Exploring the Limits of Preclassical Mechanics: A Study of Conceptual Development in Early Modern Science: Free Fall and Compounded Motion in the Work of Descartes, Galileo, and Beeckman

427 Pages·2004·9.67 MB·English

by  Peter Damerow

Sources and Studies
in the History of Mathematics and
Physical Sciences
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Brook Taylor's Work on Linear Perspective
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Redefining Geometrical Exactness: Descartes' Transformation of the Early Modern
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The Evolution of Dynamics: Vibration Theory from 1687 to 1742
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A History of Inverse Probability: From Thomas Bayes to Karl Pearson,
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Most Honourable Remembrance: The Life and Work of Thomas Bayes
A.I. Dale
Pierre-Simon Laplace, Philosophical Essay on Probabilities, Translated from the fifth
French edition of 1825. with Notes by the Translator
P. Damerow/G. FreudenthallP. McLaughlin/J. Renn
Exploring the Limits of Preclassical Mechanics: A Study of Conceptual
Development in Early Modern Science: Free Fall and Compounded Motion in the
Work of Descartes, Galileo, and Beeckman,
Second Edition
PJ. Federico
Descartes on Polyhedra: A Study of the De Solidorum Elementis
B.R. Goldstein
The Astronomy of Levi ben Gerson (1288-1344)
H.H. Goldstine
A History of Numerical Analysis from the 16th Through the 19th Century
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A History of the Calculus of Variations from the 17th Through the 19th Century
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The History of Ptolemy's Star Catalogue
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Jan de Witt's Elementa Curvarum Linearum, Liber Primus
Continued after Index
Peter Damerow
Gideon Freudenthal
Peter McLaughlin
J urgen Renn
Exploring the Limits
of Preclassical Mechanics
A Study of Conceptual Development in
Early Modem Science: Free Fall
and Compounded Motion in the Work
of Descartes, Galileo, and Beeckman
Second Edition
With 159 Illustrations
Springer
Peter Damerow Gideon Freudenthal
Max Planck Institute for The Cohn Institute for the
the History of Science History and Philosophy of
Wilhelmstrasse 44 Science and Ideas
D-lO 117 Berlin Tel Aviv University
Germany Tel Aviv 69978
[email protected] Israel
[email protected]
Peter McLaughlin J iirgen Renn
Philosophisches Seminar Max Planck Institute for
Universitiit Heidelberg the History of Science
Schulgasse 6 Wilhelmstrasse 44
69117 Heidelberg D-I0117 Berlin
Germany Germany
[email protected] [email protected]
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Library of Congress Cataloging-in-Publication Data
Exploring the limits of preclassical mechanics : a study of conceptual development in early
modem science: free falI and compounded motion in the work of Descartes, Galileo, and
Beeckman / Peter Damerow ... [et al.].-2nd ed.
p. cm. - (Sources in the history of mathematics and physical sciences)
Includes bibliographical references and index.
ISBN 978-1-4419-1917-5 ISBN 978-1-4757-3992-3 (eBook)
DOI 10.1007/978-1-4757-3992-3
1. Motion-History. 2. Mechanics-History. 1. Damerow, Peter. II. Series.
QC133.E97 2004
531'.09-dc22 2003063817
ISBN 978-1-4419-1917-5 Printed on acid-free paper.
© 2004, 1991 Springer Seiencet-Business Media New York
Originally published by Spnnger-Verlag New York, Ine. in 2004
Softcover reprint of the hardcover 2nd edition 2004
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In memoriam
Winifried Wisan
Pierre Souffrin
Preface
This book grew out of a colloquium initiated by Wolfgang Lerevre and Peter
Damerow in Berlin many years ago. In this colloquium we attempted over a
number of years to acquire an understanding of cognitive development in science
that takes account of a number of factors usually considered in isolation: the
cumulative or progressive aspects of science, its embedding in culture and
society, the cognitive content of theories, and the relationship of science to
contemporary philosophical systems. The results of our discussions are
embodied in a number of books and other publications by various members of
the colloquium - some programmatic in nature, some case studies of particular
scientific developments. Among the way stations are: Wolfgang Lerevre, Natur
theorie und Produktionsweise (Darmstadt: Luchterhand, 1978), Die Entstehung
der biologischen Evolutionstheorie (Berlin: Ullstein 1984); Peter Damerow and
Wolfgang Lefevre, Rechenstein, Experiment, Sprache (Stuttgart: Klett-Cotta
1981); Gideon Freudenthal, Atom and Individual in the Age of Newton
(Dordrecht: Reidel 1986); Peter McLaughlin, Kant's Critique of Teleology in
Biological Explanation (Lampeter: Mellen 1990); a number of papers on Galileo
by Jiirgen Renn (see Bibliography) as well as his contributions as an editor of
the Collected Papers of Albert Einstein (Princeton Univ. Press, 1987, 1989,
1992); and finally the numerous papers on cognitive development by Peter
Damerow published mainly in German, a selection of which is to appear in
English under the title, The Cultural Conditions of Thinking, as a volume of
Boston Studies in the Philosophy of Science in the near future.
