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Mathematical Treasure: The Journal of Michael of Rhodes

Frank J. Swetz (The Pennsylvania State University)

Michael of Rhodes (ca.1380-1445) was a mariner who spent his career serving the Venetian Republic. Through his ability, he rose from the position of oarsman to an armiraio, the commander of several ships. As was the custom of the time, many individuals involved in trade and business kept logs of important information. Michael maintained a log or diary of his activities considered valuable for reference. Michael’s manuscript (1434) provides insights into the Venetian practices of the period: trade, navigation, mathematics, calendrical reckoning, astrology, and shipbuilding. The Dibner Institute of Science and Technology, in conjunction with the Massachusetts Institute of Technology, conducted a research project on the manuscript’s contents. This project resulted in a website and the publication of a three-volume study in which a complete facsimile, translation, and analysis of the manuscript is presented. First discovered in 1966, the manuscript is bound as a book and contains over 200 pages.

Pepper was the most important commodity imported from the East into Europe during the Middle Ages and Renaissance eras. A page from the manuscript discusses the mathematical solution for a problem involving a shipment of the spice:

If a load of pepper weighing 400 lbs. is worth 49 ½ ducats, [how many ducats for] 315 lbs.?

The answer, using “The Rule of Three,” is found to be 38 ducats, 23 denarii, and 17 piccolos.

On the following page, Michael demonstrated other methods for solving this problem.

Michael thought so highly of the power of “The Rule of Three,” which not only solves mercantile problems but “problems of all things in the world,” that he devoted a page to discussing this rule.

Michael then discussed the new techniques of algebra, which he mistakenly attributed to an Arabic scholar “Alzebran.” At the bottom of this page, he listed the six algebraic problems that can be solved. Using our modern symbolism, these problems are the equations: \(x=a,\) \(x^2=a,\) \(x^2=x,\) \(x^2+x=a,\) \(x^2+a=x,\) and \(x+a=x^2.\)


For further reading:

Alan Stahl, Pamela Long, and David McGee. The Book of Michael of Rhodes: A Fifteenth-Century Maritime Manuscript (2009). The MIT Press.

  • Volume I: Facsimile
  • Volume II: Transcription and Translation
  • Volume III: Studies

The information and images above are presented with the cooperation of the Dibner Institute of Science and Technology and MIT Press.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Journal of Michael of Rhodes," Convergence (June 2017)