Exceptional mercantile manuscript

[Mercantile manuscript]. Libro d'Abbaco.

€ 165.000,00

Abacus books, of which the present manuscript is an excellent example, were compilations of practical and recreational mathematics, of geometrical questions and of algebra, used by merchants in Renaissance northern Italy (Folkerts, XII, 1), a tradition which flourished after Leonardo Fibonacci's "Liber abbaci" (1202/28) (Van Egmond, 6; Folkerts, XII, 1). Some three hundred extant copies were surveyed by Van Egmond in 1980, who does not record this manuscript; only two other unrecorded examples had surfaced in commerce since then (Sotheby's, 1999; and one in private hands).

While Fibonacci was responsible for first introducing Hindu-Arabic numerals to Western Europe, abacus books, which derive from the first Italian translations of his Liber abbaci, "brought the Arabic system to Western Europe and made it a part of our common heritage" (Van Egmond, 32). Several personalities of the Renaissance were educated in the abacus tradition, including Leonardo da Vinci and Luca Pacioli, whose famous mathematical "Summa" was printed in Venice in 1494, while the renowned painter and mathematician Piero della Francesca wrote his own abacus treatise (Van Egmond, 13; Folkerts, XII, 1).

While books of this kind very rarely credited sources, this specimen includes the name of Euclid (f. 126r), the only authority Fibonacci mentioned in his treatise. Moreover, some interesting material makes this manuscript stand apart: a section (f. 110r) dedicated to the first four perfect numbers, of which Fibonacci had only mentioned the first three (Sigler, II, 25), and a so-called "magic square" (f. 8v). Magic squares were introduced to late medieval Europe through the Arabic tradition and were strongly associated with astrology; examples in Latin Europe before the 1500s, especially showing no errors, are scarce (Comes, 2016).

The structure of this manuscript closely follows the one given by Van Egmond when describing the standard content of abacus books (21-26). The main corpus of the manuscript occupies ff. 1r-141v, 183r-184r (incipit: "Nomen Algus vocabitur"); ff. 189r-190r contain a table of contents, written in red ink. The various sections comprise: ff. 1v-12r: arithmetic operations; 12v-19v: conversion of different units of measure; 19v-26r: aspect ratio; 26r-29r: currency exchanges; 29r-45v: fractional numbers; 46r-71v: division of capital and interests between partners; 71v-82r: barter; 82v-86v: calculation of interest; 87r-101v: silver lineage; 102-105v: lineage of gold; 106r-113v: recreational exercises ("de numero esvariati"); 114r-125r: so-called position rule, for the solution of 1st degree equations; 126r-141v: geometrical definitions and problems. On f. 143v a different scribe has inserted, under the date 1470, a concise instruction for the production of woollen fabrics, outlining the various investment items and specifying the use of English wool as the most valuable.