Thomas Harriot's Artis Analyticae Praxis

The Practice of the Analytic Art (translation).- Preface to Analysts.- Definitions.- Section One.- Section Two.- Section Three.- Section Four.- Section Five.- Section Six.- Numerical Exegesis.- Rules for Guidance.- Commentary.- Comparative Table of Equations Solved.- Textual Emendations.

Thomas Harriot's "Artis analyticae praxis" is an essential work in the history of algebra. This is the first English translation of his work, first published in Latin in 1631. It has recently become clear that Harriot's editor substantially rearranged the work, and omitted sections beyond his comprehension. Basing their work on manuscripts in the British Library, Pentworth House, and Lambeth Palace, the commentary contains some of Harriot's most novel and advanced mathematics, very little of which has been published in the past. Commentary included with this translation relates to corresponding pages in the manuscript papers, enabling exploration of Harriot's novel and advanced mathematics. This publication provides the basis for a reassessment of the development of algebra.

From the reviews:

"The Praxis contains Harriot's most significant contribution to the theory of equations, the discovery that polynomials can be constructed as products of linear, or sometimes quadratic, factors. ... The notes that follow the translation (70 pages) offer a great deal of fine textual detail. They also contain some beautiful reproductions of the original manuscripts ... . Seltman and Goulding's translation is a welcome addition to this growing body of work." (Jackie Stedall, MathDL, September, 2007)

"The book under review is a useful English translation of a mathematically 'clean' copy ... by Robert Goulding that is enriched by a competent commentary by Muriel Seltman: it makes the mathematical content accessible to the modern reader. To that end, Harriot's notation has rightly been modernized. ... The reader finds a comparative table of equations solved, a list of textual emendations, additional information about the Harriot papers (kept in the British Library), and a select bibliography." (Eberhard Knobloch, Mathematical Reviews, Issue 2008 j)

"Seltman's and Goulding's Introduction, Commentary, and Tables are all interesting and useful. ... The book contains just three reproductions of Harriot's original work, each a full-page photograph of one of Harriot's manuscript sheets on algebra. These are interesting and give the reader a good sense of what it is like to read Harriot's work in the manuscripts themselves."(Janet Beery, British Society for the History of Mathematics, Vol. 24 March, 2009)

From the reviews:



"The Praxis contains Harriot's most significant contribution to the theory of equations, the discovery that polynomials can be constructed as products of linear, or sometimes quadratic, factors. ... The notes that follow the translation (70 pages) offer a great deal of fine textual detail. They also contain some beautiful reproductions of the original manuscripts ... . Seltman and Goulding's translation is a welcome addition to this growing body of work." (Jackie Stedall, MathDL, September, 2007)

"The book under review is a useful English translation of a mathematically 'clean' copy ... by Robert Goulding that is enriched by a competent commentary by Muriel Seltman: it makes the mathematical content accessible to the modern reader. To that end, Harriot's notation has rightly been modernized. ... The reader finds a comparative table of equations solved, a list of textual emendations, additional information about the Harriot papers (kept in the British Library), and a select bibliography." (Eberhard Knobloch, Mathematical Reviews, Issue 2008 j)

"Seltman's and Goulding's Introduction, Commentary, and Tables are all interesting and useful. ... The book contains just three reproductions of Harriot's original work, each a full-page photograph of one of Harriot's manuscript sheets on algebra. These are interesting and give the reader a good sense of what it is like to read Harriot's work in the manuscripts themselves."(Janet Beery, British Society for the History of Mathematics, Vol. 24 March, 2009)