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Preface to A Personal Record.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript
Background: The Abbaco Tradition
The Pamiers text was designed for use in commercial training schools, which flourished in this part of Europe from the 1200s through the 1500s.
These institutions were known as schools of algorisme (“algorithm”) in French, and of abbaco or abaco in Italian (a word with the general sense of “calculation”). They arose first in northern Italy, whose economy was the most vibrant in Europe during this period (Spiesser 2003, pp. 34-35). A banker and official in Florence, Italy, reported that in 1345 at least 1,000 boys in that city alone were receiving instruction in abbaco and algorismo (Biggs 2009, p. 73). Such schools also began to appear in neighboring southern France, and a few in Catalonia (the area around Barcelona, Spain) and coastal North Africa. These four regions of the western Mediterranean had extensive trade and cultural ties with one another at the time, so it isn’t surprising that they shared methods of practical mathematics and its instruction (Høyrup 2006).
Over 400 of the abbaco and algorisme works have survived. The common ancestor of many of them is Liber Abbaci (1202) by Leonardo Fibonacci of Pisa, Italy. He was only a boy, he reports, when his father, a customs official representing Pisan merchants at their trading enclave of Bugia, in what is now Algeria, brought him to the customs house there to be taught Hindu-Arabic numerals and arithmetic (Sigler 2002, pp. 3, 15). Based on place value, the Arab-style calculations could be carried out on an abacus or with pen and paper, in either case using efficient, step-by-step procedures called algorithms. Fibonacci’s book, written in Latin, introduced this new way of reckoning to European scholars. Then the techniques spread with the aid of texts, like that of Pamiers, that were written in languages more accessible than Latin. Maryvonne Spiesser (University of Toulouse), who has extensively studied the abbaco and algorisme treatises of the region, writes that the Pamiers manuscript “founded the tradition of commercial arithmetics in southern France” (2002, p. 297).
Figure 2. A 19th-century statue of Leonardo Fibonacci in his likely birthplace of Pisa, Italy. The statue, about 15 feet tall, is part of the Fortezza Camp Santo at Giardino Scotto, a fortified garden off a road called Lungarno Fibonacci along the Arno River. (Image made in 2002 by Gordon Wilson, Emeritus Professor of English, Schoolcraft College.)
Figure 3. A master teaches his pupils in this drawing from an illuminated manuscript version of Filippo Calandri’s Trattato di Arithmetica, an abbaco treatise originally printed in Florence in 1491. (Source: Biblioteca Riccardiana (Florence, Italy), Ricc. 2669, page 111 verso. Image used by permission; further reproduction is prohibited.)
Typically, such a book would give instruction in these topics:
Some of the abbaco texts (but not that of Pamiers) included discussions of more advanced or specialized topics, such as these:
Schwartz, Randy K., "'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript," Loci (July 2012), DOI: 10.4169/loci003888