The Complex Itinerary of Leibniz’s Planetary Theory: Physical Convictions, Metaphysical Principles and Keplerian Inspiration

194 Pages·2015·2.491 MB·English

by  Paolo Bussotti (auth.)

Science Networks
Historical Studies
52
Paolo Bussotti
The Complex
Itinerary of
Leibniz’s
Planetary Theory
Physical Convictions, Metaphysical
Principles and Keplerian Inspiration
Science Networks. Historical Studies
Science Networks. Historical Studies
Founded by Erwin Hiebert and Hans Wußing
Volume 52
Edited by Eberhard Knobloch, Helge Kragh and Volker Remmert
Editorial Board:
K. Andersen, Amsterdam S. Hildebrandt, Bonn
H.J.M. Bos, Amsterdam D. Kormos Buchwald, Pasadena
U. Bottazzini, Roma Ch. Meinel, Regensburg
J.Z. Buchwald, Pasadena J. Peiffer, Paris
K. Chemla, Paris W. Purkert, Bonn
S.S. Demidov, Moskva D. Rowe, Mainz
M. Folkerts, Mu¨nchen Ch. Sasaki, Tokyo
P. Galison, Cambridge, Mass. R.H. Stuewer, Minneapolis
J. Gray, Milton Keynes V.P. Vizgin, Moskva
R. Halleux, Lie´ge
More information about this series at: http://www.springer.com/series/4883
Paolo Bussotti
The Complex Itinerary of
’
Leibniz s Planetary Theory
Physical Convictions, Metaphysical
Principles and Keplerian Inspiration
PaoloBussotti
UniversityofUdine
Udine
Italy
ISSN1421-6329 ISSN2296-6080 (electronic)
ScienceNetworks.HistoricalStudies
ISBN978-3-319-21235-7 ISBN978-3-319-21236-4 (eBook)
DOI10.1007/978-3-319-21236-4
LibraryofCongressControlNumber:2015951719
SpringerChamHeidelbergNewYorkDordrechtLondon
©SpringerInternationalPublishingSwitzerland2015
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilarmethodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, express or implied, with respect to the material contained
hereinorforanyerrorsoromissionsthatmayhavebeenmade.
Coverillustration:FromWallerMsde-00215,AugustBeer:U¨berdieCorrectiondesCosinusgesetzesbei
derAnwendungdesNicol’schenPrismasinderPhotometrie,after1850.Withfriendlypermissionby
TheWallerManuscriptCollection(partoftheUppsalaUniversityLibraryCollections).
Printedonacid-freepaper
Springer International Publishing AG Switzerland is part of Springer Science+Business Media
(www.birkhauser-science.com)
Foreword
Authors like the late Eric Aiton, Domenico Bertoloni Meli, Franc¸ois Duchesneau,
Alexandre Koyre´ and many others have diligently studied, explained or criticized
Leibniz’splanetarytheory.Leibniz,itistrue,changedhisrelativeopinionsinmany
respectsinthecourseoftime.Buthealwaysadheredtosomefundamentalconvic-
tions, among them being the strong assertion that all hypotheses must be based on
mechanicalmodels.Thisisespeciallytrueofhisdifferentexplanationsofgravitythat
are closely connected with his cosmological considerations. He thus inevitably
refused Newton’s celestical mechanics because it was based on the unexplained
notionofgravity.
PaoloBussottimakesanew,comprehensiveefforttointerpretLeibniz’sdiffer-
enttrialstodevelopaconsistentplanetarytheorywellknowingthat“itisdifficultto
offeracoherentpictureofLeibniz’stheoryofmotion”.Yet,herightlyemphasizes
that Leibniz aimed at a physical-structural theory, not only at a kinematical or
dynamicaltheoryinordertounderstandtheworldsystem.
Bussotti presents a subtle analysis of Leibniz’s thinking and argumentation.
Leibniz’s natural inertia is not Newton’s inertia. Leibniz had no inertia concept
thatwascomparabletothatofNewton.Hetriedtoreplaceitbymeansofhisforces.
