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Mathematical Treasure: John Wallis’s Operum Mathematicorum Pars Prima

Sidney J. Kolpas (Delaware County Community College)

Englishman John Wallis (1616–1703) worked off and on as a chaplain—despite being independently wealthy from the age of 27—but he is best known today for his accomplishments in mathematics. During the English Civil War, he did cryptography on behalf of the Parliamentarians. Oliver Cromwell appointed Wallis to the Savilian Chair of Geometry at Oxford University in 1649, where he remained until his death and through numerous regime changes. He contributed ideas necessary for the invention of calculus, including solutions for specific infinite series, notation such as ∞ to represent infinity and 1/∞ to represent an infinitesimal quantity, and an analytic treatment of conic sections.

Although he had already published two major works in his time at Oxford, De Sectionibus Conicis (1655) and Arithmetica Infinitorum (1656), it was only in 1657 that Wallis published his inaugural address as Savilian Professor. The volume also contained Mathesis Universalis, written versions of his lectures, and a dialogue on proportions. The binding and title page of the copy owned by the author appear below.

Cover/binding of 1657 Operum Mathematicorum Pars Prima by John Wallis.

Title page of 1657 Operum Mathematicorum Pars Prima by John Wallis.

This copy of the book was owned by Euclid Speidell (d. 1702; see the inscription below: Euclid Speidell 23 May 1692).

The autograph of Euclid Speidell in the author's copy of Operum Mathematicorum Pars Prima.

The son of an English mathematics teacher who was an early adopter of logarithms, Speidell also offered his services as a teacher as well as worked as a customs official. His most famous original book was the 1688 Logarithmotechnia, or, The making of numbers called logarithms to twenty five places from a geometrical figure.

Title page of Euclid Speidell's 1688 Logarithmotechnia.

A full digitization of Speidell's work is available in the Internet Archive, which also has a full digitization of Operum Mathematicorum. In addition to the works linked above, Wallis’s 1676 Latin translations of Archimedes’ Sand Reckoner and On the Measurement of a Circle, 1685 Treatise of Algebra, and collected works (second copy) can be found in Mathematical Treasures.

Index to Mathematical Treasures


Sidney J. Kolpas (Delaware County Community College), "Mathematical Treasure: John Wallis’s Operum Mathematicorum Pars Prima ," Convergence (June 2022)