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Mathematical Treasure: Gerbert's Geometry

Frank J. Swetz (The Pennsylvania State University)

The French scholar and cleric Gerbert of Aurillac (945–1003), who later became Pope Sylvester II, acquired a background in geometry by studying Arabic sources in Spain while he was abbot of the monastery of Bobbio in northern Italy. Gerbert’s Isagoge Geometriae became the first medieval European work that included practical geometric applications in its scope. The images presented here are of a 12th-century Austrian manuscript of Gerbert’s Isagoge and of a correspondence with Adelbold.

The first page of the text opens: “Here begins Gerbert’s geometry…”

Folio 5r introduces the topic of measurement.

Folio 33r discusses the obtaining of unknown distance measurements employing a concept of “angle”.

Here is a page from a letter from Gerbert to Adelbold (Adelbaldus), the Bishop of Utrecht, discussing the correct formula for the area of a triangle (folios 51v-52v). In an article entitled “Gerbert’s Letter to Adelbold” by G. A. Miller reprinted in From Five Fingers to Infinity (pp. 224-227) and again in The European Mathematical Awakening (pp. 9–12), this letter can be read in its entirety.

Here is a discussion of the area of an isosceles triangle and the relationship of a circle’s circumference to its diameter.

The images above were obtained through the kind cooperation of the University of Pennsylvania Libraries, The Lawrence J. Schoenberg Collection of Late and Early Renaissance Manuscripts, Kislak Center for Special Collections, Rare Books and Manuscripts. Lawrence Schoenberg, a successful businessman and collector of early scientific manuscripts, donated his collection to the University. The item shown here is fully digitized and may be consulted and copied in its entirety with due credit provided, including its reference number, LJS 194.

Related Article in Convergence:

Betty Mayfield, Gerbert d'Aurillac and the March of Spain: A Convergence of Cultures, MAA Convergence (2006).


Frank Swetz (ed.), The European Mathematical Awakening: A Journey Through the History of Mathematics from 1000 to 1800. Mineola, NY: Dover, 2013.

Frank Swetz, From Five Fingers to Infinity: A Journey Through the History of Mathematics. Chicago: Open Court, 1994.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Gerbert's Geometry," Convergence (January 2019)