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Classic Texts in the Sciences

Euclid Vindicated from Every Blemish

Edited and Annotated by Vincenzo De Risi. Translated by G.B. Halsted and L. Allegri

Authors: Saccheri, Gerolamo

Editors: De Risi, Vincenzo (Ed.)

  • First complete edition of Saccheri's Euclides Vindicatus in English
  • The classical English translation by Halsted has been corrected and enriched by the important Book Two of the work (on the theory of proportions) that was missing in all the preceding editions
  • Provides a historical introduction to the birth of non-euclidean geometry
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About this book

This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work.

Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the time. In particular, the Parallel Postulate had escaped demonstration since the first attempts at it in the Classical Age, and several books on the topic were published in the Early Modern Age. At the same time, the theory of proportion was the most important mathematical tool of the Galilean School in its pursuit of the mathematization of nature. Saccheri's attempt to prove the Parallel Postulate is today considered the most important breakthrough in geometry in the 18th century, as he was able to develop for hundreds of pages and dozens of theorems a system in geometry that denied the truth of the postulate (in the attempt to find a contradiction). This can be regarded as the first system of non-Euclidean geometry. Its later developments by Lambert, Bolyai, Lobachevsky and Gauss eventually opened the way to contemporary geometry.

Occupying a unique position in the literature of mathematical history, Euclid Vindicated from Every Blemish will be of high interest to historians of mathematics as well as historians of philosophy interested in the development of non-Euclidean geometries.

Reviews

From the book reviews:

“This is the first complete English edition of Saccheri’s Euclides vindicatus of 1733, and, with 55 pages of introduction, 99 pages of notes, 11 pages of bibliography, the definitive one. … The material in the introduction and the notes is of great interest to both historians of mathematics and to mathematicians … .” (Victor V. Pambuccian, zbMATH, Vol. 1303, 2015)

Table of contents (4 chapters)

  • Introduction

    Saccheri, Gerolamo

    Pages 1-58

  • Euclid Vindicated from Every Blemish: Book One

    Saccheri, Gerolamo

    Pages 70-191

  • Euclid Vindicated from Every Blemish: Book Two

    Saccheri, Gerolamo

    Pages 192-245

  • Notes to the text

    Saccheri, Gerolamo

    Pages 249-347

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-05966-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-05965-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-319-37791-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Euclid Vindicated from Every Blemish
Book Subtitle
Edited and Annotated by Vincenzo De Risi. Translated by G.B. Halsted and L. Allegri
Authors
Editors
  • Vincenzo De Risi
Translated by
Allegri, L., Halsted, G.B.
Series Title
Classic Texts in the Sciences
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05966-2
DOI
10.1007/978-3-319-05966-2
Hardcover ISBN
978-3-319-05965-5
Softcover ISBN
978-3-319-37791-9
Series ISSN
2365-9963
Edition Number
1
Number of Pages
VII, 381
Number of Illustrations and Tables
83 b/w illustrations, 6 illustrations in colour
Topics