not use them in order, but use just a few letters which they repeated as often as necessary-as in the Baby lonian system. Unlike the Babylonians, the Romans did not invent a new symbol for every tenfold increase of number, but (more primitively) used new symbols for fivefold increases as well.
'Thus, to begin with, the symbol for "one" is 1, and "two," "three," and "four," can be written II, III, and IIII.
The symbol for five, then, is not 11111, but V. People have amused themselves no end trying to work out the reasons for the particular letters chosen as symbols, but there are no explanations that are universally accepted.
However, it is pleasant to think that I represents the up held fin-er and that V might symbolize the hand itself with all five fingers-one branch of the V would be the out held thumb, the other, the remaining fingers. For "six," "seven," "eight," and "nine," we would then have VI, VII, 'VIII, and VIIII.
For "ten" we would then have X, which (some peo ple think) represents both hands held wrist to wrist.
"Twenty-three" would be XXIII, "forty-eight" would be XXXXVIII, and so on.
The symbol for "fifty" is L, for "one hundred" is C, for "five hundred" is D, and for "one thousand" is M. The C and M are easy to understand, for C is the first letter of centum (meaning "one hundred") and M is the first letter of rnille (one thousand).
For that very reason, however, those symbols are sus picious. As initials they may have come to oust the original less-meaningful symbols for those numbers. For instance, an alternative symbol for "thousand" looks something like this (1). Half of a thousand or "five hundred" is the right half of the symbol, or (1), and this may have been con verted into D. As for the L which stands for "fifty," I don't know why it is used.
Now, then, we can write nineteen sixty-four, in Roman numerals, as follows: MDCCCCLXIIII.
One advantage of writing numbers according to this sys tem is that it doesn't matter in which order the numbers are written. If I decided to write nineteen sixty-four as CDCLIIMXCICT, it would still represent nineteen sixty four if I add up the number values of each letter. However, it is not likely that anyone would ever scramble the letters in this fashion. If the letters were written in strict order of decreasing value, as I.did the first time, it would then be much simpler to add the values of the letters. And, in fact, this order of decreasing value is (except for special cases) always used.
Once the order of writing the letters in Roman numerals is made an established convention, one can make use of deviations from that set order if it will help simplify mat ters. For instance, suppose we decide that when a symbol of smaller value follows one of larger value, the two are added; while if the symbol of smaller value precedes one of larger value, the first is subtracted from the second. Thus VI is "five" plus "one" or "six,"' while IV is "five" minus "one" or "four." (One might even say that IIV is "three," but it is conventional to subtract no more than one sym bol.) In the same way LX is "sixty" while XL is "forty"; CX is "one hundred ten," while XC is "ninety"; MC is 44 one thousand one hundred," while CM is "nine hundred."
The value of this "subtractive principle" is that two sym bols can do the work of five. Why write VIIII il you can write IX; or DCCCC if you can write CM? The year nine teen sixty-four, instead of being written MDCCCCLXIIII (twelve symbols), can be written MC@XIV (seven sym bols). On the other hand, once you make the order of writing letters significant, you can no longer scramble them even if you wanted to. For instance, if MCMLXIV is scrambled to MMCLXVI it becomes "two thousand one hundred sixty-six."
The subtractive principle was used on and off in ancient times but was not regularly adopted until the Middle Ages.
One interesting theory for the delay involves the simplest use of the principle-that of IV ("four"). These are the first letters of IVPITER, the chief of the Roman gods, and the Romans may have had a delicacy about writing even the beginning of the name. Even today, on clockfaces bear ing Roman numerals, "four" is represented as 1111 and never as IV. This is not because the clockf ace