Leibniz’smainphysicalquantitywasspeed,notacceleration.Whenheelaborated
histheoryofaharmoniccirculationandaparacentricmotionasbasicingredientsof
hisplanetarytheory,hediditwithregardtoNewton’sPrincipiamathematica.He
wantedtoofferaphysicalalternativetoNewton’sphysics.
What is more, Bussotti’s aim is to explain the internal change of Leibniz’s
concept of gravity. Leibniz finally came to the conclusion that gravity originates
fromthecirculationoftheether.Yet,theoriginofgravitywasnotcertainforhim.
Hecontinuedtowriteonituptotheendofhislife.HeattributedtoKeplertheidea
that gravity is due tothe centrifugalforce ofthe fluid.It is worth mentioning that
suchafluidisareminiscenceofPtolemy’scosmology.
ThereforeBussottijustlyconcludesthatafullunderstandingofLeibniz’splan-
etary theory is not possible without an understanding of its connection with
Leibniz’sgeneral,physical,andmetaphysicalprinciples.
v
vi Foreword
InmyeyesBussotti’slastchapterisespeciallyimportantandoriginal.Itanalyses
Kepler’s influence on Leibniz’s scientific thinking and planetary theory. Influence
doesnotnecessarilymeanagreement,thoughLeibnizhimselfconsideredhimselfas
somebody who continued Kepler’s work. For example Leibniz did not accept
Kepler’splanetarysoulsormagneticinfluences.Forhimeventheorbitoftheplanets
mightbenotanellipse.
BussottidemonstratesthatLeibnizfalselyascribedtheinsighttoKeplerthatina
curvilinearmotionabodytendstoescapealongthetangent.ButLeibnizobviously
tooktheideaoftheparacentricmotion,aswellasthatofadecompositionofplanetary
motions,intotwocomponentsfromKepler.Ontheotherhand,hewasnotinfluenced
by his countryman when he conceived of the circulatio harmonica. Both scientists
sharedtheconvictionthatharmonydeterminesthestructureoftheuniverse.
In spite of many differences between the two thinkers, Bussotti emphasizes the
similarity between their ways of thinking, of approaching the problems, and of
conceiving of the universe and of its relation with God. Bussotti teaches the reader
to see Leibniz’s metaphysics under a new perspective, to see Leibniz as a modern
Keplerian.KeplerandLeibnizsharedindeedacommonvisionoftheuniversethatwas
basedonharmony,finalcauses,andonaconceptionoftheworldasatruekosmos.
Berlin,Germany EberhardKnobloch
June2015
Preface
ThegenesisofthisbookbeginswithanAlexandervonHumboldtfellowshipthatIhad
achievedintheperiod2003–2005atLudwigMaximiliansUniversity,Munichthough
inthoseyearsIdidnotfocusonLeibniz.SomeyearslaterIextendedtheprivilegeof
thisFellowshipduringathreemonthperiodfromDecember2013toFebruary2014at
theBerlin-BrandenburgAcademyofScience,Berlin.Thehostofmyfellowshipwas
ProfessorDr.EberhardKnobloch.Intheprevioussixmonths,Ihadfrequente-mail
contactswithProfessorKnoblochandwesharedtheideathat,duringthistimeperiod
inBerlin,IwouldfocusmystudiesontheinfluenceexertedbyKepleronLeibniz’s
planetarytheory.Therefore,Ibeganmyresearchwiththisclearintention.However,
myreading ofLeibniz’s works and the existing literatureonthe subject,aswell as
discussions with ProfessorKnobloch, convinced me to extend my research beyond
thisnarrowintention.Thus,myaimwaswidenedtoframeLeibniz’splanetarytheory
insidehisphysicsandmetaphysics.Inparticular,Iwonderedifplanetarytheorywas,
forLeibniz,somethinglikeanacademicexerciseor,inanycase,asecondarypartof
hisgeneralorderofideas,scarcelyconnectedwiththewholeofhisproductionorif,in
contrast,itplayedanimportantroleinthedevelopmentofhisentirewayofthinking.
