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REPRESENTING SPACE IN THE SCIENTIFIC REVOLUTION Thenovelunderstandingofthephysicalworldthatcharacterizedthe ScientificRevolutiondependedonafundamentalshiftinthewayits protagonistsunderstoodanddescribedspace.Atthebeginningofthe seventeenthcentury,spatialphenomenaweredescribedinrelationto apresupposedcentralpoint;byitsend,spacehadbecomeacenterless void in which phenomena could be described only by reference to arbitrary orientations. David Marshall Miller examines both thehis- torical and philosophical aspects of this far-reaching development, includingtherejectionoftheideaofheavenlyspheres,theadventof rectilinear inertia, and the theoretical contributions of Copernicus, Gilbert,Kepler,Galileo,Descartes,andNewton.Hisrichstudyshows clearly how the centered Aristotelian cosmos became the oriented Newtonian universe, and will be of great interest to students and scholarsofthehistoryandphilosophyofscience. david marshall miller is Assistant Professor of Philosophy at IowaStateUniversity.Hehaspublishedarticlesinjournalsincluding PhilosophyofScienceandHistoryofScience. REPRESENTING SPACE IN THE SCIENTIFIC REVOLUTION DAVID MARSHALL MILLER UniversityPrintingHouse,Cambridgecb28bs,UnitedKingdom CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107046733 ©DavidMarshallMiller,2014 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2014 PrintedintheUnitedKingdombyClays,StIvesplc AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Miller,DavidMarshall,author. Representingspaceinthescientificrevolution/DavidMarshallMiller. pages cm isbn978-1-107-04673-3(hardback) 1. Science–History–17thcentury. 2. Science–Philosophy. 3. Space. 4. Spaceandtime. I. Title. q125.2.m55 2014 530.1–dc23 2014007595 isbn978-1-107-04673-3Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof urlsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. For my family Contents Listoffigures pagex Preface xi Noteontexts xiii 1 Introduction:centersandorientations 1 1 Thehistoriographicalproblem 4 Explanations,descriptions,frameworks,andtheories 6 Representationsofspace 9 Interrogatingtexts 12 Examples:Aristotle,Epicurus,andNewton 17 Reciprocaliteration 19 Theepistemologyandthemetaphysicsofspace Caveatsandqualifications 21 24 Planofchapters 2 Pluribusergoexistentibuscentris:explanations, descriptions,andCopernicus 27 27 Whyanewastronomy? 29 Theproblemsofastronomy 32 Eudoxus,Aristotle,andPtolemy 37 ThePtolemaiccompromise 42 TheAverroistchallenge:whereisthecenter? Copernicus’ssolution:anewcenter 47 55 Averroismredux Theexplanatoryconsequencesofdescriptions: 60 thethirdmotion Conclusion:CopernicusandtheScientificRevolution 62 3 Nonestmotusomnino:Gilbert,verticity,and theLawoftheWhole 64 Gilbert’sresponsetoCopernicus 64 66 DeMagnete,BookI vii viii Contents 69 DeMagnete,BookII 72 Instantiationsofthegeographicalrepresentationofspace DeMagnete,BooksIII–V:magneticmotions 73 DeMagnete,BookVI:theearth’smotions 76 79 Diurnalrotation:ablindalley 81 Thethirdmotion:verticityandtheLawoftheWhole 86 Conclusion 4 Respiceresinus:Kepler,orientedspace,andtheellipse 88 88 Introduction 90 Twodesiderata:descriptionsandexplanations Theexplanatoryproblem:“respectingthesines” 94 98 Anexplanatorymechanism:themagneticbalance 103 Orientedspace 106 Conclusion:theneedforrectilinearity 5 Millemovimenticircolari:fromimpetustoconserved curvilinearmotioninGalileo 110 110 Theoriginsofinertialphysics Galileo’santecedents 113 116 DeMotu 120 Neutralmotion 123 Dialogo 130 Conservedmotion 138 Discorsi 145 Conclusion 6 Directionssontentreellesparalleles:Descartesandhiscritics onorientedspaceandtheparallelogramrule 147 147 Inertiaandthecompositionofmotion Descartes’strajectory 150 Descartes’sOptics 153 160 Descartesonorientedspace:physicalconsiderations 163 Descartesonorientedspace:metaphysicalconsiderations 168 Descartesdis-oriented Fermat’sorientationoftheOptics 174 183 Conclusion 7 Inclineittoverge:Newton’sspatialsynthesis 188 188 Introduction Hooke’squery 189 Newton’searlythoughtsonorbits 191 Newton’s“grossblunder” 196 202 Applicationoftheparallelogramrule

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The novel understanding of the physical world that characterized the Scientific Revolution depended on a fundamental shift in the way its protagonists understood and described space. At the beginning of the seventeenth century, spatial phenomena were described in relation to a presupposed central po
