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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:


These images are presented through the courtesy of the Dartmouth College Libraries, Hanover, New Hampshire.

Index to Mathematical Treasures


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