In the present volume we attempt to display some aspects of the cognitive
development involved in the emergence of modem science. We study this
development in a detailed analysis of three interrelated examples at the core of
early theories of motion.
The book as a whole is both in its approach and in many of its individual
findings a genuinely collective product and reflects a common understanding
established in many years of close cooperation. Our study of early modem
mechanics at first followed some preliminary theses introduced by Freudenthal
but soon took on a life of its own and superseded our initial conceptions. The
Introduction and Epilogue were written jointly, and all other parts, while written
by individuals, have been scrutinized and criticized by the others in the group.
Damerow and Freudenthal wrote Chapter 1; Freudenthal and McLaughlin wrote
Chapter 2; Renn wrote Chapter 3. On McLaughlin fell the task of editing, some
times heavily, each of the individual chapters in order to free shared ideas from
idiosyncratic presentations.
The translations in the text and in the Documents Chapter have a checkered
history and unclear parenthood: some were originally produced by Freudenthal as
working translations for our internal discussions; translations from the Italian are
viii PREFACE
by Renn; others were first drafted by McLaughlin, with whom final respon
sibility for all French and Latin translations lies. As the only native speaker of
English in the group, McLaughlin is also responsible for all grammatical errors,
Germanisms and stylistic solecisms that remain in the text as a whole.
Since our Berlin days the four authors have been dispersed to four different
cities on three different continents. Our continuing work would not have been
possible without the generous support of a number of institutions. The home
base and main stay of the project has always been Damerow's office in the
Center for Development and Socialization at the Max Planck Institute for
Human Development and Education in Berlin. We would especially like to thank
Director Wolfgang Edelstein for constant encouragement and a kind of support of
our long-term interdisciplinary project going beyond academic hospitality. We
would also like to thank Yehuda Elkana of the Van Leer Jerusalem Institute, and
Jiirgen Mittelstrass of the Center for Philosophy and Philosophy of Science at
the University of Constance whose support over the years have made our co
operative venture feasible. Furthermore, we are grateful to the Fritz-Thyssen
Foundation (Cologne), the Minerva Foundation (Bonn), and the Edelstein Center
for the History and Philosophy of Science (Jerusalem) for financial support at
various times, and to the Institute for Advanced Study in Berlin for bringing two
of us back to Berlin for a year.
We also thank Mr. E. J. Aiton, the British Society for the History of Science,
Cambridge University Press, Mrs. I. E. Drabkin, Mr. Stillman Drake, Kluwer
Publishers, Wall & Emerson, Inc., and the University of Wisconsin Press for
permission to use or modify figures or translations. In particular, we want to
thank the Biblioteca Nazionale, Florence, for making accessible its entire col
lection of Galileo manuscripts and for permission to reproduce some of them in
facsimile. We also want to thank Franca Principe-Saba and Mara Miniati of the
Institute and Museum of the History of Science (Florence), as well as its director
Paulo Galluzzi, for the help and hospitality accorded to Renn while he studied
the Galileo manuscripts. We should also like to thank the Springer Verlag's
anonymous referee for an unusually thorough and helpful commentary on the
original manuscript.
Finally we should like to acknowledge our debt to the scores of historians and
philosophers of science whose editions, interpretations, and translations of 17th
century scientists and philosophers we have used, abused, criticized and
cannibalized.
Berlin, Boston, Constance, and Jerusalem
To the second edition 2003
In the dozen years that have passed since the first edition of this book went to
press, a great deal of research has been done on Descartes and Galileo and the ori
gins of modem science. There have also been very significant advances made in
PREFACE ix
the accessibility of sources and in technology for analyzing them. Not only have
some previously inaccessible manuscripts been edited and published, but also
many formerly scarce published works from the period are now freely accessible
on the internet. Our own research has also continued, and recent historical work
has increasingly taken up lines of thought developed in this book. In view of
these advances and because the book has been out of print for some time, we
have undertaken to produce a revised and somewhat expanded edition, in which
we incorporate some of the most important new results.
We have expanded the discussion of the doctrine of proportions in Chapter 1.
