Geometry for College Students

238 Pages·2000·2.658 MB·English

by  I. Martin Isaacs

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THE BROOSKESRI/INCE OSL E
ADVANMCAETDH EMATICS
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GEOMETRY
for
CollSetgued ents
I. Martin Isaacs
UniveorfsW iitys coMnasdiins,o n
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THOMSON LEARNING
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IsaacIs.M, a rti(dn a,t e)
Geometfroycr o llesgteu dentMsalrIt.iI ns aacs.
p. cm.
Incluidnesd ex.
ISBN0 -534-35179-4 (text)
1.G eometIr.Ty i tle
QA445. 16230 00 00-056461
516--dc21
ToD eorbah

Perface
Thsbi ookip sr imianrtifeloncyrdo elmdla etghceess mt autwdiheeonjn ytoeshd i gh­
shcoomle tagrnewydoh woi tslohe maornar beot uhatem apzrionepgose lf ri stn,ie
ccielrst,rl i,eaa snnogdt gheeeortm firugier.csI pna ratrIhi, oc tpuhelta hstwoe h aor e
preptbaocre oihmnieg-g h shocmoalt hiectmseaa wtcihfilenilrdn is sr pahtetirhooee n l p
thsehrmtea h eehniutrs ainaejdsny omm eognfte ormwyehi tt thoewifntru u srteut .ds en
Btu swhhyoa unlydo ngeem oes?tt rurOyadensyeoo cfnor ,usi tesh, ga eto metry and
idtesns dcatenrntio,egm toarreyees, ns ttooiliaesnln ginaeriectrheincnatgvui,iro gena,,t
anodt dhiesrec .sTi hspepelri anacptpiilco,iahn closea wvtseurrd,eno lo eytx plain why
iitts hf aoctre inetguseer,ot mhrabyse t eanut agolh mteo vssettr uyd enatlt e aansdt why,
unrteiclae p neotrnls ykw,nh neogow e eotmrnyo ctwod anesstr iboepe dr oepde­urly
ctaeId .t hianraklet e ttawhrsoeeto ra nmesso irmep otrhutasfanluene ntst she axtp lain
whgye eotmhrabysee n a,ns dh ocuolndttb oiea np, ua oertf th s heco couilrc rulum.
SnicEeui csdlo,2m 30ey0 earsm eahtgraboyse,t e angua eagsdo h etd usicceteni,cv e
witthhe oarnpedrm sosA.o sa fc oenqsuegnecneeo,rfa mtgeietosuorntdyse h natvse
leahrnoetwddo r vaawcl oilnduc sfoirmoh nyhspe oastnehdso t wdo e taenacdvt o id
invraeolannisigIdo.n t whoedrrsb sy,t ugdeyotimrnseygt, u cdalenenh arnto swt htion k.
Ocfo eut,rh saerorete sh ujecbertt shc aotau llbsdueo s t etode ach rdeoeaindsn,ug ctive
bugte omieests rplyele cyffi eacbteuicsivaeste e etmhosa t vhepe e rbflaneaccoetf
deapntcdho ncesrsM.ea tnoetyfnht eh eotrhweaemt s pi grneom oveeta rrdyeei etnph e
snesteht ahtaee syrss mtoe tnhoinniuogosba ,vns do meetvisemunier nssp.gTi r haerye
cnocrbeeutcsseaet ucdaeenan dtsrsita lhawyep prtornpigrsalci,ceia elrtsoewr, h eavter,
antdhc enasy e tehw ahttia a sl ltehoga epadpc etndu oaaelpslpt yeho paa pr.e n
Geeotmirssy bo ae lauulat,nsi dmof e iottfhs e oarrseeaom m sa aztsiso nee gm
alsmmtoi cruuaslI.ofn ta mc,u tchhme e c soammceonbutmel a dad beo ut most areas
omfa thisecb,mug atet eotmirusyn iiqtnuh ieat" tsm iraarvceill ses,usto a"h c enay
reabdeaip elpcytri ead,b yte huvene inn Siruteiolanyte,e dd.o es not need a great deal
omfa thesmpoahstittioiicncma aaltr oavt tehf cleatt h iaaflt i indser atwhnre ocauhg h
verotafen txyarg nilaeni,def ah oc tfsh leei inpsee sr petntodho ipepco iustsdleioea f r
thtierna getl,h teshntee h lrieanegle tolsh raoc uomgmohpn o iOnncteo. au rltgdhu aet
thfneud amtehnetooacfrlla e lcmuuf so,r eixesaq muapamllaelaz,yni b dne gau ult,i f
buutnt fuonriattn eopiltossy si ,tb aolp ep riewtci itfiahrtosseutt tu cdlaycisuBn.ltug u
thaee svtaholefutm eige cete orxytb eenydtoshsn etd r sitkaitnoegifmt t ehsnme t.sos r e
vii
viiiP REFACE
Manotyfh per ohoatfvhseoe wisnru batneldle eb geuaatwnyhtc,i hu ,n foritsu nately,
al ihtatrtldoee rp. Ne ervcleeseriw,stvee he xeptehmcaottrs eta odtfeih brsos wo ikl l
lrnet aeon tjhobeye aoutfthp yer s oa owsfe altslh o atftht eh me.so re
Isnh rowte,s hocuolndtt soit nauundetdy e gaeceoht mbreauyc sieits h iag hly
attrsaucbatjnbiedevcu cetswa eecn al efaorrnmi s to meatbhoiuntg r deeadsuocntiinvge
