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1、LecturesinPROJECTIVEGEOMETRYA.SEIDENBERGDOVERPUBLICATIONS,INC.Mineola,NewYorkBibliographicalNoteThisDoveredition,firstpublishedin2005,isanunabridgedrepublicationoftheeditionpublishedbyD.VanNostrandCompany,Inc.,Princeton,NewJersey,1962.LibraryofCongressCataloging-in-PublicationDataSeidenberg,A
2、.(Abraham),1916-Lecturesinprojectivegeometry/A.Seidenberg.GL.p.cm.Originallypublished:Princeton,N.J.:VanNostrand,1962,inseries:Theuniversityseriesinundergraduatemathematics.onoIncludesbibliographicalreferencesandindex.ISBN0-486-44618-2(pbk.)1.Geometry,Projective.2.Geometry,Analytic.I.Title.O'
3、;;QA471.S422005516'.5-dc222005051967ManufacturedintheUnitedStatesofAmericaDoverPublications,Inc.,31East2ndStreet,Mineola,N.Y.11501PREFACEThepurposeofthisbookistoprovideatextforanundergraduatecourseinProjectiveGeometry.Theaxiomaticapproachtothissubjectisundoubtedlytheproperone,butitseemsdesira
4、ble,ifnotnecessary,togypstartfromwhatthestudentknows,namelyhighschoolgeometry,andoffleadhimfromtheretonewthings.Accordingly,thefirstchapterisdevotedtointroducingsomeofthemaintopicsinasnaiveaformaspossible.Thesubjectisthenbegunonanaxiomaticbasisinthesecondchapter.;,fuseTheaxiomaticmethodbegani
5、ngeometry,andprojectivegeometryisanespeciallysuitablesubjectinwhichtoillustratetheleadingideasof.t7themethod.Inhispreviousstudies,thestudenthasbeenaskedtotakemanythingsforgranted.Here,however,heisengagedinastudyinwhichfit;alltheelementsareinclearviewfromthebeginning.PerAsidefromtheintrinsicin
6、terestofprojectivegeometry,thereisthe.+afactthatthemaineventsofalgebraicgeometry,oneoftheprincipal...branchesofmathematics,takeplaceinprojectivespaces.Thereforepro-taijectivespacesare"somethingeveryonehastoknow."Tobesure,thisbasicminimumofknowledgecanbeconveyedefficientlybydefiningapointofn-s
7、pacetobeaclass{(pxo,pxl,...,px.)}of(n+1)-tuples,etc.;buthavingcommittedourselvestotheaxiomaticmethod,weareledtoshowinghowcoordinatesmaybeintroducedonthebasisofPappus'Theorem(inthecommutativecase)andDesargues'Theorem(inthenoncommutativecase).T
