# Mathematical Treasure: Archimedes, as Translated by John Wallis

Author(s):
Frank J. Swetz (Pennsylvania State University)

Figure 1. Title page of a book containing translations by John Wallis of two of Archimedes' most important works

The book whose title page is shown above contains translations of ArchimedesSand Reckoner and On the Measurement of a Circle from Greek into Latin by John Wallis, then Savilian Professor of Geometry at Oxford University. The unique feature of this book is that it contains the original Greek text opposite its Latin version, as shown below.

Figure 2. Proposition II of On the Measurement of a Circle, in both Greek and Latin.

On the Measurement of a Circle is very brief, containing only three propositions. In Proposition II, shown above in Figure 2, Archimedes asserted that the area of a circle is to the square on its diameter as 11 is to 14. Proposition I states that the area of a circle is equal to that of a right triangle in which one of the legs has length equal to that of the radius of the circle and the other leg has length equal to that of the circumference of the circle. Proposition III compares the length of a circle’s circumference with that of its diameter. Archimedes’ result, his best surviving approximation of $\pi,$ was that the ratio of circumference to diameter is less than 3 1/7 and greater than 3 10/71.

These two images are presented courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania. You may use them in your classroom and/or for private study; for all other purposes, please obtain permission from Archives and Special Collections, Waidner-Spahr Library, Dickinson College, Carlisle, PA.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Archimedes, as Translated by John Wallis," Convergence (February 2014)