© 2015

Seventeenth-Century Indivisibles Revisited

  • Vincent Jullien


  • The first exhaustive study on the indivisibles

  • A mathematical, historical and philosophical approach of the intrusion and use of infinity in geometry during the XVIIth century

  • Written by a team of well known scholars, after long common work and discussions

  • Explains in what sense we can think about infinite, atom, continuity, indivisible in mathematics


Part of the Science Networks. Historical Studies book series (SNHS, volume 49)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Kirsti Andersen, Enrico Giusti, Vincent Jullien
    Pages 31-55
  3. Patricia Radelet-de Grave
    Pages 57-86
  4. Vincent Jullien
    Pages 87-103
  5. Tiziana Bascelli
    Pages 105-136
  6. Vincent Jullien
    Pages 165-175
  7. Vincent Jullien
    Pages 177-210
  8. Dominique Descotes
    Pages 211-248
  9. Dominique Descotes
    Pages 249-273
  10. Antoni Malet
    Pages 275-284
  11. M. Rosa Massa Esteve
    Pages 285-306
  12. Antoni Malet, Marco Panza
    Pages 307-346
  13. Antoni Malet, Marco Panza
    Pages 365-390
  14. Vincent Jullien
    Pages 451-457
  15. Jean Celeyrette
    Pages 459-463

About this book


The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign.

These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus.

The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it.

The list of authors involved in indivisibles´ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.


epistemology indivisibles modern science

Editors and affiliations

  • Vincent Jullien
    • 1
  1. 1.Département de PhilosophieUniversité de NantesNantesFrance

Bibliographic information

  • Book Title Seventeenth-Century Indivisibles Revisited
  • Editors Vincent Jullien
  • Series Title Science Networks. Historical Studies
  • Series Abbreviated Title Science Networks Hist.Studies(Birkhäuser)
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-00130-2
  • Softcover ISBN 978-3-319-37495-6
  • eBook ISBN 978-3-319-00131-9
  • Series ISSN 1421-6329
  • Series E-ISSN 2296-6080
  • Edition Number 1
  • Number of Pages VI, 499
  • Number of Illustrations 161 b/w illustrations, 70 illustrations in colour
  • Topics History of Mathematical Sciences
  • Buy this book on publisher's site
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“This book, which contains contributions by twelve historians of mathematics, provides a fascinating insight into the background and the rise of new ways of handling indivisibles in the 17th century. … The editor, Vincent Jullien, has given the book a unity that is praiseworthy and (almost) indivisible.” (William R. Shea, Mathematical Reviews, May, 2016)