Which numerals are Roman and which are Arabic. Arabic numerals

To designate numbers in Latin, combinations of the following seven characters are accepted: I (1), V (5), X (10), L (50), C (100), D (500), M (1000).

To memorize the letter designations of numbers in descending order, a mnemonic rule was invented:

We Give Juicy Lemons, Enough for Vall Ix (respectively M, D, C, L, X, V, I).

If the sign denoting a smaller number is to the right of the sign denoting a larger number, then the smaller number should be added to the larger one, if to the left, then subtract, namely:

VI - 6, i.e. 5+1
IV - 4, i.e. 5 - 1
XI - 11, i.e. 10+1
IX - 9, i.e. 10 - 1
LX - 60, i.e. 50+10
XL - 40, i.e. 50 - 10
CX - 110, i.e. 100+10
XC - 90, i.e. 100-10
MDCCCXII - 1812, i.e. 1000 + 500 + 100 + 100 + 100 + 10 + 1 + 1.

There may be different meanings for the same number. For example, the number 80 can be denoted as LXXX (50 + 10 + 10 + 10) and as XXC (100 - 20).

To write numbers in Roman numerals, you must first write down the number of thousands, then hundreds, then tens, and finally units.

I (1) - unus (unus)
II (2) - duo (duo)
III (3) - tres (tres)
IV (4) - quattuor (quattuor)
V (5) - quinque (quinque)
VI (6) - sex (sex)
VII (7) - septera (septem)
VIII (8) - octo (octo)
IX (9) - novem (novem)
X (10) - decern (decem)
XI (11) - undecim (undecim)
XII (12) - duodecim (duodecim)
ХШ (13) - tredecim (tredecim)
XIV (14) - quattuordecim (quattuordecim)
XV (15) - quindecim (quindecim)
XVI (16) - sedecim (sedecim)
XVII (17) - septendecim (septendecim)
XVIII (18) - duodeviginti (duodeviginti)
XIX (19) - undeviginti (undeviginti)
XX (20) - viginti (viginti)
XXI (21) - unus et viginti or viginti unus
XXII (22) - duo et viginti or viginti duo, etc.
XXVIII (28) - duodetriginta (duodetriginta)
XXIX (29) - undetriginta (undetriginta)
XXX (30): triginta (triginta)
XL (40) - quadraginta (quadraginta)
L (5O) - quinquaginta (quinquaginta)
LX (60) - sexaginta (sexaginta)
LXX (70) - septuaginta (szltuaginta)
LXXX180) - octoginta (octoginta)
KS (90) - nonaginta (nonaginta)
C (100) centum (centum)
CC (200) - ducenti (ducenti)
CCC (300) - trecenti (trecenti)
CD (400) - quadrigenti (quadrigenti)
D (500) - quingenti (quingenti)
DC (600) - sescenti (sessenti) or sexonti (sekstsenti)
DCC (700) - septigenti (septigenti)
DCCC (800) - octingenti (octingenti)
CV (DCCC) (900) - nongenti (nongenti)
M (1000) - mille (mille)
MM (2000) - duo milia (duo milia)
V (5000) - quinque milla (quinque milla)
X (10,000) - decem milia (decem milia)
XX (20000) - viginti milia (viginti milia)
C (100000) - centum milia (centum milia)
XI (1000000) - decies centena milia (decies centena milia).

If suddenly an inquisitive person asks why the Latin letters V, L, C, D, M were chosen to denote the numbers 50, 100, 500 and 1000, then we will immediately say that these are not Latin letters at all, but completely different signs.

The fact is that the Western Greek alphabet served as the basis for the Latin alphabet. It is to him that the three signs L, C and M go back. Here they denoted aspirated sounds, which were not in the Latin language. When the Latin alphabet was being formed, it was they who turned out to be superfluous. They were adapted to denote numbers in the Latin script. Later, their spelling coincided with Latin letters. So, the sign C (100) became similar to the first letter of the Latin word centum (one hundred), and M (1000) - to the first letter of the word mille (thousand). As for the sign D (500), it was half of the sign F (1000), and then it became like a Latin letter. The sign V (5) was only the upper half of the sign X (10).

We all use Roman numerals - we mark the numbers of centuries or months of the year with them. Roman numerals are on watch dials, including those on the chimes of the Spasskaya Tower. We use them, but we don't know much about them.

How are Roman numerals arranged?

