The Astronomical Revolution Copernicus — Kepler — Borelli

264 Pages·012.084 MB·English

by  Alexandre Koyré

ALEXANDRE KOYRfi
The Astronomical
Revolution
COPERNICUS — KEPLER — BORELLI
Translated by
Dr R. E. W. Maddison, f.s.a.
Librarian of the Royal Astronomical Society
HERMANN: PARIS
METHUEN: LONDON
CORNELL UNIVERSITY PRESS: ITHACA, NEW YORK
Translated from the original French text La revolution astronomique,
published by Hermann, Paris, in 1961, in their series Histoire de lapensie
Contents
English translation © 1973 by Hermann, Paris
Published in France by Hermann
293 rue Lecourbe 75015 Paris
Foreword
Published in Great Britain by Methuen & Co Ltd
11 New Fetter Lane, London EC4
Published in the USA, Canada and Mexico by Cornell University Press I. COPERNICUS AND THE COSMIC OVERTHROW . 13
124 Roberts Place, Ithaca, New York 14850 Introduction...................................................................................15
Chapter I. First Outline: the Commentariolus . . . . 18
II. J. G. Rheticus and the Narratio Prima . . . 29
III. De Revolutionibus Orbium Coelestium. Osiander’s
Preface and the Letter to Pope Paul III . . . 34
IV. The Cosmic Doctrine................................................43
V. The Physical Problem................................................55
Appendix........................................................................................67
Notes....................................................................................................71
II. KEPLER AND THE NEW ASTRONOMY . . . 117
Introduction.................................................................................119
I. The Beginnings.....................................................................125
Chapter I. Mysterium Cosmographicum..................................127
II. Celestial Physics OR Wo Kv4........................157
Chapter I. Kepler and Tycho B rahe........................................159
II. First Attack upon the Theory of Mars . . . 172
III. Study of the Earth’s M otion..................................180
IV. A quo moventur planetae?........................................185
V. The Motive Force....................................................197
VI. The Individual Motive F o rc e s............................215
VII. From the Circle to the O val..................................225
VIII. From the Oval to the Ellipse..................................241
IX. Astronomy with the E llipse..................................265
ISBN (Hermann) 2 7056 5648 0 III. From Celestial Physics to Cosmic Harmony . . .281
ISBN (Methuen) 0 416 76980 2
Chapter I. The Epitome Astronomiae Copernicanae . . . 283
ISBN (Cornell) 0-8014-0504-1
II. The Harmonice Mtmdi..............................................326
Library of Congress Catalog Card Number 72-13061 III. Harmony of the Universe in the Epitome . . 344
Conclusion......................................................................................362
All rights reserved. No part of this work may be reproduced or transmitted in
Appendix 1......................................................................................365
any form or by any means, electronic or mechanical, including photocopying
II......................................................................................367
and recording, or by any information storage or retrieval system, without per­
mission in writing from the original publisher. III......................................................................................371
7
CONTENTS
TIL J. A. BORELLI AND CELESTIAL MECHANICS . 465
Introduction.........................................................................467
Chapter I. The Problem of Planetary Motion . . . . 472
II. The Solar W hirlpool......................................483
III. Celestial Mechanics. Conclusion....................497
Notes..........................................................................................514
Name In d e x .........................................................................529 Foreword
In these three studies—Copernicus, Kepler, Borelli—which are
brought together in this volume, it is not my intention to review the
history of astronomy in the sixteenth and seventeenth centuries from
Copernicus to Newton, but only the history of the ‘astronomical
revolution’, that is to say, the history of the evolution and transfor­
mation of the key-concepts by means of which endeavours to reduce
to order, or ‘to save’, phenomena— ra ^aivoyxva^ salvare
phenomena—by clearly setting forth the facts that underlie and
explain the chaos of sentient appearances.
