THE DECIMAL SYSTEM OF NUMBERS 



495 



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 Eoman and the Greek systems vied with each other for popular 

 favor among European arithmeticians. 



The origin of the Eoman numerals is lost in obscurity. Un- 

 doubtedly 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 Eomans 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 ac- 

 quired a numerical sense. 



List of Roman 12ths 



Symbol 



I There were further names and 



S= symbols for &, ££, A or f, &, &, 



S A or J, i or If, fa £,, £, T i ¥ , ^ T . 



= — These were used to apply to any 



— measurements. 



Name 



Value 



as 



1 



bes 



3 = ft 



semis 



i = A 



quadrans 



i = A 



uncia 



& 



sextula 



i 



The connection between the uncise and our inches and ounces is evident. 



The Eoman 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 Eoman 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 Eoman, 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 Eussian elementary 

 schools. 



A series of parallel grooved spaces and a goodly number of pebbles 

 constitute the simplest form of one of these primitive calculating ma- 

 chines. 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 Eoman abacus the extreme right- 

 hand column represented twelfths (unciae) and three smaller columns 



