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gopd npo5 ro rdro FdpoSrou rexfupdvoue'nrrri6ou.Ecpopp6(oupre
rq yvoor4 rexvrrq.
H rlp( rrlg rcrX6rqrogr<crdrr1orrypqt, eivcr0 039m/0.10s: 0,39m/s.
l-pdgoupeu' = 0,39m/s.
H rtp( tq5 raXrirrlro5rord rr1orryprlt, eivor0,104m/0.10s= 1,04m/s.
I-pdgoupeu: : 1,04 mls.
Eivargovep6 6rr r<ordrr1lpovrrrl 6rdprcero0,8 s rroporqprlOqre
percBotrqrrlg roXdrrlros rrls ogoipog rorf 1,04 mls -0,39m/s :
0.65m/s.fpdgoupeAu : 0,65m/s
Av 0dlouprevo 6qproupyrlooupedvopdye€fogfiou vo ergpd(er ro
<ndoo ypnyopCIdyrve,rord pdoo6po, 11otrl<ryr1>0c Xperoorefvq 6r-
crpdoouperq peropolrl rq5 rcXrirqros F€rrl XpovrrqErdpxero At
orqv orroioncporqp40qre.
Au 0,65m/s
^
:ff :0.8.1m/s,
Tonqlfro our6 triyeror;rdoqenrrdluvcrq.EivqrpdyeOog6rqvu-
o;rorr16.Egdoov11xivrlorleivcreu06ypcpylynopotiprrvo ypdgou-
Hsyrorqv olyepprrrlrrprlrqg
Auqr =at
Movd6operprloeogoro Are0vdgljorrlpo povd6ov0o eivorq
povd6oroX6rrlro5(1mls)rrposrrl povd6o1p6vou(1s),6qlo6r1
(1m/s)/ 1s ror ;rnopofpepiporovoypdrpoun 1 mfs'.
O oprop<i5.lrc vo orro6oprqooupe,ritroq,r'qvdworoenrrdXuv-
on Xpnorporrorori;rerqv i6roloyrx4rrdv<oorqvorroio0eprelrc604re
11ivvororoXdrrl'ro.
F']NFPLTPAOHTHI K NHIHI
I
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e
47.
I
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e
H enrrdXuvorlevdgovttrcetpfvouo€ lltoouyrexptl.tivrllpovtrrl
orryprlrq5 xivrloqgopi(erorog o pu0p6,9perapofuigrq5 ra16rr1.
rog rard 14mryp{ exeivq.Yno}oyi(erorar6 rrlv rrp4orrlv orrofo
reiverq piorl enrrdxuvorldrov q lpovrrrl6rdprerorq5 peropolq5
reiver oro pr16dv.Iuppotri(erorpsro yprippoo, op1tr6rqg trf{15
acceleration.
H enrrdluvoqtrrqvnpri€n.H orro66prqorlpdporoptoSrcorvod-
pragiworoqq onoioeivqrxqlcpuorrdprdye{)ognpirretvo neptdXetrot
pronp6roorlyd rtl pirp4orlrq5.l-lc6g0c pnopodoopenporrtxd vo
;rerpqoouperqv rrp( rqgenrtdXuvoqg;'Evrrgtpdnogeivoro e{q5:
Boor(6pevororo iXvrlprrogeu06ypCIpHrlsrivqoqgunoloyf(oupe
rq pfoq errrrdluvorloeXpovrr66rdorqporo onoio prrropei vo Oeor-
pr10ef prrp6,ofpgtovoF€rnv dwotqrrou6cooopenporlyouprivoS.
Ie xd0e-urrdaurrl rrlv dwoto-prrp6lpcvrrd,6rdorqpoq trpqrr15
FdorlSerrrrdluvoqgpug6iverrn (nrodFsvrltrprlrq5entrd1uvor15.