Myattemptstoanswersuchquestionsarethecoreofthisbook,insidewhich,without
enteringintodetails,whichthereaderwillcontrolintherunningtext,itispossibleto
recognizethreemainconceptualcentres:
1) Description and specification of the details (in particular mathematical and
physical details) of Leibniz’s planetary theory, also considering its historical
evolution.TheChaps.2and4arededicatedtothisproblem;
2) Connection between Leibniz’s gravity theory—perhaps better to speak of
Leibniz’sideasongravityratherthanatheoryinapropersense—andplanetary
theory.ThisisthesubjectofChap.5;
3) Kepler’s influence on Leibniz. This was my original project. It is developed in
Chap. 6, where I show the influence exerted by Kepler on Leibniz’s planetary
theory, but where I try to extend the argumentation, as I attempt to prove that
vii
viii Preface
Kepler was also influential on Leibniz’s metaphysics, in particular as far as the
conceptofpre-establishedharmonyisconcerned.
Chapter1isahistoricalandconceptualintroductiontothescenariodescribedin
the book, while Chap. 3 has to be interpreted as a brief parenthesis concerning the
conceptofinertiainLeibniz,especiallyfocusingontheaspectsconnectedtoplane-
tarytheory.Tobeclear,myintentionhasnotbeentodealwiththecomplexgeneral
problemsofLeibniz’sphysics,onwhichahugeandprofoundliteratureexists.
As to the quotations, in the running text I have always offered the English
translation from original works or letters, which are almost exclusively written in
twolanguages:Latin(inmostcases)andFrench(inseveralcases).Ifnotexplicitly
specifiedotherwise,thetranslationismine.
IwishtoexpressmyparticulargratitudetoProfessorDr.EberhardKnobloch.He
followed my research in Germany and he read the whole of my work, giving me
preciousadvice.Finally,hecontacted thepublishing houseBirkha¨usertopropose
the publication of this book. Without his collaboration and precious help, this
researchwouldhavebeenneitherwrittennorpublished.
IamalsogratefultoProfessorDaniloCapecchiforhisqualified,numerousand
profoundtips,astothecontentandformofmywork.
I am indebted with Dr. Raffaele Pisano, with whom I have published several
worksandwhoalsogavemevaluablehelp.
I wish to thank Professor Niccolo` Guicciardini for an important observation
concerningChap.4andDr.StefanoGatteiforsomeadviceregardingChap.2.
Itisobviousthatpossiblemistakesorimperfectionsrestentirelyupontheauthor.
I wish to express my gratitude to the Alexander von Humboldt Foundation for
havingfinancedmyresearch-periodinBerlin.
IamgratefultotheBirkha¨userPublishingHouseforhavingacceptedmybook
forpublication.
Udine,Italy PaoloBussotti
Contents
1 AnIntroduction:TheHistorical-ConceptualReferenceFrame. . . . 1
2 DescriptionoftheMostImportantElementsofLeibniz’s
PlanetaryTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 PhysicalPresuppositions,theCirculatioharmonica
andtheMotusparacentricus. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Leibniz’sAssertions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Commentaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 TheMotusParacentricusandItsProperties. . . . . . . . . . . . . . . . . 13
2.2.1 Leibniz’sAssertions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Commentaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 EllipticalMotionandInverseSquareLaw. . . . . . . . . . . . . . . . . . 22
2.3.1 Leibniz’sAssertions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Commentaries:TwoDifferentModelsforPlanetary
Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 TheFinalDescriptionoftheSolarSystemintheTentamen. . . . . 29
2.4.1 Leibniz’sAssertions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 Commentaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 AnInterlude:Leibniz’sConceptofInertia. . . . . . . . . . . . . . . . . . . . 31
3.1 LeibnizandNaturalInertia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Leibniz:NewtonianInertiaandConatetoRecedeAlong
theTangent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 TheFinalVersionofLeibniz’sPlanetaryTheory. . . . . . . . . . . . . . . 45
4.1 ANewModelfortheconatusexcussorius. . . . . . . . . . . . . . . . . . 46
4.1.1 CircularPathandFallingBodies:Leibniz’sAssertions. . . 46
4.1.2 CircularPathandFallingBodies:Commentaries. . . . . . . . 49
4.1.3 TheNewModelfortheconatusexcussorius:Leibniz’s
Assertions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.4 TheNewModelfortheconatusexcussorius:
Commentaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
ix