Abstract: The year that saw the first publication of Oughtred's Clavis also saw the publication of an algebra of a completely different kind, the Artis analyticae praxis (1631), compiled posthumously from the papers of Thomas Harriot (c.1560-1621). Since Harriot never published any of his scientific or mathematical findings in his lifetime, it has been difficult to establish his true place in the intellectual history of the period or to judge the extent of his mathematical influence on those who came after him. Wallis believed that Harriot should have been more acclaimed than he was, and devoted no less than a quarter of A treatise of algebra to extolling him. Furthermore, he repeatedly accused Descartes of having made use of Harriot's algebra without acknowledgement, and thereby inflamed a controversy that has never been satisfactorily settled.

Keywords: Thomas Harriot, Wallis, A treatise of algebra, Artis analyticae praxis, Treatise on equations, Praxis, Descartes,