Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By Paolo Mancosu | Go to book overview

NOTES

Introduction
1.
On the application of the mathematical method in philosophy, theology, and natural philosophy see bibliography quoted in note 39 of chapter IV.
2.
In this book I have limited myself to the analysis of the disciplines of pure mathematics and thus the question of the relationship between mathematics and physics will not be addressed.
3.
The reference is to Brunschvicg ( 1912). My work has in common with Brunschvicg's book the emphasis on mathematical practice although my approach differs from his on a number of substantial issues. Brunschvicg puts more emphasis on the study of the systems of mathematical philosophy of authors like Descartes, Spinoza, and Leibniz whereas I tend to remain closer to the foundational issues; my choice of topics is consequently quite different.
4.
4. Attention to mathematical mysticism is found for instance in Strong ( 1936).
5.
I use this term rather like Becker ( 1954), although in a much wider acception.
6.
For general introductions to the history of mathematics in the seventeenth century see Boyer ( 1968), Cantor ( 1900-1901), Kline ( 1972), Montucla ( 1799-1802), Whiteside ( 1960-61), and Zeuthen ( 1966). For the rediscovery of Greek mathematical texts, see Rose ( 1975).

Chapter 1
1.
Jardine ( 1988, 686-693) gives an overview of the debates on demonstrativeregress (regressus demonstrativus), defined as "a procedure which combines an inference from an observed effect to its proximate cause with an inference from the proximate cause to the observed effect" (p. 686).
2.
Randall ( 1961, 62-63).
3.
See E. McMullin ( 1962, 52-66), B. S. Eastwood ( 1992, 84-99), and Jardine ( 1988).
4.
The best general sources for seventeenth-century mathematics are Boyer ( 1968), Cantor ( 1900-1901), Kline ( 1972), Montucla ( 1799-1802), Whiteside ( 1960-61), and Zeuthen ( 1966). Further references will be given elsewhere.
5.
I have discussed the issue in connection with whether or not Descartes' Géométrie constitutes a revolution in mathematics in Mancosu (1992b).
6.
For summary introduction to the debate the reader is referred to Jardine ( 1988) especially pp. 693-697 and Schüling ( 1969, 11.9). For bibliographical information, further references, and a detailed analysis of the authors involved in the Renaissance part of

-213-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Table of contents

Table of contents

  • Title Page iii
  • Preface vii
  • Contents *
  • Introduction 3
  • 1 - Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century 8
  • 2 - Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity 34
  • 3 - Descartes' Géométrie 65
  • 4 - The Problem of Continuity 92
  • 5 - Paradoxes of the Infinite 118
  • 6 - Leibniz's Differential Calculus and Its Opponents 150
  • Appendix 178
  • Notes 213
  • References 249
  • Index 267
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 275

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.