The Roman counting system in its modern version consists of the following basic characters:

I 1
V 5
X 10
L 50
C 100
D500
M 1000

To remember numbers that are unusual for us using the Arabic system, there are several special mnemonic phrases in Russian and English:
We Give Juicy Lemons, Enough for Everyone Ix
We Advise Only Well-Brought-Up Individuals
I Value Xylophones Like Cows Dig Milk

The system of arrangement of these numbers relative to each other is as follows: numbers up to three inclusive are formed by adding units (II, III), - the fourfold repetition of any number is prohibited. To form numbers greater than three, the larger and smaller digits are added or subtracted, to subtract, the smaller digit is placed before the larger one, to add - after, (4 = IV), the same logic applies to other numbers (90 = XC). The arrangement of thousands, hundreds, tens and units is the same as we are used to.

It is important that any digit should not repeat more than three times, so the longest number up to a thousand is 888 = DCCCLXXXVIII (500+100+100+100+50+10+10+10+5+1+1+1).

Alternatives

The ban on the fourth use of the same number in a row began to appear only in the 19th century. Therefore, in ancient texts one can see variants IIII and VIIII instead of IV and IX, and even IIIII or XXXXXX instead of V and LX. The remains of this writing can be seen on the clock, where four is often marked with exactly four units. In old books, there are also frequent cases of double subtractions - XIIX or IIXX instead of the standard XVIII in our days.

Also in the Middle Ages, a new Roman numeral appeared - zero, which was denoted by the letter N (from the Latin nulla, zero). Large numbers were marked with special characters: 1000 - ↀ (or C|Ɔ), 5000 - ↁ (or |Ɔ), 10000 - ↂ (or CC|ƆƆ). Millions are obtained by double underlining the standard digits. Fractions were also written in Roman numerals: ounces were marked with the help of icons - 1/12, half was marked with the symbol S, and everything that was more than 6/12 was added: S = 10\12. Another option is S::.

Origin

At the moment, there is no unified theory of the origin of Roman numerals. One of the most popular hypotheses is that the Etruscan-Roman numerals originated from a counting system that uses notches instead of numbers.

Thus, the number "I" is not the Latin or more ancient letter "i", but a notch that resembles the shape of this letter. Every fifth notch was marked with a bevel - V, and the tenth was crossed out - X. The number 10 in this account looked like this: IIIIΛIIIIX.

It is thanks to such a record of numbers in a row that we owe a special system for adding Roman numerals: over time, the record of the number 8 (IIIIΛIII) could be reduced to ΛIII, which convincingly demonstrates how the Roman counting system got its specifics. Gradually, the notches turned into graphic symbols I, V and X, and gained independence. Later they began to be identified with Roman letters - as they were outwardly similar to them.

An alternative theory belongs to Alfred Cooper, who suggested considering the Roman counting system from the point of view of physiology. Cooper believes that I, II, III, IIII is a graphical representation of the number of fingers of the right hand thrown out by the trader when naming the price. V - this is a set aside thumb, forming together with the palm a figure similar to the letter V.

That is why Roman numerals sum up not only units, but also add them to fives - VI, VII, etc. - this is the thumb and other exposed fingers of the hand. The number 10 was expressed using the crossing of hands or fingers, hence the symbol X. Another option is that the number V was simply doubled, getting X. Large numbers were transmitted using the left palm, which counted tens. So gradually the signs of the ancient finger count became pictograms, which then began to be identified with the letters of the Latin alphabet.

Modern application

Today in Russia, Roman numerals are needed, first of all, to record the number of the century or millennium. It is convenient to put Roman numerals next to Arabic ones - if you write a century in Roman numerals, and then a year in Arabic, then your eyes will not ripple from the abundance of identical signs. Roman numerals are somewhat archaic. With their help, they also traditionally indicate the serial number of the monarch (Peter I), the number of the volume of a multi-volume edition, and sometimes the chapter of the book. Roman numerals are also used in antique watch dials. Important numbers, such as the year of the Olympiad or the number of a scientific law, can also be recorded using Roman numerals: World War II, Euclid's fifth postulate.

AT different countries Roman numerals are used a little differently: in the USSR it was customary to use them to indicate the month of the year (1.XI.65). In the West, Roman numerals often write the number of the year in movie credits or on building facades.

In a part of Europe, especially in Lithuania, one can often find Roman numerals designating the days of the week (I - Monday, and so on). In the Netherlands, Roman numerals sometimes represent floors. And in Italy, they mark 100-meter sections of the path, marking, at the same time, with Arabic numerals each kilometer.

In Russia, when writing by hand, it is customary to underline Roman numerals from below and from above at the same time. However, often in other countries, an underscore from above meant an increase in the case of a number by a factor of 1000 (or 10,000 times with a double underscore).

There is a common misconception that modern Western clothing sizes have something to do with Roman numerals. In fact, the designations XXL, S, M, L, etc. have no connection with them: these are abbreviations of the English words eXtra (very), Small (small), Large (large).

The Roman numbering system using letters was common in ancient Rome and Europe for two thousand years. Only in the late Middle Ages it was replaced by a more convenient decimal system for calculations, borrowed from the Arabs (1,2,3,4,5 ...).

