Jacopo da Firenze and the beginning of Italian vernacular algebra
Historia Mathematica, vol 33 , no. 1 , pp. 4-42 (2006)
In 1307, one Jacobus de Florentia located at that moment in Montpellier wrote a Tractatus algorismi containing a chapter on algebra. This earliest extant algebra in a European vernacular is noteworthy in several respects: 1.For decades, every writing on algebra in Italy or Montpellier which we know about seems to have used it – whence we may conclude that neither Italy nor Montpellier harboured an earlier vernacular tradition for such interest. 2.It has nothing in common with the Latin precursors – whence we may conclude that it represents an independent inspiration from the Islamic world, furthermore not pointing toward what we may (for lack of a better term)call the “high” Arabic tradition (al-Khwarizmi, Abu Kamil,al-Khayyami), that tradition which is reflected in Latin translations.
3.It contains no single Arabism – whence we may conclude that the Arabic inspiration was not direct but mediated through a Romance-speaking area. The obvious guess (supported by supplementary evidence) is that this area was Catalonia, even though the Catalan-Provencal tradition is only known to us from considerably later sources. Further inspection of Jacopo’s algebra and other slightly later Italian writings of enigmatic origin suggest that the earliest beginnings of formal operations (on schemes and on fractions involving cossic expressions) may also have come from the same area.