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Manuscript treatise on practical arithmetic, in It

An abbacus manuscript, in Italian. Decorated manuscript on vellum. [Italy], 1419.

Signed and dated by the scribe, Joh[ann]es de Strasburg, 18 April 1419. 47 leaves: [19 2-48 56 68]. Possibly incomplete at beginning. Written in brown ink in a small upright cursive, single column, up to 51 lines (variable), section headings and paragraph marks in red, marginal initial capitals and table headings with red capital strokes. Catchwords in center of lower margins on final versos. Ten pages with geometrical diagrams (circles and triangles). Signed and dated at end "facto e chompiuto adi 18 April 1419 / [in red] Qui scripsit scribat et sember cu[m] d[o]m[i]ni vivat / Amen solamen Steyg der blin uff den lamen / Joh[ann]es de Strasburg". Modern black goatskin. Condition: First leaf wrinkled and with large stain obscuring one to two words each from 7 lines on recto, occasional small stains Provenance: "Piero (?)Strozzo," contemporary ownership inscription at end (of a member of the Florentine banking family?); several illegible or partly eradicated early inscriptions on final verso. -- Later manuscript notes with geometrical diagrams on 5 leaves at end. a very fine example of a "trattato dell' abbaco" or italian pedagogic manual of commercial mathematics, accounting and geometry. Beginning in the thirteenth century the rise of international trade and banking companies in the Italian city-states prompted the formation of vernacular schools in which commercial mathematics, accounting and writing were taught to sons of the merchant class. This was a radical departure from the humanist educational curriculum, which, if it included mathematics at all, was limited to classical or medieval Latin mathematics - algorisms for determining moveable feast days in the church calendar, or Euclidean geometry. Known as abbaco, this practical course of mathematics was recorded and transmitted in manuscript books, of which several hundred are known to survive, all in Italian, and the vast majority in institutional collections. Long thought to be abbreviated vernacular versions of the Latin Liber abbaci of the 13th-century mathematician Leonardo Fibonacci, an encyclopaedia of practical mathematics, these abbaco manuscripts, of which the earliest dated example is from 1290, may in fact derive from a more widespread culture of commercial mathematics, already known by Fibonacci, and probably flourishing in Provence and/or Catalonia before reaching Italy. From the fourteenth to the sixteenth century so-called abbaco schools flourished throughout northern Italy, in different forms, with the Florentine version being a separate two-year course of study administered to boys aged 11 to 14, while other towns integrated the abbaco teaching into the vernacular schools. The present manuscript opens with problems of addition, multiplication, and division, including fractions. ("Abbaco books. did not usually explain addition and subtraction, probably leaving this to the teacher to do" - Grendler, p. 313). It proceeds quickly to "the heart of abbaco. solving the mathematical problems of business. The ordinary abbaco book might contain four hundred problems and their solutions, of which the largest group by far were business problems (op. cit., p. 314). This manuscript is no exception. The many problems, most presented in a literary, story-telling form that is typical of the genre, relate to commercial arrangements, payment of merchandise, commercial partnerships, measurements and weights, money exchange, etc. Several schematic tables show how to calculate distances; others show different accounting methods or methods of calculating interest. A few other problems are of the "recreational" sort described by Grendler, designed to exercise purely mathematical skills. The final section, illustrated with neat diagrams, is devoted to practical geometry. Like all abbaco manuscripts, this one contains a trove of information on late medieval Italian commercial practices. The fact that the manuscript is signed and dated adds to its interest and documentary value. The concluding jingle of the scribe Johann from Strassburg is written in an unusual mixture of Italian and German. Written in the lower margins in a seventeenth- or eighteenth-century Italian hand, the later notes testify to the manuscript's continued use two or three centuries after its production. Abbaco manuscripts appear very rarely on the market. Cf. Paul F. Grendler, Schooling in Renaissance Italy (Baltimore & London 1989), chapter 11, "Learning Merchant Skills"; Warren Van Egmond, Practical Mathematics in the Italian Renaissance: a Catalog of Italian Abbacus Manuscripts and Printed Books to 1600 (Florence 1981). Cf. Paul F. Grendler, Schooling in Renaissance Italy (Baltimore & London 1989), chapter 11, "Learning Merchant Skills"; Warren Van Egmond, Practical Mathematics in the Italian Renaissance: a Catalog of Italian Abbacus Manuscripts and Printed Books to 1600 (Florence 1981).