tic which Nagl first published
in 1890.[496] The latter work, preserved to us in a parchment manuscript of
seventy-seven leaves, contains a curious mixture of Roman and [.g]ob[=a]r
numerals, the former for expressing large results, the latter for practical
calculation. These [.g]ob[=a]r "caracteres" include the sipos (zero),
[Symbol], of which, however, Radulph did not know the full significance;
showing that at the opening of the twelfth century the system was still
uncertain in its status in the church schools of central France.

At the same time the words _algorismus_ and _cifra_ were coming into
general use even in non-mathematical literature. Jordan [497] cites
numerous instances of such use from the works of Alanus ab Insulis[498]
(Alain de Lille), Gautier de Coincy (1177-1236), and others.

Another contributor to arithmetic during this interesting period was a
prominent Spanish Jew called variously John of Luna, John of Seville,
Johannes Hispalensis, Johannes Toletanus, and Johannes Hispanensis de
Luna.[499] {125} His date is rather closely fixed by the fact that he
dedicated a work to Raimund who was archbishop of Toledo between 1130 and
1150.[500] His interests were chiefly in the translation of Arabic works,
especially such as bore upon the Aristotelian philosophy. From the
standpoint of arithmetic, however, the chief interest centers about a
manuscript entitled _Joannis Hispalensis liber Algorismi de Practica
Arismetrice_ which Boncompagni found in what is now the _Bibliotheque
nationale_ at Paris. Although this distinctly lays claim to being
Al-Khow[=a]razm[=i]'s work,[501] the evidence is altogether against the
statement,[502] but the book is quite as valuable, since it represents the
knowledge of the time in which it was written. It relates to the operations
with integers and sexagesimal fractions, including roots, and contains no
applications.[503]

Contemporary with John of Luna, and also living in Toledo, was Gherard of
Cremona,[504] who has sometimes been identified, but erroneously, with
Gernardus,[505] the {126} author of a work on algorism. He was a physician,
an astronomer, and a mathematician, translating from the Arabic both in
Italy and in Spain. In arithmetic he was influential in spreading the ideas
of algorism.

Four Englishmen--Adelhard of Bath (c. 1130), Robert of Chester (Robertus
Cestrensis, c. 1143), William Shelley, and Daniel Morley (1180)--are
known[506] to have journeyed to Spain