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first book of his Geonietiy, 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, which 

 are curiously like those now in use among 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, De JSfunieroruin Divisione, by Gerbert, a 

 Benedictine monk, subsequently raised to the papal chair 

 (in 999) as Sylvester 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 

 the Saracens ; but it appears from the arguments of M. 

 Chasles and M. Henri Martin [to whose arguments the paper 

 referred in detail], that this was a mistake, and it seems on 

 the whole most probable that the abacus vrith nine figures 

 has 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 these 

 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 

 the zodiac. It is in the popularizing of them rather than 

 their introduction 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- 

 ture, to be used for inscribing dates, and, last of all, to take 

 their place in the transactions of the counting-house and 