The history of astronomy should include that of observational
astronomy, which was revived in the West by Regiomontanus and
Bernhard Walter: some attention should be given to the foundation
and work of the earliest observatories, such as those of the Landgraf
Wilhelm IV of Hessen-Kassel, and especially of Tycho Brahe; the
upheaval caused by the invention of the astronomical refracting
telescope, which opened vistas never before seen by human eye,
should be described; and the impact of the great discoveries made
by Galileo and his rivals, requires analysis___It is rather strange
that the astronomical revolution, not only as regards its origin—the
observational data of Copernicus are almost the same as those of
Ptolemy—^but also as regards its development, was almost entirely
independent of the development of observational astronomy. Kepler,
tells us that the eight minutes difference between theory and Tycho
Brahe’s observations are at the root of this Astronomia Nova... but,
in fact, this difference was of importance to him only because he was
trying to explain it within the framework of an astronomy which he
describes as ai^noXoyriTos, that is to say, within the framework of a
celestial physics conceived long before he had access to Tycho
Brahe’s observations. Interpreted within the framework of astral
kinematics—the framework of Tycho Brahe—the difference in
question would have had no serious consequence.
FOREWORD FOREWORD
The same applies to Borelli. He is assured of a place beside Coper­ they alone enable us to understand the powerful nature of the ob­
nicus and Kepler in the history of this revolution, not on account of stacles that were erected on the difficult, tortuous, uncertain path
his telescopic observations of the motion of the Medicean planets, which had led them to abandon the ancient truths in order to dis­
but because of his decision to extend the principles of the new dyn­ cover and proclaim fresh truths.
amics to astronomy—something that Galileo had not even attempted, Itinerarium mentis in veritatem is not a straight line. The road
and in which Descartes had not succeeded, f This decision was not must be traversed, no matter how circuitous or mazelike; blind
motivated by his own observations, nor by those of others. At most, alleys must be negotiated; wrong paths must be retraced in order to
one can say that it resulted from the cumulative effect of telescopic discover the facts of the quest and hence the truth. Then, with
observations which sounded the knell of the closed universe, and Kepler, we can acknowledge that the ways by which the mind attains
substituted the boundless universe. the truth are even more wonderful than the achievement itself.
In fact, the astronomical revolution was accomplished in three Paris-Princeton.
stages, each one of which was linked with the work of one man.
With Copernicus, who brought the Sun to a standstill and launched
the Earth into the skies—^heliocentrism replaced geocentrism. With
Kepler, whose celestial dynamics—^unfortunately Aristotelian—
replaced the kinematics of circles and spheres used by Copernicus
and the Ancients. As a result, obsession with circularity was partially
overcome (though it could never be completely so in the case of a
closed universe), and ‘astronomy of the ellipse’ made its triumphal
entry into the universe. Finally, with Borelli, in a universe hence­
forth unbounded and ruled by dynamics, the unification of celestial
and terrestrial physics was completed and made manifest by aban­
donment of the circle in favour of the straight line to infinity. These
ideas of Kepler and Borelli were fructified by the genius of Newton,
and brought forth his immortal work: but that is another story,
which cannot be told here.
One further remark! As far as possible, I have allowed authors,
especially Kepler and Borelli, to speak for themselves in these studies.
The writings of Copernicus are relatively accessible to readers, but
those of Kepler and Borelli are not. For a history of scientific
thought, provided, of course, that it is not treated as a catalogue of
errors or of achievements, but as the entrancing, instructive history
of the efforts of the human mind in its search for truth, nothing can
take the place of original sources and texts. They alone enable us to
catch the spiritual and intellectual atmosphere of the period under
study; they alone enable us to appreciate at their true value the
motives and incentives which guided and impelled the authors of them;
t Cf. my Etudes Galildemes, Paris, 1939. Cartesian ideas, which fostered con­
tinental opposition to Newton for a himdred years, were important for cos­
mology and physics, but not in the least for astronomy.
10 11
I
COPERNICUS
AND THE COSMIC OVERTHROW
Introduction
The year 1543 is an important one in the history of human thought,^
for that year witnessed the publication of De Revolutionibus Orbium
Coelestium, and the death of its author, Nicolas Copernicus. ^
There is a temptation to regard this date as marking ‘the end of
the Middle Ages and the beginning of modern times’, because it
symbolizes the end of one world and the beginning of another to a
far greater extent than does the conquest of Constantinople by the
Turks, or the discovery of America by Christopher Columbus.