But, until now, Roman numerals indicate the dates on the monuments, the time on the clock and (in the Anglo-American typographic tradition) the pages of book prefaces, clothing sizes, chapters of monographs and textbooks. In addition, in Russian, it is customary to designate ordinal numbers with Roman numerals. The system of Roman numerals is currently used to designate centuries (XV century, etc.), years AD. e. (MCMLXXVII etc.) and months when indicating dates (for example, 1. V.1975), in historical monuments of law as article numbers (Carolina and others)

To designate numbers, 7 letters of the Latin alphabet were used (the first letter of the words is five, ten, fifty, one hundred, five hundred, one thousand):

I=1, V=5, X=10, L=50, C=100, D=500, M=1000

C (100) is the first letter of the Latin word centum (one hundred)

and M - (1000) - on the first letter of the word mille (thousand).

As for the sign D (500), it was half of the sign Ф (1000)

The V sign (5) is the upper half of the X sign (10)

Intermediate numbers were formed by adding a few letters to the right or left. Thousands and hundreds are written first, then tens and ones. Thus, the number 24 is written as XXIV

Natural numbers are written by repeating these digits.

At the same time, if a large number is in front of a smaller one, then they are added (the principle of addition), if the smaller one is in front of the larger one, then the smaller one is subtracted from the larger one (the principle of subtraction).

In other words, if the sign denoting a smaller number is to the right of the sign denoting a larger number, then the smaller is added to the larger; if on the left, then subtract: VI - 6, i.e. 5+1 IV - 4, i.e. 5-1 LX - 60, i.e. 50+10 XL - 40, i.e. 50-10 CX - 110, i.e. 100 + 10 XC - 90, i.e. 100-10 MDCCCXII - 1812, i.e. 1000+500+100+100+100+10+1+1

The last rule applies only to avoid the fourfold repetition of the same figure. To avoid a 4-fold repetition, the number 3999 is written as MMMIM.

There may be different meanings for the same number. So, the number 80 can be represented as LXXX (50+10+10+10) and as XXC(100-20).

For example, I, X, C are placed respectively before X, C, M to denote 9, 90, 900 or before V, L, D to denote 4, 40, 400.

For example, VI = 5+1 = 6, IV = 5 - 1 = 4 (instead of IIII).

XIX \u003d 10 + 10 - 1 \u003d 19 (instead of XVIIII),

XL = 50 - 10 = 40 (instead of XXXX),

XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33 etc.

Note:

Basic Roman numerals: I (1) - unus (unus) II (2) - duo (duo) III (3) - tres (tres) IV (4) - quattuor (quattuor) V (5) - quinque (quinque) VI (6) - sex (sex) VII (7) - septem (septem) VIII (8) - octo (octo) IX (9) - novem (novem) X (10) - decem (decem), etc. XX (20) - viginti (viginti) XXI (21) - unus et viginti or viginti unus XXII (22) - duo et viginti or viginti duo, etc. XXVIII (28) - duodetriginta (duodetriginta) XXIX (29) - undetriginta (undetriginta) XXX (30) - triginta (triginta) XL (40) - quadraginta (quadraginta) L (50) - quinquaginta (quinquaginta) LX (60) - sexaginta (sexaginta) LXX (70) - septuaginta (septuaginta) LXXX (80) - octoginta (octoginta) XC (90) - nonaginta (nonaginta) C (100) - centum (centum) CC (200) - ducenti (ducenti) CCC (300) - trecenti (trecenti) CD (400) - quadrigenti (quadrigenti) D (500) - quingenti (quingenti) DC (600) - sexcenti (seccenti) DCC (700) - septigenti (septigenti) DCCC (800) - octingenti (octigenti) CM (DCCCC) (900) - nongenti (nongenti) M (1000) - mille (mille) MM (2000) - duo milia (duo milia) V (5000) - quinque milia (quinque milia) X (10000) - decem milia (decem milia) XX (20000) - viginti milia (viginti milia) C (1000000) - centum milia (centum milia) XI (1000000) - decies centena milia (decies centena milia) "

Roman numerals often cause us difficulty.
But it is they that are usually used when numbering centuries and book chapters, when designating clothing sizes and steps in music.
Roman numerals are in our life. So it's too early to give them up. Easier to learn, understand and learn. What's more, it's easy.
So, to designate numbers in Latin, combinations of the following 7 characters are accepted: I (1), V (5), X (10), L (50), C (100), D (500), M (1000).
Why were Latin letters chosen to represent the numbers 5, 50, 100, 500 and 1000? It turns out that these are not Latin letters, but completely different characters. The fact is that the basis for the Latin alphabet (and it, by the way, exists in several versions - 23, 24 and 25 letters) was the Western Greek alphabet.