antdhn ea tomufar teh epmraoItsoteief mcc.salr tle,h a oer,rte ehafastt hp ieans s ttu,d ents
sohuclodn ttsoie nteuh ee obreepimrnsogi v tneh gdee ieortmc rslysta h;se huyol d be
tauhgothwuot n deprrso,tao anfndsd pemrohiramepp so retsvoaheunnllt ed,a rnt hey
hotwio n vaenndt p wrro.io tfes
I hslaeevceft oetirdhbs oo ksm oeo tfh e smptoearccteuh leaoirprn nel gemae s­
omreyat,nI hd a pvree sjseuitnfittcieaoodtfn eh ssf ceatu ss aiv nagr oidfei etffrye nt
techonpfir qoMuooefssi.t g lnyho orweeeradv,r,t e hk neido ufn usrspirtnihge orem
wh,iw chhirleeq buyimr oedsdet ma nodmfaa rtdhser miagctnoais rece,mra alt her
polientsstost n u.tdI srete qcuoidnreserissap obhlies ttaoip cpartweihcaoyinn ay toen e
wouwlatdnpo tr oafv caett h saeetmc so mpolbeovstuEi.evl peyrne o snfsamilao the­
maitcnisma,oos wfth odmuo n detrhssenit iganfincocdetfa e h sreel s,tou sffitnetdnh eir
fromaaxli opmroasofst oimced wlu.Lhl eaatrp nriosnohgfon suob ltaed un n rewarding
choirneesaw;tdee , x ptehscatttu wdiedlneltm psar nsobd oe ufcstaeha esri stoebnesi ng
etsbaliasrohetew hdies srioen cbrl.e edi
Thbioswo sak wraiastt etfxeoCtnro g leGl eeeotmwrhyi,ic sch o aut rhsaet
Ih atvaeu sgehvttei rmaatetlhs U e n ivoeWfrsi socintsMyiai nds,To hnce.os uer's
prinacuidpicaeoslnnto csssfeip o hoormej uanunindod re rmgarmtaahdj uwoahrtose
arsep leicziisinaen dcgao erndyuo cnFa.ot ri tchoeuimrrs,se eqt uhietr heiedsr, e but
aslaos ustbanmtiinawolhrt oiat tkhcyeeo uerlseecS tmoieovt fesh sleeuty d.es nitmsp ly
watnlotre nga emoertyw,h ile CootlhGleeereogstmeb r etyca takhuefies nyiedt t o
beam ogreen atnaldcee csb sliien trotdmoua ctthiepomrnaot thoiaafcc n oa ulir ns e
absatlrgaoecarbtd r vaac lnaccsueI.lidt mus yb eflt hifaeotr sustdote,mtsn ehs et udy
ogfe eotmirasyen x lcepenrlte patrehasmteoid rofiienucf laftbo scrto reua.src st
I havdseits siaebfidwe iettnhh ae v aitletaxhbtmalsite gb heute s df osru ac h
coeuM.ra sniyn ec lau dopifun mtbeetrproei wscitstai h nilgsnam a rpgloeiaf ns rgst oed
geommeattarelBir.ucti t h deony o ptut thf ceou wsh erei btIe gl:tsoo hnnti hnek
reaplrletytht eyoa rntedhm pesris or o tifmhnya o tpo,in sn,hi obuaeltt dh e ah eart of
geeotmcroyuf rocsroee lgs let ut.Ads eltnshooe,fy dt eevno tmeo srampecut echI ha n
thiiasnp kp rtofopro rmliaiaastnamedx iio.cMm soasstttu pdreonbdtaonsb o filtny d
tihess plelecyxii cnaaigntI,sd h tahroaept i. n ion
Theasrleoeix sstow moen fdubelor otkhasarfi tel wliestdpch cet auatrlh eorems
anedl epgroasofnb,tun to ontfeeh sseeem qsu siutieat asat beflxotetrsh g ieeotmry
couerirstI.heh a efvuoent dhm aotss ttu wdherone ttgefsiroC s rlo lGeegeoetm crlya im
troe mevmeblreiyfrto r tmtl hee iprrv eioeonxueps ot gsoeu eortmeir hnyi sghchoo l.
Fors atokhtfeieh ms a josmroeir teyva,ina edcw c limaarntecei erzsyAast. tae ixotn
inse etdheoedr,rt,e eh sfartttfao rsma p ocislnteotto h bgeei nanniidnn gtr tohdeu ces
notoipfor gnoe onfat ntldhyg e,etn tto sh e su"t"ffga oqsou dia cpskos lsiyBb celuaes.e
Ic onuolfitddn baot ohkca otv tehrreiem gdah ttae trr itiaphglahe ct et ,hs atatan rdt ed
formt hep clreaIit, ga huttghc heort usm ea tniywm ietsah t xoetu.t
PREFACE ix
Moosmfty s tusdeeemnteteodjsn yo ctoheuea,r n msda noyf btehmceevam e ry
excaibtgoeeumdote tIrtniyh s. wbhoiioacskenh ,x spiaoonmfny c u oerl seucrnteoe ts,
Ih atveretdi ro e praocsdsl ueoaclpseyos sitbhelexe p eortfih ceelsn arcsoeao nsmdo,
Ih otphema yrt e awdiaesllrfiolsdn t hgaeteo tmirasyen j n yoaabnledexi cnsibgjutc et.
Moosaftll I ,h otpheta hstooe mf y s tuadnerdne tawsdh eaorro sewr i bltele aching
hicghhmo-aostlh ewmicalotlnis vmcoeeosyt f h eaxetcm ietttnoht oe wisnrt u.d ents
Ia mg ratttoehf fleoul lor weivnifgeo wrhe ertuslhcl peo fimrm: e nts
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