I sometimes wonder if we ought not to go further and say that the
break caused by Copernicus signifies far more than the end of the
Middle Ages. Indeed, it determines the end of a period which in­
cludes not only the Middle Ages but classical antiquity too; for
only since the time of Copernicus has man ceased to be the centre of
the Universe, and the Cosmos ceased to be regulated around him.^
It is very difficult at the present time to comprehend and appreciate
the magnitude of intellectual effort, boldness and moral courage
involved in this work of Copernicus.'* To do so, we must forget the
intellectual development of succeeding centuries, and reorientate
ourselves in such a way that common sense accepts with naive,
confident certitude the direct evidence of the Earth’s immobility
and the heavens’ mobility. 5
However, to step back in time is not enough: to the force of visual
evidence must be added that of the threefold teaching and tradition
of science, philosophy and theology, as well as the threefold authority
of calculation, reason and revelation.^ Only then shall we be capable
of fully appreciating the incomparable daring of Copernican thought,
which tore the Earth from its foundations and launched it into the
heavens.^
If it be well nigh impossible to realize the magnitude of the
achievement of Copernicus without making the effort of imagin-
15
THE ASTRONOMICAL REVOLUTION COPERNICUS. INTRODUCTION
ation outlined above, it is just as difficult to grasp the extraordinary severe in his condemnation. 12 Strange to say, the Roman Catholic
and profound impression that his contemporaries must have ex­ Church made no move.
perienced on reading the work: a work which involved the destruc­ Only at a much later date, when it became evident that this work
tion of a world that everything—science, philosophy, religion— of Copernicus was not intended for mathematicians alone; when it
represented as being centred on man, and created for him*; the became clear that the blow to the geocentric and anthropocentric
collapse of the hierarchical order, which, placing this sublunary Universe was deadly; when certain of its metaphysical and religious
world in opposition to the heavens, nevertheless united them by implications were developed in the writings of Giordano Bruno,
this very opposition. only then, did the old world react. There was a twofold reaction:
The impact was too great. This fresh conception of the Universe the condemnation of Copernicus in 1616 and of Galileo in 1632,^3
seemed too hare-brained to be taken seriously. Furthermore, the which tried to suppress the new concept of the Universe: and there
greater part, if not all, of the book was too difficult for readers was the Pensees of Pascal, which essayed a reply.
lacking adequate mathematical and astronomical background.^
Copernicus said to himself: mathemata mathematicis scribmtur.
Let us leave the mathematics to the mathematicians. It is only
another hypothesis, new, yet old. A calculating device having no
more claim to truth, and therefore of no greater importance, than
those that had been previously devised by astronomers. That was
the general (and comforting) interpretation for half a century,
though there were some few exceptions,amongst whom we may
mention Tycho Brahe and Giordano Bruno, notwithstanding the
Narratio Prima of Georg Joachim Rheticus (published in 1540)
which resolutely affirmed the Copernican concept. This interpre­
tation, moreover, was put forward as that of Copernicus himself
in the very clever introduction—Ad Lectorem de Hypothesibvs
hvivs Opens—which the publisher, Andreas Osiander, wrote and
inserted anonymously at the beginning of De Revolutionibus^ and
which allowed ‘mathematicians’, i.e., professional astronomers, to
give high praise to the genius of Copernicus, and even to use his
data and methods, whilst rejecting the cosmological truth of his
system. As for the non-mathematicians, unable to appreciate the
greatness and value of the work of Copernicus, and who read the
Narratio Prima of Rheticus (or read nothing at all), these laymen
mocked the madman who doubted the immobility of the Earth;
philosophers opposed it with all the old Aristotelian arguments,
which, in their opinion, Copernicus had not refuted; and theologians
cited the undeniable authority of Holy Writ.
