After Gerbert's death, little by little the scholars of Europe came to know
the new figures, chiefly through the introduction of Arab learning. The
Dark Ages had passed, although arithmetic did not find another advocate as
prominent as Gerbert for two centuries. Speaking of this great revival,
Raoul Glaber[493] (985-c. 1046), a monk of the great Benedictine abbey of
Cluny, of the eleventh century, says: "It was as though the world had
arisen and tossed aside the worn-out garments of ancient time, and wished
to apparel itself in a white robe of churches." And with this activity in
religion came a corresponding interest in other lines. Algorisms began to
appear, and knowledge from the outside world found {124} interested
listeners. Another Raoul, or Radulph, to whom we have referred as Radulph
of Laon,[494] a teacher in the cloister school of his city, and the brother
of Anselm of Laon[495] the celebrated theologian, wrote a treatise on
music, extant but unpublished, and an arithmetic which Nagl first published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]
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