Table of contents

  1. Front Matter
    Pages i-ix
  2. The Manuscript

    1. Front Matter
      Pages 1-1
    2. P. J. Federico
      Pages 3-4
    3. P. J. Federico
      Pages 5-7
    4. P. J. Federico
      Pages 8-29
    5. P. J. Federico
      Pages 30-32
  3. Solid Geometry: The Elements of Solids

    1. Front Matter
      Pages 33-33
    2. P. J. Federico
      Pages 35-42
    3. P. J. Federico
      Pages 43-58
    4. P. J. Federico
      Pages 59-64
    5. P. J. Federico
      Pages 65-71
    6. P. J. Federico
      Pages 72-80
  4. Number Theory: Polyhedral Numbers

    1. Front Matter
      Pages 81-81
    2. P. J. Federico
      Pages 83-91
    3. P. J. Federico
      Pages 92-115
    4. P. J. Federico
      Pages 116-120
  5. Back Matter
    Pages 121-145

About this book


The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published). So many contradictory statements regarding a Descartes manuscript and Euler, by various mathematicians and historians of mathematics, were encountered that it was decided to write a separate study of the relevant part of the Descartes manuscript on polyhedra. The contemplated short paper grew in size, as only a detailed treatment could be of any value. After it was completed it became evident that the entire manuscript should be treated and the work grew some more. The result presented here is, I hope, a complete, accurate, and fair treatment of the entire manuscript. While some views and conclusions are expressed, this is only done with the facts before the reader, who may draw his or her own conclusions. I would like to express my appreciation to Professors H. S. M. Coxeter, Branko Griinbaum, Morris Kline, and Dr. Heinz-Jiirgen Hess for reading the manuscript and for their encouragement and suggestions. I am especially indebted to Dr. Hess, of the Leibniz-Archiv, for his assistance in connection with the manuscript. I have been greatly helped in preparing the translation ofthe manuscript by the collaboration of a Latin scholar, Mr. Alfredo DeBarbieri. The aid of librarians is indispensable, and I am indebted to a number of them, in this country and abroad, for locating material and supplying copies.


Descartes, Rene History of Mathematics Polyeder geometry mathematics

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5761-5
  • Online ISBN 978-1-4612-5759-2
  • Series Print ISSN 0172-6315
  • Buy this book on publisher's site