EuBuypoppnrivqorlp€oroB.pn
€nrToxuvorl
To yeyovrirq.'Evoquroorrlpr(6pevoruhv6prx6oc6pcocprlve-
rqr vs rrvqOeio' ivq rerfu;rivoerrirre6,rrpan€(r. To oqpeioA
rou Krvrlrori6raypdcperrrlv rpoxtd nou'nporfrrret, cxv€vt6oou-
p€rq oq;reia€yypogrlsrou A,,4, A, ...fu ndvo oto Xcptf.
oaa
A, Az As
a
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) . . . a Yt._+--->- a '
a-, A, f,, [o As Ae Ar Ar
H eyypagryrutv oqpeiuv A,,A.,A,...A"naprcrdvtr@ oe rpqyPanxi.s 6nord-
oeg. Ta ioa ypovtrcdnorqyara eyypag4sruv orlpeiu.tveivatr : 0.06s. l1a-
parqpqoart 6n 11xivqoqeivatennayov61ttvr1;
Arqrrrorc6voupedrr 6troro oqpeioppiorovrcrrrdvcoo€ Fto€u-
Oeio,evc6oronoordoer5crvdpreoooe66o{iro6olrdgeyypogiS6ev
e(votioeg,6tr<ogout6 ouppoivetorqv eu06.1poprprqoprcxtrqr(vqoq.
H Oeopqrrxriordqq. Or perp4oersFqSo61yo6voro ouprripoo;ro
a
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H NEPITPAOHTHI KINHIH)
48.
6rr xord rqvr<ivqorlq raX5rrlra au{dvera'i olror6lropgo, ovd foo
6qlo6r1lpovrrd 6roorrl;roro rroporqpeiror q i6rao6{qoq. Me dltro
ldyro q ;rior1enrrdxuvorl eivororoOeprl.
Ie pro eu06ypoppqr(vr1oqoov ourqv, drrou or rrpig rq5 HionS
enrrdXuvoqqe(vori6regyro 6le5 rrq lpovrrd5 6rdprcere5prerpqoer6g
rous/ rl ;rfoq enrrdXuvoq eivoriorl prerq (orryprroic)errrrdluvoq. H
errrrdluvoq e(vorouverrc6goroOepq.
O opro;rrig. Kd1e eu06ypappq rcivryor1pe ora1epry urndyuvory Aiye-
rat eo06ypapyryopaAd tnnayuvdltevq xivr1or1.Kcrd rqv rivrlo4 ou-
rr1q peropol4 tqs ralirrlrog er6qtrc6verorpr oro0rp6 puOprd,oe i-
oo 64lo611lpovrr<d6rcorrlporo ouprpoivouvic'esprrogotrds.
H e{iotooq r4g ro;16rrpag. Av eivoruoKoru o rrpd5r4g roXdr4rog
rrg Xpovrrdgorrypdgt ror to,0o roXfel
0r,: 0 : u - uo/t -to 4 u : uo* o (t-to)
Av 6eXrorlpe6rr to : 0 q olfoq 0oyiver u = uo* at. Av 6eXrofpe
ror 6rr uo: Orl oxion ypdrperor:
u=ot
I TIEPIPAOHTHI KINHII-]:
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49.
A{i(ervo noporrlprlooupedr mrlve{io<loqu : uo* ot q ra16rr1-
To fiou 0o iler mo prfMovro rrvodpevocrvrrrceipevoeivord0poroprc
i) rnS rol6rrlrog u0rror)eiXerord rqv opXq rolv
lp6vcov
ror ii) rqg noo6rrl, og ct q onoio ercppd(errrl p€rCI-
pol( rrlg roXdr4rog trdycr:rqg enrrdluvoq5.
H r{ioooq rivr;oq5.Ago,ro(qrqooup€r6po rrlv e{i-
o<ooqrivqols, rrlv e(iococrq6qlo5qnou 0o ;.rog6iver
rq Oioqrou rrvqro6oexil0elpovrrq orryp{.
Oeopod;rerr1crXioqu = uo+ dt odvrdno ouvdp-
rrlorlspe;rercxptrqrigrr1'rroXrirqro Kdrrov 1p6vo
rcoro1e6rd(oup€rrl ypocprrqnopdorooq.Ano6er-
rv6eror6'rrro eppoEdvrou OAB|0o poq6iverrqv r-
pnrnsF€r0rornorls.
To oX4paeivorrpand(ro orrdre Lx : 1/z(u0+ u) t.
Alld u : uo* of orr6re Ax : uotI 1/:rct2.