In 1539, before publication of De Revolutionibus by Copernicus,
and even of the Narratio Prima by Rheticus, Luther, no doubt in­
formed by rumour, harshly condemned the new doctrine; in 1541
Philip Melanchthon, having read the Narratio Prima^ was even more
16
17
COPERNICUS. THE COMMENTARIOLUS
Nicolaus Copernicus 8 was born 19 February 1473 at Torun (Thorn)
in West Prussia, then a Polish province. His father, also called Nico­
laus, was a rich citizen of Cracow, who had settled at Torun some
years before this town had been annexed to the Kingdom of Poland;
he acquired citizenship and even became a magistrate of Torun. His
mother, Barbara Watzelrode, came from an old aristocratic family
of the same town, and was apparently of Silesian origin. Having lost
his parents at the age of ten, Nicolaus, as well as his brother Andreas,
First Outline: the Commentariolus
was adopted by his maternal uncle, Lucas Watzelrode,^ who was at
that time a Canon of Frauenburg Cathedral, and later (in 1489)
It would be of inestimable value for the history and phenomenology became Bishop of Warmia (Ermland).
of human thought were it possible to reconstruct step by step the Was Copernicus Polish or German ? I must admit that this ques­
development of the Copernican mind. Unfortunately, it is impossible tion, or rather the importance attached to it in some quarters, appears
to do so. Copernicus has left no autobiography describing his mental to me to be somewhat irrelevant. Copernicus lived at a period
development; even the biography written by his pupil, Georg which, with few exceptions and despite the increased use of the
Joachim Rheticus, is lost; and the scant indications given in his vernacular, was not so poisoned by nationalism and nationalistic
introduction to De Revolutionibus, as well as in his fine, noble letter passions as at the present time; the period in which he lived still
to Pope Paul III, which forms the preface thereto, are most brief, enjoyed the blessings of a common culture and a common literary
and consequently difficult to interpret. As for the work itself, it is language. 10 Moreover, he lived in an Empire (medieval Poland was
presented, exactly like its first draft, the Commentariolus,^ in a state not a National State) whose subjects of various nationalities speaking
of maturity which is the despair of historians. different languages were united by and in their common adherence
However, if we must abandon any hope of writing a history of to the State {Res Publico); they knew nothing of the problem of
Copernican thought, we ought, nevertheless, to try and grasp its minorities, nor of their rights (which they enjoyed to the full); they
historical significance and nature; we ought to expose the hidden frequently intermarried and, generally speaking, got on tolerably
and acknowledged motives and incentives; and yet avoid any well with each other.
modernization. 2 To succeed in this, we must try not to regard Were it possible to ask Copernicus himself, ‘Are you Polish or
Copernicus as the forerunner of Galileo and Kepler, and so explain German?’, it is certain that he would not understand the question,“
him in the light of later developments,^ even though it is precisely and would probably reply that he was Pruthenus, meaning thereby
these developments that assure the work of Copernicus its recognized that he was a citizen of Torufi, a good Catholic, Canon of Frauen­
position in the history of ideas. burg in Warmia, and therefore a subject of the King of Poland. He
This highly important task has been rather neglected so far. In would probably add, that he used the language of learning and
fact, only occasionally has there been any serious consideration of the culture, namely Latin, for his literary correspondence but that
physics of Copernicus,® although there are excellent reviews of his in dealing with the common people or princes 13 fie naturally used
astronomy^; and a wealth of learning and ingenuity has been spent the vernacular—Polish in Cracow, German in Frauenburg or in
on secondary biographical problems, 5 or, more precisely, much effort Heilsberg,^^ and, no doubt, Italian in Padua or in Bologna.
has been wasted in trying to prove that Copernicus was Polish or Were we to persist in trying to make him understand that we are
German (the question, strictly speaking is of no importance, and looking for something else and that we are trying to explain his work
even meaningless). However, as Schiaparelli^ with his usual insight and genius by his ‘nationality’ and his ‘race’, he would probably
has said already, the Copernican problem is essentially a problem become annoyed and would declare that the idea of characterizing
of physics and cosmology. any individual by the specific or the general is quite absurd; that such
18 19
THE ASTRONOMICAL REVOLUTION COPERNICUS. THE COMMENTARIOLUS
a procedure is valid only when dealing with general (or specific) his period, an artist, savant, scholar, man of action: a humanist in the
peculiarities of individual beings; that it can be successfully applied best sense of the word.
