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# MTG4212text - E uclideaneometry G Thc s ubjectr natrero f t...

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Euclidean Geometry Thc subject rnatrer of thrs boot rs non-Eucldcr one m-usl know wna, Euc,idean Beonre,r), . "i].;llil'Jll 1i,,.;liJlil.lJ,llil;li::;i::,T::.: mofe.dimculr task th.in it ,nirhr lpp.af rniria,) r,, r:,",. ;, ."1 .*r,'",r,,"i"t";: ;;,;;;":;;;:,., ," produce thevaflou! cunEnlr] accepred desc prions. sirtch are ari based on rhc rerarnerr recenr wort ofDavid Hitberr o86: 1e.'.r). Nee,ess ro s;). fu*. g_.,.",r,,,. ;;; ;;;,;;;:;;;1";'i::,,"", to be deficient and op r for ye r orher char.acter.rzatrons l| new o I rhesc cons jde.ar ions, the rcaders ura\ no, be \umri .ed , , ,e.,r nd,,r,. Ju,r.. n., .hJ,en,,,e\.,r_ ".,..,";'',_.:; ^l^ . ::l',.."".,' shofthisror).or rhe subjec, -o - ,".,",0"ou",.i.ii;:i',",Jft ili:.ll''''t, rroridi,rg rheor s'i,h:r Ill Anlntroduction to Euclidean Geomerrv Geomctrf in rhe sense ol mensurrrion of ti!ui dates back to "*l mrr"""i,'"i ii"',i;",ii " T ip"lll"**'rl de\ eroped bI malr) cuhurer and :i:I,l.r *,"''r,, ;:;;;; ;i""iil:;:;"11.:;:nil j; J,i,iJT, Ii,i .J,li.: ::ii"Jll: reason, was-creared by rhe G.eeks. Hrsrrlrrlrns asr.e rhar rh€ orisn of gcomerr) ."" t". ,.,"J i".* ,,, tlrehres of Thates ol Milerus Ncirher rhe.\ or.r,i. -*npr,,r,,""u,, r*.;;;-;::;#;T,:i:::il'ii:i,li i':filiijlli:'J:Jjli,J,il: eclips€ of 585 Bc. jr is believcd thar hc ln.ed dunnr rhc;jrrh cenru,- ;it ;,i,,ili;."il;, ".." probablyt'om 'Lrd forrotrel in m.uv orher counrries.rntt cenrurres 1, r, fr ,,,,rr. ,t,"i r," "". ,- : ro a:uti.e |har borh ioundhis conr burior\ uselut a|d cared ".,g1 . p,",o.]. ,r,.",-i,, ,n" luture by ilcorTrorarng them rnroi(s cd!carionor sj.sren s;me rrrc creete orihi o"r *r-,'..^-e both the denrocraLjc tbrm of governmenr and \$e idcaof r trrat ht " r,I .r p."., ,, "",;,,p*"r,. to..e\ e.) ciLizen rhar he slr(jutd be abte ro argn. borl cogurr4 ura perurLsiverr. or,;"" ,r," ,ii" ,. srxtr cenrury Bc, rtre rask of edu.auns rhcif r.e'o{ uar.n". ,u rt " ,ii',' ."qo,.;,t il,i ;;;; ;;t,t."l s),slen u'a\ assmed by rhe Sotirjsrs. t.hel \$.er€ irrneranl pedagogucs "lro -ra.,rc, f,n.rn*,ry rrarnng their pupls mos t rn rhetorjc. Since rheJ i,,, r r,, nr, tl. ,1,,,,,.u,,n "";l ; i:,;,.",;;;:,r,., of Seometry,ro beuseful rool\inlhis rairnng. tnrlc, L,erLrontofndanr.hcrnrh.ircLrni.utur,uno was .eser red for psteriry It js let lillelt, rhat DemocrirLr\ (ca 4t0 E p.om,rgar" an ,to.i" tn"",, ;, ;.,,;;,;;,;i ;;il:,:,::1:,,illlli,ll':"Ji:fiil::[t:TJ; schoots. rr is n,ore than liketl. hou ever that hrirlen,"'*,.";, *" "; ,,lii 1,;l ;..,:;;,,"*' " Eudo.\us (408 355rBc) wa\ one of rhe Urs a.s,,uc,ure,ha,besins*',n*u,",,""**,""',i"uliii:,iLj'"xliTll",i'."";:1iilj".,:":l'i:l nas nol surlived. and our intormarion about his acconrpxrtnnrnts ^ second hand There is no doubr. ho\$ever, rhar he\rs a fiAFrxre mathen'ocirn u,ilh nncrcexcnr undcLsLandrn.r;i ,t,".;;;i";i;.-,,, h,,

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.'.; il"H::l':i iTH,::':l,1il:i i;ilii, H:tii:i:.J ii,illtxi:::,Ti.i:iI;1, :::,i ilTl wnosc content are Book' I I\ th( Jea-rerr, ur Jr. .,e. Jr J (r,. tf! Bnoh.v\|.ne||eur\ t fe.m.I r r "rut a r ur Books Vlt_IX rne ttr,rr ol nunrherr Book X rhe rheor) of trario at lumbcrs Books XI XIII: solid geomerrl ontetry. despile hrs fla\ s The nerl sedjon of rhrs '.u||.1 h: Jre\ ,r.<r|,rIir..ro..r,Jie Jno ner urll lh, I p,n,,f.. Jnd tt,<.tJtcrnrlt. i,t.r.ujr proposriions lro tarcf books oI l_.uclid rre rtso uc'u chaprers of \$is book. The readcf rs fejerftd xtcnsrve connnenrary on, Euclid,s Elzcrb lhe nrad/ahon of Enctrdcan geomerrt il can be onnL .(.tu(l Tl. . h.t .
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