in the twelfth century for the
purpose of studying mathematics and Arabic. Adelhard of Bath made
translations from Arabic into Latin of Al-Khow[=a]razm[=i]'s astronomical
tables[507] and of Euclid's Elements,[508] while Robert of Chester is known
as the translator of Al-Khow[=a]razm[=i]'s algebra.[509] There is no reason
to doubt that all of these men, and others, were familiar with the numerals
which the Arabs were using.

The earliest trace we have of computation with Hindu numerals in Germany is
in an Algorismus of 1143, now in the Hofbibliothek in Vienna.[510] It is
bound in with a {127} _Computus_ by the same author and bearing the date
given. It contains chapters "De additione," "De diminutione," "De
mediatione," "De divisione," and part of a chapter on multiplication. The
numerals are in the usual medieval forms except the 2 which, as will be
seen from the illustration,[511] is somewhat different, and the 3, which
takes the peculiar shape [Symbol], a form characteristic of the twelfth
century.

It was about the same time that the _Sefer ha-Mispar_,[512] the Book of
Number, appeared in the Hebrew language. The author, Rabbi Abraham ibn Meir
ibn Ezra,[513] was born in Toledo (c. 1092). In 1139 he went to Egypt,
Palestine, and the Orient, spending also some years in Italy. Later he
lived in southern France and in England. He died in 1167. The probability
is that he acquired his knowledge of the Hindu arithmetic[514] in his
native town of Toledo, but it is also likely that the knowledge of other
systems which he acquired on travels increased his appreciation of this
one. We have mentioned the fact that he used the first letters of the
Hebrew alphabet, [Hebrew: A B G D H W Z CH T`], for the numerals 9 8 7 6 5
4 3 2 1, and a circle for the zero. The quotation in the note given below
shows that he knew of the Hindu origin; but in his manuscript, although he
set down the Hindu forms, he used the above nine Hebrew letters with place
value for all computations.

* * * * *

{128}

CHAPTER VIII

THE SPREAD OF THE NUMERALS IN EUROPE

Of all the medieval writers, probably the one most influential in
introducing the new numerals to the scholars of Europe was Leonardo
Fibonacci, of Pisa.[515] This remarkable man, the most noteworthy
mathematical genius of the Middle Ages, was born at Pisa about 1175.[516]

The traveler of to-day may cross the Via Fibonacci on his way to the Campo
Santo,