ROMAN NUMERALS

History and use

Using letters for numbers
The Romans depicted numbers using seven letters of the alphabet as numerals

I = 1

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

In some forms of Roman numbers, D is sometimes represented by an I followed by a backwards C, a bit like this I ) , and M is represented by a C followed by an I and a backwards C. This is hard to depict in a computer font as they do not contain a backwards C but it can be approximated using parentheses like this ( I ). The derivation of this form seems to be from the use of the deep parentheses to represent larger numbers. Thus ( I ) is 1000, ( ( I ) ) is 10,000 and ( ( ( I ) ) ) is 100,000.

An alternative way of depicting larger numbers is by putting a horizontal bar over the numeral which multiplies it by 1000. Thus

On a larger scale 3,852,429 can be depicted as

However, in some cases the horizontal bar was used to show simply that the letters were being used as numbers. In other cases that was indicated by a small sign looking like two parentheses () placed above the numbers.

In medieval texts and some early printed books, the numerals are written in lower case letters and u was frequently substituted for v. In the final position of the numeral, j could be used instead of i. So 18 could be written xuiij rather than XVIII.

Forming numbers
At their simplest, numbers are formed by stringing the letters together to add up to the number required. Like this

The rule is to use the biggest numeral possible at each stage, so 15 is represented by XV not VVV nor XIIIII. It follows from this rule that numerals always go from left to right in descending order. This could still lead to some very long strings. For example, using this rule 99 would be LXXXXVIIII. So at some point a new rule was invented. A smaller value letter to the left of a larger value one is subtracted. So 4 becomes IV - which is 5 minus 1 - not IIII.

There are three rules about these smaller numerals which are placed to the left of a bigger one and subtracted.

• Only I, X, and C can be used in this way; V, L, and D cannot and of course M cannot because it is the biggest numeral anyway.
• Only one smaller number can be placed to the left. So 19 can be depicted XIX but 18 cannot be written XIIX. XIIX would have a certain ambiguity to it as it could be construed as 11+9=20 rather than 10-2+10=18.
• The subtracted number must be no less than a tenth of the value of the number it is subtracted from. So an X can be placed to the left of a C or an L but not to the left of an M or a D. Another way of looking at this rule is that each power of ten is dealt with separately. So 49 is XL IX (without the spaces), not IL

These rules limit the usefulness of the subtraction rule in reducing the length of Roman numerals. Although the year 2000 is quite neat at MM, 1999 is something else.*

The spreadsheet package Microsoft Excel has a function to depict numbers in Roman form. To get classical Roman numbers, conforming to the rules on these pages, use =ROMAN(n) where n is your number. There are four other versions of the function using progressively weirder versions of 'Roman' numbers. The fourth, ROMAN(n,4) giving what Microsoft calls the 'simplified' version. None of these four has any validity in terms of what real users of Roman numerals did and seem to have been dreamed up by programmers in Gatesville. For live conversion of real numbers into genuine Roman numerals ROMAN(A1) where A1 is the reference to the cell containing the number you want to convert.

Excel will not display numbers in Roman format without converting them to text. But another software package, Fireworkz for Windows, will do so, allowing live working spreadsheets in Roman numerals! I used Fireworkz to generate the lists of Roman numerals on the adjoining pages. For more about ths price and availability of this excellent and powerful software contact Gerald Fitton at Abacus Training.

The subtractive principle was familiar to the Romans as it was used in their calendar. Days were counted as so many before certain fixed points in the month. For example, the 9th of March was VII Id. that is the seventh day before the Ides on the 15th day (note that the Romans counted the Ides as the first day, so the 9th is the seventh NOT the sixth as you might expect). We also use a subtractive principle in time when we say quarter to eight or five and twenty to nine.

The strict rules about Roman numerals have been used only relatively recently. In earlier periods, although the subtractive principle was used, it seems that it was an alternative rather than compulsory and other forms such as VIIII for 9 and even IIXX for 18 are found. At any date exceptions can be found, as these four examples from different periods and all in Rome itself, show.