In Chapter 2 we have extended the analysis of Descartes' impact rules in order to
make the role of traditional statics more perspicuous, and we have been able to
take account of some recent research on Hobbes's theory of refraction when
discussing Descartes' defense of his derivation of the sine law. The analysis of
Galileo's early work in Chapter 3 can now specify more precisely the dates of
some of Galileo's discoveries. For instance, Galileo's recognition of the para
bolic trajectory of oblique projection - which we could only characterize as
"before 1604" - can now on the basis of new comparative manuscript evidence
be dated more precisely to 1592, thus significantly strengthening the argument.
We have also taken this occasion to review the arguments and to reexamine all
the translations in the documents section, in particular with a view to termino
logical consistency. We have made a large number of minor improvements in
both presentation and translation; and we have added five new documents and
expanded two others. The updated bibliography includes not only the new
sources and secondary literature cited in the text, but also lists all the most
important new books and anthologies relevant to the questions at issue.
With our continuing research we have incurred new debts of gratitude: In par
ticular we want once again to thank the Biblioteca Nazionale Centrale, Florence,
as well as the Istituto e Museo di Storia della Scienza which have cooperated
with us in making Galileo's notes on motion Ms. Gal. 72 freely accessible
through the Internet. We thank the late Prof. Karl Schuhmann, who generously
made available his unpublished transcriptions of Hobbes's optical manuscripts.
A number of scholars have assisted us with hints, suggestions for improvement,
corrections, and specific criticisms of the first edition text: We would like to
thank Mohamed Abattouy, Iochen Bi.ittner, Michele Camerota, Rivka Feldhay,
Raymond Fredette, Paolo Galluzzi, Enrico Gamba, Stephen Gaukroger, Enrico
Giusti, Wallace Hooper, Frank Horstmann, Daniele Napolitani, Carla Rita
Palmerino, Matthias Schemmel, Tom Settle, Alan Shapiro, William Shea, K. I.
Takahashi, Matteo Valleriani, and, in particular, the late Pierre Souffrin.
Peter Damerow Max Planck Institute for the History of Science
Gideon Freudenthal Tel Aviv University
Peter McLaughlin University of Heidelberg
liirgen Renn Max Planck Institute for the History of Science
December 2003
Contents (overview)
Introduction ... 1
Chapter 1
Concept and Inference: Descartes and Beeckman
on the Fall of Bodies ... 9
Chapter 2
Conservation and Contrariety: The
Logical Foundations of Cartesian Physics ... 71
Chapter 3
Proofs and Paradoxes: Free Fall and Projectile
Motion in Galileo's Physics ... 135
Chapter 4
Epilogue ... 279
Chapter 5
Documents ... 287
Bibliography ... 383
Indices ... 405
Contents
Introduction................................................................................ 1
Chapter 1: Concept and Inference: Descartes
and Beeckman on the Fall of Bodies ................................ 9
1.1 Introduction........................................................................... 9
1.2 The Medieval Tradition .......................................................... 12
1.2.1 Proportions .................................................................... 12
1.2.2 The "Moments" of Motion and the Quantification
of Motion by Proportions ............................................... 15
1.2.3 The Configuration of Qualities and Motions ..................... 17
1.2.4 "Impetus" as the Cause of Motion and of
Acceleration ................................................................... 22
1.3 Descartes' Proof of the Law of Fall ........................................ 24
1.3.1 Descartes' Initial Document (1618) ................................... 25
1.3.2 Beeckman's Note in his Journal (1618) ............................ 29
1.3.3 Descartes' Diary Note (1618) ........................................... 32
1.3.4 Descartes' Letters to Mersenne (1629-1631) ....................... 33
1.3.5 Later References to the Original Proof. ............................. 36
1.4 The Law of Fall Derived within the Context of the
Theory of Gravity .................................................................. 38
1.4.1 Beeckman's Commentary on Descartes' Initial
Document ...................................................................... 38
1.4.2 Descartes' Alternative "Law of Free Fall" in his
Initial Document ............................................................ 40
1.4.3 Descartes' Revised "Law of Fall" ..................................... 43
1.5 The Conceptual and Deductive Structure of
Descartes' Proof of the Law of Fall ........................................ 46
1.5.1 Conceptualization as a Condition for the Proof.. .............. .47
1.5.1.1 Conceptualization of Free Fall in Classical
Mechanics .......................................................... 47
1.5.1.2 Conceptualization of Free Fall in Descartes'
Proof ................................................................ 47
1.5.2 Geometrical Representation of Free Fall ............................ 49