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## Details

Genre/Form: | Early works to 1800 Ouvrages avant 1800 |
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Named Person: | John Wallis; John Wallis |

Material Type: | Internet resource |

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
John Wallis; Jacqueline A Stedall |

ISBN: | 0387207090 9780387207094 1441919228 9781441919229 |

OCLC Number: | 53937684 |

Description: | xxxiv, 192 p. : ill. ; 25 cm. |

Contents: | Frontispiece: Title page of the Arithmetica infinitorum 1656 -- Introduction: The arithmetic of infinitesimals by Jacqueline A. Stedall -- An advertisement of the forthcoming Arithmetica infinitorum, Easter 1655 -- To the most distinguished and worthy gentleman and most skilled mathematician, Dr. William Oughtred, Rector of the church of Aldbury in the Country of Surrey -- To the most respected gentleman Doctor William Oughtred, most widely famed amongst mathematicians, by John Wallis, Savilian Professor of Geometry at Oxford -- Doctor William Oughtred: A response to the preceding letter (after the book went to press). In which he makes it known what he thought of that method -- The arithmetic of infinitesimals or a new method of inquiring into the quadrature of curves, and other more difficult mathematical problems. |

Series Title: | Sources and studies in the history of mathematics and physical sciences. |

Other Titles: | Arithmetica infinitorum. |

Responsibility: | translated from Latin to English with an introduction by Jacqueline A. Stedall. |

More information: |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "John Wallis (1616-1703) was the most influential mathematician in England ... . in his Arithmetica infinitorum (Arithmetic of Infinites), he extended traditional algebra of finite numbers and symbols ... . The translator, Dr. Jacqueline Anne Stedall, has already accomplished important research on John Wallis and his mathematics and thus is ideally qualified for both the translation and a scholarly introduction and explanatory notes. She also supplies a glossary, a bibliography, and an index, while figures and tables are reproduced as facsimiles from the original edition." (Christoph J. Scriba, SIAM Review, Vol. 47 (2), 2005) "The author has done a superb job with the translation and accompanying introduction. Her expertise with the subject is readily apparent. She has rendered a valuable service to the mathematical community with this English translation of Arithmetica infintorum. One can sense the anticipation and excitement Newton must have felt upon first reading the work." (James J. Tattersall, Mathematical Reviews, 2005e) "Jackie Stedall is amazing. ... here is her translation of John Wallis's famous Arithmetic of Infinitesimals (Arithmetica Infinitorum, first published in 1656). Thank you, Jackie; please never stop. Wallis's subtitle gives a good summary of what the book is about: 'A New Method of Inquiring into the Quadrature of Curves, and other more difficult mathematical problems'. ... Stedall's translation gives us access once again to this fascinating book, and her introduction helps us understand its place in history. Not to be missed." (Fernando Q. Gouvea, MathDL, December, 2004) "This is an English translation of John Wallis's famous Arithmetica infinitorum of 1656, a milestone in the prehistory of the calculus, whose influence on Newton was important. The translation preceded by a historical introduction recalling Wallis mathematical contributions and the genesis of his most famous book. ... It is a very useful addition to the literature about the history of calculus." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 12 (2), 2005) "This book is famed above all for its infinite product for p, which duly appears among the final 'propositions'; and for this reason it is often regarded as a study of the quadrature of the circle. In fact it has a broader remit ... relationships between arithmetic and geometry, and between discrete and continuous magnitude, especially in connection with quantitative properties of various classical curves, surfaces and solids. ... This volume belongs to considerable recent efforts on English mathematics during the 17th century." (I. Grattan-Guinness, The Mathematical Gazette, Vol. 89 (515), 2005) "To the modern reader the 'Arithmetica infinitorum' reveals much that is of historical and mathematical interest, not least the mid seventeenth-century tension between classical geometry on the one hand, and arithmetic and algebra on the other. Newton was to take up Wallis's work and transform it into mathematics that has become part of the mainstream, but in Wallis's text we see what we think of as modern mathematics still struggling to emerge. ... a relevant text even now for students and historians of mathematics alike." (Zentralblatt fur Didaktik der Mathematik, January, 2005) Read more...

*User-contributed reviews*