• The Colosseum - constructed between 70 and 80 AD and known as the Flavian Amphitheatre - seated 55,000 people. The audience entered through 80 arches which were numbered 1 to 76 - the four principal entrances were unnumbered. Each spectator had a ticket bearing one these numbers and entered through the corresponding arch. It is said they could all enter within ten minutes.

Use of Roman numerals

Roman numerals are still used today and can be found in many places.

• They are still used in almost all cases for the copyright date on films, television programmes, and videos - for example MCMLXXXVI. You can see an example of the current copyright date written in this way on the web at the BBC site.
• They are also used to show the hours on some analogue clocks and watches. Here, though, the four is always depicted as IIII not as IV. That is said to be because the four strokes of IIII balance the VIII which is opposite to it on the left side of the face. One exception is one of the most famous clocks in the world - Big Ben in the Clock Tower in the Palace of Westminer where the British Houses of Parliament are located. The numerals are in lower case, gothic script and the 4 is depicted as iv.
• Intel, the computer chip maker, called the improved version of its Pentium processor the Pentium II.
• They can be used for the preliminary pages of book before the main page numbering gets under way. Here they numerals normally use lower case letters so pages i, iv, xi and so on.
• The Olympic Games are numbered using Roman numerals. The 1996 Olympic Games at Atlanta in the USA were called the XXVI Olympic Games showing that it is the 26th games of the modern era since the first in 1896. The 1998 Winter Games in Nagano were the XVIII Winter Games. When counting Olympic Games the ones cancelled during war in 1916, 1940, and 1944 are included.
• Monarchs are usually numbered in Roman - eg King Edward VII of England, Louis XIV of France. Popes are also numbered using Roman numerals eg John Paul II.
• This form is also sometimes seen in naming eldest sons in American family dynasties where successive generations bear the same first name.
• They are found in numbering paragraphs in complex documents to clarify which are main sections and which subsections so II.3.iv.(5). And they are used for similar reasons to show the volume number of periodicals eg vol.VI no.5. The New York Times still does this on its front page - eg VOL. CXLVII..No.51,305.
• You will sometimes find the first and second world wars referred to as World War I and World War II or even WWI and WWII.
• They can still be seen on public buildings, monuments and gravestones, sometimes when the inscription is in Latin but often just to give the date a certain gravity. On gravestones, as well as the date of death, Roman numerals can be used for the age of the deceased.
• Before the 18th century they were widely used for the publication date on printed books. Since that time they are still sometimes found on special editions.

Up until the eighteenth century Roman numerals were used in Europe for book-keeping even though the arabic numerals we use today were known and in use from around 1000 AD. There are said to be two reasons for this.

• Adding and subtracting are very easy with Roman numerals.
• Arabic numerals can more easily be mistaken or forged - a 0 can look very like a 6 or an 8 or a 9 or be turned into one by a single stroke.

Although simple arithmetic is easier with Roman numerals, multiplication and division, fractions, and more advanced mathematics are difficult and arabic numerals slowly replaced Roman ones in everyday life.

History
The history of Roman numerals is not well documented and written accounts are contradictory. It is likely that counting began on the fingers and that is why we count in tens. A single stroke I represents one finger, five or a handful could possibly be represented by V and the X may have been used because if you stretch out two handfuls of fingers and place them close the two little fingers cross in an X. Alternatively, an X is like two Vs, one upside down. Although the Latin for 100 is centum and for 1000 is mille, scholars generally do not think that C is 100 and M is 1000 because they are the initial letters of centum and mille. The use of D could be a representation of a C with a vertical line through it representing half. My own views is that M arose out of the use of () symbols to multiply by 1000. This theory is supported by the use of ( I ) for 1000 and I ) for 500. These could easily become corrupted or abbreviated into M or D which they resemble.

The use of this form for M and D is shown in this picture of a map dating from the 16th century in the geographical room at the Vatican in Rome. The date depicted here is ( I ) I ) LXXIX or M D LXXIX or 1579.

*Answer

The year before the year 2000 is MCMXCIX in Roman numerals. See also The 1999 Question

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e-mail Paul Lewis on paul@deadline.demon.co.uk