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REPRESENTING SPACE IN THE SCIENTIFIC REVOLUTION Thenovelunderstandingofthephysicalworldthatcharacterizedthe ScientificRevolutiondependedonafundamentalshiftinthewayits protagonistsunderstoodanddescribedspace.Atthebeginningofthe seventeenthcentury,spatialphenomenaweredescribedinrelationto apresupposedcentralpoint;byitsend,spacehadbecomeacenterless void in which phenomena could be described only by reference to arbitrary orientations. David Marshall Miller examines both thehis- torical and philosophical aspects of this far-reaching development, includingtherejectionoftheideaofheavenlyspheres,theadventof rectilinear inertia, and the theoretical contributions of Copernicus, Gilbert,Kepler,Galileo,Descartes,andNewton.Hisrichstudyshows clearly how the centered Aristotelian cosmos became the oriented Newtonian universe, and will be of great interest to students and scholarsofthehistoryandphilosophyofscience. david marshall miller is Assistant Professor of Philosophy at IowaStateUniversity.Hehaspublishedarticlesinjournalsincluding PhilosophyofScienceandHistoryofScience. REPRESENTING SPACE IN THE SCIENTIFIC REVOLUTION DAVID MARSHALL MILLER UniversityPrintingHouse,Cambridgecb28bs,UnitedKingdom CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107046733 ©DavidMarshallMiller,2014 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2014 PrintedintheUnitedKingdombyClays,StIvesplc AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Miller,DavidMarshall,author. Representingspaceinthescientificrevolution/DavidMarshallMiller. pages cm isbn978-1-107-04673-3(hardback) 1. Science–History–17thcentury. 2. Science–Philosophy. 3. Space. 4. Spaceandtime. I. Title. q125.2.m55 2014 530.1–dc23 2014007595 isbn978-1-107-04673-3Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof urlsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. For my family Contents Listoffigures pagex Preface xi Noteontexts xiii 1 Introduction:centersandorientations 1 1 Thehistoriographicalproblem 4 Explanations,descriptions,frameworks,andtheories 6 Representationsofspace 9 Interrogatingtexts 12 Examples:Aristotle,Epicurus,andNewton 17 Reciprocaliteration 19 Theepistemologyandthemetaphysicsofspace Caveatsandqualifications 21 24 Planofchapters 2 Pluribusergoexistentibuscentris:explanations, descriptions,andCopernicus 27 27 Whyanewastronomy? 29 Theproblemsofastronomy 32 Eudoxus,Aristotle,andPtolemy 37 ThePtolemaiccompromise 42 TheAverroistchallenge:whereisthecenter? Copernicus’ssolution:anewcenter 47 55 Averroismredux Theexplanatoryconsequencesofdescriptions: 60 thethirdmotion Conclusion:CopernicusandtheScientificRevolution 62 3 Nonestmotusomnino:Gilbert,verticity,and theLawoftheWhole 64 Gilbert’sresponsetoCopernicus 64 66 DeMagnete,BookI vii viii Contents 69 DeMagnete,BookII 72 Instantiationsofthegeographicalrepresentationofspace DeMagnete,BooksIII–V:magneticmotions 73 DeMagnete,BookVI:theearth’smotions 76 79 Diurnalrotation:ablindalley 81 Thethirdmotion:verticityandtheLawoftheWhole 86 Conclusion 4 Respiceresinus:Kepler,orientedspace,andtheellipse 88 88 Introduction 90 Twodesiderata:descriptionsandexplanations Theexplanatoryproblem:“respectingthesines” 94 98 Anexplanatorymechanism:themagneticbalance 103 Orientedspace 106 Conclusion:theneedforrectilinearity 5 Millemovimenticircolari:fromimpetustoconserved curvilinearmotioninGalileo 110 110 Theoriginsofinertialphysics Galileo’santecedents 113 116 DeMotu 120 Neutralmotion 123 Dialogo 130 Conservedmotion 138 Discorsi 145 Conclusion 6 Directionssontentreellesparalleles:Descartesandhiscritics onorientedspaceandtheparallelogramrule 147 147 Inertiaandthecompositionofmotion Descartes’strajectory 150 Descartes’sOptics 153 160 Descartesonorientedspace:physicalconsiderations 163 Descartesonorientedspace:metaphysicalconsiderations 168 Descartesdis-oriented Fermat’sorientationoftheOptics 174 183 Conclusion 7 Inclineittoverge:Newton’sspatialsynthesis 188 188 Introduction Hooke’squery 189 Newton’searlythoughtsonorbits 191 Newton’s“grossblunder” 196 202 Applicationoftheparallelogramrule

Description:
The novel understanding of the physical world that characterized the Scientific Revolution depended on a fundamental shift in the way its protagonists understood and described space. At the beginning of the seventeenth century, spatial phenomena were described in relation to a presupposed central po
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