The Works of Archimedes: Translation and Commentary

215 Pages·2017·3.849 MB·English

by  Reviel Netz

The Works of Archimedes
Translation and Commentary
VolumeII:OnSpirals
ThisisthesecondvolumeofthefirstfullyfledgedEnglishtranslation
oftheworksofArchimedes–antiquity’sgreatestscientistandoneof
themostimportantscientificfiguresinhistory.ItcoversOnSpirals
andisbasedonareconsiderationoftheGreektextanddiagrams,now
madepossiblethroughnewdiscoveriesfromtheArchimedes
palimpsest.OnSpiralsisoneofArchimedes’mostdazzling
geometricaltoursdeforce,suggestingamannerof“squaringthe
circle”and,alongtheway,introducingtheattractivegeometrical
objectofthespiral.Theformofargument,nolessthantheresults
themselves,isstriking,andRevielNetzcontributesextensiveand
insightfulcommentsthatfocusonArchimedes’scientificstyle,
makingthisvolumeindispensableforscholarsofclassicsandthe
historyofscience,andofgreatinterestforthescientistsand
mathematiciansoftoday.
revielnetzisPatrickSuppesProfessorofGreekMathematicsand
AstronomyatStanfordUniversity,andistheleadingscholarof
Archimedestoday.Hehaspublishednumerousarticlesandbooks,
manyofwhichhaveledtonewdirectionsinthestudyofthehistoryof
science,includingTheShapingofDeductioninGreekMathematics
(CambridgeUniversityPress,1999),TheTransformationof
MathematicsintheEarlyMediterraneanWorld(Cambridge
UniversityPress,2004),andLudicProof(CambridgeUniversity
Press,2009).Heisalsoproducingacompletenewtranslationofand
commentaryontheworksofArchimedes.

the works of
ARCHIMEDES
Translated into English, with commentary, and
critical edition of the diagrams
REVIEL NETZ
Patrick Suppes Professor of Greek Mathematics and Astronomy,
Stanford University
Volume II
On Spirals
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CONTENTS
ListofAbbreviationsofArchimedes’Works pageviii
ListofAbbreviationsofCitedManuscripts
andpre-HeibergEditions ix
Acknowledgments x
Introduction 1
TranslationandCommentary 15
OnSpirals 17
Appendix1 Pappus’CollectionIV.21–25 181
Appendix2 ScholiatoOnSpirals 187
Glossary 194
Bibliography 199
Index 201
vii
ABBREVIATIONS
’
OF ARCHIMEDES WORKS
SCI ThefirstbookOntheSphereandtheCylinder
Eut.SCI Eutocius’commentaryontheabove
SCII ThesecondbookOntheSphereandtheCylinder
Eut.SCII Eutocius’commentaryontheabove
SL OnSpiralLines
CS OnConoidsandSpheroids
DC MeasurementoftheCircle(DimensioCirculi)
Eut.DC Eutocius’commentaryontheabove
Aren. TheSand-Reckoner(Arenarius)
PEI,II PlanesinEquilibrium
Eut.PEI,II Eutocius’commentaryontheabove
QP QuadratureoftheParabola
Meth. TheMethod
CFI ThefirstbookOnFloatingBodies(deCorporibus
Fluitantibus)
CFII The second book On Floating Bodies (de
CorporibusFluitantibus)
Bov. TheCattleProblem(ProblemaBovinum)
Stom. Stomachion
viii
ABBREVIATIONS OF CITED
MANUSCRIPTS AND
PRE-HEIBERG EDITIONS
Manuscripts
A(reconstructedsourcemanuscriptofDEGH4)
B(Moerbeke’s Latin translation, partly ofA,partly ofadifferent
manuscript)Ottob.Lat.1850
C(TheArchimedesPalimpsest)
DLaur.XXVIII.4
EMarc.305
GPar.Gr.2360
HPar.Gr.2361
4Vat.Gr.PiiII.16
Editions
Commandino
Commandino, F. 1558. Archimedes Opera non nulla.
Venice.
Torelli
Torelli,J.1792.ArchimedisquaesupersuntOmnia.Oxford.
Nizze
Nizze,E.1824.ArchimedesvonSyrakusvorhandeneWerke.
Stralsund.
ix