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© 2007

Thomas Harriot's Artis Analyticae Praxis

An English Translation with Commentary

Book

Part of the Sources and Studies in the History of Mathematics book series (SHMP)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-16
  3. Pages 19-22
  4. Pages 23-29
  5. Pages 31-34
  6. Pages 35-48
  7. Pages 49-69
  8. Pages 71-93
  9. Pages 95-103
  10. Pages 105-130
  11. Pages 131-182
  12. Pages 183-208
  13. Pages 209-262
  14. Pages 271-278
  15. Back Matter
    Pages 279-302

About this book

Introduction

The present work is the first ever English translation of the original text of Thomas Harriot's Artis Analyticae Praxis, first published in 1631 in Latin. Thomas Harriot's Praxis is an essential work in the history of algebra. Even though Harriot's contemporary, Viete, was among the first to use literal symbols to stand for known and unknown quantities, it was Harriott who took the crucial step of creating an entirely symbolic algebra. This allowed reasoning to be reduced to a quasi-mechanical manipulation of symbols. Although Harriot's algebra was still limited in scope (he insisted, for example, on strict homogeneity, so only terms of the same powers could be added or equated to one another), it is recognizably modern.

While Harriot's book was highly influential in the development of analysis in England before Newton, it has recently become clear that the posthumously published Praxis contains only an incomplete account of Harriot's achievement: his editor substantially rearranged the work before publishing it, and omitted sections that were apparently beyond comprehension, such as negative and complex roots of equations.

The commentary included with this translation attempts to restore the Praxis to the state of Harrios draft. The authors based their work on manuscripts in the British Library, Pentworth House, and Lambeth Palace, and the commentary explores some of Harriot's most novel and advanced mathematics, very little of which has been published in the past. This publication will become an important contribution to the history of mathematics, and it will provide the basis for a reassessment of the development of algebra.

 

 

The present work is the first ever English translation of the original text of Thomas Harriot’s Artis Analyticae Praxis, first published in 1631 in Latin. Thomas Harriot’s Praxis is an essential work in the history of algebra. Even though Harriot’s contemporary, Viete, was among the first to use literal symbols to stand for known and unknown quantities, it was Harriott who took the crucial step of creating an entirely symbolic algebra. This allowed reasoning to be reduced to a quasi-mechanical manipulation of symbols. Although Harriot’s algebra was still limited in scope (he insisted, for example, on strict homogeneity, so only terms of the same powers could be added or equated to one another), it is recognizably modern.

While Harriot’s book was highly influential in the development of analysis in England before Newton, it has recently become clear that the posthumously published Praxis contains only an incomplete account of Harriot’s achievement: his editor substantially rearranged the work before publishing it, and omitted sections that were apparently beyond comprehension, such as negative and complex roots of equations.

The commentary included with this translation relates the contents of the Praxis to the corresponding pages in his manuscript papers, which enables much of Harriot's most novel and advanced mathematics to be explored. This publication will become an important contribution to the history of mathematics, and it will provide the basis for a reassessment of the development of algebra.

Keywords

History of Mathematics Isaac Newton algebra equation mathematics

Authors and affiliations

  1. 1.Greenwich UniversitySE9 2UGGreenwichUK
  2. 2.Program of Liberal StudiesNotre Dame UniversityNotre DameUSA

Bibliographic information

  • Book Title Thomas Harriot's Artis Analyticae Praxis
  • Book Subtitle An English Translation with Commentary
  • Authors Muriel Seltman
    Robert Goulding
  • Series Title Sources and Studies in the History of Mathematics
  • DOI https://doi.org/10.1007/978-0-387-49512-5
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-49511-8
  • Softcover ISBN 978-1-4939-0201-9
  • eBook ISBN 978-0-387-49512-5
  • Edition Number 1
  • Number of Pages VIII, 299
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics History of Mathematical Sciences
    Algebra
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

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)