These second forms are organically connected, whereas the first forms exhibit no connection.
During the first thousand years of the Christian era, the alphabet system held full sway; then for a period of nearly five hundred years the Roman and the Greek systems vied with each other for popular favor among European arithmeticians.
The origin of the Roman numerals is lost in obscurity. Undoubtedly the symbols are from Etruscan sources changed gradually into the similar Roman letters. It is to be noted that such changes in the forms of letters were most easily effected by copyists previous to the invention of printing. Just as the Babylonians operated with the common denominator sixty, so the Romans confined themselves to the denominator 12 (and powers of 12). The twelfth represented at first a definite concrete unit of weight or length, the uncius, which later acquired a numerical sense.
List of Roman 12ths
The connection between the unciæ and our inches and ounces is evident. The Roman numerals like their prototypes in the Attic system of Greece and the more ancient Semitic systems, left no traces upon our current arithmetic. However, the Roman system of calculating upon a reckoning table was one of the vital factors in the development of the decimal place system. This system was not peculiarly Roman, as ancient Greek reckoning tables are found in several continental museums. The Chinese suan-pan, in popular use in Chinese laundries, is familiar to most readers. A similar instrument is found in Russian elementary schools.
A series of parallel grooved spaces and a goodly number of pebbles constitute the simplest form of one of these primitive calculating machines. Any right-hand column is chosen as the units column and the successive columns to the left are designated by the symbols for the successive powers of ten. Ten pebbles in any one column are replaced by one pebble in the next column to the left. Addition and subtraction are simple operations and even multiplication with small integers is not a difficult operation. Division was an accomplishment which only masters achieved; the complicated rules given by some medieval writers on the subject lead one to suspect that the writers were concealing ignorance in obscurity. On the Roman abacus the extreme right hand column represented twelfths (unciæ) and three smaller columns
