You are here

Mathematical Treasure: Reisch’s Margarita Philosophica

Author(s): 
Cynthia J. Huffman (Pittsburg State University)

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.

Title page of 1517 edition of Gregor Reisch's Margarita philosophica.

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.

Frontispiece for 1517 edition of Gregor Reisch’s Margarita Philosophica.
Grammar chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica. Logic chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica.

Rhetoric chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica.
Arithmetic chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica. Geometry chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica.
GraMusic chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica. Astronomy chapter title page from 1517 edition of Gregor Reisch’s Margarita Philosophica.

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.

Illustration of counting board from 1517 edition of Gregor Reisch’s Margarita Philosophica.

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 \( \pi \).

Geometry example from 1517 edition of Gregor Reisch’s Margarita Philosophica. Geometry example from 1517 edition of Gregor Reisch’s Margarita Philosophica.

Ratio of circle diameter to perimeter in 1517 edition of Gregor Reisch’s Margarita Philosophica.

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

Ptolemy with Astronomy in 1517 edition of Gregor Reisch’s Margarita Philosophica.

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 images may be downloaded and used for the purposes of research, teaching, and private study, provided the Linda Hall Library of Science, Engineering & Technology is credited as the source. For other uses, check out the LHL Image Rights and Reproductions policy.

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

Cynthia J. Huffman (Pittsburg State University), "Mathematical Treasure: Reisch’s Margarita Philosophica ," Convergence (September 2019)

Dummy View - NOT TO BE DELETED

Mathematical Treasures: The Linda Hall Library