Av ouprgovrloouprevo eivqrXo: 0 on6re Ax : x rrporfrrrer q e-
€iocoon
x=uot*l/zo;l'
11onoio pag 6ivtt r4 O(.oqrou nv4ro6 oe xd)e ptAAovnx4 orry-
F4, ya rr1veu06ypappryoyaAd emrayovriyevq xivrloq.
Ilcparqp{ocrg
1. H peror6rrrorl uott 1/zort2eivord0porcryo
i) rrlg peror6nroq5 uotrrou 0o rropouokt(e ro rrvodprevoovrrreipe-
vo sv 6evurrrlpXeerrrrdluvoq
ror ii) rqg;.rerordnroqSl/zort'rrou 0q trrrpouoi'o(ero xrvodp€voq-
vrrreipevoldyo rr15enrrdXuvorlg
2. Irrg 66o e{rocbo€rsu : u0+ ot Korx,= tsot* 1/zot'ro ofppolo
rrou ovogipovrdr oe 6rovuo;.rorrrdpeyr10r1rrcpro, dvouv rrg ovri-
ororx€Solyepprrig rrpdgcogrrpog rdrrorov <i{ovox.
Av Oecopqooupredrr to: 0, Xo: 0 rcr drr ()rrpooovqrofuopdvogd{o-
vog eivoriror c6oreuo>0,T6r€:
a) erpd,oovq rore60uvon rns errrrdXuvorlgouprrrirrrer ;reereivqrqg
oplrqg roXdrqroq, 0q efvoro>0.
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50.
->
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orfs €qfocOo€rgu : uo+ qt Kqrx : uotI 1/zst6trcra odppolo 0a o-
vrlororxodvoeeenKi,qroodrnr€s.
p) erpdoovrl Korrdeuvorlrrls €TTrrdxuvongeirrorqvrie€rl 0116rK€r'-
vrlrrls opxrrlg rcrxdrrlrds(u">0)
0o eivqrq<0 (orr6reo : -lql) rar pnoporlF€vo ypdgouprerr5 66o
e{roc6oergperq poprp{:
u : uo- lolt ror X : uot - 1/zlalt'.
I' aurq rqv nepinrororl -potrovdrr ex6r1l6v€rorpro ouvepl5 eldr-
Toorl rrls roldrqrog, ro ovrrxefpevo6qlo6r1xrveiror 6troror rrro
CIpyd-q rcivqoq,orrl yl<6ooq trls guorrq5, Oecopeirorxivrloryye
ora)ep1 enrrdyuvoq. I6;.rrpovc F€ rrl guorK(, 11rrcpouoio errrrd-
XUvolSos pro euOriypoppqrivrloq ;rnopef vo 'nporotrioereire s6€rl-
oq eire etrdrrcooqrq5 raX6rqra5.
3. Av q opXrrrl rolirrlro eivor ioq pe prr16d'r,11e{iocrrorlrivqoqg
rroipverrn popqn
i)Aveivoryvcoorddrr prroriv4o4eivoropotrd,:rrrrcrXuv6pevrlr6re 4
e{iocoorlourrl pd56iverrq 0ioq (oMd Korrq ;reror6rrroq)rou rrvrl-
ro6 oe rdOepretrlovrrrrlorryprl.floporqpof;lr proovotroyioovd;re-
oo orrsrrpi5 rrlgperor6rrrorlsKqroro rerpdyrovorou Xpdvou.
ii)Avriorpogo,yrdvo crro6ei{oupe6rr prroer'06ypoppr1riv4orl1<o-
pigopp14 ro1614roeivorotrrotrderrrroluv6pevrlaprefvo 6ei{oupe
drr or ;rerororrioergrou xrvqrodeivqrqvdloyssrov rerpoyr6vcov
rarv1p6v<ov.
Aurdirove ror o Fotrrlqiogdrov epeuvorjoerrlv ele60epqnrc6o4.
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Opofui errrruluvdpevr;xiv4o4 (xo=0,t = 0, uo= 0)
x=1ot'-
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TouqvrrK€rpivouoerd0e
peMowrr4orrypn
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oerdOepellowrri onypri.
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lerirog rr ivcxpop6p6roolo, ro pdroolo oe o6yr<pronpsro
rp6Mo0c r<rvq0ei Trposro d6ocpognol6 rrroypqyopCI.
