Page:Popular Science Monthly Volume 81.djvu/616

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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:[1]

PSM V81 D616 Evolution of numeric symbols.png

After a while some of the monkish mathematicians learned of the symbol for nothing. O'Creat in the twelfth century employed it in three forms, o, ō, τ. 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 Roman characters with it, the Roman characters then acquiring a place value. Thus, when O'Creat writes 1200, he puts it I.II.τ.τ.; for 1089 he uses I. O. VIII. IX. At the beginning of the twelfth century Radulph of Laon used a mixture of Gobar and Roman 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 arithmetic, 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.

  1. From Smith and Karpinski, "The Hindu-Arabic Numerals."