Elementa geometriae

Page 49

. ~ b ' ' 4 LIBER ~~~~~~1fo1~~~~\~:~ .b.c. c.d ,c .cqmllcu:f~IQ) angulus.c. ~tlino ~qu-a~i\3 angu~o c .altcrh:~~;:oico p:opo:rionon.a .c. ad. c.c.dlc fmt~ .d .c. ~d .c .b.-: ft ~tc_rir ,ppo:tto a.c.ad.c.cJicur .d.c.ad.c .b. t p:cdkri ansuh fucnnt lld:' t.JC c~ua!ct\, otco Llloo o u ~ 03 rri:lllsuloo dTccqualw:coniung;arn cnim co~ ausulant~ ua 9' tucra.a.c. -:.c. .ftant tmca ,-11a.crunrq;·funilircr.b.c.';.C. d. hnctt \'no. a l trcrfcqucr~ur parron ~1Tc C'!Ualcln ton.pcr·t f .p1irnik ptomJbam hncam.b.c.crirq) ~c~ p:en~~~ ~em 7.quirlfi vrriufq; oicro;: tr!JU!)tdo;.-ad tnanguhun.c.b.c.plOpo.llo ~11 J . • q. P'~ p!imam buiu<> p:irni co:mn ad ipftnn dl ftcut .a.c.ad.c.c.t fccundt co~nm ad m dan flcm.d.c.lld.c.b.umnifdlll ell ptima pJnJ .~ofir~conclnfLoni!.l. <I~cunda pam ccOucrfo p1obarur .ql.a.c.ad.c.c.dl fiCI.It p:uni tnansuh ~d triangulu.b.c.c 1 .d.c.ad.c.b.ficut fmmdi lld eundem per p:nu~m bum~:-z qma poflltllll dl ~~ flr 11 .c.ad.c.cJiCII{.d.c.ad.c.b.crir o;tritifq; oicto:um triansutomm a.i rnau~lu.b. c.c. t na p1opo1tio:qnarc per p:imam l~tc1n. 9 .quinti ipft funr cqua\C>.}. fiCq; patcr (cwndaparv. · 11b:opofi<io ·••· quiUIJOllincc p:opNtionakG quod fi1.b p1hna rccron£)ulunJ cor!ri.ncrur.:cqut1 cr:ttctqolu.b 011(1 uio. 0i vcro qo tub pmm1 1 vluma courme:n~r 1cr~:~~~~111,::~~.~~~~~~~,;f~:·: ~:· ~-~contincmrrccu' ~~~ kcormcmr. (lSinr quatllol !incc.a,b.c.d.p:apmtion>llc>;:5 ttq) p;op01tio.a.ad.b .fiCut.c. ad.d. Nco g.> fupcrftcioHontatHl fub,\l."Z.d.cquatht ell fu~crficici conrmrc fub .b "<.C."< flfupcrfidctJcomcnta fub.a. -z.d.cllcquah!JfuP.fiCictcontcntefu!>.l>.-:-.c.t't co q) p:oponio.n.ad.l>.dl ficur.c:ad.d. ~lam e n ~ fupaAcics.contcnra fub.a."<.d 1 fupcrf,cicil cOr em a ful>.b .... c.5tcr':3odl.wpomo.~.ad.b.ftmr.c. nd.d. larcro tl tarnrn fupaf!Cicrii cmnr mutckefiJ.fcd 'i'\Jnguli ab ns contmttcqu:Jks:qll:ll'llqj ctt rmo; ongulonl: quare per fctia) parr(. ,; .bmuu ipf1 fnnr cqun1cil quod dl P_li mum.(l£xtiln parer per ptimam parr em nufdl; .ft cnun ipfc funt cqwa!ro. q: ocs an13uti carunt funr mti :latera carum crunt mutckcfto:quarc pwpoltio.a.ad.b. ficur.c.~d . d.quod dl fmmdum. 'llblopolirio .16'. 3(fi.Jcrinrrrcslincct.?~opouion~lco. q~ fu~ p~ima 1 rcrt ria rcct11nguh~5 conrmcmr: cquu em ct qo g lc~un.!a qu11 dntto ocfcribtmr. £lt vcro qo fi1b pnma 1 tcrn11 connu~ rur cqm1m dl ci qm1draro qti a li:cunda p:odudmr: ip!c C.6ir plopo:~i~~~~~~:~f~~~~:n't1.