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Mathematical Treasure: Works of Boethius

Frank J. Swetz (The Pennsylvania State University)

Boethius (ca. 480–524) was a high government official, writer, and translator. He was born in Rome in the Byzantine Empire and died in Pavia in the Gothic Empire, both in what is now Italy. He translated works of philosophy and mathematics from Greek to Latin and contributed to monastic education's famous quadrivium of arithmetic, geometry, astronomy, and music theory.

Boethius’s work in arithmetic was greatly influenced by the Pythagorean arithmetic of Nicomachus of Gerasa (fl. 100). Here in a 10th-century German manuscript (Harley 3595), we find the first page (folio 1) of Boethius' De institutione arithmetica:

First page of De institutione arithmetica by Boethius, 10th century

Appended to the manuscript above (Harley 3595) is an 11th-century copy of a translation by Boethius of Euclid’s Elements entitled Libri duo geometriae:

Page from 11th century copy of Libri duo geometriae by Boethius

A 12th-century manuscript (Harley MS 549) contains Book 1 of Boethius’ De institutione arithmetica. On folio 14 is a chart of multiplication facts:

Folio 14 from a 12th century manuscript of De institutione arithmetica by Boethius

Boethius’ De institutione arithmetica also appears in a manuscript from 12th-century France (Harley MS 1737). Folio 21v of this manuscript supplies an example of the author’s use of number diagrams:

Folio 21v from a 12th century manuscript of De institutione arithmetica by Boethius

The images above were obtained through the courtesy of the British Library. Further investigation of the images and their source can be obtained through the online services of the British Library. Where possible, manuscript reference numbers are given for the item being viewed.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Works of Boethius," Convergence (January 2020)