A Treatise of Algebra by John Wallis

This is the title page of the Treatise of Algebra (1685), by John Wallis (1616-1703).  This is probably the first attempt at a history of the subject of algebra, presented in the context of a text on the subject.   There is a discussion of Wallis's text in Jacqueline Stedall, A Discourse Concerning Algebra: English Algebra to 1685 (Oxford:  Oxford University Press, 2002).

A portrait of John Wallis from this text.

Among the most famous parts of this treatise is Wallis's discussion of the work of Thomas Harriot, especially his contention that René Descartes plagiarized Harriot's symbolization procedure in algebra. This discussion is summarized on the initial pages (3, 4, and 5) of Wallis's preface.  After giving a list of Harriot's discoveries in algebra, Wallis notes that there is "scarce anything in (pure) algebra in Descartes which was not before in Harriot."   Most historians did not believe Wallis, because Harriot's published work did not include a lot of what Wallis stated. But since the recent discoveries of Harriot's algebra manuscripts (newly published by Jacqueline Stedall), there is certainly some reason to believe that Wallis was correct. There is certainly some similarity between Harriot's manuscripts and Descartes' algebraic work in his Geometry.