Mathematical Treasure: Problems from the Zibaldone da Canal

Author(s):
Frank J. Swetz (The Pennsylvania State University)

The pages shown below are folios 16v and 17r of the Zibaldone da Canal (Canal’s Notebook). The Canals were a prominent Venetian merchant family. Their Notebook is a collection of varied information of importance to a 14th century merchant. While its origins can be traced back to the beginning of that century, the book itself is probably an updated copy of an earlier work and was most likely compiled later in the same century.

The volume begins with a listing of arithmetic exercises and their solutions. It appears that most of these problems were adapted from Leonardo of Pisa’s Liber Abaci (1202). After the arithmetic problems can be found an eclectic collection of practical information, including lists of weights and measures, literary extracts, lists of spices, prayers and charms, receipts, and even medical tables giving the best times for bloodletting.

The pages shown above contain three problems: numbered 47, 48 and 49 in the listing, now given in translation:

16v.  Make me this calculation: from Venice to Ancona is 200 miles. A ship is at Ancona and wants to go to Venice, and it goes in 30 days, and at Venice there is another ship that is going to Ancona, and it goes in 40 days. I ask you, if they both leave at the same time, each to go on its voyage, in how many days will the ships come together?

17r.  Two problems.

Make me this calculation: from Venice to Rome is 200 miles. At Rome is a courier, who wants to come to Venice, and he comes to Venice in 20 days. And a courier in Venice who wants to go to Rome, and he goes from Venice to Rome in 30 days. In how many days will these couriers come together? [The illustration shows the couriers having a snack, probably celebrating their encounter.]

Make me this calculation: a tree is underground, 1/2 and 1/4, and above ground there remains 20 braccia.  I ask you how long is the whole tree?

Correct solution procedures and answers are provided with the problems.

The Zibaldone da Canal has been translated fully and analyzed in detail by John E. Dotson in the following book, which is reviewed here and available for purchase here:

Dotson, John E. (editor and translator), Merchant Culture in Fourteenth-Century Venice: The Zibaldone da Canal, Medieval and Renaissance Texts and Studies, Binghamton, New York, 1994.

The image above is provided courtesy of the Beinecke Rare Book and Manuscript Library, Yale University. You may use it in your classroom; all other uses require permission from the Beinecke Library. The Mathematical Association of America is pleased to cooperate with the Beinecke Library and Yale University to make this image available to a larger audience.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Problems from the [i]Zibaldone da Canal[/i]," Convergence (August 2012), DOI:10.4169/loci003905