to a factor one million. For example:

Classical extension

Figure Roman	Value	Meaning
I	1 000	I suscrit with M or with macron suscrit
V	5 000	V M suscrit, or macron suscrit (attested from antiquity)
X	10 000	X M suscrit, or macron suscrit
L	50 000	L with M suscrit, or macron suscrit
C	100 000	C M suscrit, or macron suscrit
D	500 000	D with M suscrit, or macron suscrit
M	1 000 000	M with M suscrit, or macron suscrit
I	1 000 000	I double suscrit M, or with double macron suscrit
V	5 000 000	V Double M suscrit or double macron suscrit
X	10 000 000	X M suscrit double, or double macron suscrit
L	50 000 000	The Double M suscrit or double macron suscrit
C	100 000 000	C with double M suscrit or double macron suscrit
D	500 000 000	D Double M suscrit or double macron suscrit
M	1 000 000 000	M Double M suscrit or double macron suscrit

For other multiples of 1000, the M suscrit is extended to cover all the numbers it multiplies.
This remains true for the macron suscrit example CXLII CCCLXVIII DCCXCV represents the number 142 368 795.

However, it has many variations existed in both the path that the procedure before that model is imposed. The notation M has established itself quickly instead of CI (or CID) and I, whenever possible. Similarly M is preferred to CCI (or CCIDD or CCSD) whenever possible. It uses M rather than CID or CI unless a group of thousands is more than 4 in which case I with macron is preferred if possible to write the group writing must be consistent in the systematic use of letters with macron if they are used (in which case the letter M is not used, then the numbers being written in groups of three decimal digits transcribed using only six letters D, C, L, X, V, I)

The Latin epigraphy shows variants of this system, with a rating of counting hundreds of thousands, framing the figure on three sides. Thus, a fragment of the Fasti of Ostia found in 1941 published the census figure of Augustus and Tiberius in 14 AD. AD as follows:

CSCRK DCCCC
Which reads C (ENSA) S (unt) C (ivium) R (omanorum) K (apitum) Quadragant soles centum milia DCCCC
translated into "The Roman citizens are identified: one times one hundred forty thousand nine hundred head" is 4.1009 million .

Calculation

It may be that users of this numbering system have been induced to perform calculations, to know by heart some results. If, for example, they knew the product XII by XII, it was easy to deduce the product XII by one less or one more.

Extensions modern

The extension of the subtractive rule is sometimes used in a systematic way with symbols of lower rank to shorten up the numbers, for example IIM = 1 000 - 1 2 = 998, instead of CMXCVIII = (1 000 - 100) + (100 - 10) + 5 + 1 3 in the standard rule. Sometimes, symbols identical unit are grouped together after the subtractive symbols instead of symbols separated by these subtractive. This abbreviated representation can be obtained with the following algorithm:

• The number 3898 to represent

we break it down bit by bit in 3 000 + 800 + 90 + 8 as in the standard rule.

• converting each digit representation with the shortest (for multiples of 8 is used on the subtractive rule next decade, instead of the additive rule on the multiple of 5),

CC gives MMM M II X X C;

• reorders are all negative numbers in mind, in reverse order (from smallest to largest)

we obtain II X X CC MMMM C;

• we eliminate all the numbers that cancel each other starting with the most negative figures on the left,

MMMM II C is obtained;

• if there are groups of 3 or 4 consecutive identical symbols unit, they are reduced with the rule subtractive

II C we obtain M V, the final number is then IICM V, which reads as 5 000 - 1102 (all figures are added below the V final, which we will deduct this total).

Under those rules, we also get numbers sometimes easier to read and understand:

• IIC (100-2) instead of XCVIII (100-10 + 5 + a 3) with the standard notation for 98;
• IC (100-1) instead of XCIX (100-10 + 10-1) with the standard notation for 99;
• XM (1 000-10) instead of CMXC (1 100-10 + 000-100) with the standard notation for 990;
• XMV (1 000-10 + 5) instead of CMXCV (1 + 000-100 + 100-10 5) with the standard notation for 995;
• IM (1 000-1) instead of CMXCIX (1 000-100 + 100-10 + 10-1) with the standard notation for 999, etc..
• These graphs are not always recognized by readers.

Modern Uses

Roman numerals are still widely used today to rate the centuries and millennia, as, for example, " XXI ^Century "and" the ^Third Millennium. " There are also Roman numerals on the dials of clocks and watches. In this case, the number four is often written as IIII instead of IV for a purely aesthetic. Indeed, in so doing, the first four digits are composed only of I (I, II, III and IIII), the four following compounds of V (V, VI, VII, VIII) and the last four base X (IX, X, XI, XII). However, be advised that the spelling IIII date from Roman times and has met a long time in the inscriptions, medieval manuscripts and printed in competition with conventional IV.

Roman numerals were also once used to mark the date of construction of houses. She is still on the front of old buildings.

This is also true for the names of rulers (Louis XIV, ...)

Even now, it is common to specify the date of production of a film with Roman numerals at the end credits.

Roman numerals were abandoned in favor of the Indo-European numerals, known as " Arab ", using a decimal system for writing numbers shorter with just more letters (10 instead of 7), and include the zero positional (0). In addition, the system aligns the decimal numbers that greatly facilitates the calculations on paper.

However, the extension of scoring with single or double macron suscrit is still commonly used today over M as an abbreviation of one million (M, 10 ⁶⁾ and one billion (M, 10 ^9).

In the numbering of pages, there are sometimes Roman numerals in lowercase or more commonly in small capitals (in letterpress printing with neat):

• i, ii, iii, iv, v, vi, vii, viii, ix, x, xi, xii, xiii, ..., xl, ..., l, ..., lx, ..., xc, ..., c, ..., cd, ... d, ..., cm, ..., m.
• i, ii, iii, iv, v, vi, vii, viii, ix, x, xi, xii, xiii, ..., xl, ..., l, ..., lx, ..., xc, ..., c, ..., cd, ... d, ..., cm, ..., m.

In chemistry , denotes a roman numeral oxidation (such as copper (II)).

References

1. The characters used here to represent the ancient forms of the figures are taken from various writings by resemblance. The actual layout of characters can be directly reproduced here.
2. For the whole question, see, eg, Georges Ifrah, Universal History of Numbers, Seghers 1981, ( ISBN 2-221-50205-1 )
3. Source
4. A. Degrassi Inscriptiones Italiae, XIII, 1, p. 185
5. Mireille Cbeillac-Gervasoni , Maria Letizia Caldelas Fausto Zevi, Latin Epigraphy, Armand Colin, 2006, ( ISBN 2200217749 ), pp. 77-79
6. Claude Nicolet , Censors and publicans, economics and taxation in ancient Rome, Fayard, 2000, ( ISBN 2213602964 ), pp.189-190

See also

Bibliography

• Comparative History counts written Genevieve Gitelson, Flammarion, ( ISBN 2-08-211104-0 )
• Universal History of Numbers by Georges Ifrah, Robert Laffont, ( ISBN 2-221-05779-1 )

Related articles

• Character Map Unicode/U2150
• Number system
  • Decimal system
• Ancient Rome
• Numbers in the world
• Timing : a date is obtained by adding the Roman numerals of a text

External Links

• Tool for converting Roman and Arabic numerals
• Conversion algorithm and demonstration program (with source code)
• Matlab functions for converting Roman numerals (with source code) ( Matlab )
• Use of Unicode characters to write the Roman numerals on the web
• Book with 841 chapters numbered up DCCCXLI (1850)

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