~~:~~~,~~~~~!~ !incom.c.cico '1' fupcrt'icicu contcnta fub.lt. 'i.C .cqualiG dl quadrato.b. '< rtfupcrfiCtro contcma fub.\1.1.c.dl cqualta quadraro.b. oico cr p:opo:rio.a.ad.b.ctl ficm .b. ad.c.boc auran eft cui/ dcno per p:cccdrntcm pofira alia linea que ftt cqmtlio.b.ira q' .b. fu itt rortonc fct cnndc'ltcrtic. Vl 11b:opofi<io . •7· '!f fucrint boo tn-i!,'liult fimilco p1opouio 91tcrino ad a Ire ni. eft rlln(i; ,ppomo cniullibcr fi1i lg.rcrio ad fin1 rdatmU la~alrcn9 ouplicgra . .t.lD~rufd~~ ctJ~cy_b~q~ omnin~J} rriulincnv cOrinne ,ppmnon\lhu quJf'J c puma lld rrrna ra1 1ta crirlil~ficicG cofttruro !i11~ p:un:i gd fiJP-ficiC cOllttut .ct1 tiJcrlt ci finnliG in Hnauionc" crcarione. <i5mr ouo tnnn~nH.a.b.c. -:-.d.c.f.fumlcs cnltq; ~ cttl'minonC cquiansu!i t hue nun ,ppottionalium.5it ergo anguluu:.a.cqualia ansn!o.d. 'llllll)uhrn.b. ansnlo c. 'llliiBtdna.c.anl)ulo. f.critq) p:opOJiio.a .b.ad.d.e. oz.a.c.ad.d. f. ficur .b.c .ad.c f. oico '.V p1opo11 io trilli!Bnli.a.b.c . a~ tria"sutum.d.c. U: f~eut ,ppouio.b.c.ed :' f.oupllcara.Subiiigaf cnim Nn ooctrm.i•t o.buiua ouabua Unds.b.c. oz.c.f.rcrtt'l in cominua plopottioualitlltc que fir .c.g.,prracraaut rcfccar:t.c.b. fi .c ·S: fucrir ea maio: aut minol 'l p1odncatur !ii!C\l.g.a.crirq; pcrfcOOm parrcm.1<}.bmuu rrlan {lu!ua.ll.g.c .cqmdia triangu!o.d.c. f.ptoprcr id qt) ,ppolt'io .a.c .ad .d. f.rll flcur .c f.ad.c.g.'lllnguloo.c.rqua!io: anl)ulo.f.quarc per fctiam parro~1.1.quimi rn~n 1 guli.a.b.c.ad \'tnlq; Ulommcrir \'11\l ,ppo:tlo:fcd pcrp:imii bums ~omo man ~~~~;~~::·~~c~f.~;,:,';:~~~~~~:~~~~:~~r~~~;~~·:;,~~~~J~~::~~::~~·~~s~·,~.d~~b~ c.adtrfangulmn.d.c.f.C fintt~topolt io.b.c.ad.d.f.C~.upltc~ra qti eft ,ppohnlm. Bl aurC.c.g.fit equ:JUu.b.c.cnr pcrfcOOm QICIII.t4.bUitw rnangulus.a.b.c.cquaJ lis rriangulo.d.c.f.cqualioanrC .wo:tio c6poniwrcy cqnali ouphcata o;d rnph! car a \"d quotimfaiq) ftunpra. 31111 1 nc~ndC pn!lio~1C pofTonuu code modo 1 per c!ldl'!I1 111Cdll1 t~cmonflrore tiC fnpcrf1ctcbtw cquidlflllntium \arm! finnhbuo fmn ~~:J~~~;,~;~~~:;~~s:o~~:~~~~~~~~~:~~~~~:~~~~~~~;:~rc~~~~~~~~,:~: liter ,pponitur oc omnibuo hlefictcbua'ramilibuo n6dt~ pntcl niri oc tnangulio •. f) ;::;~:·,::~~;,:: ~~:';"~;~r·j ;,:~:;; :":,~i~r ~u~;~~:~=~~i~~~~ ~~~~~11!i::~\~:~~~~11~ ni. bniuo fmr vcriloomanifdlo~~n.n,~~~~·~odo 1Uiuu:. 6~ c f 6 b 6 ' ' ·@~ " It ' :.