Three Manuscripts

Abstract

Whatever the reason, nobody seems to have taken interest in the treatise before Warren Van Egmond inspected it in the mid-seventies during the preparation of his global survey of Italian Renaissance manuscripts concerned with practical mathematics [1976; 1980]. By then, the autonomous existence of the abbacus tradition in the fourteenth and fifteenth centuries was well-established; but Van Egmond noticed that the manuscript which Karpinski had examined (Vatican MS Vat. Lat. 4826, henceforth V) could be dated by watermarks to the mid-fifteenth century, and that the algebra chapter (and certain other matters) were missing from two other manuscripts which also claim to contain Jacopo’s Tractatus algorismi (Florence, Riccardiana MS 2236, undated;^[5] henceforth F; and Milan, Trivulziana MS 90, c. 1410; henceforth M)^[6]. Because M can be dated by watermarks to c. 1410, some 40 years before V (yet still a whole century after 1307), and since V contains rules for the fourth degree not present in the algebra of Paolo Gherardi’s Libro di ragioni from 1328, Van Egmond decided (personal communication) “that the algebra section of Vat.Lat. 4826 [was] a late 14th-century algebra text that [had] been inserted into a copy of Jacopo’s early 14th-century algorism by a mid-15th-century copyist”.

Van Egmond’s dating [1980: 148] is misleading, since it is merely the date of Jacopo’s original (which is given in all three manuscripts), not that of the manuscript.

A transcription of F was made by Annalisa Simi in [1995]. A critical edition of F and M by the late Jean Cassinet and Annalisa Simi was almost finished in 1999, but it got stuck with the publisher and is not going to appear (Maryvonne Spiesser, personal communication), for which reason I give a transcription of M with indication of all not merely orthographic variants with respect to F in the Appendix. As pointed out by Karpinski [1929a: 170], F had already been mentioned by Boncompagni in 1883 and by B. Lami, librarian of the Biblioteca Riccardiana, in 1754; however, Karpinski had not seen F and therefore could not know that it differs from V on important points.