The book is the first English translation of John Wallis’s Arithmetica Infinitorum (1656), a key text on the seventeenth-century development of the calculus. Accompanied with annotations and an introductory essay, the translation makes Wallis’s work fully available for the first time to modern readers. It shows how Wallis drew on some of the most important new ideas from the preceding twenty years, and took them forward to lay the foundations on which Newton was to build. Above all, the book displays the crucial mid-seventeenth-century shift from geometry to arithmetic and algebra as the primary language of mathematics.