Thomas Harriot's Artis Analyticae Praxis

1. Front Matter

   Pages i-viii

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2. Introduction

   Pages 1-16

3. The Practice of the Analytic Art (translation)

   Pages 17-17

4. Preface to Analysts

   Pages 19-22

5. Definitions

   Pages 23-29

6. Section One

   Pages 31-34

7. Section Two

   Pages 35-48

8. Section Three

   Pages 49-69

9. Section Four

   Pages 71-93

10. Section Five

    Pages 95-103

11. Section Six

    Pages 105-130

12. Numerical Exegesis

    Pages 131-182

13. Rules for Guidance

    Pages 183-208

14. Commentary

    Pages 209-262

15. Comparative Table of Equations Solved

    Pages 263-269

16. Textual Emendations

    Pages 271-278

17. Back Matter

    Pages 279-302

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The Artis analyticae praxis was published in 1631 in Latin. Until relatively - cently, an English edition would not have been considered necessary since most of the people who might have been expected to be interested in the text would have been able to read it in Latin. That is no longer the case and it is ?tting that an English edition should be published. It is also the case that a considerable proportion of the readership of the present volume will not be professional mathematicians, so we have tried to produce a translation that makes the mathematical content accessible to the modern reader. This is not because the algebra is intrinsically dif?cult but because it is not the kind of mathematics which is a part of today’s secondary school curriculum. A further problem lies in the fact that the book in the form in which it was - blished in 1631 may very well not conform to Harriot’s intentions for the publi- tion of his mathematical manuscript papers. This is why the book is accompanied by a Commentary which attempts to compare it with the appropriate passages in the surviving manuscript papers. The present work is a translation of the original text and not intended as a facsimile. The original has well over 300 errors (there may very well be more) and we have listed these at the end. In the interests of mathematical accessibility we have tried to produce a mathematically “clean” copy.

• History of Mathematics
• Isaac Newton
• algebra
• equation
• mathematics

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)

• Greenwich University, SE9 2UG, Greenwich, UK

  Muriel Seltman

• Program of Liberal Studies, Notre Dame University, Notre Dame, USA

  Robert Goulding

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