in those realms of nature which lack genuine individuality (for ex­ One of the most famous professors at the University of Cracow
ample, minerals, plants, animals), but not in the case of man, who, was Albert de Brudzewo (Brudzewski), a distinguished astronomer
considered as spiritual substance, cannot be characterized by features and mathematician, and author (in 1482) of a commentary on
and factors belonging to his material (or social) being, I fear that Peurbach’s Theoricae Novae Planetarum.^'^ Consequently, historians
were we to allow him to become a trifle anachronistic (as we are interested in Copernicus have not failed to establish a connection
between the two of them, and to explain the inclination Copernicus
being at the moment), he would say that all historical, Marxist or
had for astronomy as the result of Brudzewski’s influence. This is
sociological conceptions by which a man, or a work, of genius may
possible, of course, even though Copernicus does not seem to have
be ‘explained’ by heredity, race, class, position, background and a
attended the lectures of Brudzewo, who, moreover, after 1490 no
particular moment in history, could only have been invented and
longer taught astronomy as such, but ‘read’ Aristotle’s De Coelo:
maintained by barbarians completely devoid of philosophical up­
therefore, it was not with Brudzewo, but with one of the numerous
bringing. No doubt, he would add that if one wanted at all costs to
other ‘readers’ who taught the rudiments of astronomy to would-be
‘explain’ him, Copernicus, in these ridiculous terms, then the en­
practisers of the science, that Copernicus must have served his
quirer should look towards Italy, and not Poland or Germany.
apprenticeship. Albert de Brudzewo left Cracow in 1494; and
However, as we cannot entirely avoid the question, I must say
most biographies of Copernicus state that he left at about the same
that there is in fact no reason to suppose that Copernicus was not
time also, or even a little later in 1495; it is very likely that he did,
Polish. Furthermore, until the middle of the nineteenth century
but it is by no means certain. Be that as it may, in 1496 he was once
hardly anyone doubted it.^^ Only with the increasing growth of
more with his uncle, Lucas Watzelrode, Bishop of Warmia,i® who
nationalism in European thought and historical writing have certain
tried in vain to get him nominated Canon of Frauenburg Cathedral.
German historians, ready to serve the aims of German Imperialism,
In this same year, 1496, he departed for Italy in order to study law, as
made claims to Copernicus; a claim which has no more basis than
those concerning Leonardo da Vinci, Dante, Michelangelo and his uncle Lucas had done before him.20 On 6 January 1497 his name
was inscribed on the Natio Germanorum register of the University of
many others.
Bologna. Although great importance has frequently been ascribed
In 1491, we find Copernicus at the University of Cracow, where he
to this fact, it does not by any means imply that Copernicus ever
remained for three or four years. There is no need to seek the reasons
which guided his choice: the University of Cracow enjoyed a very considered himself to be a German.21 *nationes* of a medieval
university had nothing in common with nations in the modern sense
high reputation at that time. In fact, since the decline of the Uni­
versity of Prague, it had become the most important university in the of the word.22 Students who were natives of Prussia and Silesia were
automatically described as belonging to the Natio Germanorum.
east, being justly famous as a centre of scientific and classical culture.
Furthermore, at Bologna, this was the privileged ‘nation’; con­
Moreover, Cracow was not far from Torufi, and it may be assumed
sequently, Copernicus had very good reason for inscribing himself
that Copernicus still had some relations in the town where his father
on its register. Copernicus spent about three years at Bologna, where
was born.
he obtained the degree of magister artium after one year’s study.
We have no information about the course of studies followed by
Whilst there, he no doubt continued his studies in astronomy,
Copernicus at Cracow. Though it is certain that he made a thorough
though he seems to have been sufficiently advanced in this subject for
study of astronomy, we have no reason to think that he did not follow
the well-known astronomer Domenico Maria Novara to describe
the usual curriculum of the Faculty of Arts, based on dialectics and
him as non tarn discipulus quam adjutor et testis observationum.^^
philosophy. Indeed, Copernicus, even less so than Peurbach or
He studied many other subjects too; law, of course, but medicine
Regiomontanus, is not a narrow specialist, an ‘astronomico*-
and philosophy as well; he learned Greek^4; he read Plato; he
technician, but a man deeply imbued with the entire, rich culture of
21
20
THE ASTRONOMICAL REVOLUTION
COPERNICUS. THE COMMENTARIOLUS
absorbed the ‘renaissant’ mentality and was greatly influenced by have had much time to meditate, study or make calculations. Con­
the Pythagorean and Neo-Platonic inspiration which then held sway sequently, his work progressed and took form extremely slowly.
