6io THE POPULAR SCIENCE MONTHLY 



even an independent origin ; but it is now as certain as such things can 

 be, that the passage is a medieval interpolation, and was not written 

 by Boethius. The subject is exceedingly obscure, but there is reason 

 for thinking that these characters, apices, as they were called, were 

 used in Europe some time before the interpolation was made. 



However this may be, there was apparently among the Christian 

 peoples of Europe no widespread use of the ten symbols as they were 

 used by the Hindus, until the Christians borrowed them from the 

 Saracens of Spain. The date of their introduction from Spain cannot 

 be determined, but it is fairly certain that Gerbert, who as Sylvester II. 

 was Pope from 999 to 1003, brought them back from the Saracens 

 among whom he had studied. He seems to have described the nine 

 Gobar numerals without the zero :* 



After a while some of the monkish mathematicians learned of the sym- 

 bol for nothing. O'Creat in the twelfth century employed it in three 

 forms, o, 5, r. At this time when the new numerals are used the whole 

 subject is confused. Sometimes the Hindu symbols are used without 

 the zero; sometimes the Eoman characters with it, the Eoman char- 

 acters then acquiring a place value. Thus, when O'Creat writes 1200, 

 he puts it I.II.t.t. ; for 1089 he uses I. 0. VIII. IX. At the beginning 

 of the twelfth century Eadulph of Laon used a mixture of Gobar and 

 Eoman characters. About the same time an unknown German scribe 

 wrote them in a manuscript now in the Hof-Bibliothek in Vienna. 



The mathematician who had most to do with spreading the Hindu 

 numerals in Europe was Leonardo Fibonacci, a merchant of Pisa, who 

 was born in 1175. In 1202 he completed his "Liber Abaci," or arith- 

 metic, rewriting it in 1228. He it was who, when employing the Hindu 

 numerals, first clearly explained their use. The progress was furthered 

 when Alexander de Villa Dei about 1240, and Johannes de Sacrobosco 

 about 1250, wrote popular treatises. Of Sacrobosco's "Algorismus" 

 there remain now nearly one hundred manuscripts. It was due to him 

 particularly that the Hindu signs came to be known in Europe as Arabic 

 numerals. 



* From Smith and Karpinski, ' ' The Hindu-Arabic Numerals. ' ' 



