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Descartes on Polyhedra

A Study of the De Solidorum Elementis

  • Book
  • © 1982

Overview

Authors:
  1. P. J. Federico
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Part of the book series: Sources in the History of Mathematics and Physical Sciences (SOURCES, volume 4)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
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  2. The Manuscript

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • P. J. Federico
      Pages 3-4

    3. History of the Manuscript

      • P. J. Federico
      Pages 5-7

    4. Description of the Leibniz Copy

      • P. J. Federico
      Pages 8-29

    5. Date of the Original Descartes Manuscript

      • P. J. Federico
      Pages 30-32

  3. Solid Geometry: The Elements of Solids

    1. Front Matter

      Pages 33-33
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    2. Some Geometric Background

      • P. J. Federico
      Pages 35-42

    3. Translation and Commentary, Part I36

      • P. J. Federico
      Pages 43-58

    4. General Comments

      • P. J. Federico
      Pages 59-64

    5. Note on the Euler Papers of 1750 and 1751

      • P. J. Federico
      Pages 65-71

    6. Descartes and Euler

      • P. J. Federico
      Pages 72-80

  4. Number Theory: Polyhedral Numbers

    1. Front Matter

      Pages 81-81
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    2. The Figurate Numbers of the Greeks

      • P. J. Federico
      Pages 83-91

    3. Translation and Commentary, Part II

      • P. J. Federico
      Pages 92-115

    4. General Comments

      • P. J. Federico
      Pages 116-120

  5. Back Matter

    Pages 121-145
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Keywords

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.

Bibliographic Information

  • Book Title: Descartes on Polyhedra

  • Book Subtitle: A Study of the De Solidorum Elementis

  • Authors: P. J. Federico

  • Series Title: Sources in the History of Mathematics and Physical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-5759-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Hardcover ISBN: 978-0-387-90760-4Published: 01 December 1982

  • Softcover ISBN: 978-1-4612-5761-5Published: 12 October 2011

  • eBook ISBN: 978-1-4612-5759-2Published: 06 December 2012

  • Series ISSN: 0172-6315

  • Edition Number: 1

  • Number of Pages: IX, 145

  • Topics: Geometry

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