Roman numerals combine features of a tally system and a numeral system. In modern usage:
|IV is 4||but||VI is 6|
|IX is 9||but||XI is 11|
|MCM is 1900||but||MMC is 2100|
|4 =||IV||not IIII|
|9 =||IX||not VIIII|
|40 =||XL||not XXXX|
|90 =||XC||not LXXXX|
|400 =||CD||not CCCC|
|900 =||CM||not DCCCC|
|49 =||XLIX||not IL|
|99 =||XCIX||not IC|
|1999 =||MCMXCIX||not MIM|
|990 =||CMXC||not XM|
The effect is that only I's, X's and C's are subtracted, and only from, at most, the next two larger numerals. This convention greatly eases the reader's burden, by substituting recognition for calculation. For example, anyone who has been reading copyright dates on many books immediately recognizes a date beginning “MCM...” as something from the 1900's. If “MIM” were permitted, the reader would have to actually do the subtraction.
Today, Roman numerals are used mainly as an alternative to the Hindu-Arabic numerals in outlines and other instances in which two distinct sets of numerals are useful, for clock faces, for ceremonial and monumental purposes, and by publishers and film distributors who have an interest in making copyright dates difficult to read.
Perhaps the biggest difference between modern and Roman Roman numerals is that the Romans rarely used the subtraction principle. Nine was much more likely to be VIIII than IX.
A line drawn over a numeral meant that its value was to be multiplied by 1000. If lines were drawn on the top and both sides of a numeral, its value was multiplied by a hundred thousand.
In Rome and later elsewhere characters were used which we no longer have. Some examples:
|½ (alternate symbols)|
|9½ (alternate symbols)|
This system was almost the only one used in Europe until about the 11th century, and was gradually supplanted during the next 500 years by Hindu-Arabic numerals.
In the Middle Ages, a few conventions no longer used were common.
To make altering the last digit in a number more difficult, the final “i” was extended. Until recently, this practice was often represented in print by j instead of i, for example viij instead of viii.
A very common use of this technique was to indicate a number of scores. For example:
“For there is a C of vixx thereby be sold muttons and other beasts and fishes, as for herring vxx with the tale herring make a C: xM make a last; and because that a MI wyll not in a barrel, therefore xii barrels packed herring make a last.”
--MS Cotton, Vesp. E. IX (15th century)
vixx = 6 times 20, i.e., 6 score, = 120; muttons were sold by a “hundred” (“C”) of 120 pieces
vxx = 5 times 20, i.e., 5 score = 100; herring was sold by a hundred of 100 pieces
xM = 10 times 1000 = 10,000
MI = 1000
A phrase was frequently added to resolve the ambiguity. For example, from the same source as above:
"Also eels be sold by the stike, that is xxv eels, and x stikes make a gwyde, iicl by vxx." (ibid)
Here the phrase “by vxx” (five score) indicates that the “c” in the previous number means 100, so iicl is 250 (2 times 100, plus 50).
Certain types of errors are typical in reading Roman numerals in old manuscripts, due to physical damage to the text. Kemble describes some:
This [inconsistency in dates] however generally arises from the latter date having been partially abraded by age, and so misread: the want of a light line at the bottom readily transforms a V (in the old charters U) into a II; an abrasion may convert an X into a V: hence we not uncommonly find in these copies indiction IIII for VII or XV; VII for XII; XII for XV, and the like. Nor is another error at all uncommon, where a letter or contraction has been taken to be part of the date: for instance, indictione uo (uero) IIa, has often been read as if it were indictione VIIa. Again, indictione Xma has become transformed into indictione XIIIa, the strokes of the written “m” having been taken to represent three units. This cause of error is so frequent as to render multiplied examples unnecessary.1
Johannis M. Kemble.
Codex Diplomaticus Aevi Saxonici.
London: Sumptibus Societatis, 1839.
Reprinted in facsimile by Kraus Reprint Limited, Vaduz, 1964.
Volume 1, page lxxxix.
A History of Mathematical Notations.
La Salle, Illinois: Open Court, 1928 and 1929.
Republished in one volume by Dover in 1993.
Translated by David Bellos, E. F. Harding and Sophi Wood.
The Universal History of Numbers: From Prehistory to the Invention of the Computer.
John Wiley and Sons, 1999.
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