© 2016

Leibniz on the Parallel Postulate and the Foundations of Geometry

The Unpublished Manuscripts


Part of the Science Networks. Historical Studies book series (SNHS, volume 51)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Leibniz on the Parallel Postulate and the Foundations of Geometry

    1. Front Matter
      Pages 1-1
    2. Vincenzo De Risi
      Pages 3-6
    3. Vincenzo De Risi
      Pages 103-121
  3. Leibniz’ Texts on Parallel Lines

    1. Front Matter
      Pages 123-123
    2. Vincenzo De Risi
      Pages 124-179
  4. Back Matter
    Pages 181-195

About this book


This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.

This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.


Leibniz history of epistemology history of geometry non-Euclidean geometry theory of parallel lines

Authors and affiliations

  1. 1.MPI for the History of ScienceBerlinGermany

Bibliographic information

  • Book Title Leibniz on the Parallel Postulate and the Foundations of Geometry
  • Book Subtitle The Unpublished Manuscripts
  • Authors Vincenzo De Risi
  • Series Title Science Networks. Historical Studies
  • Series Abbreviated Title Science Networks Hist.Studies(Birkhäuser)
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-19862-0
  • Softcover ISBN 978-3-319-79288-0
  • eBook ISBN 978-3-319-19863-7
  • Series ISSN 1421-6329
  • Series E-ISSN 2296-6080
  • Edition Number 1
  • Number of Pages VIII, 195
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics History of Mathematical Sciences
    History of Philosophy
  • Buy this book on publisher's site
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“By bringing together all of the known relevant Leibnizian writings on the subject, De Risi has rendered a very valuable service to Leibniz scholars and historians of seventeenth-century mathematics. This volume is indispensable for anyone interested in the development of non-Euclidean geometry or the mathematical thought of Leibniz.” (Douglas M. Jesseph, Isis, Vol. 108 (3), September, 2017)