Thomas Harriot's \textit{Artis analyticae praxis}. An English translation with commentary
The book is a tribute to the new knowledge about the role of Thomas Harriot role in the changes of algebra in the 16th and the early 17th century. Overshadowed in its own time by the work of Descartes Harriot's contributions remained unrecognised. The authors argue that the contribution of Harriot's book ``Artis analyticae praxis'' to the ongoing revolution in mathematics of the late Renaissance justifies the publication of an English translation to make Harriot's ideas more accessible to modern readers. Besides Harriot's life and reputation the authors deal in the introduction with the historical background of his work mentioning the debt of Harriot to Viète and the points where the former surpassed the latter, the contents and the achievements of the ``Praxis'' plus its significance. The authors point out Harriot's notation as especially revolutionary. They characterize his algebra as the first one which was totally expressed in a purely symbolic notation. Furthermore, they found out that Harriot's algebra was associated with rigour comparable to the rigour in Euclidean geometry. Harriot listed some definitions which determine the rules for the manipulation of the algebraic quantities at the beginning of his work. The book is based on the dissertation of the authors. One of them, Goulding, was responsible for the translation, and the other, Seltman, for the commentaries. The detailed commentaries cover a quarter of the extent of Harriot's treatise. The commentaries are supplemented first by a comparative table of polynomial equations with numerical coefficients as solved by Viète, as well as by Harriot in his manuscripts and in his ``Praxis'', second, by a table of textual emendations, and third, by an appendix which gives further information about the manuscripts of Harriot's algebraic work in the British Library as well as a version of Harriot's algebra edited by Torperley. The book is closed by a selected bibliography and a combined name and subject index to the introduction and the commentary.
scientific article; zbMATH DE number 5134074