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1、ONQUATERNIONS,ORONANEWSYSTEMOFIMAGINARIESINALGEBRAByWilliamRowanHamilton(PhilosophicalMagazine,(1844–1850))EditedbyDavidR.Wilkins2000NOTEONTHETEXTThepaperOnQuaternions;oronanewSystemofImaginariesinAlgebra,bySirWilliamRowanHamilton,appearedin18instalmentsinvolumesxxv–xxxviofTheLondon,Edin
2、burghandDublinPhilosophicalMagazineandJournalofScience(3rdSeries),fortheyears1844–1850.Eachinstalment(includingthelast)endedwiththewords‘Tobecontinued’.Thearticlesofthispaperappearedasfollows:articles1–5July1844vol.xxv(1844),pp.10–13,articles6–11October1844vol.xxv(1844),pp.241–246,articl
3、es12–17March1845vol.xxvi(1845),pp.220–224,articles18–21July1846vol.xxix(1846),pp.26–31,articles22–27August1846vol.xxix(1846),pp.113–122,article28October1846vol.xxix(1846),pp.326–328,articles29–32June1847vol.xxx(1847),pp.458–461,articles33–36September1847vol.xxxi(1847),pp.214–219,articles
4、37–50October1847vol.xxxi(1847),pp.278–283,articles51–55Supplementary1847vol.xxxi(1847),pp.511–519,articles56–61May1848vol.xxxii(1848),pp.367–374,articles62–64July1848vol.xxxiii(1848),pp.58–60,articles65–67April1849vol.xxxiv(1849),pp.295–297,articles68–70May1849vol.xxxiv(1849),pp.340–343,
5、articles71–81June1849vol.xxxiv(1849),pp.425–439,articles82–85August1849vol.xxxv(1849),pp.133–137,articles86–87September1849vol.xxxv(1849),pp.200–204,articles88–90April1850vol.xxxvi(1850),pp.305–306.(Articles51–55appearedinthesupplementarynumberofthePhilosophicalMagazinewhichappearedatthe
6、endof1847.)VariouserratanotedbyHamiltonhavebeencorrected.Inaddition,thefollowingcor-rectionshavebeenmade:—inthefootnotetoarticle19,thetitleofthepaperbyCayleyinthePhilosophicalMagazineinFebruary1845waswronglygivenas“OnCertainResultsrespectingQuaternions”,buthasbeencorrectedto“OnCertainRes
7、ultsrelatedtoQuaternions”(seethePhilosophicalMagazine(3rdseries)vol.xxvi(1845),pp.141–145);asentencehasbeenaddedtothefootnotetoarticle70,givingthedateofthemeetingoftheRoyalIrishAcademyatwhichtherelevantcommunicationinfacttookplace(seetheProceedingsoftheRoyalIrishAcademy,v