Av po5porqoouv <<yruriro p1roaAon'(.gru mo ypqyopap 11
ondvrqorl rroupos dplerorou0dppqrrxvo 6c6ooup€(Kce6S
ppiorerorrovrd orrlv rorvqtroyrxq)dvar ntEru nroyp4yopa
ynri eivatpapirepo.
AnorovAprororetrq
orovfOtrltroio
'Orov o l-olrtroiogdploe vo epeuvdro cporr'6pevorqg nrc6onsrcrlv
oopdrcov4 dnotpq6n ra pap1repcrr(.Erouvrtoyprlyopa Kuprop-
lorioe qrr6luro. Er<rdgorrd ro drr oXerl(6rov p€rqv r<orvr1loyrr<r1
, erle<orpa0rigpi(egpdoooro dpyorou dltrqvo,prl6oogouAprorordlrl.
, H AprcrortfurcyEooxrl, rqv onoia 66dyrr7rceo faAtAaioc,oro l-Isvetw
: orr1ptorqgflieas, unomrlpt(t 6n ro uhrc66Auv rwv eilyerutvowpdruv
: rpotpycrrx cnd rqv avdpefq ru-wrtood,puv nrperapxtrcitv> orotyti-
1.uw. Ts rf.ooepaorotyeia,11fry,ro'Y6utp, o Arlp xtt ro l-lup6u npf.nu va
: ra,ur((ovratorq orc(.,pr1IJc'gp€ nq ouoieganrdng onokq nrlpav ro 6vo-
: pa rouc,.Torcoru6vep6,yn napderypa, e?eupt.irooav €vapeiyparuv
, reood,p<uvorotyeitavoro onob emrcparo1oero orotXeio'Y6tnp.Kd)e t-
: vctsn6 rs rrpurxpryrcdorotyeia eiyerq cpooxrl':ou0tor1ptoa orov errl
i yercXdtpo.Ilto'4tqAd r1ravro l1up,xdrru an6 aord o A4p,ycpqA6rtpa
: ro'Y6up Katrflo rcdxnan6 6Aaryravr7guoxrl 0f.or1rou o'roryeioufr1.
1LriltEuva, ndvrct,ye rq Euox7 rou AprcrortAq ro rcd1eorotyeioeOecl-
, p{ro 5n epEavi(etrqv rdoq va rcwq1{npoe r rpuoxQrou 0fo4. Av yn
I napduypa tva odspa,rou neptyet rcupiusg,ro ororytio l1up,ppe)ei yn
1rcdnotoAdyorcdru anr6ro ororyeioAr1p,0a npi',ra va av6pu ndvut dn'
: dur6. Mn n(lpa nou agryverareAetj?epr1orov ct(pcx0a ruvry)tirpog ro
; d6ogog rcat11xivryoryrr:,C0a eivat 11ouv€nen rr:,,;utrepoyr1qrou mory{-
';oo fq oe ouvuctoydyt rr10tor1orqv onoia ppt1trlxe.
: ftvtrcSrtpa Kuprapxoioc 11dnoQrl 6n 11goootxrlrcivr1or1evdqo-
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rrdpx€rpdvo n K€vrpopdlos€llrdxuvol,I orroio 6evoXeri(erot p€
rq }oyr14 rou nroyp4yopd olld pe rq'r o6rdronq preropol( or4v
rore60uvorl rr15rolirnrqs. Ano6errvrierorOecrlp4rrrddrr ro pd-
rpo rrls oytr((trat prero pdrpo rr15rcrXrir4ros Kotpe ro ;lqrog rr15
orrivog, o6;rq<ovop€rqv e{iocoorl
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xeqdtroro,orqv evdrqro yto rov 1p6vo,pllrloo;.reyro <porv6pevorrou
enovcxloprpdvovrorpreoro0epo6gpuOporigKotro loporrrlpioope
rtpto&xd. Einopreordpo 6rl q nepi<t6ogrcol11oulv6rqrq eivorro
poorr<d<ororXeiorour6rqrcxg>yro r<d0enepro6r16<porv6prevo.
