Stedall’s translation gives us access once again to this fascinating book, and her introduction helps us understand its place in history. Wallis’s subtitle gives a good summary of what the book is about: ‘A New Method of Inquiring into the Quadrature of Curves, and other more difficult mathematical problems’. here is her translation of John Wallis’s famous Arithmetic of Infinitesimals (Arithmetica Infinitorum, first published in 1656). One can sense the anticipation and excitement Newton must have felt upon first reading the work.' (James J. She has rendered a valuable service to the mathematical community with this English translation of Arithmetica infintorum. Her expertise with the subject is readily apparent. 'The author has done a superb job with the translation and accompanying introduction. She also supplies a glossary, a bibliography, and an index, while figures and tables are reproduced as facsimiles from the original edition.' (Christoph J. Jacqueline Anne Stedall, has already accomplished important research on John Wallis and his mathematics and thus is ideally qualified for both the translation and a scholarly introduction and explanatory notes. in his Arithmetica infinitorum (Arithmetic of Infinites), he extended traditional algebra of finite numbers and symbols. 'John Wallis (1616-1703) was the most influential mathematician in England. Her two previous books, A Discourse Concerning Algebra: English Algebra to 1685 (2002) and The Greate Invention of Algebra: Thomas Harriot’s Treatise on Equations (2003), were both published by Oxford University Press. She has written a number of papers exploring the history of algebra, particularly the algebra of the sixteenth and seventeenth centuries.

Stedall is a Junior Research Fellow at Queen's University. It is this sense of watching new and significant ideas force their way slowly and sometimes painfully into existence that makes the Arithmetica Infinitorum such a relevant text even now for students and historians of mathematics alike.ĭr J.A. Newton was to take up Wallis’s work and transform it into mathematics that has become part of the mainstream, but in Wallis’s text we see what we think of as modern mathematics still struggling to emerge. To the modern reader, the Arithmetica Infinitorum reveals much that is of historical and mathematical interest, not least the mid seventeenth-century tension between classical geometry on the one hand, and arithmetic and algebra on the other. He handled them in his own way, and the resulting method of quadrature, based on the summation of indivisible or infinitesimal quantities, was a crucial step towards the development of a fully fledged integral calculus some ten years later. In both books, Wallis drew on ideas originally developed in France, Italy, and the Netherlands: analytic geometry and the method of indivisibles. He was then a relative newcomer to mathematics, and largely self-taught, but in his first few years at Oxford he produced his two most significant works: De sectionibus conicis and Arithmetica infinitorum. John Wallis was appointed Savilian Professor of Geometry at Oxford University in 1649.

The arithmetic of infinitesimals