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Mathematical Treasure: Waymouth's 'Jewell of Artes'

Frank J. Swetz (The Pennsylvania State University)

In a December 2007 news release, the Beinecke Rare Book and Manuscript Library at Yale University announced its 2008 exhibit, “The Reckoner’s Art: Reading and Writing Mathematics in Early Modern England,” as follows.

In 1604, George Waymouth gave the new King of England a present. An explorer and navigator, Waymouth undoubtedly hoped to win the King’s patronage and support for his plans for a new voyage to the American coast. The present was the manuscript of a book, the “Jewell of Artes,” in which Waymouth had drawn sumptuous illustrations of the mathematical instruments in use on the battlefields of Europe, in navigation at sea, and in the houses of interested practitioners of the new science in England and abroad. Waymouth’s “Jewell” showcased the novelty, beauty, and tremendous utility of the mathematical arts in the early modern period. Although the work was never published, the manuscript was bound in the royal arms, and in 1605 Waymouth received funding for his next and last voyage to the east coast of America. Waymouth’s “Jewell” is among the many books and manuscripts in the exhibition “The Reckoner’s Art,” on view at the Beinecke Library from 16 January to February 2008.

Galley division

In the page from the "Jewell" shown above, Waymouth gave three examples of galley division. In each case, the results of the computation were checked by the use of the inverse operation of multiplication. Thus, for the first problem, we see 522785777625368 divided by 1234567, with the result 423456789.  The quotient was then multiplied by the divisor to obtain the original dividend. The use of large numbers, and particularly numbers composed of consecutive digits, was typical in textbook problems of this time. (Photo courtesy of Beinecke Library, Yale University; see restrictions on use described below.)

apothecary weights

The page above, decorated by the figure of a unicorn, provided practice with apothecary weights. (Photo courtesy of Beinecke Library, Yale University; see restrictions on use described below.)


This highly illustrated page presented a problem concerning the siege of a castle. A variety of artillery were to be used in the bombardment: 4 cannon, 8 demy-cannon, 6 culverins, 9 demy-culverins, and 5 sackers. They were to fire 10 volleys to breach the castle wall. Each required different loads of powder to fire. The question asked, ‘What is the total amount of powder needed to seize the castle?’ (Photo courtesy of Beinecke Library, Yale University; see restrictions on use described below.)

George Waymouth (c. 1585-1612) was an English ship captain and explorer, and a student of mathematics, navigation, and ship-building. In 1602 he led an unsuccessful voyage in search of the Northwest Passage, exploring the area between Greenland and Labrador. After returning to England he wrote “The Jewell of Artes,” a manuscript on navigation, shipbuilding, and fortification presented to King James I. Waymouth was then hired to lead an expedition to explore the area of “Virginia” that Bartholomew Gosnold (1572-1607) had explored (on and near what is now Cape Cod, Massachusetts), but he and his party were blown north to Monhegan in what is now Maine. They spent a month exploring the Penobscot area, just missing Samuel Champlain. They then kidnapped five natives and returned with them to England. Official chronicler James Rosier (1575-1635) wrote an account of the expedition titled "A True Relation of the most prosperous voyage made this present yeere 1605." The Penobscot Marine Museum produced a film and exhibit about the expedition in 2005.

The three images above are provided courtesy of the Beinecke Rare Book and Manuscript Library, Yale University. You may use them in your classroom, but 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 these images available to a larger audience.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Waymouth's 'Jewell of Artes'," Convergence (November 2012), DOI:10.4169/loci003951