9.3 
first book of his Geometry, describes an adaptation of the 
Abacus which really involved the system of decimal numera- 
tion, and some of the M.SS.-and as M. Chasles proves the 
best and most ancient— contain a table of nine figures, wdiich 
, x n . nl0n s us ; — more like our 
present figures indeed than are the numerals in use among 
the Moors. The next link in this chain of derivation is in a 
monkish treatise, Be Nwmerorwm Divisione, by Gerbert a 
Benedictine monk, subsequently raised to the papal chair 
. " 9) as S y lves ter II. This treatise (says M. Martin) 
does not explicitly describe the decimal numeration but 
throughout takes it for granted. Whence however did 
Gerbert learn it ? It was said, a few generations later, from 
e Saracens; but it appears from the arguments of M 
Chasles and M. Henri Martin [to whose arguments the paper 
refen ed in detail], that this was a mistake, and it seems on 
the whole most probable that the abacus with nine fio- ure s 
las come to us from the Latins, who had it in the time of 
Boethius, whose ascription of it to Pythagoras doubtless 
arose from its having been brought from India by the Neo 
Pythagoreans. Preserved by Boethius, the use of the*e 
figures with an abacus of traced columns became known to 
the more learned monkish scholars of the middle ages, and 
gradually came into use in scientific calculations, the Greek 
cypher being supplied and the columns at length dispensed 
with. For generations, probably for centuries, the signs and 
the use of them would be confined to the learned, as little 
understood by the common people as are now the signs of 
e zodiac H is in the popularizing of them rather than 
1 7 L ' mtl '. oductlon that we probably feel the value of Arab 
and Moorish influences. 
The interesting question still remains as to the date at 
which they first began to make their appearance in litera- 
e, to be used for inscribing dates, and, last of all, to take 
their place m the transactions of the counting-house and 
