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Mathematical Treasure: Van Ceulen on the Circle

Frank J. Swetz (The Pennsylvania State University)

Ludolph Van Ceulen (1540–1610) was a German-born mathematician who lived and worked in the Netherlands. Self-educated in mathematics, he taught the subject and also served as a fencing master. In 1596, Van Ceulen published a book in Dutch whose English title would be On the Circle. In this work, he found the value of π accurately to twenty decimal places, the most accurate value in existence at the time. The Dutch mathematician Willebrord Snell (1580–1626) translated Van Ceulen’s works into Latin so that it would reach a wider audience. Here is the title page of Snell’s 1619 Latin rendition of Van Ceulen’s notes on algebra and On the Circle.

On pages 18 and 19, Van Ceulen explained the operation of division involving irrational expressions.

On pages 164 and 165 are problems involving circles and triangles from Van Ceulen's posthumous Surdorum quadraticorum arithmetica, which was bound together with On the Circle.


These images are presented through the courtesy of the Dartmouth College Libraries, Hanover, New Hampshire. Images from the Linda Hall Library's copy of these books are found here and here.

Index to Mathematical Treasures


Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Van Ceulen on the Circle," Convergence (October 2019)