Mnoporjpe rc6pc vo roXuprorofpre6rr 11opolrl rurtrrrq rivrlorl ei-
vor firo rivqorl nepro6rrrl.Krourd yrari ro r<rvqr6ovd ioo Xpovlrd
6roorrlproro{ovopp(oxerot orn Odoqrou enovqxrcbvrogrqv i6ro
orprpc65rolirqro xor errrrdXuvorlrrou eiXe,6rov pproxdrov orqv
npoqyo6pevrlourq Odoq.KdOeopoAqr<r,rrfur<qr<ivrloqloporrqpi(e-
rot, ouverr<69,cxrr6xdrroro rrepio6o xor rdrroro ouXv6rqro. Mrro-
porjpepdhoro vo npooopprdoou;;erous opropofg rcov66o ;reyr-
0c6vorqv rrepinrcooqourqg rrlg rivrloq<;KGrvo tri;.red,rr:
Ilepio6og (T)ovopd(eror o lpd,vosrrou orrsrreiror yro vo 6laypo-
<pef pro neprqipero rvr6 oulvdrqrc (v) ro nrl}fr<orou oprOprorj(N)
rtrlv rrsprorpocpc6vrrou 6roypd(povrotoeXp6vot rrpogrov Xp6vot.
Eivorv : N/t rol ener6(ytot : T 0o rrivorN : 1, rrpordrrreldrt
Mrroporipeard;ro vo ouoXeriooup€'rnvnepio6op€rrlv ro16rq-
ro ornv opolrl ruxhrrl xivqoq.Ie lpdvc riv4oqgt : T (ioo ps rrlv
nepio6o)'ro ovrrrefpevo6ruypdcpeI rd{o ioo ;re2nR, 6nou RI oxrf-
vo rrls rpolrdg. Buor(6pevor,erropivtrts/ornv e{ioooq u : s / t
prropod;revo r<orolrl€ouFrsornv:
N4ovri6oyro rrlv rrepio6orivor <puolx.dro 1 s. H ou1v6'rrlrcxp€-
rptdror pe rq ;rovd6a1Hz,'nou orlproiver pio orpocpqcvd 6eurepd-
lenro (1Hz : 1 s-').Or pqXuvotr6yorXt)norForrorotivrr1;rovd6o1
rpm fiou 0o rrerpio orporpq svd lenrd.
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Tooepontrdvoerrelei ro ouvqOro;.rivorou6prtpol6yro.H oepoou-
vo6dg,rc0c65oeppiperroug enrpdreg,xtveitorpdoooro ceponld-
vo,evrilrourdXpovonaipverpipoSorrlvnrqorl. H rivrloqrrls a€po-
ouvo6o6Oecopeiroro6v0erq.Kdr qvd^oyoouppoiv€rKorF€rov €-
rrrpdrqev6grrvodpevourpivou ra0c6qcrvcx(qreirr10ioq rou. l-evt-
re6oupe.'Evooc6poeivor6uvar6vvo ouprpreriix€roe rroll6g rrvrl-
oerg.fro vo ;rrropdoouF€vd 6rarpivouperrlv x:dOepio orrd curd5,
lperd(erorvcrrrqpqFr€pi(ouyeF€rrl qcrvrooiopro5dlegrrg un6tror-
rreqon6re 0o rarolopoivoupenorq eivot11rir0epio rivqoqlolpt-
ord.
To rropo6eryporoF€Ftrqgoprrd prdoorrpo,rgipovtot.I' ivq e-
prroprx6rrtrofo,nou ro{r6e6er,o loorpdFroSovepo(ver;riooxdtro.
Oecop6vrosrrl frl oxiv4rr1,;rnopodpevc rrodprt:d'rrour6goupperi-
X€ro€6riorrvqoer5.H pic eivor11xoror6pugrlr,:ivqoq,rrou0q erre-
lo6oe av ovipcrverq oxdlo KGrro rrloio rltcxvorivqro. H dllrl eG
vorpio xfvrlorlp€TrlvrcrXrirqrorou rrloiou, exeivq6rlfo6ntou 0o
exretrodoeov ppror6rovoro rtvo6pevorrtroio,Xcopisvo perortve(-
ror priooo'gur6.
HopxntnSovefoprrloio(;
A56o6perc6porroro pi0o6o Xprlorpolroreiq Krvrlprotrrrlyro vo fi€pt-
yp<irperrrg odvOeregxrvqoerg.Baor16ep<6rr1porropopdverro (rrou
ppioreror ivo rcvr1r6>,'ro onoio orrlv nepinraroq pog oupperilet
oe nolli5 rrvqoerg.Krord;ro o unotroyropdgr<o'rpeye0c6vnou poq-
Oodvorrlv rrsprypoq4/ drr<o5q rcrXfrqrc rcxt11t;rrtr61uvor1.