in Italy, being centred at Florence, and of which his master, Novara, I have used the words, meditate and make calculations—^not
was an earnest exponent.^s Once again, it should be stressed that make observations. It must not be thought that Copernicus spent his
Copernicus was not an ‘astronomer’, but a humanist and one of the nights sweeping the skies in order to discover new facts to account
most cultivated minds of his time. for the position of the celestial bodies. Copernicus was not a Tycho
In 1500 he went to Rome (1500 was the Jubilee Year which at­ Brahe. He did make observations, of course, and they are more
tracted thousands of pilgrims to the capital of Christendom), where, numerous than was formerly believed; 63 are known to date,^i of
as Rheticus tells us, he gave a course of lectures on mathematics which only a small number was used in De Revolutionibus.^^ Instead
which undoubtedly means astronomy. It seems that Copernicus of this work, he had planned at one time to limit himself to publishing
was not anxious to return home. However, he was obliged to do so in a set of astronomical tables on the lines of the Alphonsine Tables.
order to assume the office of Canon of Frauenburg Cathedral, to In 1535, he had even prepared an Almanack calculated in accordance
which office Lucas Watzelrode had finally succeeded in having him with the heliocentric system; the data it contained were far more
elected (in 1497, apparently). accurate than those of its predecessors, and could be regarded to
In 1501 he returned to Poland, but not for long. After being offic­ some extent as proof of the reality of the system.^^
ially installed in his canonry, he asked for leave of absence to study Notwithstanding this work of a practising astronomer, and his
medicine; it was granted, 27 July 1501, and he returned to Italy. continual care to have agreement with observable ‘phenomena’—
This time he went to Padua. However, it was not at Padua, but at (Rheticus gives persuasive evidence of this in his Narratio Prima :
Ferrara, that he received his doctorate in canon law (31 May 1503). ‘ My master always has in front of him a properly compiled catalogue
After receiving the degree, he returned to Padua.^^ of observations made at all periods of time, and keeps it with his
Copernicus seems to have been very happy in Italy. Unfortunately, own observations.’)—^it is nevertheless true, and has long been
all good things come to an end, especially leave of absence. Ecclesias­ recognized, that the greatness of Copernicus does not depend on
tical chapters do not appreciate non-resident members, and Coperni­ his contribution of new facts, but on the conception and develop­
cus, even though he was the bishop’s nephew, had to abide by the ment of a new theory. It happens, that his theory, or rather his
rules. In 1503 he returned to his diocese, where he remained for the system, is based on old data, mainly of Ptolemy, much more than on
rest of his life. fresh data. In fact, his system—a fresh interpretation of observational
data—at least as far as the calculation of observable phenomena is
The life that awaited Copernicus on his return home bore no concerned, does not agree with them much better than does Ptolemy’s
resemblance to the popular conception of a canon’s life, peaceful system which he was striving to replace.^^
and serene, devoted to prayer, study and meditation. It was, on the This statement may seem surprising. However, it is a fact, that
contrary, one of activity. A medieval bishopric, particularly one like Ptolemy’s astronomy is relatively satisfactory, whilst that of Coperni­
that of Warmia,27 was as much a political as an ecclesiastical insti­ cus is hardly much better in practice for calculating the positions
tution, and was obliged to concern itself with the affairs of this of planets, when one takes into account the very large margin of
error inherent in the star catalogues then available.
world just as much as with those of the world to come. Moreover,
It must not be forgotten that observations were made not only with
Copernicus was for many years secretary and physician to Lucas
the naked eye, but also with instruments whose accuracy left much
Watzelrode, until the death of the latter in 1512; then he was ad­
to be desired 37—at least up to the time of Tycho Brahe; nor must it
ministrator of the chapter’s assets (it owned one-third of the country),
be forgotten that the Ptolemaic system from the mathematical
and resident delegate at Allenstein (Olsztyn) during which period
point of view is one of the finest and most outstanding works of the
of his career he produced a treatise on currency.^* Furthermore, he
human mind. In fact, the combination of circular motions he
had never given up the practice of medicine 2®; so, he would not
23
22