Mathematical Treasure: Reisch’s Margarita Philosophica

Written by Gregor Reisch, Margarita philosophica cu[m] additionibus nouis (Pearl of Wisdom or Philosophical Pearl) was a popular 16th-century encyclopedia/textbook. It was first published in 1503; at least 15 editions appeared. The title page below is from an edition published in 1517, which, according to the subtitle, is the fourth revision. Images from another edition can also be found in Convergence.

The book is written in the form of a dialogue between a student and teacher, and it contains many woodcuts to illustrate the content. There are twelve chapters in the book, with each of the first seven devoted to one of the disciplines from the trivium (grammar, logic, and rhetoric) and quadrivium (arithmetic, geometry, music, and astronomy). Below is the frontispiece which shows these 7 liberal arts, followed by the woodcuts for the openings of each of these seven chapters.

The image below shows a counting board followed by an explanation and examples of how to represent numbers on the board. The word “denarius” is used for the markers. (A denarius was a silver coin equivalent to the value of “10 asses”.) Graphics in the right-hand margin illustrate the examples. The first illustrates 15, with a marker on the 10 line and another in the space between 1 and 10, representing 5. The second graphic demonstrates that if there are two markers in a space (“in spacio aliquo duos denarius”), they can be replaced by one marker on the next line up (“linea immediate superioze”). The third graphic shows 30 (“triginta”) with 3 markers on the 10 line, while the final graphic shows 259 as 200 + 50 + 5 + 4.

The next three pages are from the chapter on Geometry, and looking at the third one, we see that Reisch was using \( \frac{22}{7} \) for \( \pi \).

The woodcut below shows Ptolemy, wearing a crown, with Astronomy.

All of the above images came from a book that can be viewed in person at the Rare Book Room of the Linda Hall Library in Kansas City. The call number is AE25 .R44 1517. A complete digital scan of a 1508 edition of Margarita Philosophica is on GoogleBooks.

Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The Linda Hall Library makes available all existing digital images from its collection that are in the public domain to be used for any purpose under the terms of a Creative Commons License CC by 4.0. The Library’s preferred credit line for all use is: “Courtesy of The Linda Hall Library of Science, Engineering & Technology.”

References

Ashworth, William B. Scientist of the Day – Gregor Reisch. Linda Hall Library, May 9, 2017. https://www.lindahall.org/gregor-reisch/.

Smith, David Eugene. Rara Arithmetica. 1908. Reprint; Cosimo Classics, 2007, pp. 82–84.

Index to Mathematical Treasures