them the more zealously.) At Vicenza in 1209, for example, there were Bohemians, Poles, Frenchmen, Burgundians, Germans, and Spaniards, not to speak of representatives of divers towns of Italy; and what was true there was also true of other intellectual centers. The knowledge could not fail to spread, therefore, and as a matter of fact we find numerous bits of evidence that this was the case. Although the bankers of Florence were forbidden to use these numerals in 1299, and the statutes of the university of Padua required stationers to keep the price lists of books "non per cifras, sed per literas claros,"[[538]] the numerals really made much headway from about 1275 on.
It was, however, rather exceptional for the common people of Germany to use the Arabic numerals before the sixteenth century, a good witness to this fact being the popular almanacs. Calendars of 1457-1496[[539]] have generally the Roman numerals, while Köbel's calendar of 1518 gives the Arabic forms as subordinate to the Roman. In the register of the Kreuzschule at Dresden the Roman forms were used even until 1539.
While not minimizing the importance of the scientific work of Leonardo of Pisa, we may note that the more popular treatises by Alexander de Villa Dei (c. 1240 A.D.) and John of Halifax (Sacrobosco, c. 1250 A.D.) were much more widely used, and doubtless contributed more to the spread of the numerals among the common people.
The Carmen de Algorismo[[540]] of Alexander de Villa Dei was written in verse, as indeed were many other textbooks of that time. That it was widely used is evidenced by the large number of manuscripts[[541]] extant in European libraries. Sacrobosco's Algorismus,[[542]] in which some lines from the Carmen are quoted, enjoyed a wide popularity as a textbook for university instruction.[[543]] The work was evidently written with this end in view, as numerous commentaries by university lecturers are found. Probably the most widely used of these was that of Petrus de Dacia[[544]] written in 1291. These works throw an interesting light upon the method of instruction in mathematics in use in the universities from the thirteenth even to the sixteenth century. Evidently the text was first read and copied by students.[[545]] Following this came line by line an exposition of the text, such as is given in Petrus de Dacia's commentary.
Sacrobosco's work is of interest also because it was probably due to the extended use of this work that the
term Arabic numerals became common. In two places there is mention of the inventors of this system. In the introduction it is stated that this science of reckoning was due to a philosopher named Algus, whence the name algorismus,[[546]] and in the section on numeration reference is made to the Arabs as the inventors of this science.[[547]] While some of the commentators, Petrus de Dacia[[548]] among them, knew of the Hindu origin, most of them undoubtedly took the text as it stood; and so the Arabs were credited with the invention of the system.
The first definite trace that we have of an algorism in the French language is found in a manuscript written about 1275.[[549]] This interesting leaf, for the part on algorism consists of a single folio, was noticed by the Abbé Lebœuf as early as 1741,[[550]] and by Daunou in 1824.[[551]] It then seems to have been lost in the multitude of Paris manuscripts; for although Chasles[[552]] relates his vain search for it, it was not rediscovered until 1882. In that year M. Ch. Henry found it, and to his care we owe our knowledge of the interesting manuscript. The work is anonymous and is devoted almost entirely to geometry, only
two pages (one folio) relating to arithmetic. In these the forms of the numerals are given, and a very brief statement as to the operations, it being evident that the writer himself had only the slightest understanding of the subject.
Once the new system was known in France, even thus superficially, it would be passed across the Channel to England. Higden,[[553]] writing soon after the opening of the fourteenth century, speaks of the French influence at that time and for some generations preceding:[[554]] "For two hundred years children in scole, agenst the usage and manir of all other nations beeth compelled for to leave hire own language, and for to construe hir lessons and hire thynges in Frensche.... Gentilmen children beeth taught to speke Frensche from the tyme that they bith rokked in hir cradell; and uplondissche men will likne himself to gentylmen, and fondeth with greet besynesse for to speke Frensche."