A large discourse concerning algebra: John Wallis's 1685 Treatise of algebra

Stedall, Jacqueline Anne (2000). A large discourse concerning algebra: John Wallis's 1685 Treatise of algebra. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000e2e0

Abstract

A treatise of algebra historical and practical (London 1685) by John Wallis (1616-1703) was the first full length history of algebra. In four hundred pages Wallis explored the development of algebra from its appearances in Classical, Islamic and medieval cultures to the modern forms that had evolved by the end of the seventeenth century. Wallis dwelt especially on the work of his countrymen and contemporaries, Oughtred, Harriot, Pell, Brouncker and Newton, and on his own contribution to the emergence of algebra as the common language of mathematics.

This thesis explores why and how A treatise of algebra was written, and the sources Wallis used. It begins by analysing Wallis's account of mathematical learning in medieval England, never previously investigated. In his researches on the origins and spread of the numeral system Wallis was at his best as a historian, and initiated many modern historiographical techniques. His summary of algebra in Renaissance Europe was less detailed, but for Wallis this part of the story set the scene for the English flowering that was to be his main theme.

The influence of Oughtred's Clavis on Wallis and his contemporaries, and Wallis's efforts to promote the book, are explored in detail. Wallis's controversial account of Harriot's algebra is also examined and it is argued that it was better founded than has sometimes been supposed and that Wallis had direct access to Harriot's algebra through Pell. Many other chapters of A treatise of algebra contain mathematics that can be linked or traced to Pell, a hitherto unsuspected secret of the book.

The later chapters of the thesis, like the final part of A treatise of algebra, explore Wallis's Arithmetica infinitorum and the work which arose from it up to Newton's foundation of modern analysis, and include a discussion of Brouncker's treatment of the number challenges set by Fermat. The thesis ends with a summary of contemporary and later reactions to A treatise of algebra and an assessment of Wallis's view of algebra and its history.

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