Thus, the three characters L, C, and M go back to the Western Greek alphabet. Here they denoted aspirated sounds, which were not in the Latin language. When the Latin alphabet was being formed, it was they who turned out to be superfluous. And they were adapted to denote numbers in the Latin script. Later, their spelling coincided with Latin letters. So, the sign C (100) became similar to the first letter of the Latin word centum (one hundred), and M - (1000) - to the first letter of the word mille (thousand). As for the sign D (500), it was half of the sign F (1000), and then it became similar to a Latin letter. The sign V (5) was only the upper half of the sign X (10).
In this regard, by the way, the popular theory that the name of the church office of the Pope (Vicarius Filii Dei), when replacing letters with Roman numerals, adds up to the “devil's number”, seems funny.

So, how to understand the Latin numbers?
If the sign denoting a smaller number is to the right of the sign denoting a larger number, then the smaller is added to the larger; if on the left, then subtract:
VI - 6, i.e. 5+1
IV - 4, i.e. 5-1
LX - 60, i.e. 50+10
XL - 40, i.e. 50-10
CX - 110 i.e. 100+10
XC - 90, i.e. 100-10
MDCCCXII - 1812, i.e. 1000+500+100+100+100+10+1+1.

There may be different meanings for the same number. So, the number 80 can be represented as LXXX (50+10+10+10) and as XXC(100-20).
Basic Roman numerals look like this:
I (1) - unus (unus)
II(2) - duo (duo)
III(3) - tres (tres)
IV (4) - quattuor (quattuor)
V (5) - quinque (quinque)
VI(6) - sex (sex)
VII (7) - septem (septem)
VIII (8) - octo (octo)
IX (9) - novem (novem)
X (10) - decem (decem), etc.

XX (20) - viginti (viginti)
XXI (21) - unus et viginti or viginti unus
XXII (22) - duo et viginti or viginti duo, etc.
XXVIII (28) - duodetriginta (duodetriginta)
XXIX (29) - undetriginta (undetriginta)
XXX (30) - triginta (triginta)
XL (40) - quadraginta (quadraginta)
L (50) - quinquaginta (quinquaginta)
LX (60) - sexaginta (sexaginta)
LXX (70) - septuaginta (septuaginta)
LXXX (80) - octoginta (octoginta)
XC (90) - nonaginta (nonaginta)
C (100) - centum (centum)
CC (200) - ducenti (ducenti)
CCC (300) - trecenti (trecenti)
CD (400) - quadrigenti (quadrigenti)
D (500) - quingenti (quingenti)
DC (600) - sexcenti (seccenti)
DCC (700) - septigenti (septigenti)
DCCC(800) - octingenti (octigenti)
CM (DCCCC) (900) - nongenti (nongenti)
M (1000) - mille (mille)
MM (2000) - duo milia (duo milia)
V (5000) - quinque milia (quinque milia)
X (10000) - decem milia (decem milia)
XX (20000) - viginti milia (viginti milia)
C (1000000) - centum milia (centum milia)
XI (1000000) - decies centena milia (decies centena milia)"

Elena Dolotova.

The Roman numbering system using letters has been common in Europe for two thousand years. Only in the late Middle Ages it was replaced by a more convenient decimal system of numbers, borrowed from the Arabs. But, until now, Roman numerals denote dates on monuments, time on clocks and (in the Anglo-American typographic tradition) pages of book prefaces. In addition, in Russian, it is customary to designate ordinal numbers with Roman numerals.

To designate numbers, 7 letters of the Latin alphabet were used: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Intermediate numbers were formed by adding several letters to the right or left. First, thousands and hundreds were written, then tens and ones. Thus, the number 24 was depicted as XXIV. The horizontal line above the symbol meant multiplication by a thousand.

Natural numbers are written by repeating these digits. At the same time, if a large number is in front of a smaller one, then they are added (the principle of addition), if the smaller one is in front of the larger one, then the smaller one is subtracted from the larger one (the principle of subtraction). Last Rule is used only to avoid the fourfold repetition of the same digit. For example, I, X, C are placed respectively before X, C, M to denote 9, 90, 900 or before V, L, D to denote 4, 40, 400. For example, VI \u003d 5 + 1 \u003d 6, IV \u003d 5 - 1 = 4 (instead of IIII). XIX = 10 + 10 - 1 = 19 (instead of XVIIII), XL = 50 - 10 = 40 (instead of XXXX), XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33, etc.

Performing arithmetic operations on multi-digit numbers in this notation is very inconvenient. The Roman numeral system is not currently used, except in individual cases, designations of centuries (XV century, etc.), years AD e. (MCMLXXVII etc.) and months when indicating dates (for example, 1.V.1975), ordinal numbers, and sometimes derivatives of small orders, greater than three: yIV, yV, etc.