To npoplrlparo qu'rd cvtrpercorri(ovtct qrrrj rrlv Krvqporrrq pe
rq trey6pevq(dpx4 rqg ave{opr4oiog (4 tqS enutrl4tr(og)r<ovrrvrl-
o€(l)v).
<'Orqv ivo rrvrlr6 errelei rourdlpovo nolfu:g rrv4oetgrdOe prio
crr6 ourdg e{eliooeror ove{dp'rqro o116rrg d,treg>.A5 e{er6rxe6-
oouFsro v6qpo rns CIpx4sourrjg yto raOdvourr6 ro rropcrdto
rrpoBtr(pora.
u. lrorovnpoo6ropropdrq5Odor1g.
H Oioqev6grcrvqro6-ro oroio oupperiXercrenollig rrvqoel5-
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F€rd olrd XpdvotraOopf(eror qv (povr,rorodprero rrvrlrd vd €KT€-
, le i rdOeprio.rivqorlcve(dprqro Kor6rq[,oXrrderri rov i6lo1p6vot.
I p. IXerrrcdp€rov urroloyroprdrq5 raldrrlrog (ror rrlg enrrdluv-
, orls)'
, H roXfrqro (r<or11errrrdXuvorl)rqv orroio 0o rropouordoer ro
rrvrlrd, perd orrd 1p6vo t, urroloyf(errlt on6 ro 6rovuopqrr16d-
r Opotoporolv roXurrlrtov (q rtrlv €rnroxjvoeov), rrou 0o erXero rr-
, vr1rd,ov errelodoe rdOe pfo r(vr1or1qr€Edprrlroror enf 1p6vo t.
i Mnopod;revo ypdrjoupe:
d : d, + d, +... + J"rord: d,'+ d, +... + d"
flopo6eiyproro
1. 4116rq odvOeoq66o eu06-
ypCIpJo.lvror opotrc6vxrvrloe<ov
npor0n'rer rivqoq eu06ypcppq
opoli. 'Evooolryrdpr, yro rro-
pd6erypo, fiou p€rcKrvefrcr pe
oroo;;pr|roXdrrlro u-,oe olfoq
pe rcvodprevnFdol on6 dvo rpril-
trolopri 11orroio rrveirqr Kr0u-
rr1 ;rerol6rqro oraOsp( do,er<relef riv4oq eu06ypop1.rqopotrr1.
Ecpdoov4 Uoror q Ju,eivororo0epdg,0o eivororoOepqror 110..
d.: do+ d,
Mdvo orrlv rrepirrroroqrrou do : - dr, rrpor6rrrer rcrXrirr1ropq6iv.
2. Arl-6rr1o6v0eoq pia5 eu0rjypotrFrnsopolrl5 r<orpriogeu06-
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xat6r<nqurt)ne o ZriAAyavNrpflrc(StilmanDrake)io<o<;va youpltotjpt(e peAu6rftq,
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PHILOSOPHI.€
NATURALIS
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vdrq rrou prrropo6vvo ouyKpt{Jorivpr6voprero dpyo rou
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6rrco5ouvq0f(erorvo }dyovror, pdvo pt.ra Zroryelorou Euxlei6r1
;rropo6v vc ouyrpr0o6v.'Ooo yto rrlv s'rnorqpovtKrloqpoofo rou5
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on rav e66v rou Aoppivou 0o pnpodoov vo nopoptrqOodv.
To dpyo6evrlrov xepcuvd5nou {iorrooe oe 1p6vo ov6nonro.
Iro 1p6vrorrou trporly1Orlrov,yeyov6ro ror dvOp<orrorrrpoeroipro-
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ourrl dcpepeorrlv errrcpdv€toro (4rqpo rqg Me0d6ou,rrou 0a dvor-
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pro poOproioono6io;reuoqorrd <prlooo,prxd5,Opqorceurrrigxor o-
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rpergvdporrqg r<ivqoqgror q Oeopiorq; pop6rqrc5. I' ol6rlqpo
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