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Angling may be said to be so like mathematics that it can never be fully learned.
The Compleat Angler, 1653.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript
A Fair Was Serious Business
To us, fairs are pretty much just amusements. But in Europe during the Middle Ages and Renaissance, they were serious business affairs— the major engines of economic growth.
Most towns had had a market day since ancient times— a certain day of the week set aside for buying and selling produce and other goods. But in the 1100s, the most ambitious cities in Europe began to host annual international trade fairs lasting one to three weeks, often coinciding with holy days and pilgrimages. These fairs drew buyers and sellers— in both cases mostly merchants and middlemen— from much greater distances than a market day: at a single fair, merchants from Italy, France, and the Low Countries might be found selling their wares. The most important commodities were fabrics. They ranged from coarser cloths of flax or wool to fine woven silks, a specialty of Lyon in southern France. The Lyon Fair was established by Charles VII in 1420, only a few years or so before the Pamiers text was written.
Figure 11. The lower floor of a restored medieval fondaco in Provins, northern France, which was rented by merchants and craftsmen during an annual international fair. Beginning in the 1100s, the annual fairs held in Provins and five other towns in the Champagne and Brie regions helped circulate textiles, spices, and other fine goods between northern Italy, Catalonia, and southern France, on the one hand, and northern Europe on the other. A fondaco was a combination of an inn, warehouse, and factory. (Image: Provins Office of Tourism.)
To read more about the fairs of Europe, see (Verlinden 1963, pp. 119-153).
In the following problem, two merchants arriving at a fair with some raw wool are charged a duty, or import tax, at some set rate that we aren’t told. The collected duties would be forwarded to the local or national government, helping to enrich them.
Note that the duties, and any “change” returned, could be paid either with liras or with wool itself. There are two unknowns that are requested, which can be found from the two linear relationships that are involved.
Fibonacci’s Liber Abbaci, mentioned earlier, included three consecutive maritime import problems very similar to the fair problem above. Instead of duties on wool in liras, these involve, respectively, freight charges on wool in soldi, customs on precious stones in bezants, and customs on fish in denari (see Sigler 2002, pp. 395-397).
The poor fellow in the next problem is a disgrace to the merchandising profession, since he is spending money almost as fast as he is earning it!
The author of the manuscript showed how to solve this problem by double false position. Of course, it can also be solved by inversion (“working backward”) or by algebra.
Schwartz, Randy K., "'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript," Loci (July 2012), DOI: 10.4169/loci003888